Abstract
A mathematical model of oxygen and lactic acid transport in skeletal muscle is used to test the effects of reactive hyperemia on oxygen and lactic acid concentrations following a period of ischemia. The model is based on the Krogh cylinder as the geometrical representation of the functional unit of transport, i.e., a capillary and the tissue it supplies. Included in the mathematical development of the model are the convective and diffusive transport of the chemical species, the nonlinear aspects of oxygen and lactic acid kinetics, and the reversible reaction of oxygen with hemoglobin in capillary blood and myoglobin in the tissue. The steady-state solution to the model is obtained first as the baseline for the study. Ischemia is then simulated by the cessation of capillary blood flow. This is followed by a reactive hyperemic response that is a function of the occlusion duration. The general effect of reactive hyperemia is to shorten the time intervals for initial return of tissue oxygen levels and the washout of accumulated lactic acid and to maintain tissue oxygen levels above steady-state values.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Artigue, R. S., and Hyman, W. A. Effect of myoglobin on oxygen and lactic acid transport in skeletal muscle subjected to ischemia.Annals of Biomedical Engineering 1976,4, 128.
Brin, M., Olson, R. E., and State, R. J. Metabolism of cardiac muscle: Comparative studies with L (+) and D (−) C14 lactate in duck and rat tissues.Journal of Biological Chemistry 1952,199 467.
Burton, K. S., and Johnson, P. C. Reactive hyperemia in individual capillaries of skeletal muscle.American Journal of Physiology 1972,223, 517.
Chance, B. Cellular oxygen requirements.Federation Proceedings 1957,16, 671.
Diamant, B., Karlson, J., and Saltin, B. Muscle tissue lactate after maximal exercise in man.Acta Physiologica Scandinavica 1968,72, 283.
Duling, B. R., and Berne, R. M. Longitudinal gradients in periarteriolar oxygen tension.Circulation Research 1970,27, 669.
Eggleton, G. P., Eggleton, P., and Hill, A. V. The coefficient of diffusion of lactic acid through muscle.Proceedings of the Royal Society London Series B 1928,103, 620.
Eriksson, E., and Myrhage, R. Microvascular dimensions and blood flow in skeletal muscle.Acta Physiologica Scandinavica 1972,86, 211.
Folkow, B., and Holicka, H. D. A comparison between “red” and “white” muscle with respect to blood supply, capillary surface area, and oxygen uptake during rest and exercise.Microvascular Research 1968,1, 1.
Gentry, R. M., and Johnson, P. C. Reactive hyperemia in arterioles and capillaries of frog skeletal muscle following microocclusion.Circulation Research 1972,31, 953.
Goldblatt, H. Observations upon reactive hyperemia.Heart 1926,12, 281.
Hammersen, F. The pattern of the terminal vascular bed and the ultrastructive of capillaries in skeletal muscle. InOxygen Transport in Blood and Tissue. D. W. Lubbers (Ed.), Stuttgart. Thieme, 1968.
Hermansen, L., and Wachtlova, M. Capillary density of skeletal muscle in well-trained and untrained men.Journal of Applied Physiology 1971,30, 860.
Huckabee, W. E. Relationship of pyruvate and lactate during anaerobic metabolism. Exercise and formation of O2 debt.Journal of Clinical Laboratory Investigation 1958,37, 255.
Hyman, C., Polidino, R. L., and Zimmerman, E. Local regulation of effective blood flow in muscle.Circulation Research 1963,12, 176.
Hyman, C., and Wong, W. H. Nature and mechanisms of the restoration of normal blood flow after exercise and ischemia. In O. Hudlicka (Ed.),Symposium on circulation in skeletal muscle. New York: Pergamon, 1968. P. 205.
Hyman, W. A., Grounds, D. J., and Newell, P. H. Oxygen tension in a capillary-tissue system subject to periodic occlusion.Microvascular Research 1975,9, 49.
Jobsis, F. F. Basic processes in cellular respiration. In M. W. Magoun (Ed.),Handbook of physiology, Baltimore, Md.: Williams and Wilkins, 1964. Section 3, Vol. 1, p. 63.
Johnson, P. C., and Wayland, H. Regulation of blood flow in single capillaries.American Journal of Physiology 1967,212, 1405.
Keul, J., Doll, E., and Keppler, D. Energy metabolism of human muscle.Medicine and Sport 1972,7.
Krebs, H. A. Rate control of the tricarboxylic acid cycle. In G. Weber (Ed.),Advances in enzyme regulation. Oxford: Pergamon, 1970. P. 335.
Krogh, A. The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissues.Journal of Physiology 1918–1919,52, 409.
Krogh, A. The supply of oxygen to the tissues and the regulation of the capillary circulation.Journal of Physiology 1918–1919,52, 457.
Krogh, A.The anatomy and physiology of capillaries. New Haven, Conn.: Yale Univ. Press, 1922.
Lehninger, A. L.Biochemistry. New York: Worth Publishers, 1970.
Lewis, T., and Grant, R. Observations upon reactive hyperemia in man.Heart 1925,12, 73.
Lightfoot, E. N.Transport phenomena and living systems. New York: Wiley-Interscience, 1974.
Lowenstein, J. M. The regulation of carbohydrate utilization. In F. Dickens and E. Neil (Eds.),Oxygen in the animal organisms. Oxford: Pergamon, 1964, P. 163.
Middleman, S.Transport phenomena in the cardiovascular system. New York: Wiley-Interscience, 1972.
Peaceman, D. W., and Rachford, H. H. The numerical solution of parabolic and elliptic differential equations.Journal of the Society for Industrial and Applied Mathematics 1955,3, 28.
Reneau, D. D., Jr., Bruley, D. F., and Knisely, M. H. A mathematical simulation of oxygen release, diffusion and consumption in the capillaries and tissue of the human brain. In D. Hershey, (Ed.),Chemical engineering in medicine and biology. New York: Plenum, 1967.
Schmidt-Nielsen, K., and Pennycuik, P. Capillary density in relation to body size and oxygen consumption.American Journal of Physiology 1961,200, 746.
Stainsby, W. N., and Otis, A. B. Blood flow, blood oxygen tension, oxygen uptake, and oxygen transport in skeletal muscle.American Journal of Physiology 1964,206, 858.
Whalen, W. J., and Nair, P. Skeletal muscle pO2: effect of inhaled and topically applied O2 and CO2.American Journal of Physiology 1970,218, 973.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hyman, W.A., Artigue, R.S. Oxygen and lactic acid transport in skeletal muscle. Ann Biomed Eng 5, 260–272 (1977). https://doi.org/10.1007/BF02407873
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02407873