Proyec to Final de Estudios EEBB EB - UBdiposit.ub.edu/dspace/bitstream/2445/19262/1/Sample-Specific... · 5.1 Discussion 57 5.2 ... Debido a la complejidad de la estructura y a la

Sam

A D R

IN

mple-Dyna

Bar

Autor:

Director

Realizad

Proyec

NGENIE

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F

rcelona

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do en:

cto Fin

MÁSTEN

ERÍA B

ific Cof Va

Functi

, 7 de J

Aur

Dam

InsCat

nal de E

TER N BIOMÉD

ompuasculaonalit

Julio de

ra María

mien La

tituto dtaluña (

Estudio

DICA

utationar Netty

el 2011

a Cardon

acroix

e Bioing(IBEC)

Eos

nal Fltwork

na Ocho

geniería

EEB

uid

oa

de

EBB

1

Economicsupport

The economic support from this project was provided by the European Commission

(Angioscaff FP7) 2008-2012

MasterSubjects

Biomaterials

Biomedical Imaging

Methods for Modeling and Simulating Biosystems

Tissue Engineering

Biomedical Signals (recognized credits)

Biomedical Devices (recognized credits)

Clinical Engineering and Healthcare Models (recognized credits)

PresentationsresultingfromthisStudy

Second TOPEA Summer School, Imaging in tissue regeneration, June 30 and July 1

Barcelona 2011, Parc de Recerca Biomèdica de Barcelona (PRBB).

2

3

Acknowledgements

I am glad to express my gratitude to those who have contributed to the research

performed and writing of this Master thesis.

First of all, I gratefully acknowledge the invaluable collaboration of my director and

supervisor Damien Lacroix, from the group of Biomechanics and Mechanobiology of

the Institute for Bioengineering of Catalonia (IBEC), who has guided me during the

whole year to achieve and well focus my project. It is a fortune to have him as a

supervisor.

Furthermore, I would like to thank the economic support to this study provided by

the European Commission (Angioscaff FP7) and the Institute for Bioengineering of

Catalonia (IBEC). A special thanks to Laura Nebuloni from the Swiss federal Institute

of Technology Zurich (ETHZ) for always taking the time to help me, for her patience

and cooperation.

Finally, I thankfully appreciate the several contributions provided by different people

in the group of Biomechanics and Mechanobiology such as Clara Sandino, Sara

Barreto, Andy Olivares, Andrea Malandrino, Jérôme Noailly and Cécile Perrault, and

also to Diego Reginensi and Adrià Muñoz. Thanks to their contributions have made

possible the successful development of this project.

4

5

Contents Economic support 1

Acknowledgements 3

Contents 5

List of Figures 7

List of Tables 9

Abbreviations 11

Abstract 13

Resumen 15

Chapter 1 Angiogenesis in Tissue Engineering: State of the Art 17

1.1 Introduction 17

1.2 The Principles Neo-vascular System: Structure and Function of Vascular System 18

1.3 Angiogenesis 20

1.4 Biomechanics of Angiogenesis 21

1.5 Tissue Engineering 22

1.5.1 Vascular TE 22

1.6 Image Acquisition Techniques 22

1.6.1 Principles Acquisition Techniques in Tissue Engineering 22

1.6.2 Computer Tomography (CT) 23

1.6.3 Magnetic Resonance Imaging (MRI) 23

1.6.4 Synchrotron Radiation (SR) 23

1.7 Image Processing 24

1.7.1 Three Dimensional Image Reconstruction 24

1.7.2 Mesh Construction 26

1.7.3 Computational Fluid Dynamics (CFD) 26

Chapter 2 Objective 29

Chapter 3 Materials and Methods 31

3.1 Image Acquisition 32

3.2 Segmentation and 3D Reconstruction 34

3.3 Superficial and Solid Mesh Construction 34

3.4 CFD Analysis 36

Chapter 4 Results 39

4.1 Reconstruction Analysis: 39

4.2 Superficial and Solid Mesh Construction 41

4.3 Mesh density requirement 43

6

4.4 CFD Analysis 51

4.4.1 Tail sample 51

4.4.1.1 Sub-volume (5%) 51

4.4.1.2 Sub-volume (10%)-100 DICOMS 53

4.4.1.3 Full Sample 54

4.4.2 Limb sample 56

Chapter 5 Discussion and Limitations 57

5.1 Discussion 57

5.2 Limitations 58

Chapter 6 Conclusions and Future Work 59

6.1 Conclusions 59

6.2 Future work 60

References 63

7

ListofFigures

Figure 1 Comparison between different types of blood vessels. *: Approximate numbers [9] .... 19

Figure 2 Microcirculation and interendothelial junctions [9] ...................................................... 19

Figure 3 Microenvironmental factors that can affect angiogenesis [9] ....................................... 20

Figure 4 Externally applied mechanical stresses on endothelial cells [9] .................................... 21

Figure 5 Synchrotron radiations scheme ................................................................................... 24

Figure 6 Reconstructions from CT scan of a dry cadaveric bone: (a) segmented volume of interest

mesh, (b) surface mesh generated from marching cubes algorithm, (c) rendered view of

surface mesh generated from marching cubes algorithm [24] ............................................. 25

Figure 7 Segmentation process overview [25] ............................................................................ 26

Figure 8 Methodology overview ................................................................................................. 31

Figure 9 Image acquisition process. ........................................................................................... 33

Figure 10 3D Reconstruction, superficial and solid mesh and CFD analysis (Sub-volume-Tail) .... 33

Figure 11 Full Sample Meshing .................................................................................................. 35

Figure 12 Boundary conditions. a. Tail, b. Sub-volume Tail (10%), c. Sub volume Tail (5%), d. Limb

........................................................................................................................................... 37

Figure 13 Segmentations process using Simpleware Software. a and b. Tail, c and d. Limb. ....... 39

Figure 14 3D Reconstruction of vascular networks interconnected using Simpleware. Software . 40

Figure 15 Superficial mesh (Sample 1 segment) using MIMICS. a.Bad triangles in orange, b. and c.

shows a non-smoothing surface and the loss of important components of geometry .......... 41

Figure 16 Software used in the methodology developing ........................................................... 42

Figure 17 Sample 1 sub-volume. a. Superficial mesh, b. Solid mesh .......................................... 43

Figure 18 Frontal and isometric view of Sample 1 (DC fragmentation) ........................................ 44

Figure 19. 100 DC Solid mesh section from the tail sample. a. Tetrahedral and hexahedral mesh.

b. Tetrahedral mesh. ........................................................................................................... 45

Figure 20 Number of elements, nodes and volume for two types of mesh to analyze the mesh

density require .................................................................................................................... 46

Figure 21 Mesh quality Tet and Tet-Hex elements. ..................................................................... 48

Figure 22 Full sample meshing. Number of elements, nodes, volume, and quality of the mesh .. 49

Figure 23 Number of elements, nodes, and volume from solid mesh (Sample 1 and 2) .............. 50

Figure 24 Contours of Velocity magnitude (m.s-1) (5% of Tail sample) ......................................... 52

Figure 25. Distribution of WSS (5% Tail sample) ......................................................................... 53

