Canine papillary muscle force-length-time relation (F-L-t) was investigated under pentobarbital sodium anesthesia. The time intervals taken from end diastole to any point (P) on the force-length plane was determined for isometric (t1) and isotonic (t2) systole and corrected for excitation contraction coupling duration. The ratio t1/t2, designated km, was approximately constant for widely scattered positions of P chosen systematically. The km in the 10 dogs ranged from 0.36 to 0.94 with means +/- SD of 0.66 +/- 0.16; km correlated negatively with muscle average cross-sectional area (r = -0.82; P less than 0.005). Assuming constancy of km, a general relationship was derived between (delta F/delta t)t1L, the rate of isometric force development at P; (delta L/delta t)t2F, the velocity of isotonic shortening at P; (delta F/delta L)(t1,t2)t, the stiffness; and (delta L/delta F)(t1,t2)t, the compliance of the myocardium (all taken at P) as follows (delta F/delta L)t1,t2t = -km(delta F/delta t)t1L/(delta L/delta t)t2F and (delta L/delta F)t1,t2t = -km-1(delta L/delta t)t2F/(delta F/delta t)t1t. The ratio of (delta F/delta t)t1L to (delta L/delta t)t2F defines functional proclivity and measures the differential propensity to force development relative to shortening. Thus myocardial stiffness or compliance determines functional proclivity by acting as an impedance-matching transformer that steps up or steps down force development of shortening as warranted by the loading conditions.
On radiation from convexo-concave microstrip patch antenna with impedance matching transformer
