Cortical Seizure Propagation Respects Functional Connectivity Underlying Sensory Processing

Focal epilepsy involves excessive and synchronous cortical activity that propagates both locally and distally. Does this propagation follow the same routes as normal cortical activity? We induced focal seizures in primary visual cortex (V1) of awake mice, and compared their propagation to the retinotopic organization of V1 and higher visual areas. We measured activity through simultaneous local field potential recordings and widefield imaging of a genetically encoded calcium indicator, and observed both prolonged seizures (ictal events) and brief interictal events. Both types of event were orders of magnitude larger than normal visual responses, and both started as standing waves: synchronous elevated activity in the focal V1 region and in corresponding retinotopic locations in higher areas. Following this common beginning, however, seizures, persisted and propagated both locally and into distal regions. These regions matched each other in retinot-opy. We conclude that seizure propagation respects the functional connectivity underlying normal visual processing. Focal epilepsy, also known as partial-onset epilepsy, can result from a range of congenital or acquired corti-cal lesions and frequently resists pharmacological treatment 1. Much of its morbidity results from the spread of seizure activity from a cortical focus to further cortical regions. These regions can be local and contiguous to the focus, as in the " Jacksonian march " seen in motor cortex. However, they can also be distal and ultimately involve both hemispheres and subcorti-cal centers (" secondary generalization "), causing loss of consciousness 2. It is not known whether seizures spread along the same functional circuits that support information processing during normal cortical activity 3. These circuits may not act as effective constraints during seizures. First, functional circuits rely on synaptic transmission, whereas seizures may involve non-synaptic mechanisms 4–11. Second, the flow of activity along functional circuits depends on the balance of synaptic excitation and inhibition , and seizures disrupt this balance 12–16. A related question concerns the difference between seizures (ictal events), and the numerous, brief inter-ictal discharges that characteristically occur between seizures. Seizures represent excessive neuronal firing lasting seconds or minutes and spreading locally and distally 12,17. Interictal discharges, instead, are brief and localized 18. A longstanding theory is that their duration and spread are limited by a powerful inhibitory surround 19. It is not known, however, if seizures and inter-ictal events originate in similar neuronal populations, and if their initiation differs in terms of spatial profile and temporal evolution 20. More generally, it is …

It is not known whether seizures spread along the same functional circuits that support information processing during normal cortical activity 3 . These circuits may not act as effective constraints during seizures. First, functional circuits rely on synaptic transmission, whereas seizures may involve non-synaptic mechanisms [4][5][6][7][8][9][10][11] . Second, the flow of activity along functional circuits depends on the balance of synaptic excitation and inhibition, and seizures disrupt this balance [12][13][14][15][16] .
A related question concerns the difference between seizures (ictal events), and the numerous, brief interictal discharges that characteristically occur between seizures. Seizures represent excessive neuronal firing lasting seconds or minutes and spreading locally and distally 12,17 . Interictal discharges, instead, are brief and localized 18 . A longstanding theory is that their duration and spread are limited by a powerful inhibitory surround 19 . It is not known, however, if seizures and interictal events originate in similar neuronal populations, and if their initiation differs in terms of spatial profile and temporal evolution 20 . More generally, it is not clear why seizures persist and propagate, while interictal discharges subside and stay local.
We addressed these questions in the visual cortex of the mouse, where we could readily distinguish between two scenarios of seizure propagation (Figure 1ad). Mouse visual cortex includes multiple retinotopic areas [21][22][23] , the largest of which are the primary and latero-medial areas (V1 and LM, Figure 1a). Epileptiform activity in a focal region of V1 (Figure 1b) could then spread in at least two ways: laterally or homotopically. In the first scenario, epileptiform activity propagates through local mechanisms to V1 regions that are contiguous to the focus (Figure 1c). In the second scenario, epileptiform activity propagates along longrange projections from V1 to homotopic regions of higher visual areas, i.e. regions that have the same retinotopic preference 23,24 producing one or more distinct, secondary foci ( Figure 1d). To evaluate these models of seizure propagation, we induced epileptiform activity in a focal region of V1 and used widefield imaging of genetically-encoded calcium indicators 25,26 to characterize the propagation of activity in space and time. These methods allowed us to observe both prolonged seizures (ictal events) and brief interictal events, and to relate their spatiotemporal evolution to the functional connectivity underlying normal visual processing.

