Excerpt

## Contents

Summary

Nomenclature

Contents

Acknowledgements

1 INTRODUCTION

1.1 Clinical Background/ Theory

1.2 Motivation

1.3 Hemodynamic variables

1.4 Computational Fluid Dynamics (CFD)

2 THESIS

2.1 Literature Review

2.2 Preliminary Work

2.2.1 Steady state analysis and Laminar flow

2.2.2 Geometry

2.2.3 Properties of Blood

2.2.4 Parabolic velocity profile

2.2.5 Rigid walls assumption

2.2.6 Mesh structure

2.2.7 Boundary conditions

2.3 Porosity model

2.4 Methodology

3 RESULTS

3.1 Unstented

3.1.1 Pressure

3.1.2 Wall Shear Stress

3.2 Stented

3.2.1 WSS Average 1

3.2.2 WSS Average 2

3.2.3 Pressure Inlet

3.2.4 Average Pressure 1

3.2.5 Average Pressure 2

3.3 Stented vs Unstented

3.3.1 Stent Small Artery (A2) vs Unstented

3.3.2 Stent Big Artery (A1) vs Unstented

4 Validation

4.1 Mesh independency

4.2 Wall Shear Stress

5 DISCUSSION

6 CONCLUSION

REFERENCES

## Summary

An intracranial aneurysm is a vascular disorder estimated to affect up to 5% of the global population. The use of flow diverting stents for treatment of intracranial aneurysms leads to ischemic complications. It is hypothesized that alteration in hemodynamics after placement of stents plays a vital role in ischemia (vessel occlusion). This project uses Computational Fluid Dynamics to study the alterations in hemodynamics before and after placement of stent with respect to the relative diameter of the bifurcating arteries on idealized geometries using ANSYS-CFX 15.0. Pressure and flow rate waveforms were extracted from a 1D model of the arterial tree to simulate hemodynamic conditions correctly. The results show that there are significant changes in hemodynamics (pressure and wall shear stress) before and after placement of stent. These changes are also affected by the relative diameters of the bifurcating arteries. The trends observed in hemodynamics can be interpreted by clinicians to study vessel occlusion and its relation to the relative diameters of arteries. The results have a potential to assist in treatment of aneurysms without ischemic complications.

## NomenclaturE

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## Acknowledgements

I would like to thank my parents for their unconditional support and giving me the opportunity to pursue my degree in Mechanical Engineering at The University of Sheffield.

I would also like to acknowledge my project supervisor and tutor Dr. Alberto Marzo for giving me the opportunity to work on this project. His expertise in the field of Biomechanics and Bioengineering helped me apply engineering principles to the cardiovascular system.

## 1 INTRODUCTION

### 1.1 Clinical Background/ Theory

An intracranial aneurysm (brain aneurysm) can be defined as the weakening of the walls of an artery that causes a localised dilation or ballooning of the blood vessel (1). If an aneurysm ruptures it causes blood to leak into the spaces around the brain that can lead to various ischemic complications such as nausea, vomiting and loss of consciousness (1) . In more severe cases it can lead to death of the patient almost immediately after rupture. Hence treatment without ischemic complications is vital.

Intracranial aneurysms are commonly found around the Circle of Willis, a circulatory connection of arteries in the brain. Almost a third of the aneurysms are present around MCA bifurcations (2). Aneurysms of such topography pose most difficulties to endovascular surgeons. They often demand retreatment and present complications during and after surgery.

Flow diverting stents (FDS) offer a valid alternative in treatment of intracranial aneurysms at bifurcations, when other endovascular procedures such as coiling are not possible (3). FDS operate in a way where they divert blood flow away from the aneurysm sac which reduces growth of the aneurysm (4).

Side branch (SB) occlusion after placement of stent is a serious difficulty. The ischemic complications could lead to detrimental outcomes such as cardiac death. This effect does not seem to be dependent on the FDS model. Hence, it is hypothesized that other factors such as hemodynamics and its influence on clinically relevant effects such as alterations of pressure and wall shear stress (WSS) could be the reason for vessel occlusion. Understanding the mutual significance of all variables at play could help in treatment without ischemic complications. However, no large-scale study has investigated this issue.

