Modelling Erythrocytes as Point-Like O2 Sources in a Kroghian Cylinder Model

Hoofd, Louis; Bos, Cees; Turek, Z.

doi:10.1007/978-1-4615-2468-7_117

Cited by 13 publications

(11 citation statements)

References 4 publications

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“…Oxygen supply to tissue is influenced not only by the density of capillaries but also by the number of RBCs within these capillaries, i.e., capillary hematocrit and RBC spacing. Several theoretical studies (8,12,13) have shown that as the distance between the RBCs increases, the capillary ceases to be a continuous source of oxygen. Thus oxygen flux from plasma gaps between the RBCs becomes negligible at a certain distance from the erythrocyte.…”

Section: Capillary Hematocrit and Rbc Spacingmentioning

confidence: 99%

Cardiac function, microvascular structure, and capillary hematocrit in hearts of polycythemic rats

Rakusan

Cicutti

Kolář

2001

American Journal of Physiology-Heart and Circulatory Physiology

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The effect of polycythemia on the coronary microcirculation was studied in young male rats. Two experimental models of polycythemia were employed: cobalt-induced polycythemia, which mimics hypoxia-induced changes, and erythropoietin-induced polycythemia, which circumvents these changes. In both models, baseline left ventricular function was normal, whereas maximal systolic and developed pressures were decreased. In cobalt-treated rats the left ventricular functional reserve was also compromised. Morphometric analysis of the left ventricle confirmed previously described improved geometric conditions for oxygen supply at the distal portions of capillaries (smaller domain areas and shorter capillary segments). In cobalt-treated but not in erythropoietin-treated rats, increased capillary angiogenesis was also detected. In the hearts from rats with both types of polycythemia, a small but significant increase in the formation of arterioles was found. Capillary linear hematocrit was within the normal range in both types of polycythemia despite sizeable increases in systemic hematocrit. Significant differences in red blood cell distribution within capillaries were found between proximal and distal portions in all experimental groups.

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Section: Capillary Hematocrit and Rbc Spacingmentioning

confidence: 99%

Cardiac function, microvascular structure, and capillary hematocrit in hearts of polycythemic rats

Rakusan

Cicutti

Kolář

2001

American Journal of Physiology-Heart and Circulatory Physiology

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“…The vast majority of oxygen in the blood is carried by RBCs, with the plasma carrying a small fraction of the total oxygen [78,83,85,86], which means heterogeneities in RBCs densities will cause changes in local oxygen supply [67,70,72,78,[83][84][85][86]. It has long been appreciated from theoretical models that the tissue oxygenation can vary with the passage of a single RBC, creating an erythrocyte-associated transient (EAT) in tissue oxygenation [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82]. Recent high-resolution measurements of oxygenation with phosphorescent dyes have confirmed the existence of these transients [67,72,[83][84][85][86], but these measurements require aligning the signals to the passage of the RBCs and would not be able to assay any slow oxygenation change that drive 1/f-like dynamics.…”

Section: Role Of Rbcs Spacing Variations In Generating 1/f-like Tissumentioning

confidence: 99%

“…Blood flow and arterial diameter show fluctuations in a similar frequency range as oxygen fluctuations [3]. Additionally, as oxygen is carried by red blood cells (RBCs), fluctuations in the flux of RBCs can drive erythrocyte-associated transients (EATs) in oxygen in the tissue [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82], and fluctuations in flux of these changes in local oxygenation in the cortex [83][84][85][86]. Stalls, brief stoppages in blood flow through capillaries happen sporadically and continuously in the cortex due to transient blockage of blood flow by leukocytes [87][88][89][90][91][92], which are known to greatly increase vascular resistance [93].…”

Section: Introductionmentioning

confidence: 99%

Origins of 1/f-like tissue oxygenation fluctuations in the murine cortex

Zhang

Gheres

Drew

2020

Preprint

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The concentration of oxygen in the brain spontaneously fluctuates, and the power distribution in these fluctuations has 1/f-like dynamics. Though these oscillations have been interpreted as being driven by neural activity, the origins of these 1/f-like oscillations is not well understood. Here, to gain insight of the origin of the 1/f-like oxygen fluctuations, we investigated the dynamics of tissue oxygenation and neural activity in awake behaving mice. We found that oxygen signal recorded from the cortex of mice had 1/f-like spectra. However, band-limited power in the local field potential, did not show corresponding 1/f-like fluctuations. When local neural activity was suppressed, the 1/f-like fluctuations in oxygen concentration persisted. Two-photon measurements of erythrocyte spacing fluctuations (‘stalls’) and mathematical modelling show that stochastic fluctuations in erythrocyte flow and stalling could underlie 1/f-like dynamics in oxygenation. These results show discrete nature of erythrocytes and their irregular flow, rather than neural activity, could drive 1/f-like fluctuations in tissue oxygenation.

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“…However, this "rim value" p xk in general will not be equal to the capillary, or, better, the erythrocyte, value pck. The main reason is that there is a pressure drop due to transport within the blood up to the capillary rim [6,9,20]. But also, there is disequilibrium between oxygen and oxymyoglobin-the gradient in c 0 2Mb and consequently in s is zero while the gradient in p* is not [4,5].…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…The same was done by [3] who termed this proportionality constant the "mass transfer coefficient." The average 0 2 flux is linearly proportional to the 0 2 supply area A k (see first part of (2.6)) and consequently the difference between plk and p k is also [9,11]:…”

Section: Boundary Conditionsmentioning

confidence: 99%

Calculation of oxygen pressures in tissue with anisotropic capillary orientation. I. Two-dimensional analytical solution for arbitrary capillary characteristics

Hoofd

1995

Mathematical Biosciences

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In tissue with a distinct orientation of the oxygen supplying structures, the capillaries, a mathematical description of oxygen transport is feasible in terms of two-dimensional diffusion in a plane perpendicular to the capillaries. Musclc tissue is an example of a highly anisotropic tissue. With some additional simplifying assumptions, a solution can be constructed in terms of capillary sources for arbitrary capillary characteristics, in particular, capillary locations. The solution includes facilitated diffusion by myoglobin in the tissue. For homogeneous tissue, the solution becomes explicit allowing direct calculation of tissue oxygen pressure at any location in a field of simple geometry (circular, rectangular). Also, the size of the area into which each capillary distributes its oxygen, the oxygen supply area, is readily calculated.

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Modelling Erythrocytes as Point-Like O2 Sources in a Kroghian Cylinder Model

Cited by 13 publications

References 4 publications

Cardiac function, microvascular structure, and capillary hematocrit in hearts of polycythemic rats

Cardiac function, microvascular structure, and capillary hematocrit in hearts of polycythemic rats

Origins of 1/f-like tissue oxygenation fluctuations in the murine cortex

Calculation of oxygen pressures in tissue with anisotropic capillary orientation. I. Two-dimensional analytical solution for arbitrary capillary characteristics

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