Multiscale modeling of human cerebrovasculature: A hybrid approach using image-based geometry and a mathematical algorithm

Abstract

The cerebral vasculature has a complex and hierarchical network, ranging from vessels of a few millimeters to superficial cortical vessels with diameters of a few hundred micrometers, and to the microvasculature (arteriole/venule) and capillary beds in the cortex. In standard imaging techniques, it is difficult to segment all vessels in the network, especially in the case of the human brain. This study proposes a hybrid modeling approach that determines these networks by explicitly segmenting the large vessels from medical images and employing a novel vascular generation algorithm. The framework enables vasculatures to be generated at coarse and fine scales for individual arteries and veins with vascular subregions, following the personalized anatomy of the brain and macroscale vasculatures. In this study, the vascular structures of superficial cortical (pial) vessels before they penetrate the cortex are modeled as a mesoscale vasculature. The validity of the present approach is demonstrated through comparisons with partially observed data from existing measurements of the vessel distributions on the brain surface, pathway fractal features, and vascular territories of the major cerebral arteries. Additionally, this validation provides some biological insights: (i) vascular pathways may form to ensure a reasonable supply of blood to the local surface area; (ii) fractal features of vascular pathways are not sensitive to overall and local brain geometries; and (iii) whole pathways connecting the upstream and downstream entire-scale cerebral circulation are highly dependent on the local curvature of the cerebral sulci.

Mathematical synthesis of the cortical circulation for the whole mouse brain—part II: Microcirculatory closure

“…Mathematical models of cerebral circulation for hemodynamic simulations combine biophysical principles with vascular anatomical data from medical images. Increasingly, models are becoming an indispensable research tool to integrate and reconcile direct imaging observations, [1][2][3][4][5][6] predict cerebral blood flow patterns, [7][8][9][10][11][12][13][14][15][16] oxygen-exchange from blood vessels to tissue, 11,12 elucidate mechanisms of blood flow control, and quantify disruption in pathological states. [17][18][19][20] Previously, we identified shortcomings when reconstructing vascular anatomical networks from raw image data.…”

Adaptive constrained constructive optimisation for complex vascularisation processes

“…In particular, the family of CCO algorithms addresses different types of study involving the influence of anatomical variability 44 , 49 – 53 , bifurcation asymmetries 42 , 54 , 55 , fractal properties 56 , staged-growth 46 , 57 , shear stress distribution 58 , 59 , among others 43 , 60 – 62 . Variants have also been proposed either to recreate more complex vascular networks in hollow organs 23 , 43 , 44 , 46 , 63 , 64 , or to speed-up the construction of such networks 46 , 65 . More recently, cases of territories supplied by multiple inlet vessels were the focus of attempts to tackle more realistic scenarios.…”

“…More recently, cases of territories supplied by multiple inlet vessels were the focus of attempts to tackle more realistic scenarios. In Blanco et al 45 , Ii et al 46 and Di Gregorio et al 47 , partitioning of a territory into subdomains was proposed so that the CCO algorithm could independently be applied to vascularise non-overlapping subdomains. Meanwhile, Jaquet et al 43 , 66 proposed to solve concurrency by assigning a relative flow quota for each input, while those who temporally exceed their quota are put on hold.…”

“…Meanwhile, Jaquet et al 43 , 66 proposed to solve concurrency by assigning a relative flow quota for each input, while those who temporally exceed their quota are put on hold. Additionally, the latest works focused on describing whole-organ microvasculature 46 , 67 defining multiple steps to generate a physiologically accurate tree. Each strategy defines different ad-hoc steps depending on the specific organ.…”

“…For example, the use of fractal networks to assess closure boundary conditions in hemodynamic simulations 70 , 71 , or the use of CCO networks to predict the arteriolar pressure in the brain 72 . More detailed generated networks have been proposed for heart 43 , 47 , 66 and brain 46 , 67 following a methodology specific for the organ of interest.…”