Virtual intracranial electroencephalography for epilepsy surgery using ictal magnetoencephalography

Modelling the interactions that arise from neural dynamics in seizure genesis is challenging but important in the effort to improve the success of epilepsy surgery. Dynamical network models developed from physiological evidence offer insights into rapidly evolving brain networks in the epileptic seizure. A major limitation of previous studies in this eld is the dependence on invasive cortical recordings with constrained spatial sampling of brain regions that might be involved in seizure dynamics. Here, we propose a novel approach, virtual intracranial electroencephalography (ViEEG), that combines noninvasive ictal magnetoencephalographic imaging (MEG), dynamical network models and a virtual resection technique. In this proof-of-concept study, we show that ViEEG signals reconstructed from MEG alone preserve critical temporospatial characteristics for dynamical approaches to identify brain areas involved in seizure generation. Our ndings demonstrate the advantages of non-invasive ViEEG over the current presurgical ‘gold-standard’ – intracranial electroencephalography (iEEG). Our approach promises to optimise the surgical strategy for patients with complex refractory focal epilepsy.


Introduction
Modelling complex systems like the brain is challenging 1 , particularly when studying time-evolving interactions that arise from normal and aberrant neural dynamics across multiple temporal and spatial scales 2,3,4 . Patterns of brain activation and interactions form the neural correlates of brain states and behaviour, which are fundamental to understanding the underlying mechanisms of brain function 5 .
Developing and validating mathematical and computational models of brain function and neural dynamics has been a key mission for neuroscience research in the last few decades.
Dynamical network models provide great capacity to probe the underlying mechanisms of complex neural dynamics. Inspired by early studies of excitatory and inhibitory neurons, investigators have developed dynamical models of neural mass and neural mass networks, which connect an ensemble of neural mass models into macroscopic neural systems 1,6,7,8,9 . Employing dynamical models, multiple attempts have been made to understand the mechanisms underlying normal 10,11 and pathological neural dynamics 12,13,14 . Dynamical network models have also been applied to neurophysiological data recorded from the human brain to develop speci c hypotheses towards clinical application 15,16,17,18 .
A major limitation of previous studies in this eld is the dependence on invasive intracranial electrode recordings of cortical activity when applying dynamical network models to experimental data. This can lead to insu cient sampling of brain networks with biased representation of the actual systems involved 19 . Moreover, invasive cortical recordings are relatively costly to obtain from animal models and only possible to obtain from the diseased human brain, as in epilepsy surgery planning, with inherent risks 20,21 . Non-invasive neuroimaging, such as high density electroencephalography (HDEEG) and magnetoencephalography (MEG), offer high temporal resolution and whole brain spatial coverage 22 . Unlike functional magnetic resonance imaging (fMRI), electromagnetic elds recorded over the head surface by EEG and MEG represent the linear summation of collective source activity 23 . Advances in EEG and MEG source imaging techniques have improved the capacity to project the recorded surface electromagnetic elds back to source activity with high spatial resolution when su cient signal-to-noise ratios are obtained 23,24 .
Epilepsy affects about 1% of the global population and at least one third of epilepsy patients have seizures that are refractory to medication 25,26 . While surgery can be an effective treatment for pharmacorefractory epilepsy, it is widely underused 27 . Presurgical evaluation is particularly challenging when MRI shows no clear lesion, a large complex lesion, or multiple potential epileptogenic lesions 28,29 . Such cases stand to bene t from non-invasive dynamical approaches to better characterise the brain networks involved in seizure dynamics. Here, we aim to apply a dynamical network approach to source reconstructed non-invasive ictal MEG data and we introduce the novel concept of virtual intracranial EEG (ViEEG). A set of sources, or virtual electrodes, 30 are de ned in the reconstructed individualised MRI brain where ictal source signals can be reconstructed as ViEEG signals. We then construct patient-speci c functional networks that are integrated in dynamical network models to determine the effects of the network structure on seizure transitions. Speci cally, brain regions responsible for seizure generation are identi ed by evaluating the contribution of each individual node to the network excitability, i.e., the likelihood of a particular node affecting the transition to a seizure. From this evaluation, we attempt to non-invasively de ne a virtual ictogenic zone (VIZ) and assess our ViEEG derived dynamical network models against the preoperative HDEEG and MEG ictal source localisation (ESL, MSL), the clinical intracranial EEG (iEEG) localisation, and the epileptogenic zone (EZ) as de ned by resection linked to long term postoperative outcome. In doing this, we aim to address several questions. Can we reconstruct ictal ViEEG signals that have distinct spatial and temporal characteristics of epileptiform discharges? If so, can dynamical network models using ictal ViEEG signals guide a surgical strategy that characterises the EZ while identifying brain areas that are less likely to be involved in the EZ? Finally, can dynamical network models using ictal ViEEG signals provide unique information to the current clinical localisation, including the iEEG seizure onset zone (SOZ) and HDEEG and MEG source localisation, in characterising the EZ?