Figure 26 Contours of Velocity magnitude (m.s-1) (10% of Sample 1)_Tetrahedral and mixture of

Tetrahedral an hexahedral mesh ......................................................................................... 53

Figure 27 Contours of Velocity magnitude (m. s-1) Sample 1 ..................................................... 55

Figure 28 Contours of Velocity magnitude (m. s-1). Sample 2 .................................................... 56

8

9

ListofTables

Table 1 Sample technical specifications ............................................................................. 32

Table 2 Blood Properties .................................................................................................... 36

Table 3 Boundary Conditions ............................................................................................. 36

Table 4 Volume result of segmentation and 3D reconstruction process .............................. 40

Table 5 Tail sample: Elements and nodes in superficial and solid mesh using MIMICS ........ 42

Table 6 Superficial mesh features ...................................................................................... 42

Table 7 Results Resample. Tet_Hex Mesh ........................................................................... 47

Table 8 Result Resamples. Tet_Mesh .................................................................................. 47

Table 9 Full sample meshing ............................................................................................. 49

Table 10 Elements, nodes, and volume values (Tail and limb samples) ............................... 51

10

11

Abbreviations

3D Three – Dimensional

2D Two - Dimensional

µCT Micro-Computed Tomography

CAD Computer-Aided Design

CPU Central Processing Unit

CFD Computational Fluid Dynamics

CT Computer Tomography

DC Dicom

ECM Extracellular Matrix

ECs Endothelial Cells

ETHZ Swiss Federal Institute of Technology Zurich

FE Finite Elements

FEA Finite Element Analysis

FEM Finite Element Method

MRI Magnetic Resonance Imaging

NDE Nondestructive Evaluation

PDE Partial Differential Equation

RAM Random-Access Memory

RX X-rays

STL Stereolithography

SR Synchrotron Radiation

TE Tissue Engineering

VEGF Vascular Endothelial Growth Factor

VOI Volume of Interest

WSS Wall Shear Stress

12

13

Abstract

One of the main factors to control in the development of tissue engineering

scaffolds is the growth of new blood vessels and the posterior formation of vascular

networks, which is consider as a critical factor because of the transport of nutrients

and oxygen to the surrounding cells.

Nowadays, computational modeling is presented as a useful support tool to provide

a better understanding of vascular networks functionality. Therefore, the analysis of

large-scale computational fluid flow dynamics (CFD), allows us to obtain the local

parameters associated to mechanical stimuli affecting the microenvironment

(scaffolds) and tissue involved (vascular cells). This study has developed a robust

methodology to perform a quantitative assessment of vascular networks

functionality based on numerical simulations.

The methodology to perform the CFD analyses presented in this study is based on

two different samples. The vascular networks were obtained by Synchrotron and

Micro-Computed Tomography provided by the Swiss Federal Institute of Technology

Zurich in DICOM file format.

The DICOM files were imported in Simpleware to obtain a three dimensional

reconstruction, superficial and solid mesh of the vascular networks. Due to the

complexity of the structure and the amount of data generated, an optimization

scheme was defined to reduce computing time while maintaining the accuracy of the

results.

Once the mesh was obtained, the boundary conditions and the properties of the

fluid were defined in Fluent and Tdyn to simulate blood movement from the

superior to inferior position. The results allowed us to interpret the mechanical

phenomenon involved in the angiogenesis process and the importance of cellular

responses to mechanical stimuli in tissue engineering applications.

14

15

Resumen

Uno de los principales factores a controlar en el desarrollo de andamios en

ingeniería de tejidos, es el crecimiento de nuevos vasos sanguíneos y la posterior

formación de redes vasculares dentro de los mismos. El desarrollo de estos vasos es

necesario principalmente, para transportar nutrientes y oxígeno a las células

circundantes y mantener la viabilidad de estas células al interior de los andamios.

Hoy en día, el modelado computacional se presenta como una herramienta útil en el

campo de la hemodinámica, capaz de proporcionar una mejor comprensión de la

funcionalidad de las redes vasculares en diferentes campos de la medicina y de la

bioingeniería. El análisis de la dinámica de fluidos computacional (CFD) a gran

escala, nos permite la obtención de los parámetros locales asociados a los estímulos

mecánicos que afectan el microambiente (andamios) y el tejido circundante (células

vasculares) de las redes vasculares. En este estudio se ha desarrollado una

metodología robusta para llevar a cabo una evaluación cuantitativa de la

funcionalidad de redes vasculares basada en simulaciones numéricas.

La metodología para llevar a cabo el análisis CFD presentada en este estudio está

basada en dos muestras diferentes de redes vasculares obtenidas mediante

Sincrotrón y Micro-Computer Tomography (μCT), proporcionadas por el Swiss

Federal Institute of Technology Zurich (ETHZ) en formato DICOM (DC).

Los ficheros DC fueron importados en Simpleware para obtener la reconstrucción

tridimensional de las redes vasculares, y la construcción de mallas superficiales y

sólidas de las mismas. Debido a la complejidad de la estructura y a la cantidad de

datos generados, se definió un esquema de optimización para reducir el tiempo de

cómputo y calculo mientras que se mantuvo la precisión de los resultados.

Una vez la malla fue obtenida, las condiciones de frontera y las propiedades del

fluido fueron definidas en Fluent y Tdyn para simular el movimiento de la sangre

desde la posición superior a la inferior de la red. Los resultados nos llevan a

interpretar el fenómeno mecánico involucrado en el proceso de angiogénesis en las

aplicaciones de ingeniería de tejidos y la importancia de las respuestas celulares a

los diferentes estímulos mecánicos.

16

Sample-Specific Computational Fluid Dynamics of Vascular Network Functionality 17

Chapter 1 Angiogenesis in TissueEngineering:StateoftheArt

1.1 Introduction

Biomaterials that promote angiogenesis have great potential in regenerative

medicine for rapid revascularization of damaged tissue, survival of transplanted

cells, and healing of chronic wounds. Ghannaati et al. have designed biomaterials to

promote angiogenesis from supra-molecular nanofibers formed by self-assembly to

evaluate the vascularization within these biomaterials [1].

However, the techniques used normally are not enough to induce the rapid

vascularization necessary for an adequate cellular oxygen supply. Thus, nowadays

researchers focus on the creation of μ-vascular networks within 3D tissue constructs

in vitro before implantation using in vivo models (chicken embryo and dorsal

skinfold chamber) [2].

After obtaining the vascularization within the scaffolds it is necessary to quantify

this vasculature. Some approximations have been made to quantify the total volume

of the capillary network within the scaffolds [3] characterizing μ-vessel within

scaffolds in physiological in vivo tissue engineering implant context.

However, qualitative studies of growth and performance of these μ-capillaries within

the scaffolds to report velocity, pressure and wall shear stress (WSS) profiles to

determine and analyze their functionality have not been done yet.

So far, there are only functional analysis of large vessels and simple networks and

there are not enough reports from μ-vessels and big networks. Lee et al. [4] have

done a 3D computational flow modeling of a wide angle bifurcation and they have

analyzed WSS, blood velocity, and blood pressure profiles in a chicken embryo

model.

