Quantification of brain proton longitudinal relaxation (T1 ) in lithium-treated and lithium-naïve patients with bipolar disorder in comparison to healthy controls.

BACKGROUND: Proton longitudinal relaxation (T1 ) is a quantitative MRI-derived tissue parameter sensitive to myelin, macromolecular, iron and water content. There is some evidence to suggest that cortical T1 is elevated in bipolar disorder and that lithium administration reduces cortical T1 . However, T1 has not yet been quantified in separate groups containing lithium-treated patients, lithium-naïve patients, and matched healthy controls. METHODS: Euthymic patients with bipolar disorder receiving lithium (n = 18, BDL) and those on other medications but naïve to lithium (n = 20, BDC) underwent quantitative T1 mapping alongside healthy controls (n = 18, HC). T1 was compared between groups within the cortex, white matter and subcortical structures using regions of interest (ROI) derived from the Desikan-Killiany atlas. Effect sizes for each ROI were computed for BDC vs BDL groups and Bipolar Disorder vs HC groups. RESULTS: No significant differences in T1 were identified between BDL and BDC groups when corrected for multiple comparisons. Patients with bipolar disorder had significantly higher mean T1 in a range of ROIs compared to healthy controls, including bilateral motor, somatosensory and superior temporal regions, subcortical structures and white matter. CONCLUSIONS: The higher T1 values observed in the patients with bipolar disorder may reflect abnormal tissue microstructure. Whilst the precise mechanism remains unknown, these findings may have a basis in differences in myelination, macromolecular content, iron and water content between patients and controls.

Dynamic mechanisms of neocortical focal seizure onset.

Recent experimental and clinical studies have provided diverse insight into the mechanisms of human focal seizure initiation and propagation. Often these findings exist at different scales of observation, and are not reconciled into a common understanding. Here we develop a new, multiscale mathematical model of cortical electric activity with realistic mesoscopic connectivity. Relating the model dynamics to experimental and clinical findings leads us to propose three classes of dynamical mechanisms for the onset of focal seizures in a unified framework. These three classes are: (i) globally induced focal seizures; (ii) globally supported focal seizures; (iii) locally induced focal seizures. Using model simulations we illustrate these onset mechanisms and show how the three classes can be distinguished. Specifically, we find that although all focal seizures typically appear to arise from localised tissue, the mechanisms of onset could be due to either localised processes or processes on a larger spatial scale. We conclude that although focal seizures might have different patient-specific aetiologies and electrographic signatures, our model suggests that dynamically they can still be classified in a clinically useful way. Additionally, this novel classification according to the dynamical mechanisms is able to resolve some of the previously conflicting experimental and clinical findings.

Structural connectivity in a paediatric case of anarchic hand syndrome.

BACKGROUND: "Anarchic hand" is a rare condition characterised by non-volitional, goal-directed movements of one arm. We report a case with analysis of structural and functional connectivity. CASE PRESENTATION: A 15 year old girl developed intermittent symptoms of intermanual conflict or anarchic hand as a result of traumatic brain injury during which she sustained a callosal bleed. Resting-state fMRI and DTI tractography were performed at a stage when symptoms had largely resolved. CONCLUSION: Structural connectivity between homologous superior frontal areas and functional connectivity between homologous posterior cingulate areas were significantly reduced, which may have contributed to causation. Tractography demonstrated new indirect connections between supplementary motor areas via the cerebellum, which we propose contributed to symptom resolution.

Towards a large-scale model of patient-specific epileptic spike-wave discharges.

Clinical electroencephalographic (EEG) recordings of the transition into generalised epileptic seizures show a sudden onset of spike-wave dynamics from a low-amplitude irregular background. In addition, non-trivial and variable spatio-temporal dynamics are widely reported in combined EEG/fMRI studies on the scale of the whole cortex. It is unknown whether these characteristics can be accounted for in a large-scale mathematical model with fixed heterogeneous long-range connectivities. Here, we develop a modelling framework with which to investigate such EEG features. We show that a neural field model composed of a few coupled compartments can serve as a low-dimensional prototype for the transition between irregular background dynamics and spike-wave activity. This prototype then serves as a node in a large-scale network with long-range connectivities derived from human diffusion-tensor imaging data. We examine multivariate properties in 42 clinical EEG seizure recordings from 10 patients diagnosed with typical absence epilepsy and 50 simulated seizures from the large-scale model using 10 DTI connectivity sets from humans. The model can reproduce the clinical feature of stereotypy where seizures are more similar within a patient than between patients, essentially creating a patient-specific fingerprint. We propose the approach as a feasible technique for the investigation of patient-specific large-scale epileptic features in space and time.

