AUTHOR=Mariappan Panchatcharam , B  Gangadhara , Flanagan  Ronan 

TITLE=A point source model to represent heat distribution without calculating the Joule heat during radiofrequency ablation

JOURNAL=Frontiers in Thermal Engineering

VOLUME=Volume 2 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/thermal-engineering/articles/10.3389/fther.2022.982768

DOI=10.3389/fther.2022.982768

ISSN=2813-0456

ABSTRACT=Numerous liver cancer oncologists suggest bridging therapies to limit cancer growth until donors are available. Interventional radiology including radiofrequency ablation (RFA) is one such bridging therapy. This locoregional therapy aims to produce an optimal amount of heat to kill cancer cells, where the heat is produced by a radiofrequency (RF) needle. Less experienced Interventional Radiologists (IRs) require a software-assisted smart solution to predict the optimal heat distribution as both overkilling and untreated cancer cells are problematic treatments. Therefore, two of the big three partial differential equations, (1) heat equation \citep{Pennes} to predict the heat distribution and (2) Laplace equation  \citep{Prakash} for electric potential along with different cell death models  \citep{Neil} are widely used in the last three decades. However, solving two differential equations and a cell death model is computationally expensive when the number of finite compact coverings of a liver topological structure increases in millions. Since the heat source from the Joule losses $Q_r=\sigma |\nabla V|^2$ is obtained from Laplace equation $\sigma \Delta V=0$, it is called the Joule heat model. The traditional Joule heat model can be replaced by a point source model to obtain the heat source term. The idea behind this model is to solve $\sigma \Delta V=\delta_0$ where $\delta_0$ is a Dirac-delta function. Therefore, using the fundamental solution of the Laplace equation \citep{Evans} we represent the solution of the Joule heat model using an alternative model called the point source model which is given by the Gaussian distribution
$$Q_r(x)=\sum_{x_i\in\Omega}\frac{1}{K} \sum_i c_i e^{-\frac{|x-x_i |^2}{2\sigma^2} }$$ where $K$ and $c_i$ are obtained by using needle parameters. This model is employed in one of our software solutions called RFA Guardian \citep{Philip}  which predicted the treatment outcome very well for more than 100 patients.