# Correlation between computed electric dose maps and early post-operative MRI for the evaluation of irreversible electroporation

Olivier Sutter, Luc Lafitte, Olivier Seror, Clair Poignard, Baudouin Denis de Senneville

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Olivier Sutter, Luc Lafitte, Olivier Seror, Clair Poignard, Baudouin Denis de Senneville. Correlation between computed electric dose maps and early post-operative MRI for the evaluation of irreversible electroporation. Physics in Medicine and Biology, 2025, pp.1-19. 10.1088/1361-6560/ae1802. hal-05337772

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# Correlation between computed electric dose maps and early post-operative MRI for the evaluation of irreversible electroporation

Olivier Sutter<fnref n="1" />,<fnref n="2" />, Luc Lafitte<fnref n="2" />, Olivier Seror<fnref n="1" />, Clair Poignard<fnref n="3" />†,
Baudouin Denis de Senneville<fnref n="2" />‡,†

E-mail: olivier.sutter@aphp.fr, luc.lafitte@inria.fr,
olivier.seror@aphp.fr, clair-poignard@inria.fr,
bdenisde@math.u-bordeaux.fr

†These two authors jointly supervised this work

## Abstract.

*Objective.* To correlate numerical simulations of the electric dose distribution with early post-operative MRI following irreversible electroporation (IRE) treatment of hepatocellular carcinoma (HCC).

*Approach.* A standard linear electrostatic model was employed to simulate the three-dimensional electric field (EF) distribution using real electric pulses and geometrical characteristics and intraoperative cone-beam CT (CBCT) data. Spatial registration between intraoperative CBCT and post-operative MRI was performed using both rigid and deformable methods, ranging from simple global translations based on anatomical landmarks to advanced deformable image registration (DIR) techniques accounting for elastic tissue deformations.

*Main Results.* The proposed approach was retrospectively evaluated using data from 22 patients who underwent IRE liver ablation (one patient underwent two distinct IRE procedures), resulting in a total of 23 procedures. The most accurate correspondence between predicted and observed ablation zones was achieved using a dose threshold of approximately 350 V/cm, yielding a median Dice Similarity Coefficient (DSC) around 0.74, indicative of substantial spatial overlap. Although elastic DIR approaches applied to segmented liver regions provided the highest registration accuracy, the simpler translational registration based on manually selected landmarks demonstrated surprisingly robust performance in localizing the simulated EF within the actual ablation zone.

*Significance.* These findings contribute to the standardization of IRE efficacy assessment on MRI and highlight the significant potential EF simulations to predict the extent of tissue ablation in IRE procedures for HCC. This approach may offer a valuable tool for improving intraoperative decision-making and post-operative assessment.

<footnote n="1">¹ Interventional Radiology Unit, Hôpital Avicenne, Hôpitaux Universitaires Paris Seine-Saint-Denis, APHP, Bobigny, France</footnote>

<footnote n="2">² University of Bordeaux, CNRS, INRIA, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France</footnote>

<footnote n="3">³ Inria Centre at Rennes University, F-35042, France</footnote>
**Keywords:** Interventional procedures, Electric dosimetry, Multi-modal image registration.
# 1. Introduction

Irreversible electroporation (IRE) is based on the following principle: when the magnitude of the electric field (EF) exceeds a critical threshold during a sequence of high-voltage micropulses, it induces permanent disruption of the cell membrane, ultimately leading to apoptosis (Tasu et al. 2022, Collettini et al. 2019, Narayanan et al. 2024, Rai et al. 2022, Wah et al. 2021). Importantly, this non-thermal technique preserves the integrity of the extracellular matrix and surrounding tissue architecture (Fruhling et al. 2023). Consequently, IRE is particularly well-suited for the treatment of tumors located in close proximity to critical anatomical structures such as major blood vessels and bile ducts. Clinical studies have demonstrated the safety and efficacy of IRE in patients with tumors smaller than 5 cm near large vessels or major bile ducts, where conventional thermal ablation techniques are often contraindicated due to the risk of collateral damage (Haemmerich et al. 2003, Sutter et al. 2017, Freeman et al. 2021, Meijerink et al. 2021, Lyu et al. 2019, Tasu et al. 2022).

Early evaluation of treatment efficacy represents critical information for optimizing clinical management (Distelmaier et al. 2017, Sutter et al. 2017, Ma et al. 2022, Silk et al. 2014, Bhutiani et al. 2016). For conventional ablative techniques, post-treatment follow-up is typically conducted several weeks after the procedure to assess therapeutic response, based on the presence or absence of complete necrosis of the target tumor on contrast-enhanced imaging (CT or MRI). Post-treatment assessment following irreversible electroporation (IRE) is more challenging because of a dynamic remodeling of the ablation zone, which tends to shrink more rapidly than with thermal ablation. Consequently, previous studies have suggested that, in the context of IRE, performing an MRI a few days after the procedure may enhance the evaluation of treatment efficacy. This early imaging captures the ablation zone, whose size and shape are directly related to the extent of the EF, before significant shrinkage occurs. It may also provide valuable insights into the immediate biological response of the tumor, as MRI is a well-established modality for assessing tumor changes due to its inherently high soft-tissue contrast.