Contribution of White Matter Fiber Bundle Damage to Language Change After Surgery for Temporal Lobe Epilepsy.

BACKGROUND AND OBJECTIVES: In medically refractory temporal lobe epilepsy (TLE), 30%-50% of patients experience substantial language decline after resection in the language-dominant hemisphere. In this study, we investigated the contribution of white matter fiber bundle damage to language change at 3 and 12 months after surgery. METHODS: We studied 127 patients who underwent TLE surgery from 2010 to 2019. Neuropsychological testing included picture naming, semantic fluency, and phonemic verbal fluency, performed preoperatively and 3 and 12 months postoperatively. Outcome was assessed using reliable change index (RCI; clinically significant decline) and change across timepoints (postoperative scores minus preoperative scores). Functional MRI was used to determine language lateralization. The arcuate fasciculus (AF), inferior fronto-occipital fasciculus (IFOF), inferior longitudinal fasciculus, middle longitudinal fasciculus (MLF), and uncinate fasciculus were mapped using diffusion MRI probabilistic tractography. Resection masks, drawn comparing coregistered preoperative and postoperative T1 MRI scans, were used as exclusion regions on preoperative tractography to estimate the percentage of preoperative tracts transected in surgery. Chi-squared assessments evaluated the occurrence of RCI-determined language decline. Independent sample t tests and MM-estimator robust regressions were used to assess the impact of clinical factors and fiber transection on RCI and change outcomes, respectively. RESULTS: Language-dominant and language-nondominant resections were treated separately for picture naming because postoperative outcomes were significantly different between these groups. In language-dominant hemisphere resections, greater surgical damage to the AF and IFOF was related to RCI decline at 3 months. Damage to the inferior frontal subfasciculus of the IFOF was related to change at 3 months. In language-nondominant hemisphere resections, increased MLF resection was associated with RCI decline at 3 months, and damage to the anterior subfasciculus was related to change at 3 months. Language-dominant and language-nondominant resections were treated as 1 cohort for semantic and phonemic fluency because there were no significant differences in postoperative decline between these groups. Postoperative seizure freedom was associated with an absence of significant language decline 12 months after surgery for semantic fluency. DISCUSSION: We demonstrate a relationship between fiber transection and naming decline after temporal lobe resection. Individualized surgical planning to spare white matter fiber bundles could help to preserve language function after surgery.

Interictal MEG abnormalities to guide intracranial electrode implantation and predict surgical outcome.

Intracranial EEG (iEEG) is the gold standard technique for epileptogenic zone (EZ) localisation, but requires a preconceived hypothesis of the location of the epileptogenic tissue. This placement is guided by qualitative interpretations of seizure semiology, MRI, EEG and other imaging modalities, such as magnetoencephalography (MEG). Quantitative abnormality mapping using MEG has recently been shown to have potential clinical value. We hypothesised that if quantifiable MEG abnormalities were sampled by iEEG, then patients' post-resection seizure outcome may be better. Thirty-two individuals with refractory neocortical epilepsy underwent MEG and subsequent iEEG recordings as part of pre-surgical evaluation. Eyes-closed resting-state interictal MEG band power abnormality maps were derived from 70 healthy controls as a normative baseline. MEG abnormality maps were compared to iEEG electrode implantation, with the spatial overlap of iEEG electrode placement and cerebral MEG abnormalities recorded. Finally, we assessed if the implantation of electrodes in abnormal tissue, and subsequent resection of the strongest abnormalities determined by MEG and iEEG corresponded to surgical success. Intracranial electrodes were implanted in brain tissue with the most abnormal MEG findings - in individuals that were seizure-free post-operatively (T=3.9, p=0.003), but not in those who did not become seizure free. The overlap between MEG abnormalities and electrode placement distinguished surgical outcome groups moderately well (AUC=0.68). In isolation, the resection of the strongest abnormalities as defined by MEG and iEEG separated surgical outcome groups well, AUC=0.71, AUC=0.74 respectively. A model incorporating all three features separated surgical outcome groups best (AUC=0.80). Intracranial EEG is a key tool to delineate the EZ and help render individuals seizure-free post-operatively. We showed that data-driven abnormality maps derived from resting-state MEG recordings demonstrate clinical value and may help guide electrode placement in individuals with neocortical epilepsy. Additionally, our predictive model of post-operative seizure-freedom, which leverages both MEG and iEEG recordings, could aid patient counselling of expected outcome.

