Parameter quantification for oxygen transport in the human brain

Oxygen is carried to the brain by blood flow through generations of vessels across a wide range of length scales. This multi-scale nature of blood flow and oxygen transport poses challenges on investigating the mechanisms underlying both healthy and pathological states through imaging techniques alone. Recently, multi-scale models describing whole brain perfusion and oxygen transport have been developed. Such models rely on effective parameters that represent the microscopic properties. While parameters of the perfusion models have been characterised, those for oxygen transport are still lacking. In this study, we set to quantify the parameters associated with oxygen transport and their uncertainties. We first present a multi-scale, multi-compartment oxygen transport model based on a porous continuum approach. We then determine the effective values of the model parameters. By using statistically accurate capillary networks, geometric parameters (vessel volume fraction and surface area to volume ratio) that capture the microvascular topologies are found to be 1.42% and 627 [mm ² /mm ³ ], respectively. These values compare well with those obtained from human and monkey vascular samples. In addition, maximum consumption rates of oxygen are optimised to uniquely define the oxygen distribution over depth. Simulation results from a one-dimensional tissue column show qualitative agreement with experimental measurements of tissue oxygen partial pressure in rats. We highlight the importance of anatomical accuracy through simulation performed within a patient-specific brain mesh. Finally, one-at-a-time sensitivity analysis reveals that the oxygen model is not sensitive to most of its parameters; however, perturbations in oxygen solubilities and plasma to whole blood oxygen concentration ratio have a considerable impact on the tissue oxygenation. These findings demonstrate the validity of using a porous continuum approach to model organ-scale oxygen transport and draw attention to the significance of anatomy and certain parameter values.