Recent approaches rely on physician-guided electrode placement under imaging guidance, typically using a combination of real-time imaging modalities (e.g., ultrasound, fluoroscopy, or fluoro-CT) and sequential volumetric acquisitions, while considering anatomical and procedural constraints (Marino et al. 2021, Perera-Bel et al. 2023, Cindric et al. 2021). Following needle insertion, a CT or cone-beam CT (CBCT) scan is performed to verify accurate electrode positioning (Sutter et al. 2018). At our institution, a follow-up MRI is performed three days after IRE ablation to qualitatively assess treatment outcome However, no standardized criteria currently exist for evaluating treatment efficacy based on this early post-procedural MRI.

The objective of this study is to contribute to the standardization of IRE efficacy assessment on MRI by combining computational electric field evaluation with advanced image registration techniques. Specifically, we aim to assess the potential of real-time numerical simulations of the electric field generated during an irreversible
electroporation (IRE) procedure to predict the post-operative ablation zone as visualized
on MRI.

Our contributions are threefold:

(i) To evaluate methodological strategies for the spatial registration of CBCT- and MRI-derived data acquired at different stages of the IRE patient care pathway. Particular attention is given to the impact of potential CBCT image quality degradation caused by needle insertion on the overall accuracy of the results. The reliability of simple methods based on global translation, as well as more advanced approaches involving deformable image registration (DIR) to account for elastic deformations, was evaluated.

(ii) To introduce dedicated quantitative metrics for assessing the reliability of EF dose simulations registered onto the post-operative IRE ablation zone as visualized on MRI.

(iii) To identify threshold values of EF isodose that achieve optimal spatial correspondence with post-operative ablation zone observed on MRI.

**2. Materials and Methods**

2.1. *Patient cohort.*

The dataset utilized in the present study was collected as part of the *Evalhep* Project (ClinicalTrials.gov Identifier: NCT06289712). The study protocol adhered to the ethical principles outlined in the 1975 Declaration of Helsinki. Approval was obtained from the local institutional review board (CLEA-2023-n°307), and informed non-opposition from all participants was confirmed.

The database includes all IRE procedures performed at our center between January 2022 and May 2023. In addition to clinical data, it comprises all peri-operative imaging studies and procedural reports generated by the IRE device. The proposed approach was therefore retrospectively evaluated using data from 22 patients who underwent IRE liver ablation under real-time clinical conditions. One patient underwent two separate IRE procedures, yielding a total of 23 procedures. Inclusion criteria comprised patients who underwent IRE treatment for up to three liver tumors within a single session. Only cases for which both CBCT-Needles and CBCT-noNeedles reconstructions were considered. Additionally, the presence of an early follow-up MRI, performed within three days following the procedure, was required for inclusion. Exclusion criteria included imaging studies of insufficient quality to allow accurate liver contouring or ablation zone segmentation. Patients were also excluded in cases of confluent ablation zones involving multiple tumors, as well as in instances of overlapping ablations, defined as any repositioning or pull-back of electrodes during the same session following the initial treatment cycle.
## 2.2. Data collection

### 2.2.1. IRE procedure.
IRE ablation of hepatocellular carcinoma (HCC) was performed under general anesthesia. Monopolar 19-gauges electrodes were percutaneously inserted around the tumor by an interventional radiologist using a free-hand technique, guided by a combination of real-time US and 3D Virtual Target Fluoroscopic Display, with the aim of adequate coverage of the target region (Sutter et al. 2018). Up to six electrodes were positioned as parallel as possible, in accordance with standard clinical practice guidelines. The exposed length of the active part of the electrodes was 40 mm in all cases whatever the tumor size. A pull-back of electrodes, followed by another treatment cycle, was considered in cases where the target tumor was larger than 3 cm in the electrodes' insertion axis. The energy delivery protocol consisted of a minimum 100 pulses, of 90 µs duration, between all electrode pairs with a target intensity ranging between 35 and 50 A. Pulse parameters, including the applied electric potential between active electrode pairs, were configured on the generator (NanoKnife®, AngioDynamics, Latham, NY) according to the inter-electrode distance and the “predicted current” by the generator based on 400 V test pulses. Electric pulses were synchronized with the electrocardiogram and delivered during the refractory phase of the cardiac cycle across alternating electrode pairs. During this procedure, two CBCT scans were acquired:

(i) A high-definition (16°/second rotation) contrast-enhanced CBCT acquired at the beginning of the procedure, prior electrode insertion (hereafter referred to as “CBCT-noNeedle”).

