Frank-Starling law and Bowditch phenomenon may have the common theoretical grounds

Abstract

The relationship between two different linear dimensions of the chamber (ventricle) and the two respective values of the force of contraction (which are applied to the imaginary piston in order to accelerate the initial venous inflow) is deduced as the ratio of forces which is equal to the ratio of squares of linear dimensions of the chamber; the equation is valid when the durations of both contractions (systoles) are identical. The relationship corresponds to Frank-Starling law (the right limb of parabola can be approximated to the direct proportionality of the law). When the durations of systoles are different the ratio of forces is equal to the inverse ratio of durations of systoles; the inverse proportionality permits to interpret the Bowditch phenomenon by means of the ascending asymptote of hyperbole. Stepwise shortening of systole is impossible due to extremely narrow range of variable (duration of systole), hence the shift of variable can be realized only as a leap; this leap is accompanied by the enormous rise of function (force of contraction) which can be accommodated to several contractions. Homoiometric regulation can be considered a safety device (presumably in the form of paroxysmal tachycardia with the shortened systole) in the case when heterometric regulation lacks to produce the adequate force of contraction in response to excessively distended chamber.