1
|
Pérez-Cervera A, Hlinka J. Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators. PLoS Comput Biol 2021; 17:e1008521. [PMID: 33780437 PMCID: PMC8032201 DOI: 10.1371/journal.pcbi.1008521] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2020] [Revised: 04/08/2021] [Accepted: 02/22/2021] [Indexed: 01/24/2023] Open
Abstract
The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous or endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures. Despite its simplicity, the modelling of epileptic dynamics as a slow-fast transition between low and high activity states mediated by some slow feedback variable is a relatively novel albeit fruitful approach. This study is the first, to our knowledge, characterizing the response of such slow-fast models of epileptic brain to perturbations by computing its isochrons. Besides its numerical computation, we theoretically determine which factors shape the geometry of isochrons for planar slow-fast oscillators. As a consequence, we introduce a theoretical approach providing a clear understanding of the response of perturbations of slow-fast oscillators. Within the epilepsy context, this elucidates the origin of the contradictory role of interictal epileptiform discharges in the transition to seizure, manifested by both pro-convulsive and anti-convulsive effect depending on the amplitude, frequency and timing. More generally, this paper provides theoretical framework highlighting the role of the slow flow component on the response to perturbations in relaxation oscillators, pointing to the general phenomena in such slow-fast oscillators ubiquitous in biological systems.
Collapse
Affiliation(s)
- Alberto Pérez-Cervera
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic
- Center for Cognition and Decision Making, Institute for Cognitive Neuroscience, National Research University Higher School of Economics, Moscow, Russia
- * E-mail: (AP); (JH)
| | - Jaroslav Hlinka
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic
- National Institute of Mental Health, Klecany, Czech Republic
- * E-mail: (AP); (JH)
| |
Collapse
|
2
|
Deeba F, Sanz-Leon P, Robinson PA. Unified dynamics of interictal events and absence seizures. Phys Rev E 2019; 100:022407. [PMID: 31574631 DOI: 10.1103/physreve.100.022407] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2018] [Indexed: 01/09/2023]
Abstract
The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into ∼3-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.
Collapse
Affiliation(s)
- F Deeba
- Department of Physics, Dhaka University of Engineering and Technology, Gazipur 1700, Bangladesh; School of Physics, University of Sydney, New South Wales 2006, Australia; and Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia
| | - P Sanz-Leon
- School of Physics, University of Sydney, New South Wales 2006, Australia, and Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia
| | - P A Robinson
- School of Physics, University of Sydney, New South Wales 2006, Australia, and Center for Integrative Brain Function, University of Sydney, New South Wales 2006, Australia
| |
Collapse
|
3
|
Karoly PJ, Kuhlmann L, Soudry D, Grayden DB, Cook MJ, Freestone DR. Seizure pathways: A model-based investigation. PLoS Comput Biol 2018; 14:e1006403. [PMID: 30307937 PMCID: PMC6199000 DOI: 10.1371/journal.pcbi.1006403] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Revised: 10/23/2018] [Accepted: 07/26/2018] [Indexed: 02/06/2023] Open
Abstract
We present the results of a model inversion algorithm for electrocorticography (ECoG) data recorded during epileptic seizures. The states and parameters of neural mass models were tracked during a total of over 3000 seizures from twelve patients with focal epilepsy. These models provide an estimate of the effective connectivity within intracortical circuits over the time course of seizures. Observing the dynamics of effective connectivity provides insight into mechanisms of seizures. Estimation of patients seizure dynamics revealed: 1) a highly stereotyped pattern of evolution for each patient, 2) distinct sub-groups of onset mechanisms amongst patients, and 3) different offset mechanisms for long and short seizures. Stereotypical dynamics suggest that, once initiated, seizures follow a deterministic path through the parameter space of a neural model. Furthermore, distinct sub-populations of patients were identified based on characteristic motifs in the dynamics at seizure onset. There were also distinct patterns between long and short duration seizures that were related to seizure offset. Understanding how these different patterns of seizure evolution arise may provide new insights into brain function and guide treatment for epilepsy, since specific therapies may have preferential effects on the various parameters that could potentially be individualized. Methods that unite computational models with data provide a powerful means to generate testable hypotheses for further experimental research. This work provides a demonstration that the hidden connectivity parameters of a neural mass model can be dynamically inferred from data. Our results underscore the power of theoretical models to inform epilepsy management. It is our hope that this work guides further efforts to apply computational models to clinical data.
