A three-element model describes excised cat papillary muscle elasticity

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Abstract
The three-element model for skeletal muscle has been widely applied to cardiac muscle. It consists of an active contractile element (CE) that represents the muscle's response to stimulation, in series with an elastic element (SE) and the CE and SE in parallel with another elastic element (PE). There have been problems in interpreting experimental data on muscle elasticity using this model. Data seem to indicate that SE force depends not only on instantaneous length, but also initial length; it is not only elastic. Recent experiments seem to indicate that the SE has time-varying properties; it is not passive. This paper formulates a three-element model in which phi(x) = alpha[e beta(x-x*)-1] governs the elastic elements, where phi = force, alpha, beta = spring constants, x = length, and x* = rest length, which avoids these problems. The SE and PE have the same properties. (Typical values: alpha approximately equals .045 g/mm2, beta approximately equals 5.9 mm-1 for cat papillary at 29 degrees C.). By accounting for the nonlinearity of the SE-PE interaction, this three-element model leads to predictions that agree with published data on excised papillary muscle's elastic properties.

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