Optimizing Sensor Placement for Temperature Mapping during Ablation Procedures

Abstract

Accurately mapping the temperature during ablation is crucial for improving clinical outcomes. While various sensor configurations have been suggested in the literature, depending on the sensors' type, number, and size, a comprehensive understanding of optimizing these parameters for precise temperature reconstruction is still lacking. This study addresses this gap by introducing a tool based on a theoretical model to optimize the placement of fiber Bragg grating sensors (FBG) within the organ undergoing ablation. The theoretical model serves as a general framework, allowing for adaptation to various situations. In practical application, the model provides a foundational structure, with the flexibility to tailor specific optimal solutions by adjusting problem-specific data. We propose a nonlinear and nonconvex (and, thus, only solvable in an approximated manner) optimization formulation to determine the optimal distribution and three-dimensional placement of FBG arrays. The optimization aims to find a trade-off among two objectives: maximizing the variance of the expected temperatures measured by the sensors, which can be obtained from a predictive simulation that considers both the type of applicator used and the specific organ involved, and maximizing the squared sum of the distances between the sensor pairs. The proposed approach provides a trade-off between collecting diverse temperatures and not having all the sensors concentrated in a single area. We address the optimization problem through the utilization of approximation schemes in programming. We then substantiate the efficacy of this approach through simulations. This study tackles optimizing the FBGs' sensor placement for precise temperature monitoring during tumor ablation. Optimizing the FBG placement enhances temperature mapping, aiding in tumor cell eradication while minimizing damage to surrounding tissues.

Keywords: fiber Bragg grating sensors (FBGs); laser ablation; minimal invasive surgery; sensor positioning; temperature monitoring.

Figure 1

Schematic of an FBG array, illustrating the positioning of individual sensitive elements within a single fiber (not to scale).

Figure 2

Proposed theoretical optimization method, illustrated through a practical case study. The flow includes (1) addressing the FBGs placement issue for a laser ablation procedure in the pancreas; (2) conducting a COMSOL simulation to predict temperature distribution, resulting in a map of predicted temperatures; (3) utilizing the proposed optimization method to determine optimal sensor positions based on the temperature map for effective temperature monitoring during the procedure; and (4) obtaining the coordinates for the sensor positions.

Figure 3

Relation between the j-th and $(j-1)$-th sensors in the same FBG-array. The position ${\mathit{r}}_{ij}$ is obtained from ${\mathit{r}}_{i,j-1}$ by moving $ϵ+{\delta }_{i,j-1}$ (i.e., the distance ${\delta }_{i,j-1}$ between the two spheres, plus the radius $ϵ/2$ of each sphere) toward ${\mathit{r}}_{i,j}$, i.e., along the direction described by the unit-length vector $\mathit{\gamma }({\varphi }_i,{\theta }_i)$. Iterating, the position of each sensor in an FBG-array is uniquely determined by the diameter $\eta$, by the position of the first sensor, by the angles ${\theta }_i, {\varphi }_i$, and by the distances ${\delta }_{i,j}$.

Figure 4

Temperature distribution obtained for numerical simulation carried out at 20 W in correspondence of the final ablation time (i.e., 5 min), and visualized in the plane containing the MW antenna as an example.

Figure 5

Illustrating the behavior of the objective function as it stabilizes to a specific value after a certain number of iterations. The blue curve represents the objective function, while the orange curve shows whether the solution found at a given iteration is feasible or not.

Figure 6

Illustrating the positions of FBG arrays on the temperature map resulting from the simulation. Red points indicate the positions of individual FBGs within the arrays, arranged along lines defining each FBG array.