(ii) A low-definition (40°/second rotation) unenhanced CBCT acquired with the electrodes in their final position, immediately prior to pulse delivery (referred to as “CBCT-Needles”).

### 2.2.2. Post-operative IRE assessment.
At our institution, an MRI scan is systematically performed within three days after the procedure to enable early assessment of IRE treatment efficacy. All these post-operative MR examinations were performed on two 1.5 Tesla MRI units (both OPTIMA 450W, GE Healthcare) using a standardized protocol. This included T1-weighted dual-echo sequence, T2-weighted fast spin echo sequence, diffusion-weighted imaging with b-values of 50 and 800 s/mm2 and fat-suppressed T1-weighted gradient echo sequences acquired before and after administration of gadolinium-based contrast agent (Gadoteric acid; Dotarem, Guerbet). Two arterial-phase acquisitions were systematically performed, triggered 5–7 seconds after contrast arrival in the descending aorta, followed by portal venous phase (at 70 seconds) and delayed phase (at 180 seconds).

As previously described, the IRE treatment area appears as a dual-component ablation zone, consisting of a central region of coagulative necrosis (devascularized and typically T1 hyperintense) and a peripheral inflammatory/oedematous zone, characterized by T1 hypointensity, T2 hyperintensity and progressive enhancement. Its
borders are generally well demarcated on unenhanced T1- and T2-weighted images,
allowing segmentation.

The IRE-induced ablation zone was manually segmented by an experienced
radiologist using the 3D Slicer software platform (Fedorov et al. 2012). The unenhanced
T1-weighted sequence was preferred due to its thinner slice thickness (2mm vs. 4-5mm
for T2). This segmentation served as a reference for assessing the extent of tissue affected
by EF.

2.3. Image preprocessing

2.3.1. Image standardization. All imaging datasets used in this study were resampled
to a common isotropic resolution of 1 × 1 × 1 mm³ prior to further processing.

2.3.2. Registration of the pre-insertion CBCT scan. Since accurate EF computation depends on the precise localization of electrodes in situ, and considering that electrode insertion induces liver deformation and may alter the patient's overall anatomy, EF simulations were performed within the reference space defined by the post-insertion CBCT (CBCT-Needles) image. To ensure spatial consistency, all CBCT data were aligned within this reference space. Specifically, the pre-insertion CBCT (CBCT-noNeedle) was deformably registered to the CBCT-Needles image using a deformable image registration (DIR) approach based on the EVolution algorithm, as proposed in (Denis de Senneville et al. 2016, Zachiu et al. 2017) and previously applied in (Gallinato et al. 2019). This algorithm is specifically designed for non-rigid multimodal image registration. It incorporates a similarity metric that emphasizes edge alignment, and the implementation used in this study employs a diffeomorphic transformation to preserve local topological properties, allowing for both forward and inverse application of the estimated deformation field (Yang et al. 2008).

2.3.3. *Liver segmentations.* Liver regions of interest were extracted on both CBCT-noNeedles and MRI scans using the TotalSegmentator module (Wasserthal et al. 2023) within the 3D Slicer software (Fedorov et al. 2012). Manual corrections were subsequently applied using the software's segmentation editing tools to ensure anatomical accuracy. The finalized ROIs were then converted into binary masks mapped onto a computational Cartesian grid. The binary liver masks on the CBCT-noNeedles were then propagated to the CBCT-Needles scan using the DIR algorithm detailed in Section 2.3.2.

2.3.4. Landmarks localisation in the liver. 3D landmarks were manually placed by an expert radiologist at the most reliably identifiable anatomical location near the target tumor area in both the original pre-insertion CBCT and MR images. When the tumor was clearly visible in both modalities, it was roughly segmented, and the centroid of the segmented tumor was used as the landmark. If the tumor was not adequately visible,
the landmark was instead placed at the bifurcation of the main portal vein, which is consistently identifiable in both CBCT and MR images. The landmarks identified in the enhanced CBCT-noNeedle scan were then propagated to the CBCT-Needles scan using the DIR algorithm detailed in Section 2.3.2.

### 2.3.5. Needle positions.
The coordinates of two points per needle, one at the tip and another along the shaft, were manually identified on the post-insertion CBCT scan. When feasible, corresponding needle locations were also identified on the post-operative MRI, based on the thin sheath of coagulation necrosis (appearing as T1-weighted hyper-intensity) surrounding the active portion of the electrodes. Individual MRI-visible needle tracks could then be reliably matched to their counterparts on the CBCT scan, enabling direct one-to-one correspondence between modalities. Using these landmarks, the 3D coordinates of the proximal (tumor vicinity) and distal end of the active portion of each needle (i.e., where the voltage is applied, located 4 cm from the needle tip in the used device) were determined.