18 Sample-Specific Computational Fluid Dynamics of Vascular Network Functionality

Nowadays, measure of WSS, velocity or pressure within tissue constructs to evaluate

the functionality of μ-vascular networks in vitro or in vivo is difficult and expensive.

Gödde and Kurz [5] modeled blood flow through capillary networks to determine

local pressure gradients, which were in turn used to calculate local shear stress.

Also blood flow, pressures and shear stresses on ECs have been proposed and

modeled as angiogenic stimuli [5,6].

Therefore, to perform a quantitative assessment of the functionality of the μ-

vascular network based on the numerical simulations turns out to be a useful

support tool for predicting the functionality of this new vascular network within the

scaffolds design in the Angioscaff Project and then to be compared with results

obtained in vitro and in vivo from the same project.

1.2 The Principles Neo-vascular System: Structure and Function of

Vascular System

The term angiogenesis is reserved to describe the formation of new vessels, usually

at the capillary level, by proliferation, migration, and assembly of endothelial cells

from existing capillaries or venules [7]. This new microvasculature is an extremely

adaptable structure that is capable of architectural and functional adjustments in

response to multiple biochemical and mechanical stimuli [8].

The fundamental function of the vascular system is to deliver oxygen and nutrients

to the cells and remove waste from peripheral tissues.

There are three main types of blood vessels: arteries, veins, and capillaries. All

blood vessels except capillaries have three distinct layers surrounding a central

blood carrying lumen (Figure 1) [9].

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The role of blood flow in capillary growth was first demonstrated by Clark in the late

1910s [15] by examining capillaries in the same area in tad-pole tails for many

consecutive days, Clark was able to prove that capillaries with a high velocity of flow

(and with a high shear stress) had more sprouts, but capillaries with slow flow

gradually narrowed and disappeared.

1.5 Tissue Engineering

1.5.1 Vascular TE TE is a multidisciplinary field that applies the principles of biology and engineering

in order to develop tissue substitutes to restore, maintain, or improve the function

of diseased or damaged human tissues when the body is not able to do it by itself

[16].

To date TE has been successful in producing simple avascular tissues, such as skin

and cartilage, which are thin enough for oxygen and other nutrients to diffuse

passively through to sustain the cells within them [17]. Sufficient neovascularization

in scaffold materials can be achieved through coordinated application of angiogenic

factors with indicator cells types in different biomaterials [18].

Great advances have been made in identifying the biochemical factors and

intracellular signaling pathways that mediate the control of the angiogenesis

process.

1.6 Image Acquisition Techniques

1.6.1 Principles Acquisition Techniques in Tissue Engineering

Innovative surface and volume mesh generation techniques have recently been

developed, which convert 3D imaging data, as obtained from magnetic resonance

imaging (MRI), computed tomography (CT), micro-CT, synchrotron and ultrasound,

directly into meshes suitable for use in physics-based simulations.

These techniques have several key advantages, including the ability to robustly


generate meshes for topologies of arbitrary complexity (such as bioscaffolds or

composite micro-architectures) providing meshes in which the geometric accuracy of

mesh domains is only dependent on the image accuracy and the ability for certain

problems to model material inhomogeneity by assigning the properties based on

image signal strength [19].

1.6.2 Computer Tomography (CT)

CT is a powerful nondestructive evaluation (NDE) technique for producing two

dimensional (2D) and 3D cross-sectional images of an object from flat X-ray images.

Characteristics of the internal structure of an object such as dimensions, shape,

internal defects, and density are readily available from CT images. The imaging

system produces a 2D shadowgraph image of the specimen just like a film

radiograph [20]

1.6.3 Magnetic Resonance Imaging (MRI)

In MRI the study object is placed within a high intensity magnetic field. This causes

the magnetic moments of the molecules within the object to become aligned. The

object is then irradiated with pulses of low-level microwave radiation (excitation

pulses) that cause some of the magnetic moments of the molecules to oscillate and

re-emit microwaves after each pulse. These re-emissions are measured and stored

digitally

1.6.4 Synchrotron Radiation (SR)

SR refers to an electromagnetic radiation produced when ultra-relativistic electrons

circulating in a storage ring are deviated by strong magnetic fields. The storage ring

consists of a succession of bending magnets and straight sections including

insertion devices (Figure 5) [21].

SR benefits from increased brilliance that is orders of magnitude greater than

conventional X-ray sources. This improves image quality, reduces scan time, enables

higher resolution and facilitates, also the use of monochromatic and tunable energy

(single energy) X-rays of the beam is a key point since this condition is a basic

24

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c

(a) segment

m, (c) rendere

thm [24]

data (e.g.

ound data

asks. The

phy (STL) f

esampling,

ity

intractable

ar cartesia

ughout the

step that

mes of inte

ups. (Figur

intensity v

ted volume o

ed view of su

. CT, MRI d

will then s

se describ

format, as

, cropping

25

e owing to

an grid of

e scanned

t must be

erest (VOI)

re 6).

values for

of interest

urface mesh

data, etc.),

spawn one

be how an

shown on

, etc.)

o

f

d

e

)

r

,

e

n

n

26

Seg

Ma

Sur

Me

Clearly, t

accuracy o

resolution

tissues an

1.7.2 Me

3D mesh

engineerin

usually w

meshes fo

good inte

The FE m

now, in

inconveni

structure.

1.7.3 Co

Sample

gmentation

ask filtering

rface extra

esh generat

he accura

of the initi

n but a nu

nd motion

esh Const

es are fre

ng. This in

with tetrah

or complic

rnal angle

ethod is u

image pro

ent in ma

omputatio

-Specific Com

n

g

action

tion

Figure

acy of any

ial segmen

umber of

artefacts [

truction

equently u

nvolves de

hedral or

cated dom

s, a goal th

used in mo

ocessing.

any cases

onal Fluid

mputational F

7 Segmentat

y resultant

ntation and

other fact

19].

used to pe

ecomposin

hexahed

ains is a c

hat has elu

odeling phy

This, by

the struc

d Dynami

Fluid Dynam

tion process

t model w

d this will

tors includ

erform ph

g a doma

ral eleme

challenging

uded resea

ysical phe

the use

ture obtai

cs (CFD)

ics of Vascul

overview [25

will be lar

be a funct

ding noise

hysical sim

in into a

nts. Auto

g problem

archers for

nomena o

of volume

ined does

ar Network F

5]

rgely depe

ion not jus

, poor con

mulations i

mesh of s

matically

, especially

nearly two

f conventi

etric mesh

not refle

Functionality

endent on

st of the im

ntrast betw

in science

small elem

creating

y guarante

o decades

onal and,

hes which

ct the ori

n the

mage

ween

and

ents,

such

eeing

[26]

even

h are

ginal


With the appearance of powerful and fast computers, new possibilities for replacing

time-consuming model testing and field-testing have arisen. This involves solving

the differential equations describing fluid motion, using either a finite volume or a

FE method. These methods applied for the solution of the fluid equations of motion

are named computational fluid dynamics (CFD).

