A mathematical model of the right ventricular muscle geometry and mass

Abstract

An understanding of the geometry of the right ventricular (RV) free wall is imperative for both modelling its mechanics and assessing its mass by imaging techniques such as echocardiography. In this paper, a new model of the RV free wall geometry is discussed in which the wall is assumed to have a parabolic long-axis and a circular short-axis curvature respectively. By use of analytic geometry, mathematical expressions for RV surface area, volume and mass were derived. In vitro model validation was carried out in the following manner: (1) echocardiographic images of 16 isolated calf hearts were obtained; (2) measurements were made from the images to determine the parameters required by the model; (3) wall mass was determined by use of these parameters; and (4) the calculated wall mass was then compared with actual RV wall mass (determined by weighing). The model was found to be very accurate for determination of RV free wall mass (R = 0.92); it should prove useful in the study of the stress-strain relationships for the RV and for precise quantitative assessment of RV free wall mass.