BIOMIMETIC DESIGN OF A LIVER SPECIFIC VASCULAR

NETWORK

By

OWEN BURNS

A thesis submitted in partial fulfilment of the

requirements for the award of the degree of

BACHELOR OF ENGINEERING

(Mechanical)

from

UNIVERSITY OF WOLLONGONG

FACULTY OF ENGINEERING

November 2008

ii

Acknowledgements

I wish to express my sincere gratitude to Dr Buyung Kosasih for serving as my

university thesis supervisor. I also wish to thank Dr. David Hoganson, for his guidance

and inspiration during my internship at the Tissue Engineering and Organ Fabrication

Laboratory, Centre for Regenerative Medicine. His experience and enduring

enthusiasm have proven invaluable to my own.

I wish to express my sincere appreciation to several colleagues whose friendship I

have cherished during my studies, including Dr. Howard Pryor, Elisabeth O’Doherty,

Ali Hart and Gwen Owens, their support and suggestions in all maters have been a great

source of knowledge and motivation.

I am deeply indebted to Dr Joseph P. Vacanti and Cathyrn Sundback, ScD, if not

for their willingness to take on an Aussie engineering student; this thesis project would

not have been possible.

iii

Abstract

The study of tissue engineering has been of great interest to researchers for many

years, particularly the development of techniques to facilitate the production of

biological substitutes that restore, maintain and improve tissue function. Of special

interest are the development viable artificial alternatives for liver treatment. At present

the need for liver donors far out weighs the supply, meaning those who suffer from end

stage liver failure face lengthy, painful and expensive treatment options which are also

unable to address all of the normal biological functions of the liver.

Central the concept of creating a tissue engineered liver is developing a scaffold

or support structure to hold liver cells. The native liver has an extensive bifurcating

blood vessel network which delivers oxygen and nutrients within a few hundred

microns to all of the cells in the liver. Accordingly, a main obstacle to achieving the

goal of a completely tissue engineered liver alternative is vascularisation; without an

elegant and sophistically arranged blood supply, the functionality of the biological liver

can never be achieved. The present study addressed this obstacle by investigating a

vasculature designed to mimic natural liver architecture.

The present study introduces novel methods for mapping and mathematically

controlling the vascular networks that make up artificial scaffolds and new techniques

for manufacturing silicon devices. The mathematical methods employed in the design

of these vascular networks were successfully implemented and validated using

numerical and in vitro testing. Results from the numerical simulations and in vitro

testing show excellent agreement with the design methodology.

iv

TABLE OF CONTENTS

Acknowledgements ii

Abstract iii

List of Figures vi

List of Tables viii

Notation ix

Chapter 1 INTRODUCTION

1.1 Tissue Engineering 1

1.2 Liver Structure 3

1.3 Objectives of the Present Study 7

1.4 Outline of the Dissertation 7

Chapter 2 LITERATURE REVIEW

2.1 Vascular Networks 8

2.2 Background of Vascular Network Designs 11

2.3 Biomimetic Diameter Ratios between Parent and Daughter

Vessels 15

2.4 Arterial Branching 17

2.5 Physiologic Shear 21

2.6 Biomimetic Vessel Lengths 21

2.7 Constitutive Models 22

2.7.1 Newtonian Fluids 22

2.7.2 Non-Newtonian Fluids 23

2.7.3 Viscoplastic Fluids 24

2.8 Numerical Studies of Vascular Networks 28

Chapter 3 VASCULAR NETWORK DESIGN

3.1 Design Inputs 30

3.2 Application of Murray’s law to vascular network design 32

Chapter 4 NUMERICAL SIMULATION OF VASCULAR DESIGN

4.1 Numerical simulation of vascular design 42

v

4.2 CFD Methodology 42

4.3 Mesh Independent Study 46

Chapter 5 MANUFACTURING AND TESTING METHODOLOGY

5.1 Case Study: Fast-Track Device Manufacturing

and Testing 47

5.2 Hex-Bed moulds and In Vitro Testing 51

Chapter 6 RESULTS

6.1 Pressure Distribution 55

6.2 Shear Stress Distribution 56

6.3 Flow Rate 57

Chapter 7 DISCUSSION AND CONCLUDING REMARKS

7.1 Discussion 60

7.2 Concluding Remarks and Recommendations 65

LIST OF REFERENCES 66

APPENDICES

Appendix A Vascular Network Mathematical Model 79

Appendix B Manufacturing Protocols 72

Appendix C In Vitro Test Procedure 81

vi

List of Figures

1.1 Pictorial of the liver 4

1.2 A liver lobule and segment of a liver lobule 5

1.3 Pictorial cross-section of the liver 6

1.4 Representation of a capillary bed, or vascular network 6

2.1 Early silicon mould used to make vascular networks 9

2.2 Silicone moulding of vascular layers 10

2.3 Scanning Electron Microscopy (SEM) image of boundaries of the

layers of a liver scaffold 10

2.4 First vascular network design 11

2.5 Test-Net 1 device in vivo in a rat model 12

2.6 Test-Net Alpha device 13

2.7 Fast-Track device perfused with blood 15

2.8 A sample of the enlarged tracings of arterial bifurcations from which

measurements were taken 18

2.9 An arterial bifurcation, represented schematically 19

2.10 Flow curves of a Newtonian fluid 26

2.11 Flow curves of power-law fluids 26

2.12 Flow curve of a Cross model 27

2.13 Flow curves of viscoplastic fluids 27

2.14 Predicted normalised wall shear stress distributions in a series of

constant-depth rectangular and trapezoidal manifolds 29

3.1 Single hexagonal lobule with general vascular network 34

3.2 Single vascular layer assembly 35

3.3 Schematic resistance model for one sixth segment 36

3.4 Constant depth one sixth segment of hexagonal radial model 40

3.5 Flow chart illustrating the series of events in developing a

mathematical model for the vascular network 41

4.1 Top view of Cartesian mesh for outlet header model 43

vii

4.2 Image showing the layout of the computational domain and

structure of the one sixth segment used in CFD fluid flow analysis 44

4.3 Side View of one sixth segment 45

4.4 Mesh Independent Study 46

5.1 Isometric view of Fast-Track vascular mould 47

5.2 Fast-track device assembled and perfused with de-coagulated

sheep blood 48

5.3 Fast-Track device with bubbles present in the channels 50

5.4 Fast-Track device with clamping arrangement for perfusing

and flow testing 51

5.5 Moulds for the Hex-Bed vascular layer and associated headers using

photolithography on silicon substrates 53

5.6 Single vascular layer device which has been assembled using oxygen

plasma bonding and perfused with sheep blood prior to verification

flow testing 54

5.7 Test circuit used for verification testing of Hex-Bed devices 54

6.1 Pressure distribution over one sixth segment at the design flow

rate of 0.022 ml/min 55

6.2 Shear stress distribution over one sixth segment at the design

flow rate of 0.022 ml/min 56

6.3 Error of flow rate in the capillaries in a one sixth segment 58

6.4 Normalised inlet pressure over single layer vascular network

device at various flow rates 59

7.1 Velocity profile for two pairs of capillaries branching from their

respective parent vessel 62

viii

List of Tables

6.1 Channel dimensions of rectangular, uniform depth cross-section

micro fluidic manifolds employed in numerical simulations 57

6.2 Relative diameters of channels making up the one sixth segment

having been solved for the design flow rate 57

ix

Notation

A cross-sectional area, mm2

d relative diameter of a channel / vessel, µm / mm

D area ratio, dimensionless

Dh hydraulic diameter, mm

h channel height, mm

L relative length of a channel / vessel, mm

m constant, measure of the consistency of a fluid, Pa·s

n constant, measure of the degree of non-Newtonian fluid behaviour,

dimensionless

P pressure, mmHg / Pa

p wetted perimeter, mm

Q volumetric flow rate, ml / min

R resistance, Pa·s / mm3

T temperature, °C

w channel width, mm

X branching parameter, dimensionless

area ratio, dimensionless

shear rate, sec-1

non-Newtonian apparent viscosity, Pa·s

branching angle of a channel / vessel, degrees

Newtonian viscosity, Pa·s

shear stress, Pa / dynes/cm2

1

CHAPTER 1. INTRODUCTION

1.1 Tissue Engineering

The issue of designing bio-engineered tissues and organs for human therapy is

complex, requiring a multidisciplinary approach which combines the principles of

engineering and life sciences. The overall goal of which is to develop biological

substitutes that restore, maintain and improve tissue function (Skalak and Fox, 1988;

Langer and Vacanti, 1993; Lysaght and Reyes, 2001). Three techniques have been

employed for the creation of new tissue:

1) Manipulation of isolated cells or cell substitutes that are then infused into the

damaged tissue, this avoids the many complications of surgical procedures and allows

the replacement of only those cells that supply the needed function. Its main limitations

may include failure of the infused cells to maintain their function in the recipient tissue

and immunological rejection (Langer and Vacanti, 1993; Hoganson et al., 2008).

2) Tissue-Inducing substances. This approach would likely employ signal

molecules such as growth factors to stimulate damaged tissue to repair itself. Such

growth factors would depend on the purification and large scale production of signal

molecules and the development of methods to deliver these molecules to their targets

(Langer and Vacanti, 1993).

3) Cells placed on or within matrices. The development of matrices can take two

approaches, a) cells are isolated, in a closed system, from the body by a membrane

which allows the transfer of oxygen and nutrients from the blood but prevents large

bodies such as antibodies or immune cells from destroying the functioning replacement

cells, and b) the matrices implanted are produced from natural materials such as

collagen that allow the replacement cells to grow onto, eventually replacing the host

matrices. To artificially engineer living tissues in vitro, bioactive degradable scaffolds

(matrices) have cultured cells grown on and within them, providing the physical and

chemical cues to guide their differentiation and assembly into three-dimensional (3D)

tissue (Griffith, 2000).

In studies done by Park et al. (2006) and Hoganson et al. (2008), current designs

of extracorporeal bio-artificial liver (BAL) devices have shown promise in clinical

studies and preliminary in vivo testing. The goal of these systems is to provide

temporary support to patients with liver failure who are awaiting liver transplantation.

2

Due to the livers’ regenerative capacity, some numbers of patients have shown

improvement in liver function having been given temporary hepatic support by BAL

devices (Park et al., 2006), thus avoiding a liver transplant and associated life-long

immunosuppressive therapy. However, while the various extracorporeal liver support

systems have shown success in clinical and in vivo studies, for those patients whose

livers are beyond regeneration, BAL extracorporeal devices at present are still only

bridges to liver transplants. It has been summarised that the limiting factor to BAL

extracorporeal devices is their inability to effectively and efficiently exchange oxygen

and nutrients with the target cells (Hoganson et al., 2008). While extracorporeal

devices have several advantages in liver support (Langer and Vacanti, 1993),

implantable systems, on the other hand offer the possibility of permanent liver

replacement. Using various techniques cells could be harvested from the patient, where

appropriate, avoiding bio-compatibility complications for implanted devices. However,

the greatest challenge associated with implantable devices or tissue is creating a

functional mass of engineered tissue to support the required blood flow and the

numerous functions of a normal liver. It has been hypothesised that in order to

overcome this issue, an integrated vasculature could be built as part of the tissue-

engineered organ which would provide immediate exchange of oxygen and nutrient rich

blood to the full volume of the engineered tissue (Hoganson et al., 2008). By

effectively utilising a built in vasculature as part of an engineered organ, it is the hope

that such devices would reduce and one day replace the need for organ transplants from

donor lists. This report focuses on the issue of designing vasculature as part of an

integrated scaffold.

To date, all bio-engineered liver assist devices have suffered from the formation

of thrombus (blood clotting) in vascular channels due in part to the high level of

complexity of the branching patterns naturally seen in human organs. This report, in

conjunction with research being conducted by David Hoganson M.D. (Tissue

Engineering and Organ Fabrication Laboratory, Massachusetts General Hospital) on the

creation of an optimised vascular network for the purpose of bio-engineering a human

liver with authorisation from Dr. Joseph P. Vacanti, Laboratory Director, will

investigate and address the issue of designing a vascular scaffold to allow the

unrestricted flow of blood through a device using biomimetic principles. The optimised

network designed here built upon previous design iterations and design principles

developed by the Tissue Engineering and Organ Fabrication Laboratory and was created

in close collaboration. The overall goal of this study is to design and manufacture a

3

liver assist device with incorporated vascular network that will maintain a continuing

flow of blood.

1.2 Liver Structure

The liver is one of the most complex organs in the human body; it is also the

largest, contributing about 1/50 of the total body weight, or about 1.5 kg in the average

adult human (Guyton and Hall, 2000). Accounting for two thirds of the liver mass are

hepatocytes, the predominant cell type within the liver. The liver performs numerous

critically important functions of sustaining metabolic equilibrium, including production

of bile, regulation of nutrients, synthesis of serum proteins, and metabolism and

conjunction of compounds for excretion in the bile or urine. The liver is normally

capable of regenerating after acute injury and under appropriate physiological stimuli,

regains its function (Arias et al., 2001). However, liver failure occurs when the normal

regenerative process is compromised and the remaining functional capacity of the

damaged liver is unable to sustain life. On a fundamental level the basic functions of the

liver can be divided into three categories: 1) vascular functions for storage and filtration

of blood, 2) secretory function for secreting bile into the gastrointestinal tract, and 3) its

metabolic functions concerned with the majority of the metabolic systems of the body

(Guyton and Hall, 2000). For the purpose of the present study, the vascular function for

the delivery of oxygen and nutrients and the subsequent removal of cell waste products..

Blood flows into the liver via the portal vein and hepatic artery. The total blood

flow of the liver is on average 1400 millilitres per minute; approximately 1000 ml of

blood flows from the portal vein into the organ with an additional 400 ml of inflow

from the hepatic artery (Guyton and Hall, 2000). Shown below in Figure 1.1 is an

image of the liver. After entering the liver, blood then flows through a complex system

of vessels, and ultimately out of the hepatic vein, which then connects to the heart via

the vena cava.

The average pressure of blood in the hepatic vein leading to the vena cava is

approximately zero millimetres of mercury, while the pressure in the portal vein leading

into the liver is only a few mmHg normally, in patients with end stage liver disease their

portal venous pressure is elevated and can be well over 10 mmHg. As blood flows

through the bodies’ circulation the mean pressure falls progressively from 120 mmHg to

approximately 0 mmHg. As the liver is the last organ to receive blood from the

4

circulatory system, it follows that the pressure at the hepatic vein leading to the vena

cava is approximately 0 mmHg (Guyton and Hall, 2000). This small pressure

differential indicates that resistance to blood flow across the liver is low in normal

systems, however, various pathological liver conditions can markedly alter pressure and

flow (Guyton and Hall, 2000; Park et al., 2006). The two most common causes of liver

failure are cirrhosis and fulminant hepatic failure (Park et al., 2006). Causes of

cirrhosis include alcoholism and chronic hepatitis, where as a result of chronic injury;

fibrotic tissue irreversibly replaces normal liver tissue. Fulminant hepatic failure is a

clinical syndrome defined by impaired mental and neuromuscular function; the main

causes include chemical and viral hepatitis. These conditions can cause the pressure at

the portal vein to rise as high as 20 to 40 mmHg due to significantly increased blood

flow resistance in the liver, increasing the pressure.

Figure 1.1: Pictorial of the liver. Blood flows into the liver via the portal vein and

hepatic artery. The blood then flows through a complex system of vessels, out of

the hepatic vein, which then connects to the heart via the Vena Cava (Cincinnati

Children’s Hospital Medical Centre, 2003).

The basic functioning unit of the liver is that of the liver lobule. Shown in

Figures 1.2 and 1.3, the liver lobule is approximately hexagonal in shape, several

millimetres in length, between 0.8 and 2 mm in diameter and one cell thick. A human

liver contains 50,000 to 100,000 individual lobules (Guyton and Hall, 2000). The liver

is supplied with blood from branches of the portal vein and the hepatic artery. Blood

then flows through small channels called sinusoids (a type of capillary vessel) that are

lined with hepatocytes. Hepatocytes remove toxic substances from the blood, which

then exits the lobule through the central vein, also called the hepatic venule. Each

5

hepatic venule connects to form the hepatic vein and thence into the vena cava which

directs blood flow back to the heart.

The capillary bed acts as the filtration mechanism of blood within the liver. As

can be seen in Figures 1.2 and 1.3, blood flowing from the branches of the hepatic

artery and hepatic protal vein to the hepatic venule flows through a system of small

channels called sinusoids. This system is known as the capillary bed, or vascular

network. The purpose of the vascular network is to allow the optimal transfer of

oxygen and nutrients from the blood flow to the hepatocytes that require them.

