Quantifying discretization errors for soft tissue simulation in computer assisted surgery: A preliminary study

Abstract

Errors in biomechanics simulations arise from modeling and discretization. Modeling errors are due to the choice of the mathematical model whilst discretization errors measure the impact of the choice of the numerical method on the accuracy of the approximated solution to this specific mathematical model. A major source of discretization errors is mesh generation from medical images, that remains one of the major bottlenecks in the development of reliable, accurate, automatic and efficient personalized, clinically-relevant Finite Element (FE) models in biomechanics. The impact of mesh quality and density on the accuracy of the FE solution can be quantified with a posteriori error estimates. Yet, to our knowledge, the relevance of such error estimates for practical biomechanics problems has seldom been addressed, see [25]. In this contribution, we propose an implementation of some a posteriori error estimates to quantify the discretization errors and to optimize the mesh. More precisely, we focus on error estimation for a user-defined quantity of interest with the Dual Weighted Residual (DWR) technique. We test its applicability and relevance in two situations, corresponding to computations for a tongue and an artery, using a simplified setting, i.e., plane linearized elasticity with contractility of the soft-tissue modeled as a pre-stress. Our results demonstrate the feasibility of such methodology to estimate the actual solution errors and to reduce them economically through mesh refinement.

Direct simplicial dynamics: Simulations in biomechanics

“…Therefore we cannot directly compare the numbers obtained from the two theories for the ‘same’ values of the elastic moduli. Thus approaches that attempt to quantify discretization errors, while they may be such as Reference 31, are not directly relevant to our approach and purpose. We may however be able to follow procedures such as those proposed in References 32‐35, and in particular machine learning approaches to identify the parameter values based upon data from clinical procedures as they become available.…”

Role of mechanical cues and hypoxia on the growth of tumor cells in strong and weak confinement: A dual in vitro–in silico approach

“…Homogenous FE meshes have been generated and used for the numerical simulations (linear triangular elements having a mean characteristic size of the order of 0.5 m). With fine meshing only needed in the interface zone, a local remeshing technique (34,35) would surely help in reducing computational costs as perspective improvement of the developed computational framework.…”

An open-source FEniCS-based framework for hyperelastic parameter estimation from noisy full-field data: Application to heterogeneous soft tissues

“…These ideas have been pushed forward with the goal of discriminating between discretization error and model error in a series of papers [8][9][10], where real-time error estimation method for surgical simulation and guidance are described in detail [11].…”