Collapse
Affiliation(s)
- Philippa J Karoly
- Department of Biomedical Engineering, The University of Melbourne, Parkville, Australia
- Department of Medicine, St Vincent's Hospital, The University of Melbourne, Fitzroy, Australia
| | - Levin Kuhlmann
- Brain Dynamics Lab, Swinburne University of Technology, Hawthorn, Australia
- Centre for Neural Engineering, The University of Melbourne, Parkville, Australia
| | - Daniel Soudry
- Department of Electrical Engineering, Technion, Haifa, Israel
| | - David B Grayden
- Department of Biomedical Engineering, The University of Melbourne, Parkville, Australia
- Centre for Neural Engineering, The University of Melbourne, Parkville, Australia
| | - Mark J Cook
- Department of Medicine, St Vincent's Hospital, The University of Melbourne, Fitzroy, Australia
| | - Dean R Freestone
- Department of Medicine, St Vincent's Hospital, The University of Melbourne, Fitzroy, Australia
- Seer Medical Pty, Melbourne, Australia
| |
Collapse
|
4
|
Deeba F, Sanz-Leon P, Robinson PA. Dependence of absence seizure dynamics on physiological parameter evolution. J Theor Biol 2018; 454:11-21. [PMID: 29807025 DOI: 10.1016/j.jtbi.2018.05.029] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2018] [Revised: 05/22/2018] [Accepted: 05/24/2018] [Indexed: 12/30/2022]
Abstract
A neural field model of the corticothalamic system is applied to investigate the temporal and spectral characteristics of absence seizures in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into an absence seizure-like state once a threshold is passed and a supercritical Hopf bifurcation occurs. The dynamics and spectral characteristics of the resulting model seizures are explored as functions of maximum connection strength, time above threshold, and the rate at which the connection strength increases (ramp rate). Our results enable spectral and temporal characteristics of seizures to be related to changes in the underlying physiological evolution of connections via nonlinear dynamics and neural field theory. Spectral analysis reveals that the power of the harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. It is also found that the time to reach the stable limit-cycle seizure oscillation from the instability threshold decreases with the square root of the ramp rate.
Collapse
Affiliation(s)
- F Deeba
- School of Physics, University of Sydney, NSW 2006, Australia; Center for Integrative Brain Function, University of Sydney, NSW 2006, Australia.
| | - Paula Sanz-Leon
- School of Physics, University of Sydney, NSW 2006, Australia; Center for Integrative Brain Function, University of Sydney, NSW 2006, Australia
| | - P A Robinson
- School of Physics, University of Sydney, NSW 2006, Australia; Center for Integrative Brain Function, University of Sydney, NSW 2006, Australia
| |
Collapse
|
5
|
Cocchi L, Gollo LL, Zalesky A, Breakspear M. Criticality in the brain: A synthesis of neurobiology, models and cognition. Prog Neurobiol 2017; 158:132-152. [PMID: 28734836 DOI: 10.1016/j.pneurobio.2017.07.002] [Citation(s) in RCA: 226] [Impact Index Per Article: 32.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Revised: 06/15/2017] [Accepted: 07/13/2017] [Indexed: 11/26/2022]
Abstract
Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a comprehensive theory of brain activity and cognitive function. Modelling and analysis methods for neuroscience should aim to accommodate multiscale phenomena. Emerging research now suggests that multi-scale processes in the brain arise from so-called critical phenomena that occur very broadly in the natural world. Criticality arises in complex systems perched between order and disorder, and is marked by fluctuations that do not have any privileged spatial or temporal scale. We review the core nature of criticality, the evidence supporting its role in neural systems and its explanatory potential in brain health and disease.
Collapse
Affiliation(s)
- Luca Cocchi
- QIMR Berghofer Medical Research Institute, Brisbane, Australia.
| | | | - Andrew Zalesky
- Melbourne Neuropsychiatry Centre, The University of Melbourne, Melbourne, Australia
| | - Michael Breakspear
- QIMR Berghofer Medical Research Institute, Brisbane, Australia; Metro North Mental Health Service, Brisbane, Australia
| |
Collapse
|
6
|
Ashwin P, Coombes S, Nicks R. Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2016; 6:2. [PMID: 26739133 PMCID: PMC4703605 DOI: 10.1186/s13408-015-0033-6] [Citation(s) in RCA: 104] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2015] [Accepted: 10/30/2015] [Indexed: 05/20/2023]
Abstract
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.
