Inga Altrogge

Numerical simulation of radio frequency ablation with state dependent material parameters in three space dimensions

We present a model for the numerical simulation of radio frequency (RF) ablation of tumors with mono- or bipolar probes. This model includes the electrostatic equation and a variant of the well-known bio-heat transfer equation for the distribution of the electric potential and the induced heat. The equations are nonlinearly coupled by material parameters that change with temperature, dehydration and damage of the tissue. A fixed point iteration scheme for the nonlinear model and the spatial discretization with finite elements are presented. Moreover, we incorporate the effect of evaporation of water from the cells at high temperatures using a predictor-corrector like approach. The comparison of the approach to a real ablation concludes the paper.

Towards optimization of probe placement for radio-frequency ablation

We present a model for the optimal placement of mono- and bipolar probes in radio-frequency (RF) ablation. The model is based on a numerical computation of the probes electric potential and of the steady state of the heat distribution during RF ablation. The optimization is performed by minimizing a temperature based objective functional under these constraining equations. The paper discusses the discretization and implementation of the approach. Finally, applications of the optimization to artificial data and a comparison to a real RF ablation are presented.

Optimal applicator placement in hepatic radiofrequency ablation on the basis of rare data

In this paper, a numerical procedure to determine an optimal applicator placement for hepatic radiofrequency ablation incorporating uncertain material parameters is presented. The main focus is set on the treatment of subjective and rare data-based information. For this purpose, we employ the theory of fuzzy sets and model uncertain parameters as fuzzy quantities. While fuzzy modelling has been established in structural engineering in the recent past, it is novel in biomedical engineering. Incorporating fuzzy quantities within an optimisation task is basically innovative. In our context, fuzzy modelling allows us to determine an optimal applicator placement that maximises the therapy success under the given uncertainty conditions. The applicability of our method is demonstrated by means of an example case.

Radiofrequency ablation planning beyond simulation

It is a challenging task to plan a radiofrequency (RF) ablation therapy to achieve the best outcome of the treatment and avoid recurrences at the same time. A patient specific simulation in advance that takes the cooling effect of blood vessels into account is a helpful tool for radiologists, but this needs a very high accuracy and thus high computational costs. In this work, we present various methods, which improve and extend the planning of an RF ablation procedure. First, we discuss two extensions of the simulation model to obtain a higher accuracy, including the vaporization of the water in the tissue and identifying the model parameters and to analyze their uncertainty. Furthermore, we discuss an extension of the planning procedure namely the optimization of the probe placement, which optimizes the overlap of the tumor area with the estimated coagulation in order to avoid recurrences. Since the optimization is constrained by the model, we have to take into account the uncertainties in the model parameters for the optimization as well. Finally, applications of our methods to a real RF ablation case are presented.

Modeling, Simulation and Optimization of Radio Frequency Ablation

The treatment of hepatic lesions with radio-frequency (RF) ablation has become a promising minimally invasive alternative to surgical resection during the last decade. In order to achieve treatment qualities similar to surgical R0 resections, patient specific mathematical modeling and simulation of the biophysical processes during RF ablation are valuable tools. They allow for an a priori estimation of the success of the therapy as well as an optimization of the therapy parameters. In this report we discuss our recent efforts in this area: a model of partial differential equations (PDEs) for the patient specific numerical simulation of RF ablation, the optimization of the probe placement under the constraining PDE system and the identification of material parameters from temperature measurements. A particular focus lies on the uncertainties in the patient specific tissue properties. We discuss a stochastic PDE model, allowing for a sensitivity analysis of the optimal probe location under variations in the material properties. Moreover, we optimize the probe location under uncertainty, by considering an objective function, which is based on the expectation of the stochastic distribution of the temperature distribution. The application of our models and algorithms to data from real patient’s CT scans underline their applicability.

Optimization and Fast Estimation of Vessel Cooling for RF Ablation

In this work, we present a three-dimensional (3D) model for the optimization of the probe placement in radio-frequency ablation (RFA). The model is based on a system of partial differential equations (PDEs) that describe the electric potential of the tissue and the steady state of the heat which is induced into the tissue. The PDE system is solved by a finite element approach and the optimization is performed by minimizing a temperature based objective functional under the constraining PDE systems. A well-known difficulty associated with RFA is the cooling influence of large blood vessels on the ablation result. A method is discussed, which efficiently estimates the cooling effect of those vessels, based on a precalculation of all patient-independent data and tabulation of the results.