A New Framework for Behavior Modeling of Organs and Soft Tissue Using the Boundary-Element Methods

Abstract

In this paper, a method for modeling the deformation behavior of organs and soft tissue is presented. The purpose is to predict the global deformation effect that arbitrary, time-varying external perturbations have on an organ. The perturbation might be caused by an instrument (e.g., through the surgeon's grasping and pinching actions), or it might be from organ-organ, organ-body-wall collisions in a bodily cavity. A methodology, employing (1) a surface representation based on the Boundary-Element Method—or BEM, of the deformation equations and (2) recently developed linear-algebra techniques (known as the "Hierarchical Semi-Separable" matrix representation—or HSS), is proposed. We demonstrate that the proposed framework achieves an almost linear time complexity of O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.14</sup> ), a significant speed up comparing to the traditional O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) schemes employing brute-force linear-algebra solution methods based on Finite-Element Method (FEM) formulations. Furthermore, unlike some previous approach, no restriction is placed on the external perturbation pattern and how it can change over time.