# Classification of magnetoencephalographic independent components in epilepsy by machine learning

Aurore Semeux-Bernier, Francesca Bonini, Samuel Medina Villalon, Maria

Fratello, Matthieu Kowalski, Jean-Michel Badier, Frédéric Richard,
Christian-George Bénar

► To cite this version:

Aurore Semeux-Bernier, Francesca Bonini, Samuel Medina Villalon, Maria Fratello, Matthieu Kowalski, et al. Classification of magnetoencephalographic independent components in epilepsy by machine learning. Clinical Neurophysiology, 2025, 180, pp.2111377. 10.1016/j.clinph.2025.2111377. hal-05324467

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# Classification of magnetoencephalographic independent components in epilepsy by machine learning

Aurore Semeux-Bernier<sup>a</sup>, Francesca Bonini<sup>a,b</sup>, Samuel Medina Villalon<sup>a,b ID</sup>, Maria Fratello<sup>a</sup>, Matthieu Kowalski<sup>c ID</sup>, Jean-Michel Badier<sup>a</sup>, Frédéric Richard<sup>d</sup>, Christian-George Bénar<sup>a,*</sup>

## ARTICLE INFO

### Keywords:

ICA

Interictal

Machine learning

Magnetoencephalography

Drug-resistant epilepsy

## ABSTRACT

**Objective:** Magnetoencephalography (MEG) provides valuable information for the pre-surgical assessment of patients with drug-resistant focal epilepsy, but analysis is time-consuming and subjective. Our objective was to combine Independent Component Analysis (ICA) and machine learning to ease interpretation of MEG signals.

**Methods:** We recorded 41 patients. Machine learning models were trained to classify independent components based on a set of 61 predefined features. In a first model, based on random forest (RF), we classified artifact components versus all others. In a second model, based on RF and logistic regression, we classified 4 classes (heart, noise, epileptic, physiological (i.e. normal brain activity)).

**Results:** With the first model 1, we obtained F1-score and balanced accuracy above 0.9. With the second model, balanced accuracy was above 0.8. Classification of epileptic component was above chance level, but with a moderate F1 score around 0.5 – with large variability across patients. Our analysis highlighted features based on spectrum, dipolarity, connectivity, kurtosis, regularity, as well as difficulties regarding spike detection.

**Conclusion:** Artifact classification can be performed efficiently with a combination of ICA and random forest. Distinguishing epileptic from physiological activity is more difficult, although some features show promise as biomarkers.

**Significance:** Our study demonstrates both the potential and the technical limitations of ICA classification of epileptic and artifactual components.

## 1. Introduction

In patients with drug-resistant focal epilepsy, which affects approximately 30 % of individuals with focal epilepsy, surgery may be the only effective treatment option [1]. The goal of surgery is to remove the brain regions responsible for generating seizures, known as the epileptogenic zone (EZ), which must be identified during the pre-surgical evaluation. This evaluation begins with a non-invasive phase, which includes long-term video-electroencephalographic (EEG) monitoring (Devinsky et al., 2018) and multimodal neuroimaging analysis (Rosenow and Luders, 2001). This phase, if not sufficient to precisely identify the EZ to be removed, can be followed by the implantation of intracerebral electrodes using stereo-electroencephalography (SEEG) (Bartolomei et al.,

2017).

Non-invasive recording of interictal epileptiform discharges (IEDs) using high-resolution EEG and magnetoencephalography (MEG) help delineating the EZ for direct surgical resection or guiding SEEG electrode implantation (Kasper et al., 2018; Knowlton and Shih, 2004; Rossi Sebastiano et al., 2020). Compared to EEG, MEG signals are less affected by distortions due to the skull's low conductivity. It results in MEG localization being less blurred (Gavaret et al., 2014), while requiring less complex head models for source localization (Baillet et al., 2001).

However, challenges remain in the systematic analysis and localization of IEDs. Clinical practice can be time-consuming, as each IED must be individually labeled for source localization (Laohathai et al., 2021), on large multivariate datasets typically comprising over 200

<footnote><sup>a</sup> Aix Marseille Univ, INSERM, INS, Inst Neurosci Syst, Marseille, France</footnote>

<footnote><sup>b</sup> APHM, Timone Hospital, Epileptology and Cerebral Rhythmology, Marseille, France</footnote>

<footnote><sup>c</sup> Inria, Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numériques, Gif-sur-Yvette, France</footnote>

<footnote><sup>d</sup> Aix Marseille Univ, CNRS, I2M, Marseille, France</footnote>

<footnote>* Corresponding author at: Institut de Neurosciences des Systèmes – INS, Aix-Marseille Université/ Inserm, UMR 1106, Faculté de Médecine La Timone, 27 bd Jean Moulin 13005 Marseille, France.</footnote>

<footnote>E-mail address: christian.benar@univ-amu.fr (C.-G. Bénar).</footnote>
channels. The localization process is further complicated by the simul-
taneous activation of multiple generators of both epileptic and non-
epileptic activity.

Independent component analysis (ICA) is a method of blind source separation that disentangles the signals that are mixed at the MEG sensor level (Bell and Sejnowski, 1995). This technique helps signal interpretation by reducing high-dimensional data to a smaller set of relevant independent components (ICs), each having a spatial (topography) and a temporal part (time- course). The IC time course can then be used to identify components with epileptic activity (i.e., IEDs) (Chirkov et al., 2022; Ossadtchi et al., 2004). Each epileptic component thus selected potentially represents a node in the interictal epileptic network (Malinowska et al., 2014), putatively corresponding to a single brain region if the component is dipolar (Delorme et al., 2012). Source localization is also simplified by identifying the components associated with IEDs, as localization can be performed on IC topographies rather than on individual spikes. Still, the best strategy to identify the most interesting epileptic components remains an open question. It was also shown that ICA has to be handled with care, as it can degrade source localization in some conditions (Pellegrino et al., 2020).

