*3.2. Electrode-Region Mapping*

The regions that displayed the most variance in electrode mapping across all nine patients are listed in Table 2 according to the Freesurfer region names. The majority of the variance appeared to be in the temporal regions. Manual inspection of the warped electrodes on each patient's scalp, which were overlaid on the cortex regions, indicated that individual scalp and cortex morphology contributed to the model's determination of the nearest electrode for a given region.


**Table 2.** Between patient region variance in the region to electrode mapping.

Key: L: left, R: right, bankssts: banks of the superior temporal sulcus.

#### *3.3. Structure-Function Coupling*

The structure-function coupling observed in the nine patients revealed three distinct groups with the following features. The first group (Patients 1–3, Figure 2a) had the highest laterality scores (L = 3), with coupled electrode pairs that consistently overlapped with the seizure onset zone. The second group (Patients 4–6, Figure 2b) had less well-lateralised seizures (L = 2–3), and the coupled electrode pairs overlapped with the onset side but not the exact zone. In Patient 4, only two out of three seizures were highly lateralised (L = 3) while the third was not (L = 2), and the electrode pair (PZ-O2) that did not overlap with the exact seizure onset zone was observed on the poorly lateralised seizure. Patient 4 also had three single electrodes from highly connected MRI and EEG pairs that overlapped inside the seizure onset zone (shown in heatmaps in Figure A1). Patients 5 and 6 were less well lateralised, and highly coupled electrode pairs were present both within and outside the seizure onset zone. In Patient 6, the electrode pair T3-C3 overlapped with the expected onset zone of the one poorly lateralised seizure. The third group (Patients 7–9, Figure 2c) were considered non-lateralised for most of their seizures. These patients generally displayed highly coupled electrode pairs that were inconsistent with the expected onset zone or had only a single overlapping MRI and EEG electrode rather than a pair (Patient 7). Figure 2 contains a condensed interpretation of the detailed results for each patient, shown in Appendix A. The overlapping electrode pairs with MRI z-scores (>2) and EEG z-scores (>1.8) are displayed. The most common seizure onset zone for each patient is also displayed.

**Figure 2.** Highly connected electrode pairs in structural and functional connectome. Each "head" shows a schematic of the electrode pairs for each of the nine patients (numbered 1–9 above each head). The "L" value represents each patient's overall seizure lateralisation score based on their available recorded seizures. A score of zero represented poorly lateralised seizures, whilst highly lateralised seizures received a score of three. The patients' seizures stratified them into three categories: patients 1–3 had high laterality, patients 4–6 had some seizures that were well lateralised, while others were not, and patients 7–9 had poor laterality in all seizures. The purple lines (and circled electrodes) represent the electrode pairs that displayed strong connectivity (z-scores > 2) in the structural (MRI) connectome. The orange lines (and circled electrodes) represent the electrode pairs that displayed strong connectivity (z-scores > 2) in the functional (EEG) connectome. Dotted lines in either colour represent a z-score of 1.8–2. The blue shading represents the most frequently observed seizure onset zone for a given patient, as observed from their ward EEG recordings. If a seizure did not have a specific onset region within the first 5 s, it was considered non-lateralised, even if it displayed late-lateralisation. Purple and orange circled electrodes in the blue shaded areas represent high structure-function coupling in the seizure onset zone.

#### **4. Discussion**

In this study, we obtained structural and functional connectomes from nine patients to investigate whether our model could uncover the structure-function coupling during seizure onset. We also examined the pattern and congruence of the structure-function coupling with the expected seizure onset zone. The first key finding was that patients with well-lateralised seizures displayed high structural-functional congruence consistent with the expected seizure onset zone. The second key finding was that patients who were not well-lateralised had varying coupled electrodes that were not consistently in the onset zone. The results indicate that for well-lateralised patients, connectivity data derived from dMRI can be a valuable tool to augment routine EEG observations. However, the dMRI should be interpreted in the context of other routinely collected data from the patient.

Our findings offer some compelling evidence for the use of dMRI in clinical practice. Firstly, in patients with high structure-function coupling in the expected onset zone, dMRI may provide additional support to the EEG observations. A recent work used intracranial EEG (iEEG) and dMRI to explore the relation between structure-function coupling and postsurgery seizure freedom [9]. The Authors showed that patients who achieved post-surgery seizure freedom had higher structure-function coupling pre-surgery. However, access to iEEG may not be feasible in the initial diagnosis stage. Additionally, the diagnostic yield of low-density scalp EEG (25 electrodes) has been suggested to be comparable to high-density EEG (256 electrodes) [44]. Taken together, our findings suggest that our model may be used

during the diagnosis stage to determine the suitability of surgery for newly-diagnosed patients. Notably, we provide evidence that high structure-function coupling was present for patients regardless of whether they had previously experienced an FBTC seizure. Our finding suggests that a history of infrequent FBTC seizures (present in Patients 1 and 3) does not preclude the patient from having well-lateralised structure-function coupling.

