Computational Aerodynamics of Long Segment Congenital Tracheal Stenosis with Bridging Bronchus

Limin Zhu1#, Jinlong Liu1,2#, Weimin Zhang1, Qi Sun1, Haifa Hong1, Zhou Du1, Jinfen Liu1* 1 Department of Cardiothoracic Surgery

2 Institute of Pediatric Translational Medicine Shanghai Children’s Medical Center

Shanghai Jiao Tong University School of Medicine Shanghai, China

Qian Wang Department of Medical Imaging

Shanghai Children’s Medical Center Shanghai Jiao Tong University School of Medicine

Shanghai, China

Yi Qian Australian School of Advanced Medicine

Macquarie University Sydney, Australia

Mitsuo Umezu Center for Advanced Biomedical Sciences

TWIns, Waseda University Tokyo, Japan

Abstract—Long segment congenital tracheal stenosis (LSCTS) is one of most severe malformation with high mortality rate and dismal prospective. Hypoventilation is the main issue for the death of children with LSCTS after surgical correction. However, currently, little information is available on local aerodynamics to disclose the reasons for the improvement of such therapies, especially LSCTS with distal bronchus stenoses. Here, we investigated a patient-specific model of LSCTS with complete tracheal rings and bridging bronchus (BB). Computational fluid dynamics (CFD) was applied to analyze the local aerodynamics around BB before and after tracheal surgery in inspiratory phase and expiratory phase. Average pressure drop, wall shear stress, streamlines and energy loss were calculated to evaluate the surgical outcomes. The results indicate the airflow at the trachea and BB become more turbulent in expiration phase than that in inspiration phase. The turbulence increases the workloads of respiration in expiration phase. It should be the cause for post-operative hypoventilation. To study the local aerodynamics is helpful for the improvement of surgical therapies of the LSCTS.

Keywords—congenital tracheal stenosis; computational fluid dynamics; bridging bronchus; airflow; aerodynamics

I. INTRODUCTION The left pulmonary arterial sling (PAS) is usually

associated with diffuse primary or secondary tracheobronchial abnormalities. It is one of most common congenital tracheal stenosis (CTS) presenting of complete tracheal rings and bridging bronchus (BB). The presentation of these anomalies ranges from no symptoms to severe respiratory distress, recurrent respiratory tract infections and dysphagia. Although the slide tracheoplasty (STP) has been reported as a versatile and reliable technique associated with low morbidity and mortality recently, the most challenging form of CTS is long segment congenital tracheal stenosis (LSCTS) with compromise of the carina and main stem bronchi, sometimes result in high mortality in neonates and young infants.

A patient-specific investigation based on the analysis of tracheal aerodynamics was performed. The three-dimensional (3D) tracheal models before and after surgical modified STP were reconstructed according to medical images of a patient who suffered from PAS associated with LSCTS, BB and a distal bronchial stenosis. Computational fluid dynamics (CFD) was applied to evaluate the tracheal aerodynamics around the BB at the inspiration phase and expiration phase. Average pressure drop, wall shear stress (WSS), streamlines and energy loss were calculated to quantitatively estimate the local aerodynamics in trachea and bronchus. The aim of the present study is not to investigate the aerodynamic characteristics of STP in the complex CTS, but also to find the reasons for post-operative hypoventilation on such patients.

II. MATERIAL AND METHODS

A. Generation of Geometric Models This study was approved by the local institutional review

board and regional research ethics committee of Shanghai Children’s Medical Center (SCMC) Affiliated Shanghai Jiao Tong University School of Medicine. The informed consent was obtained from the parents of a 15-month-old child, when he was diagnosed PAS associated with LSCTS with complete tracheal rings, BB with distal part stenosis and a distal part of right upper bronchial stenosis.

The patient-specific computed tomography (CT) images before and after operations were obtained for the reconstruction of the 3D tracheal models by using 16-slice multi-detector row enhanced CT scanner (Bright Speed Elite, GE Medical System, General Electric, America). Image resolution was 512×512 pixels and the slice thickness was 0.625 mm. Medical imagining software Materialise -Mimics Innovation Suite 17.0 was used to segment CT images and reconstruct the 3D tracheal geometry. Figure 1 depicts the tracheal geometry after surface refinement.