In parallel, the integration of machine learning (ML) techniques has transformed healthcare by offering innovative solutions to complex diagnostic and treatment challenges. In the field of epilepsy, it has already been used to tackle different issues (Abbasi and Goldenholz, 2019), such as seizure detection (Bhanot et al., 2022), source localization (Sun et al., 2023), image analysis for lesion detection, prediction of surgical and medical outcomes (Santos-Santos et al., 2023). In the context of interictal analysis, a set of studies performed localization of the epileptogenic zone (EZ) in MEG (Nissen et al., 2018), EEG (Ntolkeras et al., 2024) and, SEEG (Cimbalnik et al., 2019). It has been shown in interictal MEG that ML model based on predefined features could differentiate healthy from epileptic subjects (Soriano et al., 2017). Some ML studies on MEG data have also been done regarding spike detections (Pan et al., 2023).

This study aims to improve non-invasive diagnostic of drug-resistant
epilepsy by ML methods performed on MEG data. More specifically, our
main objective was to automatically identify the ICA components cor-
responding to epileptic activity, thus helping to define the interictal
epileptic network. As a secondary objective, we sought to assess whether
cerebral ICs could be separated from artifactual ICs. To reach these
objectives, we used supervised ML classification methods based on
predefined features. The training and testing of the models were based
on labels derived from visual analysis by a neurophysiologist (FB), with
expertise in the use of MEG-ICA data in the pre-surgical assessment of
epilepsy.

## 2. Material and method

2.1. Database

MEG recordings were acquired from drug-resistant patients during
the presurgical evaluation of their epilepsy at the Timone Hospital in
Marseille, consisting of approximately 10 min of interictal MEG re-
cordings in the resting state (eyes closed). The MEG data came from a
cohort of 41 drug-resistant patients. Data were organized in a Brain
Imaging Data Structure (BIDS) (Niso et al., 2018). This study has ob-
tained ethical approval from the local ethical committee (APHM:"-
PADS23-231 Apprentissage automatique pour améliorer le diagnostic
non-invasif de l'épilepsie").

The MEG system used for this study was equipped with 248 SQUID
magnetometers (4D Neuroimaging Magnes system). The sampling fre-
quency was 2034.51 Hz. For each run, Independent Component Analysis
(ICA) was performed, using the infomax algorithm (Bell and Sejnowski,
1995). ICA, which is a method for disentangling a multivariate signal
into ICs, was used here with the aim of isolating the distinct nodes of the
epileptic network that are mixed in the recorded MEG signals

(Malinowska et al., 2014). To reduce background noise, MEG signals
were filtered within the [1–100] Hz range before ICA computation. To
improve interpretability, and to be more robust by limiting amount of
data in each run, only 100 components were kept through a dimen-
sionality reduction process with principal component analysis (PCA).
This resulted in a full dataset of 4100 components.

Subsequently, for each ICA performed on each patient, an expert
MEG neurophysiologist (F.B.) reviewed and classified, components into
distinct categories based on the underlying activity, including epileptic
activity, heart activity, background noise, and normal physiological
activity. These labels were made during the day hospital routine, the
expert was not blinded to clinical data. Most cerebral components were
below IC50, and never above 70, suggesting that no information is lost
by selecting only 100 dimensions.

ICA and reviewing were performed with the in-house AnyWave
software (Colombet et al., 2015), available at meg.univ-amu.fr.

Classification was performed using supervised ML model. The
approach involves both binary and multi- class categorizations. In the
multi-class design, the following labels were assigned (Fig. 1):

• 0 for normal physiological activity

• 1 for epileptic activity

• 2 for heart activity

• 3 for background noise

In second round of review by experts blinded to clinical annotation (CGB, JMB), we also decided to divide the epileptic ICs into 2 categories the "obvious" and "non-obvious" epileptic activity. An "obvious" epileptic IC has very clear epileptic spikes when "non-obvious" ICs are more difficult to label. Fig. 1(b) gives an example of "non- obvious" epileptic ICs (in purple) and an "obvious" epileptic one (in pink) with recognizable spikes.

Multi-class design can be approached in two distinct ways. The first
consists in processing all classes simultaneously, while the second in-
volves breaking them down into distinct binary problems. In the latter
approach, noise components and cardiac artifacts are first identified

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Representation of magnetoencephalographic independent component (a) Example of time series of ICs and their corresponding labels, (b) Example of three different epileptic ICs with “non-obvious” activities in purple and “obvious” activity in pink.</figcaption></figure>
individually, then epileptic activity is distinguished from physiological activity. This multi-stage strategy enables a more nuanced classification, likely to improve the ability of the model to discern specific patterns associated with different classes. It also allows for a better interpretation of the results.

## 2.2. Features

All information dimensions of ICA components were explored: temporal, spectral, and spatial. The features were designed by considering the existing literature and based on the visual classification method of experts in neurophysiology (F. B.) and signal processing (C-G. B., J-M. B., F. R.). The features were extracted subject per subject, but the overall ML model operates single component level, without taking into account subject-specific information. Each feature was computed to provide an objective, reproducible method. To perform this study, we used different tools Bids Manager Pipeline (Jegou et al., 2022), Brainstorm (Tadel et al., 2011), AnyWave (Colombet et al., 2015), MATLAB, Python. All ML related functions are using scikit-learn Python toolbox (Pedregosa et al., 2011). The following section explains how features were computed as well as their meaning. The nomenclature is detailed in Supp. Table 1 in Supplementary Data. Features computed on time series.

### Spikes

The main transient event, in interictal activity, examined by neurophysiologists is the interictal epileptiform discharge, or “epileptic spike” (Iwasaki et al., 2005). A spike generally consists of a transient event with energy in the band [25–80] Hz followed by a slow wave in the [5–15] Hz band. Based on this principle, two detectors were tested: Delphos which was originally built to detect oscillations in stereo-encephalography (SEEG) (Roehri et al., 2018), and a detector specially developed for this study called 2B-detector (“2 bands detector”). Both detectors rely upon the identification of higher amplitude signals in the time-frequency domain.

Delphos uses image analysis, while 2B-detector relies on the simultaneous detection of extreme values in the amplitude distribution over time in two frequency bands. 2B-detector is therefore less computationally demanding. These two detectors have thresholds to tune that in order to declare a detection. Delphos has 3 thresholds, in time, frequency and amplitude dimension. 2B detector has 2 Tuckey-fence thresholds on the amplitude, one per frequency band. To adapt these detectors to our study, various values were tested on a subset of 2300 ICs from 23 subjects. The optimal set of thresholds was determined to be the one maximizing a F1-score defined as:

$$f_{\beta} = \frac{(1 + \beta^2)\text{precision} * \text{recall}}{\beta^2(\text{precision} + \text{recall})}, \quad \beta = 1 \quad (1)$$

$$\text{precision} = \frac{\text{true positive}}{\text{true positive} + \text{false negative}} \quad (2)$$

$$\text{recall} = \frac{\text{true positive}}{\text{true positive} + \text{false negative}} \quad (3)$$

The F1-score was calculated with respect to another threshold according to the number of detections for each component. This threshold was a hyper-parameter tuned for each subject. Inside a subject, components exceeding this hyper-parameter were designated as epileptic, and the labels thus obtained were compared with the expert classification and used for evaluation purposes (Semeux-Bernier et al., 2023).

