Mathematical model of erythrocytes as point-like sources

Bos, Cees; Hoofd, Louis; Oostendorp, Thom F.

doi:10.1016/0025-5564(94)00026-v

Cited by 19 publications

(16 citation statements)

References 19 publications

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“…Therefore an accurate model should also calculate the gradient in the tissue adjacent to the capillary. Modelling of an additional thin layer of tissue will suffice, since the gradients damp out quickly (Bos et aL, 1995), CONCLUSION Aroesty and Gross (1970) stated that the effect of motion is negligible. The outcome of their investigation was determined by their choice of concentrations at the gap boundaries.…”

Section: Discussionmentioning

confidence: 99%

Reconsidering the Effect of Local Plasma Convection in a Classical Model of Oxygen Transport in Capillaries

Bos

Hoofd

Oostendorp

1996

Microvascular Research

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Please be advised that this information was generated on 2018-05-09 and may be subject to change. m f c r o v a s c u l a r r e s e a r c h 51, 39-50 (1996) In 1970, Aroesty and Gross investigated the influence of local plasma convection in between two successive red blood cells (RBC) in a capillary on the local oxygen transfer into tissue by combining convectional and diffusional oxygen transport, They concluded that the effect of local plasma convection on oxygen transport in the capillaries was insignificant. Here it is shown that this result was due to their choice of flat oxygen concentration profiles as boundary conditions. In fact, the plasma motion can be of importance when more realistic oxygen concentrations are used as boundary conditions. The fluxes of oxygen through the capillary wall could be up to 50% larger as compared to those of Aroesty and Gross, especially for low hematocrit values and for maximally working muscle. Since the boundary concentrations in the model of the current paper are fixed, chosen not to be influenced by the transport processes, calculations will not show to what extent motion really enhances the oxygen transport, and should be considered as rough indications of the effect of plasma motion. The results in this investigation indicate that in capillaries motion has to be taken into account under conditions of low hematocrit or high RBC velocity.

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Section: Discussionmentioning

confidence: 99%

Reconsidering the Effect of Local Plasma Convection in a Classical Model of Oxygen Transport in Capillaries

Bos

Hoofd

Oostendorp

1996

Microvascular Research

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“…In other words, the presence of a capillary is equated to the presence of an oxygen-supplying RBC [139], although the presence of a capillary is only a necessary but not a sufficient condition for oxygen supply. In theoretical mathematical modelling the important role of the RBCs has long been taken into account; some models consider RBCs as point-like oxygen sources [14], while others assume separate homogeneous flowing regions of plasma and RBCs [149,150]. Gould & Linninger [65] reviewed such existing models against morphological data of vascular trees and as a result, presented a working model of haematocrit distribution.…”

Section: Limitation 1: Role Of the Haematocritmentioning

confidence: 99%

Image-based modelling of skeletal muscle oxygenation

Zeller‐Plumhoff

Roose

Clough

et al. 2017

J. R. Soc. Interface.

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The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo. Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange.

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“…By definition, EP is the limiting difference between p of (9) and where for the righthand part (18) and (2) have been substituted. The boundary condition is that erythrocyte pressure pE must be reached at the erythrocyte border, which was an equivalent sphere radius rsE for the stroboscope model [1]. For the present model, this location is denoted by (rEi zE); for the continuous model, it is the capillary border (rr,0).…”

Section: Representationmentioning

confidence: 99%

“…The model presented here is an extension of the two previous models [1,3], that accounts for erythrocyte movement in the capillary. The model only considers equidistant erythrocytes all moving with the same speed.…”

Section: Introductionmentioning

confidence: 99%

“…In the literature, it was mainly investigated by numerical methods for a limited number of capillaries and in simplified tissue situations. Since such numerical results cannot be easily incorporated into tissue models, we developed analytical methods [1,3] that allow an estimation of the effect on p 0 2 in various circumstances. The effect was quantified as an extraction pressure (EP; for a complete list of symbols used in this article, see Table 1), defined as follows.…”

Section: Introductionmentioning

confidence: 99%

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The effect of blood flow on oxygen extraction pressures calculated in a model of pointlike erythrocyte sources for rat heart

Hoofd

Bos

Oostendorp

1996

Mathematical Biosciences

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A mathematical description of pericapillary oxygen gradients that takes into account the particulate nature of blood is possible in terms of erythrocytes as pointlike sources. The formulation in terms of quasi-stationary sources [1] is ex tended to account for moving erythrocytes. The extended model is semianalytical and can be used to estimate the extraction pressure (EP), which quantifies the effect on partial pressure of oxygen ( p 0 2) in the tissue far from the erythrocytes. Simulations have been done for rat heart muscle tissue around a capillary. For low hematocrit (Hct; 20%) and low blood velocity EP is highest, higher than the p 0 2 drop in a surrounding typical tissue cylinder. This means that the impediment to 0 2 release close to the capillary can be larger than that to transport further into the tissue. Increasing the hematocrit decreases EP, that is, it facilitates O z release. Increasing the blood velocity decreases EP at low Hct values but has the opposite effect at high Hct values ( > 35%). For zero velocity, results are the same as with the quasi-stationary model.

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Mathematical model of erythrocytes as point-like sources

Cited by 19 publications

References 19 publications

Reconsidering the Effect of Local Plasma Convection in a Classical Model of Oxygen Transport in Capillaries

Reconsidering the Effect of Local Plasma Convection in a Classical Model of Oxygen Transport in Capillaries

Image-based modelling of skeletal muscle oxygenation

The effect of blood flow on oxygen extraction pressures calculated in a model of pointlike erythrocyte sources for rat heart

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