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Brain metabolism is highly dependent on continuous oxygen supply. Cortical microvascular networks exhibit heterogeneous blood flow, leading to non-uniform tissue oxygenation and capillary hemoglobin saturation. We recently proposed capillary outflow saturation heterogeneity (COSH) to represent effects of heterogeneity on oxygen supply to tissue regions most vulnerable to hypoxia, and showed that diffusive oxygen exchange among red blood cells within capillaries and among capillaries (diffusive interaction) significantly reduces COSH in simplified geometrical configurations. Here, numerical simulations of oxygen transport in capillary network geometries derived from mouse somatosensory cortex are presented. Diffusive interaction was found to reduce COSH by 41 to 62% compared to simulations where diffusive interaction was excluded. Hemoglobin saturation drop across the microvascular network is strongly correlated with red blood cell transit time, but the coefficient of variation of saturation drop is approximately one third lower. Unexpectedly, the radius of the tissue cylinder supplied by a capillary correlates weakly with the anatomical tissue cylinder radius, but strongly with hemoglobin saturation. Thus, diffusive interaction contributes greatly to the microcirculation's ability to achieve tissue oxygenation, despite heterogeneous capillary transit time and hematocrit distribution. These findings provide insight into the effects of cerebral small vessel disease on tissue oxygenation and brain function., Frontiers in Physiology, 9, ISSN:1664-042X

Capillary dysfunction impairs oxygen supply to parenchymal cells and often occurs in Alzheimer's disease, diabetes and aging. Disturbed capillary flow patterns have been shown to limit the efficacy of oxygen extraction and can be quantified using capillary transit time heterogeneity (CTH). However, the transit time of red blood cells (RBCs) through the microvasculature is not a direct measure of their capacity for oxygen delivery. Here we examine the relation between CTH and capillary outflow saturation heterogeneity (COSH), which is the heterogeneity of blood oxygen content at the venous end of capillaries. Models for the evolution of hemoglobin saturation heterogeneity (HSH) in capillary networks were developed and validated using a computational model with moving RBCs. Two representative situations were selected: a Krogh cylinder geometry with heterogeneous hemoglobin saturation (HS) at the inflow, and a parallel array of four capillaries. The heterogeneity of HS after converging capillary bifurcations was found to exponentially decrease with a time scale of 0.15–0.21 s due to diffusive interaction between RBCs. Similarly, the HS difference between parallel capillaries also drops exponentially with a time scale of 0.12–0.19 s. These decay times are substantially smaller than measured RBC transit times and only weakly depend on the distance between microvessels. This work shows that diffusive interaction strongly reduces COSH on a small spatial scale. Therefore, we conclude that CTH influences COSH yet does not determine it. The second part of this study will focus on simulations in microvascular networks from the rodent cerebral cortex. Actual estimates of COSH and CTH will then be given., Frontiers in Physiology, 9, ISSN:1664-042X

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.

American Journal of Physiology. Heart and Circulatory Physiology, 308 (3), ISSN:0363-6135, ISSN:1522-1539

Objective Oxygen transport to parenchymal cells occurs mainly at the microvascular level, and depends on convective red blood cell (RBC) flux, which is proportional in an individual capillary to the product of capillary hematocrit and red blood cell velocity. This study investigates the relative influence of these two factors on tissue oxygen partial pressure (PO2). Methods A simple analytical model is used to quantify the respective influences of hematocrit, RBC velocity and flow on tissue oxygenation around capillaries. Predicted tissue PO2 levels are compared with a detailed computational model. Results Hematocrit is shown to have a larger influence on tissue PO2 than RBC velocity. The effect of RBC velocity increases with distance from the arterioles. Good agreement between analytical and numerical results is obtained and the discrepancies are explained. Significant dependence of mass transfer coefficients on RBC velocity at low hematocrit is demonstrated. Conclusions For a given RBC flux in a capillary, the PO2 in the surrounding tissue increases with increasing hematocrit, as a consequence of decreasing intravascular resistance to diffusive oxygen transport from RBCs to tissue. These results contribute to understanding the effects of blood flow changes on oxygen transport, such as occur in functional hyperemia in the brain. This article is protected by copyright. All rights reserved.