CFD essentially takes the momentum, heat and mass balance equations, along with

other models describing the equipment performance, and solves them to give

information such as pressure, velocity and wall shear stress (WSS) profiles.

The basic principle of the CFD modeling method is that the simulated flow region is

divided into small cells within each of which the flow either kept under constant

conditions or varies smoothly.

In hemodynamic applications, CFD simulation of blood has been a subject of

significant research effort. Over the last decade great progress has been made in

computational modeling of blood flows to measure hemodynamic variables [27-29]



Chapter2Objective

Develop a methodology to perform a quantitative assessment of the functionality of

micro-vascular networks from synchrotron and μ-CT data in two different samples,

based on numerical simulation to estimate the mechanical stimulus that promote

the angiogenesis process in tissue engineering constructs.


Samp

Ch

The

vess

ple-Specific C

haptemain step

els networ

Image a

Image s

Superfic

CFD ana

Computationa

er3Ms used to d

rks (Figure

acquisition

segmentati

cial and so

alysis

al Fluid Dyna

Materdevelop th

e 8) were:

ion and 3D

lid meshes

Figure

amics of Vasc

ialsahe methodo

D reconstru

s construc

e 8 Methodol

cular Networ

andMology to pe

uction

tion

ogy overview

k Functionali

Methoerform the

w

ity

odse CFD anal

31

ysis of thee


3.1 Image Acquisition

The first step to perform the computational fluid dynamic (CFD) analyses presented

in this study is the image acquisition.

It was obtained by the corrosion casting method, two different samples of vessel

networks formed in the tail and the lower hind limb of a mouse, provided by ETHZ

from synchrotron and μCT data in DC files format.

Table 1 shows the technical acquisition specifications of each sample.

Table 1 Sample technical specifications

Sample 1 (Tail) Sample 2 (Limb)

Technique acquisition Synchrotron* micro-CT**

Resolution 1.4 μm 3 μm

Pixels 788 x 756 x1021 894 x 894 x 894

Nº of DICOMS 1021 894

Slice thickness (mm) 3,699219e-3 1

Sample real size (mm) 2,914x2,796x3,78 4,844x4844x4,844

Mouse section Tail*** Limb****

*Synchrotron at the Swiss Light Source (PSI, Villigen, Switzerland)

**μCT 50 (Scanco Medical AG, Bruttisellen, Switzerland)

***Proximal part

****Lower hind limb

Figure 9 shows an overview of the image acquisition process. The image acquisition

was made by the ETHZ. They have done and In vivo μ-computed tomography and

Synchrotron radiation tomography of different mice using the corrosion casting

method. They have obtained the geometry of the vessels in image slides and in

DICOM format.

Samp

The

netw

ple-Specific C

next step

works and t

Figure 10 3

Computationa

s to get a

the constr

D Reconstru

al Fluid Dyna

Figure 9

CFD analy

uction of a

ction, superf

amics of Vasc

9 Image acqu

ysis involv

a superficia

ficial and sol

cular Networ

isition proce

ve the 3D

al and soli

id mesh and

k Functionali

ess.

reconstruc

d mesh (Fi

CFD analysis

ity

ction of th

igure 10).

s (Sub-volum

33

e vascular

me-Tail)

r


3.2 Segmentation and 3D Reconstruction

Vascular segmentation and 3D reconstruction of the vascular networks geometry

were accomplished by Thresholding and FloodFill within different image processing

software: MIMICS 13.1: Materialise, Haasrode, Belgium, and Simpleware 4.2: Scan IP

module, United Kingdom.

The geometric models are generated from medical image data (Synchrotron and μCT

data). The first step in the process of model creation is the generation of a mask

that defines the region of interest (ROI). This process is known as segmentation and

can be carried out manually or automatically.

By segmentation the image is divided into parts or objects that comprise it. The

extent to which this subdivision is done depends on the particular application, when

the segmentation process have finished, it is possible to work with the objects of

interest of the application. The segmentation will lead ultimately to success or

failure of the process of analysis. In most cases, a good segmentation gives rise to a

right solution, so that should make every effort possible at the stage of

segmentation.

In this case the segmentation process was done carefully to ensure an interconnect

network. Only the connected elements of the geometry resulting of the

segmentation process were used and the non-connected structures were removed to

proceed with the construction of the superficial and volumetric mesh.

3.3 Superficial and Solid Mesh Construction

Once the 3D reconstructions of the networks are obtained, the next step it is to

construct the triangle model of the geometries in STL format. However, these

models cannot be applied by CFD packages for the generation of the required

geometric mesh. One more process is needed to convert the triangle model into

surface or solid model to facilitate CFD simulations.

The superficial mesh was obtained using different image processing software:

MIMICS 13.1 and Simpleware (Scan IP module). And the solid or volumetric mesh

Samp

was

Due

divid

full s

unde

cond

800

Then

rece

vasc

the s

ple-Specific C

obtained u

to the lar

ded into se

sample. At

er the req

dition of m

DC, 1-900

n a full me

ived from

cular netwo

same cond

Computationa

using Simp

rge size of

ections of

t First it w

quired mes

meshing to

0 DC, and 1

esh was ob

m Limb sa

ork in mor

dition was

al Fluid Dyna

pleware (Sc

f the data

100 DC f

as analyze

sh density

6 differen

1-1021 DC

btained un

mple. Als

re detail in

applied on

Figure

amics of Vasc

can IP mod

of Sample

files to ana

ed the first

y for all th

t groups o

C (Figure 1

nder the re

o, in orde

n tail sam

n this sub-s

e 11 Full Sam

cular Networ

dule).

e 1 (Tail),

alyze the m

t 100 DC, t

he DC files

of DC: 1-50

11)

equired me

er to ana

ple, a sub

sample.

mple Meshing

k Functionali

in a first

mesh dens

then a full

s received

00 DC, 1-6

esh density

lyze the f

-volume o

g

ity

step the m

sity requir

l mesh was

applying

00 DC, 1-7

y for all th

functional

of 5% was

35

model was

ed for the

s obtained

the same

700 DC, 1-

he DC files

ity of the

taken and

s

e

d

e

-

s

e

d


To obtain the mesh density required the “Resample” tool from Simpleware was used,

which is used to reduce the size of the images by lowering resolution but without

modifying sizes or features of the object. Resampling can also be useful to

artificially increase the resolution by supersampling the data.

3.4 CFD Analysis

Once the mesh was obtained the CFD analysis was performed using two different

commercial softwares: Ansys-Fluent 12.1 (United States) and Tdyn 11.0.5 (Spain).

Table 2 shows the properties of blood that were used [30] to simulate the fluid

within the different vascular networks. It was supposed a laminar Newtonian fluid

Table 2 Blood Properties

Fluid Properties (Blood)

Viscosity 0.0022 Kg.m-1s-1 *

Density 1060 Kg.m-3 **

The boundary conditions were defined in Fluent and Tdyn to simulate blood

movement from the superior to inferior position Table 3 shows the boundary

conditions used to the CFD analysis in the samples. The velocity was applied in the

superior region of the networks and the pressure outlet was applied in the inferior

region of the network (Figure 12).

