Abstract
The cerebral microvasculature plays a vital role in adequately supplying blood to the brain. Determining the health of the cerebral microvasculature is important during pathological conditions, such as stroke and dementia. Recent studies have shown the complex relationship between cerebral metabolic rate and transit time distribution, the transit times of all the possible pathways available dependent on network topology. In this paper, we extend a recently developed technique to solve for residue function, the amount of tracer left in the vasculature at any time, and transit time distribution in an existing model of the cerebral microvasculature to calculate cerebral metabolism. We present the mathematical theory needed to solve for oxygen concentration followed by results of the simulations. It is found that oxygen extraction fraction, the fraction of oxygen removed from the blood in the capillary network by the tissue, and cerebral metabolic rate are dependent on both mean and heterogeneity of the transit time distribution. For changes in cerebral blood flow, a positive correlation can be observed between mean transit time and oxygen extraction fraction, and a negative correlation between mean transit time and metabolic rate of oxygen. A negative correlation can also be observed between transit time heterogeneity and the metabolic rate of oxygen for a constant cerebral blood flow. A sensitivity analysis on the mean and heterogeneity of the transit time distribution was able to quantify their respective contributions to oxygen extraction fraction and metabolic rate of oxygen. Mean transit time has a greater contribution than the heterogeneity for oxygen extraction fraction. This is found to be opposite for metabolic rate of oxygen. These results provide information on the role of the cerebral microvasculature and its effects on flow and metabolism. They thus open up the possibility of obtaining additional valuable clinical information for diagnosing and treating cerebrovascular diseases.
Highlights
Estimates of cerebral blood flow (CBF), mean transit time (MTT), oxygen extraction fraction (OEF) and cerebral metabolic rate of oxygen (CMRO2) using imaging modalities have been widely used in clinical studies to diagnose ischaemic lesions, where CBF is the flow of blood per volume of tissue, MTT is the ratio of the cerebral blood volume (CBV) to CBF, with CBV being the volume of blood per volume of tissue, OEF is the fraction of oxygen removed from the blood in the capillary network by the tissue and CMRO2 is the product of CBF and OEF
There is no significant difference between the mean values in CBV, MTT, mean absolute deviation transit time (MADTT), OEF and CMRO2 for the three cube sizes as expected since these are determined by the morphological, blood and tissue properties, which were matched for all cube sizes
An extension to a recently developed mathematical technique to solve for the residue function in a capillary network with matching physiological topology has been developed here to solve for OEF and
Summary
Estimates of cerebral blood flow (CBF), mean transit time (MTT), oxygen extraction fraction (OEF) and cerebral metabolic rate of oxygen (CMRO2) using imaging modalities have been widely used in clinical studies to diagnose ischaemic lesions, where CBF is the flow of blood per volume of tissue, MTT is the ratio of the cerebral blood volume (CBV) to CBF, with CBV being the volume of blood per volume of tissue, OEF is the fraction of oxygen removed from the blood in the capillary network by the tissue and CMRO2 is the product of CBF and OEF. Studies using positron emission tomography have shown regions of brain tissue surviving during ischaemia Such tissue is characterised by a reduction in CBF and an increase in oxygen extraction to meet the necessary metabolic demand [1,2]. Linninger et al [4] applied this to understand oxygen exchange between blood vessels and brain cells by quantifying oxygen advection in the microcirculation, tissue oxygen perfusion and oxygen consumption. Such artificial networks have been used to develop continuum models of blood flow in capillary network [5] using a multi-scale homogenization method proposed by Shipley and Chapman [6]
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