Intracranial EEG Structure-Function Coupling and Seizure Outcomes After Epilepsy Surgery.

BACKGROUND AND OBJECTIVES: Surgery is an effective treatment for drug-resistant epilepsy, which modifies the brain's structure and networks to regulate seizure activity. Our objective was to examine the relationship between brain structure and function to determine the extent to which this relationship affects the success of the surgery in controlling seizures. We hypothesized that a stronger association between brain structure and function would lead to improved seizure control after surgery. METHODS: We constructed functional and structural brain networks in patients with drug-resistant focal epilepsy by using presurgery functional data from intracranial EEG (iEEG) recordings, presurgery and postsurgery structural data from T1-weighted MRI, and presurgery diffusion-weighted MRI. We quantified the relationship (coupling) between structural and functional connectivity by using the Spearman rank correlation and analyzed this structure-function coupling at 2 spatial scales: (1) global iEEG network level and (2) individual iEEG electrode contacts using virtual surgeries. We retrospectively predicted postoperative seizure freedom by incorporating the structure-function connectivity coupling metrics and routine clinical variables into a cross-validated predictive model. RESULTS: We conducted a retrospective analysis on data from 39 patients who met our inclusion criteria. Brain areas implanted with iEEG electrodes had stronger structure-function coupling in seizure-free patients compared with those with seizure recurrence (p = 0.002, d = 0.76, area under the receiver operating characteristic curve [AUC] = 0.78 [95% CI 0.62-0.93]). Virtual surgeries on brain areas that resulted in stronger structure-function coupling of the remaining network were associated with seizure-free outcomes (p = 0.007, d = 0.96, AUC = 0.73 [95% CI 0.58-0.89]). The combination of global and local structure-function coupling measures accurately predicted seizure outcomes with a cross-validated AUC of 0.81 (95% CI 0.67-0.94). These measures were complementary to other clinical variables and, when included for prediction, resulted in a cross-validated AUC of 0.91 (95% CI 0.82-1.0), accuracy of 92%, sensitivity of 93%, and specificity of 91%. DISCUSSION: Our study showed that the strength of structure-function connectivity coupling may play a crucial role in determining the success of epilepsy surgery. By quantitatively incorporating structure-function coupling measures and standard-of-care clinical variables into presurgical evaluations, we may be able to better localize epileptogenic tissue and select patients for epilepsy surgery. CLASSIFICATION OF EVIDENCE: This is a Class IV retrospective case series showing that structure-function mapping may help determine the outcome from surgical resection for treatment-resistant focal epilepsy.

Modelling the role of tissue heterogeneity in epileptic rhythms.

Epileptic seizure activity manifests as complex spatio-temporal dynamics on the clinically relevant macroscopic scale. These dynamics are known to arise from spatially heterogeneous tissue, but the relationship between specific spatial abnormalities and epileptic rhythm generation is not well understood. We formulate a simplified macroscopic modelling framework with which to study the role of spatial heterogeneity in the generation of epileptiform spatio-temporal rhythms. We characterize the overall model dynamics in terms of spontaneous activity and excitability and demonstrate normal and abnormal spreading of activity. We introduce a means to systematically investigate the topology of abnormal sub-networks and explore its impact on spontaneous and stimulus-evoked rhythmic dynamics. This computationally efficient framework complements results from detailed biophysical models, and allows the testing of specific hypotheses about epileptic dynamics on the macroscopic scale.