## 2.4. Multimodal registration between per- (CBCT) and post- (MR) operative data

The successful evaluation of the per-operative dose map as a predictor of the post-operative IRE ablation zone depends on establishing a reliable spatial correspondence between the per- (CBCT) and post- (MR) operative image spaces. This task presents a particular challenge due to the fundamentally different imaging modalities, which produce significantly different contrast profiles, as well as the potentially large variations in patient positioning, since the images are acquired several days apart. To address this, the following five image registration strategies were evaluated:

### 2.4.1. Global translation based on liver segmentation.
This registration strategy, referred to as “Trans/Liver-Seg” throughout the manuscript, estimates a global 3D translation by aligning the liver masks identified in Section 2.3.3. The alignment is performed by maximizing a correlation-based functional using a gradient-driven optimization approach. The centroids of the segmented liver volumes in both modalities are used as the initial estimate for the optimization.

### 2.4.2. Global translation based on manually defined landmarks.
This registration strategy, referred to as “Trans/Landmarks”, estimates a global 3D translation based on the displacement of manually placed landmarks in the CBCT-Needles and MR images, as described in Section 2.3.4.

### 2.4.3. Non-rigid registration based on pre-insertion CBCT and MR images.
This registration strategy, referred to as “DIR/CBCT-noNeedles”, refines the global translation described in Section 2.4.2 by subsequently applying the DIR algorithm, as previously described in Section 2.3.2, to the CBCT-noNeedles and MR images.
2.4.4. Non-rigid registration based on post-insertion CBCT and MR images. This registration strategy, referred to as “DIR/CBCT-Needles”, refines the global translation described in Section 2.4.2 by subsequently applying the DIR algorithm, as previously described in Section 2.3.2, to the CBCT-Needles and MR images.

2.4.5. Non-rigid registration based on liver segmentations. The registration strategy, referred to as “DIR/Liver-Seg”, first estimates an initial global translation by aligning the centroids of the segmented liver volumes from both modalities, as described in Section 2.3.3. This is followed by the application of the DIR algorithm, detailed in Section 2.3.2, to the segmented liver masks.

2.5. Electric field computation to assess the IRE ablation zone

In this study, we hypothesize that numerical simulations of the EF can serve as an early estimator of the ablation zone resulting from IRE. This section outlines the numerical methods implemented, as well as the strategy used to define the ablation zone as visualized in post-operative MRI.

2.5.1. Electric field computation Following the approach described in (Gallinato et al. 2019, Gallinato et al. 2020, Tasu et al. 2023), the standard linear static model was employed to simulate the 3D EF distribution during the IRE procedure, using a grid size of 100 × 100 × 100. Electrode geometry was reconstructed based on the manufacturer’s specifications (AngioDynamics). For a configuration involving N inserted electrodes, the EF dose map corresponding to the isoline I is defined as:

$$ \forall \mathcal{I} \in \mathbb{R}, \quad M_{\text{dose}}(\mathcal{I}) = \left\{ x \in \Omega : \max_{(k_+, k_-) \in \{1, \dots, N\} \times \{k_+, 1, \dots, N\}} (\|\nabla \phi^{k_+, k_-}(x)\|_2 \ge \mathcal{I}) \right\}. \quad (1) $$

where the $N(N-1)/2$ functions $\phi^{k_+,k_-}$ represent the electrostatic potentials resulting from the activation of the electrode pair $\Gamma_{k_+}, \Gamma_{k_-}$ for $(k_+, k_-) \in \{1, \dots, N\} \times \{k_+ + 1, \dots, N\}$. $\| \cdot \|_2$ is the Euclidean norm. More specifically, each potential $\phi^{k_+,k_-}$ satisfies:

$$ \forall l \in \{1, \dots, N\}, \quad \left\{ \begin{array}{l} -\nabla \cdot (\sigma \nabla \phi^{k_+,k_-}) = 0, \text{ in } \Omega, \\ \phi^{k_+,k_-}|_{\Gamma_{k_+}} = +V/2, \quad \phi^{k_+,k_-}|_{\Gamma_{k_-}} = -V/2, \\ \phi^{k_+,k_-}|_{\Gamma_l} = \alpha_l, \quad \text{such that} \quad \int_{\Gamma_l} \sigma \nabla \phi^{k_+,k_-} \cdot \text{ndx} = 0, \quad \text{for } l \neq k_-, k_+ \\ \partial_n \phi^{k_+,k_-}_{\partial \Omega} = 0. \end{array} \right. \quad (2) $$

2.5.2. IRE ablation zone prediction from EF. In this study, we adopted a deliberately simple and interpretable strategy to predict the extent of post-operative IRE ablation
zone visible on MRI, using the simulated EF distribution. Specifically, we reconstructed regions of the simulated volume exceeding predefined electric field thresholds. The isodose volume was then used as surrogate predictions of the IRE ablation zone extent as it can be observed on post-operative imaging.

