Transmural Variation and Anisotropy of Microvascular Flow Conductivity in the Rat Myocardium

Abstract

Transmural variations in the relationship between structural and fluid transport properties of myocardial capillary networks are determined via continuum modelling approaches using recent three-dimensional (3D) data on the microvascular structure. Specifically, the permeability tensor, which quantifies the inverse of the blood flow resistivity of the capillary network, is computed by volume-averaging flow solutions in synthetic networks with geometrical and topological properties derived from an anatomically-detailed microvascular data set extracted from the rat myocardium. Results show that the permeability is approximately ten times higher in the principal direction of capillary alignment (the ‘longitudinal’ direction) than perpendicular to this direction, reflecting the strong anisotropy of the microvascular network. Additionally, a 30% increase in capillary diameter from subepicardium to subendocardium is shown to translate to a 130% transmural rise in permeability in the longitudinal capillary direction. This result supports the hypothesis that perfusion is preferentially facilitated during diastole in the subendocardial microvasculature to compensate for the severely-reduced systolic perfusion in the subendocardium.

Multi-scale homogenization of blood flow in 3-dimensional human cerebral microvascular networks

“…The magnitudes of the errors in these values from the converged permeability ‫ܭ(‬ ) range from around 25 % to 1.6 %. This is in contrast to the error in the mean calculated by Smith et al which has a maximum value of around 70 % for a 100 x 100 x 21.6 µm 3 voxel (Smith et al, 2014). The lack of a sharp increase in permeability at smaller cube sizes is likely to be due to the more random, isotropic nature of the cerebral microvasculature, as opposed to the more aligned myocardial capillaries modelled by Smith et al It is also likely that the much larger density of the longitudinally aligned myocardial capillaries will have partially accounted for this difference.…”

“…It was found that the permeability of the capillaries in the three principal directions was highly isotropic, with less than 1.2 % variation in their converged values. This was due to the "mesh-like" structure of the capillary network, and confirms that when modelling the cerebral microvasculature a 2-dimensional simplification of the model is not a valid assumption, unlike when modelling coronary capillary networks (Smith et al, 2014).…”

“…It is therefore expected that as voxel size increases, the calculated permeability will tend to a converged asymptotic macro permeability, similar to that observed by Smith et al for their simulations of capillary networks in the rat myocardium (Smith et al, 2014).…”

“…In a similar study, Smith et al used the same homogenization methods applied here on synthetic rat coronary capillary networks (Smith et al, 2014). The network was assumed to be 2-dimensional with orthogonal connections between capillaries.…”

“…Therefore, determining the REV of a network is important to minimise computation time. Smith et al have previously used the averaging techniques derived by Shipley and Chapman on a model of non-leaky rat myocardial capillaries (Smith et al, 2014).…”