Systems biology tools for toxicology.

An important goal of toxicology is to understand and predict the adverse effects of drugs and other xenobiotics. For pharmaceuticals, such effects often emerge unexpectedly in man even when absent from trials in vitro and in animals. Although drugs and xenobiotics act on molecules, it is their perturbation of intracellular networks that matters. The tremendous complexity of these networks makes it difficult to understand the effects of xenobiotics on their ability to function. Because systems biology integrates data concerning molecules and their interactions into an understanding of network behaviour, it should be able to assist toxicology in this respect. This review identifies how in silico systems biology tools, such as kinetic modelling, and metabolic control, robustness and flux analyse, may indeed help understanding network-mediated toxicity. It also shows how these approaches function by implementing them vis-à-vis the glutathione network, which is important for the detoxification of reactive drug metabolites. The tools enable the appreciation of the steady state concept for the detoxification network and make it possible to simulate and then understand effects of perturbations of the macromolecules in the pathway that are counterintuitive. We review how a glutathione model has been used to explain the impact of perturbation of the pathway at various molecular sites, as would be the effect of single-nucleotide polymorphisms. We focus on how the mutations impact the levels of glutathione and of two candidate biomarkers of hepatic glutathione status. We conclude this review by sketching how the various systems biology tools may help in the various phases of drug development in the pharmaceutical industry.

A spatially extended model for macroscopic spike-wave discharges.

Spike-wave discharges are a distinctive feature of epileptic seizures. So far, they have not been reported in spatially extended neural field models. We study a space-independent version of the Amari neural field model with two competing inhibitory populations. We show that this competition leads to robust spike-wave dynamics if the inhibitory populations operate on different time-scales. The spike-wave oscillations present a fold/homoclinic type bursting. From this result we predict parameters of the extended Amari system where spike-wave oscillations produce a spatially homogeneous pattern. We propose this mechanism as a prototype of macroscopic epileptic spike-wave discharges. To our knowledge this is the first example of robust spike-wave patterns in a spatially extended neural field model.

Early deviation from normal structural connectivity: A novel intrinsic severity score for mild TBI.

OBJECTIVE: Studies of outcome after traumatic brain injury (TBI) are hampered by the lack of robust injury severity measures that can accommodate spatial-anatomical and mechanistic heterogeneity. In this study we introduce a Mahalanobis distance measure (M) as an intrinsic injury severity measure that combines in a single score the many ways a given injured brain's connectivity can vary from that of healthy controls. Our objective is to test the hypotheses that M is superior to univariate measures in (1) discriminating patients and controls and (2) correlating with cognitive assessment. METHODS: Sixty-five participants (34 with mild TBI, 31 controls) underwent diffusion tensor MRI and extensive neuropsychological testing. Structural connectivity was inferred for all participants for 22 major white matter connections. Twenty-two univariate measures (1 per connection) and 1 multivariate measure (M), capturing and summarizing all connectivity change in a single score, were computed. RESULTS: Our multivariate measure (M) was able to better discriminate between patients and controls (area under the curve 0.81) than any individual univariate measure. M significantly correlated with cognitive outcome (Spearman ρ = 0.31; p < 0.05). No univariate measure showed significant correlation after correction for multiple comparisons. CONCLUSIONS: Heterogeneity in the severity and distribution of injuries after TBI has traditionally complicated the understanding of outcomes after TBI. Our approach provides a single, continuous variable that can fully capture individual heterogeneity. M's ability to distinguish even mildly injured patients from controls and its correlation with cognitive assessment suggest utility as an imaging-based marker of intrinsic injury severity.

Investigating Brain Network Changes and Their Association With Cognitive Recovery After Traumatic Brain Injury: A Longitudinal Analysis.