*Research supported by the Project funded by China Postdoctoral ScienceFoundation (No. 2014T70420, P.I.: Jinlong Liu), the Fund of The ShanghaiCommittee of Science and Technology (No.14411968900, P.I.: Jinlong Liu), the Medicine-Engineering Project of Shanghai Jiao Tong University (No.YG2014MS63, P.I.: Jinlong Liu) and the Fund of Shanghai Jiao TongUniversity School of Medicine (No. 14XJ10039, P.I.: Jinlong Liu).

Jinfen Liu is the corresponding author. Phone: +86-21-5881-5377; Fax: +86- 21-5089-1405; E-mail: liujinfen2007@aliyun.com

# Co-first Author: Limin Zhu and Jinlong Liu

(a) Pre-operation

(b) Post-operation

Figure 1. 3D patient-specific tracheal models before and after surgical corrections.

In Model 1, there were three stenoses in patient’s trachea. Due to the difficulty of surgeries, the main stenosis, LSCTS, in trachea was surgically corrected. However, the other two stenoses were uncorrected; Stenosis 1 and Stenosis 2 in Model 2.

B. CFD Analysis

1) Governing equations of flow The 3D incompressible Navier-Stokes (N-S) equation and

continuity equation governs the airflow in trachea. The motion of airflow can be described by the following equations defined below.

( ) ( )

( )=∂∂+

∂∂

+∂∂

+∂∂

∂∂+

∂∂−=

∂∂+

∂∂

0jj

ii

j

j

i

jiji

ji

uxt

fx

u

xu

xxp

uux

ut

ρρ

μρρ (1)

where 3,2,1, =ji , 321 ,, xandxx represent coordinate axes,

ji uu , and p are the velocity vector and the pressure in the point of the fluid domain, ρ and μ are airflow density and viscosity, t is time. The term if expresses the action of body forces. We assumed airflow to be a Newtonian fluid with constant density ( ρ = 1.161 kg/m3) [1] and viscosity ( μ=1.864×10-5 kg/m s) [2] and the body forces were omitted.

We found the maximum Reynold value was about 3500. The airflow in this patient-specific tracheal geometry should be turbulence flow. To solve the problem of turbulence flow, we used the Wilcox model ω−k [3], which was validated perfectly for the complex airflow in trachea [4]. The Wilcox

ω−k model can be described by the equations of the kinetic energy of turbulence (Eq. (3)) and the specific dissipation rate (Eq. (4)) defined below:

Eddy Viscosity

ωρμ k

T = (2)

Turbulence Kinetic Energy

( )∂∂+

∂∂+−

∂∂=

∂∂+

∂∂

jT

jj

iij

jj x

kx

kxu

xk

utk μσμωρβτρρ ** (3)

Specific Dissipation Rate

( )∂∂+

∂∂+−

∂∂=

∂∂+

∂∂

jT

jj

iij

jj xxx

ukx

ut

ωσμμβρωτωαωρωρ 2 (4)

Closure Coefficients

95=α ,

403=β ,

1009* =β ,

21=σ ,

21* =σ

whereijτ is the Reynolds stress tensor. It is given by,

ijijTij kS δρμτ322 −= (5)

whereijS is the mean strain-rate tensor,

jiδ≠=

=jj

iifiif

,0,1 , is

Kronecker delta.

Wall shear stress (WSS), which is difficult to be acquired by direct measurements, is accepted as one reason for the damage to the trachea [5, 6]. It is a manifestation of the interaction between the airflow and trachea. The equation for WSS in a Newtonian fluid is given by:

0=∂∂−=

y

xwall y

uμτ (6)

where μ is viscosity, xu is the velocity of the fluid near the boundary, and y is the height above the boundary.