Results
We generated transgenic mice expressing a genetically-encoded calcium indicator (GCaMP3 or GCaMP6) in excitatory neurons of the cortex [27][28][29] , and implanted a head-post and a cranial window spanning the left parietal bone, which we thinned to facilitate optical access 26 . After recovery and a period of habituation, we head-fixed the mice over a treadmill where they were free to run while we performed visual stimulation, widefield imaging, and electrophysiological recordings ( Figure 1e).
We first used widefield imaging of GCaMP fluorescence to measure activity evoked by visual stimulation, and mapped the retinotopic organization of V1 and higher visual areas (Figure 1f). For each mouse we aligned the salient features of the retinotopic map 26 on a reference map of the areal organization of the mouse visual cortex 30 . This procedure identified multiple visual areas (Figure 1f) including V1 and adjacent area LM, which is thought 31 to be homologous to primate area V2.
We then elicited focal epileptiform discharges by blocking GABAA receptors in a small region of V1 (Figure 1g). GABAA receptors were blocked by including picrotoxin (10 mM) in a pipette inserted into medial V1 via a small craniotomy. We applied no pressure, so that the picrotoxin solution would diffuse minimally beyond the tip of the pipette (resistance 0.5-3 MΩ). We targeted layer 5 because its extensive recurrent, horizontal and columnar connectivity enable it to evoke prolonged depolarization across layers 32 , making it a promising location for triggering translaminar epileptiform events.
Within minutes of pipette insertion, recordings of local field potential (LFP) made from the same pipette revealed robust epileptiform events (Figure 1i-n). These events consisted of intermittent seizures (Figure 1i, red triangles) separated by sequences of brief discharges (Figure 1i, blue triangles). These epileptiform events were mirrored by large amplitude GCaMP optical signals ( Figure 1l). They were also typically accompanied by pronounced increases in pupil dilation (Figure 1h,m) and by bouts of running (Figure 1n).
Based on their duration, these epileptiform discharges could be readily categorized into distinct classes (Figure 2). The distribution of epileptiform discharge duration was bimodal (Figure 2a, p <0.001, Wilcoxon rank sum test, n=5 mice), with a median duration of 8.6 s for seizures, and 0.5 s for interictal events. Interictal events occurred on average 13.4 ± 3.7 times per minute (n = 5 recordings in 5 animals), much more frequently than seizures, which occurred about once per minute (1.0 ± 0.2 events/min). Interictal events were slightly larger on average (Figure 2b, p <0.001, Wilcoxon rank sum test, n = 5 mice) and were followed by briefer periods of relative LFP quiescence than seizures  Figure 2b) , but this onset was followed by a rapid escalation of high-frequency activity, with a large increase in power between 8 and 30 Hz (Suppl. Figure  2b,e). The increase in power near 10 Hz was consistent across events and animals (Suppl. Figure 2i).
These epileptiform events were faithfully tracked by large fluorescence signals, which dwarfed those seen during normal visual processing (Figure 2g). The peak fluorescence changes (ΔF/F) seen during epileptiform events were 125±22% for interictal events and 175±50% for seizures. These signals were much larger than those evoked by visual stimuli 26,33 (Figure 2g), which peaked at 4±1%. Yet, they bore close relation-ship to the LFP (Suppl.  The fluorescence signals allowed us to study the spatial spread of epileptiform events, and revealed profound differences between ictal and interictal events ( Figure  3a-c). The transient fluorescent signals seen during interictal events were localized in V1 with a smaller peak in LM (Figure 3a). They involved a region that was markedly smaller than the region that could be activated by visual stimuli (Figure 3b, Suppl. Movie 1). Seizures, instead, progressively invaded the entire visual cortex and beyond (Figure 3c, Suppl. Movie 2). Interictal and ictal events had similar origins: 94±4% of events started in V1, close to the pipette used to apply picrotoxin and record LFP (starting positions were within a radius of 0.32±0.12 mm).  