Weibull distribution function for cardiac contraction: integrative analysis.
The Weibull distribution is widely used to analyze the cumulative loss of performance, i.e., breakdown, of a complex system in systems engineering. We found for the first time that the difference curve of two Weibull distribution functions almost identically fitted the isovolumically contracting left ventricular (LV) pressure-time curve [P(t)] in all 345 beats (3 beats at each of 5 volumes in 23 canine hearts; r = 0.999953 +/- 0.000027; mean +/- SD). The first derivative of the difference curve also closely fitted the first derivative of the P(t) curve. These results suggest the possibility that the LV isovolumic P(t) curve may be characterized by two counteracting cumulative breakdown systems. Of these, the first breakdown system causes a gradual pressure rise and the second breakdown system causes a gradual pressure fall. This Weibull-function model of the heart seems to give a new systems engineering or integrative physiological view of the logic underlying LV isovolumic pressure generation.
Araki
J
J
Department of Physiology II, Okayama University Medical School, Okayama 700-8558, Japan. jaraki@med.okayama-u.ac.jp
Matsubara
H
H
Shimizu
J
J
Mikane
T
T
Mohri
S
S
Mizuno
J
J
Takaki
M
M
Ohe
T
T
Hirakawa
M
M
Suga
H
H
D000818:Animals; D001794:Blood Pressure; D004285:Dogs; D008955:Models, Cardiovascular; D009200:Myocardial Contraction / Q000502:physiology*; D013995:Time; D016277:Ventricular Function, Left