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Bibliography: leaves 249-279. / xv, 279 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--The University of Adelaide, Dept. of Applied Mathematics, 1999

In this thesis, a parallel solver was developed for the modelling of blood flow through a number of patient-specific geometries. A locally conservative Galerkin (LCG) spatial discretisation was applied along with an artificial compressibility and characteristic based split (CBS) scheme to solve the 3D incompressible Navier-Stokes equations. The Spalart-Allmaras one equation turbulence model was also optionally employed. The solver was constructed using FORTRAN and the Message Passing Interface (MPI). Parallel testing demonstrated linear or better than linear speedup on hybrid patient-specific meshes. These meshes were unstructured with structured boundary layers. From the parallel testing it is clear that the significance of inter-processor communication is negligible in a three dimensional case. Preliminary tests on a short patient-specific carotid geometry demonstrated the need for ten or more boundary layer meshes in order to sufficiently resolve the peak wall shear stress (WSS) along with the peak time-averaged WSS. A time sensitivity study was also undertaken along with the assessment of the order of the real time step term. Three backward difference formulae (BDF) were tested and no significant difference between them was detected. Significant speedup was possible as the order of time discretisation increased however, making the choice of BDF important in producing a timely solution. Followed by the preliminary investigation, four more carotid geometries were investigated in detail. A total of six haemodynamic wall parameters have been brought together to analyse the regions of possible atherogenesis within each carotid. The investigations revealed that geometry plays an overriding influence on the wall parameter distribution. Each carotid artery displayed high time-averaged WSS at the apex, although the value increased significantly with a proximal stenosis. Two out of four meshes contained a region of low time-averaged WSS distal to the flow divider and within the largest connecting artery (internal or external carotid artery), indicating a potential region of atherosclerosis plaque formation. The remaining two meshes already had a stenosis in the corresponding region. This is in excellent agreement with other established works. From the investigations, it is apparent that a classification system of stenosis severity may be possible with potential application as a clinical diagnosis aid. Finally, the flow within a thoracic aortic aneurysm was investigated in order to assess the influence of a proximal folded neck. The folded neck had a significant effect on the wall shear stress, increasing by up to 250% over an artificially smoothed neck. High wall shear stresses may be linked to aneurysm rupture. Being proximal to the aneurysm, this indicated that local geometry should be taken into account when assessing the rupture potential of an aneurysm.

Background. Extensive studies have been conducted to simulate blood flow in the human vasculature using nonlinear equations of pulsatile flow in collapsible tube plus a network of vessels to represent the whole vasculature and the cerebral circulation. For non-linear models numerical solutions are obtained for the fluid flow equations. Methods. Equations of fluid motion in collapsible tubes were developed in the presence of gravitational force (Gforce). The Lax-Wendroff and MacCormack methods were used to solve the governing equations and compared both in terms of accuracy, convergence, and computer processing (CPU) time. A modified vasculature of the whole body and the cerebral circulation was developed to obtain a realistic simulation of blood flow under different conditions. The whole body vasculature was used to validate the simulation in terms of input impedance and wave transmission. The cerebral vasculature was used to simulate conditions such as presence of G-force, blockage of Internal Carotid Artery (ICA), and the effects on cerebral blood flow of changes in mean and pulse pressure. Results. The simulation results for zero G-force were in very good agreement with published experimental data as was the simulation of cerebral blood flow. Both numerical methods for solutions of governing equations gave similar results for blood flow simulations but differed in calculation performance and stability depending on levels of G-force. Simulation results for uniform and sinusoidal G-force are also in good agreement with published experimental results, Blood flow was simulated in the presence of a single (left) carotid artery obstruction with varying morphological structures of the Circle of Willis (CoW). This simulation showed significant differences in contralateral blood flow in the presence or absence of communicating arteries in the CoW. It also was able to simulate the decreases in blood flow in the cerebral circulation compartment corresponding to the visual cortex in the presence of G-force. This is consistent with the known loss of vision under increased acceleration. Conclusions. This study has shown that under conditions of gravitational forces physiological changes in blood flow in the systemic and cerebral vasculature can be simulated realistically by solving the one-dimentional fluid flow equations and non-linear vascular properties numerically. The simulation was able to predict changes in blood flow with different configurations and properties of the vascular network.