## 2.6. Evaluation metrics

### 2.6.1. Assessment of multimodal registration.
To assess the quality of the alignment between per-operative CBCT and post-operative MRI data, the following metrics were defined to evaluate both the accuracy of the global liver overlap and the local registration error near the ablation zone. The latter was assessed using manually placed internal liver landmarks (section 2.3.4) and the identification of the distal endpoints of the electrodes' active surfaces (section 2.3.5). For each metric, the mean and standard deviation across patients were reported.

#### Liver contour overlap.
The Dice Similarity Coefficient (DSC) was used to quantify the spatial overlap between the liver segmentation on the per-operative CBCT and the corresponding liver volume on the post-operative MRI, propagated using the deformation field estimated through multimodal image registration (see Section 2.4):

$$DSC_{\text{liver}} = \frac{2 \cdot |M_{\text{CBCT}} \cap M_{\text{MRI} \to \text{CBCT}}|}{|M_{\text{CBCT}}| + |M_{\text{MRI} \to \text{CBCT}}|} \quad (3)$$

where $M_{\text{CBCT}}$ denotes the binary liver segmentation mask from intra-operative CBCT, $M_{\text{MRI} \to \text{CBCT}}$ the binary liver mask from post-operative MRI. The operator $\cap$ represents the intersection of the two sets (i.e., the voxel-wise intersection, and $| \cdot |$ denotes the cardinality of a set (i.e., the number of voxels it contains).

#### Needle localisations.
The Target Registration Error (TRE) between the proximal and distal endpoints of the electrodes' active surfaces, as identified in both CBCT and MRI, was computed. When multiple electrodes were simultaneously visible in both CBCT and MRI, the mean TRE across was calculated as follows:

$$\text{TRE}_{\text{needles}} = \frac{1}{N} \sum_{i=1}^{N} \left( \frac{1}{2} \left( \| \mathbf{p}_{i,1}^{\text{CBCT}} - \mathbf{p}_{i,1}^{\text{MRI}} \|_{2} + \| \mathbf{p}_{i,2}^{\text{CBCT}} - \mathbf{p}_{i,2}^{\text{MRI}} \|_{2} \right) \right) \quad (4)$$

where $N$ is the total number of electrodes simultaneously visible in both CBCT and MRI, $\mathbf{p}_{i,1}^{\text{CBCT}}$ and $\mathbf{p}_{i,1}^{\text{MRI}}$ are the 3D coordinates of the proximal endpoint of the active contact of electrode $i$, identified in CBCT and MRI, respectively, $\mathbf{p}_{i,2}^{\text{CBCT}}$ and $\mathbf{p}_{i,2}^{\text{MRI}}$ are the 3D coordinates of the distal endpoint of electrode $i$ identified in CBCT and MRI, respectively.

### 2.6.2. Assessment of IRE ablation zone.
To quantify the ability of EF numerical dosimetry to predict post-operative IRE ablation zone, the following dedicated metrics
were defined and computed across multiple isodose threshold levels (isodose values regularly sampled between 200 V/cm and 600 V/cm were evaluated in the scope of this study). These thresholds reflect the reliability of dose delivery at varying EF magnitude in relation to the observed IRE ablation zone response.

*Predicted/measured IRE ablation zone overlap.* To assess the spatial correspondence between the dose distribution and post-operative IRE ablation zone, the DSC was calculated between the segmented IRE ablation zone in the MRI and the isodose region corresponding to various dose thresholds from the per-operative dose map, as follows:

$$ \forall d \in \mathbb{R}, \quad \text{DSC}_{\text{ablation}}(d) = \frac{2 \cdot |M_{\text{ablation}} \cap M_{\text{dose}}(d)|}{|M_{\text{ablation}}| + |M_{\text{dose}}(d)|} \quad (5) $$

where $M_{\text{ablation}}$ denotes the binary mask of the IRE ablation zone region segmented on post-operative MRI, $d$ a scalar dose threshold (e.g., in V/cm) used to define the map $M_{\text{dose}}(d)$ as defined in (1).

*Isodose/IRE ablation zone contour distance.* The Hausdorff Distance was used to quantify the spatial discrepancy between the IRE ablation zone segmented on the post-operative MRI and the isodose contours from the per-operative EF magnitude, as follows:

$$ \text{HD}_{\text{ablation}} = \max \left\{ \max_{x \in \partial M_{\text{ablation}}} \min_{y \in \partial M_{\text{dose}} \ge t} \|x - y\|_2, \max_{y \in \partial M_{\text{dose}} \ge d} \min_{x \in \partial M_{\text{ablation}}} \|y - x\|_2 \right\} \quad (6) $$

where $\partial M$ denote the boundary of mask $M$.

