Cavity detection in biomechanics by an inverse evolutionary point load BEM technique

Abstract

An efficient solution of the inverse geometric problem for cavity detection using a point load superposition technique in the elastostatics boundary element method (BEM) is presented in this article. A superposition of point load clusters technique is used to simulate the presence of cavities. This technique offers tremendous advantages in reducing the computational time for the elastostatics field solution as no boundary re-discretization is necessary throughout the inverse problem solution process. The inverse solution is achieved in two steps: (1) fixing the location and strengths of the point loads, (2) locating the cavity geometry. For a current estimated point load distribution, a first objective function measures the difference between BEM-computed and measured deformations at selected points. A genetic algorithm is employed to automatically alter the locations and strengths of the point loads to minimize the objective function. Upon convergence, a second objective function is defined to locate the cavity geometry modelled as traction-free surface. Results of cavity detection simulations using numerical experiments and simulated random measurement errors validate the approach in regular and irregular geometrical configurations.

Inverse Vof Meshless Method for Efficient Nondestructive Thermographic Evaluation

“…This allowed for accurate and efficient identification of subsurface cavities without the need of regenerating geometries or BEM interpolation matrices. This technique was later extended by Ojeda, Divo, and Kassab [25] for biomechanical applications of cavity detection in cortical bones. In this case, the deformation field difference with respect to a measured field at the exposed boundaries was minimized by using an elastostatics BEM code and employing a variety of differently shaped anchored grid patterns (AGP) that adapt to the shape of the internal cavity using the efficient singularity superposition idea.…”