Dynamical modulation of hypersynchronous seizure onset with transcranial magneto-acoustic stimulation in a hippocampal computational model.

Hypersynchronous (HYP) seizure onset is one of the frequently observed seizure-onset patterns in temporal lobe epileptic animals and patients, often accompanied by hippocampal sclerosis. However, the exact mechanisms and ion dynamics of the transition to HYP seizures remain unclear. Transcranial magneto-acoustic stimulation (TMAS) has recently been proposed as a novel non-invasive brain therapy method to modulate neurological disorders. Therefore, we propose a biophysical computational hippocampal network model to explore the evolution of HYP seizure caused by changes in crucial physiological parameters and design an effective TMAS strategy to modulate HYP seizure onset. We find that the cooperative effects of abnormal glial uptake strength of potassium and excessive bath potassium concentration could produce multiple discharge patterns and result in transitions from the normal state to the HYP seizure state and ultimately to the depolarization block state. Moreover, we find that the pyramidal neuron and the PV+ interneuron in HYP seizure-onset state exhibit saddle-node-on-invariant-circle/saddle homoclinic (SH) and saddle-node/SH at onset/offset bifurcation pairs, respectively. Furthermore, the response of neuronal activities to TMAS of different ultrasonic waveforms revealed that lower sine wave stimulation can increase the latency of HYP seizures and even completely suppress seizures. More importantly, we propose an ultrasonic parameter area that not only effectively regulates epileptic rhythms but also is within the safety limits of ultrasound neuromodulation therapy. Our results may offer a more comprehensive understanding of the mechanisms of HYP seizure and provide a theoretical basis for the application of TMAS in treating specific types of seizures.

Examining the low-voltage fast seizure-onset and its response to optogenetic stimulation in a biophysical network model of the hippocampus.

Low-voltage fast (LVF) seizure-onset is one of the two frequently observed temporal lobe seizure-onset patterns. Depth electroencephalogram profile analysis illustrated that the peak amplitude of LVF onset was deep temporal areas, e.g., hippocampus. However, the specific dynamic transition mechanisms between normal hippocampal rhythmic activity and LVF seizure-onset remain unclear. Recently, the optogenetic approach to gain control over epileptic hyper-excitability both in vitro and in vivo has become a novel noninvasive modulation strategy. Here, we combined biophysical modeling to study LVF dynamics following changes in crucial physiological parameters, and investigated the potential optogenetic intervention mechanism for both excitatory and inhibitory control. In an Ammon's horn 3 (CA3) biophysical model with light-sensitive protein channelrhodopsin 2 (ChR2), we found that the cooperative effects of excessive extracellular potassium concentration of parvalbumin-positive (PV+) inhibitory interneurons and synaptic links could induce abundant types of discharges of the hippocampus, and lead to transitions from gamma oscillations to LVF seizure-onset. Simulations of optogenetic stimulation revealed that the LVF seizure-onset and morbid fast spiking could not be eliminated by targeting PV+ neurons, whereas the epileptic network was more sensitive to the excitatory control of principal neurons with strong optogenetic currents. We illustrate that in the epileptic hippocampal network, the trajectories of the normal and the seizure state are in close vicinity and optogenetic perturbations therefore may result in transitions. The network model system developed in this study represents a scientific instrument to disclose the underlying principles of LVF, to characterize the effects of optogenetic neuromodulation, and to guide future treatment for specific types of seizures.

The seizure classification of focal epilepsy based on the network motif analysis.

Due to the complexity of focal epilepsy and its risk for transiting to the generalized epilepsy, the development of reliable classification methods to accurately predict and classify focal and generalized seizures is critical for the clinical management of patients with epilepsy. In order to holistically understand the seizure propagation behavior of focal epilepsy, we propose a three-node motif reduced network by respectively simplifying the focal region, surrounding healthy region and their critical regions as the single node. Because three-node motif can richly characterize information evolutions, the motif analysis method could comprehensively investigate the seizure behavior of focal epilepsy. Firstly, we define a new seizure propagation marker value to capture the seizure onsets and intensity. Based on the three-node motif analysis, it is shown that the focal seizure and spreading can be categorized as inhibitory seizure, focal seizure, focal-critical seizure and generalized seizures, respectively. The four types of seizures correspond to specific modal types respectively, reflecting the strong correlation between seizure behavior and information flow evolution. In addition, it is found that the intensity difference of outflow and inflow information from the critical node (connection heterogeneity) and the excitability of the critical node significantly affected the distribution and transition of the four seizure types. In particular, the method of local linear stability analysis also verifies the effectiveness of four types of seizures classification. In sum, this paper computationally confirms the complex dynamic behavior of focal seizures, and the study of criticality is helpful to propose novel seizure control strategies.

