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POLITECNICO DI MILANO
Facoltà di Ingegneria Industriale e dell’Informazione
Corso di Laurea Specialistica in Ingegneria Biomedica
THE NEOAORTA IN PATIENTS WITH
TRANSPOSITION OF THE GREAT ARTERIES
AFTER ARTERIAL SWITCH OPERATION:
IMAGING AND COMPUTATIONAL STUDY
Relatore: Prof. Francesco MIGLIAVACCA
Correlatore: Ing. Daria COSENTINO
Ing. Silvia SCHIEVANO
Ing. Giovanni BIGLINO
Tesi di Laurea Specialistica di:
Matteo CASTELLI, matr. 765535
Lorenzo DE NOVA, matr. 765741
Anno Accademico 2011-2012
Index
SUMMARY I
SOMMARIO XVI
CHAPTER 1 – INTRODUCTION : THE CLINICAL PROBLEM 1
1.1 TRANSPOSITION OF THE GREAT ARTERIES ............................................... 2
1.2 SURGICAL REPAIR OF TGA: THE ARTERIAL SWITCH
OPERATION......................................................................................................... 4
1.3 POSTOPERATIVE COMPLICATIONS .............................................................. 7
1.4 SURGICAL REPAIR OF TGA: AN ALTERNATIVE
OPERATION......................................................................................................... 9
CHAPTER 2 – AIM OF THE STUDY 12
CHAPTER 3 – STATE OF THE ART 14
3.1 4D MAGNETIC RESONANCE IMAGING ...................................................... 15
3.1.1 PRINCIPLES ............................................................................ 15
3.1.2 PREVIOUS WORK .................................................................. 16
3.2 COMPUTATIONAL ANALISYS ...................................................................... 19
3.2.1 COMPUTATIONAL FLUID DYNAMICS ............................. 19
3.2.2 LUMPED PARAMETER NETWORK (LPN) ........................ 20
3.2.3 MULTI-DOMAIN APPROACH .............................................. 22
3.2.4 PREVIOUS WORKS ............................................................... 23
CHAPTER 4 – MATERIALS AND METHODS I : EXPERIMENTAL 26
4.1 ANATOMICAL MODELS ................................................................................. 27
4.2 HYDRAULIC CIRCUIT ..................................................................................... 31
4.2.1 PUMP ....................................................................................... 32
4.2.2 ARTERIAL COMPLIANCE .................................................... 34
4.2.3 VASCULAR RESISTANCE .................................................... 35
4.2.4 ATRIAL RESERVOIR ............................................................ 38
4.2.5 PRESSURE MEASURING EQUIPMENT .............................. 38
4.2.6 FLOW MEASURING EQUIPMENT ...................................... 40
4.2.7 DATA ACQUISITION AND DATA ANALYSIS .................. 43
4.3 MAGNETIC RESONANCE (MR) ..................................................................... 44
4.3.1 ACQUISITION ......................................................................... 44
4.3.2 DATA EXTRACTION ............................................................. 46
4.4 ASSESSING THE EFFECT OF COMPLIANCE: COMPLIANT
TGA MODEL ...................................................................................................... 49
CHAPTER 5 – MATERIALS AND METHODS II :
COMPUTATIONAL 52
5.1 ANATOMICAL MODELS ................................................................................. 53
5.1.1 AN ADDICTIONAL CASE ..................................................... 53
5.2 MESH AND SENSITIVITY ANALYSIS .......................................................... 54
5.3 CFD SIMULATION............................................................................................ 57
5.3.1 WORKING HYPOTHESIS ...................................................... 58
5.3.2 BOUNDARY CONDITIONS .................................................. 58
CHAPTER 6 - RESULTS 65
6.1 EXPERIMENTAL RESULTS ............................................................................ 66
6.1.1 CONSIDERATIONS ON TEMPORAL RESOLUTION FOR
4D FLOW ACQUISITIONS ................................................................ 66
6.1.2 4D FLOW RESULTS: TGA AND CONTROL GEOMETRIES
68
6.1.3 THE EFFECT OF COMPLIANCE: DISTENSIBLE
PHANTOM .......................................................................................... 70
6.2 COMPUTATIONAL RESULTS ........................................................................ 72
6.2.1 MODEL VALIDATION .......................................................... 73
6.2.2 QUALITATIVE COMPARISON BETWEEN 4D FLOW AND
CDF SIMULATIONS .......................................................................... 81
6.2.3 THE EFFECT OF THE AORTIC ARCH GEOMETRY: CFD
COMPARISON BETWEEN TGA, CONTROL AND SPIRAL
GEOMETRIES ..................................................................................... 86
CHAPTER 7 - DISCUSSION 99
CHAPTER 8 – CONCLUSIONS AND FUTURE WORK 108
REFERENCES 114
List of Figures Figure 1.1 - Schematic representation of the heart with TGA, highlighting the origin of the
great vessels from the incorrect ventricle [yorksandhumberhearts.nhs.uk]. .............................. 2
Figure 1.2 - Rashkind procedure: the balloon catheter is inserted into the septal defect and
inflated. After inflation, the catheter is pulled back through the hole [http://www.hakeem-
sy.com]......................................................................................................................................... 5
Figure 1.3 - Schematic representation of the arterial switch operation, including relocation of
coronary buttons [http://radiology.rsna.org]. ............................................................................. 7
Figure 1.4 - Fluoroscopy visualisation of an acute aortic arch, or gothic arch, as a result of
arterial switch operation. The enlarged aortic root (indicated by the yellow arrow) and the
indentation resulting from repositioning of the pulmonary arteries following the Lecompte
procedure (red arrow) can also be appreciated. Image modified from [Agnoletti et al., 2007]. . 9
Figure 1.5 - Comparison between normal heart (C), TGA (A), ASO with Lecompte (B) and spiral
ASO (D). It is possible to appreciate how the spiral procedure restores a more physiological
anatomy than the traditional arterial switch operation [image form Chiu et al.,2002]. ........... 10
Figure 3.1 - 3D flow visualisation of a control patient highlighting cohesive systolic streamlines
[Baker er al., 2012]. ................................................................................................................... 16
Figure 3.2 - Particle traces emitted from the SVC show how the blood is distributed between
the p-RPA, d-RPA and main PA [Bachler et al.,2012]. ................................................................ 18
Figure 3.3 - A simple example of LPN model (top) and its electrical-hydraulic analogy (bottom):
flow (f) and pressure (P) are represented by electric current (i) and voltage (V). ...................... 20
Figure 3.4 - Lumped model of a short pipe: flows and pressures in the district are regulated by
the NS equations [Laganà, 2002]. ............................................................................................. 22
Figure 3.5 - Inlet (left) and outlet (right) lumped parameter network used to study the fluid
dynamics in the aortic arch [Kim et al., 2008]. .......................................................................... 23
Figure 3.6 - Velocity magnitude at peak systole (A), late systole (B), diastole (C). .................... 24
Figure 3.7 - Mean wall shear stress at peak systole. ................................................................. 24
Figure 4.1 - Screenshot of the Mimics interface, showing anatomical reconstruction of the TGA
aortic arch. 3D geometry (bottom right panel) is reconstructed from 2D MR images (top and
bottom left panels). ................................................................................................................... 28
Figure 4.2 - Detail of the port for the pressure catheter. It allows for access the aortic arch in a
very easy way. ........................................................................................................................... 29
Figure 4.3 - Control (left) and TGA (right) models manufactured by means of rapid prototyping.
It is possible to appreciate geometries differences among the two models: the yellow arrow
highlights the enlarged aortic root in the TGA model; the red arrows point the different aortic
arches. The green arrow indicates the point of insertion of a pressure catheter on the
ascending aorta (on the TGA model). Finally silicone was used to attach the model to Tygon
tubes, as can also be appreciated from these images. .............................................................. 30
Figure 4.4 - Experimental circuit: II indicates the compliant chambers, III one of the four taps
implementing the resistances, and IV the atrial reservoir. ........................................................ 31
Figure 4.5 - Schematic representation of the circuit. P represents the pulsatile pump, C the
compliant chambers, R the non-linear resistances. The arrow indicates the direction of the
flow. ........................................................................................................................................... 32
Figure 4.6 - Harvard Apparatus pulsatile blood pump used for the experiments: A) inlet, B)
outlet. Also indicated, the position of the ball valve that regulates the flow. ........................... 33
Figure 4.7 - Inflow waveform: it is obtained setting the stroke volume and the heart rate
respectively at 90 ml and 70 bpm. ............................................................................................. 34
Figure 4.8 - Schematic representation of the circuit using for characterising the resistances.
The red and the blue arrow indicate the position of the pressure catheters to measure pressure
values before and after the tap. ................................................................................................ 36
Figure 4.9 - Characteristic curves, with the respective equations, of the resistances: carotid
(blue), innominate and subclavian (red), descending aorta (green). ......................................... 38
Figure 4.10 - Catheter tip dimension compared with a match. ................................................. 39
Figure 4.11 – Pressure catheter manual calibration: on the ‘x’ axis the output of the console in
Volts (V) and on the ‘y’ axis the associated pressure in mmHg. ................................................ 39
Figure 4.12 - Catheter position: the yellow arrow indicates the dedicated port for the pressure
catheter. It is possible to see the light blue little pipe, fixed to the model with silicone, along
which the catheter is guided into the model. ............................................................................ 40
Figure 4.13 - Transit time ultrasound theory of operation: a schematic representation. On the
left: cross-talk between the crystals mounted inside the probe. On the right: position of the
probe, snugly clumped to the Tygon tube. ................................................................................ 41
Figure 4.14 - Flow-probe calibration: on the ‘x’ axis the output of the flow-meter in Volts (V)
and on the ‘y’ axis the associated flow in L/min. ....................................................................... 41
Figure 4.15 - The yellow arrow points at the flow-probe position, which is the inlet of the
phantom. ................................................................................................................................... 42
Figure 4.16 - The yellow arrow underlines the flow-probe artefact in MR scan, visible in the
aortic root. ................................................................................................................................. 43
Figure 4.17 - AcqKnowledge interface: pressure curve is shown in purple, flow curve in red. .. 44
Figure 4.18 - Data extraction via Osirix : magnitude (right) and phase (left). The enlightened
circles in the left image are the inlet (top) and the descending aorta (bottom), while the two
big grey circles are the two bottles full of water positioned in the scanner to simplify the
identification of the model. ....................................................................................................... 47
Figure 4.19 - 3D mask and planes in the TGA model. The numbers indicate the planes for the
velocity analysis: 1-2 inlet, 3 aortic roots, 4 ascending aorta, 5-6 descending aorta. ............... 48
Figure 4.20 - Particle seeds at different locations along the 3D model then used to generate
streamlines and pathlines. ......................................................................................................... 49
Figure 4.21 - Compliant TGA geometry. Clearly the new model was printed starting from the
same STL file used for the rigid one. Thus the only differences are the properties of the two
different materials. .................................................................................................................... 50
Figure 5.1 - Comparison of three different geometries: TGA, control and “spiral”. Images at the
bottom represent the 3D volumes recostructed in Mimics. The aorta is shown in red and the
pulmonary arteries are shown in blue. ...................................................................................... 54
Figure 5.2 - Mesh example at the inlet of the model: it is possible to notice the 5 layers of
prisms. ....................................................................................................................................... 55
Figure 5.3 - Sensitivity analysis: variation of the power dissipation index with the number of
elements in the mesh. There is no significant difference between 900000 elements mesh and
1200000 element mesh. ............................................................................................................ 56
Figure 5.4 - Control (right), TGA (central) and spiral (left) geometries meshed with tetrahedral
elements. The different colours represent different portions of the models separated by planes
used to evaluate the fluid dynamics at 1)aortic root, 2)ascending aorta, 3)descending aorta. 57
Figure 5.5 - TGA geometry: inlet (A) and outlets (B, C, D, E). ..................................................... 59
Figure 5.6 - TGA (top) and control (bottom) velocities imposed at the inlet of the 3D
geometries during the CFD simulation. ..................................................................................... 60
Figure 5.7 - 3D geometry of the TGA patient coupled with the LPN. ......................................... 60
Figure 5.8 - LPN implemented at each of the outlet branch: Qin, Qin2, Qt, Qx represent the
flows, P, Pt, Patrium the pressures; R2 and Rt are linear resistances, while R1 is flow-
dependant; C and Ct are compliances. ...................................................................................... 61
Figure 6.1 – Flows at the inlet of the model acquired with the Standard (blue) and High
Resolution (red) 4D Flow sequences, compared with the OsiriX 2D acquisition (green). .......... 67
Figure 6.2 – Qualitative comparison of the streamlines of the High Resolution (left) and the
Standard (right) 4D flow sequences. The first image shows a noisier background and visibly
less number of streamlines than the Standard one. .................................................................. 68
Figure 6.3 - Streamlines in the TGA geometry (left) compared with streamlines in the control
geometry (right) at t= 0.2 s (systolic peak). The range of velocity goes from 0 to 1.38 m/s for
both images. The yellow arrow indicates the jet impinging the aortic root. ............................. 69
Figure 6.4 - Streamlines in the TGA geometry (left) compared with streamlines in the control
geometry (right) at t= 0.6 s (diastole). The range of velocity goes from 0 to 1.38 m/s for both
images. ...................................................................................................................................... 69
Figure 6.5 - TGA compliant model (left) and TGA rigid model (right). As expected there are no
shape differences between the two phantoms. The only difference is represented by the
material used for the rapid prototyping process. ...................................................................... 71
Figure 6.6 – The compliant TGA model (left) is connected with the pulsatile pump. The
pressure effect is clearly visible, as the model did not retain its original shape, especially in the
aortic root. The TGA rigid model (right) was placed next to the compliant one in order to
better appreciate the geometric differences. ............................................................................ 71
Figure 6.7 - Pressure waveform comparison between the rigid TGA model (red) and the
compliant one (blue). As expected the second one in more damped than the first one, as a
result of the additional proximal compliance implemented by the distensible phantom.......... 72
Figure 6.8 - Computational (red) and experimental (blue) flow waveforms comparison in TGA’s
subclavian for a cardiac cycle (T=0.8 s). .................................................................................... 75
Figure 6.9 - Computational (red) and experimental (blue) flow waveforms comparison in TGA’s
innominate for a cardiac cycle (T=0.8 s). ................................................................................... 76
Figure 6.10 - Computational (red) and experimental (blue) flow waveforms comparison in
TGA’s carotid for a cardiac cycle (T=0.8 s). ................................................................................ 76
Figure 6.11 - Computational (red) and experimental (blue) flow waveforms comparison in
TGA’s descending aorta for a cardiac cycle (T=0.8 s). ............................................................... 77
Figure 6.12 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s subclavian for a cardiac cycle (T=0.8 s). ...................................................................... 77
Figure 6.13 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s innominate for a cardiac cycle (T=0.8 s). .................................................................... 78
Figure 6.14 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s carotid for a cardiac cycle (T=0.8 s). ........................................................................... 78
Figure 6.15 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s descending aorta for a cardiac cycle (T=0.8 s). ........................................................... 79
Figure 6.16 - Computational (red) and experimental (blue) pressure waveforms comparison in
TGA’s aortic arch for a cardiac cycle (T=0.8 s). .......................................................................... 80
Figure 6.17 - Computational (red) and experimental (blue) pressure waveforms comparison in
control’s aortic arch for a cardiac cycle (T=0.8 s). ..................................................................... 80
Figure 6.18 - Temporal instants considered for the comparison displayed in the cardiac cycle. :
t1 represents the early systole, t2 the systolic peak, t3 the late systole and t4 the diastole. ...... 81
Figure 6.19 - 4D flow streamlines (left) compared with CFD streamlines (right) at t1= 0.1 s
(early systole) in the TGA model. The range of velocity is the same for both images. .............. 82
Figure 6.20 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.2 s
(peak systole), in the TGA model. The range of velocity is the same for both images. It is clearly
visible in both of them the flow jet hitting the wall. .................................................................. 82
Figure 6.21 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.4 s (late
systole), in the TGA model. The range of velocity is the same for both images. Once again in
both of them it is possible to appreciate a flow jet impinging on the aortic wall...................... 83
Figure 6.22 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.6 s,
(diastole), in the TGA model. The range of velocity is the same for both images. ..................... 83
Figure 6.23 – 4D flow streamlines (left) compared with CFD streamlines (right) at t1= 0.1 s
(early systole) in the control model. The range of velocity is the same for both images. .......... 84
Figure 6.24 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.2 s,
(peak systole), in the control model. The range of velocity is the same for both images. It is
clearly visible in both of them the flow jet flowing smoothly towards the upper branches. ..... 85
Figure 6.25 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.4 s (late
systole), in the control model. The range of velocity is the same for both images. Once again in
both of them it is possible to appreciate a flow jet flowing towards the subclavian artery. ..... 85
Figure 6.26 - 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.6 s
(diastole), in the control model. The range of velocity is the same for both images ................. 86
Figure 6.27 - CFD innominate flow waveforms comparison between TGA (red), control (blue)
and spiral (green) geometries for a cardiac cycle (T=0.8 s). ...................................................... 88
Figure 6.28 - CFD carotid flow waveforms comparison between TGA (red), control (blue) and
spiral (green) geometries for a cardiac cycle (T=0.8 s). ............................................................. 89
Figure 6.29 - CFD subclavian flow waveforms comparison between TGA (red), control (blue)
and spiral (green) geometries for a cardiac cycle (T=0.8 s). ...................................................... 89
Figure 6.30 - CFD descending aorta flow waveforms comparison between TGA (red), control
(blue) and spiral (green) geometries for a cardiac cycle (T=0.8 s). ............................................ 90
Figure 6.31 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.1 s. ..... 91
Figure 6.32 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.2 s. .... 92
Figure 6.33 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.4 s. ..... 93
Figure 6.34 – Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.6 s. .... 94
Figure 6.35 - Front view of the WSS in control (left), TGA (central), spiral (right) models. The
range of wall shear stress goes from 0 to 35 Pa. ....................................................................... 95
Figure 6.36 - Lateral view of the WSS in control (left), TGA (central), spiral (right) models. The
range of wall shear stress goes from 0 to 35 Pa. ....................................................................... 95
Figure 6.37 –Velocity vectors at peak systole (t=0.2s) in the control model . ............................ 97
Figure 6.38 - Velocity vectors at peak systole (t=0.2s) in the TGA model . ................................ 97
Figure 6.39 - Velocity vectors at peak systole (t=0.2s) in the spiral model. ............................... 98
Figure 7.1 - Control (right), TGA (central) and spiral (left) geometries. ................................... 104
Figure 7.2 - WSS in control (left), TGA (central), spiral (right) models. .................................... 105
Figure 8.1 - Coarsen mesh on the inlet face of the TGA model, used for the pixel by pixel
imposition of the velocity......................................................................................................... 113
List of Tables
Table 4.1 - Compliance values per each outlet of the model. .................................................... 35
Table 4.2a - Pressure drop in carotid. ........................................................................................ 36
Table 4.2b - Pressure drop in innominate and subclavian. ... Errore. Il segnalibro non è definito.
Table 4.2c - Pressure drop in descending aorta .................... Errore. Il segnalibro non è definito.
Table 5.1 - Pressure drop (ΔP) across each non-linear resistance. Q indicates flow-rate. ......... 62
Table 5.2 - Linear resistances of the LPN. .................................................................................. 63
Table 5.3 - Compliances of the LPN. .......................................................................................... 63
Table 6.1 - Mean flows calculated by OsiriX software (left) and Fluent simulation (right) at
every outlet for the TGA model. ................................................................................................. 73
Table 6.2 - Mean flows calculated by OsiriX software (left) and Fluent simulation (right) at
every outlet for the control model. ............................................................................................ 74
Table 6.3 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at every
outlet for the TGA model. The following percentages are computed relatively to the inlet flow.
................................................................................................................................................... 74
Table 6.4 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at every
outlet for the control model. The following percentages are computed relatively to the inlet
flow. ........................................................................................................................................... 75
Table 6.5 - Mean flows calculated by Fluent at every outlet of the TGA (left), control (central)
and spiral (right) models. ........................................................................................................... 87
Table 6.6 - Flow split calculated by Fluent at every outlet of the TGA (left), control (central) and
Spiral (right) models. The following percentages are computed relatively to the inlet flow. .... 87
Table 6.7 – Mean pressure calculated at each outlet of the control (left), TGA (central) and
spiral (righ) models. ................................................................................................................... 96
List of Abbreviations
List of Abbreviations
2D : Two-Dimensional
3D : Three-Dimensional
4D : Four-Dimensional
ASO : Arterial Switch Operation
BAV : Bicuspid Aortic Valve
BSA : Body Surface Area
CFD : Computational Fluid Dynamics
LPN : Lumped Parameter Network
MR : Magnetic Resonance
MRI: Magnetic Resonance Imaging
ODE : Ordinary Differential Equation
PA : Pulmonary Artery
ROI : Region of Interest
RPA : Right Pulmonary Artery
SVC : Superior Vena Cava
TGA : Transposition of the Great Arteries
List of Abbreviations
UDF : User Defined Function
VA : Ventriculo-Arterial
WSS : Wall Shear Stress
SNR : Signal to Noise Ratio
HR : Heart Rate
SV : Stroke Volume
Summary
II
INTRODUCTION
Transposition of the Great Arteries (TGA) is the most common cyanotic
congenital heart disease in neonates. The incidence of the disease is estimated
as 20-30 cases per 100,000 live births every year, with a 60-70% male
predominance. It involves ventriculo-arterial (VA) discordance, with the aorta
originating from the right ventricle and the main pulmonary artery (MPA) from
the left ventricle. The pulmonary and systemic circulations thus function in
parallel rather than in series, resulting in insufficient oxygen supply to the
tissues and excessive right and left ventricular workload. This scenario is
incompatible with prolonged survival unless oxygenated and deoxygenated
blood is mixed at some anatomic level. As soon as the condition of the
newborn is stabilised, typically by an atrial septostomy facilitating blood
mixing, it is possible to proceed with the arterial switch operation (ASO),
repositioning the great vessels in their physiological site.
