Analytical description of force-time and force-velocity relations of isometric contractions in feline isolated heart muscle and in the intact heart.

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Abstract
The function T = T1 + T2 exp { - ((.DELTA. - t)/.alpha.-m} is proposed to describe both the growing phase of the isometric tension-time curve and the pre-ejection pressure time curve of an isovolumic contraction. This 2-fold use of the proposed function permits one to relate the dynamics of intact heart to the dynamics of papillary muscle. Isometric force velocity relations are obtained from this function for the Maxwell and Voigt models. Contractile element velocity given as a function of stress is split into 2 factors: a step-like function and Fung''s equation. Analysis of their asymptotic behavior under limiting values of T1 and comparison with published experimental results lead to the hypothesis that Fung''s equation, obtained as outlined above, describes the isotonic force-velocity relation of the contractile element at a given preload. The interplay of the Maxwell and Voigt model in relating some dynamic variables is analyzed. In particular, a force-velocity relation is introduced which proves to be independent of preload but sensitive to inotropic interventions and easily obtainable from isometric tension time (or pressure time) records alone; Vmax extrapolated from this relation is proposed as an index of contractility. The specificity and sensitivity of some commonly used contractility indices are analyzed as an aid in assigning physical meaning to different parameters used in the formalism.