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.

Validity of the force-velocity relation for muscle contraction in the length region, l less than or equal to l-o

Considerable attention has been directed to the characteristic force-velocity relation discovered by A. V. Hill in the study of muscle kinematics. Models of contractile process were tested on the basis of their compatibility with the Hill equation. However, almost all the isotonic data have been restricted to one length, l(0), the maximum length with almost no resting tension; the velocities measured are those initial values when the load begins to move. The force-velocity curve extrapolates to zero velocity for isometric tension, but only for the tension at that one length. Very few efforts have been made to study the profiles of the curves throughout the range of lengths over which shortening takes place. In examining the length region, l </= l(0), for an isotonically contracting muscle, not only is the force-velocity relation valid for the initial reference length, l(0), but also for any other length. The analysis in this report indicates that the constants a/P(0) and b/l(0) remain fixed throughout the length change of afterloaded isotonic shortening in the Rana pipiens sartorius muscles.