A simplified coronary model for diagnosis of ischemia-causing coronary stenosis.

BACKGROUND AND OBJECTIVE: The functional assessment of the severity of coronary stenosis from coronary computed tomography angiography (CCTA)-derived fractional flow reserve (FFR) has recently attracted interest. However, existing algorithms run at high computational cost. Therefore, this study proposes a fast calculation method of FFR for the diagnosis of ischemia-causing coronary stenosis. METHODS: We combined CCTA and machine learning to develop a simplified single-vessel coronary model for rapid calculation of FFR. First, a zero-dimensional model of single-vessel coronary was established based on CCTA, and microcirculation resistance was determined through the relationship between coronary pressure and flow. In addition, a coronary stenosis model based on machine learning was introduced to determine stenosis resistance. Computational FFR (cFFR) was then obtained by combining the zero-dimensional model and the stenosis model with inlet boundary conditions for resting (cFFRr) and hyperemic (cFFRh) aortic pressure, respectively. We retrospectively analyzed 75 patients who underwent clinically invasive FFR (iFFR), and verified the model accuracy by comparison of cFFR with iFFR. RESULTS: The average computing time of cFFR was less than 2 s. The correlations between cFFRr and cFFRh with iFFR were r = 0.89 (p < 0.001) and r = 0.90 (p < 0.001), respectively. Diagnostic accuracy, sensitivity, specificity, positive predictive value, negative predictive value, positive likelihood ratio, negative likelihood ratio for cFFRr and cFFRh were 90.7%, 95.0%, 89.1%, 76.0%, 98.0%, 8.7, 0.1 and 92.0%, 95.0%, 90.9%, 79.2%, 98.0%, 10.5, 0.1, respectively. CONCLUSIONS: The proposed model enables rapid prediction of cFFR and exhibits high diagnostic performance in selected patient cohorts. The model thus provides an accurate and time-efficient computational tool to detect ischemia-causing stenosis and assist with clinical decision-making.

Extracting the transition network of epileptic seizure onset.

In presurgical monitoring, focal seizure onset is visually assessed from intracranial electroencephalogram (EEG), typically based on the selection of channels that show the strongest changes in amplitude and frequency. As epileptic seizure dynamics is increasingly considered to reflect changes in potentially distributed neural networks, it becomes important to also assess the interrelationships between channels. We propose a workflow to quantitatively extract the nodes and edges contributing to the seizure onset using an across-seizure scoring. We propose a quantification of the consistency of EEG channel contributions to seizure onset within a patient. The workflow is exemplified using recordings from patients with different degrees of seizure-onset consistency.

Spontaneous transitions to focal-onset epileptic seizures: A dynamical study.

Given the complex temporal evolution of epileptic seizures, understanding their dynamic nature might be beneficial for clinical diagnosis and treatment. Yet, the mechanisms behind, for instance, the onset of seizures are still unknown. According to an existing classification, two basic types of dynamic onset patterns plus a number of more complex onset waveforms can be distinguished. Here, we introduce a basic three-variable model with two time scales to study potential mechanisms of spontaneous seizure onset. We expand the model to demonstrate how coupling of oscillators leads to more complex seizure onset waveforms. Finally, we test the response to pulse perturbation as a potential biomarker of interictal changes.

Band power modulation through intracranial EEG stimulation and its cross-session consistency.