Traumatic brain injury (TBI) can result in acute cognitive deficits and diffuse axonal injury reflected in white matter brain network alterations, which may, or may not, later recover. Our objective is to first characterize the ways in which brain networks change after TBI and, second, investigate if those changes are associated with recovery of cognitive deficits. We aim to make initial progress in discerning the relationships between brain network changes, and their (dys)functional correlates. We analyze longitudinally acquired MRI from 23 TBI patients (two time points: 6 days, 12 months post-injury) and cross-sectional data from 28 controls to construct white matter brain networks. Cognitive assessment was also performed. Graph theory and regression analysis were applied to identify changed brain network metrics after injury that are associated with subsequent improvements in cognitive function. Sixteen brain network metrics were found to be discriminative of different post-injury phases. Eleven of those explain 90% (adjusted R 2) of the variability observed in cognitive recovery following TBI. Brain network metrics that had a high contribution to the explained variance were found in frontal and temporal cortex, additional to the anterior cingulate cortex. Our preliminary study suggests that network reorganization may be related to recovery of impaired cognitive function in the first year after a TBI.

Human cortical folding across regions within individual brains follows universal scaling law.

Different cortical regions vary systematically in their morphology. Here we investigate if the scaling law of cortical morphology, which was previously demonstrated across both human subjects and mammalian species, still holds within a single cortex across different brain regions. By topologically correcting for regional curvature, we could analyse how different morphological parameters co-vary within single cortices. We show in over 1500 healthy individuals that, despite their morphological diversity, regions of the same cortex obey the same universal scaling law, and age morphologically at similar rates. In Alzheimer's disease, we observe a premature ageing in the morphological parameters that was nevertheless consistent with the scaling law. The premature ageing effect was most dramatic in the temporal lobe. Thus, while morphology can vary substantially across cortical regions, subjects, and species, it always does so in accordance with a common scaling law, suggesting that the underlying processes driving cortical gyrification are universal.

Computer modelling of connectivity change suggests epileptogenesis mechanisms in idiopathic generalised epilepsy.

Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence diagnosis based on MRI is challenging. Anatomical abnormalities underlying brain dysfunctions in IGE are unclear and their relation to the pathomechanisms of epileptogenesis is poorly understood. In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissues in vivo. Analysing white matter structures of 32 subjects we incorporated our in vivo findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis. Patients with IGE have significant bilateral alterations in major white-matter fascicles. In the cingulum, fornix, and superior longitudinal fasciculus, tract integrity is compromised, whereas in specific parts of tracts between thalamus and the precentral gyrus, tract integrity is enhanced in patients. Combining these alterations in a logistic regression model, we computed the decision boundary that discriminated patients and controls. The computational model, informed with the findings on the tract abnormalities, specifically highlighted the importance of enhanced cortico-reticular connections along with impaired cortico-cortical connections in inducing pathological seizure-like dynamics. We emphasise taking directionality of brain connectivity into consideration towards understanding the pathological mechanisms; this is possible by combining neuroimaging and computational modelling. Our imaging evidence of structural alterations suggest the loss of cortico-cortical and enhancement of cortico-thalamic fibre integrity in IGE. We further suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit for reversing the mechanisms leading to epileptogenesis.

White matter microstructural properties in bipolar disorder in relationship to the spatial distribution of lithium in the brain.

BACKGROUND: Lithium treatment is associated with an increase in magnetic resonance imaging derived measures of white matter integrity, but the relationship between the spatial distribution of brain lithium and white matter integrity is unknown. METHODS: Euthymic patients with bipolar disorder receiving lithium (n = 12) and those on other medications but naïve to lithium (n = 17) underwent diffusion imaging alongside matched healthy controls (n = 16). Generalised fractional anisotropy (gFA) within white matter was compared between groups using a standard space white matter atlas. Lithium-treated patients underwent novel multinuclear lithium magnetic resonance imaging (7Li-MRI) to determine the relative lithium concentration across the brain. The relationship between 7Li-MRI signal intensity and gFA was investigated at the resolution of the 7Li-MRI sequence in native space. RESULTS: Lithium-treated bipolar disorder and healthy control groups had higher mean white matter gFA than the bipolar disorder group treated with other medications (t = 2.5, p < 0.05; t = 2.7, p < 0.03, respectively). No differences in gFA were found between patients taking lithium and healthy controls (t = 0.02, p = 1). These effects were seen consistently across most regions in the white matter atlas. In the lithium-treated group, a significant effect of the 7Li-MRI signal in predicting the gFA (p < 0.01) was identified in voxels containing over 50% white matter. LIMITATIONS: Cross-sectional evaluation of a relatively small cohort. CONCLUSIONS: The higher gFA values observed in the lithium-treated bipolar disorder group suggests that long-term lithium is associated with greater white matter integrity. Our novel analysis supports this further, showing a positive association between white matter gFA and the spatial distribution of lithium.

