Simulation of Radio-Frequency Ablation using Composite Finite Element (CFE) Methods

The radio-frequency (RF) ablation of primary and metastatic tumors has become a promising treatment as an alternative to chemotherapy, radiotherapy and surgical resection. Together with appropriate mathematical, physical and biochemical models which describe the process, the success of the treatment can be estimated or even optimized. The goal is to reduce the recurrency rate by a complete destruction of the malignant tissue.

In this work we consider RF-ablation 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, which delivers a power of 30W - 200W at a frequency of f = 500KHz. Once the generator is switched on, an electric current warms the tissue close to the probe up to temperatures of more than 60°. 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 critial temperatures can only be achieved by propagation of heat away from the source. Thereby the perfusion of the surrounding tissue by large vessels and capillary blood flow has a significant cooling effect which needs to be modeled properly. 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 simultaneously.

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The figure shows a schematic sketch of the computational domain and the the inscribed structures. On this computational domain we are solving the following equations:

Electric potential

We compute the electric potential of the RF probe with

where is the electric conductivity of the tissue and the boundary conditions at the electrodes of the probe.

Temperature distribution

The distribution of temperature within the tissue is computed using the heat-equation (bioheat-transfer equation)
where is the thermal conductivity of the different materials.

Heat Sources and Sinks

The right hand side of the above bioheat-transfer equation consists of the following heat source and sink:

• Heating by the electric current  
• Cooling by perfusion (blood flow)  

For the application of the model to real data, we have taken a vessel segmentation from a real CT scan and placed the applicator into the setting. Click on the image to load a movie showing the configuration of vessels and applicator. Left: Potential (0.0 Volt) of one bipolar RF probe. Click on the image to load a movie showing the potential distribution. Since the probe is placed very close to the vascular structure, the 0 Volt isosurface is forced to not lie exactly between the electrodes of the probe, because the vessels have different electrical properties than the rest of the tissue.
 
Right: Potential (0.0 Volt) of three simultaneously running RF-probes. Click on the image to load a movie showing the potential distribution.
Left: The 330K isosurface of the heat distribution is shown at the time (t=0.01) for one cooled bipolar probe as shown above. Please click on the image to load a movie which shows the evolution of the 330K temperature isosurface in time.