MICCAI original investigationMultiscale Optimization of the Probe Placement for Radiofrequency Ablation
Section snippets
A model for the simulation of RF ablation
We consider the computational domain to be a cuboid Ω ⊂ ℝ3 with boundary Γout = ∂Ω in which a tumor Ωtu ⊂ Ω and vascular structures Ωv ⊂ Ω are located. Further, we assume that a mono- or bipolar RF probe is applied in Ω, whose position (of the active zone’s center) and direction are variables (which we would like to optimize later on). Later on we will extend this model to a fixed cluster of probes, in which the rotation of the cluster becomes an additional
Objective functions
The aim of the therapy is the complete destruction of the tumor with minimum amount of affected native tissue. In this work, we focus on temperature based objective functions, which measure the “quality” of a given temperature distribution. We consider the tissue to be destroyed if it is heated above a critical high temperature Tcrit = 60°C. Thus for an optimal outcome of the ablation the temperature shall be high in the region of the tumor Ωtu and close to body temperature in the native tissue
Optimizing the probe placement
Formally, the objective function f can be considered as a function of the temperature distribution T, where T is a function of the heat source Qrf, and Qrf is a function of the optimization parameter . Hence, we write To optimize the probe location, we are looking for u ∈ U such that · ·(u) becomes minimal.
Obviously, in certain situations the uniqueness of a minimizing configuration is not guaranteed (eg,
Discretization with finite elements
The solutions of the elliptic boundary value problems Eq (5a), (5b), (10) are numerically computed with a finite element method on a three-dimensional uniform Cartesian grid. Below we introduce a multiscale optimization algorithm to accelerate the minimization of the objective function. Therefore it is convenient to assume that we work on an octree grid (ie, a hexahedral grid with 2L × 2L × 2L cells for some L ∈ ℕ). Note that this is in fact no restriction because every Cartesian grid can be
Numerical results
In this section, we present the application of our optimization to artificial settings as well as to geometries obtained from real computed tomography scans. Let us first verify the performance of our algorithm in a case where the correct solution is qualitatively obvious. To this end, let Ω be a domain of extent 60 × 60 × 60 mm3 that we discretize as described in the previous section with a fine grid of 1203 grid cells (which is embedded into an octree grid of level L = 7). A tumor domain Ωtu
Conclusions and future work
We have discussed a multiscale model for the optimization of the placement of mono- and multipolar probes in RF ablation. The optimization minimizes an objective function that penalizes temperatures below Tcrit aiming at a uniform tumor heating. For the modeling of blood perfusion, the model uses a weighted variant of the approach of Pennes (14), which prescribes a high perfusion rate inside vessels and a small perfusion rate for capillary blood flow. The performance of the algorithm is
Acknowledgments
The authors thank the VICORA team and in particular T. Stein and A. Roggan from Celon AG for valuable hints and fruitful discussions on the topic. Also, we would like to thank the team from MeVis-Research, in particular A. Weihusen, F. Ritter, and finally S. Zentis and C. Hilck for preprocessing the computed tomography scans.
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