Current Trends in Mathematical Modeling of High-Temperature Thermal Therapies

We are delighted to present this special issue of The Open Biomedical Engineering (TOBEJ) focused on the current trends in mathematical modeling of high-temperature thermal therapies (ablation therapies). Clinical application and research of these therapies has seen rapid growth in the last decade, particularly for applications of cardiac arrhythmia (cardiac catheter ablation) and cancer treatment (tumor ablation). The general goal of these therapies is destruction of unwanted tissue (e.g. cancer tissue) via image-guided application of heat – typically via an applicator steered to the target location. Mathematical modeling of these therapies has become an important research tool, allowing investigation of underlying biophysics, as well as development of new medical devices. This special issue presents papers on current research directions from several of the major contributors to this field. While not all heating modalities are covered, many concepts presented are applicable to other modalities (e.g. laser, focused ultrasound). Most of the presented papers are related to tumor ablation, and one of the papers is discussing cardiac ablation. One of the essential features is the assessment of ablation zone (or thermal lesion) size. In this regard, Dr. Chang presents a study where the current methods used for predicting tissue injury (iso-temperature contours, cumulative equivalent minutes, and Arrhenius formulation) are exhaustively compared. Despite the fact that the study is focused on radiofrequency (RF) ablation, many of the presented concepts and conclusions can be applied to modeling studies of therapies based on other energy types. Drs. Saito and Ito present initial results on the possibility of monitoring the thermal lesion progress during microwave ablation by assessing the reflection coefficient change of the microwave antenna. Results are presented using mathematical models with experimental validation. Their results suggest that the proposed method could be used to improve monitoring during the procedure. Inadequate monitoring capabilities during tumor ablation procedures are currently one of the primary limitations. In addition to monitoring, prediction of the thermal lesion dimensions before treatment would be of great benefit to aid the physician in treatment planning. Dr. Preusser's group is working on this topic, where they work towards computer-assisted optimization of the procedure (i.e. finding the optimal applicator location for a given patient, and locating regions that are not heated sufficiently). The paper by this group published in this special issue by Kröger et al. presents a method that predicts the effect of large vessels via a rapid algorithm that can potentially be …