A reduced order explicit dynamic finite element algorithm for surgical simulation

Real-time simulation of viscoelastic tissue behavior with physics-guided deep learning

Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by computational cost. In this application scenario, which typically involves transportable simulators, the computing hardware severely constrains the size or the level of details of the simulated scene. To address this limitation, data-driven approaches have been suggested to simulate mechanical deformations by learning the mapping rules from FEM generated datasets. Prior data-driven approaches have ignored the physical laws of the underlying engineering problem and have consequently been restricted to simulation cases of simple hyperelastic materials where the temporal variations were effectively ignored. However, most surgical training scenarios require more complex hyperelastic models to deal with the viscoelastic properties of tissues. This type of material exhibits both viscous and elastic behaviors when subjected to external force, requiring the implementation of time-dependant state variables. Herein, we propose a deep learning method for predicting displacement fields of soft tissues with viscoelastic properties. The main contribution of this work is the use of a physics-guided loss function for the optimization of the deep learning model parameters. The proposed deep learning model is based on convolutional (CNN) and recurrent layers (LSTM) to predict spatiotemporal variations. It is augmented with a mass conservation law in the lost function to prevent the generation of physically inconsistent results. The deep learning model is trained on a set of FEM datasets that are generated from a commercially available state-of-the-art numerical neurosurgery simulator. The use of the physics-guided loss function in a deep learning model has led to a better generalization in the prediction of deformations in unseen simulation cases. Moreover, the proposed method achieves a better accuracy over the conventional CNN models, where improvements were observed in unseen tissue from 8% to 30% depending on the magnitude of external forces. It is hoped that the present investigation will help in filling the gap in applying deep learning in virtual reality simulators, hence improving their computational performance (compared to FEM simulations) and ultimately their usefulness.

Finite-element kalman filter with state constraint for dynamic soft tissue modelling

This research work proposes a novel method for realistic and real-time modelling of deformable biological tissues by the combination of the traditional finite element method (FEM) with constrained Kalman filtering. This methodology transforms the problem of deformation modelling into a problem of constrained filtering to estimate physical tissue deformation online. It discretises the deformation of biological tissues in 3D space according to linear elasticity using FEM. On the basis of this, a constrained Kalman filter is derived to dynamically compute mechanical deformation of biological tissues by minimizing the error between estimated reaction forces and applied mechanical load. The proposed method solves the disadvantage of costly computation in FEM while inheriting the superiority of physical fidelity.

Extended Kalman Filter Nonlinear Finite Element Method for Nonlinear Soft Tissue Deformation

BACKGROUND AND OBJECTIVE

Soft tissue modelling is crucial to surgery simulation. This paper introduces an innovative approach to realistic simulation of nonlinear deformation behaviours of biological soft tissues in real time.

METHODS

This approach combines the traditional nonlinear finite-element method (NFEM) and nonlinear Kalman filtering to address both physical fidelity and real-time performance for soft tissue modelling. It defines tissue mechanical deformation as a nonlinear filtering process for dynamic estimation of nonlinear deformation behaviours of biological tissues. Tissue mechanical deformation is discretized in space using NFEM in accordance with nonlinear elastic theory and in time using the central difference scheme to establish the nonlinear state-space models for dynamic filtering.

RESULTS

An extended Kalman filter is established to dynamically estimate nonlinear mechanical deformation of biological tissues. Interactive deformation of biological soft tissues with haptic feedback is accomplished as well for surgery simulation.

CONCLUSIONS

The proposed approach conquers the NFEM limitation of step computation but without trading off the modelling accuracy. It not only has a similar level of accuracy as NFEM, but also meets the real-time requirement for soft tissue modelling.

Towards real-time finite-strain anisotropic thermo-visco-elastodynamic analysis of soft tissues for thermal ablative therapy

BACKGROUND AND OBJECTIVES

Accurate and efficient prediction of soft tissue temperatures is essential to computer-assisted treatment systems for thermal ablation. It can be used to predict tissue temperatures and ablation volumes for personalised treatment planning and image-guided intervention. Numerically, it requires full nonlinear modelling of the coupled computational bioheat transfer and biomechanics, and efficient solution procedures; however, existing studies considered the bioheat analysis alone or the coupled linear analysis, without the fully coupled nonlinear analysis.