### Event-locked index

Based on the detection time of Delphos in the time series of each IC, an event-locked index (ELI) can be computed. It consists in averaging around the detection (+/- 200 ms) the different events, labeled as

“spike”, inside a component and inter-components. Inter-components averaging is based on a window defined around the detection of spikes of another component. Component averaging allows testing the consistency of detection within a component. Inter-component averaging allows measuring the response of a component to occurrence of events in another IC. These averages were compared to zero with a t-test (computed in MATLAB), and we kept only the maximum t-value across time. This gives a square matrix of dimension equal to the number of ICA components. The features extracted are the diagonal of the matrix, the sum on the line and the sum on the column.

### Kurtosis

Signals with a high kurtosis value indicate the presence of peaks, which lead to a non-Gaussian distribution (heavy tails) (Robinson et al., 2014). In this study, it was computed using the kurtosis function from the Python toolbox `scipy.stats`.

### Entropy

The entropy of a time series is a quantitative measure characterizing the complexity of its structure. Here, we used permutation entropy that has been found useful in the context of epilepsy (Bratu et al., 2024).

Unlike traditional entropy measures, permutation entropy considers the order or arrangement of values within the time series, rather than focusing solely on their magnitude. It is based on the Shannon entropy computed on the ordinal distribution of the time series. The Shannon entropy is:

$$H(X) = - \sum_{x \in X} p(x) \log_b p(x) \quad (4)$$

Where X is here the discrete random variable representing the possible patterns of the signal. A pattern is defined by two embedding dimensions: a number d of points, and τ distance between consecutive values of the signal to be extracted.

By considering the respective amplitudes of consecutive data points, permutation entropy considers structures that may not be captured by other measures. It is therefore useful for estimating the level of complexity in a given signal.

To compute permutation entropy, a Python module called `ordpy` (Pessa and Ribeiro, 2021) was used, using its default settings (d = 3, τ = 1). The `ordpy` package is specifically designed for calculating ordinal patterns and related measures. It is using the symbolic encoding method proposed by (Bandt and Pompe, 2002). This method is very demanding in terms of computation, and because of the high sampling frequency, requires the decimation of signals by a factor of 5 before processing.

### Regularity

A measure that can characterize the regularity of a function is the Hölder regularity condition. A function f, defined on a Euclidean space, is α-Hölder continuous, if it satisfies for every x and y the following condition:

$$|f(x) - f(y)| \le C|x - y|^\alpha \quad (5)$$

Where α the exponent and C the intercept are both real and $C > = 0, \alpha > 0$. The measure of the exponent is obtained by applying a linear regression to the empirical semi-variogram of the signal computed at different scales. In practice, we computed the exponents twice within two different scale ranges, one in [7–50] samples and the other in [1–150] samples. Besides, regularity was computed on a sliding window of 1 s, resulting in one Hölder intercept and one exponent per window. Moreover, to look at the overall homogeneity of the signal, we compared the regularity computed on the whole signal with the distribution of regularity computed on each window, with a Fisher statistic. This gives
us 4 features: the mean and standard deviation of the Hölder exponent across windows, the coefficient of variation of the Hölder intercept (standard deviation divided by the mean) and the Fisher statistic.

## Connectivity

A connectivity measure that has been used extensively on epileptic data is the h2 non-linear correlation measure (Lopes Da Silva et al., 1989). The h2 consists in a piecewise linear cross-correlation, estimating the non-linear association between two components, as well as the associated delay. The time series is segmented into windows. For each window, an h2 value is computed at different delays with respect to the other component. The h2 value retained per window is the maximum of all h2s at different delays. In the present study, we used 2-second windows with a 1 s overlap, and delays between signals ranging between 0 ms and 100 ms. Then, to build a summary matrix of h2 associated to the links between ICs and their directionality we used two methods.

The first directionality measure is the directionality index proposed by (Wendling et al., 2001). It is based on the signs of the difference between h2 from component 1 to 2 and from component 2 to 1 and the sign of the differences in delays. If we found that 1 is leading 2, then the median h2 value across bins is set in the summary matrix in position (1,2), and 0 in position (2,1). If we do not find a leading component, the average h2 value is set to both positions. We introduce here a second directionality measure, considering the delays only for the windows with high h2 values. The directionality is assessed with a sign test across windows of delays with high h2 values. If it is significant, the median of the considered delays values is set in the summary matrix with the same logic as the first measure.

Finally, other features consist in descriptive statistics (mean, standard deviation) of the distribution of h2 across time per IC. To separate the meaningful in- formation of the h2 matrix, a non-negative matrix factorization with 2 components (one keeping the information, the other the “noise”) was performed. This method is explained in the next section.

## Non-negative matrix factorization

Non-negative matrix factorization (NMF) permits to extract meaningful patterns that repeat within a 2D positive image (time-frequency or space-time for example) (Laroche et al., 2015; Lee and Seung, 1999). NMF decomposes an image into different components (whose number is chosen by the user), with a constraint of positivity. The positive constraint is important to use, as decomposing a positive image into components could lead in positive and negative signals that compensate each other. This is a useful constraint that is often used for unsupervised classification.

With this technique we tried 2 different approaches on the ICA time courses. The first approach consists in using NMF on the whole ICA data of a subject to capture links between ICA components. Here, the 2D image is constructed by stacking the envelopes of all the ICs. Each NMF component has a profile across components and a time-course. The goal was to regroup automatically ICs based on their type of activity (without any a priori on the frequency bands). For each IC, we computed the absolute value of the Hilbert envelope of the signal filtered using the `filtfilt` MATLAB function. NMF was computed on the resulting image (number of ICs x number of time points), using scikit-learn with default parameters (Frobenius divergence), by decomposing the image into 10 NMF components. Then, for each ICA, we retained the maximum value across the 10 NMF components. This measures whether this component is involved in at least one NMF component, meaning that it has been regrouped by NMF as acting in relation with other components.

