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THE PROCESS OF THE DEVELOPMENT OF HYPOXIA IN AN ABNORMAL BLOOD FLOW

  • Received : 2007.10.19
  • Accepted : 2008.01.04
  • Published : 2008.03.25

Abstract

Interrupted blood flow diminishes the concentration of oxygen in tissues. Hypoxia first appears in the region distal to the capillaries and grows throughout the entire t issue. However, the time-wise evolution of hypoxic area is diverse when some of capillaries are blocked in a multi-capillary domain with different oxygen squirt. The process of the development of hypoxia through time course is analyzed mathematically in the domain. Each source in steady state is controlled by a time sensitive function to simulate the occlusion.

Keywords

Blood occlusion;Capillary;Hypoxia

References

  1. Carslaw, H.S. and Jaeger. J.C. Conduction of heat in solids Oxford At The Clarendon Press, Second Edition, 1959.
  2. Clark, P.A., Kennedy, S.P., and Clark Jr. A., Buffering of muscle tissue in $PO_2$ levels by the oxygen field from many capillaries, in: K. Rakusan, et al. (Eds.) Oxygen transport to tissue XI, Adv. Exp. Med. Biol., 248, 1989, pp165. https://doi.org/10.1007/978-1-4684-5643-1_21
  3. Gonzalez-Fernandez, J.M. and Atta, S.E. Concentration of oxygen around capillaries in polygonal regions of supply, Math. Biosci., Vol 13, 1972, pp 55-69. https://doi.org/10.1016/0025-5564(72)90023-5
  4. Fletcher, J.E. A model describing the unsteady transport of substrate to tissue from the microcirculation, SIAP, Volume 29, Issue 3, 1975, pp449-480. https://doi.org/10.1137/0129038
  5. Gradshteyn, I.S. and Ryzhik, I.M. Tables of Integrals Series and Products, fifth ed., Academic Press, San Diego, 1994.
  6. Krogh, A. The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue, J. Physiol., Vol 52, issue 6, May 1919, pp 409-415. https://doi.org/10.1113/jphysiol.1919.sp001839
  7. Millard, C.A. and Gorman, A.D. A model for substrate concentrations in tissue surrounding single capillaries, Mathl. Comput. Modelling, Vol. 25, No 11, 1997, pp1-7.
  8. Salathe, E.P. and Wang, T-C The development of anoxia following occlusion, Bulletin of Math. Bio., Vol 44, issue 6, 1982, pp 851-877. https://doi.org/10.1007/BF02465185
  9. Salathe, E.P., Gross, J.F., and Wang, T-C. Mathematical analysis of oxygen transport to tissue, Math. Biosci., 51, 1980, pp89-115. https://doi.org/10.1016/0025-5564(80)90092-9
  10. Salathe, E.P. Mathematical modelling of oxygen transport in skeletal muscle, Math. Biosci., 58, 1982, pp171-184. https://doi.org/10.1016/0025-5564(82)90071-2
  11. Wang, C.Y. and Bassingthwaighte, J.B. Capillary supply regions, Math. Biosci., Vol 173, issue 2, Oct 2001, pp 103-114. https://doi.org/10.1016/S0025-5564(01)00074-8
  12. Whiteley, J.P., Gavaghan, D.J., and Hahn, C.E.W. Mathematical modelling of oxygen transport to tissue, J. Math. Biol., 44, 2002, pp503-522. https://doi.org/10.1007/s002850200135