Computational Modeling of Oxygen Transport in the Microcirculation: From an Experiment-Based Model to Theoretical Analyses

Abstract

Oxygen supply to cells by the cardiovascular system involves multiple physical and chemical processes that aim to satisfy fluctuating metabolic demand. Regulation mechanisms range from increased heart rate to minute adaptations in the microvasculature. The challenges and limitations of experimental studies in vivo make computational models an invaluable complement. In this thesis, oxygen transport from capillaries to tissue is investigated using a new numerical model that is tailored for validation with experimental data. On this basis, theoretical analyses of tissue oxygenation and intravascular oxygen distribution are conducted with applications to blood flow regulation mechanisms and heterogeneity in microvascular networks. The computational model developed here employs moving red blood cells (RBCs) in the frame of reference of the tissue. This key feature enables direct result comparison to oxygen measurements in capillaries and tissue. Thus, the first model validation with micrometric-resolution measurements of oxygen partial pressure (PO2) in vivo could be performed. This novel technique is used to describe the complex relation between hemoglobin saturation and plasma PO2 which manifests itself by the presence of erythrocyte-associated transients. Dynamic regulation mechanisms of microvascular blood flow in the brain were modeled. The effect of individual pericyte-induced capillary dilations was investigated in a simple capillary network. Although a slight increase in tissue PO2 was observed, multiple dilations need to simultaneously occur to produce a response comparable to the effect of arteriolar dilations. The dependence of tissue oxygenation on hematocrit and blood velocity was also described. Based on analytical tools supported by the computational model, the relative influence of hematocrit was demonstrated to be stronger. The complex topology of microvascular networks entails a certain degree of heterogeneity in oxygen supply. Excessive variations in RBC transit times through the microvasculature have been associated to conditions such as diabetes, Alzheimer’s disease and hypertension. Their relation with hemoglobin saturation heterogeneity was modeled based on the computational and analytical tools developed here. Diffusive interaction within and between capillaries was shown to lead to a considerable reduction of hemoglobin saturation heterogeneity at the scale of neighboring capillaries. These findings may substantially affect the interpretation of RBC transit time measurements in health and disease. The state-of-the-art technique for high-resolution oxygen measurements in vivo is currently two-photon phosphorescence lifetime microscopy (2PLM). To address uncertainties related to photochemical consumption of oxygen, a numerical model for 2PLM that includes oxygen diffusion and removal by organic molecules was devised. The ensuing potential underestimation of PO2 can be quantified, thereby allowing to choose experimental parameters to avoid systematic errors and photodamage of the region of interest. This model, along with the rest of this thesis, considerably improves the synergy between theoretical modeling and experimental studies in the context of microvascular oxygen transport.