The second approach is at the level of each ICA component. Here, we used time-frequency analysis to construct an image based on a given IC. Each NMF component has a spectral signature and a time-course. The NMF was thus applied to the short-term Fourier transform (STFT) of the

IC signal, computed using *LFTAT* MATLAB toolbox (Průša et al., 2014). We used 2 s Hann window with a time shift of 12 ms for the STFT. The NMF was computed on the module of STFT with a MATLAB code proposed by (Févotte et al., 2009) that recommends using the divergence of Itakura-Saito for time-frequency signals. We decomposed each IC into two NMF components, with the hypothesis that one will represent the main information of the signal (i.e. spikes), and the other the noise (background) part. By observing the different spectral and temporal profiles we decided to extract the kurtosis (from the time series), the frequency and width of the second peaks of highest amplitude (from the spectral profile).

### 2.2.1. *Spectral features*

Having used the temporal information contained in the ICA, one can also extract the characteristics associated within the signal frequency content. To do this, the discrete Fourier transform (DFT) of the signal is calculated. The DFT has been computed using the Python module `scipy signal` over 5-second windows with a 2.5-seconds overlap. Following these calculations, features were extracted from the average spectrum over all windows.

## Power Spectrum Density

Power spectral density (PSD) is a measure that quantifies the distribution of energy in different frequency bands, including delta [1-4] Hz, theta [4-8] Hz, alpha [8-12] Hz, beta [15-30] Hz, and gamma [40-100] Hz. It is calculated by dividing the energy in each frequency band by the total energy of the entire spectrum in the [1-100] Hz band. This division provides a normalized representation of the energy distribution, quantifying the relative contributions of the different frequency bands to the overall signal.

## Fitting oscillations and one-over-F

We computed the “Fitting Oscillations and One-Over- F” (FOOOF) measure in order to better characterize the important features of the spectrum. The FOOOF process thus separates each spectrum into an aperiodic component, capturing the 1/f behavior, and a periodic component, representing the peaks emerging from the aperiodic component. The process was implemented using a Python module (Donoghue et al., 2020). The fit of the aperiodic component has to be done on a frequency range. Different fits have been tried. Either on the whole band [1-100] Hz, or decomposed in 2 bands, first [1-40] Hz and [40-100] Hz. If the aperiodic fit was not done on the whole frequency range, a suffix with the corresponding frequency range has been added to the feature name.

By removing the aperiodic component, the spectrum becomes flat, and the 1/f effect is attenuated. The power spectral density (PSD) is then calculated on this flat spectrum using the same frequency bands as the previous features, providing a more nuanced view of the energy distribution across frequencies. In the periodic component, FOOOF analysis captures crucial features such as peak amplitude and width. We thus extracted from the periodic component the amplitude of the highest peak and its corresponding frequency. This gives indications of the dominant frequency present in the signal.

## Spectral Entropy

When examining the spectral characteristics of various activities, distinct patterns and peaks of activation become apparent in different frequency bands (Inouye et al., 1991). Spectral entropy can be used as a quantitative measure for characterizing the variability and complexity of spectral patterns, enabling a better understanding of the unique spectral characteristics associated with different types of activity (motor, cardiac, noise, epileptic, ...). We used the spectral entropy function from the python toolbox `AntroPy` (raphaelvallat.com/antropy/
)

### 2.2.2. Feature based on spatial topography

The last feature is based on the spatial part of ICA components which corresponds to the columns of the unmixing matrix. If an ICA component corresponds to a focal brain source, then the ICA topography will be dipolar (Delorme et al., 2012). The “dipolarity” of a topography thus gives an indication on whether the component corresponds to a single brain source.

Given the known positions of each MEG sensor, it becomes possible to solve the inverse problem and to perform source localization on the ICA topographies. Here, the Brainstorm software was used (Tadel et al., 2011), with an overlapping sphere head model and a 2 mm grid discretization of source locations. A straightforward dipole fit was applied. The time course of the dipole *J* is estimated using the generalized least squares method:

$$J = (L^T WL)^{-1} L^T WF \quad (6)$$

with *L* the leadfield (obtained through the forward problem), *F* as the topography, and *W* the whitening matrix derived from the noise covariance matrix.

#### Dipolarity.

The feature derived from the dipole fit source localization is its goodness of fit, indicating the “dipolarity” of a given topography. This metric is used to measure how effectively a single dipole explains the observed topography. The value ranges between 0 and 1. It is computed using the formula:

$$GOF = 1 - \frac{\text{residualvariance}}{\text{totalvariance}} \quad (7)$$

$$\text{residualvariance} = \sum_{n} (F - \hat{F})^2 \quad (8)$$

where *n* is the number of sensors, *F* the field recorded and *F* the field estimated using the estimated time course of the dipole:

$$\hat{F} = L\hat{J} \quad (9)$$

A value close to 1 indicates that the dipole is a strong candidate for the source of the observed topography. Under the assumption that most of brain ICs are dipolar (Delorme et al., 2012), low dipolarity value can be taken as an indication that a given IC does not represent a brain source.

### 2.3. Feature selection

In summary, the dataset comprises 61 features per IC. We had to select the best calculation method for each feature (e.g. “smooth” or not) and the best subset of features that provides the optimal performance for the problem at hand. There are several methods of feature selection, both model-dependent and model-agnostic. The Mean Decrease in Impurity (MDI) is based on the working principle of random forest. Two highly correlated variables will have similar MDIs for a fairly large number of estimators (Chavent et al., 2021). It is thus easier to interpret, as the extracted features are strongly colinear. MDI quantifies the importance of features using the Gini index, which reflects the decrease in heterogeneity after a split. For a particular feature, this is the sum, within a tree, of the decrease in impurity in all nodes that perform a split based on that feature. The average of all trees in the random forest model is then calculated. The impurity measure or Gini index is:

$$H(Q_m) = \sum_{k} p_{mk} (1 - p_{mk}) \quad (10)$$

With $Q_m$, the data at the node *m*, $p_{mk}$ the proportion of class *k* in node *m*.