Dataset and Ethics
The study was based on the dataset in Plummer et al 31  had drug-resistant focal epilepsy with either no visible MRI lesion (10 patients) or a complex lesion (3 patients). Each patient had an hour-long simultaneous HDEEG (ANT Waveguard® 72-94 electrode cap including 12-electrode inferior temporal array, 10-10 positions) acquired on one of two EEG ampli er systems (ANT ASAlab®, Enschede; Compumedics SynampRT®) and MEG (Elekta Triux® 306 sensors, 102 magnetometers, 204 planar gradiometers), sampled at 1000Hz or 5000Hz with anti-aliasing lter set at 330Hz or 1650Hz respectively. Bad channels for all MEG data were checked prior to applying temporal extension to signal source separation (tSSS) using Max lter® v2.2.10-15 (Elekta Oy, Helsinki) for interference suppression (correlation limit 0.98 and sliding window of 10 seconds). Independent onesecond interval clock triggers acquired on each system were used to synchronise HDEEG and MEG o ine, veri ed by comparing ECG channel signal phase from each independent modality. MEG head coils, HDEEG electrode positions, and PAN (pre-auricular, nasion) co-ordinates were digitised (Polhemus Fastrak®) in common space for MRI co-registration; digitised points were cross-validated with optical sensor tracking (NDI Polaris Vicra®). Applying a second-order bandpass Hann FFT lter (1-100Hz), seizures were independently marked by a neurologist (C.P.) and a clinical scientist (S.V.) using Curry 7® (Compumedics Neuroscan®, Hamburg). A total of 36 ictal MEG events were captured from 12 patients (interictal-only activity in one MRI-normal patient) ( Table 1). Pre-operative MPRage MRI was acquired as part of clinical investigation as well as post-operative CT to con rm resection margins. A post-iEEG implantation CT scan con rmed implantation locations in the seven patients who had iEEG grids or strips -Patient 7 had an intraoperative depth electrode and four patients (Patients 2, 3, 6, 8) went straight to surgery based on non-invasive data. As raw iEEG recordings were not available to us for two external patients (only iEEG reports for Patients 7, 9) we were able to compare ViEEG to iEEG results in six patients (Patients 1,4,5,10,11,12). Based on ndings from Plummer et al 31 , ictal early-MSL preceded early-ESL in six patients (Patients 1, 3, 4, 5, 10, 11), while ictal early-ESL preceded early-MSL in ve patients (Patients 2, 6, 8, 9, 12) Ictal discharges were not localisable in one patient (Patient 7) ( Table 1). Using standardised low resolution tomographic analysis (sLORETA), Plummer et al 31 found there is usually a lead-lag relationship between early-MSL and early-ESL for a given averaged ictal discharge and it was the earliest solution (de ned as the rst occurring early-MSL or early-ESL solution from discharge take-off that explained 90% of the signal variance) that was the best predictor of the EZ.