Although ASO restores normal blood flow, several long-term complications
can arise and the long-term effects are not fully appreciated yet as this
procedure was introduced in the 1980s. In particular the hemodynamics might
be greatly affected by anatomical features such as enlarged aortic root and
acute aortic arch angulation, typical of TGA repaired by ASO.
AIM OF THE STUDY
The aim of this work is to create a validated computational model of the neo-
aorta following ASO and use this validated model to compare the local fluid
dynamics in different anatomies.
Particular attention was given to the result of the Lecompte maneuver, during
which the main pulmonary artery and its branches are brought forward and the
aorta is moved posteriorly, generating a greatly different anatomical
arrangement. It has been suggested that retaining the spiral shape of the aorta,
otherwise compromised during the Lecompte manoeuvre, could be beneficial,
so this scenario was also explored.
The workflow adopted in this study is summarised in Figure a: starting from
clinical data, 3D models are generated both for the experimental and the
Summary
III
computational study, using the experimental data to validate the computational
model and taking forward the study in-silico, evaluating different geometries.
Figure a – Summary of the workflow adopted in this study.
MATERIAL AND METHODS I: EXPERIMENTAL
An experimental approach was chosen because an in-vitro study can provide
controllable and reproducible data.
Anatomical models:
The study was carried out at a patient-specific level. A patient with TGA
corrected with ASO and an age-matched healthy control case were selected (15
years old, 1.7 m2 BSA, male). Both patients underwent MR examinations and
their anatomies were reconstructed in 3D from MR data using commercial
software (Mimics, Materialise, Leuven, Belgium). The final models include the
aortic root, the ascending and descending aorta, and the brachiocephalic
branches (i.e. innominate, left carotid and left subclavian arteries).
The 3D volume can be exported as a Standard Triangle Language (STL) file
compatible with the rapid prototyping technique known as PolyJet technology,
allowing to manufacture 3D models. A transparent and robust resin (Watershed
11122; DSM Somos, Elgin, IL) was used for the printing process (Figure b).
Summary
IV
Figure b - Control (left) and TGA (right) models manufactured by means of rapid prototyping
from MR data, showing the indentation on the ascending aorta (AAo) in the TGA model.
Hydraulic circuit:
The models are inserted in a mock circulatory loop (Figure c), consisting of a
pulsatile pump with adjustable stroke volume and heart rate, four Windkessel
elements and four metered needle-pinch valves at every outlet of the model, in
order to replicate arterial compliance and vascular resistance, respectively,
and a reservoir implementing atrial pressure (= 9 mmHg).
Figure c - Schematic representation of the circuit.
Summary
V
Each Windkessel component consists of a Perspex cylinder, with a 3-way valve
fitted at the top in order to control the volume of air, regulating the stiffness of
the circuit. The range of pressure at the inlet was set to 115/60 mmHg
according to cuff pressure data measured in the TGA patient. The resistance
elements have the advantage of being easily adjustable, albeit strongly flow-
dependent, thus implementing non-linear curves. They were previously
characterized imposing a range of flows and measuring the pressure drop
across the tap . They were set in order to split the flow physiologically: 55% to
the descending aorta and 45% to the upper branches.
As the circuit had to be inserted inside the MR scanner for 4D flow
acquisitions, all the ferromagnetic parts were located in the control room,
adjacent to the scanner. In order to guarantee hygiene and safety of the scanner
in the event of leakages, water was the flowing medium for performing the
experiments. Hydraulic seal between the model, the pipes and the compliant
chambers was ensured using silicon.
The measuring equipment consisted of a high-fidelity factory-calibrated fiber
optic catheter (Samba Preclin; Vastra Frolunda, Sweden) and an ultrasonic
flow probe (Transonic; Ithaca, NY, USA), both accurately calibrated before the
experiments. Pressure and flow tracings were recorded with a data acquisition
system (BIOPAC, Goleta, CA, USA) at 250 Hz.
Magnetic Resonance:
MR acquisitions were performed with a 1.5 T scanner (Avanto; Siemens,
Erlangen, Germany). Firstly, phase-contrast data was acquired for 2D
quantification of flow-velocity. The images were taken in 4 different planes,
always perpendicular to the flow: inlet, descending aorta, innominate and
subclavian arteries. Moreover, 4D (i.e. 3 spatial dimensions in time)
acquisitions were performed. Two different sequences were tested: a standard
sequence (provided by Siemens, 15 minutes acquisition) and a higher temporal
and spatial resolution sequence (1 hour 10 minutes acquisition). OsiriX
Imaging Software (Pixmeo; Geneva, Switzerland), a DICOM viewer
specifically designed for navigation and visualization of medical images, was
used for quantification of flow from phase-contrast data using a previously
Summary
VI
validated in-house written plug-in. Mean velocity for the 4 above-mentioned
planes were obtained dividing each flow by the area of the region of interest
(ROI). The difference between the inlet and the other 3 measured flows
provided a measure of carotid flow. 4D data were analysed by means of the
Siemens 4D Flow software. A 3D mask was created and 6 planes of interest
were drawn (two at the inlet of the model, one in the aortic root, one before and
one after the upper branches, and one in the descending aorta) gathering
information on flow and velocity. The evolution of particle traces and
streamlines, originated by particle seeds placed in the 3D mask, was recorded
in order to obtain temporal information.
Assessing the effect of compliance:
The main shortcoming of using a rigid model is that the compliant behaviour of
blood vessels is not considered. In order to account for this and evaluate how
local fluid dynamics are affected, a compliant TGA phantom was also
manufactured, using a rubber-like commercially available compound
compatible with PolyJet rapid prototyping, namely TangoPlus FullCure 930.
The new compliant TGA geometry was connected to the same hydraulic circuit
used for the rigid models, so that the only difference in the experiment was
represented by the material of the phantom.
MATERIALS AND METHODS II: COMPUTATIONAL
Anatomical models:
The two geometries used for the CFD simulations were the same as those
printed for the in-vitro study. In order to better understand how geometric
differences could affect the hemodynamics in the aortic arch and to better
evaluate the effect of the Lecompte maneuver, an additional patient with a
different anatomical arrangement was taken into consideration. This patient
had TGA repaired with ASO but the Lecompte maneuver was not performed in
this instance. This resulted in the aorta preserving a more spiral curvature
(Figure d). This case presented an enlarged aortic root, typical of TGA patients,
but the aortic arch is more similar to the control geometry, and is hereby
referred to as “spiral” geometry.
Summary
VII
Figure d - Comparison of three different geometries: TGA, control and “spiral”. The aorta is
shown in red and the pulmonary arteries are shown in blue.
CFD simulations:
The STL files of the geometries obtained from Mimics were imported in ICEM
(Ansys Inc., Canonsburg, PA), in order to build the finite volume mesh
(900,000 tetrahedral elements with 5 boundary prism layers) as shown in
Figure e.
Figure e - Control (left), TGA (centre) and spiral (right) geometries meshed with tetrahedral
elements. The different colour is due to the presence of three planes, created in order to
evaluate the fluid dynamics at these positions.
Summary
VIII
Computational simulations were run using commercial finite volumes software
(Ansys Fluent 14, Fluent Inc.©, Lebanon, NH). The second order upwind
method was chosen to solve the convective terms of the Navier-Stokes
equations in 3D fluid domains, with SIMPLE algorithm to solve the pressure-
velocity coupling. The solver is an implicit “Least square cell method” (1st
order, temporal increment = 10-4
s). Water was used as flowing medium (ρ=
1000 Kg/m3, μ= 1 cP) and laminar flow motion conditions were observed in all
cases. In order to reach asymptotic behaviour in the results, 5 cardiac cycles
per simulation were replicated for a total of 400,000 time-steps.
Each of the 3 aortic models (TGA, control and spiral) presented 5 boundary
faces: one aortic inlet, three brachiocephalic outlets (Innominate, Carotid,
Subclavian), and one descending aorta outlet. An 11 term Fourier series was
used to impose at the inlet of the model the same velocities measured during
the experiments (Vmean = 0.9 m/s, ranging from -0.8 m/s and 2.8 m/s). In order
to provide the necessary boundary conditions, each outlet was coupled with a
lumped parameter network (LPN, in Figure f). The LPN reproduced exactly the
experimental circuit described above.
Figure f - LPN implemented at each outlet branch. The first part of the network is different for
each outlet: C stands for the compliant chamber, R1 represents the non-linear resistance of the
taps, R2 the distributed resistances of the tubes. The second part of this LPN is common to
every outlet: Ct and Rt represent the overall compliance and resistance of the circuit.
EXPERIMENTAL RESULTS AND DISCUSSION
All hydrodynamic experiments and data acquisition were performed
successfully. The mock circuit proved to be suitable for the representation of
the downstream districts of the circulatory system and pressure and flow values
are in the physiological range, setting adequate boundary conditions.
Summary
IX
Consideration on temporal resolution for 4D flow acquisition:
There were no substantial differences between the flows acquired with the two
sequences. In both cases the mean flow (OsiriX Qmean= 5.5 L/min, Standard
Qmean= 5.5 L/min, HighRes Qmean= 7 L/min) and the amplitude of the signals
(OsiriX Qpeak= 17 L/min, Standard Qpeak= 15 L/min, HighRes Qpeak= 20 L/min)
were comparable with those measured with OsiriX from traditional 2D
Cartesian phase-contrast flow acquisitions, which represented our reference
values. The high resolution sequence was noisier and slightly overestimated the
systolic peak. From a qualitative point of view, images from the high resolution
sequence did not provide any additional information compared to the standard
one, and exhibited a noisier background, likely due to compromised signal-to-
noise ratio (SNR), as well as a smaller number of streamlines, which could not
represent adequately the fluid dynamics in the arch. As the results obtained
from the 15 minute acquisition were satisfactory as validation data for the
computational study, these were further analysed.
4D flow results: TGA vs. control anatomy:
Qualitative fluid dynamics differences between different geometries can be
appreciated thanks to 4D flow visualisation, in particular streamlines analysis.
Overall, the TGA model exhibited more chaotic flow in both systolic and
diastolic phases. In systole (Figure g) a high velocity jet was clearly visible,
impinging on the enlarged aortic root wall. This was not observed in the
control model.
Summary
X
Figure g - Streamlines in the TGA geometry (left) compared with streamlines in the control
geometry (right) at systole.
Compliant TGA model:
Noticeable geometric changes were observed in the compliant model, once
pressurised, due to the highly distensible nature of TangoPlus. The geometry
did not retain its original shape. As the aim of the work is to study the effect of
a specific geometry on the fluid dynamics, this material was deemed as not
suitable. The model was also prone to tear and, prior to inserting the model in
the MR scanner for data acquisition, structural failure of the material occurred
in correspondence of the aortic arch. Pressure data was acquired prior to
failure, showing a damped pressure waveform, as expected due to the
additional proximal compliance.
COMPUTATIONAL RESULTS AND DISCUSSION
Model validation:
There were no substantial differences between the flows acquired during the
experiments and the one calculated by the CFD simulations, both for the TGA
and the control geometries. The computational model replicated appropriately
the experimental hydrodynamic environment. Flow distribution results were in
excellent agreement, with a maximum difference in the flow split in the TGA’s
subclavian of 3.5%. Overall distributions and flow tracings in the
computational models were in good agreement with in-vitro data. Satisfactory
Summary
XI
agreement was also noted in terms of pressure tracings and pressure values:
experimental and computational mean pressures matched both in the TGA
model (84.6 mmHg vs. 85.7 mmHg) and in the control model (87.0 mmHg vs.
83.2 mmHg).
Qualitative comparison between 4D flow and CFD simulations:
A good agreement between 4D flow and CFD was assessed for both TGA and
control geometries (Figure h). In particular, CFD showed the same flow jet
impinging at the top of the aortic root wall in the TGA model, and the
surrounding whirl visible in 4D flow images. In the control model it is possible
to observe the uniform flow jet in the aortic root, smoothly reaching the upper
branches, as in the 4D flow data. All the ranges of velocities are comparable in
terms of magnitude and distributions, both in systole and in diastole.
Figure h – 4D flow streamlines (left) compared with CFD streamlines (right) at systole for the
TGA (top) and the control (bottom) geometries.
CFD anatomical assessment: TGA, control and spiral geometries
The mean flows at each outlet and the flow split in the three geometries are
comparable: the difference is around 1%, with a maximum of 1.1% in the
Summary
XII
subclavian arteries. Pressures in the TGA model are similar to the control, with
a maximum difference in the subclavian artery (3.7%). Comparing the spiral
and the control geometries, the difference in flow split is around 1%, with the
largest variation in the carotid (2.5%) and differences in flow and pressure
waveforms are negligible at every face of the models.
Streamlines highlighted the differences between the geometries. In systole
(Figure i), the control model exhibited a streamlines pattern which follows the
geometry, while in the TGA and the spiral geometries the flow jet, surrounded
by low-velocity whirling streamlines, hits the wall, losing velocity before
reaching the upper branches and causing a chaotic trend of the flow. In diastole
it is possible to underline a more chaotic streamlines trend in the enlarged root
of both the TGA and spiral geometries compared to the control.
This fluid dynamic feature, characterized by low velocities and recirculation,
could be important from a clinical point of view, since it can promote particles
deposition and consequently thrombus, clotting and plaques formation, thus
increasing long-term risk of atherosclerosis.
Figure i - Control (left), TGA (central) and spiral (right) velocity streamlines at systole.
In TGA and spiral geometries the area interested by a WSS > 25 Pa
(green/yellow) is more extended than in the control model, reaching values
Summary
XIII
around 35 Pa (red), particularly where the root narrows (Figure l). The risk of
high WSS is a mechanical damage of the inner vessel wall, which could
weaken the vessel and possibly initiate a lesion.
Figure l - WSS in control (left), TGA (central), spiral (right) models.
In both TGA and spiral roots the velocity vectors (Figure m) showed more
complex dynamics than in the control model, with presence of secondary
flows. While higher velocities in the control model are clustered in the centre
of the surface, in the other two they have a random distribution. In the
ascending aorta, the effect of the sudden shrinking after the enlarged root is
clearly visible.
Figure m – Velocity vectors in control (left), TGA (central), spiral (right) anatomies.
Summary
XIV
CONCLUSIONS
This study provides a reliable methodology for hemodynamic evaluations in
patient-specific models, highlighting how new techniques like 4D MR flow can
help in clinical analysis. Moreover CFD simulations, validated against in-vitro
data, proved to be a useful tool to study complex geometries in order to help
clinicians to evaluate the patients’ conditions and potentially assess novel
procedures. This methodology provides results that are coherent with clinical
ranges from patients’ data and from the literature. The results thus have clinical
relevance. The anatomical features of TGA, mainly the enlarged aortic root
(common to the “spiral” model, in which the Lecompte maneuvre was not
performed), have an unfavourable hemodynamic effect.
FUTURE WORK
Statistical analysis:
It is important to include more patients in the study in order to draw
conclusions on the statistical significance of the findings. Additional patients
can be implemented in the CFD simulations, whose reliability has been proven
in the validation study. Increasing the number of both TGA and healthy cases,
it is possible to characterize this congenital heart disease with statistical
confidence and potentially gather insight into long-term effects which at
present are lacking due to the absence of long-term follow up clinical data.
Compliant model:
A compliant model, reflecting the distensible behaviour of real vessels, would
be helpful to further understand the fluid dynamics, especially local
hemodynamics in the aortic root. The material must be deformable but also
able to withstand physiological pressures for the whole duration of the MR
acquisition. In this study Tango Plus suffered structural failure, so finding
alternative materials warrants future investigation.
Provided that significant differences are observed between rigid and compliant
phantoms, it is possible to account for such compliant behaviour also in the
computational simulations, using a fluid-structural interaction (FSI) approach.
One problem typically related to this tool is the lack of information on the
Summary
XV
elastic characteristics of natural vessels. However, using an artificial material,
thoroughly characterised experimentally, all the elastic characteristics could be
implemented in the FSI simulations.
Pixel by pixel inlet imposition:
4D MR flow is a novel technique providing a breath of hemodynamic
information, and it is appealing to try and develop methods of data extraction
in order to refine the computational simulations. For example, imposing
velocities values to each element of the mesh at the inlet of the computational
model, instead of the spatial average, could allow to obtain a more detailed
characterization of complex fluid dynamics. It is possible, from MR data, to
extract the velocity in each of the pixels of the inlet face, in the three
components x, y and z. The effect of this different inlet on the local fluid
dynamics, such as better characterising whirling and recirculation in the aortic
root, warrants further study.
Sommario
XVII
INTRODUZIONE
La Trasposizione delle Grandi Arterie (TGA) è una grave cardiopatia
congenita, cianotica che si manifesta alla nascita. Tale patologia, la cui
incidenza è stimata intorno ai 20-30 casi all’anno per ogni 100.000 nati vivi ha
una predominanza per il sesso maschile del 60-70%. È caratterizzata da una
discordanza arterio-ventricolare, con l’aorta che ha origine dal ventricolo
destro e l’arteria polmonare dal ventricolo sinistro. La configurazione
anatomica che ne risulta prevede un funzionamento in parallelo tra circolazione
polmonare e sistemica, piuttosto che in serie.
Questa situazione è incompatibile con la vita, a meno di comunicazioni tra i
due circoli, polmonare e sistemico, che permettano al sangue deossigenato di
miscelarsi con il sangue ossigenato. Per questo motivo, in tali pazienti, viene
eseguita una settostomia atriale alla nascita, necessaria per stabilizzare le
condizioni del neonato prima di procedere con l’operazione che riposiziona i
grandi vasi nei loro siti fisiologici, chiamata appunto “operazione di inversione
arteriosa” (Arterial Switch Operation, ASO). Nonostante l’operazione di
inversione delle grandi arterie ripristini una normale disposizione delle
strutture cardiache, numerose complicazioni a lungo termine possono insorgere
e per di più gli effetti a lungo termine non sono ancora ben noti dal momento
che il primo caso di ASO è stato riportato all’inizio degli anni Ottanta. In
particolare, è stato notato come le caratteristiche anatomiche tipiche di pazienti
TGA trattati con ASO, quali la radice aortica allargata e la acuta angolazione
dell’arco aortico, potrebbero influenzare l’emodinamica nel distretto aortico.
OBIETTIVO DELLO STUDIO
L’obiettivo di questo lavoro è di creare un modello computazionale della
neoaorta a seguito di ASO, di validarlo, e infine di usarlo per valutare come
differenti anatomie possono influenzare la fluidodinamica locale.
Particolare attenzione è stata posta sulla Lecompte maneuver, manovra
chirurgica nella quale l’arteria polmonare e le sue diramazioni vengono
spostate anteriormente all’aorta, generando una inusuale disposizione
anatomica con l’aorta in posizione posteriore e compressa dalle arterie
Sommario
XVIII
polmonari. In letteratura è stato suggerito che il mantenimento di una
disposizione più fisiologica potrebbe giovare da un punto di vista
emodinamico: è stato pertanto suggerito di ricreare la curvatura naturale
dell’arco aortico, altrimenti compromessa dalla Lecompte maneuver. In questo
lavoro è stata modellata e analizzata anche questa anatomia.
In Figura a è stato riportato uno schema riassuntivo del lavoro svolto: partendo
da dati clinici, sono stati generati i modelli 3D da usare sia per lo studio
sperimentale che per quello computazionale. I risultati sperimentali sono stati
usati per validare il modello computazionale che, una volta validato, è stato
applicato allo studio delle diverse anatomie indagate.
Figura a – Rappresentazione schematica del lavoro svolto.
MATERIALI E METODI SPERIMENTALI
E’ stato scelto un approccio sperimentale dato che uno studio in-vitro è in
grado di fornire dati controllabili e riproducibili.
Modelli anatomici:
Lo studio è stato svolto a livello patient-specific. Per apprezzare le differenze
emodinamiche, sono stati selezionati due soggetti della stessa età e con
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XIX
caratteristiche fisiche comparabili (15 anni, 1.7 m2 BSA, maschi): un paziente
TGA corretto con ASO e un controllo sano.
Di entrambi i pazienti, i dati di risonanza magnetica erano disponibili e sono
stati utilizzati per ricostruirne le anatomie 3D, usando un software
commerciale (Mimics, Materialise, Leuven, Belgium). I modelli finali
includono la radice aortica, l’aorta ascendente e discendente e le arterie
brachiocefaliche (anonima, carotide sinistra e succlavia sinistra).
Il volume 3D creato per ogni modello può essere esportato come un file
Standard Triangle Language (STL), compatibile con la tecnica di
prototipazione rapida, conosciuta come tecnologia PolyJet, che permette di
stampare modelli fisici 3D. Per il processo di stampaggio è stata scelta una
resina rigida e trasparente (Watershed 11122; DSM Somos, Elgin, IL) (Figura
b).
Figura b – Modello di controllo (sinistra) e TGA (destra) stampati con la tecnica di
prototipazione rapida a partire da immagini di MR, che mostrano la posizione dell’aorta
ascendente (AAo) nel modello TGA.