Pearson correlation coefficient was computed between all features to interpret MDI scores. Subsequently, hierarchical clustering can be done which permits the selection in each group (defined with a heuristic threshold) features with the highest MDI. Features chosen following this analysis were fed to the ML model, others were discarded.

### 2.4. Standardization across patients

Using ML techniques, we intend to find a model that can be generalized across patients. Hence, to ensure robustness across patients, we need to standardize the features. Standardization method can improve uniformity and limit the cardinality (number of unique values) of each feature. Each feature can thus be first standardized individually within each subject, then in a second step standardized all together across subjects.

The first standardization was not necessary for all features, as some of them are by definition already standardized. To check the usefulness of this first step, we compare MDI score of features with and without standardization. For the second step of the standardization process, the scaler was fitted solely on the training dataset.

### 2.5. Machine learning model

In this study, various ML models were explored, including logistic regression, support vector machines (SVM) neural networks and ensemble model, specifically random forest (RF). Different model parameters were tested. They were chosen empirically by looking at the performance of the model in normal condition versus chance level. The chosen parameters are detailed in Supp. Table 2 in Supplementary Data. There is a large imbalance between class labels as there are very few epileptic components. The imbalance is taken into account during model training by specifying it in the model parameters with the ‘balanced’ option of scikit-learn.

The normal condition performance is assessed by separating the dataset in 2 subsets: 80 % of the data to train the model and 20 % to test it. No subject could be part of both the training and testing set, which means that the imbalance between classes is preserved. The performance score is then computed by comparing the true labels with the predicted labels of the test set. Because it is an imbalanced problem, the chance level is determined by training and testing the model (on two different subsets), with the outputs of the training dataset randomly shuffled. The model therefore attempts to fit the input to a random output.

To get an idea of a model’s robustness, the training and testing process was repeated 100 times with random splits of the dataset, while accounting for its imbalanced nature. This approach results in a distribution of performance scores.

Two performance scores were used to evaluate the models: balanced accuracy, a traditional ML measure and, the F1-score, detailed in equation (1). The choice of F1-score was motivated by the highly imbalanced nature of the data set, with an average of 30 % of physiological ICs, 6 % of epileptic ICs, 2 % of cardiac ICs, 62 % of noise ICs. This metric can be computed for each class separately, but we mostly focused on the F1 for the epileptic class.

The obvious and non-obvious epileptic ICs were kept together for the classification task because not doing do would have further increased the imbalanced nature of the data. Linear mixed models were used to evaluate the monotonous behavior of the selected features from physiological to non-obvious to obvious ICs.

The best model was selected based on the comparison with chance level of the performance score distributions (with 80 % / 20 % split, see above). As our final goal is to predict ICs at the level of a single subject, we then used a leave-one-out design. This consists in training the model on all subjects but one and tests it on the remaining one. This allowed testing the performance at the level of single subjects, as well as a better understanding of the variability across subjects.
# 3. Results

## 3.1. Brain/no brain discrimination

In Fig. 2, we can see confusion matrices that are the result of the four binary classification tasks. Each classification task was performed using a RF model, and the confusion matrix corresponds to the result of the model on the testing set. The binary classifications of ICs related to heart artifact and noise versus the other components reach a balanced accuracy and F1 score above 0.90. But as shown in Fig. 2(d), the binary classification of ICs between physiological and epileptic activity has lower performance, with a balanced accuracy of 0.54 and an F1 score of 0.51 with a RF model.

For each classification problem, we can see in Fig. 3 the value of MDI associated to each feature put in the RF model. The stronger the value, the more the feature decreases the impurity after a split. The prefix “norm” means that the standardized version (inside a subject) has been selected. For the spectral features, the suffix “smooth” is a reminder that the spectral features were obtained from the mean spectrum computed with a sliding window. The stars represent the needed features for each classification task according to the function SelectFromModel.

For the classification task of heart artifacts and noise components, few features stand out from the others. For the heart IC classification, it is the coefficient of variation between spike detections and the spike rate obtained with the Delphos detector, for the noise it is the number of the IC (which are sorted by the proportion of energy they represent in the total signal) another regularity. When it comes to the binary problem between physiological and epileptic components, there is no feature having the same degree of importance as in the previous classification. This underlines the fact that no feature is discriminating enough to permit a real separation between physiological and epileptic components. Nevertheless, the best features according to MDI index are:

* Dipolarity

* IC number (reflecting the energy within the original signal)

* PSD in delta and theta band

* H2 connectivity measures in the broad band [1—45] Hz

* Delphos detections

* Aperiodic components of the spectrum computed with FOOOF

* Kurtosis measures (with and without NMF)

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Confusion matrix binary classification with RF, (a) Noise components vs others, (b) heart artifact components vs others, (c) non-brain components, i.e. heart and noise confounded, vs brain activity, (d) Within brain activity, classification between epileptic components and physiological activity.</figcaption></figure>

It is important to note that only non-linear connectivity measures are selected by our model. Fig. 3 gives a hint of how effective spike detection is. For the epileptic classification, the features linked to spike detection have lower MDI than for the heart classification. For all the classification problem, the feature “mean importance eli” that represents the significance of the average of spike detections inside an IC in comparison to zero has low MDI. This could indicate that the detectors did not only detect spikes, but also cardiac bursts.

## 3.2. Difficulty to perform automatic spike detection

The difficulty of performing spike detection relatively to physiological activity appears to be a critical issue in our ML models. We have chosen to focus on the result of Delphos detector. Fig. 4(a) represents the distribution of detected spikes number for 3 categories: brain activity (orange), heart activity (gray) and noise activity (green). We can see that the heart ICs have more detections than the other two categories.

As shown before, the issue concerning spike features is for the classification of brain activity: between physiological and epileptic activity. To investigate this question, we used the distinction between obvious and non-obvious epileptic ICs. Fig. 4(b) corresponds to a more detailed analysis of “brain” boxplot of (a), when the brain ICs are separated between physiological, non-obvious and obvious epileptic activity. A Mann-Whitney test did not find a significant difference between non-obvious and obvious ICs. The significant differences observed between epileptic ICs and physiological ICs could be caused by the large sample size of the physiological group. Indeed, there are 1216 physiological ICs, 186 “non-obvious” ICs and 85 “obvious” ICs.

