Tim David

One-dimensional and three-dimensional models of cerebrovascular flow

The Circle of Willis is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. One-dimensional (1D) and three-dimensional (3D) computational fluid dynamics (CFD) models of the Circle of Willis have been created to provide a simulation tool which can potentially be used to identify at-risk cerebral arterial geometries and conditions and replicate clinical scenarios, such as occlusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic autoregulation using a proportional-integral (PI) controller to modify efferent artery resistances to maintain optimal efferent flow rates for a given circle geometry and afferent blood pressure. The models can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures. The 1D model is particularly relevant in this instance, with its fast solution time suitable for real-time clinical decisions. Results show the excellent correlation between models for the transient efferent flux profile. The assumption of strictly Poiseuille flow in the 1D model allows more flow through the geometrically extreme communicating arteries than the 3D model. This discrepancy was overcome by increasing the resistance to flow in the anterior communicating artery in the 1D model to better match the resistance seen in the 3D results.

Endothelial Nitric Oxide Synthase and Calcium Production in Arterial Geometries: An Integrated Fluid Mechanics/Cell Model

It is well known that atherosclerosis occurs at very specific locations throughout the human vasculature, such as arterial bifurcations and bends, all of which are subjected to low wall shear stress. A key player in the pathology of atherosclerosis is the endothelium, controlling the passage of material to and from the artery wall. Endothelial dysfunction refers to the condition where the normal regulation of processes by the endothelium is diminished. In this paper, the blood flow and transport of the low diffusion coefficient species adenosine triphosphate (ATP) are investigated in a variety of arterial geometries: a bifurcation with varying inner angle, and an artery bend. A mathematical model of endothelial calcium and endothelial nitric oxide synthase cellular dynamics is used to investigate spatial variations in the physiology of the endothelium. This model allows assessment of regions of the artery wall deficient in nitric oxide (NO). The models here aim to determine whether 3D flow fields are important in determining ATP concentration and endothelial function. For ATP transport, the effects of a coronary and carotid wave form on mass transport is investigated for low Womersley number. For the carotid, the Womersley number is then increased to determine whether this is an important factor. The results show that regions of low wall shear stress correspond with regions of impaired endothetial nitric oxide synthase signaling, therefore reduced availability of NO. However, experimental work is required to determine if this level is significant. The results also suggest that bifurcation angle is an important factor and acute angle bifurcations are more susceptible to disease than large angle bifurcations. It has been evidenced that complex 3D flow fields play an important role in determining signaling within endothelial cells. Furthermore, the distribution of ATP in blood is highly dependent on secondary flow features. The models here use ATP concentration simulated under steady conditions. This has been evidenced to reproduce essential features of time-averaged ATP concentration over a cardiac cycle for small Womersley numbers. However, when the Womersley number is increased, some differences are observed. Transient variations are overall insignificant, suggesting that spatial variation is more important than temporal. It has been determined that acute angle bifurcations are potentially more susceptible to atherogenesis and steady-state ATP transport reproduces essential features of time-averaged pulsatile transport for small Womersley number. Larger Womersley numbers appear to be an important factor in time-dependent mass transfer.

Numerical Simulation of Local Blood Flow in the Carotid and Cerebral Arteries Under Altered Gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.

A computational model of hemodynamic parameters in cortical capillary networks.

The analysis of hemodynamic parameters and functional reactivity of cerebral capillaries is still controversial. To assess the hemodynamic parameters in the cortical capillary network, a generic model was created using 2D voronoi tessellation in which each edge represents a capillary segment. This method is capable of creating an appropriate generic model of cerebral capillary network relating to each part of the brain cortex because the geometric model is able to vary the capillary density. The modeling presented here is based on morphometric parameters extracted from physiological data of the human cortex. The pertinent hemodynamic parameters were obtained by numerical simulation based on effective blood viscosity as a function of hematocrit and microvessel diameter, phase separation and plasma skimming effects. The hemodynamic parameters of capillary networks with two different densities (consistent with the variation of the morphometric data in the human cortical capillary network) were analyzed. The results show pertinent hemodynamic parameters for each model. The heterogeneity (coefficient variation) and the mean value of hematocrits, flow rates and velocities of the both network models were specified. The distributions of blood flow throughout the both models seem to confirm the hypothesis in which all capillaries in a cortical network are recruited at rest (normal condition). The results also demonstrate a discrepancy of the network resistance between two models, which are derived from the difference in the number density of capillary segments between the models.

