Distribution of oxygen partial pressure in a two-dimensional tissue supplied by capillary meshes and concurrent and countercurrent systems

Metzger, Hermann

doi:10.1016/0025-5564(69)90039-x

Cited by 22 publications

(9 citation statements)

References 6 publications

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“…We model each capillary district as an array of N u identical capillary pipes with radius R cap and length L cap arranged in parallel (Takahashi et al 2009;Liu et al 2009). The parameter R cap is set equal to 3 µm and N u and L cap are chosen to reproduce the main geometrical features of the real anatomical capillary mesh, specifically the total lateral capillary surface exposed to solute filtration and the capillary density in the tissue as done in Metzger (1969). Denoting by N l the number of arteriole/venule pairs digging into the layer l, l = 4, 6, each capillary district is supposed to cover an area equal to Ω t,xy /N l , so that a capillary density in the plane and an equivalent lateral surface can be computed and, consequently, the parameters N u and L cap .…”

Section: Capillary Pleximentioning

confidence: 99%

Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

Causin

Guidoboni

Malgaroli

et al. 2015

Biomech Model Mechanobiol

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Section: Capillary Pleximentioning

confidence: 99%

Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

Causin

Guidoboni

Malgaroli

et al. 2015

Biomech Model Mechanobiol

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“…Electrodes larger than this are likely to interfere with the microcirculation or give a mixture of capillary and tissue rather than a true extravascular value. Neo-Krogh models with varying capillary geometries and diffusional interaction have been developed (Metzger, 1969;Grunewald and Sowa, 1978;Schubert et al, 1978) and predicted random PO 2 histograms have been compared with the data. There is agreement in cases of low oxygen consumption but not in the more interesting situations.…”

Section: Oxygenmentioning

confidence: 99%

In Vivo Comparison of Non-Gaseous Metabolite and Oxygen Transport in the Heart

Rose

Goresky

Bach

et al. 1988

Oxygen Transport to Tissue X

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“…Accordingly, in this study, the distributed model may be insufficient for a descrip tion of brain microcirculation. Metzger (1969) has considered the oxygen diffusion from two-and three-dimensional capillary structures in the form _.1…”

Section: Perspectivementioning

confidence: 99%

Tracer Disposition Kinetics in the Determination of Local Cerebral Blood Flow by a Venous Equilibrium Model, Tube Model, and Distributed Model

Sawada

Sugiyama

Iga

et al. 1987

J Cereb Blood Flow Metab

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Tracer distribution kinetics in the determination of local cerebral blood flow (LCBF) were examined by using three models, i.e., venous equilibrium, tube, and distributed models. The technique most commonly used for measuring LCBF is the tissue uptake method, which was first developed and applied by Kety (1951). The measurement of LCBF with the 14C-iodoantipyrine (IAP) method is calculated by using an equation derived by Kety based on the Fick's principle and a two-compartment model of blood-tissue exchange and tissue concentration at a single data point (Sakurada et al., 1978). The procedure, in which the tissue is to be in equilibrium with venous blood, will be referred to as the tissue equilibration model. In this article, effects of the concentration gradient of tracer along the length of the capillary (tube model) and the transverse heterogeneity in the capillary transit time (distributed model) on the determination of LCBF were theoretically analyzed for the tissue sampling method. Similarities and differences among these models are explored. The rank order of the LCBF calculated by using arterial blood concentration time courses and the tissue concentration of tracer based on each model were tube model (model II) less than distributed model (model III) less than venous equilibrium model (model I). Data on 14C-IAP kinetics reported by Ohno et al. (1979) were employed. The LCBFs calculated based on model I were 45-260% larger than those in models II or III. To discriminate among three models, we propose to examine the effect of altering the venous infusion time of tracer on the apparent tissue-to-blood concentration ratio (lambda app). A range of the ratio of the predicted lambda app in models II or III to that in model I was from 0.6 to 1.3. In the future, there may be a need to determine which model should be used to calculate the LCBF based on this discriminator and to develop another discriminator by using multiple data points based on positron emission tomography.

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Distribution of oxygen partial pressure in a two-dimensional tissue supplied by capillary meshes and concurrent and countercurrent systems

Cited by 22 publications

References 6 publications

Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

In Vivo Comparison of Non-Gaseous Metabolite and Oxygen Transport in the Heart

Tracer Disposition Kinetics in the Determination of Local Cerebral Blood Flow by a Venous Equilibrium Model, Tube Model, and Distributed Model

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