Figure 1.2: A liver lobule and segment of a liver lobule. (Cunningham and Van

Horn, 2003)

6

Figure 1.3: Pictorial cross-section of the liver. Connecting the Hepatic Artery

and Hepatic Portal Vein to the Hepatic Vein (Fernandes and Barker, 2003).

Figure 1.4: Representation of a capillary bed, or vascular network (Microsoft®

Encarta®, 2008).

Shown in Figure 1.4 is a basic representation of a capillary bed. Blood flowing

from the artery on the left hand side branches into a number of arterioles which in turn

each branch in succession to form capillaries; each branching is known as a bifurcation.

7

Each bifurcation from a single vessel into two or three, creates a step down in the

relative diameter and length in the vessel. From the capillaries, the branching reverses,

multiple capillaries are joined to become venules and multiple venules join to become a

vein each time two or more vessels merge to form one, the diameter and length of the

successive vessel will be relatively larger. This phenomenon is called arterial branching

or arterial bifurcating and will be discussed in Chapter 2.

1.3 Objectives of the Present Study

The objectives of the present study are:

1) to investigate the characteristics and mathematical representation of naturally

occurring human arterial vasculatures,

2) to investigate the optimal design parameters for designing microfluidic networks,

3) to design an optimised vascular network based on previous network designs and

research,

4) To manufacture the liver device using the optimised vascular network,

5) To test the newly developed liver device and assess against the design principles,

6) To analyse and discuss the results obtained from testing and previous studies in

order to develop recommendations for future studies.

1.4 Outline of the Dissertation

Chapter 2 reviews the various literatures concerning the methods used for

mimicking natural systems including vascular networks and arterial branching and

constitutive blood models. Chapter 3 discusses the methodology to designing vascular

networks based on biomimetic principles. Chapter 4 investigates the numerical study of

the vascular network using Computational Fluid Dynamics (CFD). Chapter 5 outlines

and discusses the methodology and manufacturing of vascular networks, liver assist

devices and testing. Chapter 6 presents the results of experimental studies performed on

the optimised liver scaffold with integrated vascular network. Chapter 7 discusses

various aspects of the project, gives conclusions of the present study and

recommendations for future investigations.

8

CHAPTER 2. LITERATURE REVIEW

2.1 Vascular Networks

In the human body and especially in organs, vascular networks serve as the

optimum transfer function for oxygen and nutrients to pass from the blood stream to the

tissues and cells that require them. Vascular networks are made up of arteries, arteriole,

capillaries, venule and veins. Capillaries are the smallest of the bodies’ blood vessels,

measuring 5 – 10µm in diameter, which connect arterioles and venules, and facilitate

the optimum interchange of water, oxygen, carbon dioxide and many other nutrient and

waste chemical substances between blood and the surrounding tissues. The liver is an

exception to the typical capillary size in that the sinusoids or capillary like vessels I the

liver are approximately 30µm in diameter. The important dimension contributes to the

much lower resistance of the liver compared to other organs. Figure 1.4 is an example

of the arrangement of a vascular network.

Replicating this artificially, scaffolds are developed and used to serve as

replacement vascular networks. Scaffolds are porous, degradable structures fabricated

from either natural materials (collagen, fibrin) or synthetic polymers (polyglycolide,

polylactide, polylactide coglycolide). Scaffolds can be created as sponge like sheets,

gels, or highly complex structures with intricate pores and channels fabricated using

specialised manufacturing technologies and techniques. Virtually all scaffolds used in

tissue engineering incorporate vascular network systems that to a lesser or greater

degree mimic and function as a natural one would, and are intended to degrade slowly

after implantation in the patient and be replaced by new tissue (Griffith et al., 2002).

Within the human body vascular networks are three dimensional, where

branching of vessels occurs in the X, Y and Z planes. The vascular network of arteries,

capillaries and veins is incredibly complex and duplicating it exactly is neither practical

nor can be accomplished with available manufacturing processes. However, its basic

principles can be utilised within the limits of the current manufacturing processes

available. As such, the first step in developing an artificial scaffold with an integrated

vascular network was to identify a method to manufacture vascular networks.

Photolithography is used to make computer chips and has been adapted to make planar

moulds for vascular networks, creating channels as small as 10µm. UV light is used to

9

etch a series of channels in a silicon wafer with the channels determined by the photo

mask. Figure 2.1 shows a photo of one of the first silicon moulds created.

Figure 2.1: Early silicon mould used to make vascular networks (Hoganson et al.,

2007).

From the silicon mould, the vascular network is made by casting clear silicone

rubber over the mould, upon removal the mould then has the vascular network

imprinted in the material, a technique commonly known as soft lithography. A

schematic of the manufacturing of a silicone vascular network is shown in figure 2.2.

The resulting vascular network made out of silicone has a series of channels but an open

top; it is not a sealed network. The same moulding process that is used to create the

vascular layer of the scaffold is used to create a second open chamber for the

hepatocytes. This compartment is called the parenchymal chamber in a liver device and

has an open top.

10

Figure 2.2: Silicone moulding of vascular layers (Hoganson et al., 2007).

To close the system, a porous membrane is placed over the open top of the

vascular network and sandwiched between the parenchymal chamber which is placed

on the opposite side of this membrane. Thus, blood flows through the vascular network

and exchanges oxygen and nutrients across the thin porous membrane with the

hepatocytes in the parenchymal chamber. Shown in Figure 2.3 is a scanning electron

microscopy (SEM) image of a cross-section of a liver scaffold. The parenchymal

chamber has multiple posts which support the top of the chamber and maintain the

desired height. The membrane is made of porous polycarbonate.

Figure 2.3: Scanning Electron Microscopy (SEM) image of boundaries of the

layers of a liver scaffold (Hoganson et al., 2007).

11

This fundamental manufacturing process has been used to manufacture all of the

liver devices to date and has been optimised with each progressive design of the

vasculature.

2.2 Background of Vascular Network Designs

Once a manufacturing process was identified, initial vascular network designs

were implemented as a proof of concept for this novel approach to tissue engineering.

The first vascular network was designed by engineers at Draper Laboratory (Kaihara et

al., 2000), this initial network shown in Figure 2.4.

Figure 2.4: First vascular network design (Shin et al., 2000).

Testing of the initial designs from the Draper Laboratory revealed that the

network had too high a resistance to blood flow at arterial pressure, stimulating blood

clotting in network channels. Multiple other early designs were developed at Draper

Laboratory but were not representative of the natural capillary structures of the body.

These realisations lead the Vacanti Laboratory to collaborate with computational

biologists from the Massachusetts Institute of Technology (MIT) who then developed a

design of a vascular network with a fractal branching pattern designed for arterial blood

pressure. This vascular network with its parenchymal chamber was designated as the

Test-Net 1 device

The Test-Net 1 vascular network was tested in vivo in a rat model, where much

was learned about the scaffold and the utility of the design; however the design was not

12

suitable for larger animal studies. Shown in Figure 2.5 below is a Test-Net One devise

in vivo in a rat model.

The next generation device, Test-Net Alpha was designed by engineers at Draper

Laboratories in collaboration with computational biologists at MIT. The Test-Net

Alpha was designed for arterial input pressure but used more theoretical fluid dynamic

principles rather than attempting to mimic the fractal branching pattern of the vascular

system of the body. This design allowed the vascular network to be stacked, creating a

three dimensional thick tissue engineered structure, which allowed the device to be

seeded with a much larger number of liver cells which was more representative of the

number of cells needed to support or replace the liver function of a patient. Figure 2.6

below show a Test-Net Alpha device perfused with blood.

Figure 2.5: Test-Net 1 device in vivo in a rat model (Hoganson et al., 2007).

Due to low blood flow rate through the Test-Net Alpha device with portal inlet

pressure, there was inadequate performance in portal in vivo studies. The fundamental

challenge with the in vivo studies has been blood clotting in the device. To date, the

longest period of blood flow before clotting is 72 hours. The development of thrombus

is a complex issue for which there are many contributing factors. The low blood flow

rate seen in the device during in vivo testing led to stasis in some of the channels which

would stimulate thrombus formation. Secondly, the device is made from silicone which

is a foreign material in the body like all foreign materials in the blood stream, this leads

to a degree of platelet activation within the blood. Platelet activation and adherence

within the device leading to thrombus formation is likely a significant contributing

13

factor. The third significant factor in the early animal studies was the use of catheters

placed in the portal vein and inferior vena cave. These catheters directed the blood

from the portal vein through the device and back to the inferior vena cava. Although

they simplified the operation, they consisted of long small diameter tubing which does

not have a proven history of long term patency as a vascular graft. Finally, in the early

animal studies, a conservative use of anticoagulants was utilised. It was recognised that

a more aggressive anti-coagulant strategy may be useful in maintaining blood flow

through the device.

(a) (b)

Figure 2.6: Test-Net Alpha device (a). (b) Multi-layer Test-Net Alpha device

(Hoganson et al., 2007).

To significantly lower the likelihood of blood clotting within the device, these

four contributing factors were systematically addressed. Firstly, a proven strategy for

delivery of blood to the device from the portal vein and returning it back to the inferior

vena cava was established through an improved surgical model and anticoagulation

regimen. The correction for the identified issues of low blood flow in the device and

the use of a foreign material, silicone, led to a fundamental question: if the vascular

network of the device was designed to mimic the natural branching pattern of blood

vessels and the device had and adequate blood flow rate, would the silicone vascular

network remain patent? The first step in answering this question was to develop an

optimal design of the vascular network to be then tested with silicone.

14

After an extensive review and testing of the vascular networks developed,

researchers at the Vacanti Laboratory identified six key parameters that would best

facilitate the ability to design successful networks. It was decided that mimicking the

branching patterns seen in human organs would best accommodate the patent flow of

blood through the vascular networks; incorporation of these with hemodynamic

principles and theoretical fluid dynamics led to the establishing the following

fundamental design principles.

I. Biomimetic diameter ratios between parent and daughter vessels,

II. Optimal bifurcation branching angles,

III. Physiologic shear in vessels

IV. Biomimetic vessel length,

V. Shear stress profile at bifurcations, and,

VI. Vascular channel spacing for adequate nutrient and oxygen transfer.

The Fast-Track device and its associated vascular network were designed using

the six fundamental design principles to minimise blood clotting with the goal of

maintaining blood flow in a silicone device for longer than 28 days. To readily achieve

this, two compromises were made in designing the Fast-Track device. Firstly, since the

goal was to achieve optimal blood flow, the vascular network was designed very simply

as to more clearly understand the benefits of the improved biomimetic design. As a

result, the network had less than ideal surface area coverage for transfer of nutrients and

oxygen to hepatocytes on the adjacent parenchymal chamber. Secondly, although the

device was designed with blood flow necessary to support 30% of the mass of the liver,

due to the smaller amount of surface area coverage realised, the device can only support

a much smaller fraction of the liver function. Again, this compromise was made in

order to create ideal conditions to understand the benefit of improving the blood flow in

the device with a biomimetic designed vascular network. Figure 2.7 shows a Fast-

Track device that has been perfused with blood.

15

Figure 2.7: Fast-Track device perfused with blood.

2.3 Biomimetic Diameter Ratios between Parent and Daughter Vessels

A significant portion of the branching vasculature in the human circulatory and

respiratory systems obey Murray’s law (Sherman, 1981), which states that the cube of

the diameter of the parent vessel is equal to the sum of the cubes of the daughter

vessels. Where Murray’s law is complied with, there is shown to be a functioning

relationship between vessel diameter and volumetric flow, average linear velocity of

flow, velocity profile, channel-wall shear stress, Reynolds number and the pressure

gradient in the individual vessels. In the case where homogeneous, full-flow sets of

vessels are being investigated it is also seen that a relationship is also established

between vessel diameter and the conductance, resistance and cross-sectional area of a

full-flow set (Sherman, 1981). In almost all organisms, the arrangement of the vessels

is influenced by general physical laws as well as by the specific physiological

requirements of the organism. In terms of the physics of transport systems, dimensions

of the associated mechanisms are of great importance. Like the laws of Poiseuille and

Lick, which arose within a biological context, Murray’s law is a general physical

principle of great utility in the description of biological bulk transport systems

(Sherman, 1981). Murray determined that physiological vascular systems within the

body have achieved an optimum arrangement such that the least possible amount of

16

biological work is needed to transport blood in every segment of vessels within the

circulatory and respiratory systems.

The derivation of Murray’s law was developed without any assumptions

regarding the symmetry of the branching system, and is therefore a general law, which,

within the confines of its assumptions, applies to branching systems of all forms. The

two assumptions made by Murray were; (a) that the systems are arranged to minimise

energy output, and (b) that the energy output is that which results from two terms

associated with (i) Poiseuille flow, where energy output is proportional to f2r

-4; and (ii)

volume of the systems, where maintenance energy is proportional to r2. Alternately, the

law applies to a system of given volume that is arranged to minimise resistance, where

resistance is proportional to r-4

.

In any vessel segment (of unit length) obeying Poiseuille’s law, the flow through

the segment is proportional to the pressure difference and to the fourth power of the

vessel radius. In systems designed to have optimum mass transport characteristics,

those obeying Murray’s and Poiseuille’s law, any vessel segment within the system will

have flow that is proportional to the pressure difference and to the forth power of the

radius. When considering a single vessel segment within the system, for the system to

remain optimal, if the radii of the target vessel is changed in order to maintain flow, the

radii of both vessels upstream and downstream of the targeted vessel need to be altered

proportionally to maintain uniform flow conditions.

A system following Murray’s law allows for prediction of some other

characteristics of the system. The following characteristics hold for a system obeying

Murray’s law (Sherman, 1981):

Volumetric Flow

In every vessel of a system governed by Murray’s law, the fluid flow is

proportional to r3 (Murray’s law)

Velocity of flow

The average velocity of a fluid in a Murray system will be proportional to r

(Murray, 1926a) since (a) the flow is proportional to r3, and (b) the cross-sectional area

of a vessel is proportional to r2. Therefore, since the maximum velocity of the fluid (at

the centre of the vessel) is twice the average velocity in laminar flow, the maximum

velocity of flow is also proportional to the vessel radius.

Velocity Profile

Since in a Murray’s system the maximum velocity of fluid in a vessel (at the

centre) is proportional to the vessel radius, then the parabolas describing the velocity

17

profiles in all the vessels are similar to one another because the flow has a similar shape

in every vessel of a Murray system.

Vessel-Wall Shear Stress

Because the velocity-profile parabolas are all similar to one another in a Murray

system, the rate of change of velocity nearing a vessel wall will be the same for all

vessels at a given distance. As a result, systems described by Murray’s law will have

uniform shear stress profiles.

Reynolds Number

In any system, the Reynolds number is proportional to velocity of flow times the

vessel radius. In a Murray system, the average velocity is proportional to r, therefore

average Reynolds number is proportional to the square of the radius.

Pressure Gradient

In a segment where flow obeys Poiseuille’s law, the flow of fluid is proportional

to the pressure gradient, or pressure difference per unit length, times the forth power of

the vessel radius. In Murray systems, the flow is proportional to the cube of the vessel

radius; therefore the pressure gradient will be proportional to r-1

(neglecting the small

effects from changes in kinetic energy in the fluid).

Conductance and Resistance

The conductance in a full-flow set of vessels is proportional to the sum of the

radii to the forth power; 4r . Where the full-flow set is homogeneous, the

conductance is proportional to nr4. Since nr

3 is constant in a Murray optimum system,

it follows that nr4 must be proportional to r. Therefore the conductance is proportional

to r for homogeneous, full-flow sets in a Murray system. By taking the reciprocal of

conductance, the resistance will be proportional to r-1

, which agrees with the long-

established fact that the greatest source of resistance in an arterial tree is the in the

smallest vessels.

2.4 Arterial Branching

In a study by M. Zamir and N. Brown (1992), angiography (X-ray imaging) was

used to map the characteristics of arterial branching in various parts of the

cardiovascular systems of humans, pigs and rabbits as a means to analyse the geometric

relationships that govern the structure of arterial bifurcations. To accomplish this, x-ray

images were enlarged at the sites of branching and measurements were made of the

18

branching angles and branch diameters. The measured results were compared with

‘optimum’ values for branching angles and branch diameters that have been predicted

by various theoretical studies (Murray, 1962a,b: Kamiya and Togawa, 1872: Kamiya et

al., 1974: Rodbard, 1975: Uylings, 1977: Zamir 1976a,b, 1977, 1978).