OBJECTIVE: Direct electrical stimulation of the brain through intracranial electrodes is currently used to probe the epileptic brain as part of pre-surgical evaluation, and it is also being considered for therapeutic treatments through neuromodulation. In order to effectively modulate neural activity, a given neuromodulation design must elicit similar responses throughout the course of treatment. However, it is unknown whether intracranial electrical stimulation responses are consistent across sessions. The objective of this study was to investigate the within-subject, cross-session consistency of the electrophysiological effect of electrical stimulation delivered through intracranial electroencephalography (iEEG). APPROACH: We analysed data from 79 epilepsy patients implanted with iEEG who underwent brain stimulation as part of a memory experiment. We quantified the effect of stimulation in terms of band power modulation and compared this effect from session to session. As a reference, we made the same measurements during baseline periods. MAIN RESULTS: In most sessions, the effect of stimulation on band power could not be distinguished from baseline fluctuations of band power. Stimulation effect was consistent in a third of the session pairs, while the rest had a consistency measure not exceeding the baseline standards. Cross-session consistency was highly correlated with the degree of band power increase, and it also tended to be higher when the baseline conditions were more similar between sessions. SIGNIFICANCE: These findings can inform our practices for designing neuromodulation with greater efficacy when using direct electrical brain stimulation as a therapeutic treatment.

Dynamical Features of a Focal Epileptogenic Network Model for Stimulation-Based Control.

Much attention has been dedicated to clinical research of focal epilepsy, but the ability to derive a successful seizure control strategy based on unique dynamical features of the electroencephalogram is an unsolved problem. In this work, we introduce a basic model of spontaneous seizure dynamics and construct from it to a network model of focal-onset seizure dynamics. The full model is composed of coupled oscillators with scale-free network connectivity and a common slow variable. We find that global parameter changes and variation of the connectivity can drive the model from a quiescent state to recurrent seizures, and, eventually, to a permanent-seizure-state. Based on network synchronization features we design a stimulation scheme for the control of the fraction of nodes with strongest phase locking is proposed. Simulations lead to the identification of optimal stimuli for a given type of dynamics. Our results contribute to the development of a rational strategy for the non-surgical treatment of drug-resistant epilepsy.

Effects of brain-derived neurotrophic factor and noise on transitions in temporal lobe epilepsy in a hippocampal network.

Brain-derived neurotrophic factor (BDNF) has recently been implicated in the modulation of receptor activation leading to dynamic state transitions in temporal lobe epilepsy (TLE). In addition, the crucial role of neuronal noise in these transitions has been studied in electrophysiological experiments. However, the precise role of these factors during seizure generation in TLE is not known. Building on a previously proposed model of an epileptogenic hippocampal network, we included the actions of BDNF-regulated receptors and intrinsic noise. We found that the effects of both BDNF and noise can increase the activation of N-methyl-D-aspartate receptors leading to excessive C a 2 + flux, which induces abnormal fast spiking and bursting. Our results indicate that the combined effects have a strong influence on the seizure-generating network, resulting in higher firing frequency and amplitude. As correlations between firing increase, the synchronization of the entire network increases, a marker of the ictogenic transitions from normal to seizures-like dynamics. Our work on the effects of BDNF dynamics in a noisy environment might lead to an improved model-based understanding of the pathological mechanisms in TLE.

Network dynamics in the healthy and epileptic developing brain.

Electroencephalography (EEG) allows recording of cortical activity at high temporal resolution. EEG recordings can be summarized along different dimensions using network-level quantitative measures, such as channel-to-channel correlation, or band power distributions across channels. These reveal network patterns that unfold over a range of different timescales and can be tracked dynamically. Here we describe the dynamics of network state transitions in EEG recordings of spontaneous brain activity in normally developing infants and infants with severe early infantile epileptic encephalopathies (n = 8, age: 1-8 months). We describe differences in measures of EEG dynamics derived from band power, and correlation-based summaries of network-wide brain activity. We further show that EEGs from different patient groups and controls may be distinguishable on a small set of the novel quantitative measures introduced here, which describe dynamic network state switching. Quantitative measures related to the sharpness of switching from one correlation pattern to another show the largest differences between groups. These findings reveal that the early epileptic encephalopathies are associated with characteristic dynamic features at the network level. Quantitative network-based analyses like the one presented here may in the future inform the clinical use of quantitative EEG for diagnosis.

Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients.

Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients in response to stimulation. Even when using the same stimulation parameters in the same patient, wide variability in the duration of transient response has been reported. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well understood. To investigate the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and excitable states, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell there before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. Based on the analysis, we propose an explanation of why stimulation induced epileptiform activity may vary between trials, and predict how the variability could be related to ongoing oscillatory background activity. We compare our dynamic mechanism with other mechanisms (such as a slow parameter change) to generate excitable transients, and we discuss the proposed excitability mechanism in the context of stimulation responses in the epileptic cortex.

