Modeling of Oxygen Transport in the Microcirculation

Adrien Lücker, Patrick Jenny, Bruno Weber (University of Zurich)

Abstract

Oxygen transport to tissue is a fundamental function of the cardiovascular system. Gas and nutrient exchange mostly occur at the smallest blood vessels due to their large surface area. Oxygen supply to cells involves multiple processes that aim to satisfy fluctuating metabolic demand. In the brain, the regulation of oxygen transport at the capillary level is still poorly understood, partly due to the challenges faced by experimental techniques. Computational models provide an invaluable complement to in vivo studies by improving our understanding of the underlying physical phenomena. Following recent improvements in experimental methods, we developed a new numerical model for oxygen transport that is tailored for validation with experimental data.

Oxygen Transport Model

Oxygen transport involves chemical binding with hemoglobin in red blood cells (RBCs), convective and diffusive transport as well as metabolic consumption in the tissue. This gives rise to coupled transport equations for oxygen partial pressure (PO₂) and hemoglobin saturation. To solve them, a method based on overlapping meshes for RBCs moving through capillaries was developed, with a fixed mesh being employed for the oxygen equation. These features facilitates result comparison with PO₂ measurements using two-photon phosphorescence lifetime microscopy, since the presence of moving RBCs is resolved by this technique.

The Distribution of Oxygen in Capillaries

Enlarged view: Longitudinal profiles of PO2 — Longitudinal profiles of PO₂ at various radial positions. The black rectangles indicate the RBC positions.

The oxygen distribution in blood plasma is complex due to the nonlinearity of the chemical reaction with hemoglobin and the presence of individual RBCs. However, its understanding is essential to relate measurements of plasma PO₂ with the actual blood oxygen content. The simulated variation of PO₂ in the capillary shown in the figure agrees well with oxygen measurements based on two-photon microscopy. Besides, we show that the amplitude of these fluctuations mainly depends on the spacings between RBCs and the metabolic oxygen consumption.

The Heterogeneity of Hemoglobin Saturation

Capillaries in the cerebral cortex form complex interconnected vascular networks. While a certain degree of blood flow heterogeneity is generally observed, excessive variations in RBC transit times through the capillaries have been associated to conditions such as Alzheimer’s disease, diabetes and hypertension. We used our oxygen transport model to analyze the heterogeneity of hemoglobin saturation in capillary networks as shown in the video below. Our results demonstrate that diffusive interaction within and between capillaries lead to a substantial reduction of hemoglobin saturation heterogeneity. These findings affect the interpretation of RBC transit time measurements in health and disease.

Source Codes

external page 2POD (2-Photon phosphorescence with Oxygen Diffusion) is a MATLAB library for the simulation of phosphorescence decays in two-photon microscopy with oxygen diffusion and consumption by organic molecules.

The library external page O2RBC is an OpenFOAM extension for oxygen transport from red blood cells. It also features a Python library for pre- and postprocessing of simulations, including data visualization.