Energy loss (EL), the energy difference between the tracheal inlet and the outlet, is useful for evaluating inspiration workload. Given pressure and flow rate of the inflow and outflow, EL can be calculated by:

outletinlet EEEL −=

+−+=outlet

oooinlet

iii QuPQuP 22

21

21 ρρ (7)

where P is the static pressure, u is the velocity, and Q is the flow rate. i indicates the inlet. o indicates the outlet.

2) Mesh generation The grid-generation software, ANSYS -ICEM 14.0, was

applied to produce mixed grids. Three-layer body-fitted prismatic grids were created in the near-wall regions with an average nodal space that increased by a ratio of 1.2. The distance of the first prismatic layer to the tracheal surface was fixed at 0.0024 mm. This scheme accurately measured WSS and improved the resolution of the relevant scales in airflow motion. A tetrahedral mesh covered the remainder of the domain.

To find the best mesh for CFD analysis, grid-sensitivity verification were performed and found that grid numbers of about 0.5 million in steady simulation would make the most efficient mesh. Table 1 lists the mesh information for each model used in the present study.

TABLE I. MESH INFORMATION FOR EACH MODEL

MODEL MODEL 1 MODEL 2

TOTAL ELEMENTS 793,126 786,573

TOTAL NODES 240,192 262,620

3) Boundary conditions The pulsatile velocity profile of airflow in one respiration

cycle was used as inlet condition for the simulation of airflow in the patient-specific model; Model 1. To compare the geometric effects caused by LSCTS on stenoses, we imposed the same velocity curve as inlet condition of Model 2. Figure 2 shows these data in one respiration cycle.

Figure 2. Airflow velocity in one respiration cycle

To fully develop the flow boundary layer, we extended the inlet domain upstream to twenty times the size of the trachea. At the outlets, we extended airway diameter forty times in a normal direction to allow sufficient recovery of air pressure in each branch. A zero pressure was assumed at all the outlets according to Ho CY et al. [2].

4) Calculations

The finite volume solver package, ANSYS -FLUENT 14.0, was applied to solve the problem of unsteady airflow in each model. We assumed tracheal wall consisted of rigid surfaces with no-slip conditions. The semi-implicit (SIMPLE) method was chosen to solve the discretized 3D incompressible N-S equations. A second-order upwind scheme was used in the calculations. For convergence criteria, the relative variation of the quantities between two successive iterations was smaller than the pre-assigned maximum, 10-5.

III. RESULTS Figure 3 compared the average pressure drop of Stenosis 1

and Stenosis 2 at the phase of inspiration and expiration. An obvious decrease was obtained at Stenosis 1 after the surgical correction of main stenosis in trachea. However, an increase of average pressure drop was found at Stenosis 2. This indicates the surgical correction has a large effect on the BB.

(a) Average pressure drop at Stenosis 1

(B) Average pressure drop at Stenosis 2

Figure 3. The comparison of average pressure drop of Stenosis 1 and Stenosis 2 at the phase of inspiration and expiration.

Local aerodynamics was investigated. Table 2 displays the WSS and streamlines at the maximum velocity of airflow at the inspiration phase and expiration phase. High WSS of trachea was relieved after the surgical correction. It indicates the

damage of the airflow to the trachea was redbe flow smoothly. However, a relatively found at Stenosis 2, especially at the phase of

Flow separation occurred around Stenosicorrection. Large rotating flow was created area of BB to trachea. This implied an agradient may create to increasing flow rotaexpiration. By the surgical correction of thetrachea, the rotating flow was weakened aHowever, the airflow in the trachea became rat expiration.

TABLE II. AERODYNAMIC ANALYSIS (WSS AND

INSPIRATION E

duced. The air can large still can be f expiration.

s 2 before surgical at the connection

abnormal pressure ation especially at e main stenosis in around Stenosis 2. revolved especially

D STREAMLINES)

EXPIRATION

Figure 4 graphs the averagand expiration. After the corrsharp decrease of EL was achibreath was reduced.

Figure 4. The comparison of Averaexpiration.

IV. DISC

With the development of thof CTS has improved recently these children can be challengpresentation. The presence osignificant risk factor for deathexperience in our medical centSTP in the complex case of CTwhich is unfeasible to operationthe complex cases with severcause severe hypercapnia durinafter STP.

