Theoretical Series Elastic Element Length in Rana pipiens Sartorius Muscles

Abstract

A B S T R A C T Assuming a two component system for the muscle, a series elastic element and a contractile component, the analyses of the isotonic and isometric data points were related to obtain the series elastic stiffness, dP/dl,, from the relation, dP dP dt dP 1From the isometric data, dP/dt was obtained and shortening velocity, v, was a result of the isotonic experiments. Substituting (Po --P ) / T for dP/dt and (P0 --P ) / ( P + a) times b for v, dP/dl, = (P + a) /bT, where P < P0, and a, b are constants for any lengths l ~ l0 (Matsumoto, 1965). If the isometric tension and the shortening velocity are recorded for a given muscle length, 10, although the series elastic, l,, and the contractile component, 1,, are changing, the total muscle length, l0 remains fixed and therefore the time constant, T. Integrating, f v e dP 1 f z , o P + a -b T ~o dl~'the stress-strain relation for the series elastic element, is obtained; l,,0 ----ls + lo0 where /co equals the contractile component length for a muscle exerting a tension of P0-For a given P / P o , ls is uniquely determined and must be the same whether on the isotonic or isometric length-tensiontime curve. In fact, a locus on one surface curve can be associated with the corresponding locus on the other.