A new framework for assessing subject-specific whole brain circulation and perfusion using MRI-based measurements and a multi-scale continuous flow model

Abstract

A large variety of severe medical conditions involve alterations in microvascular circulation. Hence, measurements or simulation of circulation and perfusion has considerable clinical value and can be used for diagnostics, evaluation of treatment efficacy, and for surgical planning. However, the accuracy of traditional tracer kinetic one-compartment models is limited due to scale dependency. As a remedy, we propose a scale invariant mathematical framework for simulating whole brain perfusion. The suggested framework is based on a segmentation of anatomical geometry down to imaging voxel resolution. Large vessels in the arterial and venous network are identified from time-of-flight (ToF) and quantitative susceptibility mapping (QSM). Macro-scale flow in the large-vessel-network is accurately modelled using the Hagen-Poiseuille equation, whereas capillary flow is treated as two-compartment porous media flow. Macro-scale flow is coupled with micro-scale flow by a spatially distributing support function in the terminal endings. Perfusion is defined as the transition of fluid from the arterial to the venous compartment. We demonstrate a whole brain simulation of tracer propagation on a realistic geometric model of the human brain, where the model comprises distinct areas of grey and white matter, as well as large vessels in the arterial and venous vascular network. Our proposed framework is an accurate and viable alternative to traditional compartment models, with high relevance for simulation of brain perfusion and also for restoration of field parameters in clinical brain perfusion applications.

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“…On the macro-scale, full organ models of blood flow in the brain have been developed [30,31]. These models treat the microvasculature in the brain as a continuous porous medium, effectively smoothing out the local topology and variations in blood flow.…”

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“…We, therefore, use homogenized models for the distribution of number and size of penetrating vessels over the cortex and for the downstream microvascular beds. Such homogenized models are based on porous media physics and include a description of perfusion in terms of Darcy's law, considering the anisotropic nature of the vascular bed (46,47). Essentially all arteries, but notably the arterioles have significant resistance for perfusion.…”

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“…the exchange of oxygenated blood with deoxygenated blood in the capillary bed. The driving force for perfusion is the pressure difference between the two compartments [8].…”

“…However, the computational cost of this approach limits its applicability at a clinically relevant scale. In a recent study [8], Hodneland et al treat vessels as a 1D network model and the capillary bed as a 3D continuum model, thus decreasing significantly the computational cost and allowing for full brain simulations. It must be mentioned, however, that 1D models have a reduction in accuracy when compared to full 3D models, in particular when applied to describe large vessels [9].…”

“…The purpose of the fluid distribution function is to reflect the micro-vessel structure surrounding each terminal node. Differently from [8], we look at the impact of nonlinear interactions between pressure and flow, as well as the role of vessel bifurcations in the flow network. Our model was developed with a minimum number of boundary conditions and unknown parameter settings to obtain result purely from governing equations and the given anatomy.…”