Collapse
Affiliation(s)
- Peter Ashwin
- Centre for Systems Dynamics and Control, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, Exeter, EX4 4QF, UK.
| | - Stephen Coombes
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
| | - Rachel Nicks
- School of Mathematics, University of Birmingham, Watson Building, Birmingham, B15 2TT, UK.
| |
Collapse
|
7
|
van Dijkman SC, Alvarez-Jimenez R, Danhof M, Della Pasqua O. Pharmacotherapy in pediatric epilepsy: from trial and error to rational drug and dose selection - a long way to go. Expert Opin Drug Metab Toxicol 2016; 12:1143-56. [PMID: 27434782 DOI: 10.1080/17425255.2016.1203900] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
INTRODUCTION Whereas ongoing efforts in epilepsy research focus on the underlying disease processes, the lack of a physiologically based rationale for drug and dose selection contributes to inadequate treatment response in children. In fact, limited information on the interindividual variation in pharmacokinetics and pharmacodynamics of anti-epileptic drugs (AEDs) in children drive prescription practice, which relies primarily on dose regimens according to a mg/kg basis. Such practice has evolved despite advancements in pediatric pharmacology showing that growth and maturation processes do not correlate linearly with changes in body size. AREAS COVERED In this review we aim to provide 1) a comprehensive overview of the sources of variability in the response to AEDs, 2) insight into novel methodologies to characterise such variation and 3) recommendations for treatment personalisation. EXPERT OPINION The use of pharmacokinetic-pharmacodynamic principles in clinical practice is hindered by the lack of biomarkers and by practical constraints in the evaluation of polytherapy. The identification of biomarkers and their validation as tools for drug development and therapeutics will require some time. Meanwhile, one should not miss the opportunity to integrate the available pharmacokinetic data with modeling and simulation concepts to prevent further delays in the development of personalised treatments for pediatric patients.
Collapse
Affiliation(s)
- Sven C van Dijkman
- a Division of Pharmacology , Leiden Academic Centre for Drug Research , Leiden , The Netherlands
| | - Ricardo Alvarez-Jimenez
- a Division of Pharmacology , Leiden Academic Centre for Drug Research , Leiden , The Netherlands
| | - Meindert Danhof
- a Division of Pharmacology , Leiden Academic Centre for Drug Research , Leiden , The Netherlands
| | - Oscar Della Pasqua
- b Clinical Pharmacology and Discovery Medicine , GlaxoSmithKline , Stockley Park , UK.,c Clinical Pharmacology and Therapeutics , University College London , London , UK
| |
Collapse
|
8
|
Discovery and Validation of Biomarkers Based on Computational Models of Normal and Pathological Hippocampal Rhythms. VALIDATING NEURO-COMPUTATIONAL MODELS OF NEUROLOGICAL AND PSYCHIATRIC DISORDERS 2015. [DOI: 10.1007/978-3-319-20037-8_2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
|
9
|
Woldman W, Terry JR. Multilevel Computational Modelling in Epilepsy: Classical Studies and Recent Advances. VALIDATING NEURO-COMPUTATIONAL MODELS OF NEUROLOGICAL AND PSYCHIATRIC DISORDERS 2015. [DOI: 10.1007/978-3-319-20037-8_7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
|
10
|
Freestone DR, Karoly PJ, Nešić D, Aram P, Cook MJ, Grayden DB. Estimation of effective connectivity via data-driven neural modeling. Front Neurosci 2014; 8:383. [PMID: 25506315 PMCID: PMC4246673 DOI: 10.3389/fnins.2014.00383] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Accepted: 11/09/2014] [Indexed: 01/12/2023] Open
Abstract
This research introduces a new method for functional brain imaging via a process of model inversion. By estimating parameters of a computational model, we are able to track effective connectivity and mean membrane potential dynamics that cannot be directly measured using electrophysiological measurements alone. The ability to track the hidden aspects of neurophysiology will have a profound impact on the way we understand and treat epilepsy. For example, under the assumption the model captures the key features of the cortical circuits of interest, the framework will provide insights into seizure initiation and termination on a patient-specific basis. It will enable investigation into the effect a particular drug has on specific neural populations and connectivity structures using minimally invasive measurements. The method is based on approximating brain networks using an interconnected neural population model. The neural population model is based on a neural mass model that describes the functional activity of the brain, capturing the mesoscopic biophysics and anatomical structure. The model is made subject-specific by estimating the strength of intra-cortical connections within a region and inter-cortical connections between regions using a novel Kalman filtering method. We demonstrate through simulation how the framework can be used to track the mechanisms involved in seizure initiation and termination.
