A new approach to defining regional work of the ventricle and evaluating regional cardiac function: Mean wall stress-natural logarithm of reciprocal of wall thickness relationship

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Abstract
A new method of defining regional mechanical work done by a unit volume of myocardium of the ventricular wall and evaluating regional cardiac function is proposed. This method uses the relationship between mean wall stress (σ) and the natural logarithm of the reciprocal of wall thickness (ln(1/H)). 1/H at a point on the epicardial surface is proportional to the regional area (A) of the ventricular wall containing that point. The value for regional work obtained from the relationship between theσ and lnA orσ and ln(1/H) has a true dimension of work, i.e., [J/m3]. Theσ — ln(1/H) relationship was studied in ten anesthetized dogs. Wall thickness and internal diameter of the left ventricle were measured with ultrasonic dimension gauges. Regional work per unit volume of myocardium multiplied by the total myocardial volume of the left ventricle correlated well with the total mechanical work of the entire left ventricle calculated from the pressure-volume relationship during pressure loading, contractility change, and volume loading. During pressure loading, the end-systolicσ — ln(1/H) relationship showed linearity. After bolus injection of isoproterenol theσ — ln(1/H) loop shifted to the left. We concluded that theσ — ln(1/H) relationship provides a method of characterizing regional function normalized to the unit volume of myocardium. In addition, our methods have a potential for echocardiographic application.