Real-time multi-physics modeling of radio-frequency electrosurgical procedures

Abstract

Electrosurgery utilizing radio-frequency (RF) alternating current is increasingly being utilized to perform a variety of surgical and other therapeutic procedures. However, the underlying mechanisms of electrosurgical cutting and damage have not been thoroughly understood, a factor that likely contributed significantly to the incidence of RF electricity-related surgical complications. Hence, physically realistic simulations of electrosurgery are becoming a necessity for safe and effective use as also to develop new devices and procedures. Such interactive simulations demand real-time modeling of coupled electro-thermo-mechanical physics, multiscale interactions, and topology modifications with a very high degree of realism. To cope with these challenges, methods that are numerically efficient and robust have to be developed. However, incorporating topology changes with these algorithms for interactive simulations is challenging, and the intra- and extracellular vaporization that results in precise cutting of tissue has not been modeled.

Finally, we present acceleration strategies for the solution of multi-physics problem to achieve real-time simulation of RF activated tissue dissection. First, an efficient block preconditioner is proposed to solve coupled electro-thermo-mechanical problem using Krylov subspace based iterative solver (e.g. GMRES). The block preconditioning technique effectively deflates the spectrum of the system matrix, resulting in an exponential convergence of GMRES iterations. Next, we propose a data-driven approach that leverages the approximation power of deep learning neural networks with the precision of standard solvers to further accelerate computations. The electro-thermal problem is solved using GMRES with the deflation-based block preconditioner. The mechanical deformation due to intra- and extracellular water evaporation is predicted using a convolutional neural network (CNN) with a highly customized architecture, trained using a supervised learning framework to map a nonlinear relationship between the pore pressure and deformation field for evolving tissue topology. The simulation results show significant improvement in the computational time for the hybrid approach when compared to standard solution approach using block-preconditioned GMRES and a parametric solution approach using a proper generalized decomposition (PGD)-based reduced order model; with the accuracy comparable to the ground truth obtained using standard solution approaches.

This approach provides greatly increased visual resolution of thermal effects, yet remains physically accurate. However, a major limitation of this approach is that it still requires dynamic triangulation to provide sub-finite-element graphical rendering. To overcome this issue, we propose a novel physics-driven level set approach to capture the interfacial evolution of tissue damage to reduce meshing and re-meshing complexity. An important aspect of this work is the derivation of the level set evolution equation from the Second Law of Thermodynamics, which is consistent with Griffith’s fracture evolution criterion. The damage parameter that determines the interfacial evolution of tissue damage is characterized by solving an inverse problem that seeks to minimize the difference between the predicted and experimentally measured topological information, i.e. signed distance of a spatial point from the damaged interface. Controlled electrosurgical experiments are performed on the fresh ex vivo porcine liver to obtain the topological information of damaged tissue. Example problems are shown to simulate tissue dissection with a fixed and moving active electrode.

In this thesis, we propose a multi-physics model to study the effects of RF activation on the thermo-mechanical response of soft tissues. A thermodynamically consistent continuum model for soft tissues is presented within the framework of small deformation linear thermoelasticity. The micromechanical model based equation-of-state describes the thermodynamic states such as temperature, and pressure arising from evaporation of intra- and extra-cellular water by absorbing heat due to Joule heating. A tissue damage model is employed to describe tissue dissection due to cellular wall rupture, with effective thermal and mechanical quantities, and incremental effective heat generation at a macroscopic spatial point obtained from the micromechanical model. The multi-physics model is validated with experimental data from thermal ablation experiments on porcine liver tissue.

We propose two algorithms for electrosurgical cutting based on a dual mesh algorithm and a level set method to model tissue dissection based on critical temperature and energy-based criteria, respectively. Modeling of electrosurgical cutting is complicated as the cut must follow the motion of the electrosurgical tool, but must also evolve in width and depth. The actual depth and extent of tissue injury are dependent upon many factors including power density, electrode size and shape, and nature of the tissue being dissected. First, we introduce a dual mesh algorithm for rendering partially vaporized tissue (i.e. tissue at temperature above critical boiling temperature under ambient condition) at spatial resolutions much finer than the underlying tetrahedral mesh.