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Figure 1.1: Middle Cerebral Artery bifurcation aneurysm treated with stent. A, B: are conventional 3D angiograms that show the aneurysm. C: follow up angiogram after placement of stent shows aneurysm disappearing. The white arrows show the placement of the stents. D: shows significantly changed orientation of parent and bifurcating artery (5)

### 1.2 Motivation

About 1.5 to 5% of the global population has or will develop an aneurysm (6). They can prove to be fatal as they may cause internal bleeding. Once an aneurysm bleeds the chance of death is 30 to 40% (7). Even if the aneurysm is treated the chance of moderate to severe brain damage is 20 to 35% (8).

This project is part of research collaboration between INSIGNEO, University of Sheffield and Hopital Bretonneau, Tours, France. It aims to investigate the effects of flow diverting stents on intracranial artery bifurcations with a focus on bifurcating vessels diameter on hemodynamics and occlusion. The identification of the strongest variables of interest has the potential to make an impact on the treatment of aneurysms and serve as a guidance tool to Neurologists whilst treating a patient.

### 1.3 Hemodynamic variables

Hemodynamics, or study of blood flow, provides mechanical triggers that are transduced into biological signals leading to geometric changes in the artery. There is strong evidence that suggests that hemodynamics affect the behaviour of the inner most layer of the artery, the endothelium (9). Endothelial cells transduce mechanical signals caused by hemodynamics into biological signals that maintain vascular equilibrium (10).

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Figure 1.2: Endothelial cells at the inner wall of the artery (11)

The hemodynamic conditions inside blood vessels lead to the development of superficial stresses near the wall vessels. This is a shear stress due to blood flow; it is applied by the blood against the vessel wall. Shear stress plays an important role in the pathogenesis of aneurysms. Vessel wall remodelling as a result of shear stress alteration contributes to the development of an aneurysm (12).

The determination of shear stresses on a surface is based on the fundamental fluid mechanics assumption, according to which the velocity of the fluid upon the wall surface is zero (no-slip condition). This leads to the establishment of velocity gradient.

The shear stress is the simply the velocity gradient multiplied by the viscosity of the fluid.

illustration not visible in this excerpt

Equation 1.1

Endothelial cells are sensitive to changes in the levels of WSS and may lead to vessel wall remodelling (13). Hence, analysing alterations in WSS is important to understand the clinically relevant outcomes.

Pressure is exerted by the blood flow upon the walls of the arteries. A pressure gradient is what drives any type of flow. Alterations in pressures can cause arteries to open and close. If the blood pressure is too high, the muscles in the artery wall will respond by pushing back harder, this makes the artery walls thicker. Increased thickness leads to less space for the blood to flow through which would increase the pressure even further (14).

Large elevations in mean arterial blood pressure can increase wall tension to a level that leads to rupture. It is possible that before rupture the vessel wall may have biologically remodelled and deteriorated over time decreasing wall strength to such a level that even a small increase in pressure could push the wall tensile stress over the limit and rupture the wall (15).

A sudden reduction in pressure may also cause ischemic complications. If the pressure inside the artery is much lower in comparison to the intracranial pressure it may cause the artery to occlude. Hence, analysing alterations in pressure before and after placement of FDS could help understand clinically relevant outcomes.

### 1.4 Computational Fluid Dynamics (CFD)

CFD is a methodology that uses numerical methods to analyse fluid flows. One of the advantages of using CFD to analyse this problem is that it enables to mimic the effect of the stent and capture its effects without having to conduct surgery.

CFD is based on the fundamental governing equations of fluid dynamics namely continuity, momentum and the energy equation.

For a steady, laminar incompressible flow the equations reduce to Continuity equation

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Equation 1.2

It is a mathematical expression denoting conservation of mass in the physical domain.

Navier Stokes equation

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Equation 1.3

[illustration not visible in this excerpt]Is the convection (inertial) term

[illustration not visible in this excerpt]Is the diffusion term (transport of fluid from high to low gradients)

[illustration not visible in this excerpt]Is the source term; pressure gradient that drives the flow

This Navier Stokes equation describes the motion of viscous fluids. The two equations have been presented in the form after valid assumptions about the blood flow have been made. (Section 2.2)

Since in this project there is no modelling of heat transfer and the temperature gradient in the body is negligible only the continuity and momentum equations are considered for this analysis.

The software being used to conduct CFD analysis for this project is ANSYS CFX 15.0. CFX is a coupled solver; it uses the control volume finite element method that uses coupled equations to solve pressure and velocity in the domain. CFX was chosen for its ease to implement the complex boundary conditions (Section 2.2.7) required in this project.

How CFD works? Why is it used?