As depicted, Delphos detector seems to detect heart burst activity as the mean of the gray distribution corresponds to the mean cardiac frequency. But it is unlikely in the studied dataset to observe more than 100 epileptic spikes in a given IC.

## 3.3. Impact of obvious spikes in an IC

The previous results about spike detection are in line with what we observe in Fig. 3, where the last column corresponds to MDI for the classification problem between physiological, “non-obvious” and “obvious” epileptic activities. The 2 last columns of Fig. 3 present the behavior of the most important features depending on the brain type activity. Fig. 5 depicts the t-statistic for the 10 features with the biggest MDI when we fit each feature individually with the categorical variable (physiological, non-obvious epileptic and obvious epileptic) a linear model using *fitdlme* function from MATLAB. This allows finding when a feature has a regular progression (either increasing or decreasing) across categories. The stars represent the case where the p value is significant. Every feature has a significant p value, except for the two related to kurtosis, which also have very low t-statistics (even though it was found important in conjunction with other parameters, see Fig. 3). This representation allows finding the features that have the expected behavior when linked to the presence of clear spikes. We can see that delta and theta power, aperiodic component of the FOOOF, tend to increase with the presence of clear spikes in ICs. On the opposite beta power and connectivity tend to decrease.

## 3.4. Classification performance with a subset of features

Based on the previous MDI measure (see Fig. 3), we have used SelectFromModel function for each classification problem. We concatenated the selected 35 features and performed a hierarchical clustering to reduce the number of features to 15 features (see section 3.5 for the feature correlation matrix). Supp. Fig. 1 in Supplementary Data shows the performance score of different ML models in comparison to chance level in different configurations (binary or multi-labels classification, with oversampling or not). The F1-score is computed only for the epileptic class. We observed that RF models obtain high precision but
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Feature importance, Gini importance of the different features, each column represents a different classification problem. The features are grouped by type. The stars represent the features selected by the RF model.</figcaption></figure>

low recall whereas logistic regression models obtain high recall but low precision. We thus decided to use an ensemble model composed by an RF and logistic regression model using VotingClassifier. The best score is achieved in the multi-label classification design with SMOTE oversampling from scikit-learn toolbox.

In Fig. 6 the detail of the performance of this particular model is shown (details are presented in Supp. Fig. 2 in Supplementary Data). The separation from chance level is clear, and the model appears to achieve good balanced accuracy (median: 0.72). Nevertheless, the F1-score for the epileptic class is low (median: 0.49). This is linked to the low precision of the model, potentially due to the lack of relevant features to separate physiological ICs from epileptic ICs. As expected after the results of Fig. 2 and Fig. 5, the result of F1-score for the heart and noise classes have a median of 0.95 and 0.93 respectively.

The difference between normal condition and chance level changes from one class to the other. This was expected as the class population size largely differs across classes. Moreover, the gap between the

balanced accuracy score and the F1-score underlines the ambiguity of these measures. Indeed, a good balanced accuracy score, even though designed for handling imbalanced datasets, does not mean that a model will actually be efficient for all classes as it is a global measure across classes.

### 3.5. Heterogeneity between subjects

After the selection of the best set of features and the best model, we can perform a leave-one-out study. The model is trained on all subjects but one and tested on the remaining one. Fig. 7 represents the performance of the testing part for each subject. When observing the results subject per subject in the leave-one-out design one can see a strong heterogeneity in the performance of the model with 19 subjects with a F1-score above 0.5. This can be considered as a net improvement in comparison to the first RF model presented in Fig. 2. This strong heterogeneity does not depend on the number of epileptic ICs per subject,
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Spike detections distribution across classes (a) Boxplots showing the distribution of the number of spikes detected as a function of the type of IC, with brain activity in orange, cardiac activity in gray and noise activity in green. (b) Boxplots showing the details of the orange distribution of the number of spikes detected in brain activity: the yellow distribution concerns physiological ICs, the purple distribution concerns “non-obvious” epileptic ICs and the pink distribution concerns “obvious” epileptic ICs.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Behavior of the most important features for the cerebral ICs, Linear mixed-effects t-statistic results of the most important features for the classification of epileptic ICs. The purple stars represent significant $p \le 0.0001$ after Bonferroni correction.</figcaption></figure>

the type of epilepsy, the output of the surgery nor the presence of a lesion (Supp. Fig. 3 and 4 in Supplementary Data).

To understand the cause of this strong heterogeneity, we fitted and tested an ML model for each subject individually i.e., in overfitting conditions). Because it seems that heart artifact and noise ICs were not an issue for the classification result (see Fig. 2), we decided to redo the classification by focusing only on cerebral ICs (i.e. physiological and epileptic). To prevent excessive overfitting, we selected on the whole population a subset of features from the most important ones identified in this binary problem (15 features, as in section 3.4). Fig. 8(a) is a clustermap of the Pearson coefficient correlation between the selected features.

In order to test whether the same thresholds can be used across

subjects, we looked at the variability of the logistic regression coefficients when we fit a model inside a subject and during the leave-one-out design. The resulting coefficients are shown in Fig. 8 (b). The orange distribution corresponds to the distribution of “ideal” coefficient (in overfitting condition), whereas the pink distribution corresponds to the coefficients found in the leave-one-out design (thus avoiding overfitting). From this figure we can see the spread of coefficient values, sometimes of opposite sign. This indicates the difficulty to effectively find a common set of features or common thresholds across subjects.

In order to test whether the same features are useful across subjects, we used a feature selection method within each subject. A logistic regression model was thus fitted using SequentialFeatureSelector function for each subject. As seen in Fig. 8 (c), the large variability in the proportion of times a given feature was selected indicates that, from one subject to another, the best set of features to characterize epileptic IC is not the same. Only some were selected each time, particular the out-strength directionality, the Hölder exponent and the FOOOF offset.

# 4. Discussion

## 4.1. Classification results

MEG is a non-invasive method that has proven its utility in the pre-surgical evaluation of drug-resistant epilepsy. While applying ICA to MEG data helps reduce dimensionality and can improve the detection and localization of interictal epileptic activity (Malinowska et al., 2014; Pizzo et al., 2019), identifying the epileptic components of interest remains a challenge (Malinowska et al., 2014; Pizzo et al., 2019). In the present study, which is at our knowledge the first using ML methods to classify epileptic activity on MEG ICs, the main objective was to identify automatically the ICs involved in the epileptic network. A secondary objective was to separate brain-related ICs from noise and heart artifacts.

