Oxygen delivery through capillaries

Go, Jaegwi

doi:10.1016/j.mbs.2006.09.021

Cited by 5 publications

(5 citation statements)

References 7 publications

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“…Also, we discuss the effect of the fractional order of the derivatives as well as the influence of external forces on delivery of oxygen from capillary to tissues. Previously, the general mathematical model for diffusion of oxygen, as given by Srivastava and Rai [3] omitted external force.…”

Section: Mathematical Model For Oxygen Diffusionmentioning

confidence: 99%

“…In abnormal blood circulation, cells in the area most distal to the capillary at the venous end begin to suffer from hypoxia when perfusion levels drop to critically low values [1][2][3][4]. The insufficient oxygen delivery to tissue may interrupt metastasis and destroy part of the muscle.…”

Section: Introductionmentioning

confidence: 99%

“…However, should the oxygen tension gradient become affected or oxygen concentration levels in capillary become very low, insufficient oxygenation may lead to hypoxia. Previously, Go [3] used a mathematical model for oxygen delivery through capillaries in which the longitudinal diffusion of solute in capillaries was neglected and also it was assumed that the diffusion of oxygen and the consumption rate of oxygen are the same everywhere, which is an unrealistic simplification for clinical situations [1], as shown in Fig.1. The diffusion processes will differ in different places.…”

Section: Introductionmentioning

confidence: 99%

“…The diffusion processes will differ in different places. Go [3] also identified that physical exertion boosts oxygen consumption rate but leads to depletion in oxygen from some cells and that cells engulfing capillaries can utilize or preserve more oxygen than required for a subsequent cycle. Srivastava and Rai [4] removed all the shortcomings discussed above and presented a new mathematical model for diffusion of oxygen of all types, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Study of Oxygen Diffusion From Capillary to Tissues During Hypoxia With External Force Effects

Srivastava

Tripathi

Bég

2017

J. Mech. Med. Biol.

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A mathematical model to simulate oxygen delivery through a capillary to tissues under the influence of an external force field is presented. The multi-term general fractional diffusion equation containing force terms and a time dependent absorbent term is taken into account.Fractional calculus is applied to describe the phenomenon of sub-diffusion of oxygen in both transverse and longitudinal directions. A new computational algorithm, i.e. the New Iterative Method (NIM) is employed to solve the spatio-temporal fractional partial differential equation subject to appropriate physical boundary conditions. Validation of NIM solutions is achieved with a Modified Adomian Decomposition Method (MADM). A parametric study is conducted for three loading scenarios on the capillary-radial force alone, axial force alone and the combined case of both forces. The results demonstrate that the force terms markedly influence the oxygen diffusion process. For example the radial force exerts a more profound effect than axial force on subdiffusion of oxygen indicating that careful manipulation of these forces on capillary-tissues may assist in the effective reduction of hypoxia or other oxygen depletion phenomena.

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Section: Mathematical Model For Oxygen Diffusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Study of Oxygen Diffusion From Capillary to Tissues During Hypoxia With External Force Effects

Srivastava

Tripathi

Bég

2017

J. Mech. Med. Biol.

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“…The relationship above states that the rate approaches 1 for large oxygen concentration and grows without bound for small oxygen concentration. Alternative forms can be found in (Go, 2007). Particular forms of the representation of oxyhemoglobin dissociation do not affect the analysis.…”

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confidence: 99%

Substrate Transport in Cylindrical Multi-Capillary Beds with Axial Diffusion

2023

LiB

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It is known that in oxygen concentration proles for capillary beds of skeletal muscles, radial diusion most likely has considerably more eect on oxygen transport in long and parallel capillary beds than axial diusion. However, axial diusion may still play a signicant role in oxygen transport in tissue, especially in relatively short pathways. Our model adds to known solutions the component of axial diusion to multi-capillary beds inside a tissue cylinder, where arbitrary characteristics include random locations and uneven oxygen strengths. Discussion of the solutions for oxygen supply in multicapillary beds near the arterial ends, in the central regions, and near the venous ends in capillaries is introduced in the remainder of the article. To account for relatively small longitudinal diusivities, we use perturbation methods to solve the associated governing equations.

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A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissues

Srivastava

2010

Mathematical and Computer Modelling

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Oxygen delivery through capillaries

Cited by 5 publications

References 7 publications

Numerical Study of Oxygen Diffusion From Capillary to Tissues During Hypoxia With External Force Effects

Numerical Study of Oxygen Diffusion From Capillary to Tissues During Hypoxia With External Force Effects

Substrate Transport in Cylindrical Multi-Capillary Beds with Axial Diffusion

A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissues

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