DISCRETE GRADIENT METHOD FOR IMAGE-BASED BIOMECHANICAL STRESS ANALYSIS ¹⁾

This paper proposes a discrete gradient method for the stress analysis for biological systems. A point-cloud is taken as the geometric input instead of the conventional CAD model. Before applying the discrete gradient method on the point-cloud model, the neighboring relationship is defined among points as well as the volume occupied by each point. The gradient interpolation vectors, which can approximate the gradient of a function, are defined for each point in the form of the generalized finite difference. The pointwise strain is calculated by using the discrete differentials involving the nodal displacements of a set of neighboring points. A mechanical solver using the discrete gradient method for finite strain elasticity is developed in weak form. It can be shown that this solver retains the similar accuracy and convergence rate of bilinear quadrilateral finite elements, with a locking-free behavior, and is more tolerant to the mesh distortion. An e±cient method is developed to extract the point-cloud model from medical images. Since a material constituent comprises pixels within a certain range of gray-scale values, the pixels within given thresholds are isolated and an initial point-cloud is formed. The physical coordinates are inferred from the image resolution. The Delaunay tessellation and the barycentric subdivision are utilized to provide the neighboring relation and the point volume. A static analysis of the abdominal aortic aneurysm inflation is carried out to demonstrate the usefulness of the method. Despite the use of the tessellation, the method is not element-based because the element-wise assumed solution is never constructed. A distinct feature of this method is that the entire process is completed with a minimal user interference or even fully automatically. This is significant for applications where a timely analysis is desired.