Circuito idraulico:
I modelli sono stati montati in un circuito idraulico (Figura c), consistente in
una pompa pulsatile con un volume di eiezione e un range di frequenza
cardiaca regolabili, quattro elementi Windkessel e quattro valvole a rubinetto
ad ogni uscita dei modelli, per riprodurre rispettivamente la distensibilità delle
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XX
arterie e la resistenza vascolare, e una riserva il cui battente idraulico
rappresenta la pressione atriale (9 mmHg).
Figura c – Rappresentazione schematica del circuito.
Ogni componente Windkessel è costituita da un cilindro in Perspex, con una
valvola a tre posizioni nella parte superiore per controllare il volume di aria
contenuto nel cilindro, regolando così la rigidezza del circuito. Le valvole a
rubinetto sono state regolate in modo da ottenere un intervallo di pressione
all’ingresso del circuito di 115/60 mmHg, in accordo con la pressione misurata
nel paziente TGA, e una divisione fisiologica del flusso con il 55% in aorta
discendente e 45% nei vasi brachiocefalici. Gli elementi resistivi utilizzati
hanno il vantaggio di essere facilmente controllabili, sebbene fortemente
dipendenti dal flusso. Le loro curve caratteristiche non lineari sono state
ottenute imponendo diversi flussi e misurando la caduta di pressione a cavallo
del rubinetto.
La parte centrale del circuito è progettata priva di componenti metallici in
modo da poter essere inserita ed usata in uno scanner per risonanza magnetica.
I componenti ferromagnetici come la pompa, le console degli strumenti di
misurazione e il laptop sono stati posizionati nella stanza adiacente allo
scanner. Per questioni di sicurezza e igiene dello scanner nell’eventualità di
perdite, come fluido di prova è stato scelto di utilizzare acqua durante gli
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XXI
esperimenti. Le guarnizioni idrauliche, i modelli, i tubi e le camere complianti
sono state sigillate utilizzando silicone.
La strumentazione per le misurazioni è composta da un catetere di pressione a
fibra ottica (Samba Preclin; Vastra Frolunda, Sweden) e un flussimetro ad
ultrasuoni (Transonic; Ithaca, NY, USA), entrambi accuratamente calibrati
prima degli esperimenti. Pressioni e flussi sono stati registrati con un sistema di
acquisizione di dati (BIOPAC , Goleta, CA, USA) a 250 Hz.
Risonanza Magnetica:
Le acquisizioni sono state effettuate con uno scanner da 1.5 T (Avanto;
Siemens, Erlangen, Germany). Per prima cosa sono stati acquisiti dati a
contrasto di fase per le quantificazioni 2D di flusso e velocità in 4 diversi piani,
scelti perpendicolari al flusso in corrispondenza dell’ingresso del modello,
dell’aorta discendente, anonima e succlavia. Successivamente sono state
acquisite due diverse sequenze 4D (le 3 dimensioni spaziali nel tempo): una
standard (fornita dalla Siemens, della durata di 15 minuti) e una con
risoluzione spaziale e temporale aumentate (della durata di 1 ora e 10 minuti).
Il software OsiriX Imaging (Pixmeo; Geneva, Switzerland), progettato per la
navigazione e la visualizzazione di immagini mediche, è stato utilizzato per la
quantificazione di flussi da dati a contrasto di fase usando un plug-in
precedentemente scritto e validato dal gruppo di ricerca del Great Ormond
Street Hospital di Londra. Le informazioni sulle velocità nei quattro piani
descritti prima sono state ottenute dividendo i flussi per l’area delle rispettive
regioni di interesse (ROI). La misura del flusso in carotide è stata ottenuta
sottraendo al flusso in ingresso i 3 flussi calcolati alle altre uscite. I dati 4D
sono stati analizzati per mezzo del software Siemens 4D Flow. Dopo aver
creato una maschera 3D, sono stati disegnati 6 piani di interesse (2 all’ingresso,
1 in radice aortica, 2 lungo l’arco aortica, rispettivamente prima e dopo i vasi
brachiocefalici e uno in aorta discendente) per estrarre dati su velocità e flussi.
Infine, per studiare l’evoluzione temporale delle particelle di flusso lungo
l’arco aortico e le sue diramazioni, sono state riprodotte le streamlines
registrate nel modello scegliendo opportuni piani di origine nella maschera 3D.
Sommario
XXII
Stima dell’effetto della distensibilità:
Il principale limite nell’uso di modelli rigidi consiste nel trascurare la
deformabilità fisiologica dei vasi. Per studiarne l’effetto sulla fluidodinamica
locale, è stato perciò stampato lo stesso modello TGA ma con un un materiale
gommoso, e quindi distensibile, commercialmente disponibile e compatibile
con la prototipazione rapida, chiamato Tango Plus FullCure 930. La nuova
geometria TGA deformabile è stata connessa allo stesso circuito idraulico
utilizzato per i modelli rigidi, in modo da valutare la sola influenza del
materiale.
MATERIALI E METODI COMPUTAZIONALI
Modelli anatomici:
Le stesse due anatomie stampate per gli studi in-vitro sono state utilizzate per
le simulazioni CFD. Per meglio comprendere come le differenze geometriche
possono influenzare l’emodinamica nell’arco aortico e valutare l’effetto della
Lecompte maneuver, è stato considerato un ulteriore paziente, con una diversa
disposizione anatomica. È un paziente TGA che ha subito una ASO senza
Lecompte maneuver. Il risultato è una disposizione anatomica differente
(Figura d), con l’aorta che mantiene una curvatura più fisiologica. Anche
questo caso presenta una radice aortica allargata, tipica dei pazienti TGA, ma
l’arco aortico è più simile alla geometria di controllo. Questa geometria è
definita, nel nostro studio, con il nome di “spiral”.
Sommario
XXIII
Figura d - Confronto tra le tre diverse geometrie: TGA, controllo e “spiral”. L’aorta è colorata
in rosso, mentre l’arteria polmonare in blu.
Simulazioni CFD:
I file STL delle geometrie, ottenuti da Mimics, sono stati importate in ICEM
(Ansys Inc., Canonsburg, PA), per creare le mesh a volumi finiti (900000
elementi tetraedrici con 5 strati di prismi al contorno), come mostrato in Figura
e.
Figura e - Controllo (sinistra), TGA (centrale) and spiral (destra) con mesh ad elementi
tetraedrici. I diversi colori corrispondono a 3 piani, creati in ciascuna geometria per valutare la
fluidodinamica in quelle posizioni.
Sommario
XXIV
Le simulazioni computazionali sono state effettuate con un software
commerciale per simulazioni a volumi finiti (Ansys Fluent 14, Fluent Inc. ©,
Lebanon, NH). Il metodo scelto per risolvere i termini convettivi delle
equazioni di Navier-Stokes nel dominio fluido 3D è il metodo Upwind di
secondo ordine, con l’algoritmo SIMPLE per risolvere l’accoppiamento
pressione-velocità.
Il metodo di risoluzione adottato è il metodo “Least square cell” (primo ordine,
incremento temporale = 10-4
s). Il fluido scelto per le simulazioni è l’acqua (ρ=
1000 Kg/m3, μ= 1 cP) e condizioni di moto laminare sono state verificate in
ogni simulazione. Per raggiugere un comportamento asintotico dei risultati,
sono stati simulati 5 cicli cardiaci, corrispondenti a 40000 passi temporali.
Ognuno dei 3 archi aortici modellati (TGA, controllo e spiral) presenta 5 facce:
una di ingresso, e quattro di uscita (anonima, carotide, succlavia e aorta
discendente). Le velocità misurate durante gli esperimenti sono state imposte
come ingresso del modello grazie a una serie di Fourier a 11 termini (Vmedia =
0.9 m/s, con intervallo da -0.8 m/s e 2.8 m/s). Per fornire le adeguate
condizioni al contorno ogni uscita è stata accoppiata ad una rete a parametri
concentrati (Figura f). Questa rete riproduce esattamente il circuito
sperimentale precedentemente presentato.
Figura f - Rete a parametri concentrati ad ogni uscita del modello.La prima parte della rete è
diversa per ogni uscita: C indica la camera compliante, R1 rappresenta la resistenza non lineare
del rubinetto, R2 la resistenza distribuita dei tubi. La seconda parte della rete è in comune tra
tutte le uscite: Ct e Rt rappresentano la complianza e la resistenza totali del circuito.
RISULTATI SPERIMENTALI E DISCUSSIONE
Tutti gli esperimenti idrodinamici e le acquisizioni sono stati condotti con
successo. Il circuito idraulico si è rivelato adatto a rappresentare i distretti a
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XXV
valle del sistema circolatorio. Le pressioni ed i flussi ottenuti si trovano tutti in
un intervallo di valori fisiologico.
Considerazioni sulla risoluzione temporale delle acquisizioni 4D flow:
Non sono state notate differenze sostanziali tra i flussi acquisiti con le due
sequenze. I valori di flusso medio (OsiriX Qmedio=5.5 L/min, Standard
Qmedio=5.5 L/min, HighRes Qmedio=7 L/min) e l’ampiezza dei segnali (OsiriX
Qmax=17 L/min, Standard Qmax=15 L/min, HighRes Qmax=20 L/min) sono
confrontabili con quelli estratti da OsiriX tramite l’acquisizione standard 2D in
contrasto di fase, utilizzata come termine di paragone. La sequenza ad alta
risoluzione ha fornito risultati più rumorosi e ha leggermente sovrastimato il
picco sistolico.
Da un punto di vista qualitativo le immagini estratte tramite l’acquisizione ad
alta risoluzione non hanno fornito nessuna informazione aggiuntiva rispetto
alla sequenza standard, e addirittura hanno mostrato uno sfondo rumoroso,
dovuto al rapporto segnale-rumore compromesso, e un numero inferiore di
streamlines, che potrebbero quindi non rappresentare in modo completo la
fluidodinamica nell’arco aortico.
Risultati del 4D flow: anatomia TGA vs. controllo:
Le differenze qualitative tra le due diverse geometrie possono essere
apprezzate grazie alla visualizzazione del 4D flow, e in particolare tramite
l’analisi delle streamlines. Complessivamente, il flusso nel modello TGA
risulta essere più caotico sia in sistole che in diastole. In sistole (Figura g), il
getto ad alta velocità che impatta contro la parete della radice aortica,
chiaramente visibile nella geometria patologica, è assente nel modello di
controllo.
Sommario
XXVI
Figura g - Streamlines durante la sistole nella geometria TGA (sinistra) confrontate con il
modello di controllo (destra).
Modello TGA distensibile:
Una volta messo sotto pressione, sono stati osservati importanti cambiamenti
nella forma del modello distensibile, a causa della grande deformabilità del
materiale. In particolar modo la radice aortica ha perso la forma originale. Dal
momento che lo scopo del lavoro è studiare gli effetti di una specifica
geometria sulla fluidodinamica, questo materiale si è rivelato inadatto. Prima di
inserire il modello dentro lo scanner, inoltre, il materiale è andato incontro a
cedimento strutturale. I valori di pressioni sono stati acquisiti prima del
cedimento, mostrando, come previsto, una forma d’onda più smorzata a causa
dell’aumento della compliance prossimale.
RISULTATI COMPUTAZIONALI E DISCUSSIONE
Validazione del modello:
Non essendoci differenze sostanziali tra i flussi acquisiti durante gli
esperimenti e quelli calcolati dalle simulazioni CFD, né per la geometria TGA
né per quella di controllo, possiamo affermare che il modello computazionale
replica correttamente le condizioni idrauliche sperimentali. Le distribuzioni dei
flussi tra le uscite sono in ottimo accordo, con una differenza massima del
3.5% nell’arteria succlavia del modello TGA. L’andamento temporale dei
Sommario
XXVII
flussi conferma che la simulazione CFD riproduce in maniera soddisfacente le
condizioni del set-up sperimentale. Inoltre è apprezzabile una soddisfacente
corrispondenza per quanto riguarda le pressioni medie e il loro tracciato nel
tempo, sia per il TGA (85.7 mmHg dal test sperimentale vs. 84.6 mmHg dalla
simulazione) che per il controllo (87.0 mmHg dal test sperimentale vs. 83.2
mmHg dalla simulazione).
Confronto qualitativo tra il 4D flow e le simulazioni CFD:
La corrispondenza tra i risultati del 4D flow e quelli computazionali è ottima,
sia per il modello TGA che per il controllo (Figura h). In particolare il CFD
mostra lo stesso getto che impatta contro l’apice della radice aortica nel
modello TGA e gli stessi vortici circostanti che si notano nelle immagini del
4D flow. Nel modello di controllo è possibile osservare il getto, uniforme
lungo l’intero arco aortico, che scorre verso le arterie brachiocefaliche, identico
a quello mostrato dal 4D flow. Gli intervalli di velocità sono confrontabili sia
in termini di valore assoluto che di distribuzione, in sistole come in diastole.
Figura h – Confronto tra le streamlines ottenute dal 4D flow (sinistra) e quelle ricavate dalla
simulazione CFD (destra) in sistole nel modello TGA (in alto) e nel controllo (in basso).
Sommario
XXVIII
Confronto CFD tra i modelli TGA, di controllo e “spiral” :
Il flusso medio ad ogni uscita e la sua ripartizione sono confrontabili nelle tre
geometrie: la differenza è intorno all’1%, con un massimo di 1.1% in
succlavia. La pressione nel modello TGA è molto simile a quella nel controllo,
con una variazione massima in succlavia (3.7%). Confrontando la geometria
spiral con il controllo, la differenza è intorno all’1%, con la più grande
variazione in carotide (2.5%). La stessa situazione si può osservare per le
forme d’onda di flussi e pressioni, dove le differenze sono trascurabili in ogni
faccia dei modelli. Le streamlines mettono in evidenza le differenze tra le
geometrie. In sistole (Figura i) si nota come, mentre nel controllo le linee di
flusso seguono la geometria, nel modello TGA e in quello spiral un getto ad
alta velocità, circondato da vortici a bassa velocità, colpisce la parete perdendo
velocità prima di raggiungere le arterie brachiocefaliche e causando un
andamento casuale del flusso. In diastole è possibile evidenziare l’andamento
meno ordinato delle streamlines nella radice aortica del modello TGA e spiral,
se confrontate con il controllo.
Questa situazione fluidodinamica, caratterizzata da basse velocità e ricircoli,
può essere importante da un punto di vista clinico, poiché promuove la
formazione di coagulo, di trombo o placca, aumentando il rischio a lungo
termine di arteriosclerosi.
Sommario
XXIX
Figura i - Streamlines in sistole nei modelli di controllo (sinistra), TGA (centrale) e spiral
(destra)
Nelle geometrie TGA e spiral, l’area caratterizzata da valori di sforzo alla
parete più alti di 25 Pa (giallo/verde) è più estesa rispetto al modello di
controllo, e il WSS raggiunge persino valori intorno ai 35 Pa, specialmente
dove la radice si stringe (Figura l). Alti valori di sforzo alla parete possono
causare danni meccanici alla parete interna dei vasi [Chien et al., 1998 and
Shyyy ,2001], che può portare all’ indebolimento degli stessi e potenzialmente
a un inizio di lesione.
Figura l - Sforzo alla parete nel modello di controllo (sinistra), TGA (centrale) e spiral
(destra).
Sommario
XXX
I vettori di velocità (Figura m) nella radice sia del modello TGA che nello
spiral mostrano una fluidodinamica più complessa che nel controllo, con
presenza di flussi secondari. Mentre le zone ad alta velocità sono concentrate al
centro della radice del controllo, negli altri due modelli hanno una
distribuzione casuale. In aorta ascendente l’effetto del brusco restringimento è
chiaramente visibile.
Figura m – Vettori di velocità nella radice aortica, in aorta ascendente e in aorta discendente
dei modelli di controllo (sinistra), TGA (centrale) e spiral (destra).
CONCLUSIONI
Conclusioni:
Questo studio fornisce un metodo affidabile per la valutazione
dell’emodinamica in modelli patient-specific, evidenziando come la nuova
tecnica di 4D MR flow possa essere utile per l'analisi clinica. Inoltre le
simulazioni CFD, validate con i risultati in-vitro, si sono dimostrate uno
strumento valido per studiare geometrie complesse e aiutare i medici a valutare
le condizioni del paziente ed eventualmente a testare virtualmente procedure
chirurgiche innovative. Questo metodo ha fornito risultati confermati da ogni
simulazione e coerenti con gli intervalli fisiologici presenti ini letteratura. I
risultati hanno una grande rilevanza dal punto di vista clinico. Le caratteristiche
anatomiche derivanti dalla correzione della trasposizione delle grandi arterie, in
particolare la radice aortica dilatata (comune al modello “spiral”, in cui la
Sommario
XXXI
Lecompte maneuver non è stata effettuata), hanno dimostrato avere un effetto
negativo sull’emodinamica.
SVILUPPI FUTURI
Analisi statistica:
Sarebbe interessante includere ulteriori pazienti nello studio, in modo da poter
tratte conclusioni di rilevanza statistica da un punto di vista clinico. Le
simulazioni CFD, la cui affidabilità è stata provata in questo studio, sarebbero
quindi la metodologia da usare per l’analisi di nuove anatomie patient-specific.
Aumentando il numero sia di pazienti TGA che di casi fisiologici, sarà
possibile caratterizzare questa patologia cardiaca congenita con confidenza
statistica, intuendo potenzialmente gli effetti a lungo termine ad oggi ancora
sconosciuti per l’assenza di un adeguatamente esteso follow-up clinico.
L’effetto della distensibilità:
Un modello distensibile, che rispecchia il comportamento deformabile dei vasi
fisiologici, sarebbe d’aiuto per capire meglio la fluidodinamica, e in particolare
l’emodinamica locale nella radice aortica. Il materiale da usare per stampare
tali modelli deve essere deformabile, ma anche capace di resistere sotto
pressione per il tempo richiesto dalll’acquisizione delle immagini di risonanza
magnetica. In questo studio il Tango Plus ha subito un cedimento strutturale,
quindi la ricerca di materiali alternativi deve essere oggetto di eventuali
indagini future.
Purché un analisi sperimentale con un circuito idraulico mostri differenze tra i
modelli rigidi e distensibili, è possibile tenere conto del comportamento
distensibile anche nelle simulazioni computazionali, sfruttando un approccio di
interazione fluido-struttura (FSI). Un problema solitamente legato a questo
strumento è la mancanza di informazioni sulle proprietà elastiche del vaso
naturale. Utilizzando un materiale artificiale, approfonditamente caratterizzato
sperimentalmente, tutte le proprietà elastiche possono essere implementate
nelle simulazioni FSI
Sommario
XXXII
Imposizione pixel per pixel del flusso in ingresso:
Four-Dimensional MR flow è una tecnica nuova, in grado di fornire utili
informazioni emodinamiche. E’ interessante cercare di sviluppare nuovi metodi
di estrazione dei dati, in modo da migliorare le simulazioni computazionali. Per
esempio, imporre valori di velocità a ogni elemento della faccia di ingresso del
modello computazionale, invece del valore medio, potrebbe permettere di
caratterizzare la complessa fluidodinamica della radice aortica in modo più
dettagliato. Dalle immagini di risonanza magnetica è infatti possibile estrarre il
valore della velocità nelle sue tre componenti x, y e z in ogni pixel della faccia
di ingresso. L’effetto di questo tipo di ingresso sulla fluidodinamica locale, ad
esempio per caratterizzare meglio i ricircoli e i vortici all’interno della radice
aortica, potrebbe essere oggetto di studi futuri.
Chapter 1 Introduction: the clinical problem
2
1.1 TRANSPOSITION OF THE GREAT ARTERIES
Transposition of the Great Arteries (TGA) is the most common cyanotic
congenital heart disease in neonates [Lincon et al., 1984]. The incidence of the
disease is estimated as 20-30 cases per 100,000 live births every year, with a
60-70% male predominance [Kalogeropoulos et al., 2009].
Although the aetiology of this congenital disease is still unknown, some risk
factors have been identified:
- Mother’s age > 40 years
- Alcoholism
- Diabetes
- Poor nutrition during pregnancy
- Rubella or other viral illness during pregnancy.
The hallmark of TGA is ventriculo-arterial (VA) discordance, whereby the
aorta arises from the right ventricle and the pulmonary artery (PA) arises from
the left ventricle (Figure 1.1) [Warnes, 2006].
Figure 1.1 - Schematic representation of the heart with TGA, highlighting the origin of the
great vessels from the incorrect ventricle [yorksandhumberhearts.nhs.uk].
Chapter 1 Introduction: the clinical problem
3
This anatomical arrangement impacts on the way blood circulates throughout
the body; in fact, the pulmonary and systemic circulations function in parallel
rather than in series. Oxygenated pulmonary venous blood returns to the left
atrium and left ventricle, but it is recirculated to the pulmonary vascular bed
via the abnormal pulmonary arterial connection to the left ventricle.
Deoxygenated systemic venous blood returns to the right atrium and right
ventricle where it is pumped to the systemic circulation, effectively bypassing
the lungs.
This parallel circulation results in insufficient oxygen supply to the tissues and
excessive right and left ventricular workload [Allen et al., 2007]. It is
incompatible with prolonged survival unless oxygenated and deoxygenated
blood are mixed at some anatomic level, such as in the presence of atrial or
ventricular septal defects acting as left-to-right shunts [Planche et al., 1998].
In approximately 60% of patients, the aorta is anterior and to the right of the
pulmonary artery, while a subset of patients presents the aorta located in front
and to the left of the pulmonary artery. These two types of configurations are
referred to as dextro-transposition of the great arteries (d-TGA) and levo-
transposition of the great arteries (l-TGA).
