Computational Modelling of Capillaries in Neuro-Vascular Coupling
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
The analysis of hemodynamic parameters and functional reactivity of cerebral capillaries is still controversial. The detailed mapping of tissue oxygen levels on the scale of micrometers cannot be obtained by means of an experimental approach, necessitating the use of theoretical methods in this investigating field. To assess the hemodynamics and oxygen transport in the cortical capillary network, 2D and 3D generic models are constructed (non-tree like) using random voronoi tessellation in which each edge represents a capillary segment. The modelling presented here is based on morphometric parameters extracted from physiological data of the cortex in which the spatial distribution of the diameter of the capillary is based on a Modified Murray method. This method led to a proper link between the diameter topology and flow pattern such that the maximum efficiency for flowing blood is concluded in the model of cortical capillary network. The approach is capable of creating an appropriate generic, realistic model of a cerebral capillary network relating to each part of the brain cortex because its geometrical density is able to vary the capillary density. The pertinent hemodynamic parameters are obtained by numerical simulation based on effective blood viscosity as a function of hematocrit and microvessel diameter, ESL (endothelial surface layer) effect, phase separation and plasma skimming effects. Using a solution method of the Green's function, the model is numerically developed to provide different simulations of oxygen transport for varying perfusion and metabolism in a mesoscale model of the cortical capillary network, bridging smaller and larger scale phenomena. The analysis of hemodynamic parameters (blood flow rate, velocity and hematocrit) demonstrates a consistency with the experimental observation. The distribution pattern of wall shear stress (WSS) in the network model supports the physiological data which in turn represents a proper matching between the hemodynamics and morphometrics in the cerebral capillary network. The distributions of blood flow throughout the 2D and 3D models seem to confirm the hypothesis in which all capillaries in a cortical network are recruited at rest (normal condition). The predictions showed a heterogeneous distribution in the flow pathways (aspect of length and inflow) and the pertinent transit time of red blood cell (RBC) in the network model which is dependent on varying perfusion rates. The analyses of oxygen transport in the model has demonstrated that oxygen levels in the tissue are sensitively dependent on the microvascular architecture and flow distribution. Unlike the homogeneous compartmental models, the mesoscale model presented in this study led to a prediction of tissue PO2 gradients throughout the tissue and a spatial distribution of tissue PO2 on the micron-scale for varying perfusion and metabolism. The predicted nonlinear changes in the oxygen extraction fraction (OEF) of the model as a function of the perfusion rate provide a basis for the quantitative interpretation of functional magnetic resonance imaging (fMRI) studies in terms of changes in local perfusion. The model is capable of predicting the brain oxygen metabolism under both normal and disease states, particularly, local hypoxia and local ischemia caused by misery perfusion syndrome. The hypoxic states for different perfusion rates and oxygen consumption rates demonstrated that in a significant decrease in brain perfusion (as can occur in stroke), the tissue hypoxia can be avoided by a moderate reduction in oxygen consumption rate. Increasing oxygen consumption rates (a realization of spatiotemporal stimulation of neural tissue) with respect to maintaining the tissue PO2 in the model led to a predicted flow-metabolism coupling in the model which supports the experimental studies of somatosensory and visual stimulation in humans by positron emission tomography (PET) and functional MRI (magnetic resonance imaging). A disproportionately large increase in blood supply is required for a small increase in the metabolic utilization (oxygen consumption rate) which in turn, is strongly dependent on the resting OEF such that the magnitude of the blood flow increases in the higher resting OEF.