A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia

Chung Seon Yi, Aaron L. Fogelson, James P. Keener, Charles Peskin

Research output: Contribution to journalArticle

Abstract

The response of tissue to ischemia (cessation of blood flow and deprivation of oxygen) includes swelling of the intracellular space, shrinkage of the extracellular space, and an increase in the extracellular potassium concentration. The responses of cardiac and brain tissue to ischemia are qualitatively different in that cardiac tissue shows a rise in extracellular potassium over several minutes from about 5 to 10-12 mM followed by a plateau, while brain tissue shows a similar initial rise followed by a very rapid increase in extracellular potassium to levels of 50-80 mM. During hypoxia the flow of blood (or perfusate) is maintained and, while there is a substantial efflux of potassium from cells, there is little accumulation of potassium in the interstitium. A mathematical model is proposed and studied to try to elucidate the mechanism(s) underlying the increase in extracellular potassium, and the different time courses seen in neural and cardiac tissue. The model involves a Hodgkin-Huxley-type description of transmembrane ion currents, allows for ion concentrations as well as volumes to change for both the intracellular and extracellular space, and includes coupling of damaged tissue to nearby healthy tissue. The model produces a response to ischemia much like that seen in neural tissue, and the mechanism underlying this response in the model is determined. The same mechanism is not present in cardiac ion models, and this may explain the qualitative difference in response shown in cardiac tissue.

Original languageEnglish (US)
Pages (from-to)83-106
Number of pages24
JournalJournal of Theoretical Biology
Volume220
Issue number1
DOIs
StatePublished - 2003

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Hypoxia
Ischemia
Potassium
ischemia
hypoxia
Cardiac
Tissue
potassium
Intracellular Space
extracellular space
ions
Extracellular Space
Ions
blood flow
Swelling
Brain
Blood
Blood Flow
Shrinkage
brain

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia. / Yi, Chung Seon; Fogelson, Aaron L.; Keener, James P.; Peskin, Charles.

In: Journal of Theoretical Biology, Vol. 220, No. 1, 2003, p. 83-106.

Research output: Contribution to journalArticle

Yi, Chung Seon ; Fogelson, Aaron L. ; Keener, James P. ; Peskin, Charles. / A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia. In: Journal of Theoretical Biology. 2003 ; Vol. 220, No. 1. pp. 83-106.
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