A Dynamic Finite Element Surface

This paper presents a physics-based approach to anatomical surface segmentation, reconstruction, and tracking in multidimensional medical images. The approach makes use of a dynamic \balloon" model|a spherical thin-plate under tension surface spline which deforms elastically to t the image data. The tting process is mediated by internal forces stemming from the elastic properties of the spline and external forces which are produced from the data. The forces interact in accordance with Lagrangian equations of motion that adjust the model's deformational degrees of freedom to t the data. We employ the nite element method to represent the continuous surface in the form of weighted sums of local polynomial basis functions. We use a quintic triangular nite element whose nodal variables include positions as well as the rst and second partial derivatives of the surface. We describe a system, implemented on a high performance graphics workstation, which applies the model tting technique to the segmentation of the cardiac LV surface in volume (3D) CT images and LV tracking in dynamic volume (4D) CT images to estimate its nonrigid motion over the cardiac cycle. The system features a graphical user interface which minimizes error by aaord-ing specialist users interactive control over the dynamic model tting process.