Seizures, instead, behaved as standing waves only at first, when they closely resembled interictal events, and then propagated extensively (Figure 3h-i). A standing wave model with the spatial profile of interictal events was appropriate to describe the beginning of the ictal events, but it became patently inadequate af-ter a few hundred milliseconds (Figure 3i-j): it progressively overestimated the activity at the focus (negative residual, Figure 3j), while underestimating the activity in the surrounding region (positive residual, Figure 3j). Consequently, the quality of this model's predictions deteriorated sharply with time ( Figure 3g,h). Seizures, thus, start as standing waves just as interictal events, but then they progressively propagate beyond the common initial spatial profile to engage wider regions of cortex.
The common spatial profile of interictal and early ictal events typically encompassed not only the focus, but also one or more distinct regions that were homotopic, i.e. that shared the same retinotopic preferences (Figure 4a-d). For instance, two distinct lobes are clearly visible 60-100 ms into the example epileptiform events (Figure 3a, c). The first lobe lies in area V1 and the second in area LM (Figure 4a). To characterize these two lobes, we drew a line connecting V1 to LM along the direction of maximal change in preferred horizontal position obtained when retinotopy was mapped ( Figure  4b). The profile of activation along this line was bimodal (Figure 4c), with the activation in V1 being 8±2 times higher and ~2 times wider than in LM (n = 4 mice, Suppl. Figure 4a-d). Crucially, the two activations involved regions with matching retinotopic preference (Figure 4d). The retinotopic preferences of the two peaks, indeed, were not significantly different (p= 0.4, Wilcoxon signed rank test), and the retinotopic preferences of the two peaks were significantly correlated (r = 0.48, p<0.001, Suppl. Figure 4e, f).
These observations indicate that two factors determine the spatial profile of interictal events and early seizures: one local, causing lateral spread and one distal, causing homotopic spread (Figure 4e-i). The local factor could, in principle, arise from disinhibition (spread of picrotoxin, loss of GABAA receptor electrochemical driving force, or depolarization block of interneurons), from local excitatory circuits, or from nonsynaptic mechanisms; its impact falls off with cortical distance (Figure 4e). The distal factor, by contrast, arises from the same axonal and synaptic organization that supports functional connectivity, whose impact decreases with retinotopic distance (Figure 4h). We combined these two effects into a simple multiplicative model (Figure 4e,g,h), and found that with only 6 parameters the model provided good fits to the data (Figure 4f). The function of retinotopy, in particular, was described by one key parameter, the angular standard deviation σ. As this parameter grows, the function becomes closer to a constant, and retinotopy plays a lesser role in the profile of the epileptiform events. When fitting the data, σ consistently took values <40 deg (Figure 4i) implying an important contribution of retinotopy (Figure 4h), which in turn produced a clear secondary peak in activity (Figure 4f). Homotopic connectivity thus plays a key role in determining the spatial profile of interictal events and early seizures. Retinotopic modulation was present in all mice, but the strength of its contribution varied across animals (Figure 4d), possibly reflecting experimental variability in the induction of the focus and levels of expression or sensitivity of the calcium indicator.
These same two factors -lateral and homotopic -also determined the subsequent evolution of seizures, when the standing wave gave way to escalating propagation of activity (Figure 5a-d). As we have seen, seizures propagated to engage most of the visual cortex, and often beyond, producing activity levels comparable to those observed at the focus (Figure 5a). The pattern of propagation can be seen by following the activity of individual loci between the focus in area V1 and the homotopic location in area LM (Figure 5b, c). In the example shown, the focus in V1 had a retinotopic preference ~100 degrees away from the middle of the visual field, which is indicated in orange in the map of retinotopy ( Figure 5b). Accordingly, at that location the calcium traces show ictal activity with the earliest onset ( Figure 5c, top arrow). This activity progressively invades further V1 locations, eventually reaching the border with area LM, where receptive fields are in the middle of the visual field (0 degrees, Figure 5c, blue traces). Well before having reached those areas, however, the seizure has already reached a distal region: the portion of LM with the same retinotopic preference as the focus (Figure 5c, bottom arrow). For instance, 6 to 8 s into the event, the ictal activity shows a bimodal profile, being stronger in the homotopic regions in LM than in regions of V1 that are closer to the focus ( Figure  5d). The two factors, lateral and homotopic, both contributed approximately linearly to the time course of seizure propagation (Figure 5e-j). To measure the time it took for a seizure to invade each pixel, we defined a 'delay to seizure invasion' as the time taken for the pixel to reach 60% of its maximum activity. Consistent with the observations made above, a map of this quantity shows activations occurring earlier in the V1 focus and in the homotopic region in LM than in other locations ( Figure 5h) and a plot of delay along a line from V1 to LM shows delay growing with distance while displaying two distinct troughs (Figure 5e). When averaging these measures across mice, we found that delay strongly correlated with distance (r = 0.81, p < 10 -7 , n = 64 seizures in 4 mice), with an average propagation speed of 0.48 ± 0.03 mm/s (Figure 5f). However, closer inspection of this linear prediction based on distance shows that it underestimates the delays of proximal territories and overestimates those of distal territories (Figure 5f). The corresponding residuals were highly correlated with retinotopic distance from the focus (r = 0.82, p < 10 -24 , Figure 5g). Indeed, if delay to cortical invasion were solely due to cortical distance, it would grow radially from the focus and display concentric rings (Figure 5i). The map of residuals instead reveals that it underestimates delays in territories retinotopically close to the focus, especially in higher visual areas (Figure 5j, blue negative residual), and overestimates delays in distal territories in V1 and in regions outside the visual areas (Figure 5j, red positive residual). These results indicate that delay to ictal invasion depends approximately linearly on two factors: one lateral, which grows with distance in cortex, and one homotopic, which grows with distance in visual preference.
Homotopic factors also played a key role in the timing of the prominent individual oscillatory waves of activity seen during seizures (Figure 6). Once a territory was invaded by seizure activity, it displayed striking fast oscillations in the range of 6-11 Hz, evident both in the LFP and in the GCaMP fluorescence (Figure 6a, c , Figure 5a , Suppl. Figure 3a). These oscillations continued until the seizure spread to the entire visual cortex and be-yond, after which we occasionally observed more diverse patterns (such as spiral waves 34,35 ). To isolate the fast oscillations from the slow spreading activity, we filtered the traces in that frequency range, and used the Hilbert Transform to compute the amplitude and phase of the oscillation for the LFP and for each pixel at each time point (Figure 6a, c) . During an epoch starting 3.4±0.1 s after seizure initiation and lasting 3.7±0.8 s (Figure 6a, c), the seizure focus acted as a pacemaker for the oscillations: each oscillatory wave started at the focus and propagated on the surface of the cortex. The spatiotemporal pattern of these oscillations was highly stereotypic (Figure 6b, d): the map of their delay was consistent across oscillations ( Figure 6c) and closely related to the map of retinotopy (Figure 6b). Accordingly, the average oscillation shows activity progressively entraining a larger region of cortex, propagating homotopically like the slow wave of seizure recruitment (Suppl. Movie 3). Similar results were seen in other mice: in all cycles the LFP and GCaMP signatures of the oscillations were consistent (Figure 6g, h, m) and maps of delay were strikingly similar to the retinotopic maps (Figure 6d-g). Just like the slow spread of seizure activity, therefore, the fast oscillations that characterize this activity propagate along the same functional circuits that support neural signals during normal cortical activity.

