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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 &lt; P(0), and a, b are constants for any lengths l &lt;/= 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.

Theoretical Series Elastic Element Length in Rana pipiens Sartorius Muscles