Table 3 Boundary Conditions

Boundary Conditions

Velocity (inlet) 1 mm s-1

Pressure (Outlet) 0 Pa

Samp

Fi

ple-Specific C

gure 12 Bou

Computationa

ndary condit

al Fluid Dyna

tions. a. Tail,

amics of Vasc

b. Sub-volum

cular Networ

me Tail (10%

k Functionali

), c. Sub volu

ity

ume Tail (5%)

37

), d. Limb


Samp

Ch

4.1

The

in F

preli

of t

cont

To o

the

vasc

used

main

ple-Specific C

hapteRecons

results ob

Figure 13

iminary se

the sampl

taining onl

Figure 13 S

obtain the

entire geo

cular netwo

d the Flood

n model.

Computationa

er4Rstruction

btained fro

. We obta

gmentatio

e, and th

y connecte

Segmentation

red mask

ometry is r

orks. And t

dfild tool

al Fluid Dyna

ResultAnalysis

om the seg

ained two

n of the va

he green

ed structur

ns process u

it is neces

reconstruc

to obtain t

to elimina

amics of Vasc

tss:

gmentation

o different

ascular ne

mask sho

res in the v

sing Simplew

ssary to us

ted withou

the green m

ate the str

cular Networ

n process o

masks: t

tworks, th

ows the s

vascular ne

ware Software

se the Thr

ut losing a

mask in th

uctures th

k Functionali

of the two

the red m

at include

segmentat

etwork.

e. a and b. T

eshold too

any import

e segment

at were no

ity

o samples

mask cont

the entire

tion of th

Tail, c and d.

ol to make

tant segm

tation proc

ot connec

39

are shown

tained the

geometry

he images

Limb.

e sure that

ent of the

cess it was

ted to the

n

e

y

s

t

e

s

e

40

The result

real size o

was prese

Figure

Table 4 s

reconstru

segments

The perce

structure

process w

The differ

volume is

of the rec

Sample

ts of the 3

of the two

erved almo

14 3D Recon

shows the

ctions pro

.

Table 4

Volu

Volu

Diffe

entage of d

in Sample

with a large

rence of v

possible b

onstructed

-Specific Com

3D reconst

samples a

ost entirely

nstruction of

result of

cess of the

4 Volume res

ume mask

ume mask

erence vol

difference

e 1 is 0,17

e volume o

volume in

because th

d geometry

mputational F

ruction of

are shown

y.

f vascular net

the volum

e two sam

ult of segme

red (mm3)

green (mm

ume (%)

between t

748% whic

of interconn

the Sampl

his Sample

y structure

Fluid Dynam

the interc

in Figure

tworks interc

me obtaine

ples with t

ntation and

Samp

2,28

m3) 2,284

0,174

the volume

ch corresp

nected stru

e 2 is a li

is a sub-s

es belong t

ics of Vascul

onnected v

14. The v

connected us

ed from th

their non-c

3D reconstru

ple 1 Sa

8 1,

4 1,

4 3,

e of non-c

ond to an

ucture.

it bit high

election of

to this com

ar Network F

vascular ne

olume of b

sing Simplew

he segmen

connected

uction proces

ample 2

630

570

681

onnected

improved

er (3,681%

f a bigger

mplete sam

Functionality

etwork and

both struct

ware. Software

ntation and

and conne

ss

and conne

d segment

%). This lo

one, and s

mple.

d the

tures

e

d 3D

ected

ected

ation

ss of

some

Samp

4.2

Duri

softw

supe

num

large

Usin

109

geom

and

Unit

Also

analy

sam

The

show

also

analy

Fig

ple-Specific C

Superf

ng the re

ware MIMI

erficial me

mber of ele

e samples

g the Sam

elements

metry from

huge amo

(CPU).

o to impro

ysis, that

ples.

superficia

wn in Figu

a bad no

ysis accord

gure 15 Supe

shows a

Computationa

ficial and

econstruct

ICS have

esh as pro

ements on

with a big

mple 1 as e

(Table 5)

m the orig

ount of me

ove the su

makes m

al mesh ob

ure 15. He

on-smooth

ding to ou

erficial mesh

a non-smoot

al Fluid Dyna

Solid Me

ion proce

limitations

oblems wi

n the surfa

amount o

example, it

with man

ginal mode

mory Rand

perficial m

more ineff

btained us

ere we can

hing surfac

r requirem

(Sample 1 s

hing surface

amics of Vasc

esh Const

ss we fin

s in the t

ith the qu

ace and so

of DC files.

t was obta

ny flipped

el. These c

dom-acces

mesh with

ficient app

sing MIMIC

n see the f

ce, which

ments.

egment) usin

and the loss

cular Networ

truction

nd some d

hree-dime

uality of t

olid mesh

ained a vol

elements

cause pro

s memory

MIMICS it

plied the

CS from a

flipped ele

do not a

ng MIMICS. a

s of importan

k Functionali

drawbacks

nsional re

the genera

were foun

umetric m

and with

blems for

(RAM) and

t is necess

same pro

sub-volum

ments, the

llow us to

a.Bad triangle

nt componen

ity

s, for exa

econstructi

ated mesh

nd, mainly

mesh with a

a huge lo

graphic p

d Central P

sary a lon

otocol wit

me of tail

e bad cont

o continue

es in orange,

nts of geomet

41

ample, the

on of the

h and the

y with the

around 50

oss of the

processing

Processing

ng time of

h another

Sample is

tours, and

e the CFD

b. and c.

try

e

e

e

e

0

e

g

g

f

r

s

d

D

42

Ta

Sa

Due to the

develop t

reconstru

The softw

shown in

With Simp

Due to vis

here, beca

structure

Table 6

samples.

Sample

able 5 Tail sa

ample 1

e limitatio

his metho

ction, supe

ware used

Figure 16

pleware we

sualization

ause of the

in both sa

shows the

Sup

-Specific Com

ample: Eleme

Mes

Superfici

Solid (Tet

ns expose

odology. Si

erficial and

in each st

6.

Figure 16 So

ere obtaine

n limitation

e number

amples.

e features

T

perficial m

Elements

Nodes

mputational F

ents and node

sh type

al

trahedral)

d previous

impleware

d solid me

tage of bu

oftware used

ed the supe

ns, the com

of element

of the su

Table 6 Super

mesh

Fluid Dynam

es in superfi

Ele

5.595.

50.080

sly with MI

was used

shing.

uilding the

in the metho

erficial me

mplete tai

ts it is not

uperficial m

rficial mesh f

Sampl

42.706

22.647

ics of Vascul

cial and solid

ements

500.000

0.500.000

MICS, only

d in the se

e methodo

odology deve

esh of the t

l and limb

t possible t

mesh obta

features

e 1

.038

.252

ar Network F

d mesh using

Nod

2.764.30

9.492.70

y Simplewa

egmentatio

ology for C

eloping

two sampl

b meshing

to differen

ained from

Sample 2

9.389.79

4.134.23

Functionality

g MIMICS

des

00.000

00.729

are was use

on process

CFD analys

es (Figure

are not sh

ntiate the e

m tail and

2

2

2

ed to

s, 3D

sis is

e 17).

hown

entire

limb

Samp

4.3

The

the

volu

mes

mee

The

no in

In o

the S

to a

was

The

in Fi

ple-Specific C

Mesh d

3D recons

computer

me). The

h. Assumi

t defined o

points are

nformation

ur case, th

Sample 1;

nalyses th

made in th

Frontal an

gure 18.