A four variable constitutive equation was developed utilizing the method first presented by Schneck and Walburn. Spearman rank correlation coefficients were calculated on whole blood samples within a narrow range of hematocrit to investigate further the effect of the various plasma constituents on whole blood viscosity. Viscosity measurements were made on one hundred anticoagulated blood samples of known hematocrit and chemical composition. The constitutive equation was developed using a power law functional form similar to that employed by Schneck and Walburn. This equation contains two parameters, the consistency index and the non-Newtonian index. A computerized multiple regression technique with apparent viscosity as the dependent variable was used to determine the particular form of these parameters. The one, two and three variable models developed confirmed the results of the previous work of Schneck and Walburn. The four variable model included the total lipids in combination with the concentration of total protein minus albumin and hematocrit. Spearman rank correlation coefficients showed the highest correlations between whole blood viscosity and the plasma constituents to be those of the globulins, total protein and fibrinogen. The constitutive equation developed did not show as high a correlation between experimental data and theory as did the Schneck-Walburn three variable model. The addition of a fourth variable did produce a statistically significant increase over the best three variable model of the present study. / M.S.

It was generally accepted that the rate of formation of cerebrospinal °uid (CSF) is independent of intraventricular pressure [26], until A. Sahar and a host of other scientists challenged this belief. A. Sahar substantiated his belief that the rate of (CSF) formation actually depends on intraventricular pressure, see A. Sahar, 1971 [26]. In this work we show that CSF formation depends on some other factors, including the intraventricular pressure. For the purpose of this study, we used the capillary blood °ow model proposed by K.Boryczko et. al., [5] in which blood °ow in the microvessels was modeled as a two-phase °ow; the solid and the liquid volume phase. CSF is formed from the blood plasma [23] which we assume to be in the liquid volume phase. CSF is a Newtonian °uid [2, 23]. The principles and methods of e®ective area" developed by N. Sauer and R. Maritz [21] for studying the penetration of °uid into permeable walls was used to investigate the ¯ltrate momentum °ux from the intracranial capillary wall through the pia mater and epithelial layer of the choroid plexus into the subarachnoid space. We coupled the dynamic boundary equation with the Navier-Stoke's constitutive equation for incompressible °uid, representing the °uid °ow in the liquid volume phase in the capillary to arrive at our model. / Mathematical sciences / M.Sc.

It was generally accepted that the rate of formation of cerebrospinal °uid (CSF) is independent of intraventricular pressure [26], until A. Sahar and a host of other scientists challenged this belief. A. Sahar substantiated his belief that the rate of (CSF) formation actually depends on intraventricular pressure, see A. Sahar, 1971 [26]. In this work we show that CSF formation depends on some other factors, including the intraventricular pressure. For the purpose of this study, we used the capillary blood °ow model proposed by K.Boryczko et. al., [5] in which blood °ow in the microvessels was modeled as a two-phase °ow; the solid and the liquid volume phase. CSF is formed from the blood plasma [23] which we assume to be in the liquid volume phase. CSF is a Newtonian °uid [2, 23]. The principles and methods of e®ective area" developed by N. Sauer and R. Maritz [21] for studying the penetration of °uid into permeable walls was used to investigate the ¯ltrate momentum °ux from the intracranial capillary wall through the pia mater and epithelial layer of the choroid plexus into the subarachnoid space. We coupled the dynamic boundary equation with the Navier-Stoke's constitutive equation for incompressible °uid, representing the °uid °ow in the liquid volume phase in the capillary to arrive at our model. / Mathematical sciences / M.Sc.