Modeling of radiofrequency tumor ablation

Temperature comparison of perfused (blue) and unperfused (red) RFA simulation model in the liver; RFA energy was switched off after 10 seconds; temperature was measured at electrode’s tip (arrow). Blood perfusion limits the temperature increase in the tissue -> cooling effect

Thermal ablative therapies are used to treat malignant tumors in liver, kidney, lung and bone tissues. During RF ablation treatment, a thin electrode is placed directly into the tumor using ultrasound, computed tomography or magnetic resonance imaging guidance. An RF generator connected to an antenna creates an electromagnetic field in the surrounding tissue which causes heat due to ionic friction. Due to the blood flow e.g. in the liver cooling occurs (heat is dragged away by the blood) an limits the temperature increase. The perfusion effect can be mathematically modeled with the "bio-heat equation" which was first introduced by Pennes in 1948. 

The bio-heat equation is solved with: 

 

ρ is the density (kg·m^-3), c is the specific heat (J·kg^-1·K^-1), k is the thermal conductivity (W·m^-1·K^-1), J is the electric current density (A·m²), E is the electric field intensity (V·m^-1) and Q_P (W·m^-3), is the heat loss due to blood perfusion. The energy generated by the metabolic processes, is usually neglected since it is orders of magnitude lower than Q_P.

 

T_bl is the temperature of the blood (assumed to be 37 °C), ρ_bl is the blood density (kg·m^-1), c_bl is the specific heat of human blood (J·kg^-1·K^-1), and w_bl is the blood perfusion. 

The image in the top shows a RFA model that I created in COMSOL4.0 to compare temperature distribution in perfused and unperfused liver.

Links:

COMSOL - http://www.comsol.com/

My ablation laboratory - http://www.musc.edu/ablation/