Multiscale Optimization of the Probe Placement for Radiofrequency Ablation

doi:10.1016/j.acra.2007.07.016

Academic Radiology

Volume 14, Issue 11, November 2007, Pages 1310-1324

An extended version of a talk was presented at the MICCAI Conference (Copenhagen, October 2006). The presented results are part of a collaboration of CeVis, MeVis-Research, and a variety of clinical partners in research projects and the national research networks VICORA and FUSION funded by the German Research Foundation and the Federal Ministry of Education and Research.

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Rationale and Objectives

We present a model for the optimal placement of mono- and bipolar probes in radiofrequency (RF) ablation. The model is based on a system of partial differential equations that describe the electric potential of the probe and the steady state of the induced heat distribution.

Materials and Methods

To optimize the probe placement we minimize a temperature-based objective function under the constraining system of partial differential equations. Further, the extension of the resulting optimality system for the use of multiple coupled RF probes is discussed. We choose a multiscale gradient descent approach to solve the optimality system.

Results

This article describes the discretization and implementation of the approach with finite elements on three-dimensional hexahedral grids.

Conclusion

Applications of the optimization to artificial test scenarios as well as a comparison to a real RF ablation show the usefulness of the approach.

Section snippets

A model for the simulation of RF ablation

We consider the computational domain to be a cuboid Ω ⊂ ℝ³ with boundary Γ_out = ∂Ω in which a tumor Ω_tu ⊂ Ω and vascular structures Ω_v ⊂ Ω are located. Further, we assume that a mono- or bipolar RF probe is applied in Ω, whose position $\bar{x} \in Ω$ (of the active zone’s center) and direction $\bar{a} \in S^{2} = {x \in ℝ^{3} : | x | = 1}$ 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 T_crit = 60°C. Thus for an optimal outcome of the ablation the temperature shall be high in the region of the tumor Ω_tu 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 Q_rf, and Q_rf is a function of the optimization parameter $(\bar{x}, \bar{a}) = : u \in U : = Ω \times S^{2}$ . Hence, we write $\begin{array}{l} Q_{rf} = Q (u), Q : U \to L^{2} (Ω), \\ T = T (Q_{rf}), T : L^{2} (Ω) \to H^{1} (Ω) \end{array}$ To optimize the probe location, we are looking for u ∈ U such that $F : U \to ℝ, u \mapsto F (u) := f$ · $T$ · $Q$ (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 2^L × 2^L × 2^L 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 Ω_tu

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 T_crit 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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View full text

MICCAI original investigationMultiscale Optimization of the Probe Placement for Radiofrequency Ablation

Rationale and Objectives

Materials and Methods

Results

Conclusion

Section snippets

A model for the simulation of RF ablation

Objective functions

Optimizing the probe placement

Discretization with finite elements

Numerical results

Conclusions and future work

Acknowledgments

Untersuchungen zur Dosimetrie der hochfrequenzstrominduzierten interstitiellen Thermotherapie in bipolarer Technik, vol 22

Three-dimensional finite-element analyses for radio-frequency hepatic tumor ablation

IEEE Trans Biomed Eng

Investigation of the influence of blood flow rate on large vessel cooling in hepatic radiofrequency ablation

Biomed Tech

A new nonlinear elliptic multilevel FEM applied to regional hyperthermia

Comp Vis Sci

A three-dimensional finite element model of radiofrequency ablation with blood flow and its experimental validation

Ann Biomed Eng

On the modelling of perfusion in the simulation of RF-ablation

SimVis

Optimale Steuerung partieller Differentialgleichungen

Theorie und Numerik restringierter rungsaufgaben

MICCAI original investigation
Multiscale Optimization of the Probe Placement for Radiofrequency Ablation