Virtual iEEG
We propose a novel concept (ViEEG) that consists of multiple virtual electrodes or virtual sensors guided by HDEEG and MEG source imaging 30,32 . An example of ViEEG de ned for a patient is given in Fig. 1. ViEEG was de ned using similar electrode con gurations to iEEG, such as grid, strip and depth arrays, and a uniform spacing (10mm) between virtual electrodes to allow a direct comparison between iEEG and non-invasive ViEEG. In this study, ViEEG was de ned for each patient solely using information from MSL 31 (not ESL), while blinded to other clinical information. Thus, the locations of ViEEG electrodes extensively covered MSL of averaged ictal discharges (early-, mid-upstroke and late-peak phase solutions) 31 . ViEEG comprising over 500 virtual electrodes is less computationally feasible for dynamical modelling and so we did not de ne ViEEG to cover the whole brain in this study. We used Curry 8® (Compumedics Neuroscan®, Hamburg) software and pre-operative MRI scans to generate realistic boundary element method models with a single layer, i.e., inner skull surface 33 . Ictal ViEEG signals were reconstructed using a linearly constrained minimum variance beamformer technique 34 . Technical details of MEG signal processing and source reconstruction are presented in Supplementary material (ViEEG signal reconstruction). A total of 25 from 36 seizures could be reconstructed using ViEEG with distinct morphological and spatial characteristics from background activity (Supplementary Table 5). Eleven seizures reconstructed from the ictal MEG data did not present identi able morphological features of epileptiform discharges and hence were excluded from analysis. ViEEG con gurations are presented in Supplementary Figs. 5-16.

Blinded Analysis
To ensure the validity of ViEEG and dynamical network models, M.C. was blinded to the surgical outcomes, pathology, iEEG ndings, and ESL solutions; M.C. had no knowledge of which solution (early-ESL or early-MSL) was the earliest solution for each patient when de ning ViEEG. All other team members were blinded to the locations and con gurations of ViEEG. When analysing and modelling ictal ViEEG signals, D.G. was blinded to clinical information, including resection margins, iEEG ndings, source localisation and surgical outcomes, and ViEEG locations and con gurations. Only time-series of ictal ViEEG signals (no information on ViEEG locations, resection margin, pathology or surgical outcomes) were given to construct functional networks and apply dynamical network models. Patient information was de-identi ed and patient numbers were randomised from the previous publication 31 . Clinical information and ViEEG con gurations were only unblinded to D.G., W.W. and J.T. after results from network models were nalised.

Dynamical Network Models and Virtual Resection
Functional networks were constructed from ictal ViEEG signals using two connectivity methods, amplitude envelope correlation (AEC) and mutual information (MI) 17,35,36,37,38 . Both methods do not conservatively correct eld leakage effects in reconstructed source signals 36 . Similar to connectivity analysis of iEEG data, we treated each ViEEG electrode as a node and connectivity between a pair of nodes expressed by the edge-strength. A surrogate correction threshold was then applied to functional networks to preserve edges that were statistically signi cant 37 . Next, a generative dynamical network model was integrated to each node, simulating the change of network excitability when a node was virtually resected from the network 17,39 . Speci cally, we calculated the change in time that the network spends in the seizure state over the total simulation time after a node is removed from the network structure. The effect of the removal of a node is quanti ed by the so-called Node Ictogenicity (NI), where a positive NI indicates the removal of that node effected a decrease in the seizure-likelihood. This model has been presented previously 17,40,41,42 . The set of nodes that have signi cantly large (Mann-Whitney-Wilcoxon U-test and Bonferroni-Holms correction survival) and positive NI values relative to other nodes is de ned as the Virtual Ictogenic Zone (VIZ). Any nodes outside the VIZ are de ned as non-ictogenic nodes. For each MEG seizure, our approach identi ed two VIZs (AEC-VIZ and MI-VIZ) from AEC and MI constructed networks. Each VIZ also has two aspects, 'hotspot' and 'boundary'. We de ned a VIZ hotspot as nodes in the top 20% NI values among all VIZ nodes and boundary as the outer line of the VIZ. The VIZ hotspot (or top NI value nodes) has been shown to better predict the EZ, while the VIZ boundary can capture the entirety of the EZ and identify non-ictogenic brain areas that are less likely to overlap with the EZ 17,41,42 . See also Supplementary material (Network model).