Computationa

Figure 17 S

density re

struction i

memory,

efficiency

ng a set o

optimal co

e very close

n for recon

hree-dimen

in a first s

e mesh de

he first 10

nd isometr

al Fluid Dyna

Sample 1 sub

equireme

s the proc

maintainin

of the al

of points

nditions fo

e to each o

nstruction

nsional rec

step the m

ensity req

0DC at the

ric view of

amics of Vasc

b-volume. a.

ent

cess throug

ng their p

gorithm is

misrepres

or meshing

other, the

constructio

model was

uired for t

e top of the

Tail Samp

cular Networ

Superficial m

gh which r

physical ch

s what de

ented, the

g.

noisy poin

on is perfo

divided int

the full sa

e Sample 1

ple DICOM

k Functionali

mesh, b. Solid

real object

haracteristi

efines the

ere will be

ts and red

ormed bas

to sections

ample. The

1.

CS fragme

ity

d mesh

ts are repr

ics (size, s

quality of

e points th

dundant po

sed the lar

s of 100 D

e mesh op

entation ca

43

roduced in

shape and

f the final

hat do not

oints, offer

rge size of

Dicom files

ptimization

an be seen

n

d

l

t

r

f

s

n

n

44

The mesh

from volu

informatio

mesh ar

reconstru

The aim

informatio

and/or to

our case,

best resul

Sample

Figure

hing used

umetric re

on about s

e not m

ction of co

to achiev

on, and tu

o much in

meshing w

lts in this s

-Specific Com

18 Frontal a

is tetrahed

constructi

superficial

mutually e

omplex sol

ve is the c

urn, the m

formation

with optim

study beca

mputational F

and isometric

dral and he

on, as op

aspects of

each excl

lid structur

collection

mesh too

on the str

mum result

ause it is th

Fluid Dynam

c view of Sam

exahedral

pposed to

f the 3D s

usive, fat

res.

of structu

much sim

ructure, th

ts in the m

he most co

ics of Vascul

mple 1 (DC fr

meshes b

triangular

tructures.

te compl

ures that

mple data,

is avoids a

mesh tetrah

ommonly u

ar Network F

agmentation

ecause the

r meshes

Therefore

ementary

have as

preventin

a greater a

hedral bec

used in CFD

Functionality

n)

ey are shie

as we pro

e, both typ

allowing

much pos

ng acute a

nalysis tim

ause it ha

D analysis.

elded

ovide

es of

the

ssible

angle

me. In

s the

Samp

In b

only

elem

orde

analy

a

b

Fig

In o

the v

mes

It w

resa

mixt

The

(Tetr

100D

ple-Specific C

rief, two t

y tetrahedr

ments were

er to find t

ysis (Figur

ure 19. 100

rder to ob

vascular n

h and the

was used v

mple, and

ture of tetr

number o

rahedral a

DC segme

Computationa

types of m

al element

e obtained.

he best co

re 19).

DC Solid me

btain an ad

etworks, i

quality of

values of

d it was o

rahedral an

f elements

and a mix

nt are show

al Fluid Dyna

meshes wit

ts and mes

In both ca

mpromise

sh section fr

dequate m

t was app

the elemen

resamplin

obtained t

nd hexahe

s and node

xture of te

wn in Figu

amics of Vasc

h differen

shes with

ases the m

between c

rom the tail s

Tetrahedral

mesh densi

lied differe

nts was ve

g from 1

two meshe

dral eleme

es and the

etrahedral

ure 20.

cular Networ

t elements

a mixture

mesh densi

calculation

sample. a. Te

mesh.

ity without

ent values

rified at ea

(without

es from e

ents)

volume o

and hexa

k Functionali

s were ana

of tetrahe

ty was var

n time and

etrahedral an

t losing im

of resam

ach point o

resample

each case

btained fo

ahedral ele

ity

alyzed. Me

edral and h

ied param

accuracy o

nd hexahedra

mportant f

ple in bot

of resampl

- w/o) to

(Tetrahed

or each typ

ements) in

45

eshes with

hexahedral

etrically in

of the CFD

al mesh. b.

features of

h types of

e.

o 2 times

dral and a

pe of mesh

n the first

h

l

n

D

f

f

s

a

h

t

46

Figure 20 N

The num

resamplin

The mixed

both mes

elements

Sample

Number of e

bers of el

ng increase

d tetrahed

shes at re

(Table 7).

-Specific Com

lements, nod

lements d

es.

ral and he

esample fr

mputational F

des and volum

r

ecrease in

xahedral m

rom 2 tim

Fluid Dynam

me for two ty

require

n both typ

mesh, reac

mes, passi

ics of Vascul

ypes of mesh

pes of me

ches a lowe

ng to 12

ar Network F

h to analyze t

shes when

er number

million to

Functionality

the mesh de

n the valu

of elemen

o 2 millio

nsity

ue of

nts of

on of


In both types of meshes, the number of nodes decrease when the value of

resampling increase in a similar way. Both cases pass to 5 million (without resample)

to around 700,000 nodes at resample from 2 times (Table 7, Table 8).

Table 7 Results Resample. Tet_Hex Mesh

DICOMS Resample Number ele. Nº Tet Nº Hex Nodes Volumen(mm3)

1-100

W/O 12.965.527 10.434.756 2.530.771 5.227.177 1,89E-01

1,1 10.139.959 8.302.720 1.837.239 3.992.863 1,88E-01

1,2 8.110.333 6.744.622 1.365.711 3.127.902 1,78E-01

1,3 6.644.638 5.593.585 1.051.053 2.522.301 1,88E-01

1,4 5.445.852 4.634.108 811.744 2.038.914 1,86E-01

1,5 4.544.994 3.900.913 644.081 1.684.046 1,86E-01

1,6 3.885.296 3.359.525 525.871 1.430.184 1,88E-01

1,7 3.297.241 2.874.161 423.080 1.201.527 1,86E-01

1,8 2.850.326 2.499.305 351.021 1.031.512 1,87E-01

1,9 2.491.161 2.199.341 291.820 894.803 1,87E-01

2 2.204.834 1.957.575 247.259 786.397 1,89E-01

Table 8 Result Resamples. Tet_Mesh

DICOMS Resample Elements Nodes Volumen (mm3)

1-100

W/O 23.149.531 5.227.177 1,89E-01

1,1 16.995.056 3.852.017 1,80E-01

1,2 13.060.842 2.982.006 1,78E-01

1,3 10.089.351 2.307.677 1,74E-01

1,4 8.717.743 2.038.914 1,88E-01

1,5 7.142.543 1.684.046 1,86E-01

1,6 5.948.193 1.414.231 1,87E-01

1,7 4.978.765 1.193.347 1,86E-01

1,8 4.252.708 1.027.209 1,87E-01

1,9 3.629.084 883.920 1,86E-01

2 3.184.789 780.818 1,89E-01

It was verified that volume was kept constant whatever the amount of mesh density

and the type of element mesh. In both cases the volume remained constant with

small differences between the values obtained, ranging from 0,174 mm3 to 0,189

mm3.