Wall Shear Stress Modulation of ATP/ADP Concentration at the Endothelium

AbstractA mathematical model of ATP/ADP reaction at the surface of the endothelium for any two-dimensional or axisymmetric nonsingular functional form of the wall shear stress has been presented. Excellent agreement is obtained with the numerical solution for the parallel plate case. For spatially varying wall shear stress, such as the stagnation point flow and a backward facing step the ATP concentrations are shown to have a maximum at the stagnation point streamline and the reattachment point respectively. Increasing the Reynolds number increases both the ATP and ADP concentrations. For the backward facing step significant spatial variations occur in the concentration. Hence, a strong controlling factor for physiological kinetic values is the geometry of the arterial vessel since this determines the wall shear stress and thence the transport to the reactive surface. The area of high concentration also occurs where the wall shear stress is low (limiting case is zero shear stress). Atherosclerotic plaques are known to occur in areas of low wall shear stress and at vessel bifurcations where the wall shear stress is spatially varying. The ATP/ADP concentrations at these particular points may very well contribute to the formation of plaques.

Lumped Parameter and Feedback Control Models of the Auto-regulatory Response in the Circle of Willis

The Circle of Willis (CoW) is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. A 1-dimensional model of the CoW has been created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or string-like circulus vessels, or arterial infarctions. The model captures cerebral haemodynamic auto-regulation by using a proportional-integral-derivative (PID) controller to modify efferent resistances and maintain optimal efferent flowrates for a given circle geometry and afferent blood pressure. Results match limited clinical data and results obtained in prior studies to within 6%. In addition, a set of boundary conditions and geometry is presented for which the auto-regulated system cannot provide the necessary efferent flowrates and perfusion, representing a condition with increased risk of stroke and highlighting the importance of modelling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.

Dynamic myogenic autoregulation in the rat kidney: a whole-organ model

A transient 1D mathematical model of whole-organ renal autoregulation in the rat is presented, examining the myogenic response on multiple levels of the renal vasculature. Morphological data derived from micro-CT imaging were employed to divide the vasculature via a Strahler ordering scheme. A previously published model of the myogenic response based on wall tension is expanded and adapted to fit the response of each level, corresponding to a distally dominant resistance distribution with the highest contributions localized to the afferent arterioles and interlobular arteries. The mathematical model was further developed to include the effects of in vivo viscosity variation and flow-induced dilation via endothelial nitric oxide production. Computer simulations of the autoregulatory response to pressure perturbations were examined and compared with experimental data. The model supports the hypothesis that change in circumferential wall tension is the catalyst for the myogenic response. The model provides a basis for examining the steady state and transient characteristics of the whole-organ renal myogenic response in the rat, as well as the modulatory influences of metabolic and hemodynamic factors.

A Computational Model of Oxygen Transport in the Cerebrocapillary Levels for Normal and Pathologic Brain Function

The oxygen exchange and correlation between the cerebral blood flow (CBF) and cerebral metabolic rate of oxygen consumption (CMRO2) in the cortical capillary levels for normal and pathologic brain functions remain the subject of debate. A 3D realistic mesoscale model of the cortical capillary network (non-tree like) is constructed using a random Voronoi tessellation in which each edge represents a capillary segment. The hemodynamics and oxygen transport are numerically simulated in the model, which involves rheological laws in the capillaries, oxygen diffusion, and non-linear binding of oxygen to hemoglobin, respectively. The findings show that the cerebral hypoxia due to a significant decreased perfusion (as can occur in stroke) can be avoided by a moderate reduction in oxygen demand. Oxygen extraction fraction (OEF) can be an important indicator for the brain oxygen metabolism under normal perfusion and misery-perfusion syndrome (leading to ischemia). The results demonstrated that a disproportionately large increase in blood supply is required for a small increase in the oxygen demand, which, in turn, is strongly dependent on the resting OEF. The predicted flow-metabolism coupling in the model supports the experimental studies of spatiotemporal stimulations in humans by positron emission tomography and functional magnetic resonance imaging.

Comprehensive clinical assessment of home-based older persons within New Zealand: an epidemiological profile of a national cross-section.

Objective: Since 2012, all community care recipients in New Zealand have undergone a standardised needs assessment using the Home Care International Residential Assessment Instrument (interRAI‐HC). This study describes the national interRAI‐HC population, assesses its data quality and evaluates its ability to be matched.

Computer Model of Nucleotide Transport in a Realistic Porcine Aortic Trifurcation

Adenosine triphosphate (ATP) is a ubiquitous blood borne agonist which is responsible for the regulation of vascular tone via purinogenic signalling pathways. The present study models the transport of ATP in a realistic porcine aortic trifurcation, which includes multiple branches and bifurcations. The focus of the present study is understanding how pulsatile flow effects mass transfer, observing both mean and transient variations. Unlike in the many idealized models which model transport of low diffusion coefficient species, the realistic geometry leads to very different mass transfer characteristics. These include spiral patterns in the distribution of low concentration fluid. Furthermore, the mean ATP distribution was found to be elevated compared with the steady state; this is attributed to the effects of convective mixing. The results strongly implicate that under certain conditions mass transport in pulsatile flow exhibits different hydrolysis characteristics at the endothelium compared with steady state. Transient variations throughout the the cardiac cycle were found to be small. This small transient response is primarily due to low ATP diffusivity.