At each branch site the diameters of the two daughter vessels were measured

three times and the results was averaged and expressed in terms of the diameter of the

parent vessel; thereby expressing each measured bifurcation in terms of two relative

diameters instead of three absolute ones. The centres of the diameters were then used to

generate the centre line of the vessel near the branching site. In cases where the centre

lines were curved due to not uniformly straight vessels, the tangent lines to the curves

were used to generate three straight lines from which the branching angles ө1 and ө2

were defined. Figure 2.8 illustrates how these measurements were taken. The

measured values for the diameters and angles were thus presented in relation to the

parent vessel as relative diameters (d1/d0) and (d2/d0) and branching angles ө1 and ө2,

where d0 refers to the parent diameter and d1 and d2 the daughter diameters, and ө1 and

ө2 the bifurcation angles for the daughter vessels.

Figure 2.8: A sample of the enlarged tracings of arterial bifurcations from which

measurement s were taken (Zamir and Brown, 1982).

19

A 1989 study by Fanucci et al. on the branching of human arterial bifurcations,

defined a series of area relationships were by the theoretical optimal characteristics for

angles and diameters of human arterial bifurcations could be compared. Based upon

morphologically normal arteries and studied angiographically, Fanucci et al. defined

two area ratios beta and D (see Figure 2.10) which defines the surface area of a vessel at

different locations following a bifurcation. The area ratio equals the sum of cross-

sectional areas of the two daughter branches divided by that of the parent artery and

characterises the change in cross-sectional area associated with the continuous

branching for aorta to capillaries. From this, an area ratio value greater than one

represents an ‘expansion’ in relative vessel surface area and a value lower than one, an

effective ‘narrowing’ relative to the original. The average of the value should be

greater than one to achieve an increase in cross-sectional area which is representational

of the morphology of normal branching from an artery to a capillary network. The area

ratio is conventionally defined away from the junction region, and as a result is

considered as a more ‘global’ design aspect of the arterial tree rather than a more ‘local’

bifunctional geometry. Conversely, the area ratio D is described by the diameters of the

daughter vessels at the bifurcation apex, making it a local aspect measurement. The

placement of measurements of the area ratios and D can be seen in Figure 2.9.

Figure 2.9: An arterial bifurcation, represented schematically. Show are the

diameters d1, d2 and d0 are taken to calculate the area ratio (solid line) and the

area ratio D (dashed line) (Fanucci et al., 1989).

20

The results obtained from both studies, (Zamir and Brown, 1982; Fanucci et al.,

1989) are largely qualitatively consistent with theoretical results; however, there are

small discrepancies that warrant discussion. Both theoretical and actual measurements

in the Zamir and Brown (1982) study were made on same vascular beds. As a result,

data scatter could lie with the actual measurements rather than the vessel actual angles

of vascular beds themselves. Also, inconsistencies between the theoretical and

measured data could have resulted in the manual assignment of tangent lines to identify

the branching angles in non-uniform arterial branching and the selection of the

appropriate diameters to use. Additionally, the perspective of the particular

angiographic image of the vascular bed used for these measurements may have caused

distortion of the branching angles. These errors appear to largely stem from errors in

judgement which are thus random in nature and would lead to scatter on both sides of

the theoretical curves.

In the Fanucci et al. (1989) study, theoretical values of the area ratios of both

and D were compared against measured values on the same set of human arterial

bifurcations. Results shoe a direct link between the optimality of theoretical models and

the measured values found in human arterial bifurcations. Also, the area ratio D had a

better correlation to the theoretical models generated than that of the area ratio ,

however because the cross-sectional areas measured for the area ratio D are much

higher than those of the area ratio they may not have the same relevance and more

data is necessary to confirm this..

Most importantly, the Fanucci et al. (1989) study describes an alternate method to

determine the relationships between arterial bifurcations in the human system. While

this method will not be used in the present study, is could be used in further studies to

create a more physiologically accurate model for the vascular bed. A major hurdle to be

faced is the minimisation or elimination of clotting in the vascular channels which in

previous devices has occurred at the vessel bifurcation. As noted by Fanucci et al.

(1989) there is a greater correlation between theoretical and measured values at the

smaller channel diameter bifurcations due to the pressure increases associated with a

reduction in channel diameter. This is an important conclusion, as maximising the

number of capillaries in the vascular bed design will be critical for a high level of

surface area in relation to vessels.

21

2.5 Physiologic Shear

The specific ranges of vessel shear stress created in the liver are unknown.

Although the relative size of vessels in the liver suggest shear rates would be similar to

those observed in the venous system, approximately 0.1 to 0.6 Pa (1-6 dynes/cm2), the

structure of the liver vessels is more closely representative of normal arterial

architecture which have a shear rate range of approximately 1 to 7 Pa (10-70 dynes/cm2)

(Malek et al., 1999). Due to the relative size of the vessels, the low volumetric flow

rate and low pressure differential, the shear rates in the liver are expected to be in the

high venous, low arterial range approximately 0.4 to 2.5 Pa (4-25 dynes/cm2).

2.6 Biomimetic Vessel Lengths

In the body, vessels have characteristic relationships between relative vessel

diameters and lengths, typically, the smaller the blood vessel diameter, the shorter the

length. Although there is not a great deal of data associated with the relationship

between relative vessel diameters and their lengths; Milnor (1989) amassed a data set

for observed lengths at various diameters of the arterial and venous blood vessels. To

derive biomimetic length for the different diameter channels in the vascular network,

this data was extrapolated via a 3rd

order polynomial best fit analysis. In the Fast-Track

design, the vascular network was created using these absolute lengths or proportionally

smaller lengths, with preservation of length relationships between channels of different

diameters. This 3rd

order polynomial will again be utilised in the current design,

however, it is expected that scaling of the channel lengths in the vascular network will

be necessary due to the relative size and density of the vasculature being created.

In a study conducted by Emerson et al. (2005), vascular trees were studied

composed of square, rectangular and trapezoidal cross-sections, similar studies on

vascular network design have also been conducted by Pries et al. (1995), Janakiraman

et al. (2006) and Barber and Emerson (2008). The aims of these studies were to

present a theoretical basis for understanding and controlling flow behaviour in

symmetric tree-like structures designed using vascular principles. However, in all three,

only symmetric vascular networks were considered for general ‘lab on a chip’

applications. In the current study it is expected that certain aspects of the design will

deviate from symmetric in order meet the geometrical constraints. Emerson et al.

22

(2005) noted that the proportionality of vessel lengths to diameters is not an essential to

exploit biomimetic design principles, but deviations will affect the flow resistance and

pressure distribution within the vasculature. There three studies also fail to address the

effect of varying vessels within individual generations of the vascular network. It is

expected that such variances in vessel lengths will likely cause variability in the flow

characteristics within the network, thus becoming a key aspect in the current

investigation.

2.7 Constitutive Blood Models

The subject of rheology describes the deformation of matter when under applied

stress. On a theoretical basis, rheology illustrates the relationship between flow and

deformation behaviour, and internal structures of materials that can not be described

using classical fluid mechanic or elasticity principles. In the case of fluids, this area of

study is also known as Non-Newtonian fluid mechanics. The viscous properties of

whole blood can then be characterised in terms of the rheological properties and

separated into three conditions; Newtonian, general non-Newtonian and as a

viscoplastic fluid (Kim, 2002). The characteristics of blood that significantly impact on

the nature of its flow include shear-thinning and yield stress.

2.7.1 Newtonian Fluids

Newtonian fluids are defined as those whose shear stresses, when plotted at a

given temperature, against the shear rate will give a straight line with a constant slope

that is independent of the shear rate; as seen in Figure 2.10. Newtonian fluids, for

example water, air, ethanol and benzene, are the basis for all classical fluid mechanics.

The simplest constitutive equation of these fluids is Newton’s law of viscosity

(Middleman, 1968; Bird et al., 1987: Munson et al., 1998);

(2-1)

where is the Newtonian viscosity and is the shear rate or rate of strain.

However, fluids such as paint, foods, polymers and blood show non-Newtonian

viscosity characteristics.

23

2.7.2 Non-Newtonian Fluids

Non-Newtonian fluids are those that do not follow the relationship between shear

stress and shear rate shown by Newtonian fluids. Aqueous solutions of fine particles

such as red blood cells (RBC) in blood, high molecular weight polymers or polymer

melts and suspensions are usually characterised as non-Newtonian. General non-

Newtonian fluids do not have a constant slope curve when the shear stress is plotted

against the shear rate. When the viscosity of a fluid decreases with increasing shear rate

the fluid is called shear thinning. Conversely, if the viscosity increases as the fluid is

placed under a high shear rate, the fluid will be considered shear-thickening (Kim,

2002).

The power-law model is one of the most widely used general non-Newtonian

constitutive models, and can be described as (Middleman, 1968; Bird et al., 1987:

Munson et al., 1998);

nm (2-2)

where m and n are power law constants.

m, a constant, is a measure of the consistency of the fluid; the greater the value of

m the higher the viscosity of the fluid. The constant, n, is a measure of the degree of

non-Newtonian behaviour; the greater the divergence from unity, the more distinctive

the non-Newtonian characteristics of the fluid (Kim, 2002).

The viscosity of a power-law fluid can be described as (Middleman, 1968; Bird et

al., 1987; Munson et al., 1998);

1 nm (2-3)

where is the non-Newtonian apparent viscosity. However, the power-law

model does not have the capability to describe a fluid in terms of its yield stress (Kim,

2002). If n < 1, the apparent viscosity of a fluid will decrease shear rate increases, and

the fluid will be shear-thining. If n > 1, the fluid will become shear-thickening where

the apparent viscosity of the fluid will increase with the shear rate. When n = 1, the

fluid will behave as a Newtonian fluid. The three cases of power law models are

illustrated in Figure 2.11. The main disadvantage of the power-law model is that it does

not adequately express the viscosity of many non-Newtonian fluids at regions of very

24

high or low shear. Since n is typically less than one, goes to infinity at a very low

shear rate rather than to a constant, 0 , as is often observed experimentally (Kim, 2002).

In order to overcome the inability of the power-law to model Newtonian regions

of shear-thinning fluids at very high and low shear rates, Cross (1965) proposed the

following equation (Ferguson and Kemblowski, 1991; Cho and Kensey, 1991;

Macosko, 1994);

nm

1

0 (2-4)

where 0 and are the viscosities at very low and high shear rates,

respectively, and m and n are model constants.

At transitional rates of shear, fluids described by the Cross model will behave like

a power-law model, as illustrated in Figure 2.12. However, the Cross model does,

unlike the power-law model, produce Newtonian viscosities ( 0 and ) at both very

low and high shear rates (Kim, 2002).

2.7.3 Viscoplastic Fluids

A viscoplastic fluid is a class of non-Newtonian fluids that will not flow under the

application of very small shear stresses. The critical value, yield stress of the fluid,

must first be exceeded before the fluid will flow. As a result, a viscoplastic fluid is a

solid when the shear stress is less than the yield stress.

The Bingham plastic model is one of the simplest representations of viscoplastic

fluids, and can be described as (Bird et al., 1987; Ferguson and Kemblowski, 1991;

Macosko, 1994);

yBm ,ywhen (2-5)

0 ,ywhen (2-6)

where y is a constant that is the yield stress, and Bm is a model constant that is

described as the plastic viscosity.

25

The characteristics of a fluid with a yield stress whose viscosity is independent of

the shear rate, can be described using the Bingham-plastic model, as shown in Figure

2.13; however, the Bingham-plastic model does not have the capability to describe the

shear-thinning characteristics of non-Newtonian fluids (Kim, 2002).

Based on a two phase suspension of a solid and piped fluid, the Casson (1959)

model describes the flow of viscoplastic fluids and exhibits both the yield stress and

shear-thinning non-Newtonian viscosity characteristics of the fluid. Mathematically,

the Casson model can be defined as (Bird et al., 1987; Ferguson and Kemblowski,

1991; Cho and Nensey, 1991; Macosko, 1994);

ky ,ywhen (2-7)

0 ,ywhen (2-8)

For materials such as food products and blood, the Casson model will provide a

better representation of a fluid than the Bingham plastic model (Fung, 1990; Cho and

Kensey, 1991).

The Herschel-Bulkley model is an extension of the power-law model that goes on

to include the yield stress of the fluid. (Herschel and Bulkley, 1926)

y

nm ywhen , (2-9)

0 ywhen , (2-10)

where m and n are model constants.

The Herschel-Bulkley model, like the Casson model, shows the characteristics of

both the yield stress and shear-thinning non-Newtonian viscosity of fluids. The

Herschel-Bulkley model has been the most widely used to describe the rheological

behaviour of food products and biological liquids (Ferguson and Kemblowski, 1991),

which have also been shown to give a better fit to many biological fluids than the

power-law or the Bingham plastic models (Kim, 2002).

26

Figure 2.10: Flow curves for a Newtonian fluid; (a) Shear Stress vs. Shear Rate.

(b) Viscosity vs. Shear Rate (Kim. 2002).

Figure 2.11: Flow Curves of power-law fluids. (a) shear-thinning fluid (n < 1). (b)

Newtonian fluid (n = 1). (c) shear-thickening fluid (n > 1) (Kim, 2002).

27

Figure 2.12: Flow curve for a cross model (Kim, 2002).

Figure 2.13: Flow curves of viscoplastic fluids, where (a) represents a fluid

modelled using the Casson or Herschel-Bulkley model, and (b) a fluid modelled

with the Bingham model (Kim, 2002).

28

2.8 Numerical Studies of Vascular Networks

Murray’s law was originally developed for cardiovascular systems composed of

multi-diameter circular pipes. While this provides a useful method for describing

cardiovascular systems, manufacturing vascular networks of circular cross-section is not

practical. In studies by Emerson et al. (2006) and Barber and Emerson (2008), tree-like

models of micro-channels have been proposed that mimic the geometrical properties of

vascular systems. A theoretical approach was first used to form a basis for controlling

the flow properties within the symmetric system based on biomimetic principles;

detailed numerical modelling followed showing excellent agreement to the application

of theoretical work (Emerson et al., 2005; Barber and Emerson, 2008). It was the aim

of these studies to introduce a measure of control into design microfluidic lab-on-chip

systems based on biomimetic principles. Cieslicki (1999) and Barber et al. (2006) have

demonstrated that Murray’s law can be generalised by defining a branching parameter,

X, which governs the change in diameter of each consecutive generation;

3

1

3

0

2d

dX (2-11)

When X is equal to one, the bifurcations obey Murray’s law and the flow

characteristics in each generation will be identical. Where X is less than one, the flow

characteristics will have a diminishing effect, for example, the wall shear stress will

reduce in each segment of the network. Conversely, where X is greater than 1, the wall

shear stress will increase in each segment of the network (Emerson et al., 2006).

In these studies, Murray’s law was extended to include rectangular and

trapezoidal geometries since a direct analogy can be shown to the hydraulic diameter.

The numerical simulations considered tree-like branching networks of square,

rectangular and trapezoidal cross-sections that were restricted to four generations (n =

0,1,2,3), and where the length of the each segment was proportional to its hydraulic

diameter. An example of the predicted normalised wall shear stress distributions in

constant-depth rectangular and trapezoidal networks can be seen in Figure 2.14.

Simulations conducted assumed a mean velocity of 0.01 ms-1

in all inlet channels of

pure water with a dynamic viscosity of 0.001 kg m-1

s-1

, with assumed laminar fully

developed flow in each segment.

29

In circular pipes the stress distribution around the circumference will be uniform,

conversely, in a non-circular channels, as seen in Figure 2.14, the wall shear stress will

vary around the wetted perimeter. This difference can be taken into account by

considering the average shear stress around the perimeter of the channel. Where non-

circular channels are considered the hydraulic diameter can be used when defining

terms for the mean tangential wall shear stress and other fluid flow characteristics

(Barber and Emerson, 2008). Thus a measure of control can be introduced when

designing microfluidic networks. Where there are applications for all three cases shown

above, the current study will use a branching parameter of one in order to maintain

uniform flow conditions throughout the network. It can be seen in Figure 2.14 that for

case where X is equal to one, the wall shear stress varies slightly with bifurcation level.

This is inevitable since the channel aspect ratio changes at each bifurcation level.

However, the average wall shear stress around the perimeter remains constant

throughout the network. The overall flow characteristics within a network will be

unaffected by the shape of the channels (Barber and Emerson, 2008).

Figure 2.14: Predicted normalised wall shear stress distributions in a series of

constant-depth rectangular and trapezoidal manifolds (Barber and Emerson,

2008).

