Tim Kröger

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.

Simulation of Radiofrequency Ablation Including Water Evaporation

We present a new approach for the simulation of radiofrequency (RF) ablation, which takes the vaporization of water into account. This vaporization has an important influence on the outcome of the ablation process due to the significant smaller electric conductivity in the gaseous domain. Therefore the development of a gaseous domain around the RF probe leads to a decreased induction of heat into the surrounding tissue. We discretize the mathematical model by using composite finite elements to solve the resulting partial differential equations. A level set method is used for the tracking of the moving boundary between the tissue containing gaseous water and the tissue containing liquid water.

Matching of anatomical tree structures for registration of medical images

Many medical applications require a registration of different images of the same organ. In many cases, such a registration is accomplished by manual placement of landmarks in the images. In this paper, we propose a method which is able to find reasonable landmarks automatically. To achieve this, bifurcations of the vessel systems, which have been extracted from the images by a segmentation algorithm, are assigned by the so-called association graph method and the coordinates of these matched bifurcations can be used as landmarks for a non-rigid registration algorithm. Several constraints to be used in combination with the association graph method are proposed and evaluated on a ground truth consisting of anatomical trees from liver and lung. Furthermore, a method for preprocessing (tree pruning) as well as for postprocessing (clique augmentation) are proposed and evaluated on this ground truth. The proposed method achieves promising results for anatomical trees of liver and lung and for medical images obtained with different modalities and at different points in time.

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.

Workflow oriented software support for image guided radiofrequency ablation of focal liver malignancies

Image guided radiofrequency (RF) ablation has taken a significant part in the clinical routine as a minimally invasive method for the treatment of focal liver malignancies. Medical imaging is used in all parts of the clinical workflow of an RF ablation, incorporating treatment planning, interventional targeting and result assessment. This paper describes a software application, which has been designed to support the RF ablation workflow under consideration of the requirements of clinical routine, such as easy user interaction and a high degree of robust and fast automatic procedures, in order to keep the physician from spending too much time at the computer. The application therefore provides a collection of specialized image processing and visualization methods for treatment planning and result assessment. The algorithms are adapted to CT as well as to MR imaging. The planning support contains semi-automatic methods for the segmentation of liver tumors and the surrounding vascular system as well as an interactive virtual positioning of RF applicators and a concluding numerical estimation of the achievable heat distribution. The assessment of the ablation result is supported by the segmentation of the coagulative necrosis and an interactive registration of pre- and post-interventional image data for the comparison of tumor and necrosis segmentation masks. An automatic quantification of surface distances is performed to verify the embedding of the tumor area into the thermal lesion area. The visualization methods support representations in the commonly used orthogonal 2D view as well as in 3D scenes.

Matching of tree structures for registration of medical images

Many medical applications require a registration of different images of the same organ. In many cases, such a registration is accomplished by manually placing landmarks in the images. In this paper we propose a method which is able to find reasonable landmarks automatically. To achieve this, nodes of the vessel systems, which have been extracted from the images by a segmentation algorithm, will be assigned by the so-called association graph method and the coordinates of these matched nodes can be used as landmarks for a non-rigid registration algorithm.

Hierarchical matching of anatomical trees for medical image registration

Today, tomographic images are used in medical applications more and more. To support physicians in diagnosis and treatment, a registration of two images taken at different points in time or under different conditions is needed. As the structure of the vessel or airway trees is relatively stable between two image acquisitions, they provide a good basis for the automatic determination of landmarks. In this work, a hierarchical tree search algorithm is proposed, which efficiently computes a matching between branchpoints of anatomical trees, which can be used as landmarks for an elastic registration. The algorithm is designed to be general and robust in order to be applicable to a variety of different datasets, which are acquired by different sensors or under different conditions. The validation of the algorithm against manually created ground truth data leads to a 80.9% rate of correctly matched branchpoints. Allowing a tolerance of 5 mm, the rate increases to 89.9%. The runtime for 50-700 vertices is about 1-45 seconds.

Stability of the 8-tetrahedra shortest-interior-edge partitioning method

We consider a tetrahedron partitioning method, known in the literature as the 8-tetrahedra shortest-interior-edge partition. For this method, which is a variant of Freudenthal’s algorithm in three space dimensions, we prove that the infinite series of refined meshes (for any given initial mesh) is stable in the sense that the degree of degeneracy of the cells remains bounded. We give an explicit estimate in terms of a standard shape quality measure introduced by Liu and Joe. Furthermore, we show that our estimate is sharp. The estimate also holds for Freudenthal’s algorithm (in three space dimensions) provided that it is initialized appropriately. Numerical experiments confirm our result as well as its sharpness.

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.

Towards a verified simulation model for radiofrequency ablations

The simulation of radiofrequency ablations (RFA) can predict the achievable coagulation area and thus provide useful information for treatment planning, especially in cases in which the heat distribution can be limited by vascular cooling effects. A strong reliability of the numerical simulation results is essential for clinical use In this paper, we present a novel experimental procedure for the verification of RFA simulation systems in a lifelike environment without requiring animal tests. RF ablations are performed within isolated, perfused porcine livers, the corresponding configurations are reconstructed and simulated on a computer, and the resulting pathoanatomical coagulations are compared to their simulated counterparts with consideration of vascular cooling effects. We have applied this procedure for an initial verification of an existing RFA simulation system. The results are presented and discussed in this paper.