Discussion
By exploiting the potential of widefield imaging and of genetically encoded calcium indicators, we were able to study the spatiotemporal evolution of epileptiform activity in the awake cortex and relate this evolution to the underlying functional architecture. Focal picrotoxin injections induced prolonged seizures with clear behavioral correlates, separated by numerous brief interictal events. In the first few hundred milliseconds from their onset, the two types of discharge were extremely similar: they were standing waves of activity with a fixed spatial profile. Afterwards, however, interictal events subsided while seizures went on to invade much of visual cortex and beyond. Individual fast waves of activity within seizures also spread in a similar manner. Strikingly, all of these epileptiform phenomena respected the functional connectivity of the visual cortex observed during normal sensory processing. Specifically, the phenomena were shaped by a combination of two factors, one local and dependent on cortical distance from the focus, and one distal and dependent on homotopic relationship with the focus. Both factors determined the shape of the common spatial footprint characteristic of interictal events and of seizure onset (Figure 4). Both factors determined the slow spread of the seizures ( Figure 5). Both factors also determined the fast spread of the prominent oscillations that accompany the seizures ( Figure 6).
These local and distal factors likely reflect different mechanisms. Distal propagation must rely on synaptic barrages transmitted from the seizure focus through long-range, excitatory pathways connecting homotopic regions. Local propagation, in addition, can involve collapse of local inhibition 12,13 , although evidence exists for a host of non-synaptic mechanisms such as gap junctions among neurons 11 or astrocytes 10 , alterations in the electrochemical gradients of chloride 8,9 or potassium 7 , endogenous electric fields 5,6 and defective astrocyte calcium signaling 4 .
The combination of widefield imaging and genetically encoded calcium indicators represents a substantial advance over electrophysiological recordings performed at a few sites 36,3738 , and complements the measures that can be obtained with high-density electrode arrays 12 . Widefield imaging has long been recognized as a promising alternative, and has been applied to measure hemodynamic signals 3,39 ,voltage-sensitive fluorescent dyes 40 , or organic calcium dyes 41 . These techniques, however, provide much weaker signals than genetically encoded calcium indicators. These indicators can be targeted to specific types of neurons, have high signal to noise ratios and provide a faithful representation of the underlying neural activity, with appropriate spatial and temporal resolution 28,26,42 . Indeed, the signal to noise ratio of the calcium indicators used here allowed single trial analysis without the need to average responses. Recording in awake animals, moreover, avoided the confounding effects of anesthesia.
These differences in methods may explain a difference between our results and those of earlier studies. Whereas we found a strong relationship between the propagation of epileptiform activity and the underlying functional architecture, previous widefield imaging studies found only a weak relationship 40 or no relationship 3,39 . In addition to the choice of indicators, these differences could be easily due to differences in the neural systems under study. For instance, it is likely that the functional connectivity between two regions having the same retinotopic preference across visual areas is stronger than the connectivity between two regions having the same orientation preference within area V1.
We did not observe decreases in fluorescence in regions surrounding epileptiform activity, as one might have expected from an "inhibitory surround" 19 . This finding may seem to be in contradiction with an earlier study of hemodynamic signals, which were found to be decreased in the region around the focus 3 . Neither our study nor the previous study, however, employed the ideal methods to probe inhibition. Indeed, decreases in hemodynamic signals cannot be interpreted as increases in inhibition, because: interneuron activation has the opposite effect 43 . Our methods, likewise, are not ideal to study inhibition: we measured calcium signals only in excitatory neurons, and these signals reflect mostly supra-threshold activity and may be insensitive to hyperpolarization below threshold. The question of what interneurons do in the region surrounding the focus thus remains open and can be addressed in future studies by genetically targeting those neurons for widefield imaging.
The striking similarity that we found between interictal events and the onset of seizures suggests that the two are mechanistically related. Interictal events have long been recognized as an electrophysiological marker of epilepsy 16 , but have no or only subtle clinical correlates 44 . They have been proposed either to prevent seizure initiation 18 or to act as a prelude to seizures 45 . It has, furthermore, been proposed that interictal events dominated by GABAergic signaling give way to glutamatergic pre-ictal events 20 . Our results do not reveal any detectable differences between interictal events and seizures during the first few hundred milliseconds: both are well modeled as standing waves involving the same temporal profile over a fixed spatial territory. It remains to be determined whether a qualitative or quantitative difference in the underlying cellular mechanisms lead to these events dying down (and thus become interictal) or turning into propagating seizures. A plausible distinction is that seizures result from escape from an inhibitory restraint 46 . Indeed, the smaller peak of activity in LM during interictal discharges is consistent with a barrage of feed-forward activity that fails to recruit a self-sustaining discharge. To test this hypothesis, once again, it would be useful to express the calcium indicator in inhibitory neurons and compare their activity in interictal events and seizures.
The seizures induced in our preparation bear numerous similarities with seizures observed in patients. Their speed of propagation across the cortex, ~0.5 mm/s, is consistent with measurements obtained with high-density electrode arrays from seizures recorded in humans with cortical epilepsy 12 . However, propagation to LM is consistent with recruitment of more distant areas at short latency. Moreover, our results demonstrate that cortico-cortical connections that support higher visual processing have an important role in determining the propagation of seizures originating in V1. The involvement of higher-order visual cortex is consistent with seizures seen in occipital epilepsy, which commonly includes both elemental symptoms in specific areas of the visual field and more complex visual hallucinations 47 , which might be expected from the engagement of higher visual areas.
Our characterization of the spatiotemporal flow of activity in epileptic discharges provides a platform for further understanding the mechanisms of epilepsy and for testing therapeutic approaches. In particular, the techniques and results introduced here may help shed light on the mechanisms of secondary generalization of partial-onset seizures. Secondary generalization sharply reduces the efficacy of surgical removal of the primary lesion 48 and is thus a hallmark of refractory epilepsy, with substantial impact on quality of life and increased risk of mortality 49,50 . Although secondary generalization ultimately involves subcortical structures 2 it is commonly preceded by invasion of neighboring regions of cortex 51 . The techniques introduced here may make this process amenable to study, and may provide a benchmark to identify and test novel therapeutic targets.

