# Feasibility of Temperature Control by Electrical Impedance Tomography in Hyperthermia

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

^{2}) and Glenn (age: 84, height: 1.73 m, BMI: 20.4 kg/m

^{2}) anatomical models [35]. Two anatomical models were used to assess the impact of intersubject variability, as well as the importance of using personalized reference models. The models were discretized using a tetrahedral mesh in EIDORS v3.9. We first describe single iteration reconstruction using EIDORS. In Section 2.2, we present novel reconstruction approaches capable of overcoming the limitations of existing methods in our application of interest, their implementation, and the investigation scenarios. While considering the high heterogeneity of the human body, we then determined if the reconstruction accuracy improved when using a tissue-dependent penalty (TiD) parameter. A sensitivity analysis regarding the location and size of the simulated region was also performed.

#### 2.1. Single Iteration Reconstruction

#### 2.2. Pipeline and Simulation Setup

#### 2.3. Investigation Scenarios

#### 2.3.1. Tissue-Dependent Penalty

#### 2.3.2. Region Location and Size

#### 2.3.3. Impact of Inaccurate Reference Model

#### 2.3.4. Voltage Measurement Noise

#### 2.4. Simulated HT Treatment Reconstruction

- We performed two thermal simulations of a one-hour treatment (${T}_{Opt}$ and ${T}_{Pess}$) using the same specific absorption rate (SAR) distribution. The Pennes bioheat equation (PBE) [41] with temperature-dependent perfusion models was used for the thermal simulations (see Equation (8)). The applied power level was the same in both cases, but the temperature-dependent perfusion models for muscle, fat, and tumor tissues were different (see Figure 4), to illustrate the impact of perfusion uncertainty;
- We translated the temperature increase to a modified conductivity map, which included a component directly related to temperature ($\Delta {\sigma}_{temp}$) and a perfusion-related indirect component ($\Delta {\sigma}_{perf}$);
- We reconstructed and analyzed the changes in conductivity based on the “ground truth” temperature simulation (${T}_{Pess}$), using the conductivity at 37 °C as the reference model (Scenario 1) or the conductivity for the “planned” ${T}_{Opt}$ (Scenario 2). The reconstructed conductivity was then converted into a reconstructed temperature estimation map.

^{3}), c is the specific heat capacity (J/kg°C), k is the thermal conductivity (J/(s·m·°C)), ${w}_{b}$ is the perfusion rate (kg/(s·m

^{3})), ${\rho}_{b}$ is the density of blood, ${c}_{b}$ is the specific heat capacity of blood, ${q}_{m}$ is the metabolic heat generation rate (J/(s·m

^{3})), and ${q}_{ext}$ is the electromagnetic power deposition. ${w}_{b}$ can be temperature dependent to account for vasodilation.

#### 2.4.1. Change in Conductivity Due to Temperature Increase

#### Disentangling Temperature and Perfusion

#### 2.4.2. Reconstruction Scenarios

## 3. Results

#### 3.1. Reconstruction Time

#### 3.2. Investigation Scenarios

#### 3.2.1. Tissue-Dependent Penalty

#### 3.2.2. Multiple Regions

#### 3.2.3. Impact of Inaccurate Reference Model

#### 3.2.4. Voltage Measurement Noise

#### 3.3. Simulated HT Treatment Reconstruction

#### 3.3.1. Personalized Reference Model

#### 3.3.2. Temperature and Perfusion Mapping

#### 3.3.3. Summary of Temperature Reconstruction Accuracy

_{c}= 2%/°C. The limitations of the reconstruction accuracy estimations are discussed in Table 4.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the implemented reconstruction pipeline and the scenarios investigated in this study. Boxes with continuous outlines represent data, while the dotted ones represent processes. First, the actual and the reference model are generated, based on a discretized dielectric model of the patient and electrodes. Reconstruction proceeds through multiple iterations of forward ($FWD$) and inverse ($INV$) problem solving. The reconstruction results have been analyzed to study the impact of reconstruction approaches, noise, as well as reference model realism and accuracy.

**Figure 2.**(

**a**) FEM model of the Duke anatomical model torso with electrode locations indicated in green; (

**b**) slices of the modified model $\Delta \sigma (\%)$ for a heated region in the liver; (

**c**) locations and sizes of the different heated region scenarios; (

**d**) setup featuring changes outside the prior region.

**Figure 3.**Simulated HT treatment in the Duke and Glenn anatomical models. Five modular applicator elements were placed circumferentially around the tumor, and their phases and amplitudes were optimized to preferentially heat the tumor. Two different anatomical models were used to investigate the impact of anatomical variability, as well as the impact of using a nonpersonalized reference model for reconstruction.

