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

Abstract

Microcirculation in skeletal muscle determines both blood flow distribution and O2 transport. The partial pressure of oxygen (PO2) is a prime candidate to assess in tissue, as PO2 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 (SO2) measurements, are unable to directly assess skeletal muscle tissue PO2. Instead, modern microcirculatory O2 analysis relies on biophysical models to recreate tissue PO2 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 O2 diffusion, capillary O2 convection, tissue O2 consumption, and capillary-tissue O2 transfer. This model was developed to study an IVVM protocol involving a controlled exposure of skeletal muscle using an O2 exchange chamber. In the protocol studied, hemodynamic parameters in the skeletal muscle region near to the O2 chamber are experimentally shown to exhibit substantial variations. The prevailing theory is capillary perfusion limits the depth of penetration of the chamber O2, and local hemodynamic parameter responses serve to regulate capillary SO2 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 PO2 distributions and was solved using traditional math techniques such as operator decoupling and Fourier decomposition, and exhibited the ability to rapidly and accurately calculate PO2 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 O2 transport, to observe the interaction of both skeletal muscle layers. This is achieved by assuming baseline hemodynamic parameters in the layer far from the O2 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 O2 chamber will be modelled by the a-priori fixing of parameters in the region far from the O2 chamber and allowing near-layer parameters to be perturbed. Several parameters, including capillary density φ, velocity vB, inlet saturation SIN, hematocrit HT, 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 O2 profiles will be visualized, as well as the conditions under which the capillary SO2 is homogenized in both layers of skeletal muscle.