It was necessary to check the mesh quality in both cases to ensure the accuracy of

the results to decide the mesh density used to perform the CFD analysis. The quality

of a mesh depends on the quality of its elements, which in turn depends on the

application.

48

Figure 21

quality in

In-

wh

can

an

Th

ele

The resam

meshes, s

the super

Finally, re

obtained

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The CFD

distributio

shown tha

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Sample

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this study

-out aspec

en used fo

n lead to n

important

e edge le

ment from

mple of 1.

suggesting

ficial and s

esults indi

with 5,94

of tetrahed

re necessa

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at CFD sim

instead of

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he mesh

y is related

ct ratio gi

or finite el

numerical

t feature of

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6 times ha

g these res

solid mesh

Figure 21

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Fluid Dynam

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rately

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Samp

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ple-Specific C

sideration

number o

ahedral me

Figure 22 Fu

Resample1,6

Computationa

to the nec

of elements

esh of the f

ull sample me

Nº DIC

e

1-501-601-701-801-90

1-10

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essary mat

s, nodes, t

full tail sam

eshing. Num

Table

COMS E

00 300 400 400 500 6

021 8

amics of Vasc

thematics

the volume

mple are s

ber of eleme

e 9 Full samp

Elements

4.553.0991.923.8959.980.9918.522.5158.453.3671.250.605

cular Networ

involved.

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ents, nodes, v

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Nod

9 8.3375 10.135

12.1075 14.2007 16.6505 19.781

k Functionali

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igure 22 a

volume, and

es V

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.737

ity

ality obtain

and Table

quality of th

Volume (m

1,03 1,24 1,47 1,72 1,99 2,34

49

ed for the

9.

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mm3)

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50

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and the n

number o

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limb sam

nodes, an

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A full tetr

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e 1 and 2)

d 19 millio

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ribed

o the

of DC

r the

e

o the

ents,

of 1.6

on of

with a


resample of 1.6 times with a reduction of 71% of elements and 69% of nodes density

in the full sample 1 (tail).

With the limb sample, a full tetrahedral mesh was obtained with 16 million of

elements, and 4 millions of nodes without loss of volume of structures futures

(1,27) with a resample of 1.6 times with a reduction of 71% of elements and 69% of

nodes density in the full limb sample .Table 10

Table 10 Elements, nodes, and volume values (Tail and limb samples)

Elements Nodes Volume (mm3)

w/o Resample Sample 1 279.148.673 63.981.293 2,28 Sample 2 57.683.223 12.962.545 1,58

Resample 1,6 Sample 1 81.250.605 19.781.737 2,28 Sample 2 16.789.608 4.007.760 1,55

Reduction (%) Sample 1 71 69 0,17 Sample 2 71 69 1,27

4.4 CFD Analysis

4.4.1 Tail sample

4.4.1.1 Sub-volume (5%)

In order to better understand the behavior of the vascular network of tail sample, it

was extracted a volume corresponding to 5% and it was analyzed the results of

blood velocity and WSS. In this case we used the same boundary condition proposed

above.

Using CFD analysis, we visualized velocity profiles and calculated wall shear stress

along the vessels wall.

I. Velocity profile

The velocity profile of this network shows a distribution of fluid flow on different

planes. We can see the heterogeneity of fluid flow distribution in the vessels, and

the direction of the blood movement. This is the highest velocity is 3 times higher

52

than the i

Velocity v

observe c

vascular s

velocity d

increase

velocity eq

In conclus

in a 2D cr

vessels, a

velocity in

II. Wa

Figure 25

sub-volum

large vess

Sample

nlet veloci

values insid

changes in

sections. F

decreases

in the velo

quals to ze

Figure

sion, the v

ross-sectio

and the dir

nlet.

all Shear S

5 shows th

me, with a

sels with va

-Specific Com

ty.

de the ves

n the vasc

For examp

in this se

ocity was

ero.

e 24 Contour

velocity pro

on. We can

rection of

Stress

he distribu

maximum

alues arou

mputational F

ssels range

cular netwo

le we can

ection and

observed.

s of Velocity

ofile of this

n see the h

the blood

ution of th

m value of 1

nd to 0.5

Fluid Dynam

e from 1 t

ork veloci

see that i

d, in the

. Finally it

magnitude (

s network

heterogene

d’s movem

he wall she

1.039 Pa a

Pa.

ics of Vascul

to 3 m.s-1

ty with th

ncreasing

region wi

t was obse

(m.s-1) (5% of

shows a d

eity of fluid

ent. This

ear stress

and a distr

ar Network F

(Figure 24

e change

the vesse

th a sma

erved in s

Tail sample)

istribution

d flow dist

is a scale

(WSS) in t

ribution ins

Functionality

4) Also we

in size o

l diameter

ll diamete

some vess

)

n of fluid fl

tribution in

of 3 time

the tail sa

side one o

e can

f the

r, the

er an

els a

low a

n the

s the

mple

of the

Samp

4.4.

Here

optim

I.

F

ple-Specific C

1.2 Sub

e we can

mization p

Velocit

Figure 26 Co

Computationa

F

-volume

see the

process des

ty profile

ntours of Ve

al Fluid Dyna

igure 25. Dis

(10%)-10

results f

scribed ab

locity magnit

Tetrah

amics of Vasc

stribution of

00 DICOM

for the tw

bove (Sectio

tude (m.s-1) (

hedral an hex

cular Networ

WSS (5% Tail

MS

wo types

on 3.3 Mes

10% of Samp

xahedral mes

k Functionali

sample)

of meshe

sh Density

ple 1)_Tetrahe

h

ity

es obtaine

Requires)

edral and mi

53

ed in the

.

xture of

e


Velocity values inside the vessels range from 1 and 3 m.s-1. As it was showed in the

Sample 1 sub-volume of 5%, in some vessels the velocity is equal to zero.

To perform the CFD analysis we have used a Window Server 2008 R2 Enterprise with

two processors Intel (R) Xeon(R) 3GHz and 48GB of memory RAM. Finally it was

observed similar qualitatively results in the CFD analysis of these two meshes; we

decided to use tetrahedral elements to perform the CFD analysis of the other

samples.

4.4.1.3 Full Sample

I. Velocity profile

The velocity profile of this network shows a distribution of fluid flow on different

planes. (Figure 27) We can see the heterogeneity of fluid flow distribution in the

vessels, and the direction of the blood’s movement. This is a scale of 3 times the

velocity inlet.

Velocity values inside the vessels range from 1 and 3 m. s-1. As it was showed in 5%

and 10% sub-volume, in some vessels the velocity is equal to zero, mainly in the

small lateral vessels.

It was observed that the velocity is higher inside the small capillaries than the larger

ones.

