Mathematical modeling of the heart using magnetic resonance imaging

A hybrid three-dimensional solid mathematical model of cardiac ventricular geometry developed using magnetic resonance (MR) images of an in vivo canine heart is discussed. The modeling techniques were validated using MR images of an ex vivo heart and direct measurements of cardiac geometry and mass properties. A spin-echo MR sequence with in-plane resolution of 1.0 mm was used to image the canine heart in eleven short-axis planes at contiguous 5-mm intervals. Contour points on the epicardial, left ventricle (LV), and right ventricle (RV) boundaries were selected manually at each slice level. A boundary representation geometric model was constructed by fitting third-order nonuniform rational B-spline surfaces through each set of surface points. Compared to the anatomic specimen (AS), volume errors of the ex vivo model were 0.3, 1.5, and 5.8% for the LV cavity, RV cavity, and total enclosed volumes, respectively. Comparison of cross-sectional areas of the AS and the model at ten levels demonstrated mean model errors of 4.1, 2.5, and 2.9% for the LV, RV, and epicardial boundaries, respectively.