## 2.7. Statistical analysis.

A Wilcoxon signed-rank test was conducted to assess whether the differences in metrics across the various image registration strategies described in Section 2.4 were statistically significant. A significance threshold of $p = 0.05$ was applied.

## 2.8. Hardware and implementation details.

All implementations for image pre-processing and deformable image registration (DIR) were performed using Python 3.10. Visualization of results was carried out using the 3D Slicer software platform (Fedorov et al. 2012). Time performance benchmarks were conducted on a standard laptop equipped with an Intel® Core™ i9-10980HK CPU and an NVIDIA GeForce RTX 3080 GPU.
# 3. Results

## 3.1. Multimodal registration between per- and post-operative data

Figure 1 presents a comparison of liver contour alignment quality achieved by the different registration strategies under evaluation. As anticipated, incorporating elastic deformation leads to improved alignment of liver contours (see Figure 1d and the light grey boxplots in Figure 1e), compared to approaches based solely on global translation (see Figure 1c and the white boxplots in Figure 1e). Additionally, the liver contours demonstrate comparable overlap when the DIR algorithm is applied to needle-free images (DIR/CBCT-noNeedles) and to images with inserted needles (DIR/CBCT-Needles), as shown in Figure 1e (the difference is not statistically significant, with a *p*-value of 0.075). Furthermore, the direct incorporation of pre-segmented liver masks into the data fidelity term of the registration functional (DIR/Liver-Seg) leads to statistically significantly improved performance compared to methods that rely solely on MR and CBCT image intensities (i.e., DIR/CBCT-noNeedles and DIR/CBCT-Needles). All comparisons yielded statistically significant differences with *p*-values less than $10^{-6}$.

Figure 2 focuses on registration accuracy in a region located closer to the targeted tumor area using manually identified needle positions as a surrogate. When using global translation alone (no elastic refinement), manually annotated landmarks by an experienced radiologist (Trans/Landmarks) yield similar alignment than the alternative approach based on liver contours (Trans/Liver-Seg): the difference is not statistically significant, with a *p*-value of 0.78. Notably, the highest registration accuracy in this region is once again achieved using the two-step approach, in which an initial global translation is followed by a DIR refinement applied specifically to the segmented liver masks, as implemented in the DIR/Liver-Seg method. All comparisons yielded statistically significant differences, with *p*-values less than $10^{-2}$.

## 3.2. Computation of the electric field amplitude

Figure 3 presents metrics designed to evaluate both the quality of dose alignment with the IRE ablation zone visible on the postoperative MRI and the accuracy of early IRE ablation zone prediction during IRE therapy. Using the DIR/Liver-Seg method, it can be observed that an isodose value around 350 V/cm yields the best overlap between the IRE ablation zone visualized on the postoperative MRI and the IRE ablation zone predicted online from the EF dose (see Figure 3a). With this isovalue, it is noteworthy that the DICE coefficients between measured and predicted IRE ablation zone reach values around 0.74, indicating a substantial degree of overlap. The superiority of methods incorporating elastic deformation is evident (see Figure 3b and 3c). Nevertheless, the simple global translation approach guided by manually defined landmarks (Trans/Landmarks method) performed remarkably well within the ablation zone.
<figure><img src="image_3.png" /><figcaption>Figure 1: Comparison of registration performance along liver boundaries across different strategies. (a) Representative intraoperative CBCT acquired during IRE ablation immediately after needle insertion, with the segmented liver overlaid in green. (b) Postoperative MRI of the same patient acquired three days after IRE, with the segmented liver overlaid in red. (c) Overlay of CBCT and MRI liver contours after translational registration based on liver segmentation (“Trans/Liver-Seg”). (d) Overlay of CBCT and MRI liver contours after deformable image registration based on liver segmentation (“DIR/Liver-Seg”). (e) Quantitative comparison of CBCT/MRI liver segmentation overlap across the patient cohort, using registration approaches based solely on global translation (i.e., “Trans/.” strategies, white boxplots) and those incorporating local deformable refinement (i.e., “DIR/.” strategies, light grey boxplots).</figcaption></figure>