As a first result, we show that classical ML models perform well for separating artifactual from cardiac and from brain activity. Indeed, we observed that no epileptic ICs were confounded with cardiac ICs, indicating that the features proposed in the present study are efficient for identifying heart artifacts and noise components. We thus achieved, with a random forest model, similar results to those obtained using more complex methods based on neural networks with predefined features (Rong and Contreras-Vidal, 2006) or deep learning with convolutional
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Detail of the best model, *VotingClassifier* in the multi-labels design composed by a logistic regression and RF models with *SMOTE* oversampling, the purple distribution represents the score of the model in normal training condition, the yellow one represents the score of the model in chance level condition. The balanced accuracy is a score that takes into account the global classification of the four classes. The models have been trained and tested 100 times.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Performance achieved for the chosen model in the leave-one-subject-out design study. The yellow curve corresponds to recall, the pink one corresponds to precision and the blue one to the F1-score. The dashed blue line corresponds to the balanced accuracy score. The subjects have been sorted by ascending F1-score.</figcaption></figure>

neural networks (Treacher et al., 2021). The proposed method, given its robustness in selecting artifactual ICs, could therefore be included into an automatic pipeline in order to reject noise-related ICs and clean the MEG signal.

As a second result, we observed that separation between physiological and epileptic classes was more difficult, with a higher level of false negatives and false positives. Previous studies conducted on EEG (Ntolkeras et al., 2024) or intracerebral (SEEG) data (Cimbalnik et al., 2019; Klimes et al., 2019; Jose et al., 2023) have shown the potential of ML to localize the EZ. However, these studies used the area under the ROC curve (AUC, revealing high values above 0.9), which, may not be a suitable metric to identify the epileptic regions or signals. Indeed, the ROC is hampered by the intrinsic imbalance between positive classes (corresponding to very few pathological epileptic sources) and negative classes (corresponding to abundant physiological sources) (Klimes et al., 2019; Jose et al., 2023). We used instead the F1 classification score – a reliable measure in clinical practice – which low value reveals the difficulty in isolating the epileptic components from other brain-related components. Nonetheless, although the performance was not as high as expected, our ML approach allowed investigating the potential of features to provide interesting information about the underlying epileptic signal.

The biggest challenge of this study was the substantial variability observed across patients. While some recordings contained very few IEDs, others had numerous IEDs with a morphology varying along time

and across ICs. As a matter of example, in Supp. Fig. 5,6,7 in Supplementary Data, three snapshots of different MEG patient recordings with the prediction of our ML model. Some ICs were marked by the expert in the clinical context and by comparison with other recordings. These difficult cases motivated us, in the second clinically blinded review, to separate the epileptic ICs into obvious and non-obvious activities. The labeling of independent components (ICs) demands significant clinical expertise, especially in borderline cases, which we deliberately chose not to exclude in order to reflect real-world clinical complexity.

## 4.2. Feature selection

Different methods for feature selection have been used in previous studies, such as fast correlation-based filter (Li et al., 2023) and statistical comparison (Cimbalnik et al., 2019; Ntolkeras et al., 2024). As there seems to be no consensus on feature selection, we decided to investigate random forests, an established and easy-to-use ML method.

We investigated different types of features. The most straightforward is spike detection, which is a difficult topic due to variability of spikes within and across patients. We found based on MDI score that it is an important feature, however more for separating artifactual from signal than for actual detection of epileptic nature of ICs. We also found that, similarly to Nissen et al. (Nissen et al., 2018), non-linear connectivity measures and PSD in delta band are significantly linked to epileptic ICs.

In addition, we incorporated into the model non-classical features
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Heterogeneity of parameters and features across subjects (a) Clustermap based on Pearson correlation coefficient between features (b) Logistic regression coefficient variability when testing the model in overfitting condition (fit and test on the same subject) versus leave-one-subject-out design with only selected features. Here the classification task is binary: between physiological and epileptic ICs (c) percentage of times a feature has been voted for in a logistic regression model (number divided by 41, number of subject). The classification task here is also binary: between physiological and epileptic ICs.</figcaption></figure>

based on non-negative matrix decomposition, spectrum aperiodic parameters and Hölder regularity. These features emerged as important, as indicated by Gini importance measure, representing a novel finding that warrants further exploration in feature engineering in epilepsy, and possibly representing new biomarkers for epilepsy. In this regard, to address this issue of identifying biomarkers for epileptic pathological signal (Ramantani et al., 2023), we analyzed the features deemed significant within a large list of putative markers using linear modeling to assess their behavior based on the type of ICs: physiological (non-pathological brain sources), non-obvious epileptic, or obvious epileptic.

We hypothesized that a useful feature should have a monotonous behavior across these three categories.

### 4.3. Features as putative biomarkers

Among the features tested, h2 connectivity has shown a monotonous behavior, decreasing significantly from physiological, to non-obvious then to obvious ICs, that is, in the presence of clear spikes. This is consistent with previous studies showing that epileptic brain regions, although intrinsically more connected, are less connected to the rest of
the brain, and with the fact that such a connectivity pattern is associated to good surgical out- come. (Bettus et al., 2008; Englot et al., 2015; Lagarde et al., 2018; Aydin et al., 2020; Corona et al., 2023) However, as pointed out by two reviews (Englot et al., 2016; Xu et al., 2021), this is a subject of debate, as some studies found higher connectivity of epileptic regions with the rest of the brain. Results may also vary based on the method used for computing connectivity and clinical characteristics. Increase in delta and theta power has been observed within obvious compared to non-obvious epileptic and physiological ICs, indicating that slow activities are linked to the presence of clear spikes. Theta power has also been found as an important marker in (Bettus et al., 2008). How- ever, in this latter study focusing exclusively on patients with mesial temporal lobe epilepsy, a decrease of theta power was observed when the mesial structures are part of the epileptogenic zone. In contrast, in (Westin et al., 2022), an increase in the MEG signal of delta and theta power was demonstrated before and up to onset time of spikes. In- creases in the interictal delta band in the EZ has also been observed in (Lundstrom et al., 2019) and in (Lundstrom et al., 2018), the latter also describing an increased coupling between slow and fast activities such as interictal spikes. Interestingly, we also observed that epileptic ICs exhibit lower beta power than physiological ICs, which may in turn be related to the observed relative increase in slow oscillation.

