Parameter quantification for oxygen transport in the human brain

Background and objective: 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. Methods: Effective parameter values of a continuum-based porous multi-scale, multi-compartment oxygen transport model are systematically estimated. In particular, geometric parameters that capture the microvascular topologies are obtained through statistically accurate capillary networks. Maximum consumption rates of oxygen are optimised to uniquely define the oxygen distribution over depth. Simulations are then carried out within a one-dimensional tissue column and a three-dimensional patient-specific brain mesh using the finite element method. Results: Effective values of the geometric parameters, vessel volume fraction and surface area to volume ratio, are found to be 1.42% and 627 [mm2/mm3], 2 /mm 3 ], respectively. These values compare well with those acquired from human and monkey vascular samples. Simulation results of the one-dimensional tissue column show qualitative agreement with experimental measurements of tissue oxygen partial pressure in rats. Differences between the oxygenation level in the tissue column and the brain mesh are observed, which highlights the importance of anatomical accuracy. 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. Conclusions: The findings of this study demonstrate the validity of using a porous continuum approach to model organ-scale oxygen transport and draw attention to the significance of anatomy and parameters associated with inter-compartment diffusion.