Acknowledgements
We thank Michael Okun and Daisuke Shimaoka for assistance in experimental setup and data analysis, and Charu Reddy for animal husbandry and histology. This work was supported by the Wellcome Trust (095669-Z-11-Z) and Epilepsy Research UK. L.F.R. was funded by the Wellcome Trust PhD programme in Neuroscience at UCL. M.C. holds the GlaxoSmithKline/Fight for Sight Chair in Visual Neuroscience.

Methods
All experimental procedures were conducted according to the UK Animals Scientific Procedures Act (1986). Experiments were performed at University College London, under personal and project licenses released by the Home Office following appropriate ethics review.
All data analysis was performed in MATLAB (The Math-Works Inc.).

Transgenic lines
Emx1::Cre-flex-GCaMP3 mice were generated by crossing the following two transgenic lines: Emx1-IRES-Cre, expressing Cre recombinase under the Emx1 promoter (catalog #005628, The Jackson Laboratory); and a reporter Ai38-GCaMP3 line (catalog #014538, The Jackson Laboratory), carrying a floxed copy of the GCaMP3 gene under the strong CAG promoter in the Rosa26 locus. Offspring expressed GCaMP3 in excitatory neurons of the neocortex and hippocampus 29,25 .
Rasgrf-dCre-CaMKIIa-TTA-TITL-GCaMP6f triple transgenics 28 were generated by breeding Rasgrf-dCre, CamKII-tta and Ai93(TITL-GCaMP6f) mice. Three weeks before imaging, TMP was orally administered for 3 consecutive days to trigger dCre-mediated recombination. With this system, flex-GCaMP6f recombination was induced only in Rasgrf positive neurons, while transcription was further restricted to CaMKIIa expressing neurons that also expressed the transcription factor TTA. As a result, GCaMP6 expression was selective to pyramidal neurons located in layers 2/3 and sparsely in layer 5.
Although GCaMP6f allows for the detection of population activity with higher signal to noise ratio than GCaMP3, the cortical activations studied here were so massive that this made little difference. We thus present data obtained with both indicators.

