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Front. Physiol. | doi: 10.3389/fphys.2018.00420

The Relation between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 1: Theoretical Models

  • 1Department of Mechanical and Process Engineering, ETH Zürich, Switzerland
  • 2Department of Physiology, University of Arizona, United States
  • 3Institute of Pharmacology and Toxicology, Universität Zürich, Switzerland

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 hetero- geneity (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.

Keywords: Capillary transit time heterogeneity, hemoglobin saturation, oxygen transport, computational modeling, red blood cells, Microcirculation, Hematocrit, Blood flow

Received: 28 Nov 2017; Accepted: 04 Apr 2018.

Edited by:

Joseph L. Greenstein, Johns Hopkins University, United States

Reviewed by:

Daniel Goldman, University of Western Ontario, Canada
Ranjan K. Dash, Medical College of Wisconsin, United States
Leif Østergaard, Center of Functionally Integrative Neuroscience and MINDLab
David Robert Grimes, Queen's University Belfast, United Kingdom  

Copyright: © 2018 Lücker, Secomb, Weber and Jenny. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Adrien Lücker, ETH Zürich, Department of Mechanical and Process Engineering, Zurich, 8092, Switzerland,