Statistical Analysis
A mixed-effects logistic regression model was employed to evaluate the statistical signi cance of nodallevel (virtual electrode) concordance between a VIZ (hotspot and boundary) and clinical localisation (resection margin, iEEG SOZ and HDEEG-MEG source localisation) based on odds ratios (OR) with 95% con dence intervals (CI). Akaike Information Criterion (AIC) 43 and Bayesian Information Criterion (BIC) 44 were reported. We also calculated the precision and recall of respective boundaries and hotspots of AEC-VIZ and MI-VIZ in predicting the resection margin and the earliest source localisation solution when seizures are grouped based on long-term (at least 24-month follow-up) surgical outcomes (seizure-free and non-seizure-free. F-scores, the harmonic mean of precision of VIZ hotspot and recall of VIZ boundary, were reported. See also Supplementary material (Statistical analysis).

Data Availability
All data are available upon request.

Results
Twelve patients with 25 seizures captured by simultaneously acquired HDEEG and MEG were included in our analysis (Table 1, Supplementary Table 5).

Clinical features of ictal ViEEG signals
The rst question we addressed is whether we can reconstruct ictal ViEEG signals with distinct clinical characteristics to enable dynamical network models to identify brain areas that are involved and not involved in increased in silico seizure likelihood. In Fig. 2, we demonstrate a side-by-side comparison of ViEEG and iEEG signals from Patient 5. Ictal waveforms from ViEEG can be visually identi ed solely from sources in anterior hippocampal and basal temporal structures, which is consistent with the iEEG SOZ. Representative ictal ViEEG signals of 25 seizures are shown in Supplementary Figs. 5-16.

VIZ hotspot and boundary characterise the EZ and predict the clinical localisation
The next question we asked is whether the VIZ can devise a strategy that characterises the EZ with su cient precision and recall. Successful prediction of the EZ by the VIZ hotspot is demonstrated in Fig.   2. Although the VIZ boundary is much more extensive than the EZ, it captures the entirety of the EZ and also identi es non-ictogenic brain areas. The dynamical network models (using two different network inference techniques, AEC-VIZ and MI-VIZ) obtain high recall in predicting the EZ (Supplementary Fig. 4 for seizure-free group). Mixed-effects logistic regression models suggest AEC-VIZ and MI-VIZ signi cantly predict the resection margin at nodal level (Fig. 6A). F-scores (harmonic mean of precision of VIZ hotspot and recall of VIZ boundary) for MI-VIZ (median=0.75) in predicting the EZ (i.e., resection margin for seizure-free patients) suggest our approach helps delineate the EZ and identify non-ictogenic brain regions based on recall of MI-VIZ (Fig. 6B, Supplementary Fig. 4). The spatial overlap between the VIZ and clinical localisation are demonstrated on a per patient and per seizure basis in Supplementary Table  3 and Supplementary Table 4. Furthermore, we nd AEC-VIZ and MI-VIZ hotspots and boundaries predict the iEEG SOZ and the early-MSL solution (Fig. 6A Supplementary Fig. 6), Patient 6 ( Supplementary Fig 10), Patient 11 (Fig. 3, Supplementary Fig 15), Supplementary Fig 16).

MI-VIZ predicts the optimal source localisation solution
The earliest solution (the rst-occurring early-MSL or early-ESL sLORETA solution) has been reported as the best predictor of the EZ 31 . In this study, we are interested in whether VIZ identi ed by dynamical network models predicts the earliest solution and not just the early-MSL. AEC-VIZ and MI-VIZ signi cantly predict the earliest solution (Fig. 6A, Supplementary Table 1 and Supplementary Table 2). Speci cally, we nd that the MI-VIZ predicts the early-ESL instead of early-MSL in three patients -Patient 6 ( Fig. 4, Supplementary Fig. 10), Patient 8 ( Supplementary Fig. 12), and Patient 12 seizure 1 (Fig. 5,   Supplementary Fig. 16) -out of the total ve patients who have early-ESL as the earliest solution. This is also demonstrated in Fig. 6A as higher ORs are seen for MI-VIZ hotspot and boundary prediction of the earliest solution against the early-MSL alone (also see Supplementary Table 1 and Supplementary Table  2).