Collapse
Affiliation(s)
- Dean R Freestone
- Department of Medicine, St. Vincent's Hospital Melbourne, The University of Melbourne Fitzroy, VIC, Australia ; NeuroEngineering Laboratory, Department of Electrical and Electronic Engineering, The University of Melbourne Parkville, VIC, Australia
| | - Philippa J Karoly
- Department of Medicine, St. Vincent's Hospital Melbourne, The University of Melbourne Fitzroy, VIC, Australia ; NeuroEngineering Laboratory, Department of Electrical and Electronic Engineering, The University of Melbourne Parkville, VIC, Australia
| | - Dragan Nešić
- NeuroEngineering Laboratory, Department of Electrical and Electronic Engineering, The University of Melbourne Parkville, VIC, Australia
| | - Parham Aram
- Department of Automatic Control and Systems Engineering, University of Sheffield Sheffield, UK
| | - Mark J Cook
- Department of Medicine, St. Vincent's Hospital Melbourne, The University of Melbourne Fitzroy, VIC, Australia
| | - David B Grayden
- NeuroEngineering Laboratory, Department of Electrical and Electronic Engineering, The University of Melbourne Parkville, VIC, Australia ; Centre for Neural Engineering, The University of Melbourne Parkville, VIC, Australia
| |
Collapse
|
11
|
van Putten MJAM, Zandt BJ. Neural mass modeling for predicting seizures. Clin Neurophysiol 2013; 125:867-8. [PMID: 24326320 DOI: 10.1016/j.clinph.2013.11.013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2013] [Revised: 11/18/2013] [Accepted: 11/19/2013] [Indexed: 12/01/2022]
Affiliation(s)
- Michel J A M van Putten
- Department of Neurology and Clinical Neurophysiology, Medisch Spectrum Twente and Clinical Neurophysiology group, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente, Enschede, The Netherlands.
| | - Bas-Jan Zandt
- Neuroimaging group, MIRA-Institute for Biomedical Technology and Technical Medicine, University of Twente, Enschede, The Netherlands.
| |
Collapse
|
12
|
Altered resting state brain dynamics in temporal lobe epilepsy can be observed in spectral power, functional connectivity and graph theory metrics. PLoS One 2013; 8:e68609. [PMID: 23922658 PMCID: PMC3724835 DOI: 10.1371/journal.pone.0068609] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2012] [Accepted: 05/30/2013] [Indexed: 02/04/2023] Open
Abstract
Despite a wealth of EEG epilepsy data that accumulated for over half a century, our ability to understand brain dynamics associated with epilepsy remains limited. Using EEG data from 15 controls and 9 left temporal lobe epilepsy (LTLE) patients, in this study we characterize how the dynamics of the healthy brain differ from the "dynamically balanced" state of the brain of epilepsy patients treated with anti-epileptic drugs in the context of resting state. We show that such differences can be observed in band power, synchronization and network measures, as well as deviations from the small world network (SWN) architecture of the healthy brain. The θ (4-7 Hz) and high α (10-13 Hz) bands showed the biggest deviations from healthy controls across various measures. In particular, patients demonstrated significantly higher power and synchronization than controls in the θ band, but lower synchronization and power in the high α band. Furthermore, differences between controls and patients in graph theory metrics revealed deviations from a SWN architecture. In the θ band epilepsy patients showed deviations toward an orderly network, while in the high α band they deviated toward a random network. These findings show that, despite the focal nature of LTLE, the epileptic brain differs in its global network characteristics from the healthy brain. To our knowledge, this is the only study to encompass power, connectivity and graph theory metrics to investigate the reorganization of resting state functional networks in LTLE patients.
Collapse
|