FAU Erlangen-Nuremberg

Optimization and Optimal Control of Therapy Parameters for Radio-Frequency Ablation

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Project leaders

FB 03, AG Optimierung u. optimale Steuerung
Uni Bremen

Tel: 0421 218-4813
Fax: 0421 218-4235

Email: bueskens@math.uni-bremen.de


Center of Complex Systems and Visualization (CeVis)
Uni Bremen
Universitaetsallee 29
28359 Bremen

Tel: 0421 218-7707
Tel: 0421 218-7711 (Sekr.)
Fax: 0421 218-4236

Email: preusser@cevis.uni-bremen.de


Additional applicant

FB 03, Mathematik mit Schwerpunkt Dynamische Systeme
Uni Bremen

Tel: 0421 218-3552
Fax: 0421 218-4236

Email: heinz-otto.peitgen@cevis.uni-bremen.de


DFG funded assistants

Hanne Tiesler (Uni Bremen)


Inga Altrogge (Uni Bremen)

Tim Kroeger (Uni Bremen)


For various tumor-diseases (liver-, lung-, bone-tumors, kidney-carcinoma), for which a surgical therapy is not possible due to the extent of the tumor or the general state of the patient, local and minimally invasive techniques have been established as alternative forms of the treatment. The so-called thermo-ablation treatments try to destroy the malignant tissue by local heating or cooling. Examples of local heating techniques are the radio-frequency-ablation (RF-ablation), laser induced thermo-therapy or focused ultrasound. Promising results in the treatment of liver tumors have been achieved during the last years with thermo-ablation using laser-radiation or radio-frequency-current. Within the field of interventional radiology the percutaneous minimal-invasive tumor-therapy with thermo-ablation is a young but continuously advancing method with high therapeutic potential.

The clinical relevance of these approaches is clearly visible in publications up to date. The treatment with RF-ablation is very widely used. Recurrence rates and median survival times have been investigated by various authors for patients with hepatocellular carcinoma, hepatic metastases as well as colorectal liver metastases which have been treated by RF-ablation.


The focus of the envisaged project is the RF-ablation of the liver with bipolar systems: a probe, internally cooled and containing two electrodes, is placed in the vicinity of the malignant tissue. The electrodes are connected to a generator, and an electric current warms the tissue close to the probe up to temperatures of more than 60° C. Consequently the proteins of the heated tissue denaturate and its cells die. The treatment is successful, if all tumor cells are destroyed by the denaturation of their proteins. In areas distant from the probe the critical temperatures can only be achieved by propagation of heat away from the source. Thereby perfusion (blood flow) of the surrounding tissue by large vessels and capillary blood flow has a significant effect. To enlarge the volume of coagulated tissue (i.e. denaturated proteins) and to decrease the influence of perfusion the tumor can be penetrated with multiple probes (at most 2-3) simultaneously.

For a reliable treatment with RF-ablation, a planning of the therapy and monitoring of the intervention is indispensable. In the interest of the patient it must be ensured in advance, that a tumor will be destroyed completely by the therapy and the achieved result must be controlled intra- and post-interventional.

During the last decade the numerical simulation of RF-ablation has been modeled by several authors. Such models consist of a system of partial differential equations for electric potential, tissue temperature and tissue damage. The equations are coupled nonlinearly and the physical properties of the tissue under consideration depend on the temperature, the dehydration state and the protein status of the cells. However, in the field of RF-ablation no results exist on the optimization of treatment parameters or the parametric sensitivity analysis to assess the computed solution.

The project aims at several targets: The design of appropriate objective functionals which measure the quality of an ablation process. Furthermore the identification of the patient-individual material properties. These include the electric and thermal conductivities as well as densities and heat capacities. Moreover the project aims at an optimization and optimal control of the RF-probe's positioning and electric potential. Since the mathematical model describing the ablation process is a system of PDEs which are coupled in a complex way, increasing levels of modeling, discretization and optimization will be considered. Finally the postoptimal calculation of so-called parametric sensitivity differentials of the optimal solutions with respect to model data and perturbations will be considered at the different levels. This information plays an important role in the analysis of partial results as aforementioned and might be a helpful tool in the assessment of optimal solutions for users.

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