The results of present studafter the surgical correction of maverage pressure drop in Stendifferent results. The reason odrop in Stenosis 2 after surgerrestriction and flow redistributiairway after main stenosis enland streamlines indicate that great effects in the expiratory significant restriction of airflostenosis, CO2 retention and hclinical experience, this phenobecome an obvious problem period in gas exchange, especphase during positive pressurepatient with residual main dexpiratory limitation will be therespiratory acidosis and needoxygenation. It seemed that themajor issue for immediately relife quality.

e EL at the phase of inspiration rection of the main stenosis, a ieved. It means the workload of

age EL at the phase of inspiration and

CUSSION

he technique of STP, the survival [7-10]. However, the surgery in ged due to their heterogeneous

of bronchial stenosis is still a h [7, 10]. Based on the clinical er, the operative survival rate of TS with distal bronchia stenosis, n, was significantly low, because re distal bronchial stenosis can ng the early postoperative period

dy disclosed local aerodynamics main stenosis in the trachea. The nosis 1 and Stenosis 2 shows f the increasing of the pressure

ry should be the release of flow ion to the distal part of the main largement. The results of WSS the turbulence of airflow have phase, which will result in the

ow from the distal parts of the hypercapnia. According to our omenon will be aggravated and during the early postoperative

cially in the passive expiratory e mechanical ventilation. To the distal bronchial stenosis, such e reason of failure of ventilation, d of extracorporeal membrane e flow turbulence should be the

ecovery after STP and long-term

In clinic, it will be confused for the decision-making of surgical strategy of complex CTS with distal bronchus stenosis because of the unpredictable outcome for these children. The calculated results are reasonable to explain the clinical outcomes and disclose the reasons why several children died from severe hypoventilation after STP. Recent methods of diagnosis for CTS, including bronchoscopy, bronchography and multidetector computed tomography (MDCT) [11-13], can only provide the static imagine modalities of the main airway. The dynamic information is unavailable, especially in the diagnosis by bronchography and MDCT. Therefore, to predict the outcome for surgical intervention of the stenotic bronchus remained still unclearly. The technique of CFD will be a promising tool for the evaluation of the severe abnormalities at trachea and bronchus by providing local aerodynamics, such as pressure drops, WSS, airflow distribution and energy loss rate. Combined with computer-aided design (CAD), CFD can be potentially used for the investigation of virtual surgeries [14- 16]. Based on the results of virtual surgeries, the possible results of the aero flow dynamic after surgical repair will be evaluated before surgical procedure. The patient-specific enlargement of trachea lumen will be studied in future, from which the boundary diameter of the main airway lumen surgical treatment will be indicated In the case of complex CTS with main distal bronchial stenosis, an additional therapy for the stenotic bronchus, such as balloon dialation and/or stent implantation, should be applied more initiatively. In the case of high risk of sever residual stenosis of the distal branches of the airway, contingency plans such as ECMO should be prepared before surgical procedure performed. It can be performed depending on the information of patient’s status and local aerodynamics provided by CFD prediction.

V. CONCLUSION The approach of computational aerodynamic analysis by using CFD technique is a potential noninvasive tool to provide airflow information in trachea for the evaluation of surgical outcomes. Different bronchial stenosis has influence on airflow dynamics after surgical corrections, especially at expiration phase. The computational aerodynamics can be served as a helpful tool to disclose local detailed airflow information for further surgical therapies.

ACKNOWLEDGMENT We would like to express our great gratitude for the support

of the Project funded by China Postdoctoral Science Foundation (No.2014T70420, P.I.:Jinlong Liu), the Fund of The Shanghai Committee of Science and Technology (No.14411968900, P.I.:Jinlong Liu), the Medicine-Engineering Project of Shanghai Jiao Tong University (No. YG2014MS63, P.I.:Jinlong Liu) and the Fund of Shanghai Jiao Tong University School of Medicine (No. 14XJ10039, P.I.:Jinlong Liu).

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