# 4. Discussion

## 4.1. Multimodal registration between per- and post-operative data

The primary objective of this study was to evaluate the potential of real-time numerical simulations of the electric field generated during IRE procedures to provide insights into the post-operative ablation zone, as visualized on MRI. Achieving accurate image registration is a critical step in this process, particularly for aligning intra-operative data with post-operative imaging to evaluate treatment effects. While our main objective is
<figure><img src="image_4.png" /><figcaption>Figure 2: Correspondence between electrode positions on CBCT and MRI, used as a surrogate for assessing local registration performance within the ablation zone across different strategies. (a) Representative intraoperative unenhanced CBCT showing the distal ends of two of the six electrodes used for IRE of a 32 mm HCC in the right liver lobe. The estimated virtual needle trajectories are overlaid as red dashed lines in the inset. (b) Corresponding postoperative T1-weighted MRI showing the ablation zone as a well-defined hypointense region, with the needle tracks visible as linear hyperintensities. The virtual trajectories of the two electrodes are overlaid as red dashed lines. (c) Quantitative comparison of the Target Registration Error (TRE) computed between the proximal and distal endpoints of the electrodes' active tips, as identified in both CBCT and MRI, across the patient cohort. Results are reported for registration strategies based solely on global translation (i.e., “Trans./.” strategies, white boxplots) and those refined through local deformable image registration (i.e., “DIR./.” strategies, light grey boxplots).</figcaption></figure>

to predict the ablation zone and determine an optimal isodose threshold, this study contributes to identifying key elements for optimizing multimodal image registration approaches adapted to IRE procedures. Furthermore, these findings may be particularly valuable for the registration of preoperative MRI data onto intraoperative CBCT images,
<figure><img src="image_5.png" /><figcaption>Figure 3: Quantitative evaluation of intraoperative EF dose relative to the postoperative IRE ablation zone. (a) Spatial overlap between the IRE ablation zone delineated on postoperative MRI and the IRE ablation zone predicted intraoperatively from EF dose, computed for EF isodose threshold levels regularly sampled between 200 V/cm and 600 V/cm. (b) Dice coefficient (DSC) quantifying the overlap between the segmented IRE ablation zone on MRI and the 350 V/cm EF isodose region (higher values indicate better agreement). (c) Corresponding Hausdorff Distance (HD) between the predicted and observed ablation zones (lower values indicate better agreement). (d-f) Representative example illustrating the overlay of the 350 V/cm EF isodose region (green) and the postoperative IRE ablation zone (red), obtained using the DIR/Liver-Seg registration method, shown in the axial (d), coronal (e), and sagittal (f) planes.</figcaption></figure>
including segmentations of tumor regions and organs at risk.

The presence of needles, low-dose levels in CBCT, and metallic artifacts marginally impact the overall performance of DIR methods across the entire liver (Figure 1e). Interestingly, in some patients, the presence of needles in the CBCT-Needles image provided valuable imaging features that facilitated image matching with MRI-visible needle tracks (Figure 2c). Advanced DIR techniques based on liver contours offer clear benefits over simple translations both at the liver boundaries and more locally within the ablation region. The computational cost of the multi-modal DIR algorithm on our test platform was approximately 5 minutes. However, in the case of the DIR/Liver-Seg approach, which yielded the best results in our experiments, this duration must be supplemented by the time required for liver segmentation. Notably, although the TotalSegmentator algorithm (Wasserthal et al. 2023), applied to the CBCT-noNeedle image to mitigate artifacts present in post-insertion scans, provided a useful initial estimate of the liver segmentation within a few minutes, extensive manual corrections by an expert radiologist were necessary to achieve the required level of accuracy. Consequently, the DIR process is still far from fully automated. Further advances in automatic segmentation are essential to enable a truly autonomous DIR pipeline. Nevertheless, the current results are encouraging and outline a clear path toward this goal.

It is noteworthy that the registration error metric based on manually identified electrode positions (as used in Figure 2) yields relatively high values, with a median error of approximately 8 mm for the best-performing registration strategy. This elevated error is likely primarily attributable to inaccuracies in manual electrode localization by the radiologist and is further compounded across both CBCT and MRI images in the calculation of equation (4). While the absolute error values in millimeters may therefore be largely overestimated, this metric remains appropriate in the context of this study, where the primary objective is to compare the relative performance of different registration methods.

## 4.2. Computation of the electric dose map

The insights gained from the registration quality metrics generalize well to the accuracy of the IRE ablation zone predictions (Figure 3). Interestingly, despite the overall superior performance of DIR-based methods, the simple global translation approach guided by manually defined landmarks performed remarkably well in mapping the EF dose within the ablation zone. Notably, when using global translation alone (i.e., without elastic refinement), the mapping was more accurate when guided by manually placed landmarks from an experienced radiologist, compared to translation estimated from liver segmentation masks. This can be attributed to the proximity of the manually selected landmarks to the region of interest, which improves local alignment within the ablation zone. Given that elastic deformation-based methods share a common limitation in accurately assessing motion quality, such straightforward landmark-based
techniques may represent a viable alternative, particularly when manual annotations
(which nonetheless require the involvement of a specialized radiologist) are available.
To this end, the optimal approach is to use the tumor itself as a landmark when it is
visible on CBCT. If this is not possible, the portal vein bifurcation may serve as an
alternative, although its distance from the tumor can be a limitation. In neither is
visible, other anatomical landmarks, such as vascular bifurcations or surgical clips, may
be considered as surrogate markers.