The Navier Stokes and Continuity equations are partial differential equations that can be applied to any fluids problem. Engineers rely on the conservation principles of mass, momentum and energy to define a fluids problem scientifically using physics. After defining the boundary conditions these equations become problem specific. Due to the complex and non-linear nature of these equations no analytical solution exists, but engineers require solutions only at a set number of discretized points in the solution domain. The process of generating these discretized points in the domain is called meshing. The conservation equations, in their algebraic form, are solved at each node in the solution domain marching from the inlet to the outlet. If a solution is required between the positions of two nodes then interpolation is used.

The solution provides information on the properties of interest such as magnitudes and distribution of pressure and WSS in the domain.

## 2 THESIS

### 2.1 Literature Review

Throughout the years intensive research has been dedicated on the role of hemodynamics in arterial pathologies. From CFD analysis, it can be seen that the arterial segments are greatly affected by complex hemodynamic forces such as alterations of pressure and WSS (16). These hemodynamic forces may encourage vascular remodelling of the arterial structure by interacting with the endothelial cells (9) . Both these factors are significantly affected by the vessel geometry and may show differences with respect to the geometry (17).

Shear stress is the tangential force of the flowing blood on the endothelial surface of the blood vessel. It is created by flow of the viscous blood over the endothelial cell surface. The blood flow in contact with the endothelial surface is relatively still compared to the increased velocity in the centre of the vessel. Shear stress is thought to affect only the inner surface of the vessels, that is, the endothelial monolayer (18).

The stretching forces exerted by the shear stress gradient would weaken the intercellular contact between the endothelial cells, leading to the initiation of destructive remodelling. It can be assumed that the initial destructive changes in the vessel wall, like rupture of the internal elastic lamina and weakening of the muscular layer, take place at the region of the highest hemodynamic stress (19). This identifies as a region to watch when analysing results.

The vascular endothelium becomes irregular in shape due to low WSS. This irregularity weakens the smooth muscle of the artery, which is responsible for the contraction and dilation of the artery (20) and could be a possible reason for occlusion. Low WSS promotes endothelial proliferation and shape change but it is also responsible for secretion of substances that promote vasoconstriction (21).

High shear stress, as found in laminar flow, promotes endothelial cell survival, alignment in the direction of flow and secretion of substances that promote vasodilation and anticoagulation (22). High shear stress is a relative term in this case, if it exceeds the acceptable range it would damage the vessel wall. Hence, it is speculated that there is a range of values of WSS that exhibits healthy behaviour of the endothelium.

The magnitude of the shear stress vector is directly proportional to blood flow and fluid viscosity and inversely proportional to vessel radius to the power of 3. Consequently, blood vessels with high flow and small diameters are exposed to high shear stress, while vessels with low flow and large diameters are exposed to low shear stress (18). Hence, the effect of relative diameter of the bifurcating artery would play an important role in distribution of WSS.

Long-term alterations in the maintenance and structure of vessel function by shear occur through regulation of protein synthesis and gene expression; exposure to altering levels of shear stress may affect these functions and ultimately result in thickening of the artery (23).

Intracranial arteries have reduced or even missing external elastic lamina because arteries upstream from the cerebral arteries dampen the majority of the pulsatile blood flow. The vascular smooth muscle is usually reduced or disorganized at bifurcations (24). This restructuring makes bifurcations weaker and more susceptible to damage with changes in pressure, shear stress, and flow rates (24).

Pressure is created by cardiac contraction, which produces the hydrostatic force of the blood within the blood vessel. This force is transmitted to all layers of the blood vessel unlike WSS which only affects the innermost layer. The effect of transmural pressure on the responsiveness of vascular smooth muscle was studied using rats that lead to chronic occlusion of one external iliac artery (25). The arterial pressure in the occluded leg was reduced to approximately half of that in the opposite unoccluded leg, suggesting that pressure is an important hemodynamic variable when studying vessel occlusion.

Based on both experimental and clinical observations, it is known that atherosclerotic lesions (thickening of arterial wall) have the propensity to form in areas of changing shear stress vectors (18). Although flow in the centre of the arterial lumen is rapid and laminar, the blood near the arterial wall, known as the boundary layer, has slower flow, longer particle resident times, and variable cyclic flow patterns. Areas of boundary layer separation and low shear force generally occur at the outer wall of arterial bifurcations, leading to more prominent degradation of wall of arteries; areas exposed to high shear stress, such as flow dividers, have diminished exposure to substances that cause arterial wall degradation and exhibit the least lipid accumulation (26).