Samp

ple-Specific CComputationa

Figure 2

al Fluid Dyna

27 Contours o

amics of Vasc

of Velocity m

cular Networ

magnitude (m

k Functionali

m. s-1) Sample

ity

e 1

55

56

4.4.2 Lim

I. Ve

The veloc

planes (Fi

vessels, a

velocity in

Velocity v

As it was

network t

the volum

The meth

has one p

the basis

Sample

mb samp

locity pro

Fig

city profile

igure 28).

and the dir

nlet.

values insid

showed in

the vessels

me have vel

odology fo

potential li

of the ge

-Specific Com

le

ofile

gure 28 Cont

of this n

. We can s

rection of

de the vess

n Sample

s are not w

locity equa

or automa

imitation,

eometry, a

mputational F

tours of Velo

etwork sh

see the he

the blood

sels range

1, in some

well conne

al to zero.

ted mesh

the fact th

and not o

Fluid Dynam

ocity magnitu

ows a dist

eterogenei

d’s movem

from 1 an

e vessels t

cted, may

generation

hat the co

on the bas

ics of Vascul

ude (m. s-1). S

tribution o

ty of fluid

ent. This

d 3 m. s-1

the velocity

be that is

n described

mputation

sis of the

ar Network F

Sample 2

of fluid flo

flow dist

is a scale

.

y is equal

why a big

d in the pr

al mesh is

expected

Functionality

ow on diffe

tribution in

of 3 time

to zero In

g percentag

revious Se

s generate

flow feat

erent

n the

s the

n this

ge of

ction

ed on

ures.


Chapter5DiscussionandLimitations

5.1 Discussion

In the velocity results in both samples, it was observed in some vessels a velocity

equals to zero. This possibly means that these vessels are not well trained and

connected to the rest of the network, and the blood cannot pass through these

vessels. Theoretically the cells that surround these "non-functional" vessels do not

receive the nutrients and oxygen from the blood necessary to survive.

The values of WSS obtained with the CFD analysis were within the physiological

range found in the human body reported in literature [36]. There is a vast amount of

experimental evidence demonstrating that externally applied mechanical stresses

(fluid shear stress, stretch, and pressure) regulate cytoskeletal organization, signal

transduction, gene expression, and a wide variety of EC functions, including

migration, proliferation, and ECM remodeling, which suggests a role of extrinsic

stresses in angiogenesis.

In fact, many studies have shown that fluid shear stress and stretch can affect the

production and/or activity of the endogenous biochemical factors, although most of

these investigations were not conducted in the context of angiogenesis. [9]

With numerical simulations we can measure the WSS in each point of the network

and we can predict that the cells surround this vessels could be stimulated

mechanically and in response to this stimulus, the angiogenesis process could be

continue.

This is a promising study that involves concurrent research groups either by

analyzing the profiles of cellular and molecular biology of the process of

angiogenesis, another investigation group the process behind the regenerative

engineering of angiogenesis in the physiological phenomena and we systematizing

the study as a computational model and its potential applications in improving the

understanding of the process of new blood vessels.


5.2 Limitations

Some limitations were found in the development of this project.

Both the time meshing as the CFD analysis time was quite long due to the density

and quality of the mesh required in both samples. To make starting the simulation it

was required the use of servers with special technical features.

On the other hand, the results of CFD analysis cannot be interpreted entirely as a

physiological behavior, since the boundary conditions were imposed on the

development of the methodology does not correspond to “real” conditions in both

samples, because in the process of image acquisition, was not taken into account

the position of the sample, which could not be identified clearly the direction of

movement of the blood.

In addition, the samples that were sent to us to perform the CFD analysis

correspond to sub-groups of larger samples, so it may have been lost of information

from the actual geometry of both samples.

Similarly, the method used for the acquisition of such data (corrosion casting ) have

certain limitations when it comes to micro-capillary samples, like in this case, since

the polymer sometimes fails to fully invade the vessels and the images acquired

reported vessels not connected when it really should be in the original sample.

It is also important to note that our computational simulation treated the blood as a

Newtonian fluid and discounted the mechanical effects of blood cells or biochemical

molecules, which it will take it into account in the future work to continue whit this

project.


Chapter6ConclusionsandFutureWork

6.1 Conclusions

• A methodological approach for automatic 3D geometric analysis and

generation of a tetrahedral computational mesh from Synchrotron and μCT data of

vascular networks from a tail and a limb of a mouse was defined. The computational

mesh is intended for numerical analysis of blood flow within these vascular vessels.

• This methodology was applied to images from Synchrotron and μCT but it

can be applied in general to other volumetric data, especially where the DICOM

standard is used. The methodology we set up for mesh generation allowed

producing computational mesh that shows good resolution and element skewness.

• The proposed technique is fast, accurate and reproducible, and can be a

useful tool for the evaluation of micro-vascular networks fluid dynamics.

• Results in different networks indicate the heterogeneity of fluid flow

distribution within the vessels with values ranging between 0 and 3 times the inlet

velocity. Respect to the vessels with a velocity equal to zero m s-1 means that these

vessels are not well connected to the rest of the network, and the blood cannot pass

through them and in this case the cells that surround these "non-functional" vessels

do not receive the nutrients and oxygen from the blood necessary to survive.

• The values of WSS obtained are within the physiological range found in the

human body reported in literature. Results indicate the heterogeneity of WSS

distribution within the vessels. These mechanical stimuli play an important role in

angiogenesis regulating the cytoskeletal organization, as a signal transduction, in

gene expression, and a wide variety of EC functions, including migration,

proliferation, and ECM remodeling.


6.2 Future work

The short term future plan to continue with the development of this project involves

some important task.

Task 1: The next step will be to make a comparison of in silico results with in vivo

results on many different samples to determine the functionality of the angiogenic

process in tissue regeneration.

Task 2: Also it is necessary to obtain data in different time points of growth to

validate the methodology and to define realistic and accurate boundary conditions

to ensure a proper physiological interpretation of the results. Then it will necessary

to perform several analyses on different vascular networks to investigate the

angiogenic functionality of the scaffolds

Task 3: Once the methodology has been assessed in different samples it will be

define a validation of the model building a scale prototype of a sub-volume network,

to quantify the fluid flow distribution inside the vessels to compare the obtained

results, with the CFD results.

Task 4: Simulate the behavior of endothelial cells around blood vessels included in

the angiogenesis process using numerical simulation, to quantify the exchange of

oxygen from the vessels into the cells, in order to relate the functionality of vascular

networks during angiogenesis in different scaffolds with the gas exchange

necessary for the preservation of cells and tissue surrounding these vessels.

Task 5: In order to evaluate the functionality of the vascular networks development

within the scaffolds design in the Angioscaff Project, it will perform CFD analysis of

the resulting samples in different points of growth to quantify the volume of

functional network.


Sept-Dec 11 Janu-Sept 12 Sept-Dec 12 Janu-Sept 13 Sept-Dec 13

Task 1

Task 2

Task 3

Task 4

Task 5



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Documents

Proyec to Final de Estudios EEBB EB - UBdiposit.ub.edu/dspace/bitstream/2445/19262/1/Sample-Specific... · 5.1 Discussion 57 5.2 ... Debido a la complejidad de la estructura y a la