Left ventricular mechanics related to the local distribution of oxygen demand throughout the wall.

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Abstract
The complex interactions between left ventricular mechanics and the oxygen demand is studied by relating the left ventricular transmural oxygen demand to the myocardial structural and dynamic characteristics. The study utilizes a recent model of left ventricular contraction, which is based on a nested shell spheroidal geometry, a fan-like fibrous structure, the twisting motion of the left ventricle over its long axis, a transmural electrical activation propagation and the basic laws of sarcomere dynamics. The local "axial" stress (in the direction of the fibers) and the instantaneous sarcomere length are used to calculate the spatial distribution of the intramural oxygen demand per beat Vo2(y), where y is the distance from the endocardium. The normalized local sarcomere stress-length area SLAn(y) is related linearly to Vo2(y) by: Vo2(y) = K1 X SLAn(y) + K2, where K1 and K2 are constants. The calculations show a transmural metabolic gradient which is characterized by higher values of Vo2(y) in the endocardial layers than in the epicardial layers. Shorter endocardial sarcomeres and the twisting motion of the left ventricle around the long axis decrease the metabolic gradient across the wall, while a slow transmural electrical propagation wave as well as a wider angle of distribution of the fan-like fiber architecture increases the transmural metabolic gradient. Integration of the local oxygen demand across the left ventricular wall yields global values in agreement with those based on Suga's pressure-volume area approach. The model thus provides a qualitative and quantitative tool to assess the relation of the local and global oxygen demand to the complex left ventricular structure, fiber mechanics, and the dynamics of contraction.