30

CHAPTER 3. VASCULAR NETWORK DESIGN

3.1 Design Inputs

The present goal, for use of this device as a bridge to transplant, is to support 30%

of the mass of the liver. Using current available technology, the device would be much

larger than could fit within the available space in the abdomen to support this liver

mass; as an interim goal, the device will be designed to support 10% of liver mass. The

liver scaffold vascular layers will be manufactured in a single plane, with mass attained

by stacking the vascular layers. Adjacent to the vascular layers and separated by a thin

porus membrane, the parenchymal chamber will hold the target tissue cells. Therefore,

the mass required for the device can be adjusted by altering the number of vascular

layers.

The tissue engineered liver was designed to receive up to 30% of the normal

blood inflow from the portal vein and then reconnect the ‘treated’ blood outflow to the

inferior vena cava. The vascular network was designed to specifically mimic the

architecture of the liver thereby achieving a high degree of surface area coverage

corresponding to the vascular channels. The vascular network has a liver-specific radial

design which has been grouped into eight interconnecting hexagonal beds which share

common inlets. To achieve the goal to create an optimal vascular network design that

will minimise blood clotting, the fundamental design principles that govern blood

vessels in the body will be mimicked. In order to minimise blood clotting, the channels

of the designed vascular network are larger than that of the normal liver sinusoids. To

support 10% of the liver mass, approximately 30% of the total liver blood flow will be

targeted with the smallest channels being ~60µm in diameter as compared to native

liver sinusoids which are ~30µm in diameter. Therefore, the flow to mass ratio will be

much larger than that of the normal liver.

An underlying consideration in designing the vascular network is to ensure that

the flow of blood through the device experiences the same physiological conditions that

are normally occurring in the liver. To achieve this, the device will adhere to the five

biomimetic design principles, discussed in Chapter 2, that target uniform flow of blood

in the liver. The following points illustrate:

31

1. The relative diameters of the channels of the vascular layer will follow Murray’s

law.

2. Targeting the shear stress profile at channel bifurcations, a physiologic bifurcation

angle of 45º will be utilised to optimise the flow as it divides at the bifurcations.

3. The shear rate in the vascular layer will mimic that seen in the liver, which is

likely to be in the high venous, low arterial shear stress range, approximately 0.8

to 2.5 Pa (8-25 dyns/cm2).

4. Channel lengths will be calculated in terms of the relative diameters using a 3rd

order polynomial attached to a data set of biomimetic channel lengths of arterial

diameters and corresponding vessel lengths.

5. Through iterative design, the velocity profiles at the bifurcations will been made

relatively uniform by adjusting the radius of curvature of all aspects of the

bifurcation.

6. In vascular networks native and artificial, the presumed maximum distance for

consistent oxygen diffusion is approximately 200µm. To optimise nutrient and

oxygen transfer in the liver scaffold a minimum channel spacing distance of

150µm has been selected. The ideal distance between channels in the vascular

network is 150-200µm, however, due to the other physiological design

parameters and the geometrical constraints, we will aim to have <10% of the

channels separated by a distance >200µm from another channel.

7. The vascular layer will be designed at a constant depth of 74µm.

8. The vascular layer is fed by a two stage header system, the first stage branching

from the inlet nozzle to 8 channels, the second stage branching into 28 to feed the

8 hexagonal beds of the vascular layer. A first stage 8:1 header will then used to

reconnect the 8 outlets of the vascular layer to the outlet nozzle.

In order to determine the percentage of liver function that can be sustained by the

device, the number of hepatocytes in the device will be compared to the number of

hepatocytes in a normal liver. In the device, the hepatocytes are housed in a planar

chamber adjacent to the vasculature, meaning that the number of hepatocytes in the

device is dependent on the surface area of oxygen and nutrient exchange between the

vascular layer and parenchymal chamber. As such, the mass of the liver, and therefore

the percentage of liver function that is supported, is dependent on the surface area of the

device. Research has shown (Hoganson et al., 2007), that human hepatocytes form a

confluent polarized monolayer with a density of 7 x 109 hepatocytes / m

2. Ten percent

32

of the human liver is approximately 1.6 x 1010

hepatocytes. Given the number of

hepatocytes measured per meter square in vivo, this would require 2.29 m2 of surface

area for the device. Based upon these calculations, the current design will support ~3%

of hepatocytes required for organ function. However, while these are ultimately

important considerations for the design of a final liver support device, this report is

focusing only on the design for the vasculature, and at this time does not account for the

amount of hepatocytes within the device.

Blood flow to the liver via the portal vein is approximately 900 ml/min. To

support 30% of liver flow, the device will be designed for a total blood flow rate of 300

ml/min; for a device consisting of 284 layers, this correlates to a flow rate per layer of

1.06 ml/min. Layers will be assembled into a number of modules for ease of

manufacture and testing. The inferior vena cava (IVC) pressure varies with respirations

and in a normal human is approximately zero, but has also been shown to fluctuate

higher. Therefore the design outlet pressure of the device will be set at 3 mmHg,

representing a small degree of safety factor for the inconsistent ICV pressure. In the

target population, those with end stage liver failure, it is expected for the portal venous

pressure to be at least 10 mmHg; the chosen value thus represents a reasonable choice

for the minimal pressure input to the device. With these design conditions it is our aim

that the shear stress in the vasculature network be 1-2.5 Pa (10-25 dyns/cm2).

3.2 Application of Murray’s law to vascular network design

The branching structures found in the mammalian circulatory and respiratory

systems follow design principles which minimise the amount of biological work needed

to allow flow fluid. The relationship between the relative diameters of parent vessels

and the diameter of daughter vessels was first derived by Murray using the principle of

minimum work. This relationship known as Murray’s Law states that the cube of the

diameter of the parent vessel (d0) is equal to the sum of the cubes of the diameters of the

daughter vessels (d1, d2… dN). That is;

3

2

3

1

3

0 ddd (3-1)

Where Murray’s law is observed, a functional relationship exists between vessel

diameter and volumetric flow, average linear velocity of flow, velocity profile, vessel-

33

wall shear stress, Reynolds number and the pressure gradient in individual vessels4. In

homogeneous, full-flow sets of vessels a relationship is also established between vessel

diameter and the conductance, resistance and cross-sectional area. This system for

defining the vascular network is only applicable where the diameters of the branching

vessels d1 and d2 are equal in each generation of the vascular network. As such

Murray’s law can be simplified to;

3

1

3

0 2dd (3-2)

In order to achieve the required spacing for oxygen diffusion, a general vascular

network was first designed using the six biomimetic principles based upon a single

hexagonal lobule with radial flow. All channels of the vascular network have been

arranged using the six biomimetic design principles set out above based on a smallest

channel diameter of 75µm. Figure 3.1 illustrates a single hexagonal lobule with general

vascular network.

From the single hexagonal lobule, a vascular layer was constructed by connecting

eight lobules, as seen in Figure 3.2. The vascular layer consists of eight lobules sharing

common inlets that are supplied with blood by a two stage header system. The first

stage header receives blood from a single tube, dividing flow equally into eight

channels before flowing radially outwards to the second stage header. Entering the

second stage header, the blood divides from eight to twenty eight channels as it reaches

the vascular layer. Blood then flows radially inwards, through each of the eight

hexagonal beds to eight outlets, whereupon it then converges through the outlet header

into a single tube.

34

Figure 3.1: Single hexagonal lobule with general vascular network. Channels of

the vascular network have been calculated using the six biomimetic design

principles set out above based on a minimum channel diameter of 75µm.

From the general vascular network, a system of equations was derived to

calculate the required channel diameters to meet the design flow rate. In order to model

the flow characteristics of the vascular network, a one sixth segment was analysed to

develop an electrical resistance analogue model, shown in Figure 3.3, whereby branches

1, 2 and 3 are symmetrical across the axis of the inlet and outlet. This model defines the

resistance in terms of an entire branch (three descending generations and three

ascending). From Figures 1 and 2(b), it can be seen that the first two generations of

vessels are not of equal length; corresponding to the resistance model in Figure 3.3,

these are vessels are named L1A, L2A and L3A and L1B1 and L1B2, L2B1 and L2B2, and L3B1

and L3B2. In generations A and B, there will be differing flow characteristics due to the

unequal vessel lengths, it is these vessels which have been targeted in the methodology

as vessels they will cause the flow to be non-uniform in branches 1, 2 and 3.

35

(b)

(a)

Figure 3.2: (a) Single vascular layer assembly. The eight interconnecting

hexagonal lobules of the vascular layer are feed by a two stage inlet header

system consisting of a 1 to 8 first stage header and a 8 to 28 second stage header.

A 1 to 8 inlet header is used to connect the 8 outlets of the vascular layer to a

single tube. (b) One Sixth segment of the vascular layer.

36

Figure 3.3: Schematic resistance model for one sixth segment. Due to the

restrictions of the hexagonal geometry the lengths of vessels A and B are not

equal. This leads to a situation where the flow rate in vessels of generation A and

B are not the same, which in turn means that the shear stress profile will not be

uniform within all vessels.

The resistance seen in branch 1 is defined as;

E

DDCCCCBB

A R

RRRRRRRR

RR

21432121

1 11

1

1111

1

11

1 (3-3)

It thereby follows that for there to be equal flow characteristics in all branches of

the network the resistance in each branch must also be the same. Therefore;

321 RRR (3-4)

Next, the flow through each branch in terms of the resistance to flow was defined

in order to generate and expression based upon the relative diameters and lengths of

37

each individual vessel in each branch. In order to define the flow of blood in the

vascular network Poiseuille’s equation was used;

4

128

d

LQP

(3-5)

Poiseuille’s equation allows for the modelling of blood flow due to the fact that at

very low shear rates blood will behave as a viscoelastic fluid; therefore, for the fluid to

flow, the shear stress on the fluid must be greater than its yield stress. However, at

higher shear rates, the flow of blood behaves as a Newtonian fluid (when the shear

stress is greater than its yield stress) (Nichols et al., 2005).

By rearranging the Poiseuille equation and combining equations (3.3) and (3.5),

flow can be expressed in terms of each individual vessel as follows;

4

1

4

2

1

4

1

1

4

2

1

4

1

2

4

2

1

1

1

4

1

88

11

128A

E

D

B

D

B

C

B

C

B

B

B

B

BA

A

d

L

L

d

L

d

L

d

L

d

L

d

L

dd

L

Q

P

(3-6)

Concentrating on branch 1, to solve for the diameter of vessel LA based upon the

relative diameters of vessels LB1 and LB2. Murray’s law and Poiseuille’s equation must

be combined. Based upon the principle of minimum work, this allows for the flow in

each vessel to be equated to the next based upon their relative diameters and lengths.

Using Poiseuille’s equation to define the flow, two assumptions were made in order to

simplify the mathematical model. Firstly, the flow in vessels L1A, L2A and L3A

considered equal. Secondly, the pressure differential at each bifurcation is also

considered equal throughout the network, which makes the viscosity constant.

Although a certain amount of error is expected due to these two assumptions, it is

expected that the resulting error will be reduced by employing a number of iterative

steps later in the calculations. With these assumptions, Poiseuille’s equation can be

reduced to;

4

2

2

4

1

1

B

B

B

B

d

L

d

L (3-7)

By combining equations (3.1) and (3.7), the diameter of vessel LA in can be

expressed in terms of vessels LB1 and LB2 as follows;

38

3

2

43

2

14

2

3

B

B

BBA d

L

Ldd

(3-8)

Again investigating branch 1, the diameter of vessels LB1 and LB2 must then be

expressed in terms of L1A for the flow rate to be conserved in each generation of

vessels. For practical purposes, LB1 was fixed and LB2 was equated in terms of LB1.

Combining equations (3-6) and (3-8), an equation where the diameter of LB2 can be

calculated in terms of the resistance in branch 1 and in relation to the relative diameter

of LB1 results. Combining equations (3-6) and (3-8) gives;

21

21212

34

43

2

1

4

2

8

2

1

128

BB

BDBCB

B

B

EAB

LL

LLLLL

L

L

LL

P

Qd

(3-9)

Having resolved LB2 in terms of LB1 and the resistance in branch 1, the relative

diameter of vessel LA can be calculated using equation (3-8) and then verified by

Murray’s law; this justification is valid as Murray’s law maintains uniform flow

conditions. An example of the full derivation for the mathematical methodology can be

found in Appendix A. In the second and third branches, the same methodology was

used to calculate the relative diameters; first L2B2 was defined in terms of L2B1 and then

recalculated for the other vessels.

Thus far the channel diameters have been calculated for circular, multi-depth

cross-sections. In this project the vascular moulds are to be made using

photolithography on silicon substrates. Creating multi-depth systems using

photolithography would require multiple exposures to create multiple depths, this can

cause a great deal of misalignment in the geometry, and thus a uniform depth system

will be made. In order to preserve the uniform flow conditions of a Murray system with

a constant depth, the widths of the vascular channels can be calculated using the

hydraulic diameter relationship discussed in Chapter 2. Emerson et al. (2005) and

Barber and Emerson (2008) have shown that there is a relationship that allows for

uniform depth systems to be made that maintain the same uniform flow conditions of a

Murray system. Using the channel diameters, determined from the above method, as

39

the hydraulic diameter, the widths of the respective channels can be found as the depth

is constant. The hydraulic diameter can be written as;

P

ADh

4 (3-10)

where Dh is the hydraulic diameter, A is the cross-sectional area and p is the

wetted perimeter.

The width for a channel with a rectangular cross-section can thus be described as;

h

h

Dh

hDw

24

2

(3-11)

where h is the hight of a channel and w is the width.

In this way, a uniform depth system can be created while maintaining the flow

conditions required to mimic the liver architecture and thus blood flow conditions.

Figure 3.4 shows the one sixth segment which has been modelled for the required

design flow rate using the above methodology.

In designing the headers to supply fluid to and from the vascular layer, Murray’s

law was applied, the channels within the first and second stage headers were first

calculated and then the outlet header was determined. In order to simplify the design,

all three headers were made to be of uniform depth, photolithography can then be used

to manufacture the positive moulds in all cases. All the channels within the header

layers are straight with 90° bends connecting one layer to the next. Figure 3.5

illustrates a flow chart, or series of events for the mathematical process described

above.

40

Figure 3.4: Constant depth one sixth segment of hexagonal radial lobule. The

system is composed of rectangular channels with a uniform depth of 75μm and

channel widths form 50μm to 153μm.

The final design of the vascular network and liver device in this project has been

coined the ‘Hex-Bed’ design due to its geometry. As such, reference to the Hex-Bed

design or device refers to the vascular layer and device having been designed in this

thesis project.

41

Figure 3.5: Flow chart illustrating the series of events in developing a

mathematical model for the vascular network.

A general vascular network was set out for a nominal hexagonal lobule

diameter of 20 mm using the six biomimetic principles, and based on a

capillary diameter of 75 µm (Figure 3.1).

An electrical resistance analogue model was developed and applied for a one

sixth segment of a hexagonal lobule. The resistance expression considers

each branch of the one sixth segment separately (Equation 3-3).

An expression was derived from Poiseuille’s equation that relates the length

and diameter of a vessel to another in parallel. This expression was

combined with Murray’s law in order to describe the relationship of daughter

vessels of different lengths that have branched from a single parent vessel

(Equation 3-8).

From Equations (3-6) and (3-8), an expression was developed that describes

the diameter of one daughter vessel in generation B, in terms of its pair, the

resistance in the branch and the flow through that branch.

The diameter of vessel A can thus be in calculated from Equation (3-8) and

verified by Murray’s law.

Branches 2 and 3 can be assessed in the same fashion.

The widths for channels composed of uniform depth, rectangular cross-

section can be determined from the hydraulic diameter using Equation (3-

11).

The diameters of the inlet and outlets for the vascular network can then be

determined using Murray’s law.

42

CHAPTER 4. NUMERICAL SIMULATION OF VASCULAR

DESIGN

4.1 Numerical simulation of vascular network

In order to validate the design method discussed in Chapter 3, a comprehensive

series of computational fluid dynamics (CFD) simulations have been performed on the

vascular network and headers using the non-Newtonian Herschel-Bulkley blood model

with a density of 1049.5 kg/m3 and the COSMO FloWorks® CFD software package

existing within SolidWorks®. The purpose of the CFD analysis was three-fold; firstly,

to assess the flow conditions and confirm that the vascular network met the design

inputs and specifically the biomimetic design principles discussed previously.

Secondly, to determine the pressure differences that occur across the vascular network,

over the inlet and outlet headers and over a single vascular layer device in totality,

determining the pressure drops over the network and a single layer device will allow for

an in vitro device to be assessed against the CFD model. Thirdly, the flow rate in each

capillary vessel needed to be measured to determine the amount of error in the flow, and

thus whether the shear stress profile for the network is uniform.

