Simultaneous Topology and Stiffness Identification for Mass-Spring Models Based on FEM Reference Deformations

Abstract

Abstract. Mass-spring systems are of special interest for soft tissue modeling in surgical simulation due to their ease of implementation and real-time behavior. However, the parameter identification (masses, spring constants, mesh topology) still remains a challenge. In previous work, we proposed an approach based on the training of mass-spring systems according to known reference models. Our initial focus was the determination of mesh topology in 2D. In this paper, we extend the method to 3D. Furthermore, we introduce a new approach to simultaneously identify mesh topology and spring stiffness values. Linear elastic FEM deformation computations are used as reference. Additionally, our results show that uniform distributions of spring stiffness constants fails to simulate linear elastic deformations.

A Survey on Statistical Modeling and Machine Learning Approaches to Computer Assisted Medical Intervention: Intraoperative Anatomy Modeling and Optimization of Interventional Procedures

“…To solve the problem, the large dataset is partitioned into several small sub-datasets, and the simulator is constructed by multiple networks, each of which is trained by using its corresponding sub-dataset. When external forces caused by surgical instruments are used as input data of the simulator, the approximation or the imitation of the FEM simulation may be achieved by using mass-spring model [90] and FreeForm Deformation (FFD) [91]. In this case, the parameters in the mass-spring and FFD models are adjusted by fitting the deformations of these models to the FEM simulations used as training data.…”

Example-based dynamic skinning in real time

“…These methods fit parameters from static poses, while our fitting algorithm learns the dynamical properties of materials from animation sequences, rendering our task more challenging as the problem becomes highly non-linear. Bianchi et al [2004] proposed simultaneous identification of the topology and stiffness of mass-spring models based on finite element method (FEM) reference deformations. Our deformable model inherits the topology of the user-provided surface mesh to best fit the traditional graphics hardware pipeline.…”

Automatic preparation, calibration, and simulation of deformable objects

“…Bianchi et al [9] later demonstrate the recovery of spring constants, and the 2D calibration of a mass-spring system to a finite element reference model. They do not extend their calibration to 3D, and do not provide a mechanism for handling the exponential growth in optimization complexity associated with 3D objects and complex topologies.…”

“…[9], [39]) have allowed stiffness constants to vary at each node, which links optimization complexity directly to mesh resolution and presents an enormous optimization landscape.…”