Surgical procedures
Using aseptic techniques, animals were chronically implanted with a thinned skull cranial window under isoflurane anesthesia. 0.05mL Rimadyl (Carprofen 5% w/v) was administered before surgery as an anti-inflammatory and analgesic. During the procedure, eyes were protected with ophthalmic gel (Viscotears Liquid Gel, Alcan) and the body temperature maintained around 37°C. The animal was anesthetized and mounted in a stereotaxic frame. The scalp over the dorsal skull surface was removed to expose the cranium. The left hemisphere parietal bone was thinned using a scalpel blade. Thinning proceeded until the cancellous layer of the skull, which contains blood vessels, was completely removed. A custom-made stainless steel head plate with a round imaging chamber (8 mm diameter) was then cemented over the thinned area using dental cement (Superbond). Finally, a small drop of UV cement (Norland Products Inc.) was applied inside the imaging chamber and an 8 mm glass coverslip glued onto the thinned skull region. The cement was cured with an UV LED (390nm, ThorLabs) for 20 s. The animal was allowed to recover at 37°C in an incubator and provided with Rimadyl in the drinking water (0.1 mL in 100 mL) for the three days after the surgery.
On the day of LFP recordings, the animal was anaesthetized again and a small skull screw implanted in the contralateral frontal bone, rostral to the cranial window. A silver wire previously soldered to the screw head served as a reference for electrophysiological recordings. After opening a small hole in the cranial window coverslip, a small craniotomy was performed over the target region of V1. The exposed region was finally covered with KwicKast silicone elastomer sealant. The animal was allowed to fully recover before starting the recording session. The typical recording session of epileptiform activity lasted 30-40 minutes.

Visual stimulation and retinotopic mapping
Visual stimuli were presented on three LCD monitors 26 , positioned 30 cm from the animal, arranged to span 140 degrees in azimuth and 60 degrees in elevation of the visual field contralateral to the imaged hemisphere. For retinotopic mapping, stimuli were contrastreversing gratings presented inside a rectangular window. Stimulus duration was 5 s, flickering frequency was 2 Hz, and spatial frequency was 0.03 cycles/°. To measure the preferred azimuth, the rectangular window was 60° high and 30° wide. To measure the preferred elevation, it was 20° high and 140° wide. Eye movements were monitored with CCD camera equipped with 2 infrared LEDs.
During these experiments, the pipette was pushed through the dura without applying pressure, to avoid injection of the GABAergic antagonist. The pressure inside the pipette was measured with a differential manometer. The resistance of the micropipette was monitored to ensure that insertion in the brain didn't clog the tip.
LFP signals were amplified 1,000 fold and high-passed above 0.1 Hz via a Multiclamp 700B differential amplifier (Molecular Devices). Data were digitized at 10 kHz with a Blackrock acquisition system and software. The exposure signal from the camera, TTL signals from visual stimulation software and screen photodiode signal were recorded at the same time to synchronize electrophysiological, imaging and visual stimulation data.

LFP analysis
To identify the start times of interictal discharges and seizures from the LFP recording we devised a simple supervised event detection method. The LFP trace was resampled at 100 Hz; the start of each event was assigned to the local maxima of the first derivative of the signal that exceeded 3 standard deviations from baseline; the end of each discharge was identified when its low frequency envelope returned to baseline. Finally, the results of the automatic detection were inspected visually and events classified as interictal discharges or seizures. Missed events were manually selected and artifacts removed.
Wavelet scalograms of the LFP signal were computed using the wavelet toolbox provided by Torrence and Compo (atoc.colorado.edu/research/wavelets). Power spectra and coherence of LFP and fluorescence signals were calculated using the Chronux Toolbox 52 (http://chronux.org/ ).

Widefield calcium imaging
We recorded GCaMP fluorescence with an epi-illumination system 26 . Excitation light at 480nm was provided with a blue LED light (465nm LEX2-B, Brain Vision, band-passed with a Semrock FF01-482/35 filter) and diverted onto the visual cortex via a dichroic mirror (FF506-Di03, Semrock). The emitted fluorescence was reflected by a second dichroic mirror (FF593-Di03, Semrock), passed through an emission filter (FF01-543/50-25, Semrock), and collected by a sCMOS camera (pco.edge, PCO AG). The camera was controlled by a TTL external trigger synchronized with the visual stimulation. The image acquisition rate was 50 Hz for retinotopic mapping and 70 Hz during imaging of epileptiform activity. The nominal spatial resolution of the system was 200 pixel/mm. Imaging was conducted in 20 s long sweeps, interleaved with ~10 s pauses needed to save the data to disk.

Histology and confocal imaging
To prepare the brain for tissue section, the animal was anesthetized (pentobarbital sodium, 200 mg/kg, i.p.), and the heart was perfused with PBS (0.5 ml/min) followed by a fixative (paraformaldehyde, 4%) in PBS solution. The brain was then removed and immersed in a PBS containing 30% sucrose at 4°C. Frozen coronal sections (60 µm thick) were obtained with a sliding microtome (Microm HM400R), mounted on glass slides and stained with DAPI (Vectashield). Sections were later imaged through a confocal microscope (Zeiss).