MI-VIZ predicts the EZ and clinical localisation better than AEC-VIZ
AIC and BIC were calculated from mixed-effects logistic regression models evaluating a statistical association between AEC-VIZ and MI-VIZ and the resection margin as well as the clinical localisation (Supplementary Table 1, Supplementary Table 2). Lower AIC and BIC values suggest higher predictive power for the model. As shown in Supplementary Table 2, the MI-VIZ boundary consistently has lower AIC and BIC values than the AEC-VIZ boundary in predicting the resection margin and clinical localisation. Further, the MI-VIZ hotspot has lower AIC and BIC values than corresponding AEC-VIZ hotspot values in predicting the resection, the earliest solution, early-MSL and late-MSL solutions, while AEC-VIZ hotspots better predict the iEEG SOZ and mid-MSL solution than MI-VIZ hotspots (Supplementary Table 1). Examples can be seen in Patient 6 ( Fig. 4, Supplementary Fig. 10) and Patient 12 seizure 1 (Fig. 5, Supplementary Fig. 16), where MI-VIZ hotspots predict the resection margin and the earliest solution, while AEC-VIZ hotspots do not.

Discussion
In this study we used a multi-disciplinary approach to objectively characterise the ictal brain networks from non-invasive MEG data without the risks and constraints of iEEG. We have demonstrated that non-invasive ictal ViEEG signals preserve the most important characteristics for spatial distribution and morphology. Dynamical network models and a virtual resection technique were applied to ictal ViEEG signals to identify a sub-network VIZ that helps elucidate the EZ. Alternative surgical strategies can potentially be devised from VIZ results for non-seizure-free patients. More crucially, the VIZ from MEG data alone can predict the earliest solution out of MSL and ESL, the earliest solution best informing the likely EZ in our recent study using simultaneous HDEEG and MEG data 31 .
To our knowledge, this is the rst study that reconstructs ictal source signals using a high number of spontaneous seizures captured by MEG 31 . Ictal ViEEG signals from at least one seizure per patient present distinct characteristics of ictal events, such as hyper-synchronised rhythms, clear transitions from background activity to a seizure state, and spatial patterns of seizure propagation. Such characteristics of ictal ViEEG are also con rmed by ictal iEEG data from the same patient (Fig. 2). These ndings also support previous studies that show epileptic activity from deep structures can be detected and reconstructed using MEG 45,46 . From the 36 seizures recorded by MEG, 11 seizures do not present identi able morphological features of ictal activity and hence were not included in the analysis. We suspect that compared to source localisation, source reconstruction may require higher SNRs to resolve identi able ictal features in source space. As well, certain geometries of anatomical structures, such as gyral areas, may impair MEG source reconstruction accuracy. These 11 seizures might be amenable to source reconstruction with corresponding ictal HDEEG signals (the subject of our future work in a larger cohort). Ictal source signals have been reconstructed using ictal scalp EEG in prior studies 47,48,49 .
However, as opposed to MEG, scalp EEG signals are more distorted when the electrical eld propagates through inhomogeneous head tissue. More sophisticated techniques are needed to process and analyse the EEG signals in source space 49 .
This study demonstrates proof-of-concept that dynamical network models using ViEEG signals identify a sub-network VIZ that provide a valid characterisation of the EZ and prediction of the clinical localisation. This nding is signi cant for the following reasons. First, it demonstrates the feasibility of translating dynamical network models developed from iEEG to non-invasive ViEEG. Second, our proposed approach also identi es non-ictogenic brain areas that are less likely to overlap with the EZ, which may help clinicians ne-tune clinical hypotheses to be tested using invasive approaches. Third, our approach is data-driven and requires less human input compared to routine clinical investigations, making it a more objective assessment. As opposed to the original work of Goodfellow et al 17 that only analysed the rst seizure from each patient, we analysed all seizures that were successfully reconstructed from ictal MEG data. This lends con dence to our approach, as consistency of VIZ hotspots was found between seizures for a given patient -refer to Patient 2 ( Supplementary Fig. 6), Patient 8 ( Supplementary Fig. 12), and Patient 11 (Supplementary Fig. 15).
