Practical applications of models of oxygen supply, diffusion, and consumption: past, perspectives, and problems.

It is the objective of this paper to describe, what models of oxygen supply, diffusion, and consumption have been and can be used for and to discuss some common problems in employing mathematical models of O2 transport. In a first part, four typical fields for model applications are selected from the wide variety of former investigations and are illustrated with some recent examples.

[1]  W. Federspiel,et al.  A model study of intracellular oxygen gradients in a myoglobin-containing skeletal muscle fiber. , 1986, Biophysical journal.

[2]  C. Honig,et al.  Intracellular PO2 in long axis of individual fibers in working dog gracilis muscle. , 1988, The American journal of physiology.

[3]  J. L. Frierson,et al.  Active and passive capillary control in red muscle at rest and in exercise. , 1982, The American journal of physiology.

[4]  K. Rakušan,et al.  Capillary length, tortuosity, and spacing in rat myocardium during cardiac cycle. , 1992, The American journal of physiology.

[5]  A Krogh,et al.  The supply of oxygen to the tissues and the regulation of the capillary circulation , 1919, The Journal of physiology.

[6]  K. Groebe,et al.  Glucose diffusion coefficients determined from concentration profiles in EMT6 tumor spheroids incubated in radioactively labeled L-glucose. , 1994, Advances in experimental medicine and biology.

[7]  J D Hellums,et al.  The resistance to oxygen transport in the capillaries relative to that in the surrounding tissue. , 1977, Microvascular research.

[8]  A Krogh,et al.  The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue , 1919, The Journal of physiology.

[9]  C. Honig,et al.  O2 gradients from sarcolemma to cell interior in red muscle at maximal VO2. , 1986, The American journal of physiology.

[10]  L. Hoofd,et al.  Calculation of oxygen pressures and fluxes in a flat plane perpendicular to any capillary distribution. , 1989, Advances in experimental medicine and biology.

[11]  C. R. Taylor,et al.  Capillary blood transit time in muscles in relation to body size and aerobic capacity. , 1994, The Journal of experimental biology.

[12]  C. Ellis,et al.  The Krogh cylinder geometry is not appropriate for modelling O2 transport in contracted skeletal muscle. , 1983, Advances in experimental medicine and biology.

[13]  C. Ellis,et al.  Muscle capillary-to-fiber perimeter ratio: morphometry. , 1991, The American journal of physiology.

[14]  A. Groom,et al.  Capillary diameter and geometry in cardiac and skeletal muscle studied by means of corrosion casts. , 1983, Microvascular research.

[15]  K. Groebe.  A versatile model of steady state O2 supply to tissue. Application to skeletal muscle. , 1990, Biophysical journal.

[16]  P. Johnson,et al.  Capillary network geometry and red cell distribution in hamster cremaster muscle. , 1982, The American journal of physiology.

[18]  W. Mueller‐Klieser,et al.  Method for the determination of oxygen consumption rates and diffusion coefficients in multicellular spheroids. , 1984, Biophysical journal.

[19]  A Krogh,et al.  The rate of diffusion of gases through animal tissues, with some remarks on the coefficient of invasion , 1919, The Journal of physiology.

[20]  S. Kennedy,et al.  Buffering of muscle tissue PO2 levels by the superposition of the oxygen field from many capillaries. , 1989, Advances in experimental medicine and biology.

[21]  R. J. Stark,et al.  Effect of ionophore A23187 on cytosolic Ca2+ and enzyme secretion. , 1982, The American journal of physiology.

[22]  C L Odoroff,et al.  Capillary recruitment in exercise: rate, extent, uniformity, and relation to blood flow. , 1980, The American journal of physiology.