Quantitative Analysis of the Control of Cardiac Output in the Isolated Left Ventricle
Authors: ROBINSON DAVID A. 
Published: June 2012

A mathematical description of the hemodynamics of the ventricular cycle has been developed, based on the properties of myocardium. The functions and coefficients in the equations of this description have been evaluated quantitatively for the left ventricle of the 10 kg dog. By computer solution of these equations, the response of the ventricle in terms of end diastolic volume, stroke volume, mean arterial pressure, and stroke work to various changes such as filling pressure, contractility, systemic resistance, and arterial compliance has been recorded. The analysis includes homeometric autoregulation as well as naturally exhibited Frank-Starling regulation and successfully predicts much of the static and dynamic behavior of the isolated, supported, paced left ventricle. The major features of the analysis and results are as follows:

1) The notion of conceptually dividing the ventricle into two chambers to correspond to the conceptual division of the myocardium into a series elastic and a contractile component is introduced in order that ventricular mechanics may be viewed in the light of the extensive knowledge on muscular mechanics.

2) The force-velocity relationship of muscle makes itself felt in ventricular dynamics as an hydraulic resistance across which occurs the pressure drop from isometric pressure (about 300 mm Hg) to the pressure actually seen in the ventricle. Its value (for the 10 kg dog) is about 2.5 mm Hg/ml/sec which is considerably higher than the dynamic impedance of the arterial load (0.403 mm Hg/ml/sec at the fundamental frequency). This implies that the left ventricle resembles a flow pump more closely than commonly supposed. It further implies that cardiac output is relatively independent of pulse propagation and reflections, blood inertia, and arterial compliance.

3) A decrease in systemic resistance or a positive inotropic effect makes the heart smaller while increasing stroke volume. The combination (as in exercise) leads to increased stroke work from a smaller end diastolic volume in agreement with observations made on intact animals.

4) The fact that the isometric pressure volume curve of the ventricle (a reflection of the length tension curve of myocardium) exhibits greater pressures for larger volumes (over most of the physiological range) indicates that the ventricle is potentially capable of doing more stroke work from a larger end diastolic volume. Whether it does so in fact depends entirely on the conditions of the arterial load. This is the weak point of a too literal interpretation of Starling's law of the heart. No statement concerning stroke work and end diastolic volume can be complete or correct without specifying the nature of the load on which this work is to be done. In fact without homeometric autoregulation (a liberty to be taken only in a computer simulation) Starling's law is rapidly and grossly disobeyed in a pressure run (increasing systemic resistance). With restoration of homeometric autoregulation, Starling's law is again obeyed but dichotomized since the heart does more stroke work from a given end diastolic volume in a pressure run than in a flow run (increasing filling pressure).

5) An additional result of this investigation is the demonstration (quantitative) that concepts and measurements drawn from a wide variety of sources in the literature on muscle and cardiovascular functions are not incompatible and, when integrated into a comprehensive analytical description of the cardiac cycle, combine to produce cardiac behavior patterns in general agreement with experimentation.