4.2 CFD Methodology

The boundary conditions set for each of the layers, including the vascular layer,

consists of the outlet pressure and the inlet volumetric flow rate. As stated in the design

inputs, the outlet pressure for the liver assist device is 3 mmHg with an inlet volumetric

flow rate of 1.06 ml/min. The computational expenditure of running CFD analysis on

the entire single vascular layer device is impractical due to the mesh requirements; as a

result, the CFD analysis was broken down, and each layer of the device was computed

separately using ideal flow rates. Starting from the outlet header and finishing with the

first stage inlet header, the boundary conditions for each layer were determined.

Considering first the outlet header, the boundary conditions were; outlet pressure

3 mmHg with an inlet flow rate of 0.1325 ml/min. The Cartesian mesh for the outlet

header contained 0.43 million nodes corresponding to approximately 52,000 fluid cells

43

and ~57,000 partial cells. A top view of the outlet header model and its mesh is shown

in Figure 4.1.

Figure 4.1: Top view of Cartesian mesh of the outlet header model.

In order to determine the outlet pressure for the vascular layer, the inlet pressure

to the outlet header was selected as a goal for the CFD simulation. This enables the

boundary conditions to be set while determining selected characteristics of the system.

By selecting the inlet pressure to the outlet header as a goal, the boundary conditions for

the vascular layer are thus determined.

Again using the ideal inlet volumetric flow rate for the vascular layer, and the

vascular outlet pressure determined from the outlet header simulation, the boundary

conditions for the vascular layer were determined. Figure 4.2 shows the one sixth

segment that has been modelled using the design method set out in Section 2.1 which, at

this stage, has not yet been adjusted for flow uniformity. For the flow analysis, the

model represents the actual vessels that the blood flows through. The arrows indicate

the direction of flow; the fluid divides down the six branches that make up generation A

and bifurcates into generations B and then C. Flow then converges, forming

generations D and E before exiting the vascular layer through the central outlet.

44

Figure 4.2: Image showing the layout of the computational domain and structure

of the one sixth segment used in CFD fluid flow analysis. The arrows indicate the

direction of fluid flow. The arrows indicate the direction of flow; the fluid divides

down the six branches that make up generation A and bifurcates into generations

B and then C. Flow converges forming generations D and E and thus exits the

vascular layer through the central outlet.

The Cartesian mesh representing the vascular layer consists of approximately 2

million nodes, 25,000 fluid cells and 26,000 partial cells. Figure 4.3 shows the

Cartesian mesh looking at the vascular network outlet in the YZ axis, side view. Using

automatic mesh refinement tools within the COSMOS® package, the mesh can be

refined in areas where stress concentrations will occur. Figure 4.3 highlights the outlet

to the vascular layer where there is a 90° change in direction of the fluid flow. The

mesh refinement level for the channel has been selected based on the mesh independent

study, however, it can be seen that the refined mesh continues into the outlet channel.

This allows the area of stress concentration to be assessed in greater detail. The same

technique has been used at points of stress concentrations within the vascular network.

The velocity and shear profiles for the bifurcations of channels are going to be of great

interest in terms of the channel curvatures. The curvatures of channels and bifurcation

apex regions are expected to have the greatest departure from uniform flow conditions.

45

(a)

(b)

Figure 4.3: (a) Side view of one sixth segment. (b) Enlarged section of one sixth

segment showing the automatic refinement of mesh at stress concentration areas.

Following completion of the CFD simulations of the one sixth segment, it was

established that there was not uniform flow throughout the network; due to the

assumptions made when developing equations (3-7) and (3-9), a 36% capillary flow

error resulted. To ensure a uniform flow distribution within all channels of the network,

the maximum error specified in the design inputs was not to exceed 10% of the flow

rate. To correct the flow, capillary diameters were adjusted by either increasing or

decreasing the flow resistance and thus matching the actual flow rate to the design flow

rate. To make these adjustments, equation (3-7) was altered to consider the flow rate on

the diameter to the forth power instead of the channel length;

44

Current

Actual

New

Design

d

Q

d

Q (4-1)

Measuring the flow rate of the fluid in each capillary the channel widths were

adjusted to the design flow rate; all other channels in the network were then recalculated

in terms of the new capillary diameters using Murray’s law.

46

Using the goal orientated pressure-flow method, the two stage inlet headers were

also analysed in order to determine the inlet pressure to the single layer device. In

determining the inlet pressure to the device, the CFD model can then be compared to an

in vitro model by measuring the inlet pressures at various flow rates. This CFD process

was repeated for flow rates of 0.25 and 4.0 ml/min.

4.3 Mesh Independent Study

The meshes representing the vascular geometries contained approximately 0.2 –

1.6 million grid nodes (5 or more fluid cells) depending on the geometric cross-section

of the channel. The COSMOS FloWorks® software uses a finite-volume algorithm to

solve the non-linear Navier-Stokes equation governing the conservation of mass and

momentum within the fluid and a Cartesian mesh geometry system which bases the

mesh resolution upon the number of fluid cells across a given vascular geometry. The

choice of grid resolution was based upon a mesh independent study conducted on a

channel of rectangular cross-section, 74µm in depth and 50µm wide. CFD flow tests

were run at a flow rate of 0.001 ml/min with varying mesh cell resolutions. These tests

illustrated the convergence of flow in a channel of equivalent cross-section to the

smallest channel in the vascular model in relation to the mesh resolution and can be

seen in Figure 4.4. As evident from figure 4.4, the flow rate in the channel converges

on the set flow rate at approximately 4 fluid cells. In order to keep the computational

cost of the simulations to a minimum while maintaining the accuracy of the results, a

five fluid cell resolution was used to define the cross-section for all channels.

Mesh Independent Study

�

0

0.0005

0.001

0.0015

0.002

0.0025

1 2 3 4 5 6 7 8 9

Number of Fluid Cells

Flo

w R

ate

(ml/m

in) CFD Values Set Inlet Flow Rate

Figure 4.4: Mesh Independent Study. A channel with a depth of 74µm and width

50µm was used to test mesh independence.

47

CHAPTER 5. MANUFACTURING AND TESTING

METHODOLOGY

5.1 Case Study: Fast–Track Device Manufacture and Testing

The manufacturing of the Fast-Track mould utilised a process known as electrical

discharge machining or simply EMD. This process was chosen as it allowed channels

to be machined at varying depths and widths with smooth transitioning. Figure 5.1

shows an isometric photo of the Fast-Track vascular network mould.

Figure 5.1: Isometric view of Fast-Track vascular mould

While EMD does provide a means to machine multi-depth channels, the surface

finish left on the vascular network faces adversely affected the ability to bond the

respective layers. An approach called Plasma Activation was employed to bond

network faces together permanently with much greater strength than previous methods,

and will be discussed in more detail later in the chapter.

The layers were made by casting Polydimethylsiloxane (silicone) over the

vascular and head moulds and cured in an oven for 2 hours at a temperature of 70°C.

Upon removal, the silicone layers with the imprinted vascular pattern are semi-ridged.

The Fast-Track Device consists of three layers; the Header, a blank (or interstitial layer)

and the Vascular Network layer. The Header layer constitutes the inlet to the device. It

has a central inlet with six radial branches. Radiating out are the six Header channels,

with the outlets at the edge of the mould corresponding to the opposing inlets to the

vascular network. The ‘Blank’ is placed in between the Header and the Vascular

Network, separating the inlet channels of the Header from the Vascular Network.

48

During assembly the Blank has six holes punched in it, facilitating the connection of the

Header outlets to the vascular network inlets. Figure 5.2 the complete assembly of the

Fast-Track device, complete with inlet and out let nozzles and completely perfused with

de-coagulated sheep blood.

Figure 5.2: Fast-Track device assembled and perfused with de-coagulated sheep

blood

Initially PDMS was used as a ‘glue’ to bond the layers together. The process is

known as spinning, as involved placing 1 ml of PDMS on a silicon wafer which was

then spun at 1000rpm for 30 seconds, which then had layers stamped on it. The

respective layers could then be aligned and placed together, and cured in an oven for 2

hours at 70°C. It was thought that by producing a thin enough film, the amount of

silicone that would seep into the channels of the vascular layer would be negligible.

This proved to be incorrect. Regardless of how thin the silicone was spun, several of

the capillary channels would be blocked. This method was therefore unsatisfactory, and

a new method utilising activated plasma treatment was identified that could be used to

‘bond’ the layers together without any interstitial ‘glue’.

Plasma treatments can be used for a wide range of applications, notably for

removal of weak boundary layers, cross-linking of surface molecules and the generation

of polar groups. Oxidation of the polymer is responsible for the increase in polar

groups which is directly related to the adhesion properties of the polymer surface.

49

Bonding occurs by the sharing of electrons by molecules on the surface of the two

layers being placed in contact. The time for deactivation and thus bonding of layers

when treated is directly related to the level of treatment exposure. Therefore, the higher

the activation level, the longer it will take for the surface molecules to deactivate and

thus bond. Simply, the higher the level of activation treatment, greater the time needed

for successful bonding to occur. While extensive research was not conducted on the

activation levels and bonding properties due to time constraints, there was no difference

found between activation time and bond strength. Once complete deactivation has

occurred, the bond between layers is covalent and therefore stronger then the bonding

between PDMS molecules. The parameters adjusted to alter the activation level were

Radio Frequency (RF) Power, Pressure, Activation gas flow and time. It was

discovered that by using a low power, pressure, gas flow and a shot time period, layers

could be treated and successfully bonded in a relatively short time.

Successful bonding of vascular layers for the Fast-Track device proved difficult

due to the poor surface finish of EDM. A clamping step was introduced to the assembly

process where bonded layers were clamped between aluminium plates using C-clamps

in order to force 100% contact between layers. After successful plasma treatment and

assembly of the layers, PDMS was used to glue the nozzles in place at the inlet and

outlets of the Fast-Track Device and a thick bead run around the circumference of the

device, sealing the rim of the three layers together. Full details of the manufacture

process can be found in Appendix B.

In order to validate the design of the Fast-Track device, flow testing was required

to compare the inlet pressures to the devises at given flows against the solutions

obtained from FloWorks® during CFD modelling. In order to collect accurate data, the

test circuit was designed to replicate as close to human conditions for the blood as

possible. In the human body, blood flows at 37°C, when the temperature varies

physiological changes to the blood will affect the viscosity, shear rate and yield stress.

A water bath held at 37°C was used to hold the blood temperature in the circuit. The

temperature drop from the reservoirs though the test circuit and to the device was

considered negligible due to the relatively short time of testing. Blood flow in the body

is pulsatile due to the beating of the heart. For the purpose of testing the Fast-Track

Device a pulsatile flow was not chosen, instead constant flow delivery system was

implemented using one 60 ml syringe placed in a variable flow syringe pump.

In previous attempts to test the Fast-Track device the presence of bubbles and air

occlusions in the channels of the vascular networks proved to be a major problem. It

50

was thought that running water though the devices at a high enough flow rate would

push all bubbles from the channels, this was not the case. If a bubble is present in a

channel it effectively blocks that channel, forcing the fluid to travel though unrestricted

channels, increasing the resistance in the network and therefore spiking the pressure.

Figure 5.3 show one such Fast-track Device that still has bubbles present in numerous

channels indicated by the red rectangle.

Figure 5.3: Fast-Track Device with bubbles present in channel, indicated by the

red rectangle.

Bubble entrapment was found to be due to two factors; the fluid delivery system

and residual bubbles in the circuit. A bubble trap was placed in the test circuit before

the device to remove bubbles from the fluid before it reached the device. The use of

plasma treatment for bonding the layers significantly increased the strength of the

device. A pressurising step was thus introduced, where the test circuit was sealed and

pressurised, any remaining air bubbles were perfused through the silicone of the device

and circuit components. The rate of perfusion is directly related to the pressure applied

to the system, the higher the pressure applied, the shorter the time needed to complete

perfusion of the device and test circuit. Despite the increased strength to the device as a

result of plasma treatment, devices were still rupturing during perfusion. Since the key

purpose of the Fast-track device was to validate the design principles, the plasma

51

bonding of the layers could therefore be augmented with a clamping arrangement that

ensured the device could not rupture during in vitro testing. Once the clamping

arrangement was implemented, rupture of the devices was prevented and perfusing

times were significantly reduced. Figure 5.4 shows the clamping arrangement used for

perfusing of the Fast-Track Devices.

Figure 5.4: Fast-Track Device with clamping arrangement for perfusing and flow

testing.

5.2 Hex-Bed Moulds and In Vitro Testing

Photolithography was used to manufacture the moulds for the Hex-Bed design.

Photolithography was chosen for its high precision and excellent quality of surface

finish on the silicon substrate. Figure 5.5 illustrates the moulds of the vascular network

and headers. The silicon substrates with the aforementioned networks were placed in

petrii dishes for silicone casting of the device layers. The silicon substrates were first

secured to the base of the petrii dish with adhesive tape at the edges of the substrate in

order to secure the substrate for multiple silicone layer castings. Plasma activation

treatment was used in bonding the respective layers of the Hex-bed device. Due to the

high surface finish associated with photolithography, bonding of the silicone layers was

found to be excellent. Full details of the manufacturing procedure for the Hex-Bed

device can be found in Appendix B.

52

In order to validate the CFD of the vascular network, in vitro testing was done on

single vascular layer devices. Figure 5.6 shows a photo of an assembled single layer

device which has been perfused with sheep blood prior to verification flow testing.

Blood enters the device through the tubing on the near side of the photo and flows

radially outwards through the eight branches of the first stage header. Entering the

second stage header, the blood divides between eight to twenty eight channels.

Reaching the vascular layer, blood flows radially inwards through each of the eight

hexagonal beds to eight outlets whereupon the blood then converges through the first

stage outlet header to the tube on the far side of the device.

An in vitro test circuit was developed with a fixed outlet pressure of 3 mmHg

inside an incubator held at 37°C. The devices were first perfused with water and

pressurised to remove bubbles and air pockets from the channels of the vascular

network. Flow data using water as a medium was then colleted so as to later compare

against blood data. The system was then perfused with heparin anticoagulated sheep

blood. A pressure transducer was placed at the inlet to the device, and blood pumped

through the device using a syringe pump over a range of flow rates while the inlet

pressure was measured. A photo of the test circuit inside the incubator can be seen in

figure 5.7. On the left, a syringe can be seen filled with blood and loaded in the syringe

pump used for the flow testing. Due to the very low flow rates in the device, only one

60 ml syringe is needed to run a single flow test over the range of flow rates. The

vertical syringe to the right of the pump is the bubble trap that prevents air pockets

reaching the device from the syringe pump. Immediately to the left of the bubble trap,

seen as a metal tube is the pressure transducer and its readout. This pressure transducer

reads the inlet pressure to the device over the range of flow rates. To the right of the

bubble trap a single layer Hex-Bed device can be seen with blood being pumped

through it. The device has been placed on a plastic beaker with the base removed in

order to keep the vascular layer horizontal. The device must be kept horizontal in order

to keep the pressure uniform in across the branches of the vascular layer and headers. If

the device were on its side then there would be a higher pressure at the bottom of the

device and could increase the likelihood thrombus formation. On the right hand side of

the photo is a beaker used to collect the blood. Not seen in the photo is the pump used

to pressurise and thus perfuse air bubbles from the device and test circuit. Each Hex-

Bed device was flow tested three times using water as a control, and then blood. The

results of the flow testing were correlated with those results obtained from the

numerical study using CFD and are presented in Chapter 6.

53

(a)

(b)

(c)

Figure 5.5: Moulds for the Hex-Bed vascular layer and associated headers using

photolithography on silicon substrates. (a) Vascular layer. (b) First Stage

Header. (c) Second Stage Header.

54

Figure 5.6: Single vascular layer device which has been assembled using oxygen plasma

bonding and perfused with sheep blood prior to verification flow testing. Blood enters the

device through the tubing on the near side of the device seen in the photo and flows radially

outwards through the eight branches of the First Stage Header. Entering the Second Stage

Header the blood divides from eight to twenty eight channels. Reaching the Vascular layer,

blood flows radially inwards through each of the eight hexagonal beds to eight outlets. The

flow of blood converges through the outlet header to the tube on the far side of the device.

Figure 5.7: Test circuit used for verification testing of Hex-Bed devices. Test circuit consists

of, from left to right; a syringe pump, pressure transducer and readout, bubble/pressure

chamber, hex-bed device and waste container. Not seen in the photo is the perfusing pump

which sits outside the incubator.

55

CHAPTER 6. RESULTS

6.1 Pressure Distributions

Figures 6.1 shows the pressure profile generated from the CFD analysis. Figure

6.1 confirms the assumption that the pressure drop over the vascular layer is constant;

however it also indicates a non-uniform pressure drop between the vessel generations.

