Model‐based analysis of microcirculatory parameters affecting O ₂ transport in skeletal muscle subjected to fixed surface PO ₂

Microcirculation in skeletal muscle determines both blood flow distribution and O 2 transport. The partial pressure of oxygen (PO 2 ) is a prime candidate to assess in tissue, as PO 2 variations herald a functionality decline in skeletal muscle. Traditional non‐invasive microcirculatory techniques such as Intra‐vital Video Microscopy (IVVM) allowing for blood velocity and capillary saturation (SO 2 ) measurements, are unable to directly assess skeletal muscle tissue PO 2 . Instead, modern microcirculatory O 2 analysis relies on biophysical models to recreate tissue PO 2 distributions. (Ellis et al, Microcirc 2012 , 19:5). Recently, a continuous coupled partial differential equation (PDE) model of two layers of skeletal muscle coupled via diffusion at their boundaries was developed accounting for tissue O 2 diffusion, capillary O 2 convection, tissue O 2 consumption, and capillary‐tissue O 2 transfer. This model was developed to study an IVVM protocol involving a controlled exposure of skeletal muscle using an O 2 exchange chamber. In the protocol studied, hemodynamic parameters in the skeletal muscle region near to the O 2 chamber are experimentally shown to exhibit substantial variations. The prevailing theory is capillary perfusion limits the depth of penetration of the chamber O 2 , and local hemodynamic parameter responses serve to regulate capillary SO 2 in skeletal muscle; this would be towards either a fixed target value or homogeneity with neighboring capillary modules. The coupled PDE two‐layer model was developed for steady‐state PO 2 distributions and was solved using traditional math techniques such as operator decoupling and Fourier decomposition, and exhibited the ability to rapidly and accurately calculate PO 2 distributions in skeletal muscle which agreed with experimental values. (Afas and Goldman, Vasc Bio 2020 ). The solution affords for the unique ability not allowed in previous convection‐diffusion analytic models of O 2 transport, to observe the interaction of both skeletal muscle layers. This is achieved by assuming baseline hemodynamic parameters in the layer far from the O 2 chamber and allowing the near layer to take on a range of parameter variations; these variations can be compared to experimental observations. In this study, the behavior of both layers of skeletal muscle adjacent to an O 2 chamber will be modelled by the a‐priori fixing of parameters in the region far from the O 2 chamber and allowing near‐layer parameters to be perturbed. Several parameters, including capillary density φ, velocity v B , inlet saturation S IN , hematocrit H T , and tissue consumption μ will have this variation method applied from previous baselines (Afas et al, Math Biosci 2021 , in press ), and the resultant two‐layer O 2 profiles will be visualized, as well as the conditions under which the capillary SO 2 is homogenized in both layers of skeletal muscle.

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