The Hausdorff distance, employed in this study to evaluate the intra-operative
prediction of the IRE ablation zone, is a relevant metric as it captures both under-
and over-coverage between the predicted and reference segmentations. Although under-
coverage is the primary concern in the context of liver ablation, over-coverage becomes
critically important in broader clinical scenarios, particularly when organs at risk are in
close proximity. Quantifying both aspects is essential to avoid unnecessary IRE damage
to surrounding healthy tissues.

In this study, a simple dose thresholding approach was used to predict the IRE
ablation zone. While this method provides a practical and easily implementable solution,
future studies may explore the potential benefits of incorporating more advanced
techniques, such as radiomics-based analysis or deep neural networks, to improve the
accuracy and robustness of IRE ablation zone prediction.

Although T2-weighted images often provide good contrast for delineating the IRE
ablation zone, the typically large slice thickness required for these sequences limits
the reliability of accurate 3D segmentation. In contrast, T1-weighted sequences, while
offering less favorable contrast for visualizing the IRE ablation zone, generally permit
thinner slices, enabling more precise volumetric reconstructions. Therefore, while T2-
weighted imaging may support qualitative assessment, but T1-weighted sequences were
more appropriate for quantitative 3D segmentation in the context of this study.

Future studies are required to determine which of the histologically defined
zones corresponds to the IRE ablation zone visualized on MRI following IRE. Such
investigations would deepen our understanding of the biological significance of MRI
signal changes and support the development of more accurate imaging-based endpoints.
Establishing this correlation is crucial not only for improving the interpretation of post-
procedural imaging and validating MRI as a reliable tool for assessing the true extent of
IRE-induced cytotoxicity, but also for refining EF-based predictions of the IRE ablation
zone.

In this study, we deliberately restricted ourselves to a numerical model that does not
account for the varying electrical conductivities of different tissues (e.g., liver, tumor, and
blood vessels). This choice was motivated by the observation that the ablation zone, as
visualized on the postoperative MRI acquired three days after treatment, did not appear
sufficiently precise to allow visual identification of the impact of such conductivity
heterogeneities within the ablation area. It is worth noting that the omission of the
tumor's conductivity, which differs from that of the liver, is not necessarily a limitation
in this context. Since the tumor is entirely encompassed within the targeted ablation
zone, the heterogeneity in conductivity is unlikely to affect the outcome when predictions
are based on an isodose threshold, as is done in this study.

**5. Conclusion**

This study demonstrates the promising synergetic combination of numerical simulations of the electric field generated during IRE procedures with early post-operative imaging for quantitative assessment of the ablation zone. Using a straightforward dose-thresholding approach at approximately 350 V/cm, we observed the highest correspondence between predicted and observed ablation zones, with median DSC around 0.74, indicating a substantial degree of spatial overlap.

In addition, this work highlights key aspects for optimizing multimodal image
registration strategies tailored to IRE procedures. While advanced elastic DIR methods
applied to relevant liver segmentations yielded the highest registration accuracy, a
simpler global translation approach based on manually defined anatomical landmarks
performed surprisingly well in localizing the electric field dose within the ablation zone.
Given that elastic registration techniques often struggle to accurately capture complex
motion and to reliably quantify the quality of the results, landmark-based methods
may represent a practical and robust alternative, particularly when expert manual
annotations are available.

An on-going study lies on the acceleration of the computational framework for
per-operative numerical assessment of IRE. Our recent work demonstrated that, by
leveraging deep learning to initiate the matrix inversion process, it is possible achieve
a tenfold speedup over conventional numerical approaches, without compromising
accuracy on clinically relevant datasets. These advances, combined with the
development of physics-informed loss functions to ensure smooth gradient transitions
and the integration of larger computational grids, open promising perspectives for
incorporating simulation-based tissue conductivity characterization into the clinical
workflow of electroporation-based therapies (Sutter et al. 2023).

**Acknowledgements**

The authors acknowledge Kylian Desier for his helpful discussions and valuable insights.

This research has been conducted with the partial financial support of the Plan
Cancer MECI PC_MECI_21CM119_00 and the Institut National du Cancer (INCa)
(PLBIO n°2023-156). C. Poignard was also partly granted by the ANR projects
IMITATE and MIRE4VTACH. The Bernoulli lab between AP-HP and Inria yielded
a crucial help to O. Séror, O. Sutter, B. Denis de Senneville and C. Poignard, through
the projects NEPA and EVALHEP.
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