Because it is the wall shear stress in the vessels that governs the design criteria, the

pressure distribution is not a critical factor in the design in this study.

Figure 6.1: Pressure distribution over one sixth segment at the design flow rate of

0.022ml/min. Pressure range over the vascular layer is 8.065mmHg to

3.69mmHg, a pressure drop of 4.375mmHg.

56

6.2 Shear Stress Distribution

Figure 6.2 shows the shear profile generated from the CFD analysis.

Demonstrated is excellent shear stress uniformity within the network, 1.2–2.3 Pa (12-23

dyns/cm2) throughout, and shows the shear stress range to be within the target shear

profile of high venous and low arterial as specified in the design inputs. Slightly higher

shear rates can be seen in the inside branches where there is a slightly higher resistance

of flow due to the relative channel diameters.

Figure 6.2: Shear stress distribution over one sixth segment at the design flow

rate of 0.022ml/min. Shear stress values range from 1.2 to 2.3Pa (12-

23dynes/cm2) within the vasculature. Shear stress at the inlet/outlets is

approximately 0.00005 Pa (0.0005 dynes/cm2). The shear stress plot shows the

shear stress range to be high venous and low arterial, which is the target shear

profile, specified in the design inputs.

57

6.3 Flow Rate

From the general vascular network developed in Chapter 3, the vessel dimensions

for each branch in their respective generation within the network calculated are

presented in Table 6.1.

Table 6.1: Channel dimensions of rectangular, uniform depth cross-section microfluidic

manifolds employed in numerical simulations. The inlet channel (n = 0)was calculated using

Murray’s law where there are six daughter vessels made up of 2 sets of vessels, 1, 2 and 3’.

The outlet channel (n = 0) was calculated using Murray’s law where the outlet flow is that for

the six segments making up a single hexagonal bed.

Vessel Generation

Vessel Widths (mm)

Branch 1 Branch 2 Branch 3

1 2 1 2 1 2

Inlet 0.74

A 0.143 0.143 0.146 0.146 0.153 0.153

B 0.078 0.084 0.076 0.088 0.080 0.090

C 0.051 0.054 0.050 0.056 0.052 0.057

D 0.078 0.084 0.076 0.088 0.080 0.090

E 0.143 0.143 0.146 0.146 0.153 0.153

Outlet 1.35

Table 6.2 shows the relative diameters of the channels in the vascular layer after

having been altered to correct the flow rate through the network. It needs to be noted

that the dimensions presented in Tables 6.1 and 6.2 are the widths of the channels and

not the hydraulic diameters.

Table 6.2: Relative diameters of channels making up the one sixth segment having been solved

for the design flow rate.

Vessel Generation

Vessel Widths (mm)

Branch 1 Branch 2 Branch 3

1 2 1 2 1 2

Inlet 0.74

A 0.137 0.137 0.145 0.145 0.163 0.163

B 0.077 0.080 0.080 0.084 0.086 0.092

C 0.050 0.052 0.052 0.052 0.055 0.058

D 0.077 0.080 0.080 0.080 0.086 0.092

E 0.137 0.137 0.145 0.145 0.163 0.163

Outlet 1.35

58

Figure 6.3 shows a comparison of the flow rate through each capillary before and

after recalculation of capillary diameters. The error in flow was reduced from 36% to

8.7%, a 27.3% reduction in error. The error bars on the design flow rate curve indicate

a ±5% variation in flow within the capillaries.

Flow Rate in Capillaries

0.0007

0.00078

0.00086

0.00094

0.00102

0.0011

12 11 10 9 8 7 6 5 4 3 2 1 1' 2' 3' 4' 5' 6' 7' 8' 9' 10' 11' 12'

Capillary

Flo

w R

ate

(ml/m

in)

Design Flow Rate Origninal Flow Rate Iterated Flow Rate

Figure 6.3: Error of flow rate in the capillaries in a one sixth segment. Error

bars on the design flow rate indicate a ±5% variation in flow within the

capillaries.

Figure 6.4 shows a comparison between the CFD predicted inlet pressures

and those determined from the in vitro verification testing. The inlet pressure for

the in vitro testing is clearly higher than that of the CFD, indicating that there is a

greater resistance to flow within the devices as compared to the resistance seen in

the CFD model. The difference in inlet pressure between the blood verification

and the CFD is negligible at a flow rate of 0.25ml/min, but the difference

increases from a flow rate of 0.25-2ml/min until becoming close to constant with

the CFD curve at flow rates >2ml/min. The error bars shown on the blood

verification and CFD curves indicate one standard deviation. At the design flow

rate there is a difference in inlet pressure of 6.43mmHg.

The difference between the CFD and in vitro results for water on the other

hand are not as predicted. As can be seen the in vitro testing is lower than the

CFD. So low in fact that it is below the outlet pressure for the device for flow

rates less than 2 ml/min. This disparity is mostly likely a calibration issue with

the pressure transducer used to measure the inlet pressure. This being the case it

59

is not possible to ascertain what the inlet pressure distribution for water is going

to be for a silicone device. It is highly unlikely that the in vitro testing would

have shown results for water greater than 2 or 3 mmHg than the CFD. This is due

to the fact that water has been selected as the control fluid because of its

Newtonian properties. The two curves for the water results however, are very

close to parallel, indicating that the predicted and in vitro results have an excellent

agreement, but the calibration has been skewed for the water testing.

8 Lobule Liver Vascular Network Verification Testing

0.0

10.0

20.0

30.0

40.0

50.0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Flow Rate (ml/min)

Inle

t P

ress

ure

(m

mH

g)

Water Blood CFD blood CFD Water

Figure 6.4: Normalised inlet pressure over single layer vascular network device

at various flow rates. Data collected shows that the pressures gained from the in

vitro testing are higher than those from the CFD analysis. This indicates that

there is a greater resistance to flow within the devices as compared to the

resistance seen in the CFD model for the blood. The error bars shown on the

blood verification and CFD curves indicate one standard deviation. The curves

for the water, both CFD and invitro show that the in vitro results are lower than

the CFD.

60

CHAPTER 7. DISCUSSION AND CONCLUDING REMARKS

7.1 Discussion

This study set out to design an optimised liver specific vascular network device,

the end purpose of which is to be able to artificially create a tissue engineered liver that

can support and or replace a failing liver in a human. This would be achieved by

creating a vasculature that would facilitate the optimum transfer of oxygen and nutrients

to liver cells housed in an adjacent parenchymal chamber. The first step in developing

the vascular network was to identify those characteristics of the liver that facilitate

continuos flow of blood. Blood, being viscoplastic fluid is a very complex, there are

very specific conditions for which the device must adhere to in order to maintain blood

flow. Identified were six biometric design principles that must be adhered to in order to

control the flow of blood. These six design principles were utilised in order to develop

a vascular network that is targeted towards mimicking the natural architecture and flow

condition of the liver. Exactly duplicating the complex system of arteries, capillaries

and veins that make up vascular networks exactly is neither practical, nor can be

accomplished with available manufacturing processes. However, by employing the six

biomimetic principles of vascular design, a network was designed and manufactured to

accomplish the task of mimicking the physiological conditions seen in the human liver.

From identifying the biomimetic principles that govern blood flow, a

mathematical model was derived that describes the flow of blood through a generalised

vascular network. Through the use of numerical simulations, this general network was

optimised in order to satisfy the design inputs of the artificial liver scaffold. CFD

simulations were crucial in validating the methodology of the mathematical models

developed to describe the vascular network. Through the use of CFD simulations, we

were able to assess the vascular network in terms of the flow characteristics through the

network. Several aspects were targeted as being fundamental to achieving the design

inputs; pressure distribution within the network, velocity and shear stress profiles and

the flow rate of blood within the capillaries. Results from the CFD simulations showed

excellent agreement with the design methodology. The one exception to this was the

flow rates seen in the capillaries which were not uniform. Through the use of CFD

simulations, the flow rate in the capillaries was measured and it was found that there

was an error in flow rate across the one sixth segment that was being analysed. This

61

error in flow rates in the capillaries was expected due to a certain number of

assumptions made in the design methodology. These assumptions were necessary in

developing a solvable system of equations. The error of flow rate in the capillaries was

corrected to within the 10% (see Figure 6.3), as specified in the design inputs, by

adjusting the capillary diameters in terms of the design flow rate and the actual flow

rate measured.

As specified in the design inputs for the Hex-Bed device, the optimum distance

between channels was to be between 150-200μm, however, the spacing in between

generations A and B, and D and E is greater than 200μm. The general vascular network

was designed for the capillaries to be set for the minimum channel spacing, with all

other channels then set within the available geometry based upon the biometric design

principles. Due to the adherence to the biomimetic principles and the radial design

geometry, the channels within generations A, B, D and E could not be arranged within

the design spacing of 150-200μm. In generations A, B, D and E, the spacing ranges

from 150-800μm. As such, for future iterations of the vascular design, these distances

will be targeted. While the distances for generations A, B, D and E are not within the

design limits that were specified, it still remains that the overwhelming majority of the

surface area of the vascular bed in its entirety is within 150μm. Vascular networks

within the body are far more complex than what current technology would allow us to

create. In this design only vessel bifurcating from parent to two daughter vessels was

considered. Murray’s law however can be used to describe bifurcations to the nth

daughter vessel (Sherman, 1981). Naturally occurring vessels will also bifurcate at

numerous locations and angles along their branch segment, where only single

bifurcations are considered in this study. It is hoped that from the base of understanding

that has been gained from this study, vascular designs of much greater complexity will

be achievable in the future that maintain physiologic flow conditions.

Pressure, velocity and shear profiles from the CFD simulations showed excellent

agreement to the design inputs both before and after adjustments were made in the

capillary widths. Velocity and shear profiles have shown that there is still room for

adjustment in the layout of the design. While the shear profile was excellent in terms of

the range of shear, there are still sections of bifurcating channels that could be adjusted

in order to eliminate low velocity regions, or ‘dead-zones’. Figure 7.1 shows the

velocity profile for two pairs of capillaries branching from their respective parent

vessels. At the apex of each bifurcation there is an area of low velocity indicated by

light blue on the shear range. Low velocity regions can also be seen at the outside

62

curvature of the capillaries as they bend. Low velocity regions such as these are ‘hot

spots’ for platelet adherence and stasis formation of blood within the vasculature. The

range of shear within the vascular network lies within the target shear rates, with an

excellent agreement to the shear profile. Platelet activation is hoped to be minimal

within the network. Platelet activation studies are needed to further assess where in the

network platelet activation and stasis formation will occur.

Figure 7.1: Velocity profile for two pairs of capillaries branching from their

respective parent vessel.

While the general vascular network developed was based on a Murray system, as

evident from the velocity profile shown in Figure 7.1, there will be a slight decrease in

wall shear stress as the vessel diameter decreases. This is likely due to the relative

lengths of the vessels, those in generations A and B, the vessel lengths are not the same.

Also attributing to a decrease in wall shear stress in generations B and C is because of

the increase in cross-sectional area that occurs as part of bifurcating vessels. This can

be seen in Figure 7.1 where the velocity decreases as the flow of blood divides. To

create a more uniform profile for velocity and therefore shear stress, the diameter of the

parent vessel could be reduced just before the bifurcation. Decreasing the diameter of

the parent vessel would increase the velocity of blood as it enters the two daughter

vessels. The velocity and shear stress profiles for the bifurcation would thus be

preserved to a great extent.

63

Positive feature moulds were made of the Hex-Bed vasculature and headers using

photolithography on silicon substrates. Single layer vascular network devices were then

manufactured (see Appendix B) using silicone and a plasma activation bonding

techniques. The advent of plasma bonding for silicone devices has proven to be

instrumental in the testing of silicone devices. Previous methods of manufacturing have

proven unreliable as they considerably diminish the integrity of the vascular networks.

The development of plasma activation bonding used in manufacturing these devices

signifies a great step forward in manufacturing technologies for medical devices and

silicone materials in other areas.

From the testing of the Fast-Track device, the test circuit for the Hex-Bed device

has been improved to reduce the variability that was seen in previous test circuits. The

in vitro testing has showed interesting findings. As shown in Figure 6.4, there is a

marked increase in the pressures measured from the verification testing to the pressures

determined from the CFD analysis. At a flow rate of 0.25ml/min the difference is

minimal, but it rises until a flow rate of 2m/min at which point the difference is close to

constant. This indicates that there is a greater resistance to flow within the devices as

compared to the resistance seen in the CFD model. This difference is most likely

caused by a misalignment of the device layers during assembly. Oxygen plasma

bonding was chosen as the method for assembly as it provides a permanent bond

between the layers while maintaining the integrity of the vascular channels. However,

once treated with energised oxygen, the bonding of the layers is instantaneous making

alignment of the inlets and outlets of the respective layers extremely difficult, even

under magnification. All devices were assembled by hand; introducing an assembly

alignment mechanism or ‘jig’ would greatly reduce the error in alignment and thus

would reduce the resistance of flow within the devices, bringing the in vitro pressure

versus flow down closer to the CFD.

Contributing to the misalignment effects on the increased pressure from the in

vitro testing, surface tension within the vasculature could account for a significant

amount of the variance between the CFD and in vitro flow results. In channels as small

as those being employed in the current design, the effect of surface tension on the

resistance of fluid flowing through the channel will likely be significant. The effects of

surface tension within the vascular layer were not accounted for in the CFD simulations,

as such it is expected that surface tension effects have a great influence on the resistance

in the network, and will increase with the velocity of the fluid. This could account for

64

the large amount of error seen between the CFD and in vitro results for blood within the

network at higher flow rates.

Murray’s law was originally developed for cardiovascular systems composed of

multi-diameter circular pipes. In the current study, Murray’s biological principle in

conjunction with others has been used to design a constant-depth artificial vascular

network composed of rectangular cross-sections. The current thesis project shows

excellent agreement to Emerson et al. (2006) and Barber and Emerson (2008), where

Murray’s law was adapted to describe vascular systems composed of rectangular and

trapezoidal cross-sections. The enabling element in transitioning between describing

circular and rectangular vascular networks is forming a working relationship between

the hydraulic diameter and wetted perimeter of channels within the network.

65

7.2 Concluding Remarks and Recommendations

The present study has set out a novel method for designing a liver specific

scaffold based on biomimetic principles. A practical design methodology was

developed from theory, and was validated by numerical studies. Results from the

numerical studies show excellent agreement with the design methodology and literature.

This design process, utilising CFD as an incorporated approach to vascular design

illustrates an extensive forward step in the creation tissue engineered scaffolds with

integrated vasculatures.

Novel manufacturing techniques were utilised in the assembly of in vitro test

devices. Data from the in vitro testing shows good correlation to the numerical studies.

However, further development is needed in designing alignment techniques for scaffold

layer assembly in order to reduce misalignment errors. The utilisation of plasma

activation bonding used in manufacturing of in vitro devices signifies a great step

forward in manufacturing technologies for tissue engineered scaffolds.

In order to further assess the physiological capability of the Hex-Bed vasculature,

platelet activation and stasis formation studies are needed to determine where thrombus

formation would likely occur within the vasculature.

It is hoped that from the base of understanding that has been gained from this

study, vascular designs of much greater complexity will be achievable in the future that

maintain the physiologic flow conditions experienced by the liver.

It is recommended that future studies focus on:

1) Investigating the representation of liver specific vascular branching patterns in

order to mimic them artificially to a greater degree,

2) Increasing the packing density of channels within vascular networks, and;

3) To investigate the effects of surface tension within vascular networks, and;

4) Developing the manufacture of vasculatures, whereby the relative diameters of

channels are reduced in order to decrease the volume to liver mass ratio and thus

increase the capacity of the tissue engineered liver.

66

List of References:

Arias I.M., Boyer J.K, Chisari F.V., Fasusto N., Schacter D., Shafritz D.A. (2001) The

liver: biology and pathobiology.

Barber R.W., Cieslicki K., Emerson D.R. (2006). Using Murray’s law to design

artificial vascular microfluidic networks. In: Design and Nature III: Comparing design

in nature with science and engineering. WIT Press, Southampton. p. 245-254.

Barber, R.W., Emerson, D.R. (2008). Optimal design of microfluidic networks using

biologically inspired principles. Research Paper, Microfluidic Nanofluid 4: p. 179-19

Bird R.B., Armstrong R.C., Hassager O. (1987). Dynamics of Polymeric Liquids.

Wiley, New York, Vol 1.

Casson N. (1959). Rheology of Disperse System. Pergamom, London.