In addition, most TGA patients (regardless of the spatial orientation of the
great arteries) exhibit a subaortic infundibulum, absence of subpulmonary
infundibulum, and fibrous continuity between the mitral valve and the
pulmonary valve [Shrivastava et al., 1976]. However, several exceptions have
been observed and cannot be placed in the above classifications [Allen et al.,
2007].
With regard to ventricular morphology, the patient’s ventricles have normal
shape and thickness in presence of atrial-septal defect at birth, otherwise the
right ventricular wall is considerably thickened, with such thickening
increasing with growth. Within few weeks, the right ventricle often becomes
enlarged and hypertrophied. The wall of the left ventricle, instead, begins to
thin and becomes compressed [Planche et al., 1998].
The aortic valve plane is rightward and anterior relative to the pulmonary
trunk. The fibrous continuity of the leaflets of the atrio-ventricular and the
Chapter 1 Introduction: the clinical problem
4
ventriculo-arterial valves is located on the right side rather than on the left side
[Planche et al., 1998].
Coronary arterial anatomy in TGA patients is not only significantly different
from the normal circulatory arrangement, but it can also vary substantially
within this patients’ group. In most cases, the coronary arteries originate from
the aortic sinuses contiguous to the pulmonary trunk and run directly toward
the atrio-ventricular groove following a normal course. In other cases, they
originate from different sinuses and have an intramural course, or can be
characterised by abnormal looping around the vessels [Planche et al., 1998].
Another anatomical consideration concerns the pulmonary trunk, which can be
larger than the descending aorta, particularly in those cases presenting a
ventricular septal defect. Either isthmic coarctation or interrupted aortic arch
are very common in hearts with ventricular septal defect [Planche et al., 1998].
Following from these considerations, TGA clearly results in a complex
anatomical and physiological arrangement and, if untreated, this pathology
leads to a 30% mortality rate in the first week of life, 50% in the first month,
and 90% by the end of the first year [Allen et al., 2007]. On the other hand,
short-term and midterm survival rate exceeds 90% in cases of successfully
palliated or corrected TGA [Allen et al., 2007].
1.2 SURGICAL REPAIR OF TGA: THE ARTERIAL
SWITCH OPERATION
Repair of TGA has been attempted since the 1950s. The most successful
procedures were introduced in 1958 by A. Senning [Senning, 1959] and in
1963 by W.T. Mustard [Mustard, 1964]. Both approaches consisted in
redirecting blood flow within the atria: the former has the advantage of not
using foreign material (i.e. atrial patch), the latter of being simpler to manage
post-operatively [Kostantinov et al., 2004]. The Senning or Mustard procedures
thus represent an ‘atrial switch’ and have been used to palliate TGA until a new
procedure, referred to as ‘arterial switch’, was introduced in 1980. The first
successful arterial switch operation (ASO) was reported by Jatene [Jatene,
Chapter 1 Introduction: the clinical problem
5
1982], and it proved to be more beneficial than the atrial correction [Planche et
al., 1998], as it avoids arrhythmias and dysfunctions of the systemic ventricle.
This thesis will focus solely on patients who underwent ASO procedure, as
described below.
In the first day of life, the primary step undertaken to treat a newborn with
TGA defect is to perform a Rashkind balloon atrial septostomy [Warnes,
2006]. This mini-invasive procedure uses a balloon catheter to enlarge the
foramen ovale (i.e. the hole allowing communication between the atria in the
fetal circulation) in order to prevent its sealing, otherwise naturally occurring
soon after birth. This facilitates blood mixing and increases oxygen saturation
(Figure 1.2).
Figure 1.2 - Rashkind procedure: the balloon catheter is inserted into the septal defect and
inflated. After inflation, the catheter is pulled back through the hole [http://www.hakeem-
sy.com].
After 10-15 days, the aorta and main pulmonary artery can be surgically
repositioned (Figure 1.3) performing the actual arterial switch, which requires
cardiopulmonary bypass and aortic cross clamping.
Chapter 1 Introduction: the clinical problem
6
One particularly challenging feature of ASO is the relocation of the coronary
arteries, in order to avoid cardiac hypoxemia and ischemia of the myocardium.
The left and right coronary arteries ostia are visualized and excised from the
aortic root, with adjacent aortic wall, as "buttons". In abnormal looping course
the dissection of the coronary trunk is extended, in order to avoid any stretch or
kink during the relocation. The coronary artery buttons are then shifted
posteriorly and implanted into the facing sinuses of the main pulmonary artery
root. The left coronary artery is allocated in a low position and the right
coronary artery in a high position, in order to reduce the risk of distortion. A
lateral relocation could prevent compression by the pulmonary bifurcation.
The aorta is transected in the middle of the ascending portion, in order to lessen
the amount of reconstructed aorta posteriorly below the transferred pulmonary
artery bifurcation. The pulmonary trunk is transected 5–10 mm below its
bifurcation. Next, the main pulmonary artery and its branches are brought
forward (“Lecompte maneuver”), and the distal aorta is moved posteriorly
[Planche et al., 1998]. The distal aorta is now anastomosed (termino-terminal
anastomosis) to the root of the pulmonary valve. Reconstruction of the
pulmonary artery is then undertaken, utilising a patch of cryopreserved
pulmonary artery homograft.
Closure of the atrial septal defect completes the arterial switch repair [Planche
et al., 1998].
Chapter 1 Introduction: the clinical problem
7
Figure 1.3 - Schematic representation of the arterial switch operation, including relocation of
coronary buttons [http://radiology.rsna.org].
1.3 POSTOPERATIVE COMPLICATIONS
Although arterial switch restores normal blood flow with mixing of oxygenated
and deoxygenated blood, and 90% 10-year survival has been reported to date,
indicating the success of the surgery [Warnes, 2006], several long-term
complications can arise. It should be noted that since this procedure has been
performed for only approximately 30 years, there are no long-term survivors so
far, and the possible extent of long-term complications is not fully appreciated
yet [Cohen et al., 2010].
Aortic wall abnormalities in surgically repaired TGA are likely due to
anomalous aorticopulmonary septation, damage to the vasa vasorum, and
surgical manipulations during ASO. Vasa vasorum transections during the
procedure, with consequent blood flow inhibition, can induce necrosis followed
by dilatation, This can lead to impaired distensibility of the neoaorta, and both
Chapter 1 Introduction: the clinical problem
8
invasive and imaging-based studies have reported reduced aortic distensibility
in this group of patients [Ntsinjana et al., 2012]. Kinking of the coronary
arteries could also occur, because of the spatial arrangement of the vessels,
which does not respect the physiological one. Physical manipulations during
ASO, such as the reimplantation of the coronary arteries and suturing of the
two main vessels, can also lead to scarring and changes in the neoaortic root
wall, resulting in progressive aortic dilatation. Aneurysm formation and aortic
dissection have also been attributed to the ASO surgical handlings [Grotenhuis
et al., 2008].
After ASO, the neoaortic wall (the former pulmonary artery) is exposed to
higher systemic pressures. Concern has been raised about the ability of the
pulmonary root to adapt to a systemic pressure load. A study by Co-Vu et al.
discussed the risk for the native pulmonary root to dilate when implanted in the
aortic position, because of the histologic differences inherent to the vessel
walls of the pulmonary and aortic arteries. Also, no evidence of stabilization in
the root dimensions has been observed yet, around 15-20 years postoperatively
[Co-Vu et al., 2012].
Both aortic distensibility and aortic dimensions are crucial parameters affecting
aortic valve dynamics. Decreased distensibility of the aortic root increases
stress and strain on the neoaortic valve leaflets, therefore predisposing for
aortic valve dysfunction [Grotenhuis et al, 2008]. In addition, the risk for
neoaortic valve regurgitation appeared to increase with length of time after the
operation, which parallels the risk for neo-aortic root dilation [Co-Vu et al.,
2012].
Furthermore, the relocation of the ascending aorta onto the pulmonary valve
might create an abnormally acute angulation of the aortic arch (Figure 1.4) as a
consequence of the Lecompte maneuver. This postoperative morphological
feature has been suggested to induce enhanced systolic wave reflection and
consequent ascending aortic dilatation [Agnoletti et al., 2007]. The acute
angulation of the aortic arch, also referred to as “gothic” arch, has been
associated with compromised exercise capacity in these patients [Ou et al.,
2008]. Furthermore, the increased impedance due to a stiffer and abnormally
Chapter 1 Introduction: the clinical problem
9
shaped aortic arch is likely to impinge on the VA coupling, as recently
indicated by Biglino et al. Thus, it has been suggested that TGA repair by ASO
can also have consequences on pumping efficiency and energetics [Biglino et
al., 2013].
Figure 1.4 - Fluoroscopy visualisation of an acute aortic arch, or gothic arch, as a result of
arterial switch operation. The enlarged aortic root (indicated by the yellow arrow) and the
indentation resulting from repositioning of the pulmonary arteries following the Lecompte
procedure (red arrow) can also be appreciated. Image modified from [Agnoletti et al., 2007].
1.4 SURGICAL REPAIR OF TGA: AN
ALTERNATIVE OPERATION
In a normal anatomy, the aorta and the main pulmonary artery present a spiral
spatial arrangement, while the ASO with Lecompte maneuver, as described in
paragraph 1.3, does not maintain the spiral relationship of the great arteries.
Chapter 1 Introduction: the clinical problem
10
This has been indicated as one of the main causes for some of the clinical
complications in repaired TGA [Chiu et al., 2002]. For this reason, a modified
ASO by a so-called “spiral reconstruction” (Figure 1.5) has been advocated to
potentially help in avoiding coronary kinking.
Figure 1.5 - Comparison between normal heart (C), TGA (A), ASO with Lecompte (B) and
spiral ASO (D). It is possible to appreciate how the spiral procedure restores a more
physiological anatomy than the traditional arterial switch operation [image form Chiu et
al.,2002].
The three main differences of the spiral procedure with respect to the previous
technique have been described by the group who introduced it as follows: (1)
the aorta is amputated obliquely so that a larger left lip can be used as the floor
of the pulmonary pathway; (2) the right posterior part of the pulmonary trunk is
divided to make a larger flap to be everted to the left and a more leftward
pulmonary pathway after neoaortic anastomosis and posterior attachment
Chapter 1 Introduction: the clinical problem
11
(suturing the caudal edge of the right pulmonary artery to the posterior
neoaorta) accordingly; (3) the posterior attachment site is ascertained after
release of the aortic cross-clamp, as in the previous technique (Figure 1.6).
However, to facilitate exposure, the aorta is cross-clamped again distal to the
deepest site of attachment and then stitched from the right [Chiu et al., 2002].
Therefore, this procedure restores the high-pressure ascending aorta to its
natural location, reducing the acute angulation of the aortic arch due to the
Lecompte maneuver and all the resulting issues, such as arch hypoplasia and
neocoarctation.
Chapter 2 Aim of the study
13
As appreciated in Chapter 1, where the clinical problem of TGA and the
associated complications were briefly presented, the anatomy and physiology
of patients with repaired TGA are clearly very complex.
From a surgical point of view, the palliation and repair of this congenital heart
defect has evolved from the Senning and Mustard procedures (i.e atrial
switches) to the ASO with Lecompte modification, and recent attempts at
improving the hemodynamics post-repair (e.g. spiral surgery) suggest that
surgery for repairing TGA could still be optimised.
Moreover, from a clinical point of view, it has emerged that morphological
implications (such as the dilated aortic root and the angulation of the aortic
arch) are likely linked with some of the complications observed in TGA
patients in their teenage or early adulthood.
Gathering additional hemodynamic information by means of engineering tools
in order to systematically evaluate the neo-aorta in this patients’ population is
thus clinically important, not only to enhance knowledge of the fluid dynamics
in TGA, but also to predict potential problems that may arise later on in life in
these patients.
Taking advantage of state-of-the-art engineering tools, both experimental and
computational, this study aims to:
1) create a validated computational model of the neo-aorta following
ASO;
2) use the validated model to highlight differences in the local fluid
dynamics in different anatomies.
From a methodological point of view, hydrodynamic experimental data will be
acquired using magnetic resonance (MR) imaging, with a novel technique
known as 4D MR flow and using patient-specific phantoms. The study is then
taken forward in-silico, whereby a multi-scale modelling approach will be
adopted, including patient-specific 3D anatomy and physiology in the
simulations. As a modelling paradigm, the computational model will be
validated against experimental data. These approaches, their advantages and
their application in this specific context are described more in detail in the
following chapters.
Chapter 3 State of the art
15
3.1 4D MAGNETIC RESONANCE IMAGING
3.1.1 PRINCIPLES
Magnetic Resonance (MR) imaging techniques provide non-invasive, highly
accurate anatomic depictions of the heart and vessels. Traditionally, MR
imaging of flow is accomplished using methods that resolve two spatial
dimensions (2D) in individual slices, adding functional information to the
anatomical data. Quantitative flow assessment is an important element of
cardiovascular MR studies in patients with congenital heart disease, and in
many cases information about blood flow is required in multiple arterial and
venous vessels [Kilner et al., 2010]. This conventional 2D method offers the
advantage of a sequential acquisition of flow data in different vessels with
individually adjusted velocity encodings [Nordmeyer et al., 2010]. However,
repeated planning and acquisition can be time-consuming. In addition, data
analysis is limited to those vessel sections that were targeted when planning the
scan.
A new technique, i.e. four-dimensional magnetic resonance imaging flow
acquisition (4D MR flow), allows to obtain 3D morphological information as
well as blood flow velocities in 3 directions for each voxel at each measured
time point of the cardiac cycle. It thus provides detailed quantitative flow and
vessel wall parameters with complete vascular coverage, also allowing
additional measurements of hemodynamic parameters such as shear stress,
vortex formation, or pressure fields. Therefore, it is a reliable and resourceful
tool to quantify blood flow in patients with congenital heart diseases [Uribe et
al., 2009].
One major indication of using 4D flow application in congenital heart disease
would be the diagnostic work-up of complex cases that require multiple
quantitative flow acquisitions in arterial and venous vessels with normal and
abnormal flow patterns [Nordmeyer et al., 2010]. Compared to the
conventional 2D method, this reduces scan time, making the protocol less time
extensive and demanding for the patient; indeed, planning and acquisition of
imaging planes perpendicular to the target vessels are not necessary.
Chapter 3 State of the art
16
Furthermore, data analysis is not limited to the acquired single predefined 2D
imaging plane and, thus, would help avoiding incomplete or falsely registered
datasets [Nordmeyer et al., 2010].
The 4D flow software offers a new and time efficient tool to evaluate 4D data,
and has demonstrated its potential for analysis of arterial and venous
hemodynamics [Barker et al. 2010].
3.1.2 PREVIOUS WORK
Four-dimensional flow MRI analysis has been used in several recent studies to
investigate fluid dynamics in different cardiovascular application.
One example is an interesting study which exploits 4D flow acquisitions to
investigate aortic hemodynamics in bicuspid aortic valve (BAV) patients,
comparing specific valve morphology (i.e. fusion of the right-left coronary
cusp) with control cases matched for age and aortic size [Barker at al., 2012].
Steady-state free precession cine imaging has been used to identify the valve
lesion morphology in all BAV patients. Co-registration of the 2D valve images
with the flow data allowed to visualise the valve cups morphology in parallel
with the 3D blood flow pattern in the aorta. The 3D visualisation was based on
streamlines at peak systole (Figure 3.1).
Figure 3.1 - 3D flow visualisation of a control patient highlighting cohesive systolic
streamlines [Baker er al., 2012].
Chapter 3 State of the art
17
Four-dimensional flow MR can measure and visualise aortic 3D blood flow
patterns such as flow jets, vortex or helical flow patterns. It was observed that
BAV and cusps fusion morphology alter the hemodynamic environment, in
particular post-valvular blood jets. This in turn leads to abnormal wall shear
stress (WSS), with an elevated or asymmetrical WSS along the circumference
of the aortic wall, with consequent vascular remodelling. This study highlights
the utility of 4D MR flow for investigating the structure-function relationship
between a type of valve morphology and downstream flow characteristic, in a
congenital scenario.
Moreover, current quantification methods only allow measurement of net flow
through a vessel of interest. Estimation of flow contributions from a particular
vessel, when more than one source of flow is present, is not possible.
Using this 4D flow technique Bachler et al. (2012) analysed the flow
distribution in patients with pulmonary atresia and intact ventricular septum
after ‘‘one-and-a-half ventricle repair’’ with placement of a bidirectional Glenn
shunt [Bachler et al., 2012]. In particular, they estimated flow contribution
from the superior vena cava (SVC) toward the right pulmonary artery (RPA)
distal to the cavopulmonary anastomosis (d-RPA) and toward the RPA
proximal to the cavopulmonary anastomosis (p-RPA), thus avoiding any blood
flow streaming from the main pulmonary artery. Different regions of interest
(ROI) were defined and used as emitter planes of particle traces. Such particles,
travelling along the cardiovascular structures according to the velocity field
distribution acquired by the 4D flow sequence, allowed to characterise the
hemodynamic ‘‘baffle’’ between the pulmonary circulation and the Glenn
anastomosis. The blood flow distribution (Figure 3.2) suggests that the
palliated pulmonary circulation has poor efficiency because most of the blood
flow ejected by the ventricle moves back to the heart during the diastolic phase.
Furthermore, bidirectional Glenn anastomosis of the SVC showed poor
efficiency because most of its blood flow contribution was directed into the PA
and not into the lungs.
Chapter 3 State of the art
18
Figure 3.2 - Particle traces emitted from the SVC show how the blood is distributed between
the p-RPA, d-RPA and main PA [Bachler et al.,2012].
In 2012, Valverde and co-workers took advantage of 4D velocity acquisition
sequences to evaluate systemic-to-pulmonary collateral flow and flow
distributions in patients with single-ventricle physiology [Valverde et al.,
2012]. A whole-heart 4D velocity and 2D flows MR data were acquired in
aorta, caval veins and pulmonary arteries. The 4D velocity acquisition was
validated with the 2D velocity technique by comparing the flows measured in
each individual vessel, and time efficiency of both techniques was evaluated.
Good agreement was obtained in the measured flows, and significantly shorter
4D velocity acquisition-time was observed. Indeed, the duration of the single
4D velocity acquisition sequence (12:34±03:42 min) was significantly shorter
than the average time to satisfactorily obtain five individual 2D flow scans
(17:28±04:24 min), which increases with the number of scans needed.
Chapter 3 State of the art
19
3.2 COMPUTATIONAL ANALISYS
3.2.1 COMPUTATIONAL FLUID DYNAMICS
Computational fluid dynamics (CFD) is a very useful tool to investigate
complex fluid dynamic scenarios. In the last years, the considerable
improvements in computer technology increased the number of computational
studies to the detriment of in vitro analyses. The main advantage of CFD
simulations is the possibility of a complete representation of fluid dynamic
variables in 3D domains such as flows, pressures and velocity distributions,
shear stresses and energy losses. Also, from an economical point of view, costs
of computational analyses are lower than costs of experimental setups. The
major drawback of this method is the long-time taken by the simulation to
converge, which depends on the accuracy needed, on the complexity of the
problem, and on the computational resources available.
The computational method is based on the solution of the Navier Stokes (NS)
equations and of the mass balance equation in each volume of the grid in which
the 3D domain is divided. The 3D NS equations are:
{( )
}
where ρ is the fluid density, vi is the component of the velocity vector in the
specified Cartesian direction (i =x, y, z), t is the time, Fi is the vector of the
external body forces operating on the fluid, p is the pressure and μ is the fluid
viscosity [Dubini, 2009].
The continuity equation is shown below:
and becomes as follows
Chapter 3 State of the art
20
for incompressible fluids (constant density ρ).
Two are the key factors for obtaining detailed and reliable descriptions of the
fluid dynamics in any specific case: the boundary conditions and the
representation of the 3D domain. In cardiovascular applications, the boundary
conditions to be prescribed at the boundary faces of the 3D model are typically
values or tracings of pressure, velocity and flow-split derived from medical
exams such as catheterism, MR scans, echo measurements. Regarding the 3D
volume, it is possible to mimic complicated patient specific geometries,
obtained by advanced medical imaging techniques, such as magnetic resonance
(MR) and computerised tomography (CT) [Coveney et al., 2011].
Hence, in order to computationally reproduce patient-specific fluid dynamics,
medical images with high resolution and time-varying boundary conditions are
required for achieving adequate accuracy and reliable outcomes.
3.2.2 LUMPED PARAMETER NETWORK (LPN)
Lumped parameter models are efficient tools for the representation of complex
hydraulic networks like the cardiovascular system. This method is based on the
analogy with electric networks, where pressure and flow are identified with
electric voltage and electric current, while capacitors (C), resistors (R) and
inductors (L) correspond to vessel wall compliance, viscous dissipation in the
vessel, and fluid inertial features (Figure 3.3).
Figure 3.3 - A simple example of LPN model (top) and its electrical-hydraulic analogy
(bottom): flow (f) and pressure (P) are represented by electric current (i) and voltage (V).
Chapter 3 State of the art
21
The equations describing the behaviour of each lumped parameter are the
following:
( )
where L is the length of the conduit, r the radius in the undeformed
configuration, h the wall thickness, µ the fluid viscosity, ρ the fluid density, σ
the Poisson ratio and E the Young modulus [Laganà et al., 2002].
This approach allows an immediate calculation of flow distribution, pressure
drops and their waveforms in all the cardiovascular districts modelled. The
hemodynamics in each district is described through a system of differential
equations deduced from the NS equations after appropriate simplifications: the
convective terms of the NS equations are neglected; the fluid is considered
incompressible and in a laminar regime; the velocity distribution across a
section and the velocity variation along a conduit are replaced with mean
velocity values on the sections. The whole vascular tree can be split in several
essential compartments, depending on the grade of accuracy needed for the
study undertaken: a larger number of blocks accounts for a more precise
cardiovascular system description, but at the same time the number of
parameters’ values to be estimated increases.
