The analysis of circulatory system using polynomials has two characteristic features; it can combine various parameters of the circulatory system in a global sense to form a mathematical description, w hich, in turn, suggests a clue to solving the regulatory question. Thus, a research was porformed to investigate the relationship among cardiac output (
F), heart rate (
H) and blood pressure (
P), abbreviated as
FHP relationship, using the polynomial models consisting of methematical and biological models. The former is general mathematical expression of FHP relation while the latter implies some biological mechanisms, i. e., in our study a tonus which, corresponding to the tonic activity of an assumed cardiac output center, are introduced here in the form T=aH+bP where a and b are constants. Then cardiac output is given by
F=k0+k1T+k2T2 where k
0, k
1 and k
2 are constants, which can be determined by the least square method. The equation with highest correlation coefficient of those between cardiac outputs observed and calculated by the equations of various coefficients b (for a=1), was adopted actually as a biological model.
Ten dog experiments resulted in the coefficient of 0.977 on average for the methematical and 0.959 for the biological model. These high correlations and the small difference between them suggest that the relation, expressed by the biological equation, among the circulatory parameters can be well applied to the actual circulatory phenomenon in the aorta. This is veryfied by the figures representing the
FHP relationship observed. Furthermore, the biological equation indicates that cardiac output increases with increasing heart rate while it decreases with increasing blood pressure in most cases under the conditions induced by infusion with noradrenaline, isoproterenol and acetylcholine.
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