TY - JOUR
T1 - A mathematical study of volume shifts and ionic concentration changes during ischemia and hypoxia
AU - Yi, Chung Seon
AU - Fogelson, Aaron L.
AU - Keener, James P.
AU - Peskin, Charles S.
N1 - Funding Information:
The authors are grateful to Alex Kralios and Alan Weinstein for helpful discussions. This work was supported, in part, by NSF grant DMS-9805518 and a John Simon Guggenheim Memorial Foundation Fellowship to Fogelson and NSF grant DMS99-700876 to Keener.
PY - 2003
Y1 - 2003
N2 - 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.
AB - 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.
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U2 - 10.1006/jtbi.2003.3154
DO - 10.1006/jtbi.2003.3154
M3 - Article
C2 - 12453453
AN - SCOPUS:0037211066
SN - 0022-5193
VL - 220
SP - 83
EP - 106
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
IS - 1
ER -