Feasibility of Temperature Control by Electrical Impedance Tomography in Hyperthermia

Abstract

We present a simulation study investigating the feasibility of electrical impedance tomography (EIT) as a low cost, noninvasive technique for hyperthermia (HT) treatment monitoring and adaptation. Temperature rise in tissues leads to perfusion and tissue conductivity changes that can be reconstructed in 3D by EIT to noninvasively map temperature and perfusion. In this study, we developed reconstruction methods and investigated the achievable accuracy of EIT by simulating HT treatmentlike scenarios, using detailed anatomical models with heterogeneous conductivity distributions. The impact of the size and location of the heated region, the voltage measurement signal-to-noise ratio, and the reference model personalization and accuracy were studied. Results showed that by introducing an iterative reconstruction approach, combined with adaptive prior regions and tissue-dependent penalties, planning-based reference models, measurement-based reweighting, and physics-based constraints, it is possible to map conductivity-changes throughout the heated domain, with an accuracy of around 5% and cm-scale spatial resolution. An initial exploration of the use of multifrequency EIT to separate temperature and perfusion effects yielded promising results, indicating that temperature reconstruction accuracy can be in the order of 1 ∘C. Our results suggest that EIT can provide valuable real-time HT monitoring capabilities. Experimental confirmation in real-world conditions is the next step.

Keywords: conductivity reconstruction; perfusion estimation; temperature monitoring.

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 4

Current flow at different frequencies and fluid distribution in the human body [42] (left); optimistic and pessimistic perfusion models for muscle, fat, and tumor tissue [14,43] (right).

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 ($T_{rec1}$, using the reference conductivity at 37 °C) and Scenario 2 ($T_{rec2}$, 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.