Regulatory agencies such as the US FDA must examine new medical devices to ensure that they are safe and effective. Sometimes, devices work successfully despite the fact that the mechanism of how they work isn't fully understood. In these cases, the FDA performs basic research to fill in these knowledge gaps.
Such is the case with the latest radio frequency (RF) ablation probes, which physicians insert into tissue with the intent to ablate (destroy) tissue in the region of the probe. These devices operate in the frequency range of 460-550 kHz to deliver alternating current into the tissue surrounding the probe. The RF energy is converted to heat when ions in tissue vibrate, and damages cells by raising the local temperature to as much as 100°C. Given all the factors that can vary in animal and clinical studies, computational modeling of ablation scenarios seems the most cost-effective and efficient means to study ablation. However, computational models can account only for known and characterizable factors, which include intrinsic tissue properties such as electrical conductivity, heat capacity, density, and perfusion (blood flow), and external factors such as the stimulus voltage, time, and the maximum ablation temperature.
Historically, researchers have relied on simple models that use temperature data to predict the size and shape of necrosed tissue regions. These models calculate the electromagnetic field and then a thermal solver predicts temperature. Because these models assume constant tissue electrical and thermal properties, they correlate poorly with clinically observed volumes of necrosed tissue. Protein denaturation occurs at ablation tissue temperatures, resulting in a cessation in local blood flow and an irreversible thermodynamic change in the relationship between the tissues' electrical properties and temperature. Thus, historical models have been of limited value to physicians who must anticipate lesion size for treatment planning.
The FDA's Isaac Chang has developed a model for ablation devices that takes into account changes in the properties of tissues as a function of temperature. In addition to calculating the temperature at each spatial location over time, it calculates thermal exposure and cumulative tissue damage. It uses these results to vary the tissues' intrinsic electrical properties, which feed back into the calculations of temperature for following time steps.
Because tissue properties change constantly during ablation, ablation problems can be solved only as time-dependent models. For his modeling, Chang needed a tool that could handle both electromagnetics and thermal effects simultaneously, and chose FEMLAB modeling software from COMSOL. He used the iterative time-dependent solver on a model consisting of 8,787 nodes and 42,045 elements. Each iteration calculates the electric field from the probe, the current density, heat flux, and the resulting tissue temperature. It also calculates tissue conductivity and SAR (specific absorption rate). The model solves the problem for a 15-minute ablation every 2 seconds, and continues to solve solutions for 15 minutes postablation.
FEMLAB creates a geometry and a nonuniform mesh, but tissue exposure is unique for each point in the model and must be tracked at each location. Tracking cumulative tissue damage lends itself to a uniform rectilinear grid. Normally, finite element meshing and rectilinear gridding aren't compatible, so to avoid incompatibilities researchers typically employ the finite difference method, which also uses rectilinear gridding.
Chang developed a technique to rectify these incompatibilities. He starts with a finite element mesh and calculates temperature at a specific time step. He then uses FEMLAB's meshgrid postprocessing function to convert the mesh into a rectilinear grid. He passes that data into Matlab, which calculates thermal exposure and cumulative cell damage. The algorithm compares cumulative cell damage at each location in the rectilinear grid to a threshold; if it is exceeded, blood flow ceases. It then uses the percent cell damage to calculate changes in the tissue's electrical properties. Once the Matlab algorithm completes, it saves an augmented logical array for tissue perfusion and another of updated electrical conductivity to a swap file. At the subsequent time step, FEMLAB calls a command to interpolate specific values of electrical conductivity and blood perfusion at node locations in the finite element mesh.
The resulting temperature-dependent electrical conductivity is highly non-uniform and can vary as much as 200% over the course of an ablation (see figure). This may lead to significant underestimation of SAR and significant temperature differences in the absence of tissue perfusion. In addition, tissue perfusion directly affects the resulting temperature and indirectly changes the electrical conductivity and SAR.
(Note: References to the software used in the research should not be construed as the FDA's endorsement of this software or the company that manufactures it.)