**Figure 5.**Conductivity changes reconstruction pipeline for two investigated EIT scenarios: EIT attempts to reproduce the voltage measurement signal of the “actual” model by reconstructing temperature and perfusion changes with regard to the reconstruction reference. (Scenario 1) uses the conductivity at 37 °C as reconstruction reference, while (Scenario 2) uses the modified conductivity as predicted by computational modeling of induced heating, perfusion response, and resulting conductivity change (but wrongly assuming an “Optimistic” perfusion, while the “actual” conductivity change is based on the “Pessimistic” perfusion model). Scenario 2 also employs masking based on the predicted temperature increase (prior region) to improve reconstruction.

**Figure 6.**(

**a**) “Tissue-dependent Penalty” and “Fixed Penalty” values. (

**b**) Plot by tissue of the fitted relationship between reconstructed ($\Delta {\sigma}_{rec}$) versus reference ($\Delta \sigma $) changes in conductivity using “Fixed Penalty” (dashed line) and “Tissue-dependent Penalty” (solid line).

**Figure 7.**(

**a**) Reconstructed conductivity $\Delta {\sigma}_{rec}$ (%) for the P1 setup from Figure 2 and (

**b**) its deviation from the actual conductivity change ($\Delta {\sigma}_{err}=\Delta {\sigma}_{rec}-\Delta \sigma $) for all the setups P1–P5, as shown in Table 1 and illustrated in Figure 2, (right), using three iterations, tissue-dependent (TiD) penalty, and Hp = 0.01.

**Figure 8.**Reconstructed deviation in an inaccurate reference model (large inserted air sphere) for a fixed prior region using three iterations (

**left**) and an adaptive prior region using 1 + 1 + 3 iterations (

**right**)—note the different scale in the upper left graph.

**Figure 9.**Impact of electrode voltage SNR (see Section 2.3.4 for the SNR calculation) on the reconstruction accuracy using three iterations for four levels of SNR (10, 20, 30, 40 dB), and in the 20 dB SNR case for varying combinations of reconstruction parameters (hyperparameter and penalty)—note the different scale in the 10 dB SNR case.

**Figure 10.**Reconstruction results from realistic HT treatment modeling (LF, Duke anatomical model): (

**a**) axial slice from the thermal simulation with the optimistic perfusion model (${T}_{Opt}$), (

**b**) axial slice from thermal simulation with the pessimistic perfusion model (${T}_{Pess}$) and (

**f**) difference between ${T}_{Pess}$ and ${T}_{Opt}$; (

**c**,

**d**) reconstructed temperature results from Scenario 1 (${T}_{rec\phantom{\rule{0.166667em}{0ex}}1}$, using the reference conductivity at 37 °C) and Scenario 2 (${T}_{rec\phantom{\rule{0.166667em}{0ex}}2}$, using the reference conductivity $\Delta \sigma ({T}_{Opt})$), as calculated from the reconstructed $\Delta {\sigma}_{rec}$ in (

**h**,

**i**), respectively; (

**e**) temperature estimation error for both scenarios; (

**g**) $\Delta \sigma ({T}_{Pess})$ with its direct temperature-related ($\Delta {\sigma}_{temp}$) and the perfusion-related $\Delta {\sigma}_{perf}$ contributions.

**Figure 11.**(

**a**) Reconstructed mean and standard deviation of conductivity ($\Delta {\sigma}_{err}$) and (

**b**) estimated temperature error (${T}_{err}$). Reconstructions were performed for the Duke and Glenn anatomical models, for low frequency (LF) and high frequency (HF) current injection, using the conductivity map at 37 °C as the reference (baseline for EIT difference reconstruction) or the one predicted by thermal simulations with the (inaccurate) optimistic perfusion model (${T}_{Opt}$). Mean and standard deviation of temperature error for muscle, fat, tumor, the prior region mask, and all tissues combined are shown. TiD penalty and Hp = 0.01 were used.