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.

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.

A meeting of two chronobiological systems: circadian proteins Period1 and BMAL1 modulate the human hair cycle clock.

The hair follicle (HF) is a continuously remodeled mini organ that cycles between growth (anagen), regression (catagen), and relative quiescence (telogen). As the anagen-to-catagen transformation of microdissected human scalp HFs can be observed in organ culture, it permits the study of the unknown controls of autonomous, rhythmic tissue remodeling of the HF, which intersects developmental, chronobiological, and growth-regulatory mechanisms. The hypothesis that the peripheral clock system is involved in hair cycle control, i.e., the anagen-to-catagen transformation, was tested. Here we show that in the absence of central clock influences, isolated, organ-cultured human HFs show circadian changes in the gene and protein expression of core clock genes (CLOCK, BMAL1, and Period1) and clock-controlled genes (c-Myc, NR1D1, and CDKN1A), with Period1 expression being hair cycle dependent. Knockdown of either BMAL1 or Period1 in human anagen HFs significantly prolonged anagen. This provides evidence that peripheral core clock genes modulate human HF cycling and are an integral component of the human hair cycle clock. Specifically, our study identifies BMAL1 and Period1 as potential therapeutic targets for modulating human hair growth.

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.

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.

The importance of modeling epileptic seizure dynamics as spatio-temporal patterns.

The occurrence of seizures is the common feature across the spectrum of epileptic disorders. We describe how the use of mechanistic neural population models leads to novel insight into the dynamic mechanisms underlying two important types of epileptic seizures. We specifically stress the need for a spatio-temporal description of the rhythms to deal with the complexity of the pathophenotype. Adapted to functional and structural patient data, the macroscopic models may allow a patient-specific description of seizures and prediction of treatment outcome.

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.

A prototypic mathematical model of the human hair cycle.

The human hair cycle is a complex, dynamic organ-transformation process during which the hair follicle repetitively progresses from a growth phase (anagen) to a rapid apoptosis-driven involution (catagen) and finally a relative quiescent phase (telogen) before returning to anagen. At present no theory satisfactorily explains the origin of the hair cycle rhythm. Based on experimental evidence we propose a prototypic model that focuses on the dynamics of hair matrix keratinocytes. We argue that a plausible feedback-control structure between two key compartments (matrix keratinocytes and dermal papilla) leads to dynamic instabilities in the population dynamics resulting in rhythmic hair growth. The underlying oscillation consists of an autonomous switching between two quasi-steady states. Additional features of the model, namely bistability and excitability, lead to new hypotheses about the impact of interventions on hair growth. We show how in silico testing may facilitate testing of candidate hair growth modulatory agents in human HF organ culture or in clinical trials.

Self-organised transients in a neural mass model of epileptogenic tissue dynamics.

Stimulation of human epileptic tissue can induce rhythmic, self-terminating responses on the EEG or ECoG. These responses play a potentially important role in localising tissue involved in the generation of seizure activity, yet the underlying mechanisms are unknown. However, in vitro evidence suggests that self-terminating oscillations in nervous tissue are underpinned by non-trivial spatio-temporal dynamics in an excitable medium. In this study, we investigate this hypothesis in spatial extensions to a neural mass model for epileptiform dynamics. We demonstrate that spatial extensions to this model in one and two dimensions display propagating travelling waves but also more complex transient dynamics in response to local perturbations. The neural mass formulation with local excitatory and inhibitory circuits, allows the direct incorporation of spatially distributed, functional heterogeneities into the model. We show that such heterogeneities can lead to prolonged reverberating responses to a single pulse perturbation, depending upon the location at which the stimulus is delivered. This leads to the hypothesis that prolonged rhythmic responses to local stimulation in epileptogenic tissue result from repeated self-excitation of regions of tissue with diminished inhibitory capabilities. Combined with previous models of the dynamics of focal seizures this macroscopic framework is a first step towards an explicit spatial formulation of the concept of the epileptogenic zone. Ultimately, an improved understanding of the pathophysiologic mechanisms of the epileptogenic zone will help to improve diagnostic and therapeutic measures for treating epilepsy.