It is interesting to note that the aperiodic parameters of the FOOOF analysis (exponent and off set) increase with the presence of obvious spikes, suggesting the importance of these parameters as putative markers. It has been shown that aperiodic parameters of the spectrum are of pathophysiological relevance (Donoghue et al., 2020; Mon- temurro et al., 2024) and particularly can be linked to the balance be- tween excitatory and inhibitory activity (Gao et al., 2017).

In summary, the three classes of features – namely the decrease in h2 connectivity, the increase in the theta-delta PSD along with a decrease in beta power, and the increase of the aperiodic component of the FOOOF – demonstrate a consistent behavior across both epileptic ICs and subjects. This suggests that these features may serve as biomarkers for epilepsy, even though the present study shows that it is difficult to find common thresholds across patients. Previous ML studies have performed feature selection (Soriano et al., 2017; Cimbalnik et al., 2019) but none have specifically investigated the detailed behavior of these features depending on the type of activity (obvious, non-obvious, physiological), making it challenging to compare our findings against the literature.

## 4.4. Limitations

A key methodological limitation concerns the labeling of epileptic components, which was based on the assessment of a single expert. Although we reviewed and refined the labels (distinguishing between obvious and non-obvious epileptic IC), the absence of multiple expert annotations limits the objectivity and reproducibility of our ground truth. Labels were assigned with access to clinical information, which, while potentially enhancing their clinical relevance, introduces a risk of bias in model evaluation. This likely contributed to the moderate per- formance scores, as our models were benchmarked against highly contextualized expert judgments. Nonetheless, we view this clinically informed labeling as a strength, since it reflects realistic diagnostic reasoning and likely improves the ground truth. Future studies could include annotations from multiple blinded experts to quantify inter-rater variability and check label reliability. Confirming false negatives with an external source of information, such as intracerebral EEG, would further strengthen model validation. Additionally, multicenter datasets would be valuable, as MEG interpretation practices may differ across centers. A larger, more diverse dataset would also allow for more detailed classification of epileptic ICs, including the distinction between obvious and non-obvious patterns, which was not feasible in our current dataset due to the limited number of epileptic ICs.

A technically limiting factor we encountered was the reliability of spike detection. Automatic spike detection on surface signals is a

difficult topic. Other studies have found that specificity is of particular concern, even with sophisticated deep learning methods (Fernández-Martín et al., 2024; Mouches et al., 2024). One factor that influences the results of detection and more globally the ML model results is the subject state (Chybowski et al., 2024). Indeed, subjects were all asked to lie down quietly, but depending on their arousal state and on level of drowsiness their signals can vary very significantly (Díaz-Negrillo, 2013; Dellavale et al., 2023). Thus, a single run of 10 min may not permit to obtain equivalent resting state between subjects. Consequently, more or less spikes (or with inconsistent and stable waveform) can be observed from one run to another within the same subject, and hence the threshold to put across subjects may not be the same. It is possible that the spike rate influences the quality of ICA decomposition, which needs further investigation. The morphology of spikes could be another interesting feature (Huneau et al., 2013), which could be the scope of future studies.

Our goal in the present study was to identify interictal activity, i.e. that related to the irritative zone, even though the final aim of presur- gical evaluation is the definition of the epileptogenic zone. As the relationship between the interictal epileptic network and the EZ is not straightforward (Bartolomei et al., 2016), further study using a ground truth based on SEEG recordings would be needed. SEEG data would also enable the exploration of additional connectivity metrics beyond h2, which was the only one tested here. Another open question concerns the stability of the interictal epileptic network within a patient across different runs. In the present study, we did not have two runs labeled per subject therefore we kept only one per subject. Future work should investigate the stability of the interictal network across runs.

## 5. Conclusion and perspectives

The classification of magnetoencephalographic ICs in the context of pre-surgical analysis has a high variability across patients. As sensitivity is high, our method could still help clinical decision by outlying putative epileptic ICs. Moreover, the classification of artifactual ICs achieved a very good F1 score, suggesting that one could perform automatic artifact rejection. Feature selection can also outline putative biomarkers from the non- invasive interictal signals.

Despite the relatively limited performance of the ML model in identifying epileptic components, other venues exist to improve its predictive ability. As one of the difficulty concerns the subjectivity of the ground truth (i.e., clinician labeling), it would be interesting to carry out IC labeling based on the location of the EZ (Cimbalnik et al., 2019; Jose et al., 2023), or using simultaneously obtained SEEG signals (Pizzo et al., 2019; Velmurugan et al., 2022). To further test the generalization of ML models, it would be necessary to train and test them on data from different MEG centres (Cimbalnik et al., 2019; Jose et al., 2023). Addi- tional information to feed the model could be provided in order to improve identification of the epileptic ICs, namely subject age, state of vigilance, anti-seizure medication, since the electrophysiological signal is known to depend on these clinical parameters.

Finally, it would be interesting to try deep learning on the raw signal to investigate whether such model can generalize better across patients and help finding features that were not considered a priori. Deep learning has already been used in epilepsy in a supervised framework (Ren et al., 2021; Mouches et al., 2023). It would be interesting to use unsupervised learning, which was used in sleep staging (Banville et al., 2021) or task classification (Zhu et al., 2023) with non-linear ICA. Another possibility would be to combine feature extraction with a deep neural network as was done previously for artifact classification (Rong and Contreras-Vidal, 2006). However, these methods may require larger dataset and would be more difficult to interpret – even if the field of explainable AI is growing (Linardatos et al., 2020). A promising future path lies with the Optically Pumped Magnetometers, a new MEG tech- nology allowing patient movement, potentially leading to larger cohorts and longer runs of data (Pedersen et al., 2022).
## Funding

This work is supported by a Ph.D. grant from the Laënnec Institute of Aix-Marseille Université. This project has received funding from the Excellence Initiative of Aix-Marseille Université – A*Midex, a French "Investissements d'Avenir programme" AMX-21-IET-017 and from the French National Agency for Research through the BMWs project (ANR-20-CE45-0018) and the MEO project (ANR-22-CE19-0012). It was performed on a platform member of the France Life Imaging network (grant ANR-11-INBS-0006).

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.clinph.2025.2111377.

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