For example, the differential equations solving the network shown in Figure
3.4 are the following:
Chapter 3 State of the art
22
Figure 3.4 - Lumped model of a short pipe: flows and pressures in the district are regulated by
the NS equations [Laganà, 2002].
If the input and all the parameters of the network (R, L, C) are known,
pressures and flows can be obtained [Laganà et al., 2002].
Because of the approximations in the NS equations previously explained, LPNs
are unable to represent 3D spatial distribution and local values of the
hemodynamic variables, but are extremely fast and low demanding in terms of
computational power.
3.2.3 MULTI-DOMAIN APPROACH
In hemodynamics, as in many other engineering or scientific fields, a problem
can show peculiar behaviours at different scales. Therefore, a crucial issue is
choosing the right scale to approach the problem, which could be too large to
observe events occurring at the microscale, or too small to evaluate accurately
macroscopic phenomena. Simulating all the relevant dimensions of a problem
would require a too large number of variables and technological resources.
A multi-domain approach could be very useful, as it consists in incorporating
the 3D geometry of the only district of interest, solved with the CFD methods,
in a LPN reproducing the whole vascular tree or just the districts proximal to
the considered 3D part. The resulting network provides the 3D geometry with
realistic boundary conditions, and the LPN with the local fluid dynamic
variables [Laganà et al., 2002].
Chapter 3 State of the art
23
The boundary conditions will thus consider the behaviour of the downstream
districts and their interaction with the upstream computational domain. Indeed,
the blood flow and the pressure in the aortic arch are strictly linked to the
values in the whole arterial system.
Lumped parameter models can be used with closed multi-domain models,
where the network provides both inlet and outlet boundary conditions, and
open multi-domain models, in which the inlet is imposed from the outside.
3.2.4 PREVIOUS WORKS
An interesting work by Kim et al. studied the fluid dynamics in a pediatric
aorta coupling the 3D volume with a LPN, and comparing the results obtained
from the model with physiological flow-rate and pressure fields [Kim et al.,
2008]. The 3D geometry (meshed with 1916167 elements) included the aortic
arch and the main upper branches (left and right carotids and left and right
subclavian arteries). The open lumped parameter networks coupled at the inlet
and at all the outlets of the 3D domain are shown in Figure 3.5.
Figure 3.5 - Inlet (left) and outlet (right) lumped parameter network used to study the fluid
dynamics in the aortic arch [Kim et al., 2008].
This model allowed the analysis of several variables, such as mean flow rates
and pressures at inlet and outlets, shear stress and velocity fields in the whole
3D geometry. The results confirmed the reliability of this multi-domain
methodology. Mean flow rates and mean pressures were evaluated in all outlet
faces along the cardiac cycle. The computed cardiac output was 3.5 L/min
compared with the 3.6 L/min of the subject. Computed pressures ranged from
62 to 106 mmHg. The upper branches, as expected, experienced retrograde
flow in diastole, while the descending aorta had positive flow in the same
a)Inlet coupled to lumped parameter heart model b)Outlets coupled to 3-element Windkessel models
Chapter 3 State of the art
24
instants. These values and all the waveforms are physiologically realistic.
Volume rendered velocity magnitude showed complex flow features related to
the high inertia of the blood, especially in late systole when the flow was
decelerating (Figure 3.6B). The mean wall shear stress increased where the
flow jet hits the wall of the vessels, and decreases in the descending aorta, as
shown in Figure 3.7.
Figure 3.6 - Velocity magnitude at peak systole (A), late systole (B), diastole (C).
Figure 3.7 - Mean wall shear stress at peak systole.
Chapter 3 State of the art
25
In 2008, Karmonik and co-workers demonstrated the potential role of CFD in
therapeutic decision making of vascular pathologies of the human aorta
[Karmonik et al., 2008]. Computational models built using patient-specific
geometries and patient-specific inflow boundary conditions obtained from MRI
were used to simulate two cases: A) a mobile thrombus in the aortic arch in a
patient with ischemic stroke, B) an abdominal aortic aneurysm repaired with an
endoluminal graft. Blood flow pathlines, wall shear stresses (WSS), dynamic
pressures, blood velocity and flow particle resident times were calculated. In
all the cases, tracings and absolute flow values obtained by CFD simulations
were in good agreement with literature. In case A, flow lines intersecting the
thrombus were found to enter the left common carotid artery, providing
additional evidence on the danger represented by the thrombus: it may be a
potential source for emboli, and in case of upstream dislocation to the cerebral
circulation via the left common carotid it may be cause ischemic stroke. Wall
shear stress magnitudes computed in correspondence of the thrombus showed
high values that are favourable for emboli shedding. Also, flows predicted by
the simulations confirmed the favourable conditions for these emboli to reach
the cerebral circulation.
In case B, the analysis was focused on the WSS distribution on the wall of an
endoluminal graft, and at healthy proximal and distal segments. The results
revealed high WSS values at the landing zone and at the section of the
endoluminal graft located in the right iliac artery. Disturbed flow patterns and
increased flow particle transient times were spatially correlated with the
regions of elevated WSS. The existence of these flow disturbances suggested
the need for an intervention i.e. enlarging the endoluminal graft diameter by
angioplasty.
Chapter 4 Materials and methods I: experimental
27
In order to study the hemodynamic of the neo-aorta in patients with surgically
repaired TGA, an experimental approach was chosen because an in-vitro study
can provide controllable and reproducible data.
The complexity of an experimental setup varies according to the problem at
hand and depending on the purposes of the study, influencing the choice of
model (e.g. pure resistance, lumped parameter model, distributed, linear model
or distributed, non-linear model) [Skalak, 1972].
Experimental setups for hydrodynamic testing can take the form of mock
circulatory loops, whereby a network of tubing and lumped resistive and
compliant elements are assembled to reproduce a part or the whole of the
circulatory system. Such mock loops can include a detailed anatomical element
if a specific morphology is deemed important or is being investigated.
Anatomical elements can be either idealised [Vismara et al., 2009] or patient-
specific [Biglino et al., 2012]. An arrangement including a detailed 3D
component and lumped elements representing the remainder of the circulation
can be broadly defined as “multi-scale” [Quarteroni et al., 2001]. This patient-
specific approach was chosen to study the geometry effects in the
hemodynamic combining hydrodynamic data with the imaging potential of 4D
MR flow, previously discussed in 3.1.
4.1 ANATOMICAL MODELS
As the study was carried out at a patient-specific level, a suitable patient with
TGA corrected with ASO was selected (15 years old, 1.7 m2 BSA, male). In
order to appreciate the features of TGA hemodynamics, an age-matched
healthy control case was also selected (15 years old, 1.7 m2
BSA, male). The
control case was identified from a list of subjects screened at Great Ormond
Street Hospital in London for assessment of possible hereditary
cardiomyopathy. Both cases underwent MR examinations of their cardiac
function and their anatomies were reconstructed in 3D from MR data using
commercial software (Mimics, Materialise, Leuven, Belgium).
For the purpose of the reconstructions, the MR images are viewed in 2D, in
three projection planes (transverse, coronal and sagittal) and the software
Chapter 4 Materials and methods I: experimental
28
ultimately allows to render a 3D volume ( Figure 4.1). As the study focused on
the aortic region, segmentation of the images was performed selecting the
appropriate region of interest by a thresholding operation and defining the
boundaries of the grayscale in the image. This step was followed by a “region-
growing” operation and detailed refinements to the 3D model were completed
on a pixel by pixel basis. Similar procedures for creating 3D vascular models
have been reported in the literature [Thayyil et al. 2009, Schievano 2007].
Figure 4.1 - Screenshot of the Mimics interface, showing anatomical reconstruction of the
TGA aortic arch. 3D geometry (bottom right panel) is reconstructed from 2D MR images (top
and bottom left panels).
The final model includes the aortic root, the ascending and descending aorta
and the brachiocephalic branches (i.e. innominate, left carotid and left
subclavian arteries). In order to adjust surface irregularities, a smoothing
operation was finally performed using a shrinkage compensation factor.
As the software allows for adding CAD elements to the 3D models by means
of Booleans operations, a small cylinder was positioned in the ascending aorta
(Figure 4.2) as an access port for a pressure catheter, allowing for pressure
measurements in the aortic arch, as further described in 4.2.5.
Chapter 4 Materials and methods I: experimental
29
Similarly, the brachiocephalic vessels, the inlet in the aortic root and the outlet
at the descending aorta were all modified using CAD elements in order to
facilitate insertion and connection of the 3D phantom into the mock circulatory
system.
Figure 4.2 - Detail of the port for the pressure catheter. It allows for access the aortic arch in a
very easy way.
The 3D volume can be exported as a Standard Triangle Language (STL) file
compatible with 3D printing. In particular, the rapid prototyping technique
known as PolyJet technology [Ibrahim et al. 2008] was used to manufacture 3D
rigid models suitable for insertion in a mock circulatory loop. A transparent
and robust resin (Watershed 11122; DSM Somos, Elgin, IL) was used for the
printing process. Both the TGA and the control model are shown in Figure 4.3.
Chapter 4 Materials and methods I: experimental
30
Figure 4.3 - Control (left) and TGA (right) models manufactured by means of rapid
prototyping. It is possible to appreciate geometries differences among the two models: the
yellow arrow highlights the enlarged aortic root in the TGA model; the red arrows point the
different aortic arches. The green arrow indicates the point of insertion of a pressure catheter
on the ascending aorta (on the TGA model). Finally silicone was used to attach the model to
Tygon tubes, as can also be appreciated from these images.
Rigid models, admittedly not reproducing realistic vessel wall distensibility
and the associated recoil effect, have been used in several studies in the
literature for investigating vascular anatomies [Biglino et al., 2012], providing
valuable hemodynamic data, and it should also be noted that they serve the
purpose of collecting validation data for a computational study where the 3D
models in the CFD study also present rigid walls.
The transparency of the resin allows to see air bubbles in the circuit, thus
facilitating de-airing operations, and to control the correct positioning of the
pressure catheter in the aortic arch.
Chapter 4 Materials and methods I: experimental
31
4.2 HYDRAULIC CIRCUIT
In order to understand how the geometric differences between a TGA and a
healthy aorta affect the fluid dynamic in the aortic arch, a hydraulic circuit was
built (Figure 4.4).
It consists of:
I. Pulsatile pump
II. Compliance chambers
III. Resistances
IV. Atrial reservoir.
Figure 4.4 and Figure 4.5 show an image and a schematic representation of the
circuit.
Figure 4.4 - Experimental circuit: II indicates the compliant chambers, III one of the four taps
implementing the resistances, and IV the atrial reservoir.
Chapter 4 Materials and methods I: experimental
32
Figure 4.5 - Schematic representation of the circuit. P represents the pulsatile pump, C the
compliant chambers, R the non-linear resistances. The arrow indicates the direction of the flow.
The circuit was built so to be compatible with MR imaging. For this reason,
there is no metal in the components inserted into the scanner. All the
ferromagnetic parts (i.e. the pulsatile pump, consoles of measuring equipment,
laptop, data acquisition system) are located in the adjacent control room.
Tubing, cables and connections are facilitated by a hole in the wall between the
two rooms.
In order to guarantee hygiene and safety of the scanner in the event of
leakages, water was the fluid chosen for performing the experiments, although
other solutions (e.g. mix of water and glycerine) present more similar
properties to blood, especially in terms of viscosity [Gonzalez et al., 2011].
Hydraulic seal between the model, the pipes and the compliant chambers was
ensured using silicon.
4.2.1 PUMP
A Harvard Apparatus pulsatile blood pump (Figure 4.6) was used to simulate
the pumping action of the heart. The pulsatile output closely simulates the
Chapter 4 Materials and methods I: experimental
33
ventricular action of the heart thanks to silicone rubber-covered heart-type ball
valves. This action provides physiological advantages in blood flow for
perfusion in cardiovascular and haemodynamic studies.
Figure 4.6 - Harvard Apparatus pulsatile blood pump used for the experiments: A) inlet, B)
outlet. Also indicated, the position of the ball valve that regulates the flow.
This pump has an adjustable stroke volume range between 15 and 100 ml and a
frequency range between 10 and 100 bmp.
The outflow of the pump was connected to the inlet of the model while the
inflow of the pump was connected to the outlet of the reservoir. Sufficiently
long braided pipes, previously filled with water to avoid bubbles, were used to
allow the Harvard Pump sitting in the control room.
The pump heart rate (HR) and stroke volume (SV) were set in accordance to
patient’s data, which was derived from the MR examination report. Patient-
specific settings for the TGA case were: HR = 70 bpm and SV = 90 ml. The
waveform at the inlet of the model, obtained with the settings described, is
shown in Figure 4.7.
.
Chapter 4 Materials and methods I: experimental
34
Figure 4.7 - Inflow waveform: it is obtained setting the stroke volume and the heart rate
respectively at 90 ml and 70 bpm.
4.2.2 ARTERIAL COMPLIANCE
Arterial compliance was simulated by using Windkessel (= “air chamber” in
German) elements, according to the theory of compliant air element. Perspex
cylinders (volume = 1324.69 cm3) were thus attached at each outlet of the
model, in order to implement the natural compliant behaviour of the system.
Each chamber has a 3-way valve fitted at the top in order to control the amount
of air, regulating the stiffness of the circuit. Adjustments to the amount of air
can be easily performed to adjust in turn the lumped compliance.
Increasing the stiffness of the whole system rises the amplitude of the pressure
waveform. The range of pressure at the inlet was set between 60 and 115
mmHg according to cuff pressure data measured in the TGA patient.
The 4 compliance values were obtained using the formula:
in which V is the volume of air in each cylinder, Pm is the mean pressure of the
patient (77 mmHg) and Patm the atmospheric pressure (760 mmHg). The values
are shown in Table 4.1, where height refers to the part of each cylinder full of
air.
-10
-5
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
Chapter 4 Materials and methods I: experimental
35
Table 4.1 - Compliance values per each outlet of the model.
Height
[cm]
Diameter
[cm]
Volume
[cm3]
Pm+Patm
[Pa]
C
[m3/Pa]
INNOMINATE 5.5 7.5 242.8 111588.8 2.2 E-09
CAROTID 5.0 7.5 220.8 111588.8 2.0 E-09
DESCENDING AORTA 4.5 7.5 198.7 111588.8 1.8 E-09
SUBCLAVIAN 7.0 7.5 309.1 111588.8 2.8 E-09
4.2.3 VASCULAR RESISTANCE
Metered needle-pinch valves were positioned after each compliance chamber
to simulate the resistance of downstream districts of the circulation. Such taps
have the advantage of being easily adjustable with reproducible settings,
allowing for regulation of the mean pressure in the circuit. However, they are
strongly flow-dependent and thus implement a non-linear resistance.
Resistances were set in order to split the inflow according to the following
physiological indicative proportions: 55% in descending aorta and 45% in the
upper branches (of which 15% innominate, 20% subclavian and 10% carotid).
Flow measurements at each outlet for quantifying flow distribution were
performed using the ultrasonic flow probe described in 4.2.6. The resistances
were characterized using a simple continuous flow circuit (as in Figure 4.8).
Chapter 4 Materials and methods I: experimental
36
Figure 4.8 - Schematic representation of the circuit using for characterising the resistances.
The red and the blue arrow indicate the position of the pressure catheters to measure pressure
values before and after the tap.
Imposing known flows with a continuous pump (Q) the pressure drop across
the tap (R) was measured with two pressure catheters (Table 4.2).
Table 4.2a - Pressure drop in carotid.
Flow
[L/min]
Pbefore
[mmHg]
Pafter
[mmHg]
0.31 15.30 13.14
0.33 15.54 13.03
0.55 25.56 13.76
0.66 32.12 13.91
0.95 53.91 14.87
1.25 84.30 16.63
1.42 104.35 17.37
1.46 108.85 17.66
1.99 189.87 21.93
Chapter 4 Materials and methods I: experimental
37
Table 4.2b- Pressure drop in innominate and subclavian.
Flow
[L/min]
Pbefore
[mmHg]
Pafter
[mmHg]
0.46 15.54 13.61
0.80 25.60 14.65
1.07 37.42 15.90
1.38 55.25 18.03
1.84 89.13 22.08
1.89 91.90 22.96
2.07 109.24 25.39
2.60 161.87 30.17
2.78 180.73 30.61
Table 4.2c – Pressure drop in descending aorta.
Flow
[L/min]
Pbefore
[mmHg]
Pafter
[mmHg]
0.23 9.47 12.58
0.45 10.38 13.11
1.42 16.69 16.48
1.48 17.37 17.07
2.40 30.14 24.51
2.60 34.32 27.08
3.25 42.19 29.95
4.09 60.16 32.45
4.50 70.35 45.26
.
Chapter 4 Materials and methods I: experimental
38
Using these data to produce pressure drop-flow curves, interpolating them with
a second order polynomial, it was possible to obtain the characteristic curves of
each resistance (Figure 4.9).
Figure 4.9 - Characteristic curves, with the respective equations, of the resistances: carotid
(blue), innominate and subclavian (red), descending aorta (green).
4.2.4 ATRIAL RESERVOIR
All outlets of the 3D model drain to a reservoir representing an ‘atrial
reservoir’, positioned between the outlet of the model and the pump, and
implementing atrial pressure. This chamber is filled with water and the level of
water was set to guarantee a pressure of 9 mmHg, given by the hydraulic head.
4.2.5 PRESSURE MEASURING EQUIPMENT
Pressure in the aortic arch was measured by means of a high-fidelity factory-
calibrated fiber optic catheter (Samba Preclin Samba sensors AB; Vastra
Frolunda, Sweden). The transducer technology is based on a pressure sensitive
optical interferometer (Fabry-Perot manufactured in silicon). The sensor
element (0.36-0.42 mm of diameter) is mounted at tip of an optical fiber (0.25-
0.40 mm of diameter) (Figure 4.10).
y = 42.913x2 - 0.621x
y = 1.6396x2 - 1.71x
y = 19.886x2 - 0.9766x
0
20
40
60
80
100
120
140
160
180
0 1 2 3 4 5
Pre
ssu
re d
rop
[m
mH
g]
Flow [L/min]
carotid
descending aorta
innominate and subclavian
Chapter 4 Materials and methods I: experimental
39
Figure 4.10 - Catheter tip dimension compared with a match.
Calibration of the pressure catheter was carried out prior the experiments with
the methods of ‘column of water’, associating the console’s read-out in Volts
with known heights of water implementing known hydrostatic pressure values
(1 mmHg = 1.36 cmH2O). Thus, a correlation between pressure read in Volts
by the catheter and the corresponding mmHg value was established (Figure
4.11).
Figure 4.11 – Pressure catheter manual calibration: on the ‘x’ axis the output of the console in
Volts (V) and on the ‘y’ axis the associated pressure in mmHg.
y = 84.445x - 121.16 R2 = 0.9999
-20
0
20
40
60
80
100
120
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
Pre
ssu
re [
mm
Hg]
Output [V]
Chapter 4 Materials and methods I: experimental
40
The catheter was positioned in the ascending aorta, as shown in Figure 4.12,
through the appropriate port created in Mimics.
Figure 4.12 - Catheter position: the yellow arrow indicates the dedicated port for the pressure
catheter. It is possible to see the light blue little pipe, fixed to the model with silicone, along
which the catheter is guided into the model.
4.2.6 FLOW MEASURING EQUIPMENT
Flow at the inlet of the model was evaluated with an ultrasonic flow probe
(Transonic 400-Series Multi-Channel Flowmeter Consoles & Modules for
Laboratory Research).
Four transducers (piezoelectric crystals) within the flow probe alternately emit
sound rays to form an ultrasound beam. As the beam transverses a vessel, each
ray undergoes a phase shift in transit time proportional to the average velocity
of the liquid times the path length over which this velocity is encountered.
With wide-beam ultrasonic illumination the receiving transducers integrate
these velocity and yields volume flow (Figure 4.13).
Chapter 4 Materials and methods I: experimental
41
Figure 4.13 - Transit time ultrasound theory of operation: a schematic representation. On the
left: cross-talk between the crystals mounted inside the probe. On the right: position of the
probe, snugly clumped to the Tygon tube.
Calibration of the flow probe was performed prior the experiments with the
method of ‘timed collection’. This was performed by setting increasing flows
with a continuous pump (Sicce Multifunction Pump 2500) and measuring the
amount of water (mL) per minute gathered with a measuring cylinder and
comparing these values with the respective Volts measured by the probe
(Figure 4.14).
Figure 4.14 - Flow-probe calibration: on the ‘x’ axis the output of the flow-meter in Volts (V)
and on the ‘y’ axis the associated flow in L/min.
y = 2.0044x - 0.0097 R² = 0.9998
-1
0
1
2
3
4
5
6
0 0.5 1 1.5 2 2.5 3
Flo
w [
L/m
in ]
Output [V]
Chapter 4 Materials and methods I: experimental
42
The probe was positioned at the inlet of the model, in order to verify the
stability of the inflow during the experiment (Figure 4.15). A thin layer of
Vaseline was used to improve acoustic coupling.
Figure 4.15 - The yellow arrow points at the flow-probe position, which is the inlet of the
phantom.
This specific flow probe was designed by the manufacturer to be MR
compatible, thus including special connectors and cables. This should have
allowed simultaneous flow acquisitions during MR scanning. However,
preliminary testing highlighted that the presence of the probe was still causing
image artefacts, as in Figure 4.16.
