Mathematical Analysis of Oscillatory and Non-oscillatory Recovery of Contractility after a Rested-State Contraction and Its Modification by Calcium
Recovery of contractility after a rested-state contraction in rat ventricle proceeded in two phases and is described by equations that are solutions of a nonhomogeneous second-order differential equation. The recovery can be characterized by a damping ratio defined in terms of the constants of the homogeneous portion of the differential equation. When calcium concentration was elevated, the usual smooth recovery curve underwent oscillatory variation and thus became less damped. There was a shift in phase between oscillation in recovery and in resting tension after a rested-state contraction. A control system is proposed to regulate relaxation and subsequent recovery of contractility. Possible mechanisms for an effect of calcium on such a control system are discussed.
- Received July 7, 1969.
- Accepted October 7, 1969.
- © 1969 American Heart Association, Inc.