A Mathematical Simulation of Oxygen Release, Diffusion, and Consumption in the Capillaries and Tissue of the Human Brain

ReneauJr., Daniel D.; Bruley, Duane F.; Knisely, Melvin H.

doi:10.1007/978-1-4757-4748-5_6

Cited by 77 publications

(39 citation statements)

References 40 publications

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“…Although it accounts for less than 4 % of an adult human body weight, it consumes about 15-17 % of the total used oxygen of the human body [18].…”

Section: Anatomy Of the Human Brainmentioning

confidence: 99%

“…About 57 % of the human brain is made up of grey matter whereas 43 % is white matter [17]. However, the grey matter consumes more than 80 % of the total oxygen used by the brain [18].…”

Section: Brain Tissuementioning

confidence: 99%

“…The oxygen supply of brain tissue can be described by the so called Krogh cylinder [18], which is shown in fig. 3.4.…”

Section: Krogh Cylindermentioning

confidence: 99%

“…Oxygenated blood cells flow through the capillaries and after dissociation into the blood, oxygen diffuses into the tissue. The point "Lethal corner" marks the point in the Krogh cylinder with the lowest oxygen content (adapted from [18]). a capillary with radius r c , which is surrounded by a tissue cylinder with radius r t .…”

Section: Krogh Cylindermentioning

confidence: 99%

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Mathematical modeling of human brain physiological data

et al. 2013

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“…Although it accounts for less than 4 % of an adult human body weight, it consumes about 15-17 % of the total used oxygen of the human body [18].…”

Section: Anatomy Of the Human Brainmentioning

confidence: 99%

“…About 57 % of the human brain is made up of grey matter whereas 43 % is white matter [17]. However, the grey matter consumes more than 80 % of the total oxygen used by the brain [18].…”

Section: Brain Tissuementioning

confidence: 99%

“…The oxygen supply of brain tissue can be described by the so called Krogh cylinder [18], which is shown in fig. 3.4.…”

Section: Krogh Cylindermentioning

confidence: 99%

Section: Krogh Cylindermentioning

confidence: 99%

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Mathematical modeling of human brain physiological data

et al. 2013

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“…Steady-state models at the cellular and subcellular levels (24,25,35,39) cannot be used to analyze tracer transients. The models by Reneau et al (41) and Bassingthwaighte et al (3) take into account both axial and radial diffusion, but are costly computationally because of the finite difference methods used. The linear axially-distributed model by Rose and Goresky (44) gives good descriptions of tracer transients for oxygen, but does not distinguish erythrocytes from plasma, nor account for the formation of tracer-labeled water.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear model for capillary-tissue oxygen transport and metabolism

Yipintsoi

Bassingthwaighte

1997

Ann Biomed Eng

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Oxygen consumption in small tissue regions cannot be measured directly, but assessment of oxygen transport and metabolism at the regional level is possible with imaging techniques using tracer 15 O-oxygen for positron emission tomography. On the premise that mathematical modeling of tracer kinetics is the key to the interpretation of regional concentration-time curves, an axiallydistributed capillary-tissue model was developed that accounts for oxygen convection in red blood cells and plasma, nonlinear binding to hemoglobin and myoglobin, transmembrane transport among red blood cells, plasma, interstitial fluid and parenchymal cells, axial dispersion, transformation to water in the tissue, and carriage of the reaction product into venous effluent. Computational speed was maximized to make the model useful for routine analysis of experimental data. The steady-state solution of a parent model for nontracer oxygen governs the solutions for parallel-linked models for tracer oxygen and tracer water. The set of models provides estimates of oxygen consumption, extraction, and venous pO 2 by fitting model solutions to experimental tracer curves of the regional tissue content or venous outflow. The estimated myocardial oxygen consumption for the whole heart was in good agreement with that measured directly by the Fick method and was relatively insensitive to noise. General features incorporated in the model make it widely applicable to estimating oxygen consumption in other organs from data obtained by external detection methods such as positron emission tomography.

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