Secondly, in the patients with poorly lateralised seizures, the structure-function coupling was more predominant in the ipsilateral hemisphere. However, the presence of structure-function coupling in the contralateral hemisphere was unsurprising, given their laterality score. In these patients, dMRI may provide additional information that can guide the placement of additional electrodes in longer ward recordings. However, a more extensive structure-function coupling model may be needed to understand whether the poor laterality can be attributed to the equally high structural connectivity in both hemispheres or some other biophysical phenomenon. Further, our model demonstrated a specific region with high structure-function coupling for Patient 8, who was initially considered poorly lateralised on EEG. Such cases highlight that dMRI may offer endorsement of a specific onset zone to support an otherwise inconclusive EEG recording.

Interestingly, the presence of high structure-function coupling in an electrode pair containing a middle electrode (FZ, CZ, PZ) was observed in several patients with a seizure laterality score of 2 or lower. For example, patients 5, 7, 8 and 9 had at least one middle electrode in the electrode pairs that showed high structure-function coupling. Their poor seizure lateralisation could be due to the electrophysiological activity beneath the middle electrode, which may drive the contralateral seizure propagation.

Given the scope of the current work, some methodological considerations may aid the interpretation of the results. Firstly, the mapping method did not appear to impact the results as well-lateralised patients had a similar number of variances in the electrodeto-region mapping as the less well-lateralised patients, for whom the structural data provided little additional information. However, laterality alone may not account for the results from patients who displayed high structure-function coupling congruent with the expected onset zone. Our selection of time window and bandwidth may have impacted the coherence score. The one-second window was perhaps not brief enough to capture the highly coherent initial EEG activity. We observed high coherence in the ipsilateral hemisphere at the 0–100 millisecond (ms) scale for some patients. The lengthy time window may have confounded this high coherence.

Further, the proposition that microscopic signal aberrations in EEG may not be observed from a macroscopically normal EEG signal is worth considering [2]. The uncertainty of empirical, visual evaluation of EEG to localise the seizure onset zone has been shown [45]. Thus, in the current work, the true onset zone for some individuals may not be observable on the raw EEG, yet may have been captured in the processed EEG coherence data. However, such postulations must be verified using high-definition EEG or intracranial/stereo EEG. Alternatively, since we combined microscopic MRI and EEG data, it is also possible that our model captured the genuine seizure onset zone. Supposing the seizure began in a different region, it could have fused in millisecond time with other active regions and thus was visually revealed in a different region on the raw EEG. Such an explanation is conceivable for individuals with FBTC or multi-onset seizures and is a topic for future investigation.

Lastly, it is feasible that the structural topology has a diminished relationship with the functional activity in some individuals. Numerous mechanisms mould the seizure propagation pathways, and within-patient variance has been shown [46]. Lateralisation may be inextricably linked to the seizure duration. However, based on our experimental design (i.e., time window selection) and modest sample size, it was not plausible to extrapolate any biophysical mechanisms that may be in force. The individuals in the third group may have less well-defined circuits, or a different epileptic pattern, i.e., multi-onset or deep structural connections or functional activity, that was not captured in the connectome reconstruction or on the scalp EEG. These concepts are the subject of ongoing work to further elaborate on this feasibility study and better explain the individual differences in the outcomes.

Although our methodology may explain some of the findings, potential limitations were inevitable. The generalisation of the results is limited by the small sample size, endorsing the need to extend this work to a larger cohort. The placement of the electrodes in the electrode warp and automated mapping cannot be deemed identical to the original, physical placement of the electrodes during the EEG recording. The electrode warp placements represented the expected actual electrode placement during the recording. This work highlights the possible variation inherent in demystifying the electrical signals captured on scalp EEG. There is an intrinsic between-patient variance in cortex and scalp morphology and thickness. The nature of the clinical procedure introduces further variance through the measurement estimation of different technicians during the application and re-application of electrodes.

The Curry sensor coherence algorithm is confined to broadband frequencies and does not compute coherence from narrow-band frequencies. Further, the Curry algorithm does not consider the spatial, topographical, morphological or biophysical implications of the scalp signal; it is calculated purely on the raw EEG wave. Therefore, our inverse square mapping method was constrained in accounting for the spatial and biophysical properties of the scalp signal measurements. It is possible that the single neurologist's assessment of the congruency results may introduce bias. Future work will include evaluation of the EEG data by several neurologists blinded to the methodology, and an inter-rater reliability assessment (such as the Kappa statistic). Lastly, lack of control data restricts the distinction between the structure-function coupling in seizures and normal coupling in resting state or non-ictal periods.

Indeed, linking brain structure and function remains an imperfect science, confounded by individual differences in structure-function coupling [47]. Therefore extending this study to a larger cohort, with the addition of control data, is the subject of ongoing work in our lab. The inclusion of pre-ictal and cross-hemisphere connectivity data will enable further comparison and quantification of the active electrodes across varying brain states. Additionally, using coherence matrices derived from open source software could provide a point of comparison to Curry's sensor coherence maps. Despite these restrictions, our work provides evidence that dMRI is a promising additional tool to classify patients for further investigation or surgical candidature. Our model may be practical in identifying the most active locations for sub-scalp electrodes and the patients who could benefit from ultra long-term monitoring. We show that all regions of high connectivity are not necessarily the best place for sub-scalp electrodes. We present a feasible method to distinguish patients, and patient-specific brain regions, that may be candidates for sub-scalp electrodes. With further refinement, our method could be utilised in identifying the optimal position for sub-scalp electrode placement, removing the need for more invasive EEG methods.