**Figure 12.**(

**a**) Conductivity reconstruction error ($\Delta {\sigma}_{err}=\Delta {\sigma}_{rec}-\Delta \sigma $ in %) using 16, 12, or 8 electrodes, when the actual treatment (along with the extraction of the measurement voltages) is applied to the Duke model, (

**b**) actual heating on Glenn, (

**c**,

**d**) reconstruction is performed using the Duke model as reconstruction reference, to study nonpersonalized reconstruction of heating on Glenn. While avoiding the generation of patient-specific models for reconstruction considerably reduces the involved effort, an important factor in a clinical environments, it also results in reduced reconstruction accuracy. As hyperthermia QA guidelines recommend personalized treatment planning for deep-seated tumors, personalized models are frequently available already. The important reconstruction errors in (

**a**) reflect the use of the Duke conductivity distribution at 37 °C as reconstruction reference, while the reconstruction approaches in (

**c**,

**d**) employ nonpersonalized, Duke-based treatment planning (incl. thermal modeling) instead. (

**c**) displays reconstruction results obtained using 16 electrodes with or without voltage-rescaling to compensate for the absence of a personalized reference model. (

**d**) displays reconstruction results obtained when reducing the number of electrodes to 8, using voltage-rescaling, introducing constraints (non-negative temperature changes), and applying Green’s-function-based smoothing. These measures result in increasingly accurate temperature increase estimations.

**Figure 13.**(

**a**) Preheating impedance ${Z}_{ij}$ per electrode pair (in $\Omega $) and (

**b**) impedance reduction due to heating (in %). Upper and lower triangle values correspond to the Duke and Glenn anatomical models, respectively. The numbering follows Figure 2.

**Figure 14.**Reconstruction results from multifrequency EIT on Duke and Glenn: (

**a**) cross-sectional view of the temperature error distribution; (

**b**) reconstructed perfusion versus underlying perfusion plotted separately for muscle, fat, and tumor tissues.

**Table 1.**Size and position of simulated heated region and the added air object for the case of changes outside the focus region. See Figure 2 for the location of the origin (0, 0, 0).

Simulation | P1 | P2 | P3 | P4 | P5 | Air Object |
---|---|---|---|---|---|---|

Center (x, y, z) [mm] | (−90, 20, 15) | (−90, 20, 15) | (−90, 20, 15) | (−40, 50, 15) | (30, 50, 15) | (50, 30, 15) |

Diameter [mm] | 60 | 40 | 80 | 60 | 60 | 50 |

**Table 2.**Mean and standard deviation of the electrode voltages (${v}_{ref}$) and voltage differences at each iteration of reconstruction for two cases (reconstruction using reference conductivity, ${\sigma}_{ref}$, at 37 °C and ${T}_{Opt}$).

Electrode Voltages Levels at 1 mA Injection Current | ||||
---|---|---|---|---|

Simulation | ${\mathit{v}}_{\mathit{ref}}$ | $|\mathbf{\Delta}\mathit{v}|$ at Iteration | ||

1 | 2 | 3 | ||

Reference 37 °C | 5.1 ± 4.8 mV | 390 ± 370 μV | 42 ± 45 μV | 1.7 ± 1.7 μV |

Reference ${T}_{Opt}$ | 4.7 ± 4.5 mV | 30 ± 26 μV | 0.9 ± 0.8 μV | 0.9 ± 0.8 μV |

**Table 3.**Summary of the impact of the reconstruction approach (parameters, iterations, adaptive penalties and prior regions, reference model) and scenario (generic local $\sigma $ change, detailed treatment scenario, perfusion changes, EIT frequency/frequencies) on the reconstruction accuracy (mean and standard deviation in the prior region). For the realistic HT therapy heating pattern scenarios, the worst case from the investigated Glenn and Duke scenarios is reported. Accuracy of nonpersonalized reconstruction scenarios is not reported here, since the chosen metrics are not applicable.

Temperature Estimation Accuracy | |
---|---|

Condition | Accuracy (Mean/Stddev °C) |

Ideal: generic local (spherical) $\sigma $ change | |

1-iter., No Penalty, Hp = 0.01 | −3.9/4.9 °C |

1-iter., Penalty = 0.001, Hp = 0.01 (baseline) | −0.6/1.7 °C |

1-iter., Penalty = TiD, Hp = 0.01 | −0.6/1.4 °C |

3-iter., Penalty = TiD, Hp = 0.01 | −0.1/1.1 °C |

Nonideal: noise/$\sigma $ change outside prior region | |

3-iter., Penalty = TiD, Hp = 0.01, $\sigma $ change outside prior region | Unusable with Fixed prior region; 0/2.4 °C with Adaptive prior region |