Chapter 4 Materials and methods I: experimental
43
Figure 4.16 - The yellow arrow underlines the flow-probe artefact in MR scan, visible in the
aortic root.
For this reason, the protocol of the experiment was changed, such that the flow
waveform was acquired with the probe with the model already mounted on the
table but only before inserting it into the scanner.
4.2.7 DATA ACQUISITION AND DATA ANALYSIS
During the experiments a data acquisition system (BIOPAC System Inc.,
Goleta, California) was used to record pressure and flow output data gathered
from the catheter and the probe (Figure 4.17). Data was acquired at 250 Hz
(AcqKnowledge 4.1.1, BIOPAC System Inc., Goleta, California).
Chapter 4 Materials and methods I: experimental
44
Figure 4.17 - AcqKnowledge interface: pressure curve is shown in purple, flow curve in red.
Data was saved as Microsoft Excel files for later off line analysis. Values are
reported as mean ± standard deviation.
4.3 MAGNETIC RESONANCE (MR)
4.3.1 ACQUISITION
All MR examinations were performed with a 1.5 T scanner (Avanto; Siemens
Medical Systems, Erlangen, Germany).
The TGA geometry was first tested in the scanner. After having checked with
the flow probe that the flow split corresponded with the one in the patient (see
4.2.3) and having verified there were no leaks in the circuit, it was inserted into
the MR scanner. Due to its dimension, the bucket representing the atrium was
positioned right outside the scanner at the same level of the rest of the circuit.
Once the phantom was correctly positioned in the centre of the scanner, the
pump was turned on to set appropriate pressure and flow waveforms.
Acquisitions were gated to the pump’s external trigger, via a BNC connection
cable.
Firstly, phase contrast data was acquired for 2D quantification of flow-velocity.
Imaging parameters were:
Chapter 4 Materials and methods I: experimental
45
Venc: 250 cm/s for the outlets, 500 cm/s for the inlet;
Repetition time/echo time: 29.9/2.18 ms;
Pixel spacing: 1.17 mm;
Section thickness: 5 mm;
Flip angle: 30°.
From the phase contrast MR scan two sets of images are extracted: the
magnitude and the phase, the latter encoding the velocity information.
According to the direction of the flow, increasing values of velocity are shown
in increasing grades of black or white.
The images were taken in 4 different planes, always planned as perpendicular
to the flow: inlet, descending aorta, innominate and subclavian arteries.
Moreover, the 4D (3 spatial dimension and time) acquisitions were performed.
During each scan two different sequences were tested: a standard sequence
(Siemens) and a higher temporal and spatial resolution sequence, lasting 15
minutes and 1 hour and 10 minutes, respectively.
Imaging parameters for the standard 4D sequence were:
Venc: 200 cm/s;
Repetition time/echo time: 33.4/2.5 ms;
Pixel spacing: 2.2 mm;
Section thickness: 2.2 mm;
Flip angle: 5°.
Imaging parameters for the high resolution sequence were:
Venc: 200 cm/s;
Repetition time/echo time: 21.4/3.2 ms;
Pixel spacing: 2.4 mm;
Section thickness: 1.2 mm;
Flip angle: 5°.
The same imaging protocols were adopted for the control geometry. It is
important to stress that the values of the compliances and the resistances used
to test the control model were the same as for the TGA model.
Chapter 4 Materials and methods I: experimental
46
4.3.2 DATA EXTRACTION
OsiriX Imaging Software (Pixmeo; Geneva, Switzerland) is a DICOM viewer
specifically designed for navigation and visualization of multimodality and
multidimensional images: 2D Viewer, 3D Viewer, 4D Viewer (3D series with
temporal dimension, i.e. Cardiac-CT) and 5D Viewer (3D series with temporal
and functional dimensions, i.e. Cardiac-PET-CT).
The 3D Viewer offers all modern rendering modes: multiplanar reconstruction
(MPR), surface rendering, volume rendering and maximum intensity projection
(MIP). All these modes support 4D data and are able to produce image
fusion between two different series (PET-CT and SPECT-CT display support).
OsiriX is at the same time a DICOM PACS workstation for imaging and image
processing software for medical research (radiology and nuclear imaging),
functional imaging, 3D imaging, confocal microscopy and molecular imaging.
In particular, it allows quantification of flow from phase-contrast data using an
in-house written plugin (Figure 4.18), validated in a separate study [Odille
2011].
The identification of the ROI, where the flow data is acquired, is performed
manually on one frame, preferably at peak systole when most visible and when
the edges are crisp, then, using a non-rigid registration algorithm previously
validated [Odille et al., 2011], the ROI is propagated in all frames. Using a
plug-in developed at Great Ormond Street Hospital it was possible to calculate
the instantaneous flow volume at any time in the cardiac cycle. The mean
velocity was obtained dividing the flow by the ROI area.
The difference between the inlet and the other three measured flows provides a
measure of carotid flow, as data in the carotid were not acquired.
Chapter 4 Materials and methods I: experimental
47
Figure 4.18 - Data extraction via Osirix : magnitude (right) and phase (left). The enlightened
circles in the left image are the inlet (top) and the descending aorta (bottom), while the two big
grey circles are the two bottles full of water positioned in the scanner to simplify the
identification of the model.
Four-D data were later analysed by means of the Siemens 4D Flow software.
A 3D mask of the region of interest of the model was drawn by a combination
of thresholding and segmentation operations. This region defines the volume in
which the fluid dynamics are investigated, as shown in Figure 4.19.
Chapter 4 Materials and methods I: experimental
48
Figure 4.19 - 3D mask and planes in the TGA model. The numbers indicate the planes for the
velocity analysis: 1-2 inlet, 3 aortic roots, 4 ascending aorta, 5-6 descending aorta.
Once the mask was created the velocity were computed by drawing some
planes of interest. We took 6 planes of interest: two at the inlet of the model
(planes 1 and 2), one in the aortic root (planes 3), one before and one after the
upper branches (planes 4 and 5) and one in the descending aorta (plane 6). For
each of these planes, it is possible to save a corresponding Excel file containing
the information on flow, velocity and area.
Finally we used the tools provided by the software to place particle seed on
useful planes of the geometry, as shown in Figure 4.20. Particles are seeded on
the XYZ plane on the mask with a brush function allowing manual control.
Chapter 4 Materials and methods I: experimental
49
Figure 4.20 - Particle seeds at different locations along the 3D model then used to generate
streamlines and pathlines.
The evolution of particle traces and streamlines, originated by these particle
seeds, was recorded in order to obtain temporal information. It is possible to
choose different density of the seeds and width of streamlines and particle
traces in order to have a clear and complete visualisation of the results. It is
also possible to assign a specific colour to each seed or group of seeds to
follow their path and better understand complex flow patterns or mixing of
flows of different origins.
4.4 ASSESSING THE EFFECT OF COMPLIANCE:
COMPLIANT TGA MODEL
As previously acknowledged, the models tested in the MR scanner were
printed with a robust resin, thus obtaining a rigid geometry.
The main shortcoming of using a rigid model is that the compliant behaviour of
blood vessels is not taken into consideration. An interesting addition to the
study is to account for this compliant behaviour and evaluate how local fluid
dynamics are affected, and in particular if the compliant model resembles
closer the physiological scenario than the rigid one.
Chapter 4 Materials and methods I: experimental
50
For this purpose, a compliant TGA phantom was also manufactured and
included in the study. The material chosen to replicate the compliance of the
vessels is a commercially available rubber-like material, which can be used for
PolyJet rapid prototyping, called TangoPlus FullCure 930 [Biglino et al.,
2013], suggested as suitable for manufacturing arterial phantoms. In Figure
4.21 a picture of the TangoPlus TGA model is shown.
Figure 4.21 - Compliant TGA geometry. Clearly the new model was printed starting from the
same STL file used for the rigid one. Thus the only differences are the properties of the two
different materials.
With respect to the rigid model, this material is not transparent. As a
consequence, it is more difficult to positioning the pressure catheter inside the
aortic arch, through the pressure port. To avoid this problem the little tube used
as guide to insert the catheter was cut at a length measured corresponding to
the length necessary for the tip to be inside the arch.
The new compliant TGA geometry was connected to the same hydraulic circuit
described in Chapter 4.2, with the same flow and pressure values used before
Chapter 4 Materials and methods I: experimental
51
and described in paragraphs 4.2.2 and 4.2.3. Therefore, the only overall
difference in the circuit is represented by the material of the phantom.
Chapter 5 Materials and methods II: computational
52
CHAPTER 5
MATERIALS AND METHODS II :
COMPUTATIONAL
Chapter 5 Materials and methods II: computational
53
5.1 ANATOMICAL MODELS
The two geometries used for the CFD simulations are the same as the ones
printed for the in-vitro study described in Chapter 4.1. The computational part
of the study includes an additional model, described in detail in the following
paragraph, together with the rationale for its inclusion in the study.
5.1.1 AN ADDICTIONAL CASE
In order to better understand how the geometric differences could affect the
hemodynamics in the aortic arch, with all the problems described in paragraph
1.3 arising after ASO, and to better evaluate the effect of the Lecompte
maneuver, a patient with a slightly different surgical operation was taken into
consideration in our study.
The additional patient is not age-matched with the other two. He is, a 25 year
old male with a BSA of 1.9 m2. Nevertheless, this patient was indicated by the
cardiologists at Great Ormond Street Hospital as a case of interest, warranting
inclusion in the study, and suitable for comparing aortic geomtries. In fact, this
patient had TGA repaired with ASO but a Lecompte maneuver was not
performed in this instance. This results in a different anatomical arrangement,
with the aorta preserving a more spiral curvature, albeit this cannot be striclty
considered a case of spiral surgery as described in paragraph 1.4. This case
presents an enlarged aortic root, typical of TGA patients, but the aortic arch is
more similar to the control geometry, and will be hereby referred to as “spiral”
geometry. In Figure 5.1 a comparison between the two different arterial switch
operations geometries and the control are shown including the pulmonary
arteries, and it is possible to appreciate the differences both in spatial
arrangement as well as in aortic arch morphology.
Chapter 5 Materials and methods II: computational
54
Figure 5.1 - Comparison of three different geometries: TGA, control and “spiral”. Images at
the bottom represent the 3D volumes recostructed in Mimics. The aorta is shown in red and the
pulmonary arteries are shown in blue.
5.2 MESH AND SENSITIVITY ANALYSIS
The STL files of the geometries obtained from Mimics were imported in ICEM
(Ansys Inc., Canonsburg, PA), in order to build the finite volume mesh. Given
the complex patient-specific geometries, tetrahedral elements were chosen.
Also, a wall mesh inflation (5 layers of prisms, 1.2 grow ratio, 1 mm maximum
height) was applied in order to efficiently resolve boundary layer flows, in
which viscous effects are significant (Figure 5.2).
Chapter 5 Materials and methods II: computational
55
Figure 5.2 - Mesh example at the inlet of the model: it is possible to notice the 5 layers of
prisms.
To be sure that the numerical solutions were not influenced by the chosen grid,
sensitivity analysis was undertaken. A compromise must be reached between
computational time and accuracy of results: coarse mesh could lead to
inappropriate results, while a fine mesh could require excessive time for the
simulations to converge.
Using the TGA geometry, five different element dimensions, resulting in five
different meshes of 400000, 500000, 700000, 900000 and 1200000 volumes
respectively were tested with steady CFD simulations. A constant velocity
value of 0.13 m/s was imposed at the inlet and the flow split obtained
experimentally during the tuning of the taps (55% descending aorta, 20%
subclavian, 15% innominate and 10% carotid) was set at the outlets.
The influence of the mesh was evaluated by analysing the power dissipation
index W’dissip defined as difference between the power entering and the power
exiting the 3D volume [Pennati et al., 2011; Dubini et al., 1996; Low et al.,
1993]:
W diss ∑ i
(pi
1
2vi
2ρ) ∑
(p
1
2v
2 ρ)
Chapter 5 Materials and methods II: computational
56
where the first summation is calculated at the inlet face (i), while the second
summation is evaluated at the outlet faces (o); is the density of the fluid
(water, 1000 kg/ ), Q, v and p are respectively the averaged face flows,
velocities and pressures computed during the simulations.
As it is possible to appreciate from
Figure 5.3, there is a negligible difference of 1.4% ( corresponding to W’diss=
0.10∙105 W) between the 900000 elements mesh and the 1200000 elements
mesh. For this reason the mesh with 900000 volumes was chosen for our
models.
Figure 5.3 - Sensitivity analysis: variation of the power dissipation index with the number of
elements in the mesh. There is no significant difference between 900000 elements mesh and
1200000 element mesh.
Figure 5.4 shows the control (left), the TGA (central) and the spiral (right)
geometries with the chosen tetrahedral meshes.
5.00E-05
5.50E-05
6.00E-05
6.50E-05
7.00E-05
7.50E-05
8.00E-05
300000 500000 700000 900000 1100000
W' d
iss
[W]
Number of elements
Chapter 5 Materials and methods II: computational
57
Figure 5.4 - Control (right), TGA (central) and spiral (left) geometries meshed with tetrahedral
elements. The different colours represent different portions of the models separated by planes
used to evaluate the fluid dynamics at 1)aortic root, 2)ascending aorta, 3)descending aorta.
5.3 CFD SIMULATION
All the CFD simulations in this work were run using the commercial finite
volumes software Fluent (Ansys Fluent 14, Fluent Inc. ©, Lebanon, NH). The
method used for the solution of the NS momentum equations is a second order
upwind scheme, with a standard spatial discretization for the pressure, and an
implicit “least square cell based” discretization for the gradient. A SIMPLE
(Semi-Implicit Method for Pressure Linked Equations) pressure-velocity
coupling algorithm was exploited.
Furthermore the under-relaxation factors were set, as default, to 0.3 for the
pressure and 0.7 for the momentum. In all the simulations, the absolute
convergence criterion was the residuals of mass and momentum conservation
equations to be less than 10-4
.
Chapter 5 Materials and methods II: computational
58
5.3.1 WORKING HYPOTHESIS
As for the in-vitro experiment, the fluid chosen for the simulations is water
(density ρ=1000 kg/m3, viscosity μ=1 cP), considered completely
incompressible and Newtonian.
The simulations were run under the following working hypotheses:
laminar flow conditions
isotherm conditions
no gravitational effects
rigid-wall with no-slip condition.
Apart for the mesh sensitivity analysis, where steady-state simulations were
performed, an unsteady flow regime was used for all the simulations. The time-
step for the unsteady simulations was set at 10-4
s. In order to reach asymptotic
behaviour in the results, 5 cardiac cycles per simulation were replicated for a
total of 400000 time-steps.
Monitors at the inlet and outlets of each model were set in order to collect flow
and pressure data for quantitative analysis. Also, planes were created in the
aortic arches in correspondance of the location of the pressure catheter ports of
the physical 3D models used in the mock circuit. Other two planes, one in the
aortic root and one in the middle of the descending aorta, were created in each
model in order to further investigate the fluid dynamics in these positions
(Figure 5.4).
5.3.2 BOUNDARY CONDITIONS
Each of the 3 aortic arch modelled (TGA, control and spiral) presents 5
boundary faces: one aortic inlet, three brachio-cephalic outlets (Innominate,
Carotid, Subclavian), and one descending aorta outlet, as shown in Figure 5.5.
Velocity inlet and pressure outlets boundary conditions were imposed as
described below.
Chapter 5 Materials and methods II: computational
59
Figure 5.5 - TGA geometry: inlet (A) and outlets (B, C, D, E).
5.3.2.1 INLET
The TGA and the control inlet velocity information imposed during the
experimental tests were extracted from MR measurement, through the software
OsiriX as a discrete set of data, since MR scans were segmented in 30 temporal
frames per cardiac cycle (T=0.8 s). These data were then interpolated in order
to obtain continuous functions through a Fourier series with eleven
coefficients. The two resulting velocity curves (Figure 5.6), both with a mean
velocity of 0.9 m/s and minimum and maximum values of -0.8 m/s and 2.8 m/s,
were imposed at the inlets of the TGA and control CFD models respectively.
These inflow conditions were used to replicate computationally the
experimental tests performed using the two different phantoms (TGA and
control).
Moreover, taking advantage of the computational capability of conducting
parametric studies, in order to analyse how different surgical approaches could
influence the fluid dynamics in the aortic arch of these patients, additional
simulations were run imposing the same inflow condition at the three patient-
specific models. In particular, the TGA inflow velocity was chosen as inlet
boundary condition also for the control and spiral reconstructed anatomies.
The time-varying velocity functions were imposed at the inlet through a script
written in the computer language C, and read by Fluent under the name of UDF
(user defined function).
Chapter 5 Materials and methods II: computational
60
Figure 5.6 - TGA (top) and control (bottom) velocities imposed at the inlet of the 3D
geometries during the CFD simulation.
5.3.2.2 OUTLETS
A lumped parameter network (Figure 5.7) representing the experimental circuit
was developed and coupled with the 3D geometry as shown in Figure 5.7. In
particular, the coupling was implemented through pressures and flows
information exchanged between the 0D network and the 3D domain in
correspondance of the boundary faces.
Figure 5.7 - 3D geometry of the TGA patient coupled with the LPN.
-2
-1
0
1
2
3
4
0 0.2 0.4 0.6 0.8Ve
loci
ty [
m/s
]
Time [s]
-2
-1
0
1
2
3
4
0 0.2 0.4 0.6 0.8Ve
loci
ty [
m/s
]
Time [s]
Chapter 5 Materials and methods II: computational
61
Figure 5.8 shows the details of the lumped parameter network implemented at
each of the outlet branch. All the outlet branches share the same network
typology, but the values of the parameters are characteristics for eah branch.
The variables involved are:
Qin : flow value read and averaged by Fluent on each outlet face and
imposed as inlet to the LPN at every iteration;
P : pressure calculated by the UDF and imposed at each volume of the
outlet face;
Qin2 : flow, dumped by the compliance C, going through the resistances
R1 and R2;
Qx : flows coming from the other branches;
Qt : flow resulting from the sum of all the branches entering the final
part of the LPN, common to all branches;
Pt: pressure at the junction of all the branches;
Qt2: flow, dumped by the compliance Ct, going through the common
resistance Rt;
Patrium: pressure of the right atrium, set to 9 mmHg as measured from
the experimental tests.
Figure 5.8 - LPN implemented at each of the outlet branch: Qin, Qin2, Qt, Qx represent the
flows, P, Pt, Patrium the pressures; R2 and Rt are linear resistances, while R1 is flow-
dependant; C and Ct are compliances.
The parameter values were chosen in order to replicate the experimental
circuit.
Chapter 5 Materials and methods II: computational
62
The non-linear resistance R1 corresponds to the taps of the mock circuit, and is
characterised through the pressure drop-flow relationship obtained during the
tap experimental calibration (Table 5.1).
Table 5.1 - Pressure drop (ΔP) across each non-linear resistance. Q indicates flow-rate.
polynomial
INNOMINATE ΔP=1∙1013
∙Q2-8∙10
6∙Q
CAROTID ΔP=2∙1013
∙Q2-5∙10
6∙Q
DESCENDING AORTA ΔP=8∙1011
∙Q2-1∙10
7∙Q
SUBCLAVIAN ΔP=1∙1013
∙Q2-8∙10
6∙Q
R2 is the linear resistance representing the pressure drop contribution along the
tube connecting the considered branch to the connection point with the other
branches’ extensions. Rt lumpes the final common tube connecting the outlets’
junction to the right atrium. These resistances take into account the distributed
(equation 5.2) and the concentrated (equation 5.3) pressure drops, due to the
length of the pipes, the pipes’ connections, the sudden variations of section,
etc..
where μ is the viscosity of the fluid, L and D are the length and the diameter of
the pipes, v the velocity of the fluid and k a constant depending on the kind of
concentrated drop. In Table 5.2 the values of these resistances are reported.
Chapter 5 Materials and methods II: computational
63
Table 5.2 - Linear resistances of the LPN.
R
[Pa∙s/m3]
INNOMINATE Ri=5∙107
CAROTID Rc=1∙108
DESCENDING AORTA Rd=2.5∙107
SUBCLAVIAN Rs=1∙107
COMMON SECTION Rt=8∙107
C is the compliance representing the compliant chambers of the experimental
circuit. Ct is a numerical trick necessary to stabilise the variations of the
pressure Pt, and was set to a value which do not influence pressure and flow
results. Table 5.3 shows the values chosen for the compliances.
Table 5.3 - Compliances of the LPN.
C
[ m3/Pa ]
INNOMINATE Ci=1.88∙10-9
CAROTID Cc=1.98∙10-9
DESCENDING AORTA Cs=1.48∙10-9
SUBCLAVIAN Cd=3.06∙10-9
COMMON SECTION Ct=0.36∙10-11
The linear equation (equation 5.4), the ordinary differential equations (ODE)
(equations 5.5 and 5.7), and the second order equation (equation 5.6) solving
the LPN are reported below:
( )
Chapter 5 Materials and methods II: computational
64
{ √[ ( )] }
where the apex “old” refers to the value assumed by the variable at the
previous time step; a and b are the coefficients of the pressure drop-flow
second order equation charachterising the non linear resistance R1.
The ODE are resolved through explicit Eulero numerical method (equation 5.8)
with a time-step of 10-4
s.
( ) ( ) ( )
where f*(t) is the approximation of the function at the current time-step.
As for the inlet boundary condition, the LPN equations were written in the
computer language C and included in the UDF. The UDF compiled by the
software Fluent realises the 0D-3D coupling at the boundary faces by reading
the flow value computed from the CFD simulation, by calculating the pressure
P as results of the LPN equations, and by finally imposing it at each of the
outlet faces.
