Geometric modeling of the human torso using cubic hermite elements

Abstract

We discuss the advantages and problems associated with fitting geometric data of the human torso obtained from magnetic resonance imaging, with high-order (bicubic Hermite) surface elements. These elements preserve derivative (C ¹) continuity across element boundaries and permit smooth anatomically accurate surfaces to be obtained with relatively few elements. These elements are fitted to the data with a new nonlinear fitting procedure that minimizes the error in the fit while maintainingC ¹ continuity with nonlinear constraints. Nonlinear Sobelov smoothing is also incorporated into this fitting scheme. The structures fitted along with their corresponding root meansquared error, number of elements used, and number of degrees of freedom (df) per variable are: epicardium (0.91 mm, 40 elements, 142 df), left lung (1.66 mm, 80 elements, 309 df), right lung (1.69 mm, 80 elements, 309 df), skeletal muscle surface (1.67 mm, 264 elements, 1,010 df), fat layer (1.79 mm, 264 elements, 1,010 df), and the skin layer (1.43 mm, 264 elements, 1,010 df). The fitted surfaces are assembled into a combined finite element/boundary element model of the torso in which the exterior surfaces of the heart and lungs are modeled with two-dimensional boundary elements and the layers of the skeletal muscle, fat, and skin are modeled with finite elements. The skeletal muscle and fat layers are modeled with bicubic Hermite linear elements and are obtained by joining the adjacent surface elements for each layer. Applications for the torso model include the forward and inverse problems of electrocardiography, defibrillation studies, radiation dosage studies, and heat transfer studies.