3-iter., Penalty = 0.01, Hp = 0.1, SNR = 20 dB | −0.4/3 °C |

Hyperthermia treatment scenarios, temperature increase and perfusion changes | |

3-iter., Penalty = TiD, HP = 0.01, Ref 37 °C | 0.2/1.8 °C (LF) −0.1/1.4 °C (HF) |

3-iter., Penalty = TiD, HP = 0.01, personalized Ref T_{Opt} | −0.3/1.1 °C (LF) −0.1/0.5 °C (HF) |

3-iter., Penalty = TiD, HP = 0.01, Multifrequency | −0.1/0.3 °C |

Limitation | Discussion |
---|---|

Generality | The present study focused on two anatomies, one realistic tumor location in addition to a few spherical heating cases, a fixed exposure element type and placement, and stable EIT electrode placement. While the reconstruction parameters were not particularly tweaked to obtain the presented results, it is important to investigate whether these parameters are indeed generalizable. |

Anatomical model accuracy | Personalized anatomical model generation—or intersubject variability, if presegmented models are used—affect the simulation fidelity and are likely to be one of the main sources of reconstruction errors. |

Constant ${T}_{c}$ | A constant ${T}_{c}$ = 2%/°C was used in this study. However, reported values in tissue vary between 0.6–2.1%/°C; refs. [14,46] with a typical value around 2.0%/°C. Although it is unclear how much is measurement-accuracy-related, large intertissue or intersubject variability affects the reconstruction. |

Frequency and temperature dependence of conductivity | There is a high degree of uncertainty associated with the temperature dependence of perfusion and electric conductivity. However, since this study focused on conductivity change reconstruction, this uncertainty does not affect our conclusions. If multifrequency EIT can separate direct temperature effects from perfusion-related ones, the uncertainty is reduced to that of ${T}_{c}$. |

Inaccurate conductivity values | The reference model and the model to be reconstructed use tissue properties from a tissue properties database; however, uncertainty and variability associated with these properties affect the achievable reconstruction accuracy. EIT prior to therapy application can help obtain more accurate property maps. |

Nonlocal changes of perfusion and local vascular cooling | Although we assumed that increased blood flow circulation occurred in the heated region, nonlocal effects, such as whole-body thermoregulation, convective transport by medium-sized blood vessels, and the stealing effects or blood-flow reduction in a tissue resulting from an increase in neighboring tissue were not considered. Additionally, the localized cooling by sufficiently large blood vessels is not considered by the employed PBE, which assumes distributed perfusion. |

Fixed body core temperature | In our simulations, we assumed that body-core temperature was constant. However, the high energy delivery during HT therapy can result in a body-core temperature increase which affects overall tissue temperature. |

Electrode modeling and positioning | We modeled point electrodes with precisely known locations. The impact of inaccurate electrode positioning and compensation methods have already been studied [47,48,49]. We assume that accurate placement of electrodes can be assured during treatment. Replacing the point electrodes with extended electrodes will affect the current density in the vicinity of the electrode, and thus the reconstruction sensitivity in that region; this is easily handled and not the subject of this study, which focused on EIT for deep heating monitoring. |

Fixed patient geometry | We assumed that the patient geometry did not change between the treatment model creation and the treatment administration. Precise and reproducible patient positioning is required in the clinic, and it is already a requirement for high-quality HT treatment administration. Changes in the internal organ geometry have been investigated in this study, and are handled using adaptive prior regions. Nevertheless, large changes were shown to deteriorate the reconstruction accuracy. |

Reconstruction parameter choice | Further investigations are necessary to determine if the reconstruction parameters identified in this study also provide the best reconstruction results across other scenarios. |

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**MDPI and ACS Style**

Poni, R.; Neufeld, E.; Capstick, M.; Bodis, S.; Samaras, T.; Kuster, N. Feasibility of Temperature Control by Electrical Impedance Tomography in Hyperthermia. *Cancers* **2021**, *13*, 3297.
https://doi.org/10.3390/cancers13133297

**AMA Style**

Poni R, Neufeld E, Capstick M, Bodis S, Samaras T, Kuster N. Feasibility of Temperature Control by Electrical Impedance Tomography in Hyperthermia. *Cancers*. 2021; 13(13):3297.
https://doi.org/10.3390/cancers13133297

**Chicago/Turabian Style**

Poni, Redi, Esra Neufeld, Myles Capstick, Stephan Bodis, Theodoros Samaras, and Niels Kuster. 2021. "Feasibility of Temperature Control by Electrical Impedance Tomography in Hyperthermia" *Cancers* 13, no. 13: 3297.
https://doi.org/10.3390/cancers13133297