Toward empirical evaluation of left ventricle function: a novel mathematical mapping

A strategy is developed to facilitate quantitative analysis of left ventricle morphology based on clinically measured surface geometry and muscle fiber patterns rather than lower order geometric approximations previously required. A transfer function is derived which maps measured three-dimensional ventricle surfaces and associated muscle fiber patterns to a right circular cylinder, while preserving characteristic kinematics of the system. Functional analysis of ventricular morphology at various stages of the cardiac cycle proceeds by using classical methods on the cylindrical ventricle model, with substantially reduced analytical complexity when compared to similar calculations on the real ventricle shape. Functional morphology of the real ventricle shape at any stage of the cardiac cycle is subsequently deduced by applying the inverse of the transfer function in order to map the computed right circular cylinder back to its corresponding real ventricle shape. Limitations of the method are discussed in the context of real left ventricle performance, and extension of the method for analysis of functional morphology in other biomechanical systems is explored.