Mathematical analysis of oxygen transport to tissue

Salathé, Eric P.; Wang, Tseng-Chan; Gross, Joseph F.

doi:10.1016/0025-5564(80)90092-9

Cited by 29 publications

(13 citation statements)

References 6 publications

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“…The governing equations for time-independent transport of oxygen in the tissue and the capillaries, respectively, are given by [18] (1) (2) Here P(x, y, z) is the tissue PO 2 , which is a function of all three coordinates, P i (z) is PO 2 in the ith capillary, D t , is the diffusion coefficient of O 2 in the tissue, α t , is the solubility coefficient of O 2 in the tissue, M is the O 2 consumption rate, Q i is the volumetric blood flow rate, α b is the solubility coefficient of O 2 in the blood, V c is the mean volume of RBC, f i , is the RBC flux (number of cells per second crossing any cross section in the capillary), C Hb is the oxygen-binding capacity of hemoglobin solution inside the cells, Ѱ is the oxygensaturated fraction of hemoglobin, and J i is the O 2 flux from the capillary to the tissue per unit length of the capillary per unit time. The axial diffusion in the tissue has been neglected, which can be justified when the ratio of capillary length to intercapillary distances is sufficiently large [11,29]. For the cases considered in the present paper this ratio is ∼10.…”

Section: The Modelmentioning

confidence: 98%

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

Popel

Charny

Dvinsky

1986

Mathematical Biosciences

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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.

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Section: The Modelmentioning

confidence: 98%

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

Popel

Charny

Dvinsky

1986

Mathematical Biosciences

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“…(See Appendix.) The diffusion coefficients for CO and O 2 are set to 10 times their physically measured values (Salathe and Tseng-Chan, 1980;Whitely et al, 2002). Furthermore, subcompartment 1 communicates with both the arteriolar inflow to the muscle and the venous outflow, and CO (and O 2 ) can diffuse between this subcompartment and both vascular compartments.…”

Section: Equations Of the Model: Comentioning

confidence: 99%

Prediction of the rate of uptake of carbon monoxide from blood by extravascular tissues

Bruce

Erupaka

2008

Respiratory Physiology & Neurobiology

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Uptake of environmental carbon monoxide (CO) via the lungs raises the CO content of blood and of myoglobin (Mb)-containing tissues, but the blood-to-tissue diffusion coefficient for CO (DmCO) and tissue CO content are not easily measurable in humans. We used a multicompartment mathematical model to predict the effects of different values of DmCO on the time courses and magnitudes of CO content of blood and Mb-containing tissues when various published experimental studies were simulated. The model enhances our earlier model by adding mass balance equations for oxygen and by dividing the muscle compartment into two subcompartments. We found that several published experimental findings are compatible with either fast or slow rates of blood-tissue transfer of CO, whereas others are only compatible with slow rates of tissue uptake of CO. We conclude that slow uptake is most consistent with all of the experimental data. Slow uptake of CO by tissue is primarily due to the very small blood-to-tissue partial pressure gradients for CO.

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“…It should be noted that the absence of OCTA signal may indicate absence of flow or flow that is below the detection sensitivity of the OCTA system. In addition, we explore the intercapillary distances (ICD), which have been measured to evaluate the uniformity of capillary spacing and used as an indicator of hypoxia in various organs and tissues (22)(23)(24). The normal capillary network is a uniform geometrical arrangement of blood vessels with various ICDs, and the distribution has been shown to be approximately log-normal (25).…”

Section: Introductionmentioning

confidence: 99%

Accurate estimation of choriocapillaris flow deficits beyond normal intercapillary spacing with swept source OCT angiography

Zhang¹,

Shi²,

Zhou³

et al. 2018

Quant. Imaging Med. Surg.

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Mathematical analysis of oxygen transport to tissue

Cited by 29 publications

References 6 publications

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

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

Prediction of the rate of uptake of carbon monoxide from blood by extravascular tissues

Accurate estimation of choriocapillaris flow deficits beyond normal intercapillary spacing with swept source OCT angiography

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