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Phys Med Biol. 2018 Dec 4;63(23):235026. doi: 10.1088/1361-6560/aaeef9.

An analytical solution for temperature distributions in hepatic radiofrequency ablation incorporating the heat-sink effect of large vessels.

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School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People's Republic of China.


Fast prediction of the local thermal field induced by radiofrequency ablation (RFA) plays a critical role in hepatic RFA therapy. At present, it is still a challenging task to calculate and visualize the temperature distribution of RFA in real-time, especially when the heat-sink effect of adjacent large vessels is taken into account. To achieve this, the current investigation presented an analytical solution to calculate the temperature in RFA with an execution time of 0.05 s for three dimensional thermal field reconstruction. The presented temperature distribution is a combination of temperatures in homogeneous tissue and a quantification of the heat-sink effect of adjacent blood vessels. Temperatures in homogeneous tissue is calculated from a simplified Pennes bioheat equation, where several weighting parameters in the temperature expression are determined based on some reference point temperatures from the numerical simulation. The heat-sink effect is quantified based on a temperature factor, which measures the temperature difference between the vessel and the heated tissue, and a distance factor, which measures the distance to the vessel. The proposed method is validated to be able to gain similar temperature distributions to the numerical simulation but with its computational time being orders of magnitude smaller than that of numerical simulation, which improves the efficiency of interactive planning of RFA.


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