There are many other non-uniformities in arteries. Arteries branch off like a tree. The detailed flow condition at the bifurcation is of interest because at such a site there is a stagnation point where the velocity and velocity gradient are zero, and not far away is a region of a high velocity gradient (15).

The shear stress acting on the wall is non-uniform. Highest shear in arteries is often reached in the neighbourhood of a bifurcation. Interestingly the lowest shear also occurs in this neighbourhood (at the stagnation point). Regions of low and high wall shear could be the reasons for abnormal expansion and contraction of the artery walls (15).

### 2.2 Preliminary Work

#### 2.2.1 Steady state analysis and Laminar flow

It is well known that blood flow in arteries is transient. Past papers have shown that the difference in qualitative analysis of hemodynamic variables when modelling steady state or transient is virtually indistinguishable (27). Many scientific publications have simulated blood flow in arteries using the same assumption. The time and computational power required for steady state analysis is also significantly less compared to transient analysis.

At the bifurcation region there is an increase in resistance due to local disturbance experienced by the flow. In these deviations from the Poiseulle flow the governing parameter is the Reynolds number (Re), which is the ratio of the inertial forces to the viscous forces in the flow. The Re for the given geometry and flow conditions is 300, hence flow is laminar.

#### 2.2.2 Geometry

The geometry of the bifurcating artery was modelled using Solid works. A section of the MCA was chosen as treatment of aneurysms at this location often leads to bad clinical outcomes when treated with coils, hence the use of FDS is common at this location.

A perfectly symmetrical idealized geometry was created so as to isolate the effects of diameter ratio on hemodynamic variables.

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Figure 2.1: Solid works geometry (lengths in mm)

The inlet and exit lengths are long enough to ensure that the effects of flow disturbance at the bifurcation (ex. pressure gradients in the radial direction) are negligible and the flow is fully developed after the inlet and outlets.

For laminar flow

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Equation 2.1

Using Equation 2.1, the inlet length for a Re of 300 is 90mm. Hence, there is sufficient length available for the flow to be fully developed.

How was the range of diameters chosen?

Murray’s law is a theoretical concept that relates the diameter of the parent vessel to that of the bifurcating vessels. It was derived to determine the vessel radius that required the minimum expenditure of energy by the vessel. (15) For a bifurcating artery the law reduces to

Equation 2.2

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[illustration not visible in this excerpt]is the diameter of the parent artery.

[illustration not visible in this excerpt] and [illustration not visible in this excerpt] are the diameters of the bifurcating arteries.

The range of diameters (Table 3.1, Section 3) was selected following Murray’s law.

#### 2.2.3 Properties of Blood

Blood is a Non-Newtonian fluid which means that there is a non- linear relationship between the shear stress and shear rate. Its viscosity decreases with increasing shear rate. Mathematical models in human physiology have suggested that the viscosity of blood is roughly constant for vessels with diameter larger than 1mm. (27). The arteries modelled in this project are in the range of 2.5 to 5mm. Past papers have shown that there is little difference in qualitative results when modelling blood as a Newtonian fluid. Hence blood has been modelled with a constant viscosity of 0.0035 Pa s and a density of 1060 kg/m3.

#### 2.2.4 Parabolic velocity profile

We know from Poiseulle’s law the velocity of fluid moving through a cylinder as a function of distance from the centre of the tube is given by

Equation 2.3

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Hence at the centre (r = 0) the velocity will be the fastest where R is radius of the cylinder. A uniform parabolic velocity profile has been applied at the inlet of the vessel.

The magnitude of the velocity at the inlet was applied using the formula

Equation 2.4

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For the calculated flow rate and radius of the parent artery, ms-1. This velocity was applied for all simulations.

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Figure 2.2: Parabolic velocity profile at the inlet

#### 2.2.5 Rigid walls assumption

In this project the assumption of rigid walls has been made. This is not a realistic assumption as the arterial walls are compliant. The non-uniform cross sectional area is associated with branching and elastic deformation of the artery wall in response to a non-uniform pressure (with a finite gradient). (15) To model compliance one would have to couple the CFD analysis with a structural analysis where the deformation of the wall is taken into consideration. Past papers have shown that the rigid walls assumption doesn’t affect the qualitative nature of results. Hence, for simplification this assumption has been made.

**[...]**

- Quote paper
- Sarthak Khandelwal (Author), 2015, Effect of flow diverting stents on intracranial artery bifurcations with a focus on bifurcating vessels diameter on hemodynamics and occlusion, Munich, GRIN Verlag, https://www.grin.com/document/311665

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