### Abstract

Calculations of the oxygen distribution in resting and contracting skeletal muscle are presented, based on a mathematical model and experimental data obtained on the hamster cremaster muscle [Klitzman et al., Microvasc. Res. 25:108-131 (1983)]. The model considers a slab of tissue penetrated by a regular square array of capillaries with concurrent flow. The intracapillary resistance to oxygen transport is neglected. The capillary red blood cell flux and capillary inlet oxygen tension are assumed random variables following certain probability distributions. The sensitivity of the tissue and intracapillary PO_{2} to variations of these probability distributions are investigated. The mean tissue PO_{2} decreases as the dispersion of the random variables increases, provided that their mean values remain constant. Hypoxic regions appear gradually, especially in the case of contracting muscle, as the dispersion increases. The effect of the number of capillaries in the sample on the resultant distribution of oxygen is studied systematically. The calculated tissue PO_{2} histograms are compared with previously reported PO_{2} distributions obtained experimentally for resting and contracting skeletal muscle.

Original language | English (US) |
---|---|

Pages (from-to) | 91-113 |

Number of pages | 23 |

Journal | Mathematical Biosciences |

Volume | 81 |

Issue number | 1 |

DOIs | |

State | Published - 1986 |

### Fingerprint

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics

### Cite this

*Mathematical Biosciences*,

*81*(1), 91-113. https://doi.org/10.1016/0025-5564(86)90164-1

**Effect of heterogeneous oxygen delivery on the oxygen distribution in skeletal muscle.** / Popel, Aleksander S; Charny, C. K.; Dvinsky, A. S.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 81, no. 1, pp. 91-113. https://doi.org/10.1016/0025-5564(86)90164-1

}

TY - JOUR

T1 - Effect of heterogeneous oxygen delivery on the oxygen distribution in skeletal muscle

AU - Popel, Aleksander S

AU - Charny, C. K.

AU - Dvinsky, A. S.

PY - 1986

Y1 - 1986

N2 - Calculations of the oxygen distribution in resting and contracting skeletal muscle are presented, based on a mathematical model and experimental data obtained on the hamster cremaster muscle [Klitzman et al., Microvasc. Res. 25:108-131 (1983)]. The model considers a slab of tissue penetrated by a regular square array of capillaries with concurrent flow. The intracapillary resistance to oxygen transport is neglected. The capillary red blood cell flux and capillary inlet oxygen tension are assumed random variables following certain probability distributions. The sensitivity of the tissue and intracapillary PO2 to variations of these probability distributions are investigated. The mean tissue PO2 decreases as the dispersion of the random variables increases, provided that their mean values remain constant. Hypoxic regions appear gradually, especially in the case of contracting muscle, as the dispersion increases. The effect of the number of capillaries in the sample on the resultant distribution of oxygen is studied systematically. The calculated tissue PO2 histograms are compared with previously reported PO2 distributions obtained experimentally for resting and contracting skeletal muscle.

AB - Calculations of the oxygen distribution in resting and contracting skeletal muscle are presented, based on a mathematical model and experimental data obtained on the hamster cremaster muscle [Klitzman et al., Microvasc. Res. 25:108-131 (1983)]. The model considers a slab of tissue penetrated by a regular square array of capillaries with concurrent flow. The intracapillary resistance to oxygen transport is neglected. The capillary red blood cell flux and capillary inlet oxygen tension are assumed random variables following certain probability distributions. The sensitivity of the tissue and intracapillary PO2 to variations of these probability distributions are investigated. The mean tissue PO2 decreases as the dispersion of the random variables increases, provided that their mean values remain constant. Hypoxic regions appear gradually, especially in the case of contracting muscle, as the dispersion increases. The effect of the number of capillaries in the sample on the resultant distribution of oxygen is studied systematically. The calculated tissue PO2 histograms are compared with previously reported PO2 distributions obtained experimentally for resting and contracting skeletal muscle.

UR - http://www.scopus.com/inward/record.url?scp=0022530261&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022530261&partnerID=8YFLogxK

U2 - 10.1016/0025-5564(86)90164-1

DO - 10.1016/0025-5564(86)90164-1

M3 - Article

AN - SCOPUS:0022530261

VL - 81

SP - 91

EP - 113

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -