# Field and Temperature Shaping for Microwave Hyperthermia: Recent Treatment Planning Tools to Enhance SAR-Based Procedures

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Optimal SAR Pattern Shaping

#### 2.1.1. Description of FOCO and Derived Approaches

- -
- Multi-frequency FOCO (mf-FOCO) [42], based on the idea that hotspot spatial collocations could change with frequency. Hence, by exploiting such a feature and adopting multi-frequency applicators, one could alleviate hotspots occurrence (or mitigate their impact).
- -
- Sparsity promoted FOCO (sp-FOCO) [43], introduced to address the need to optimally select the active elements of a given applicator in a patient-specific fashion. From a mathematical point of view, it implies in problem (1) the presence of a constraint in ${\U0001d4f5}_{1}$-norm, borrowed from the compressive sensing theory [44], that is:$$\parallel {I}_{n}\parallel {}_{{\U0001d4f5}_{1}}\le \delta $$
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- Multi-target FOCO (mt-FOCO) [45], aiming at uniformly shaping the SAR over an extended target area that may have irregular contours (i.e., late-stage tumors). Nowadays, this task is not efficiently addressed by the clinically adopted algorithms. From a mathematical point of view, it involves two additional constraints, that are:$$\mathcal{R}\left\{{E}_{i}\left({\mathit{r}}_{{t}_{i}},{I}_{n}\right)\right\}=\Re \left\{{E}_{i}\left({\mathit{r}}_{t},{I}_{n}\right)\right\}\mathrm{cos}{\varphi}_{i}$$$$\Im \left\{{E}_{i}\left({\mathit{r}}_{{t}_{i}},{I}_{n}\right)\right\}=\Re \left\{{E}_{i}\left({\mathit{r}}_{t},{I}_{n}\right)\right\}\mathrm{sin}{\varphi}_{i}$$
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- Average SAR-constrained FOCO (av-FOCO) [46], which enforces hotspot-preventing constraints on the average SAR distribution rather than on the voxel-vise SAR. This is related to the fact that the average SAR over IEEE peak SAR quantifiers (1 g, 10 g) [47] is physically more related to temperature rather than the punctual SAR, i.e., voxel-vise [48].

#### 2.1.2. Assessment of FOCO-Based Approaches against Clinical Data

^{3}(ΔT50 = +0.39 °C). In addition, being FOCO formulated as a convex optimization problem, the results of the optimization procedure are repeatable and achieved sensibly faster (−44%) [50].

#### 2.2. Refinement of SAR Planning via Microwave Tomography Based Quantitative EM Modelling

#### Description of the Proposed Segmented MWT

#### 2.3. Temperature-Corrected SAR Shaping

#### 2.3.1. Description of the T-Correction Approach

- Following standard HTP procedures, a SAR-based optimization is performed to maximize the power deposition on the tumor target region (centered at ${\mathit{r}}_{t}$), minimizing the risk of hotspots in the surrounding heathy tissues.
- The optimized squared magnitude of the electric field is reasonably approximated by a (multi-variate) Gaussian fitting function, with different standard deviations along the different axes and peak position ${\mathit{r}}_{0}$.
- The peak position ${\mathit{r}}_{0}$ of the Gaussian fitting function is moved in a refinement region ${\mathcal{V}}_{\mathcal{R}}$ defined around the tumor target, where a proper number of points (${N}_{RFN}$) is considered.
- For each point in the refinement region ${\mathcal{V}}_{\mathcal{R}}$, the Gaussian fitting function is used as the source term of the bioheat equation, and the following fitness function is computed:$${\tau}_{90}=\frac{\mathrm{T}90}{{\mathrm{max}}_{\mathit{r}\in {\mathcal{V}}_{\mathcal{T}}}\left\{T\left(\mathit{r}\right)\right\}}$$
- The center ${\mathit{r}}_{0}={\tilde{\mathit{r}}}_{t}$ corresponding to the maximum value of ${\tau}_{90}$ provides the shifted focusing center for a new SAR-based optimization, able to provide an improved temperature coverage of the tumor region ${\mathcal{V}}_{\mathcal{T}};$
- Point 1 is repeated to optimize the SAR on a target region centered around ${\tilde{\mathit{r}}}_{t}$.

## 3. Results

#### 3.1. D Numerical Scenario

#### 3.2. Numerical Proof-of-Concept

^{2}/m

^{2}and standard deviations ${\sigma}_{x}=18$ mm and ${\sigma}_{y}=16.5$ mm (see Figure 5a,b) (step 2). In the reported example, we limited the refinement region (step 3) to a two-dimensional circle ${\mathcal{S}}_{\mathcal{R}}$ defined on the plane $z=-15$ mm and centered around ${\mathit{r}}_{t}$. A reasonable diameter for ${\mathcal{S}}_{\mathcal{R}}$ is suggested to be: ${d}_{\mathcal{R}}=2\left({a}_{x}+\mathsf{\Delta}\right)=38$ mm, being $\mathsf{\Delta}$ the main distance between the SAR and temperature peaks (see Figure 5c) [38]. Then, the center of the Gaussian mask has been moved on ${N}_{\mathit{r}FN}=$491 centers $\left({x}_{0},{y}_{0}\right)$ equally spaced on ${\mathcal{S}}_{\mathcal{R}}$, for which a 2D version of the bioheat equation has been solved. The considered value for ${N}_{\mathit{r}FN}$ is definitely an overkill; the scale length of the spatial discretization for the refinement is reasonably given by the shift $\mathsf{\Delta}$ between the SAR and temperature maps, which in typical cases leads to a much smaller number of refinement points. The resulting ${\tau}_{90}$ parameter (3) computed for each point in ${\mathcal{S}}_{\mathcal{R}}$ is reported in Figure 5c (step 4), and the maximum value was found for $\left({\tilde{x}}_{0},{\tilde{y}}_{0}\right)=\left(-26.7,-29.8\right)$ mm (step 5). Finally, FOCO was again applied to focus the EM radiation on a target region centered around the shifted position ${\tilde{\mathit{r}}}_{t}=\left({\tilde{x}}_{0},{\tilde{y}}_{0},-15\mathrm{mm}\right)$ $=\left(-26.7,-29.8,-15\right)$ mm (step 6).

## 4. Discussion

^{3}). Lastly, FOCO-based procedures are formulated as a convex optimization problem, hence, are easier to be implemented (as no tuning of parameters is required) and much faster than PSO-based methods. As opposed to non-convex optimizers, the results are then more repeatable and computationally less cumbersome (see above). Moreover, the point target correction based on temperature analysis could further improve FOCO performance with respect to the standard FOCO and make more effective the corresponding thermal treatment.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic view of the phased antenna array surrounding the domain of interest Ω and the target volume. Each antenna is indicated by a blue triangle, while the grey area represents the target volume.

**Figure 3.**Simplified numerical testbed. (

**a**) Top view on the plane $z={z}_{t}=-15$ mm of the simple neck model implemented in COMSOL, with the considered different tissues; (

**b**) Geometry of the HTP applicator, the simplified neck, and the waterbolus; (

**c**) Reflection coefficient of a single-feed patch antenna of the simulated array.

**Figure 4.**SAR and temperature maps for the simplified testbed. (

**a**) Normalized SAR map, visualized on the plane $z=-15$ mm, optimized with FOCO for a target tumor centered around its centroid, at ${\mathit{r}}_{t}=\left(-24,-24,-15\right)$ mm (left) and the corresponding temperature map (right); (

**b**) Normalized SAR map, visualized on the plane $z=-15$ mm, optimized with FOCO for a target region centered around the corrected center ${\tilde{\mathit{r}}}_{t}=\left(-26.7,-29.8,-15\right)$ mm (left) and the corresponding temperature map (right).

**Figure 5.**SAR Gaussian approximation for the simplified testbed. Squared amplitudes of the electric field norm (see the insets) along the $\mathit{x}$ (

**a**) and $\mathit{y}$ (

**b**) axes passing through the tumor centroid, their Gaussian approximations and the temperature profiles corresponding to the exact fields, after the first FOCO optimization (no correction is introduced); (

**c**) fitness function ${\mathit{\tau}}_{\mathbf{90}}$ as a function of the Gaussian SAR focusing center on the two-dimensional refinement region ${\mathcal{S}}_{\mathcal{R}}$ (dashed circle). The boundary of the tumor region on the plane $\mathit{z}=-\mathbf{15}$ mm is highlighted by a solid circle.

**Figure 6.**Temperature maps for the realistic testbed. (

**a**) Numerical model implemented in Sim4Life with the realistic phantom Duke [67]. (

**b**) Segmented tissues on the $\mathit{z}={\mathit{z}}_{\mathit{t}}$ plane. Temperature maps on the $\mathit{z}={\mathit{z}}_{\mathit{t}}$ plane corresponding to a SAR map optimized with FOCO (

**c**,

**d**) for a target region centered around the tumor centroid ${\mathit{r}}_{\mathit{t}}$ and (

**e**,

**f**) for a target region centered around the corrected center ${\tilde{\mathit{r}}}_{\mathit{t}}$. (

**d**,

**f**) magnify the region around the tumor target of (

**c**,

**e**), respectively, with an expanded color scale. The boundary of the tumor region is highlighted by a solid green circle. From (

**c**–

**e**), an improvement of the temperature coverage is observed, as well as a significant hotspot suppression.

**Table 1.**T50, T90, and ${\tau}_{90}$ parameters for the simplified testbed (with maximal normal tissue temperature of 43 °C), corresponding to a SAR-based optimization implemented with FOCO and with a global optimization of the THQ. Pre and post prefixes refer to the temperature map before and after the application of the thermal refinement procedure.

FOCO | THQ Opt via PSO | |
---|---|---|

T50 (pre) | 42.1 °C | 42.4 °C |

T50 (post) | 42.7 °C | 42.4 °C |

T90 (pre) | 41.1 °C | 41.4 °C |

T90 (post) | 41.9 °C | 41.7 °C |

${\tau}_{90}$(pre) | 95% | 96% |

${\tau}_{90}$ (post) | 97% | 97% |

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## Share and Cite

**MDPI and ACS Style**

Bevacqua, M.T.; Gaffoglio, R.; Bellizzi, G.G.; Righero, M.; Giordanengo, G.; Crocco, L.; Vecchi, G.; Isernia, T.
Field and Temperature Shaping for Microwave Hyperthermia: Recent Treatment Planning Tools to Enhance SAR-Based Procedures. *Cancers* **2023**, *15*, 1560.
https://doi.org/10.3390/cancers15051560

**AMA Style**

Bevacqua MT, Gaffoglio R, Bellizzi GG, Righero M, Giordanengo G, Crocco L, Vecchi G, Isernia T.
Field and Temperature Shaping for Microwave Hyperthermia: Recent Treatment Planning Tools to Enhance SAR-Based Procedures. *Cancers*. 2023; 15(5):1560.
https://doi.org/10.3390/cancers15051560

**Chicago/Turabian Style**

Bevacqua, Martina T., Rossella Gaffoglio, Gennaro G. Bellizzi, Marco Righero, Giorgio Giordanengo, Lorenzo Crocco, Giuseppe Vecchi, and Tommaso Isernia.
2023. "Field and Temperature Shaping for Microwave Hyperthermia: Recent Treatment Planning Tools to Enhance SAR-Based Procedures" *Cancers* 15, no. 5: 1560.
https://doi.org/10.3390/cancers15051560