# Physiological basis for mechanical time-variance in the heart: Special consideration of non-linear function

- Authors
- Journal
- Journal of Theoretical Biology 0022-5193
- Publisher
- Elsevier
- Publication Date
- Volume
- 139
- Issue
- 4
- Identifiers
- DOI: 10.1016/s0022-5193(89)80066-9
- Disciplines

## Abstract

A relationship between ventricular pressure and volume is developed starting from basic cardiac muscle mechanics. The known and measurable properties of myocardium, such as the Hill law, the periodic excitation-contraction mechanism, and non-linear elasticity of the surrounding elastin and collagen structure, are formulated into a myofibril unit. A cylindrical geometry is chosen to represent the structure of the ventricle, using the myofibril unit as the basic building block. Pressure-volume isochrones computed from this model illustrate non-linear function in the heart which arises from both geometric effects and muscle effects. The above theory and model is linearized to provide a special study case. The behavior that resulted is that of a time-varying elastance, E( t), and, hence, can help in the interpretation of its meaning. It is found that the minimum in E( t) is the consequence of the stiffness of the myocardial fibrous network, adjusted by a geometric factor. In addition, the magnitude of E( t) is governed by myocardial contractility, a geometric factor, and the excitation-contraction mechanism, where time-dependency is imparted by periodic excitation. Since the elastic fibers are the only true elastic elements, the quantity of elastance is determined by controlled volume feedback. A circuit model is provided to illustrate this concept. The non-linear active and passive heart function curves are specified independently. These curves are required to intersect below the resting volume and result in a negative pressure at the intersection. This is found to explain the phenomenon of ventricular suction. In addition, they lead to a time-varying dead volume by virtue of time-dependent isochronal slope. Non-linear function is introduced to the model and is found to explain the variation in curvature of the ventricular isochrones.

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