METHODS

We present a coupled thermo-visco-hyperelastic finite element algorithm, based on finite-strain thermoelasticity and total Lagrangian explicit dynamics. It considers the coupled nonlinear analysis of (i) bioheat transfer under soft tissue deformations and (ii) soft tissue deformations due to thermal expansion/shrinkage. The presented method accounts for anisotropic, finite-strain, temperature-dependent, thermal, and viscoelastic behaviours of soft tissues, and it is implemented using GPU acceleration for real-time computation.

RESULTS

The presented method can achieve thermo-visco-elastodynamic analysis of anisotropic soft tissues undergoing large deformations with high computational speeds in tetrahedral and hexahedral finite element meshes for surgical simulation of thermal ablation. We also demonstrate the translational benefits of the presented method for clinical applications using a simulation of thermal ablation in the liver.

CONCLUSION

The key advantage of the presented method is that it enables full nonlinear modelling of the anisotropic, finite-strain, temperature-dependent, thermal, and viscoelastic behaviours of soft tissues, instead of linear elastic, linear viscoelastic, and thermal-only modelling in the existing methods. It also provides high computational speeds for computer-assisted treatment systems towards enabling the operator to simulate thermal ablation accurately and visualise tissue temperatures and ablation zones immediately.

NiftySim: A GPU-based nonlinear finite element package for simulation of soft tissue biomechanics

PURPOSE

NiftySim, an open-source finite element toolkit, has been designed to allow incorporation of high-performance soft tissue simulation capabilities into biomedical applications. The toolkit provides the option of execution on fast graphics processing unit (GPU) hardware, numerous constitutive models and solid-element options, membrane and shell elements, and contact modelling facilities, in a simple to use library.

METHODS

The toolkit is founded on the total Lagrangian explicit dynamics (TLEDs) algorithm, which has been shown to be efficient and accurate for simulation of soft tissues. The base code is written in C[Formula: see text], and GPU execution is achieved using the nVidia CUDA framework. In most cases, interaction with the underlying solvers can be achieved through a single Simulator class, which may be embedded directly in third-party applications such as, surgical guidance systems. Advanced capabilities such as contact modelling and nonlinear constitutive models are also provided, as are more experimental technologies like reduced order modelling. A consistent description of the underlying solution algorithm, its implementation with a focus on GPU execution, and examples of the toolkit's usage in biomedical applications are provided.

RESULTS

Efficient mapping of the TLED algorithm to parallel hardware results in very high computational performance, far exceeding that available in commercial packages.

CONCLUSION

The NiftySim toolkit provides high-performance soft tissue simulation capabilities using GPU technology for biomechanical simulation research applications in medical image computing, surgical simulation, and surgical guidance applications.

Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices

Abstract

Simulation of all phenomena taking place in a surgical procedure is a formidable task that involves, when possible, the use of supercomputing facilities over long time periods. However, decision taking in the operating room needs for fast methods that provide an accurate response in real time. To this end, Model Order Reduction (MOR) techniques have emerged recently in the field of Computational Surgery to help alleviate this burden. In this paper, we review the basics of classical MOR and explain how a technique recently developed by the authors and coined as Proper Generalized Decomposition could make real-time feedback available with the use of simple devices like smartphones or tablets. Examples are given on the performance of the technique for problems at different scales of the surgical procedure, form gene regulatory networks to macroscopic soft tissue deformation and cutting.

Real-time simulation of biological soft tissues: a PGD approach

We introduce here a novel approach for the numerical simulation of nonlinear, hyperelastic soft tissues at kilohertz feedback rates necessary for haptic rendering. This approach is based upon the use of proper generalized decomposition techniques, a generalization of PODs. Proper generalized decomposition techniques can be considered as a means of a priori model order reduction and provides a physics-based meta-model without the need for prior computer experiments. The suggested strategy is thus composed of an offline phase, in which a general meta-model is computed, and an online evaluation phase in which the results are obtained at real time. Results are provided that show the potential of the proposed technique, together with some benchmark test that shows the accuracy of the method.