Mathematical Modeling of Heterogeneity in Rat Mesenteric Arterioles ‐ A Generative, Modular Framework

Heterogeneity is a hallmark of blood vessels in the microcirculation. An extensive degree of morphological and functional variability is evident on both the cellular and the whole vessel level. The consequences of heterogeneity for the dynamical properties of arterioles is a rather unexplored theme in the field of microcirculation. We present a novel mathematical modeling framework applied to rat mesenteric arterioles. The central idea is the construction of a model generator that can be supplied with a range of morphologies, different ion channel models etc. The output of the model generator is an actual mathematical model of ‐ in this case ‐ the rat mesenteric arteriole to be simulated. Furthermore, the generation of models allows for the specification of some (or all) parameters to be drawn from a normal (or another specific) distribution. Thus, both endothelial and smooth muscle cells may be modeled to have individual properties ‐ depending on e.g. the experimentally measured standard deviations ‐ and accordingly, resemble the experimentally observed tissue heterogeneity. The modeling approach can be used to study vasoreactivity, conduction, synchronicity etc. within the vascular wall depending on the specific aim, and in particular to study the impact of heterogeneity on these phenomena.