Mathematical modeling of thermal ablation

Ablation techniques have become a widespread choice for the treatment of cancerous tumors for which surgical resection techniques have a poor prognosis. The minimally invasive nature and high success rate when performed by experienced clinicians mean that ablation is likely to remain a core technique. However, the success rate can drop off dramatically when less-experienced operators are involved, and it is particularly difficult to kill all of the tumor and only the tumor, given the dynamic nature of the processes that lead to cell death. Mathematical modeling of the response to ablation treatment has a long history. Since the seminal paper of Pennes in 1948, there have been numerous attempts to propose models that are both physiologically accurate and computationally inexpensive. All of these models are based on different principles and assumptions, which may make them suitable only for particular applications. This makes choosing a model very difficult because of the lack of understanding about what the limitations of different assumptions are likely to be and how this influences the necessary computational resources. Here we review the models available in the literature, illustrating how the different assumptions impact upon both their accuracy and computational expense. The primary intentions are to provide a critical scientific review and a practical guide for researchers wishing to use such models in clinical applications.