Chapter 6 Results
66
6.1 EXPERIMENTAL RESULTS
All hydrodynamic experiments and data acquisition were accomplished
successfully. The mock circuit proved to be suitable for the representation of
the downstream districts of the circulatory system, and pressure and flow
values are in the physiological range. Moreover, it is important to underline
that it is possible to easily substitute one 3D model to another in order to repeat
scans with different geometries. The system ran successfully for 2-3 hours
inside the MR scanner during each acquisition.
6.1.1 CONSIDERATIONS ON TEMPORAL RESOLUTION
FOR 4D FLOW ACQUISITIONS
As previously mentioned in 4.3.1, two different 4D flow sequences were
exploited during the experiments: a Standard sequence from Siemens and a
High Resolution (HighRes) sequence.
In Figure 6.1 is possible to appreciate that there are no substantial differences
between the flows acquired with the two sequences. In both cases the mean
flow (OsiriX Qmean = 5.5 L/min, Standard Qmean = 5.5 L/min, HighRes Qmean = 7
L/min) and the amplitude of the signals (OsiriX Qpeak = 17 L/min, Standard
Qpeak = 15 L/min, HighRes Qpeak = 20 L/min) are comparable with the ones
measured with OsiriX from traditional 2D Cartesian phase-contrast flow
acquisitions, which represented our reference. The high resolution sequence
was noisier, and it slightly overestimated the systolic peak.
Chapter 6 Results
67
Figure 6.1 – Flows at the inlet of the model acquired with the Standard (blue) and High
Resolution (red) 4D Flow sequences, compared with the OsiriX 2D acquisition (green).
From a qualitative point of view, the images extracted from the high resolution
sequence do not provide any additional information compared to the standard
one. Figure 6.2 shows the differences in the streamlines obtained with the two
sequences. The high resolution sequence exhibits a noisier background, likely
due to compromised signal to noise ratio (SNR), preventing a good
thresholding, as well as a smaller number of streamlines, which could not
represent adequately the fluid dynamics in the arch.
-10
-5
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
m3 /
s]
Time [s]
OsiriX 2D
4D Standard
4D HighResolution
Chapter 6 Results
68
Figure 6.2 – Qualitative comparison of the streamlines of the High Resolution (left) and the
Standard (right) 4D flow sequences. The first image shows a noisier background and visibly
less number of streamlines than the Standard one.
As the differences between the two sequences are negligible, the high
resolution was performed only on the TGA case depicted in Figure 6.2. During
all other experiments only the considerably quicker (15 minutes vs. 1 hour 10
minutes) standard sequence was acquired.
6.1.2 4D FLOW RESULTS: TGA AND CONTROL
GEOMETRIES
Siemens 4D flow software’s tools, in particular streamlines and particle traces,
represent a quick and effective method to visualise qualitative fluid dynamics
differences between the different geometries.
Chapter 6 Results
69
Figure 6.3 - Streamlines in the TGA geometry (left) compared with streamlines in the control
geometry (right) at t= 0.2 s (systolic peak). The range of velocity goes from 0 to 1.38 m/s for
both images. The yellow arrow indicates the jet impinging the aortic root.
Figure 6.4 - Streamlines in the TGA geometry (left) compared with streamlines in the control
geometry (right) at t= 0.6 s (diastole). The range of velocity goes from 0 to 1.38 m/s for both
images.
Chapter 6 Results
70
During systole, in the TGA model, a flow jet (1.38 m/s), impinging on the
enlarged aortic root and indicated by a yellow arrow in Figure 6.3 was clearly
visible. Nearby this jet, velocities are significantly lower (about 0.3 m/s) and
with a whirling or even chaotic trend.
In the control case it is not possible to identify a single flow jet hitting the
aortic wall within the streamlines, and their path is more uniform, especially in
the aortic root, compared with the TGA patient. In this case, water flows
smoothly toward the upper branches.
During the diastolic phase, the absence of a valve in the model led to
noticeable reverse flow, as it is possible to see in Figure 6.4. Once again,
during diastole the flow in the TGA model is more chaotic and whirling than in
the control one.
As the flow inlet waveforms of the two models are comparable (see paragraph
5.3.2.1), the difference in the intensity of the colours representing the velocity
values is ascribable to the enlarged root in the TGA geometry, which presents a
significantly difference in the root diameter compared with the control’s one
(DTGA=43-46 mm; Dcontrol=27-30 mm).
6.1.3 THE EFFECT OF COMPLIANCE: DISTENSIBLE
PHANTOM
While the pump was brought to the set point working condition, important
geometric changes were observed in the compliant model. In particular, at the
same flow values as per the rigid model, the shape differences between the
compliant and the rigid geometry are relevant: because of the viscoelastic
properties of Tango Plus and its highly distensible nature, the geometry visibly
dilated, not retaining its original shape. As the aim of the work is to study the
effect of a specific geometry on the fluid dynamics, this material is not suitable
for our experiments.
In Figure 6.5 and Figure 6.6 a comparison between the two models (prior to
and during pulsatile flow) is provided.
Chapter 6 Results
71
Figure 6.5 - TGA compliant model (left) and TGA rigid model (right). As expected there are
no shape differences between the two phantoms. The only difference is represented by the
material used for the rapid prototyping process.
Figure 6.6 – The compliant TGA model (left) is connected with the pulsatile pump. The
pressure effect is clearly visible, as the model did not retain its original shape, especially in the
aortic root. The TGA rigid model (right) was placed next to the compliant one in order to
better appreciate the geometric differences.
Chapter 6 Results
72
One additional problem detected, before putting the model inside the scanner
for the images acquisition, was the structural failure of the material in
correspondence of the aortic arch.
The material resulted to be not suitable for working in this range of pressure.
For these reasons, it was not possible to accomplish the image acquisition
inside the scanner.
Despite the problems described before, it was possible to acquire pressure data
in the compliant model. As expected, the compliance of the material being the
only difference, the pressure waveform is more damped than in the rigid
phantom, as shown in Figure 6.7.
Figure 6.7 - Pressure waveform comparison between the rigid TGA model (red) and the
compliant one (blue). As expected the second one in more damped than the first one, as a result
of the additional proximal compliance implemented by the distensible phantom.
6.2 COMPUTATIONAL RESULTS
All simulations converged and were compared with experimental data for
validation purposes.
50
70
90
110
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4
Pre
ssu
re [
mm
Hg]
Time [s]
Rigid model
Compliant model
Chapter 6 Results
73
For both the quantitative and qualitative analysis, the fourth cardiac cycle out
of the five cycles simulated in Fluent was selected.
6.2.1 MODEL VALIDATION
In order to verify that the lumped parameters network implemented in the UDF
reproduces the experimental circuit described in Chapter 4.2, a quantitative
comparison between flow and pressure values collected in the mock circuit and
the ones resulting from CFD simulations is necessary. For this purpose, two
CFD simulations were considered: a) TGA geometry with TGA inflow, and b)
control geometry with control inflow, in order to exactly replicate the
experimental conditions.
With regard to the flows, three comparisons were performed: mean flow, flow
distribution at the different outlets, and the flow waveforms.
Table 6.1and Table 6.2 report the mean flow comparisons at every outlet of the
TGA and the control model, respectively.
Table 6.1 - Mean flows calculated by OsiriX software (left) and Fluent simulation (right) at
every outlet for the TGA model.
Osirix
[L/min]
CFD
[L/min]
INNOMINATE 0.92 0.86
CAROTID 0.54 0.56
DESCENDING AORTA 2.92 3.02
SUBCLAVIAN 1.17 0.98
Chapter 6 Results
74
Table 6.2 - Mean flows calculated by OsiriX software (left) and Fluent simulation (right) at
every outlet for the control model.
OsiriX
[L/min]
CFD
[L/min]
INNOMINATE 0.85 0.88
CAROTID 0.59 0.58
DESCENDING AORTA 3.39 2.91
SUBCLAVIAN 0.92 0.88
The results show very good agreement and the computational model replicated
appropriately the experimental hydrodynamic environment.
Table 6.3 and Table 6.4 show the flow split at every outlet respectively in the
TGA and control model. They were calculated as percentage values relatively
to the inlet flow.
Table 6.3 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at
every outlet for the TGA model. The following percentages are computed relatively to the inlet
flow.
Osirix
[%]
CFD
[%]
INNOMINATE 16.7 15.7
CAROTID 9.9 10.3
DESCENDING AORTA 53.1 55.1
SUBCLAVIAN 21.4 17.8
Chapter 6 Results
75
Table 6.4 - Flow split calculated by OsiriX software (left) and Fluent simulation (right) at
every outlet for the control model. The following percentages are computed relatively to the
inlet flow.
OsiriX
[%]
CFD
[%]
INNOMINATE 14.6 16.7
CAROTID 10.2 11.1
DESCENDING AORTA 57.9 55.3
SUBCLAVIAN 15.9 16.9
Flow distribution results are in excellent agreement, with a maximum
difference in the flow split in the TGA’s subclavian of 3.5%. The overall
distributions in the computational models are comparable with the ones
registered in the experiments.
Finally, Figures 6.8-6.11 and 6.12-6.15 report respectively the TGA and
control flow waveforms at every outlet, with a comparison between the real
data measured in OsiriX (blue) and the simulated results (red).
Figure 6.8 - Computational (red) and experimental (blue) flow waveforms comparison in
TGA’s subclavian for a cardiac cycle (T=0.8 s).
-4
-2
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
Chapter 6 Results
76
Figure 6.9 - Computational (red) and experimental (blue) flow waveforms comparison in
TGA’s innominate for a cardiac cycle (T=0.8 s).
Figure 6.10 - Computational (red) and experimental (blue) flow waveforms comparison in
TGA’s carotid for a cardiac cycle (T=0.8 s).
-4
-2
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
-4
-2
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
Chapter 6 Results
77
Figure 6.11 - Computational (red) and experimental (blue) flow waveforms comparison in
TGA’s descending aorta for a cardiac cycle (T=0.8 s).
Figure 6.12 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s subclavian for a cardiac cycle (T=0.8 s).
0
2
4
6
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
-4
-2
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
Chapter 6 Results
78
Figure 6.13 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s innominate for a cardiac cycle (T=0.8 s).
Figure 6.14 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s carotid for a cardiac cycle (T=0.8 s).
-4
-2
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
-4
-2
0
2
4
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
Chapter 6 Results
79
Figure 6.15 - Computational (red) and experimental (blue) flow waveforms comparison in
control’s descending aorta for a cardiac cycle (T=0.8 s).
Also in terms of flow tracings, results show that the computational simulations
reproduce in a satisfactory way the flowing conditions of the experimental
setup.
With regard to pressure measurement, experimentally it was measured only in
the aortic arch. For this reason the only possible comparison is with pressure
values measured by Fluent in a plane, specifically created in the geometry, at
the same level of the dedicated port for the pressure catheter.
Figures 6.16 and 6.17 show the comparison between the experimentally (blue)
and computationally (red) obtained pressures for the TGA and the control
model, respectively.
0
2
4
6
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
OsiriX
CFD
Chapter 6 Results
80
Figure 6.16 - Computational (red) and experimental (blue) pressure waveforms comparison in
TGA’s aortic arch for a cardiac cycle (T=0.8 s).
Figure 6.17 - Computational (red) and experimental (blue) pressure waveforms comparison in
control’s aortic arch for a cardiac cycle (T=0.8 s).
Satisfactory agreement was noted in terms of pressure tracings and pressure
values. In particular, the TGA mean pressure value for the experimental curve
40
60
80
100
120
0 0.2 0.4 0.6 0.8
Pre
ssu
re [
mm
Hg]
Time [s]
Catheter
CFD
40
60
80
100
120
0 0.2 0.4 0.6 0.8
Pre
ssu
re [
mm
Hg]
Time [s]
Catheter
CFD
Chapter 6 Results
81
is 84.6 mmHg and for the computational one is 85.7 mmHg. The control model
exhibits an experimental mean pressure of 87 mmHg and a computational one
of 83.2 mmHg.
6.2.2 QUALITATIVE COMPARISON BETWEEN 4D FLOW
AND CDF SIMULATIONS
Both 4D flow Siemens software and Fluent allow visualisation of the velocity
streamlines. For a qualitative comparison of the fluid dynamics in the different
geometries, four temporal instants (Figure 6.18) out of the entire cardiac cycle
(T= 0.8 s) were considered: t1= 0.1 s (early systole), t2= 0.2 s (systolic peak),
t3= 0.4 s (late systole) and t4= 0.6 s (diastole).
Figure 6.18 - Temporal instants considered for the comparison displayed in the cardiac cycle. :
t1 represents the early systole, t2 the systolic peak, t3 the late systole and t4 the diastole.
Figure 6.19-6.22 show velocity streamlines for the TGA geometry.
-10
-5
0
5
10
15
20
0 0.2 0.4 0.6 0.8
Flo
w [
L/m
in]
Time [s]
t1
t2
t3
t4
Chapter 6 Results
82
Figure 6.19 - 4D flow streamlines (left) compared with CFD streamlines (right) at t1= 0.1 s
(early systole) in the TGA model. The range of velocity is the same for both images.
Figure 6.20 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.2 s
(peak systole), in the TGA model. The range of velocity is the same for both images. It is
clearly visible in both of them the flow jet hitting the wall.
Chapter 6 Results
83
Figure 6.21 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.4 s
(late systole), in the TGA model. The range of velocity is the same for both images. Once
again in both of them it is possible to appreciate a flow jet impinging on the aortic wall.
Figure 6.22 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.6 s,
(diastole), in the TGA model. The range of velocity is the same for both images.
Chapter 6 Results
84
Considering these results, we could verify a good agreement between the 4D
flow and CFD simulations for the TGA geometry. In particular, the CFD is
able to show the same flow jet impinging at the top of the aortic root wall, and
the surrounding whirl visible in 4D flow images. The ranges of velocities are
comparable in terms of magnitude and distributions. The correspondence is
excellent both in systole and in diastole.
In Figure 6.23-6.26 the same 4D flow and CFD velocity streamlines
comparison is repeated for the control geometry at the same time points as for
the TGA model.
Figure 6.23 – 4D flow streamlines (left) compared with CFD streamlines (right) at t1= 0.1 s
(early systole) in the control model. The range of velocity is the same for both images.
Chapter 6 Results
85
Figure 6.24 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.2 s,
(peak systole), in the control model. The range of velocity is the same for both images. It is
clearly visible in both of them the flow jet flowing smoothly towards the upper branches.
Figure 6.25 – 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.4 s
(late systole), in the control model. The range of velocity is the same for both images. Once
again in both of them it is possible to appreciate a flow jet flowing towards the subclavian
artery.
Chapter 6 Results
86
Figure 6.26 - 4D flow streamlines (left) compared with CFD streamlines (right) at t2= 0.6 s
(diastole), in the control model. The range of velocity is the same for both images
The results of CFD and 4D flow simulations show an excellent agreement for
the control geometry. The CFD exhibits streamlines comparable with 4D flow
in terms of magnitude and distribution, both in systole and diastole. In
particular, is it possible to observe the same flow jet, uniform throughout the
whole aortic root and smoothly reaching the upper branches, as in the 4D flow
data.
6.2.3 THE EFFECT OF THE AORTIC ARCH GEOMETRY:
CFD COMPARISON BETWEEN TGA, CONTROL
AND SPIRAL GEOMETRIES
For the CFD comparison, the simulations considered the three different
geometries with the same inflow and outflow boundary conditions (the TGA
inflow was chosen), as the aim was to analyse only the effects of the geometry
on the fluid dynamics.
Chapter 6 Results
87
Table 6.5 shows the mean flows of the TGA, control and spiral obtained at
each outlet face.
Table 6.5 - Mean flows calculated by Fluent at every outlet of the TGA (left), control (central)
and spiral (right) models.
TGA
[L/min]
CONTROL
[L/min]
SPIRAL
[L/min]
INNOMINATE 0.92 0.86 0.87
CAROTID 0.57 0.57 0.54
DESCENDING AORTA 3.02 2.83 2.80
SUBCLAVIAN 0.99 0.87 0.89
The differences between these values are negligible and the mean flows in the
three geometries are comparable.
Table 6.6 displays the flow split at every outlet in the three geometries.
Percentage values are computed relatively to the inlet flow.
Table 6.6 - Flow split calculated by Fluent at every outlet of the TGA (left), control (central)
and Spiral (right) models. The following percentages are computed relatively to the inlet flow.
TGA
%
CONTROL
%
SPIRAL
%
INNOMINATE 16.70 16.77 17.05
CAROTID 10.42 11.20 10.64
DESCENDING AORTA 54.89 55.17 54.90
SUBCLAVIAN 17.99 16.87 17.42
Since the aortic arch geometry was the only different variable between these
three simulations, it is possible to deduce that the less spiral arch of the TGA
patient (with the indentation typically resulting from the Lecompte maneuver)
and the enlarged root of both TGA and spiral models do not affect the flow
Chapter 6 Results
88
split, that is instead mainly governed by the downstream resistances. The
difference in the flow-split is around 1%, with a maximum of 1.12% in the
subclavian arteries of the TGA and control models.
Figure 6.27-Figure 6.30 report the flow waveforms at each outlet, comparing
TGA (red), control (blue) and spiral geometry (green).
Figure 6.27 - CFD innominate flow waveforms comparison between TGA (red), control (blue)
and spiral (green) geometries for a cardiac cycle (T=0.8 s).
Innominate flow waveforms are really similar in the three geometries, ranging
between -1.96±0.02 and 4.47±0.2 L/min.
-3
-2
-1
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8
Flo
w [
L/m
in]
Time [s]
TGA
CONTROL
SPIRAL
Chapter 6 Results
89
Figure 6.28 - CFD carotid flow waveforms comparison between TGA (red), control (blue) and
spiral (green) geometries for a cardiac cycle (T=0.8 s).
The flows in the carotid arteries exhibit values between -1.74±0.17 and
3.32±0.27 L/min. The differences between the geometries are negligible.
Figure 6.29 - CFD subclavian flow waveforms comparison between TGA (red), control (blue)
and spiral (green) geometries for a cardiac cycle (T=0.8 s).
-3
-2
-1
0
1
2
3
4
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
TGA
CONTROL
SPIRAL
-4
-3
-2
-1
0
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
TGA
CONTROL
SPIRAL
Chapter 6 Results
90
In subclavian arteries the values range from -2.32±0.5 and 4.14±0.45 L/min,
with a very similar trend between TGA, control and spiral.
Figure 6.30 - CFD descending aorta flow waveforms comparison between TGA (red), control
(blue) and spiral (green) geometries for a cardiac cycle (T=0.8 s).
Finally, the waveforms in the descending aorta, waving between 0.61±0.2 and
5.63±0.12 L/min, show no differences linked with the geometry.
A comparison between velocity streamlines in the three different geometries
(with the same inlet flow and outlet LPN) at four different temporal instants
(t=0.1s, t=0.2s, t=0.4s and t=0.8s as for Figure 6.19) is shown in Figure 6.31-
Figure 6.34.
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Flo
w [
L/m
in]
Time [s]
TGA
CONTROL
SPIRAL
Chapter 6 Results
91
Figure 6.31 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.1 s.
In early systole (t=0.1s) the velocities are increasing at the inlet but they are
still low in the rest of the geometry. In the control geometry the majority of the
streamlines has a straight path following the geometric shape, while in the
TGA and spiral geometries the streamlines follow chaotic paths in the enlarged
roots, while they recover a more regular trend after the aortic arch, in the
descending aorta.
Chapter 6 Results
92
Figure 6.32 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.2 s.
At peak systole (t=0,2 s) the three geometries show three different behaviours.
In the control model, once again, the streamlines path follows the geometry.
The velocity magnitude remains high up to the level of the upper branches.
In the TGA the flow jet is clearly visible, and, being not directed as the
curvature of the geometry, it hits the wall of the enlarged root, losing velocity
before reaching the upper branches.
Finally, in the spiral geometry, the flow jet, once again clearly visible, is
directed as the curvature, but where the enlarged root shrinks, the flow jet hits
the wall causing a chaotic trend in the streamlines. In TGA and spiral
geometries whirling streamlines, characterised by lower velocity modulus,
surround the main flow jet.
Chapter 6 Results
93
Figure 6.33 - Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.4 s.
At late systole (t=0.4 s) what described for the systolic peak is still visible. In
particular, the difference between the TGA and the spiral geometries is due to
the different orientation of the inlet: in the TGA it points towards the external
curvature of the wall, directing the flow in this way, while in the spiral the flow
jet hits the wall when the area shrinks. The reduced area increases the velocity
of the water if compared with the velocity in the enlarged root.
Chapter 6 Results
94
Figure 6.34 – Control (left), TGA (central) and spiral (right) velocity streamlines at t=0.6 s.
The image above (Figure 6.34) reports the diastole (t=0.6 s) in the three
geometries. As expected the velocities are lower than in the systolic phase. As
observed in Figures 6.27-6.30, it should be noted that the inlet face and all
outlets except for the descending aorta are characterised by retrograde flow at
this time point. Also, the more chaotic streamlines trend in the enlarged roots
of both the TGA and spiral geometries if compared to the control one should be
highlighted.
Another interesting parameter to be evaluated in this study is the wall shear
stress (WSS). Figure 6.35-Figure 6.36 report WSS distributions at systolic peak
for control, TGA and spiral geometries, respectively.
Chapter 6 Results
95
Figure 6.35 - Front view of the WSS in control (left), TGA (central), spiral (right) models.
The range of wall shear stress goes from 0 to 35 Pa.
Figure 6.36 - Lateral view of the WSS in control (left), TGA (central), spiral (right) models.
