Theoretical Series Elastic Element Length in Rana pipiens Sartorius Muscles

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(s), from the relation, See PDF for Equation From the isometric data, dP/dt was obtained and shortening velocity, v, was a result of the isotonic experiments. Substituting (P (0) - P)/T for dP/dt and (P (0) - P)/(P + a) times b for v, dP/dl(s) = (P + a) /bT, where P < P (0), and a, b are constants for any lengths l ≤ l (0) (Matsumoto, 1965). If the isometric tension and the shortening velocity are recorded for a given muscle length, l (0), although the series elastic, l(s), and the contractile component, l(c), are changing, the total muscle length, l (0) remains fixed and therefore the time constant, T. Integrating, See PDF for Equation the stress-strain relation for the series elastic element, See PDF for Equation is obtained; l (sc0) - l(s) + l (c0)where l (co) equals the contractile component length for a muscle exerting a tension of P (0). For a given P/P (0), l(s) is uniquely determined and must be the same whether on the isotonic or isometric length-tension-time curve. In fact, a locus on one surface curve can be associated with the corresponding locus on the other.