Cho Y.I., Kensey K.R. (1980). Viscoelastic effects in the falling ball viscometer. J.

Rheol. 24(891).

Cieslicki K. (1999). Resistance to the blood flow of a vascular tree-a model study.

Polish J Med Phys Eng, 5: p.161-172.

Cincinnati Children’s Hospital Medical Centre (2003). Liver Anatomy: Liver Anatomy

and Function, JPEG, accesses 20/06/2008

http://www.cincinnatichildrens.org/health/info/liver/anatomy/liver-anatomy.html.

Cross M.M. (1965). Rheology of Non-Newtonian Fluids: A New Flow Equation for

Pseudoplastic Systems. J. Colloid Sci., 20(417).

Cunningham, C.C., and Van Horn, C.G. (2003). Energy availability and alcohol-related

liver pathology. Alcohol Research & Health 27(4): p. 281–299.

Emerson D.R., Cieslicki K., Gu X., Barber R.W. (2006). Biomimetic design of

microfluidic manifolds based on a generalised Murray’s law. Lab on a Chip; 6: p. 447-

454.

Ferguson J., Kemblowski Z. (1991). Applied Fluid Rheology. Elsevier Science, London

and New York.

Fernandes K. and Barker C. (2003). Alimentary System, (2008), accessed 28/04/2008,

https://courses.stu.qmul.ac.uk/SMD/kb/microanatomy/d/alimentary/index.htm.

Fung Y.C. (1990). Biomechanics: Motion, Flow, Stress, and Growth. Springer-Verlag,

New York.

Griffith, L.G. (200). Acta Mater. 48(263)

Griffith, L.G., Naughton G. (2002). Tissue Engineering – Current Challenges and

Expanding Opportunities. Science. 295: p. 1009-1014.

67

Guyton, A. C., Hall, J. E. (2000). Textbook of MEDICAL PHYSIOLOGY. Tenth Edition.

p. 936-943. Elservier – Health Sciences Division.

Herschel W.H., Bulkley R. (1926). Measurement of consistency as applied to rubber-

benzene solution. Proc. Am. Soc. Test. Matls, 26(621).

Hoganson D.M., Pryor II H.I., Neville C, Spool I, Kulig K, Vacanti J.P. (2007). Report

on the Science of Vital Organ Engineering: Liver and Lung. Internal Report, Tissue

Engineering and Organ Fabrication Laboratory, Centre for Regenerative Medicine,

Massachusetts General Hospital.

Hoganson D.M., Pryor II H. I., Vacanti J.P. (2008). Tissue Engineering and Organ

Structure: A Vascularised Approach to Liver and Lung. International Paediatric

Research Foundation, Inc, 63(5): p. 520-526.

Janakiraman V., Mathur K., Baskaran H. (2006). Optimal Planar Flow Network

Designs for Tissue Engineered Constructs with Built-in Vasculature. Annals of

Biomedical Engineering, 35(3): p. 337-347.

Kaihara S., Borenstein J., Koka R., Lalan S., Ochoa E.R., Ravens M., Pien H.,

Cunninghm B., Vacanti J.P. (2000). Silicon micromachining to tissue engineer

branched vascular channels for liver fabrication. Tissue Eng, 6(2): p. 105-17.

Kim S. (2002). A Study of Non-Newtonian Viscosity and Yield Stress of Blood in a

Scanning Capillary-Tube Rheometer. Drexel University.

Langer, R. and Vacanti, J.P. (1993). Tissue Engineering. Science. 260: p. 920-926.

Lysaght M. J. and Reyes J. (2001). Tissue Eng. 7(485).

Macosko C.W. (1994). Rheology; Principles, Measurements, and Applications. Wiley-

VCH, New York.

Malek A.M., Alper A.L., Izumo A. (1999). Hemodynamic Shear Stress and Its Role in

Atherosclerosis. JAMA, 282: p. 2035-2042.

Microsoft® Encarta® (2008). Circulatory System. Online Encyclopaedia 2008, JPEG,

accessed 18/05/2008

http://au.encarta.msn.com/encyclopedia_761566878_2/Circulatory_System.html#howto

cite

Middleman S. (1968). The Flow of High Polymers. Intersicence, New York.

Milnor W.R. (1989). Hemodynamics, 2nd

edition. Baltimore: Williams & Wilkins.

Munson B.R., Young D.F., Okiishi T.H. (1998). Fundamentals of Fluid Mechanics.

Wiley, New York.

Nichols W.W., O’Rourke M.F., McDonald D.A. (2005). McDonald’s Blood Flow in

Arteries: theoretical, experimental and clinical principles. Hodder Arnold.

68

Park J., Toner M., Yarmush M.l., Tilles A.W. (2006). Microchannel bioreactors for

bioartificial liver support. Microfluid Nanofluid, 2: p. 525-535.

Pries A.R., Secomb T.W., Gaehtgens P. (1995). Design Principles of Vascular Beds.

American Heart Association, 77: 1017.

Sherman, T.F. (1981). On Connecting Large Vessels to Small: The Meaning of

Murray’s Law. The Rockerfeller University Press. 431(78): p.431-453

Shin M., Matsuda K., Ishii O., Terai H., Kaazempar-Mofrad M., Borenstein J., Detmar

M., Vacanti J.P. (2004). Endothelialized networks with a vascular geometry in

microfabricated poly(dimethyl siloxane). Biomed Microdevices 6(4): p. 269-78

Skalak, R. and Fox, C.F., ENDS. (1991). Tissue Engineering (Liss, New York, 1988);

R. M. Nerem, Ann. Biomed. Eng. 19(529)

Zamir M. and Brown N. (1982). Arterial Branching in Various Parts of the

Cardiovascular System. The American Journal of Anatomy, 163:295-307.

69

Appendix A – Mathematical Model Derivation

The following derivation refers to Figure 3.3;

Murray’s Law;

3

2

3

1

3

BBA ddd [1]

Poiseuille’s Equation

4

128

d

LQP

[2]

Resistance Model:

From Poiseuille’s equation the resistance of a fluid flow can be expressed as;

4

8

r

LR

[3]

As the goal is to have uniform flow conditions;

321 RRR [4]

Therefore the resistance in a singe branch will be;

E

DDCCCCBB

A R

RRRRRRRR

RR

21432121

1 11

1

1111

1

11

1 [5]

By making the assumption that the fluid is the system has a constant rate of

dynamic viscosity, equation [3] can be simplified to;

4d

LR [6]

Therefore the resistance terms in equation [5] can now be described in terms of

the ratio of the length on the diameter of the channel to the forth power. Substituting

equation [6] into [5] gives;

4

2

4

2

1

4

1

4

4

4

3

4

3

2

4

2

1

4

1

2

4

2

1

4

1

41

111

E

E

D

D

D

D

C

C

C

C

C

C

C

C

B

B

B

BA

A

d

L

L

d

L

d

L

d

L

d

L

d

L

d

L

d

L

dd

LR

[7]

By combining equations [2] and [7] the flow in a single branch can be described

in terms of the flow of fluid through it.

70

4

2

4

2

1

4

1

4

4

4

3

4

3

2

4

2

1

4

1

2

4

2

1

4

1

4

111

128E

E

D

D

D

D

C

C

C

C

C

C

C

C

B

B

B

BA

A

d

L

L

d

L

d

L

d

L

d

L

d

L

d

L

d

L

dd

L

Q

P

[8]

Once again looking at equation [2], making assumptions for uniform flow

conditions within the network, Poiseuille’s equation can be reduced to;

4

2

2

4

1

1

B

B

B

B

d

L

d

L [9]

By rearranging equation [9] we can have an expression for the diameter segment

dB1.

2

14

2

4

1

B

BBB

L

Ldd [10]

41

2

14

21

B

BBB

L

Ldd [11]

Combining equations [1] and [10] we can then find an expression for dA.

3

2

43

2

14

2

3

B

B

BBA d

L

Ldd

[12]

31

3

2

43

2

14

2

B

B

BBA d

L

Ldd [13]

From equations [1], [11] and [13], we can combine these to form an expression in

terms of the flow characteristics and the resistance of the system.

34

3

2

43

2

14

21

4

2

2

1

1

4

2

1

4

2

2

1

1

4

2

2

4

2

2

1

1

4

23

4

2

43

2

14

2

1

88

11

128

B

B

B

B

E

D

B

B

B

D

B

C

B

B

B

C

B

B

B

B

B

B

B

B

B

B

B

A

dL

Ld

L

L

d

L

L

L

d

L

d

L

L

L

d

L

d

L

L

L

d

dL

Ld

L

Q

P

[14]

71

34

43

2

13

2

21

4

2

21

21

4

2

21

4

2

2

34

2

43

2

13

2

1

8

2

B

BB

E

BBB

BD

BBB

BC

B

B

B

B

BB

A

L

Ld

L

LLd

LL

LLd

LL

d

L

dL

Ld

L

[15]

34

43

2

14

2

21

4

2

21

21

4

2

21

4

2

2

34

43

2

14

2

1

8

2

1

128

B

B

B

E

BBB

BD

BBB

BC

B

B

B

B

B

A

L

Ld

L

LLd

LL

LLd

LL

d

L

L

Ld

L

Q

P

[16]

21

4

2

2121

4

2

2

34

43

2

14

2

8

2

1

BBB

BDBC

B

B

B

BB

EA

LLd

LLLL

d

L

L

Ld

LL

[17]

21

21212

34

43

2

1

4

2

8

2

1

1

BB

BDBCB

B

B

EA

B LL

LLLLL

L

L

LL

d [18]

21

21212

34

43

2

1

4

2

8

2

1

128

BB

BDBCB

B

B

EAB

LL

LLLLL

L

L

LL

P

Qd

[19]

Using equation [19] we can now equate channel dB1 to dB1 in terms of the

resistance in branch 1 and its flow characteristics. This method can now be applied to

branch 2 and 3.

72

Appendix B – Manufacturing Protocols

B.1 Fast-Track Single Layer Device Assembly:

I. Vascular Layer Manufacturing:

1. Mix 40g of PDMS pre-polymer at ratio of 9:1 base: curing agent (36:4g)

2. Add PDMS pre-polymer to fast track vascular mould, taking care not to

cover centre raised feature

3. Degas mould in vacuum desiccator for ~15min until all bubbles are out

of PDMS pre-polymer (-82 kPa). Some bubbles may remain and most

are relieved during aeration of chamber. Manual bursting a few

remaining bubbles is acceptable.

4. Place vascular mould in oven at 70°C for 2 hours.

5. Remove mould from oven.

6. Trim PDMS layer with #11 blade scalpel immediately outside raised

circumferential feature outside the vascular pattern.

7. Remove the centre portion of the PDMS and retain.

8. Remove the trimmed outer portion of the PDMS and discard.

9. Clean mould as required using tweezers and compressed air to ensure no

residual PDMS is present.

II. Header Layer Manufacturing:

1. Mix 80g of PDMS pre-polymer at ratio of 9:1 base: curing agent (72:8g)

2. Add PDMS pre-polymer to fast track header mould, taking care not to

cover centre raised feature

3. Degas mould in vacuum desiccator for ~15min until all bubbles are out

of PDMS pre-polymer. Some bubbles may remain and most are relieved

during aeration of chamber. Manual bursting a few remaining bubbles is

acceptable.

4. Place vascular mould in oven at 70°C for 2 hours.

5. Remove mould from oven.

6. Trim PDMS layer with #11 blade scalpel outside raised circumferential

feature outside the header pattern. The cut line should be half way

between raised feature and the edge of the mould.

7. Remove the centre portion of the PDMS and retain.

8. Remove the trimmed outer portion of the PDMS and discard.

9. Clean mould as required using tweezers and compressed air to ensure no

residual PDMS is present.

III. Blank Layer Manufacturing:

1. Mix 20g of PDMS pre-polymer at ratio of 9:1 base: curing agent (18:2g)

2. Add PDMS pre-polymer to lid of 150mm Corning Petri dish.

3. Degas mould in vacuum desiccator for ~15min until all bubbles are out

of PDMS pre-polymer. Some bubbles may remain and most are relieved

during aeration of chamber. Manual bursting a few remaining bubbles is

acceptable.

4. Place vascular mould in oven at 70°C for 2 hours.

5. Remove mould from oven.

73

6. Trim PDMS layer with #11 blade scalpel immediately above raised

circumferential feature which is on the bottom of the plate.

7. Remove the centre portion of the PDMS and retain.

8. Remove the trimmed outer portion of the PDMS and discard.

9. Clean the dish as required using tweezers and compressed air to ensure

no residual PDMS is present.

IV. Nozzle Manufacturing:

1. Obtain nozzle parts from McMastercarr:

2. Thread metal nut onto nozzle until hand tight.

3. Clamp nozzle vertically in bench mounted vice. Drill out centre of

nozzle with 5mm drill bit.

4. Clamp nozzle horizontally in bench mounted vice in area of nut.

5. Using rotary cut off tool with cutting wheel bit, divide nylon nozzle part

midway through the hex portion of the nozzle.

6. Retain nozzle end portion.

7. Remove metal nut and discard threaded nylon portion.

8. Clamp nozzle end vertically in bench mounted vice with flat of part

positioned up. Trim bottom surface of flat portion until uniform.

V. Acid Cleaning of PDMS Layers:

1. All portions of acid cleaning should occur in a fume hood.

2. All layers of PMDS need to be cleaned with a dilute acid solution prior

to assembly. Only the side of the layer that will be bonded needs to be

cleaned.

3. Prepare 0.1M solution of HCl.

4. Using 200mm square aluminium tray, fill bottom of tray with 100ml of

acid solution.

5. Place layer in solution with the desired bonding surface facing down.

The layer will float on top of the solution. Soak layer for 5 minutes.

6. Remove layer from bath with forceps and dry with compressed air only

on the surface which will be bonded. Kimwipes may only be used on

surface which will be bonded.

7. For the blank layer, flip layer in bath after five minutes to treat both

sides.

8. Once layers are dry, proceed directly to assembly.

VI. Vascular Layer to Blank Layer Assembly:

1. Set plasma bonder conditions:

1. Pressure: 75mTorr

2. Power: 75W

3. Endpoint: 100

4. Time: 10 seconds

5. DC BIAS: 0

6. BP/RP: 80

7. Gas 1 flow: 0.14 m3/min (only gas 1 is used)

8. Shelf configuration: ground – positive – ground

1. Ground (right column)

2. Positive (left column)

74

2. Place vascular layer on middle shelf and blank on bottom shelf with

bonding surface. Run plasma bonder to treat layers.

3. Open plasma bonder and rotate both vascular and blank layers 90

degrees. Run plasma bonder again to treat layers. The 90 degree

rotation is to ensure 100% activation of the layers including the edges as

there is disruption of plasma treatment at the left and right edges of the

plate due to the plate ceramic supports.

4. Remove layers from plasma bonder.

5. Place 150mm aluminium blocks on lab bench with rubber side up and

cover with sheet of wax paper.

6. Place vascular layer with the pattern up on the wax paper.

7. Align the blank layer over the vascular layer.

8. Place a sheet of wax paper over the blank.

9. Apply second 150mm aluminium plate with rubber side down.

10. Lift assembly and clamp with four evenly spaced 90mm C-clamps.

Tighten C-clamps snugly using handle of adjustable wrench (spanner).

11. Leave assembly clamped for 1 hour.

12. Unclamp vascular – blank subassembly

13. Punch out holes in blank layer aligned with peripheral inlet ponds of

vascular layer with 3mm biopsy punch, taking care not to advance punch

through vascular layer.

14. Place vascular – blank subassembly between sheets of wax paper for

storage (not on Kimwipes).

VII. Vascular and Blank Layer Subassembly to Header Assembly:

1. Set plasma bonder as in step 1 of item VI.

2. Clean bonding surface of blank layer of vascular – blank subassembly

and header layer with 50mm Scotch packaging tape to remove any

particulate.

3. Place vascular – blank subassembly layer on middle shelf and header

layer on bottom shelf with bonding surface. Run plasma bonder to treat

layers.

4. Open plasma bonder and rotate both vascular – blank subassembly and

header layers 90 degrees. Run plasma bonder again to treat layers. The

90 degree rotation is to ensure 100% activation of the layers including

the edges as there is disruption of plasma treatment at the left and right

edges of the plate due to the plate ceramic supports.

5. Remove subassembly and header layer from plasma bonder.

6. Place 150mm aluminium blocks on lab bench with rubber side up and

cover with sheet of wax paper.

7. Place vascular – blank subassembly layer with the pattern up on the wax

paper.