The range of wall shear stress goes from 0 to 35 Pa.
Chapter 6 Results
96
The first difference to be noticed between the control and the other two
geometries is the area interested by a WSS higher than 25 Pa (green/yellow
colour): it is very extended in the two pathological situations, rather than in the
physiological one. In both the TGA and the spiral WSS reaches values around
35 Pa (red) at different points. In the spiral model higher values correspond to
the narrowing of the root, in a portion corresponding to the ascending aorta. In
the TGA this shrinkage is less marked, but the area interested by a high WSS is
wider.
Table 6.7 reports the values of mean pressure at each outlet of the control,
TGA and spiral geometries.
Table 6.7 – Mean pressure calculated at each outlet of the control (left), TGA (central) and
spiral (righ) models.
TGA
[mmHg]
CONTROL
[mmHg]
SPIRAL
[mmHg]
ASCENDING AORTA 85.18 86.41 84.52
INNOMINATE 85.80 87.19 85.66
CAROTID 86.33 85.31 84.17
DESCENDING AORTA 84.40 85.50 83.60
SUBCLAVIAN 81.99 85.04 82.04
As for the flow split, the outlet mean pressure is not affected by the changes in
geometry. Pressures in the TGA model are really similar to the control ones,
with a maximum variance in subclavian artery (3.7%). Comparing the spiral
and the control geometry, the difference is around 1%, with the biggest
variation in carotid (2.5%).
In Figure 6.37-6.39 velocity vectors in the aortic arch at peak systole (t=0.2s)
are shown.
Chapter 6 Results
97
Figure 6.37 –Velocity vectors at peak systole (t=0.2s) in the control model .
Figure 6.38 - Velocity vectors at peak systole (t=0.2s) in the TGA model .
Chapter 6 Results
98
Figure 6.39 - Velocity vectors at peak systole (t=0.2s) in the spiral model.
In both TGA and spiral roots the vectors show a more complex fluid dynamics
rather than in the control model, with presence of secondary flows. While
higher velocities in the control model are clustered in the centre of the surface,
in the other two they have a random distribution.
In ascending aorta the effect of the geometry is clearly visible in the spiral
model. Here, the vectors are the result of the sudden shrinking of the section in
proximity of the plane considered. In the TGA ascending aorta, as the section
variance is smaller, this effect is reduced.
.
Chapter 7 Discussion
100
This study successfully applied a modelling paradigm involving both
experimental and computational tools to tackle a complex case of congenital
heart disease. Specifically, Transposition of the Great Arteries (TGA) is a
congenital condition presenting a wide range of complications, such as aortic
root dilation [Ntsinjana et al.,2002], reduced aortic distensibility [Grotenhuis et
al., 2008] and compromised ventricular-vascular coupling [Biglino et al., 2013]
on the aortic side, and unilater pulmonary artery stenosis on the pulmonary side
[Shrivastava et al., 1976]. The full consequences and effects of TGA repaired
with the Arterial Switch Operation (ASO) are not fully appreciated yet, due to
the relatively young age of the patients. In fact, ASO was introduced in the
1980s and TGA was previously palliated with an atrial switch approach
[Jatene, 1982]. The variety of approaches shows, in itself, the complexity of
this disease and the extent to which surgeons have gone to improve the
physiology of patients born with TGA.
This work focused solely on the aortic side of the problem, using modelling
techniques to evaluate the effect of the shape of the neo-aorta in this group of
patients. Overall, a patient-specific approach was chosen. Also, a validation
study was carried out to demonstrate the reliability of the computational model,
which was later used to gather additional information on the fluid dynamics of
TGA repaired with ASO.
Following from the results presented in Chapter 6, a relatively simple and
compact mock circuit proved to be an excellent tool to study TGA
experimentally. By setting adequate R and C boundary conditions, the mock
circuit is able to accurately reproduce the pathological scenario of interest, at a
patient-specific level, according to cuff pressure measurements. The boundary
conditions in fact can be easily tuned manually adjusting the stroke volume and
the heart rate of the pulsatile pump, the volume of air in the compliant
chambers and the extent of closure of the taps used to implement vascular
resistance. Moreover, using the manufacturing technique known as rapid
prototyping, patient-specific geometries are obtained, and these can be easily
mounted into the circuit, implementing patient-specific 3D information. This is
Chapter 7 Discussion
101
important not only because it allows to take into account the variety in aortic
morphology between different patients (by testing multiple models), but also
because the study focused specifically on the hemodynamics within the neo-
aorta.
Such hemodynamic features can be appreciated experimentally by taking
advantage of the imaging technique known as 4D MR flow [Meierhofer er al.,
2012]]. This requires first of all to construct an MR-compatible mock circuit,
which was successfully achieved in this work.
Four-D MR flow can be very informative in the field of congenital defects, as
in cases of Fontan circulation [Valverde et al., 2012] as well as bicuspid aortic
valve [Barker at al., 2012]. The advantage of using this technique, instead of
standard 2D acquisitions, is that there is no need to plan flow acquisition prior
to acquiring the data, which is collected over a volume of interest. As a result,
this can make the technique time-efficient, especially in those cases where
multiple flows need to be planned and acquired [Nordmeyer et al., 2010], albeit
acquisition time remains a concerns for clinical application of 4D MR flow,
especially in children.
Furthermore the post-processing of a 4D flow dataset gives access to exquisite
flow visualisation, including streamlines and particle tracing, over the 3D
volume of interest.
Only one study recently applied 4D MR flow to the study of TGA in humans
[Hsiao et al., 2012], however there are several advantages linked to using an
experimental approach. Firstly, the use of a hydraulic circuit solves problems
related to patient’s motion, which are of particular concern especially in
younger patients and over a long acquisition (15-20 minutes, or more).
Moreover, the circuit can be kept inside the scanner for as long as required, and
this is useful if multiple acquisitions are necessary. For example, in this study a
1 hour and 10 minute long high spatial and high temporal resolution sequence
was performed on the model. The reason to perform this additional scan was to
evaluate whether increased resolution provided access to meaningful additional
Chapter 7 Discussion
102
fluid dynamic details, especially in complex geometries, such as TGA. In this
work, because of the compromised SNR, it was not possible to get more
information than from the standard sequence. This point could be tackled in the
future from an MR physics perspective, trying to acquire high resolution
sequences without compromising SNR and ongoing work in the MR unit at
Great Ormond Street Hospital is evaluating the complexities of 4D flow
acquisition. However, as the results of the ‘standard’ (15 minute) sequence
were satisfactorily informative for the hemodynamic problem under
investigation, further work in this context was deemed not necessary.
Full datasets were ultimately acquired experimentally for the TGA anatomy
and the age-matched healthy control model. In both cases, pressure values were
in agreement with cuff pressure readings obtained at the time of the clinical
MR scan (Pmean = 80 mmHg). On the other hand, flow distribution between
upper and lower body and in the different head and neck vessels was ensured to
be realistic but was not set to patient-specific values, as flow data is not
acquired in each brachiocephalic vessel in routine clinical scans, so these data
were not available.
All the experimental acquisitions of this work were carried out using rigid
models. Rigid models are easy to mount and robust. Also, transparency
associated with some of the rigid resins used for printing rigid models are
important for some visualisation studies (e.g. particle image velocimetry, PIV
[Ibrahim et al., 2009]), albeit not necessary for MR imaging. The disadvantage
of using a rigid material, on the other hand, is that it does not take into account
the compliant behaviour of the human vessels and the associated recoiling
effect in diastole. For this reason, an additional model was printed using a
commercially available compliant compound i.e. Tango Plus, as discussed in
paragraph 4.4. This material allowed to print a complex TGA geometry and
was chosen because it is compatible with PolyJet printing technique,
guaranteeing fine printing resolution (16 μm), and based on previous evidence
of realistic distensibility [Biglino, 2013]. However, the model failed to
Chapter 7 Discussion
103
withstand the range of aortic pressures that were required for the patient-
specific runs, and was also prone to tear, resulting in the model being damaged
prior to completing a full acquisition. The lack of data gathered in the
compliant model, nevertheless, did not impinge on the validation study: as the
CFD models have rigid walls, validation data was successfully provided from
the models printed in rigid resin.
As shown in the results, presented in Chapter 6, the CFD simulations are in
overall good agreement with the experiments, which allowed to proceed with
the analysis just from a computational point of view. Although it is possible to
properly set the boundary conditions also with an experimental approach, a
computational approach guarantees their stability. In fact, minor leaks can
occur while gathering experimental data, especially over long acquisitions (i.e.
multiple scans in the MR). Also, other changes are not straightforward to
monitor, e.g. if a solution of water and glycerine were used, its content is prone
to changes in viscosity with small changes in temperature.
Computationally, it is also possible to easily undertake parametric studies,
simply changing one parameter at a time in order to understand its influence on
the fluid dynamics. The only concern in this case is the computational cost of
each additional simulation, rather the time associated with re-assembling an
experimental rig. It is also possible to extract retrospectively other parameters
and values of interest at different locations in the model, not necessarily
planned beforehand, while this is not possible in an experimental study.
In this study we performed three different simulations, the only difference
among them being the 3D element in the multi-scale network. This approach is
suitable to understand how geometry alone affects the fluid dynamics,
effectively isolating one variable in a complex clinical problem. Again, the
only cost associated with this procedure is computational.
Another advantage of the CFD is the amount of information that is possible to
gather during the post-processing. Indeed, in addition to streamlines and flows,
the software can provide values and 3D visualization of several other
parameters, such as pressure distribution and wall shear stress. The values of
Chapter 7 Discussion
104
the parameters of interest can be easily obtained at every point of the geometry,
without planning it before the simulation.
In the three geometries included in this study, the shape differences, clearly
visible in the enlargement of the root and on the different aortic arch
angulation, are ascribable to the different surgical operation (Figure 7.1). The
enlarged aortic root in both the ‘TGA’ and ‘spiral’ model is a common feature
related to their diagnosis and consequent surgery, whereas the indentation on
the ascending aorta and the more acute angle of the aortic arch observed solely
in the ‘TGA’ model are to be ascribed to the Lecompte maneuvre, which was
not performed in the ‘spiral’ model.
Figure 7.1 - Control (right), TGA (central) and spiral (left) geometries.
Analysing streamlines and WSS it is possible to understand how this affects the
fluid dynamics and, consequently, which are the potential clinical implications.
First of all it is important to underline, as shown in Chapter 6, how flow split
and overall pressure distribution are not dependent on the 3D geometry but
Chapter 7 Discussion
105
only on the downstream network. On the other hand, the local fluid dynamics
are strongly affected by anatomical changes.
The influence of the enlarged root is a point of great interest as it is evident by
analysing the velocity streamlines. In the TGA and spiral geometries the result
of this shape is a high velocity flow jet, surrounded by lower velocity flows
that follow a whirling path. This fluid dynamic feature, characterised by low
velocities and recirculation areas, could be critical from a clinical point of
view, since it can promote particle deposition and consequently thrombus,
clotting and plaques formation, thus increasing the risk of atherosclerosis
[Meierhofer et al., 2012].
Moreover, in the spiral geometry, in correspondence of the shrinking after the
enlarged root, the velocity increases considerably and the fluid dynamics result
to be very chaotic, while in the TGA model the arch angulation and the overall
geometric arrangement address the flow jet to hit the aortic wall. For this
reason in the TGA ascending aorta, the velocity is quite low.
These portions of aorta of the models resulted, in our study, to show a high
WSS (Figure 7.2).
Figure 7.2 - WSS in control (left), TGA (central), spiral (right) models.
Chapter 7 Discussion
106
The risk of having high WSS is potential mechanical damage of the inner wall
of the vessel [Chien et al., 1998; Shyyy ,2001], which could in turn weaken the
vessel and possibly initiate a lesion. TGA and spiral models are subjected to
considerably higher values of WSS. In addition the interested area in which it
has a value higher than 25 Pa is more extended in the pathological scenarios
than in the physiological one.
The combination of these two factors may have an impact in long-term
pathologies, in particular the development of aortic dilatation [Poltem, 2012].
This effect, added to the already enlarged root because of the surgical
operation, may leads to structural failure of the vessels.
Another aspect of particular interest is the comparison between the different
geometries resulting from two different surgical operations. The difference in
our case is the lack of the Lecompte maneuver for the spiral geometry. The
idea in this case is to evaluate if, reproducing a more physiological
arrangement of the vessels, it is possible to obtain a positive influence on the
fluid dynamics.
Both the information collected by streamlines and WSS do not show an
improvement with respect to the TGA scenario with Lecompte maneuver. The
enlarged root of the spiral case presents vorticity as for the TGA case, but the
direction of the high velocity flow jet has a different orientation. While in the
TGA it impinges the inner wall of the aortic root, in the spiral it hits the first
section of the ascending aorta, just after the shrinkage. The WSS is
significantly high in that area (around 35 Pa) extending for a considerable
portion of the ascending aorta, and the hemodynamics result to be very
whirling. This suggests that this particular case does not show any obvious
hemodynamic improvement with respect to the TGA case.
In comparing these two models, it should be considered that they are not age-
matched. The TGA and the control models are 15 years old with a BSA of 1.7
m2, while the spiral model is reconstructed from a 25-year-old patient. The
main difference related to the age mismatch is the distensibility of the vessels.
Since the study considers rigid models, this difference does not affect the work.
Despite this difference in age, the BSA is 1.9 m2, which is not substantially
Chapter 7 Discussion
107
different from the previous two. Moreover, as this study is focused on the
effects of geometrical changes, this case is particularly interesting because
of the different approach undertaken during the surgical operation. Finally, the
compliant behaviour of the wall was not taken into account in this study,
neither experimentally nor computationally. CFD simulations assumed rigid
vessel walls, so different distensibility was not an issue. Admittedly, such
variations in vessel compliance have been reported also at young ages [Voges
et al., 2012], but these are not as meaningful as much more significant changes
in distensibility occurring later on in life.
From a methodological point of view, all simulations were performed using
water as the flowing medium. This was set to replicate the experimental part of
the study, in which water was chosen for hygiene and safety reasons related to
operating the mock loop inside the MR scanner, rather than a solution of water
and glycerol or other accepted blood analogues. This could potentially
underestimate viscous effects that may occur in the model, although no
significant narrowing is present in the three geometries that were modelled.
This could also reflect on the magnitude of the WSS, but would not affect
considerations on different WSS distribution between different anatomies
Chapter 8 Conclusions and future works
109
The aim of this thesis was to model the fluid dynamics of patients who
underwent treatment for transposition of great arteries (TGA). Specifically, the
focus was on TGA repaired by arterial switch operation (ASO). ASO is
nowadays the most common and successful procedure for patients affected by
TGA and aims to resolve the underlying issue of insufficient oxygen supply to
the tissues and excessive ventricular workload.
Two cases of ASO were modelled in this thesis, i.e. with and without
Lecompte maneuver. The latter indicates a specific arrangement following
ASO with the pulmonary arteries effectively positioned anterior to the aorta
and the pulmonary branches embracing the aorta itself, resulting also in an
indentation of the ascending aorta. These are anatomical features typical of
repaired TGA and by including a case without Lecompte manoeuvre it was
possible to appreciate the influence of the changes in aortic morphology and
anatomical arrangement.
The other main features to be addressed in a study of the neo-aorta following
ASO are mainly a) the dilated aortic root and b) the modified aortic arch
angulation. Both have been suggested to negatively affect the physiology of
these patients [Ntsinjana et al., 2012].
In order to take into account all these realistic anatomical features, patient-
specific geometries were reconstructed from MRI data and employed both in
the experimental and computational model.
Three cases were ultimately studied in detail:
i) a TGA patient who underwent the standard ASO procedure,
ii) a TGA patient who underwent the ASO procedure without the
Lecompte maneuver, also referred to as “spiral”, with reference to
the novel spiral surgery for TGA repair [Chiu et al., 2012]
iii) a healthy individual with normal aortic geometry, referred to as
“control case”, which was matched to (i) for age and BSA.
In order to tackle this congenital scenario, we proposed a methodology
involving different tools, such as hydrodynamic experiments, 4D MR flow and
Chapter 8 Conclusions and future works
110
CFD, in order to describe patient-specific hemodynamics. We used a mock
circulatory system, which included a rapid prototyped patient-specific 3D
element for both the TGA and the control cases, and tuned according to clinical
data. Four-D MR flow was acquired in these models and highlighted the
influence of changes in geometry on the hemodynamics, especially
appreciating differences in the streamlines in the aortic root and ascending
aorta.
Two CFD simulations, coupled with a LPN properly tuned in order to exactly
replicate the conditions of the experiments, were performed, thus using the
experimental data to validate the computational models. Computational results
were in excellent agreement with their experimental counterpart.
Once the computational model is validated, we could study the effect of
changing aortic geometry alone by varying the 3D element in the multi-scale
simulations and imposing the same boundary conditions to the three cases.
From our results we could conclude that aortic geometry does not affect overall
pressure and flow values, which are regulated by the whole vasculature,
especially since abrupt changes (e.g. aortic coarctation) were not present in the
models under investigation. On the other hand, the anatomy typical of repaired
TGA results in unfavourable hemodynamics. This was indicated by high values
of wall shear stress on the ascending aortic wall, with a jet impinging on the
posterior ascending aorta, as well as by noticeable areas of flow recirculation in
the dilated aortic root. Interestingly, the “spiral” case behaved more like the
TGA case, also exhibiting substantially higher WSS than the control model and
similar flow features in the dilated aortic root, albeit the angulation of the aortic
arch resembled more that of the control case. This may suggest that features
inherent to TGA (i.e. the main vessels being repositioned with the resulting
wall abnormalities) are not improved, from a hemodynamic point of view, by
retaining a more spiral geometry of the aortic arch. However, this observation
was performed only on one patient. Furthermore, this was a case of ASO
without Lecompte manoeuvre and not a case of spiral surgery as defined by
Chiu et al. [Chiu et al., 2012]. Our conclusions thus refer to the effect of the
Chapter 8 Conclusions and future works
111
anatomy alone, without drawing considerations on the actual surgical
procedure.
Nevertheless, making use of a validated methodology, it would be possible to
suggest changes in order to advice the clinicians on potential ways to improve
the surgical technique. For example, by virtually creating a range of different
surgical outcomes, it would be possible to evaluate the potential hemodynamic
benefit of each and indicating differences in the fluid dynamics.
In conclusion, this study provides a reliable methodology for hemodynamics
evaluations in patient-specific models. Experimental data were in agreement
with clinical values. A novel imaging technique (i.e. 4D MR flow) was
employed and provided insight into hemodynamic differences between the
neo-aorta post-ASO and the healthy aorta. These considerations were expanded
using CFD simulations, validated against experimental data, which proved to
be a useful tool to study complex geometries and to potentially inform
clinicians on different surgical options for a same patient.
FUTURE WORK
1.Statistics. This study included three patient-specific models, which
effectively could be considered as three cases studies. Both the experimental
and the computational results highlighted differences between the three
scenarios, however in order to comment on the statistical significance of the
results more models need to be included in the study, for each scenario. This
can be conveniently done by making use of the validated CFD model. A range
of patient-specific models could be inserted into the validated (i.e. reliable)
multi-scale model, thus running a larger amount of simulations. This study,
which would be more computationally expensive, would provide a larger
amount of data for statistical analysis comparing different patients populations.
This could strengthen considerations on the potential long-term effects of
different morphologies.
Chapter 8 Conclusions and future works
112
2.Compliant models. Certainly, one aspect to take into consideration for further
studies is the compliant behaviour of the physiological vessels. A compliant
model, reproducing closely realistic distensible behaviour, would be helpful to
further understand the fluid dynamics. While gross differences in flow split or
aortic pressure are not expected, local hemodynamics, especially in the aortic
root, could be described in greater detail. This was attempted in this study,
however the material chosen for manufacturing the compliant TGA model did
not withstand physiological pressures for the whole time needed for a full MR
acquisition and was prone to tear. The material (i.e. TangoPlus) suffered
structural failure, so different materials should be evaluated. Silicone-based
compounds may represent a valid alternative in this regard.
If significant difference were observed experimentally between a rigid and a
compliant model, it is possible to simulate such compliant behaviour also
computationally, by means of fluid-structural interaction (FSI) simulations.
One problem typically related with this tool is the lack of information of elastic
characteristic of natural vessels. It is possible to avoid this issue by using an
artificial material which experimentally reproduces the compliant behaviour of
the vessel considered. In this way the elastic characteristic would be known,
facilitating the FSI simulations.
3.Decomposing the velocity inlet. 4D MR flow is a novel imaging technique
and in this work we have suggested that it could be used not only to validate
the computational model, but also to set it. In fact, it is possible to extract from
MR data the values of the velocity in time in each of the voxels of the inlet, in
the x, y and z components. Imposing these values to each corresponding
element of the mesh at the inlet of the computational model, instead of the
spatial average as typically done, could allow to obtain a more detailed
characterisation of the complex fluid dynamics. Clearly, the time necessary for
the simulations is considerably increased, while the flow split and overall
pressure distribution would not be affected by this different approach,
potentially providing more detail on the local fluid dynamics, e.g. whirling and
recirculation in the root. A first attempt was performed in this study, making
Chapter 8 Conclusions and future works
113
use of 2D Cartesian flow acquisitions, in order to explore the methodological
aspects related to this point. In order to reduce the high computational cost a
coarsen mesh (300000 elements), shown in Figure 8.1, was considered.
However, the mesh was not fine enough for this complex simulation. Therefore
the convergence was not reached. This warrants further study.
Figure 8.1 - Coarsen mesh on the inlet face of the TGA model, used for the pixel by pixel
imposition of the velocity.
References
114
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