Ding et al 47 is the rst study to reconstruct ictal EEG source signals to localise the EZ in source space and investigated the causal interaction patterns to identify the primary epileptic sources. Recent work from Lopes et al 41 and Sohrabpour et al 49 applied network models and connectivity analysis to EEG source-space networks and demonstrated the feasibility of non-invasive lateralisation and characterisation of the EZ. Motivated by recent studies using invasive iEEG data 17,18,50,51 , our work extends the dynamical network models and virtual resection from Goodfellow et al 17 and Lopes et al 41 to ictal MEG source signals, which has achieved similar performance in characterising the EZ as Sohrabpour et al 49 but with a different imaging modality. It is also notable that we analysed the MEG data recorded from complex cases only (MRI-normal or complex lesions) using a ViEEG approach that is intuitive to clinicians given its resemblance to iEEG arrays. Future work is needed to compare different techniques using EEG and MEG source signals.
The iEEG SOZ is often regarded as a subset of the EZ 52 . This is in part because resection is often performed beyond the extent of the iEEG SOZ and includes non-SOZ electrodes to ensure the removal of the entire putative EZ. However, the resection margin between SOZ and non-SOZ electrodes is often determined by the experience of the treating team which is less objective and less amenable to hypothesis-testing. Recent network studies 17,50 indicate there may exist a regulatory mechanism surrounding the SOZ in the form of pathological dynamics that synchronise and de-synchronise the network and hence regulate seizure generation and propagation. Such regulatory mechanisms merit further consideration in the surgical work-up 50 . Our VIZ, particularly the hotspots, can non-invasively offer such an objective boundary for surgical planning. Further, ViEEG combined with dynamical network models enables hypothesis-testing to assess surgical strategies prior to resection by virtually resecting one or more nodes from the network 17,42,51,53 . For example, all non-seizure-free post-operative patients revealed pre-operative VIZ hotspots that sat outside the resection margins -Patient 1 ( Supplementary   Fig. 5), Patient 3 ( Supplementary Fig. 7), Patient 4 ( Supplementary Fig. 8), Patient 9 ( Supplementary Fig.  13), Patient 10 ( Supplementary Fig. 14), and Patient 11 (Fig. 3, Supplementary Fig. 15).
There has been a long-standing discussion on network models versus source localisation for epilepsy and epilepsy surgery 54,55 . An important question that has been raised is whether network models using EEG and MEG reconstructed source data better characterise the EZ than the solutions offered by source localisation. As demonstrated by Sohrabpour et al 49 , connectivity imaging provides similar accuracy to source localisation in determining the extent of the EZ using sophisticated source imaging algorithms on ictal HDEEG data. Our simultaneously acquired HDEEG-MEG dataset and prospective study validating the clinical utility of electromagnetic source localisation offers the unique opportunity to address such a question 31 . To the best of our knowledge, this is the rst study that comprehensively compares ndings from dynamical network modelling of ictal MEG data with source localisation solutions using simultaneous HDEEG and MEG. In our previous work, the earliest sLORETA solution of early-ESL and early-MSL best characterises the EZ than either ESL, MSL, or combined electromagnetic source localisation (EMSL) alone 31 . On combining ictal ViEEG signals from MEG alone with dynamical network models, MI-VIZ predicts the earliest solution that can be only offered by source localisation with two modalities (HDEEG and MEG data). Speci cally, MI-VIZ can predict the earliest solution better than predicting the early-MSL solution (Fig. 6A). This nding suggests dynamical network models can provide valuable information beyond source localisation using a single modality.
We also observe that our proposed approach identi es the wider extent of the VIZ to the EZ as well as inter-seizure variability. The extent of the VIZ is likely to re ect propagation of seizure activity 56 . Our previous work argues that source localisation of ictal discharges at the mid to late phase of the averaged discharge complex usually re ects areas involved in seizure propagation. Statistical analysis suggests AEC-VIZ and MI-VIZ hotspot and boundary are less likely to predict mid-MSL and late-MSL (Fig. 6A, Supplementary Table 1 and Supplementary Table 2). Hence, the VIZ is perhaps not a simple representation of seizure propagation networks but its extent could still be affected by seizure propagation. More detailed analysis of seizure propagation networks using iEEG seizures is needed to test this hypothesis.