Analysis of imaging movies
Widefield movies where first registered using a discrete Fourier transform based subpixel image registration algorithm 53 . The retinotopic mapping and epileptiform activity images where then aligned using the brain vasculature as a reference. Affine transformation was used to find the best alignment. Then we calculated ∆F/F0 movies, where the signal for each pixel x was obtained as The map of retinotopy was obtained as previously described 26 In short, the reversing gratings elicited periodic neural responses that oscillate at twice the frequency of reversal 54 . For each pixel, we measured the power of these second harmonic responses using the Fourier transform of the fluorescent trace. We then fitted a Gaussian position tuning curve to the amplitude of the responses to visual stimulation at four horizontal positions. The standard deviation for the Gaussian curve model was the one that minimized the least squared error of the fit across pixels.
To localize the cortical initiation site of each event, calcium signals were aligned by the start of the electrographic discharge. For each event, pixels were included if they showed ΔF/F increases greater than 60% of the peak ΔF/F reached in the same class of events. The center of mass of the resulting cortical area, calculated over the first 500 ms, was then taken as the site of initiation of epileptiform activity. The average retinotopic position of the focus across animals was 93±16 degrees, confirming our ability to target the medial region of V1. We restricted the analysis to events that where contained for the most part in an imaging sweep. In particular, we included seizures that where imaged for at least 6 s after their start.
To assess the slow propagation of seizures, we defined criteria to evaluate when a cortical territory was invaded by the seizing activity. The distribution of maximum florescence levels during seizure was bimodal (Suppl. Figure 5). We considered recruited to the seizure the pixels that exceeded 30% of the peak fluorescence recorded at the focus, which was a good threshold to separate the population of pixels with the highest fluorescence change (Suppl. Figure 5). We then calculated the time it took for a seizure to invade each recruited pixel, measured from the electrographic seizure onset. We called this time 'delay to seizure invasion', and we measured it as the time point at which the fluorescence at any recruited pixel reached 60% of its maximum.

Standing wave model
We modeled the fluorescence movies of epileptiform discharges as standing waves, i.e. as the product of a global time course and a single image.

= * +
To find the best standing wave approximation, we applied singular value decomposition (SVD), a matrix factorization algorithm. SVD returns the best least square approximation of a matrix as the sum of standing waves. We obtained the time course and map of the separable model from the first row and first column returned by the SVD factorization.

Modelling of the profile of interictal events
We modeled the retinotopic profile of activation elicited by interictal events as the dot product of two functions, both dependent on the cortical position x of each ROI.
The first function depends on functional connectivity, and is a Gaussian falling off with the retinotopic distance from the focus, ret(x): The second function depends on lateral spread, and is a Gaussian-like function with the numerator raised to the 4 th power to give it a flat top as it falls off with the cortical distance from the epileptic focus: (2) ⁄ + When so parametrized, corresponds to the halfwidth half-maximum of the function. We fitted the parameters , , , , , to the data by least square minimization.

Phase analysis of cortical oscillations
Movies of cortical seizures were first bandpass filtered between 6 and 11 Hz. Then we computed the analytical representation of the fluorescence time-course for each pixel, using the Hilbert transform (MATLAB function 'hilbert', Signal Processing Toolbox). The analytical signal ( ) is a representation of a real valued signal ( ) in the complex space: ( ) = ( ) + ( )( ) = ( ) ( ) Its real part is ( ), the fluorescence signal, while its imaginary part is ( )( ), the Hilbert transform of ( ). When expressed in polar form, the analytical signal ( ) has a straightforward interpretation: the modulus ( ) represents the instantaneous amplitude, or envelope, of the oscillation; the angle ( ) represents the instantaneous phase of the oscillation.

Statistical information
Data were tested for normality before choosing the appropriate statistical test. All the statistical tests used were 2 tailed test. The significance of linear regression models was tested with the F-statistic against the null hypothesis of a constant model. p = 0.05 was assumed as the threshold for statistical significance.