8. Align the header layer over the vascular –blank subassembly. Fold the

header layer and aligning two end holes and the centre hole first. After

contact, fold the edges of the header to meet the remainder of the

subassembly.

9. Place a sheet of wax paper over the header layer.

10. Apply second 150mm aluminium plate with rubber side down.

11. Lift assembly and clamp with four evenly spaced 90mm C-clamps.

Tighten C-clamps snugly using handle of adjustable wrench (spanner).

12. Leave assembly clamped for 1 hour.

75

13. Unclamp the assembly

14. Place the assembly between sheets of wax paper for storage (not on

Kimwipes).

VIII. Nozzle Attachment and Edge Gluing:

1. Mix 10g of MDX4 and apply to a Petri dish.

2. Smear MDX4 with glass slide to create thin film.

3. Stamp bottom of nozzle onto glue.

4. Stamp bottom of nozzle onto Kimwipe to remove excess glue.

5. Wipe around hole on flat of nozzle to clear MDX4 away from edge of

hole.

6. Apply nozzle to the header layer. Using a syringe, apply additional

MDX4 to the top of the nozzle base so it extends from nearly adjacent to

shaft to over the edge of the base.

7. Place the assembly in the oven at 70°C for 30 minutes.

8. Remove the assembly from the oven and place on a plastic beaker such

that the first nozzle extends into the beaker.

9. Repeat steps 2 to 6 of this section to attach a nozzle to the vascular layer.

10. Using a syringe, apply MDX4 around the circumference of the edge of

the assembly. Generously spread MDX4 around to ensure all three layers

are adequately covered.

11. Place the assembly, including the plastic beaker in the over at 70°C for

30 minutes.

12. Remove from over. The device assembly is complete. Store device in a

covered location to prevent dust from entering the nozzles.

IX. Required Equipment and Tools:

1. Nitrile or Latex gloves

2. PDMS base and curing agent (Sylgard 184 elastomer kit)

3. Fast Track vascular mould

4. Fast Track header mould

5. 150mm Corning Petri dish lid (Corning Part No 430599)

6. Digital scale

7. 100ml plastic beaker

8. 75mm wood stirring rod

9. LabConco vacuum chamber

10. GAST vacuum pump DOA P704-AA

11. Thermo Oven – Lindberg/Blue M GO135-A1

12. #11 blade with scalpel handle

13. Metal stirring spatula

14. 0.1M HCl

15. 200mm square flat bottom aluminium pan

16. Compressed air can – Compu-cessory Power Duster

17. Plasma bonder PX250 manufactured by March with associated oxygen

and nitrogen tanks.

18. 150mm square 5mm thick aluminium plates with rubber backing

(McMaster Carr)

19. 90mm C-clamps (McMaster Carr or Husky brand from Home Depot)

20. 3mm biopsy punch (Miltex REF 33-32)

21. 150mm adjustable wrench

76

22. 6.35mm nylon nozzle with 25.4mm threaded base (McMaster Carr)

23. MDX4-4210 silicone polymer base with cross linker (Factor II Inc. Part

No. A-103, www.factor2.com)

24. 30ml syringe (BD part No. REF 309650)

25. Scotch 50mm Packaging Tape

X. Additional Notes:

1. Gloves should be worn at all times while handling the moulds and

PDMS. This will prevent build-up of oils and other surface

contamination of the moulds and PDMS layers.

2. When pouring, start by pouring the PDMS on the outside of the mould

and spiralling inward.

3. When placing the moulds in the oven, place them in the centre of the

rack so they remain level.

4. When removing the PDMS layer from the moulds, after cutting the

PDMS, gently lift an edge of the PDMS with the scalpel and utilizing a

flat metal stirring rod, gently lift the edge of the layer around the

circumference.

B.2 Hex-Bed Single Layer Device Assembly:

I. Vascular Layer Manufacturing:

1. Mix 20g of PDMS pre-polymer at ratio of 9:1 base: curing agent (18:2g)

2. Add PDMS pre-polymer to Hex-Bed vascular mould.

3. Degas mould in vacuum desiccator for ~15min until all bubbles are out

of PDMS pre-polymer (-82 kPa). Some bubbles may remain and most

are relieved during aeration of chamber. Manual bursting a few

remaining bubbles is acceptable.

4. Place vascular mould in oven at 70°C for 2 hours.

5. Remove mould from oven.

6. Trim PDMS layer with #11 blade scalpel immediately outside raised

feature outside the vascular pattern.

7. Remove the centre portion of the PDMS and retain.

8. Punch out holes associated with inlets / outlets of vascular layer with

biopsy punch, taking care not to tear vascular layer around the hole on

removal of biopsy punch.

9. Leave outer portion of the PDMS, as this forms a convenient reference

for removing future layers.

10. Clean mould as required using tweezers and compressed air to ensure no

residual PDMS is present.

II. First and Second Stage Header Layer Manufacturing:

1. Mix 20g of PDMS pre-polymer at ratio of 9:1 base: curing agent (18:2g)

2. Add PDMS pre-polymer to Hex-Bed header mould.

3. Degas mould in vacuum desiccator for ~15min until all bubbles are out

of PDMS pre-polymer. Some bubbles may remain and most are relieved

during aeration of chamber. Manual bursting a few remaining bubbles is

acceptable.

77

4. Place vascular mould in oven at 70°C for 2 hours.

5. Remove mould from oven.

6. Trim PDMS layer with #11 blade scalpel outside raised feature outside

the header pattern.

7. Remove the centre portion of the PDMS and retain.

8. Leave outer portion of the PDMS, as this forms a convenient reference

for removing future layers.

9. Clean mould as required using tweezers and compressed air to ensure no

residual PDMS is present.

III. Blank Layer Manufacturing:

1. Mix 20g of PDMS pre-polymer at ratio of 9:1 base: curing agent (18:2g)

2. Add PDMS pre-polymer to lid of 150mm Corning Petri dish.

3. Degas mould in vacuum desiccator for ~15min until all bubbles are out

of PDMS pre-polymer. Some bubbles may remain and most are relieved

during aeration of chamber. Manual bursting a few remaining bubbles is

acceptable.

4. Place vascular mould in oven at 70°C for 2 hours.

5. Remove mould from oven.

6. Trim PDMS layer with #11 blade scalpel immediately above raised

circumferential feature which is on the bottom of the plate.

7. Remove the centre portion of the PDMS and retain.

8. Trim centre portion to nominal dimensions of 60 x 60mm.

9. Remove the trimmed outer portion of the PDMS and discard.

10. Clean the dish as required using tweezers and compressed air to ensure

no residual PDMS is present.

IV. Nozzle Manufacturing:

1. Obtain 3mm ID silicone tubing from McMastercarr:

2. Cut two 100mm lengths of tubing

3. Mix 40g of PDMS pre-polymer at ratio of 9:1 base curing agent (36:4g)

4. Add PDMS pre-polymer to lid of 150mm Corning Petri dish.

5. Degas mould in vacuum desiccator for ~15min until all bubbles are out

of PDMS pre-polymer. Some bubbles may remain and most are relieved

during aeration of chamber. Manual bursting a few remaining bubbles is

acceptable.

6. Place vascular mould in oven at 70°C for 2 hours.

7. Remove mould from oven.

8. Trim PDMS layer with #11 blade scalpel into square block of dimension

20 x 20 mm.

9. Remove and retain.

10. Punch hole in centres of 20x20mm PDMS blocks with a 4mm biopsy

punch.

V. Vascular Layer to Second Stage Header Layer Assembly:

1. Set plasma bonder conditions:

1. Pressure: 75mTorr

2. Power: 75W

3. Endpoint: 100

78

4. Time: 10 seconds

5. DC BIAS: 0

6. BP/RP: 80

7. Gas 1 flow: 0.14 m3/min (only gas 1 is used)

8. Shelf configuration: ground – positive – ground

1. Ground (right column)

2. Positive (left column)

2. Place vascular layer on middle shelf and blank on bottom shelf with

bonding surface. Run plasma bonder to treat layers.

3. Remove layers from plasma bonder.

4. Place 150mm aluminium blocks on lab bench with rubber side up and

cover with sheet of wax paper.

5. Place vascular layer with the pattern up on the wax paper.

6. Bend second stage header layer gently in half and align the inlets /

outlets of the central axis of the second stage header layer with the

respective ones of the vascular layer. Allow header layer to fold over

vascular with extreme care given to alignment as bonding of layers is

permanent and instantaneous.

7. Place a sheet of wax paper over the header layer.

8. Apply second 150mm aluminium plate with rubber side down.

9. Lift assembly and clamp with four evenly spaced 90mm C-clamps.

Tighten C-clamps snugly using handle of adjustable spanner.

10. Leave assembly clamped for 1 hour.

11. Unclamp vascular – header subassembly.

12. Place vascular – blank subassembly between sheets of wax paper for

storage (not on Kimwipes).

VI. Vascular and Second Stage Header Layer Subassembly to First Stage Header:

1. Set plasma bonder as in step 1 of item VI.

2. Clean bonding surface of second stage header layer of vascular – second

stage header subassembly and first stage header layer with 50mm Scotch

packaging tape to remove any particulate.

3. Place vascular – second stage header subassembly layer on middle shelf

and first stage header layer on bottom shelf with bonding surface. Run

plasma bonder to treat layers.

4. Remove subassembly and first stage header layer from plasma bonder.

5. Place 150mm aluminium blocks on lab bench with rubber side up and

cover with sheet of wax paper.

6. Place vascular – second stage header subassembly layer with the pattern

up on the wax paper.

7. Align the first stage header layer over the vascular – second stage header

subassembly. Fold the first stage header layer and aligning two end

holes and the centre hole first. After contact, fold the edges of the header

to meet the remainder of the subassembly.

8. Place a sheet of wax paper over the header layer.

9. Apply second 150mm aluminium plate with rubber side down.

10. Lift assembly and clamp with four evenly spaced 90mm C-clamps.

Tighten C-clamps snugly using handle of adjustable spanner.

11. Leave assembly clamped for 1 hour.

12. Unclamp the assembly

79

13. Place the assembly between sheets of wax paper for storage (not on

Kimwipes).

VII. Vascular and Inlet Header Subassembly to First Stage Outlet Header:

1. Set plasma bonder as in step 1 of item VI.

2. Clean bonding surface of vascular layer – inlet header subassembly and

first stage outlet header layer with 50mm Scotch packaging tape to

remove any particulate.

3. Place vascular – inlet header subassembly layer on middle shelf and first

stage inlet header layer on bottom shelf with bonding surface. Run

plasma bonder to treat layers.

4. Remove subassembly and first stage header layer from plasma bonder.

5. Place 150mm aluminium blocks on lab bench with rubber side up and

cover with sheet of wax paper.

6. Place vascular – inlet header subassembly layer with the vascular pattern

up on the wax paper.

7. Align the first stage outlet header layer over the vascular – inlet header

subassembly. Fold the first stage outlet header layer and aligning two

end holes and the centre hole first. After contact, fold the edges of the

header to meet the remainder of the subassembly.

8. Place a sheet of wax paper over the header layer.

9. Apply second 150mm aluminium plate with rubber side down.

10. Lift assembly and clamp with four evenly spaced 90mm C-clamps.

Tighten C-clamps snugly using handle of adjustable spanner.

11. Leave assembly clamped for 1 hour.

12. Unclamp the assembly

13. Place the assembly between sheets of wax paper for storage (not on

Kimwipes).

VIII. Nozzle Attachment and Edge Gluing:

1. Mix 10g of MDX4 and apply to a Petri dish.

2. Smear MDX4 on one end of 100mm tubing.

3. Insert tubing in hole of 20x20mm PDMS block.

4. Smear MDX4 with glass slide to create thin film.

5. Stamp bottom of 20x20mm block onto glue.

6. Stamp bottom of nozzle onto Kimwipe to remove excess glue.

7. Wipe around hole on flat of nozzle to clear MDX4 away from edge of

hole.

8. Apply nozzle to the header layer. Using a syringe, apply additional

MDX4 to the top of the nozzle base so it extends from nearly adjacent to

shaft to over the edge of the base.

9. Place the assembly in the oven at 70°C for 30 minutes.

10. Remove the assembly from the oven and place on a plastic beaker such

that the first nozzle extends into the beaker.

11. Repeat steps 2 to 8 of this section to attach a nozzle to the vascular layer.

12. Using a syringe, apply MDX4 around the circumference of the edge of

the assembly. Generously spread MDX4 around to ensure all three layers

are adequately covered.

13. Place the assembly, including the plastic beaker in the over at 70°C for

30 minutes.

80

14. Remove from over. The device assembly is complete. Store device in a

covered location to prevent dust from entering the nozzles.

IX. Required Equipment and Tools:

1. Nitrile or Latex gloves

2. PDMS base and curing agent (Sylgard 184 elastomer kit)

3. Hex-Bed vascular mould

4. Hex-Bed First and Second Stage header moulds

5. 150mm Corning Petri dish lid (Corning Part No 430599)

6. Digital scale

7. 100ml plastic beaker

8. 75mm wood stirring rod

9. LabConco vacuum chamber

10. GAST vacuum pump DOA P704-AA

11. Thermo Oven – Lindberg/Blue M GO135-A1

12. #11 blade with scalpel handle

13. Metal stirring spatula

14. Compressed air can – Compu-cessory Power Duster

15. Plasma bonder PX250 manufactured by March with associated oxygen

and nitrogen tanks.

16. 150mm square 5mm thick aluminium plates with rubber backing

(McMaster Carr)

17. 90mm C-clamps (McMaster Carr or Husky brand from Home Depot)

18. 3mm biopsy punch (Miltex REF 33-32)

19. 150mm adjustable wrench

20. 3 mm ID Silicone tubing (McMaster Carr)

21. MDX4-4210 silicone polymer base with cross linker (Factor II Inc. Part

No. A-103, www.factor2.com)

22. 30ml syringe (BD part No. REF 309650)

23. Scotch 50mm Packaging Tape

X. Additional Notes:

1. Gloves should be worn at all times while handling the moulds and

PDMS. This will prevent build-up of oils and other surface

contamination of the moulds and PDMS layers.

2. When pouring, start by pouring the PDMS on the outside of the mould

and spiralling inward.

3. When placing the moulds in the oven, place them in the centre of the

rack so they remain level.

4. When removing the PDMS layer from the moulds, after cutting the

PDMS, gently lift an edge of the PDMS with the scalpel and utilizing a

flat metal stirring rod, gently lift the edge of the layer around the

circumference.

81

Appendix C – In Vitro Test Procedure

I Device Testing Procedure:

1. Manually draw 20ml of water into syringe for manual priming of the

lines and vascular network from fluid reservoir.

2. Open all Three Way Check Valves (TWCV) for primary system.

3. Open Air Release Valves at the top of the Gravity/Pump Feed Chamber.

4. Prime all lines, dislodging/removing air bubbles/pockets though the Air

Release valve at the same time.

5. Manually redraw water from reservoir ~ 20 ml.

6. Prime Gravity Gravity/Pump Feed Chamber with 15ml of fluid.

7. Close lines from Feed Chamber to Syringe Pump.

8. Test pressure of Settling Pump and set to 300 kPa.

9. Close check valve at outlet of vascular network.

10. Open check valve from Settling Pump to Feed Chamber pressurising

device and perfusing air out.

11. Open pressurized Feed Chamber to Inlet of vascular network, keep

network pressurised till such time as 100% of the network channels are

full and free of air pockets / bubbles.

12. Turn off Settling Pump and close off Feed Chamber from the system.

13. Open check valves at Outlet of vascular network.

14. Set flow-rate of Syringe Pump and run, recording values of inlet pressure

to the device from the pressure transducer read-out at various flow rates.

15. Reprime test circuit with blood, repeating steps 1 to 5. The system will

not need to be re-perfused for the blood as the bubble chamber will

prevent air pockets entering the device while changing test fluid.

16. Set flow-rate of Syringe Pump and run, recording values of inlet pressure

to the device from the pressure transducer read-out at various flow rates.

II Required Equipment and Tools:

1. Fast-Track or Hex-Bed single vascular layer device.

2. Syringe Pump.

3. Three, 500 ml styrene bottles.

4. Six, 60 ml syringes.

5. Fifteen, Three Way Check Valves (TWCV).

6. GAST vacuum pump DOA P704-AA.

7. Two meters, 3 mm ID Silicone tubing (McMaster Carr).

8. Two, Omega PX209 – 30V, 15G5V Transducers.

9. Incubator

10. Nitrile or Latex gloves.

III. Additional Notes:

1. Gloves should be worn at all times while handling blood and devices.

This will prevent build-up of oils and other surface contamination on the

devices and protect the operator form accidental contact with test blood.