Two connectivity methods -linear and nonlinear coupling between signals -were employed to better understand the underlying network structures responsible for seizure generation. AEC is believed to solely characterise linear correlations between amplitude envelopes 57,58 , while MI measures both linear and nonlinear relationships by quantifying shared and unique information between two time-series 59 . Our results demonstrate that MI-VIZ outperforms AEC-VIZ in characterising the EZ and predicting the clinical localisation, which suggests a connectivity approach that captures both linear and non-linear interactions might offer more information about ictal network structures than an approach that only captures linear interactions. This nding also lends support to a previous theoretical model using nonlinear dynamics from the seizure onset zone to identify the EZ from seizure propagation and predict seizure propagation and termination 16,60 . More broadly, our evidence supports the view that ictogenesis involves complex network neural systems that are highly nonlinear across multiple temporo-spatial scales 60 .
We nd six non-seizure-free patients have at least one VIZ hotspot node outside the resection margin -Patient 1 ( Supplementary Fig. 5), Patient 3 ( Supplementary Fig. 7), Patient 4 ( Supplementary Fig. 8), Patient 9 ( Supplementary Fig. 13), Patient 10 ( Supplementary Fig. 14), and Patient 11 (Fig. 3,   Supplementary Fig. 15) -which has been previously reported using ictal iEEG data 17 . An example is given in Patient 11 (Fig. 3, Supplementary Fig. 15), where both VIZ hotspot and iEEG SOZ are superior to the resection margin and this patient is non-seizure-free with a 60% seizure reduction rate (Engel III). Our results suggest alternative surgical strategies can be devised for non-seizure-free patients with, perhaps, reduced need for invasive monitoring for those patients who are being considered for a second resection. Some VIZs also overlap eloquent cortex as occurs in Patient 10 ( Supplementary Fig. 14) and Patient 11 ( Supplementary Fig. 15), which is not accounted for in our proposed approach. The balance between seizure outcome and compromise of eloquent cortical function may be integrated into future models to better facilitate decision-making for patients and clinicians.
There are some limitations in this study. Only ictal data were analysed. This is because our dynamical network models investigate the change of cortical excitability that are more likely to be revealed during a seizure state. Our model is phenomenological and does not include details of physiology that underlies the functioning of individual epilepsy patients. Findings from our proposed approach can only serve as a statistical biomarker that offers complementary clinical information to the pre-surgical evaluation. We did not employ connectivity methods that reduce spurious connections (often introduced by volume conduction) in source space to construct functional networks because in our study we looked at dynamical network models to characterise the EZ for epilepsy surgery, instead of investigating neural mechanisms. More details on volume conduction in source-space networks are discussed in the Supplementary material (Volume Conduction and functional networks). In addition, the computational workload does not allow us to model all the sources (5000-25000 sources) at once from the whole brain at a spatial resolution (10mm) comparable to iEEG electrodes. At present, the feasible scale of networks is between 100 and 300 nodes for dynamical modelling and results to be interpreted. In a prospective fashion, ViEEG with on feasible network scale can be moved around freely and modelled iteratively across the whole-brain, although admittedly the ideal scenario is to model a ViEEG covering the wholebrain at once (refer to Considerations for ViEEG locations in Supplementary material). Our study is retrospective with a modest number of patients and seizures analysed compared to studies using iEEG seizures, although it contains one of the highest seizure counts obtained across ictal MEG studies. Our ndings motivate further investigation in methodology and clinical utility using multi-centre datasets or prospective studies to devise and optimise surgical strategies objectively and safely.

Conclusions
We have used non-invasively acquired ictal MEG data to reconstruct ViEEG signals with distinctive morphological and spatial characteristics that are comparable to patient-speci c invasively acquired ictal iEEG data. VIZ identi ed by dynamical network models using two connectivity methods (AEC and MI) can predict the resection margin and iEEG SOZ; they also devise an alternative surgical strategy for patients with suboptimal post-operative seizure control. Importantly, VIZ using ictal MEG data alone can predict optimal source localisation solutions that were previously derived from simultaneous HDEEG and MEG data. Our ndings suggest ViEEG combined with dynamical network models can provide valuable information beyond source localisation using single modality ictal MEG, thus offering unique clinical utility in the pre-surgical evaluation of complex drug refractory epilepsy cases.