Heterogeneity of trans-callosal structural connectivity and effects on resting state subnetwork integrity may underlie both wanted and unwanted effects of therapeutic corpus callostomy.

BACKGROUND: The corpus callosum (CC) is the primary structure supporting interhemispheric connectivity in the brain. Partial or complete surgical callosotomy may be performed for the palliation of intractable epilepsy. A variety of disconnection syndromes are recognised after injury to or division of the CC however their mechanisms are poorly understood and their occurrence difficult to predict. We use novel high resolution structural connectivity analyses to demonstrate reasons for this poor predictability. METHODS: Diffusion weighted MRI data from five healthy adult controls was subjected to novel high-resolution structural connectivity analysis. We simulated the effects of CC lesions of varying extents on the integrity of resting state subnetworks (RSNs). RESULTS: There is substantial between-individual variation in patterns of CC connectivity. However in all individuals termination points of callosal connections mostly involve medial and superior sensory-motor areas. Superior temporal and lateral sensory-motor areas were not involved. Resting state networks showed selective vulnerability to simulated callosotomy of progressively greater anterior to posterior extent. The default mode network was most vulnerable followed by, in decreasing order: frontoparietal, limbic, somatomotor, ventral attention, dorsal attention and visual subnetworks. CONCLUSION: Consideration of the selective vulnerability of resting state sub-networks, and of between-individual variability in connectivity patterns, sheds new light on the occurrence of both wanted and unwanted effects of callosotomy. We propose that beneficial effects (seizure reduction) relate to disruption of the default mode network, with unwanted "disconnection syndrome" effects due to disruption particularly of the somatomotor and frontoparietal RSNs. Our results may also explain why disconnection syndromes primary reflect lateralised sensory-motor problems (e.g. of limb movement) rather than midline function (e.g. tongue movement). Marked between-subject variation in callosal connectivity may underlie the poor predictability of effects of callosotomy. High resolution structural connectivity studies of this nature may be useful in pre-surgical planning of therapeutic callosotomy for intractable epilepsy.

Structural connectivity based whole brain modelling in epilepsy.

Epilepsy is a neurological condition characterised by the recurrence of seizures. During seizures multiple brain areas can behave abnormally. Rather than considering each abnormal area in isolation, one can consider them as an interconnected functional 'network'. Recently, there has been a shift in emphasis to consider epilepsy as a disorder involving more widespread functional brain networks than perhaps was previously thought. The basis for these functional networks is proposed to be the static structural brain network established through the connectivity of the white matter. Additionally, it has also been argued that time varying aspects of epilepsy are of crucial importance and as such computational models of these dynamical properties have recently advanced. We describe how dynamic computer models can be combined with static human in vivo connectivity obtained through diffusion weighted magnetic resonance imaging. We predict that in future the use of these two methods in concert will lead to predictions for optimal surgery and brain stimulation sites for epilepsy and other neurological disorders.

A computational study of stimulus driven epileptic seizure abatement.

Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.

Phase space approach for modeling of epileptic dynamics.

Epileptic electroencephalography recordings can be described in terms of four prototypic wave forms: fast sinusoidal oscillations, large slow waves, fast spiking, and spike waves. On the macroscopic level, these wave forms have been modeled by different mechanistic models which share canonical features. Here we derive a minimal model of excitatory and inhibitory processes with features common to all previous models. We can infer that at least three interacting processes are required to support the prototypic epileptic dynamics. Based on a separation of time scales we analyze the model in terms of interacting manifolds in phase space. This allows qualitative reverse engineering of all epileptic wave forms and transitions between them. We propose this method as a complement to traditional approaches to modeling epileptiform rhythms.