Modeling and Real-Time Simulation of a Vascularized Liver Tissue

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.

Estimation of boundary conditions for patient-specific liver simulation during augmented surgery

PURPOSE

Augmented reality can improve the outcome of hepatic surgeries, assuming an accurate liver model is available to estimate the position of internal structures. While researchers have proposed patient-specific liver simulations, very few have addressed the question of boundary conditions. Resulting mainly from ligaments attached to the liver, they are not visible in preoperative images, yet play a key role in the computation of the deformation.

METHOD

We propose to estimate both the location and stiffness of ligaments by using a combination of a statistical atlas, numerical simulation, and Bayesian inference. Ligaments are modeled as polynomial springs connected to a liver finite element model. They are initialized using an anatomical atlas and stiffness properties taken from the literature. These characteristics are then corrected using a reduced-order unscented Kalman filter based on observations taken from the laparoscopic image stream.

RESULTS

Our approach is evaluated using synthetic data and phantom data. By relying on a simplified representation of the ligaments to speed up computation times, it is not estimating the true characteristics of ligaments. However, results show that our estimation of the boundary conditions still improves the accuracy of the simulation by 75% when compared to typical methods involving Dirichlet boundary conditions.

CONCLUSION

By estimating patient-specific boundary conditions, using tracked liver motion from RGB-D data, our approach significantly improves the accuracy of the liver model. The method inherently handles noisy observations, a substantial feature in the context of augmented reality.

Fast simulation of stent deployment with plastic beam elements

Coronary stent deployment is a reference cardiology intervention, used to treat atherosclerosis and prevent heart attacks. The outcomes of the intervention highly depend on the accuracy of the stent apposition, which could benefit from per-operative prediction tools. In this paper, we propose a fast and mechanically realistic 3D simulation of a coronary stent expansion. Our simulation relies on the finite element method and involves serially linked beam elements to model the slender geometry of a stent. The elements are implemented with a non-linear elasto-plastic behavior, describing realistically the complex deformation of a balloon-expandable stent. As a proof of concept, we simulated the free expansion of a coronary stent. The simulation output was compared with micro-CT data, acquired experimentally during the device expansion. Results show that the plastic beam model is able to reproduce successfully the final geometry of the stent. In addition, the use of 1D elements allows to achieve a significantly lower computational time than for equivalent literature simulations, based on 3D elements. This preliminary work highlights the compatibility of our method with clinical routine in terms of execution time. Further developments include the application of the method to more advanced simulation scenarios, with the addition of a personalized artery model.

Modeling of the contrast-enhanced perfusion test in liver based on the multi-compartment flow in porous media

The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. Conceptually, computed time-space distributions of the so-called tissue density can be compared with the measured data obtained from CT; such a modeling feedback can be used for model parameter identification. The blood flow is characterized at several scales for which different models are used. Flows in upper hierarchies represented by larger branching vessels are described using simple 1D models based on the Bernoulli equation extended by correction terms to respect the local pressure losses. To describe flows in smaller vessels and in the tissue parenchyma, we propose a 3D continuum model of porous medium defined in terms of hierarchically matched compartments characterized by hydraulic permeabilities. The 1D models corresponding to the portal and hepatic veins are coupled with the 3D model through point sources, or sinks. The contrast fluid saturation is governed by transport equations adapted for the 1D and 3D flow models. The complex perfusion model has been implemented using the finite element and finite volume methods. We report numerical examples computed for anatomically relevant geometries of the liver organ and of the principal vascular trees. The simulated tissue density corresponding to the CT examination output reflects a pathology modeled as a localized permeability deficiency.

Cellular neural network modelling of soft tissue dynamics for surgical simulation

BACKGROUND

Currently, the mechanical dynamics of soft tissue deformation is achieved by numerical time integrations such as the explicit or implicit integration; however, the explicit integration is stable only under a small time step, whereas the implicit integration is computationally expensive in spite of the accommodation of a large time step.

OBJECTIVE

This paper presents a cellular neural network method for stable simulation of soft tissue deformation dynamics.

METHOD

The non-rigid motion equation is formulated as a cellular neural network with local connectivity of cells, and thus the dynamics of soft tissue deformation is transformed into the neural dynamics of the cellular neural network.

RESULTS

Results show that the proposed method can achieve good accuracy at a small time step. It still remains stable at a large time step, while maintaining the computational efficiency of the explicit integration.

CONCLUSION

The proposed method can achieve stable soft tissue deformation with efficiency of explicit integration for surgical simulation.