Application of a Second‐Order Control‐Systems Model to Investigate Effects of Impaired Capillary Signalling in Skeletal Muscle on Regulation of Capillary Blood Flow Velocity and Tissue Oxygenation

Abstract

Microcirculation is the main region of the vasculature where oxygen (O2) is transferred directly from blood to metabolically active tissue. Tissue O2 partial pressure (PO2) in the microcirculation has been historically infeasible to measure, but critical as an indicator of capillary and surrounding tissue health. Thus, theoretical modelling of capillary‐tissue O2 transport is crucial as a complement to in vivo experiments in exploring structure‐function relationships in microvascular networks (Ellis et al, Microcirc 2012, 19:5). To properly complement experiments which stimulate O2 flow‐dependent regulation systems, modelling of microcirculatory O2 transport requires incorporation of knowledge on regulatory mechanisms.Capillary networks modulate their blood velocity to recruit sufficient O2 delivery in many local O2 conditions; this has led to the conclusion that endothelium signals upstream to arterioles in an O2‐dependent manner (Ghonaim et al, Microcirc 2021, e12699). Recently, a second‐order control systems model was developed to investigate the interaction between capillary‐tissue O2 transport and O2‐dependent blood flow regulation under an externally applied O2 stimulus. This utilized elements from previous arteriolar diameter alteration models in response to skeletal muscle O2 gradients, as well as elements from a recently developed continuous‐capillary O2 transport model (Afas et al, Math Biosci 2021, 333:108535).The control systems model aimed to predict modulations in blood velocity through endothelial signalling which homogenized outlet capillary PO2 in skeletal muscle. The model demonstrated that variations in O2 transport parameters such as capillary network density and tissue O2 consumption rate had varying effects on the averaged blood velocity in a small skeletal muscle segment perfused by a capillary network. In addition, the externally supplied PO2 had an effect on both blood velocity and the tissue‐capillary O2 balance. While the tissue‐capillary PO2 balance and velocity adaptation were investigated, the endothelial signalling parameters were not reported (Afas & Goldman, Vasc. Bio. 2021, conference).The present study investigates implications of capillary network metric variations on the endothelial signal communicated upstream to modulate capillary blood flow in response to various muscle surface PO2 levels. Constraints imposed by pathogenic impairment of endothelial signalling will be investigated and interpreted in the context of capillary flow regulation.