Computational models in epilepsy

Computational models in epilepsy mainly focus on describing an electrophysiological manifestation associated with epilepsy called seizures. For this purpose, computational neurosciences use differential equations to reproduce the temporal evolution of the signals recorded experimentally. A book published in 2008, Computational Neuroscience in Epilepsy.{{Cite book|url=https://www.worldcat.org/oclc/281558250|title=Computational neuroscience in epilepsy|date=2008|publisher=Academic|others=Ivan Soltesz, Kevin Staley|isbn=978-0-12-373649-9|edition=1st|location=Amsterdam|oclc=281558250}} summarizes different works done up to this time. The goals of using its models are diverse, from prediction to comprehension of underlying mechanisms.{{Cite journal|last=Lytton|first=William W.|date=August 2008|title=Computer modelling of epilepsy|journal=Nature Reviews Neuroscience|language=en|volume=9|issue=8|pages=626–637|doi=10.1038/nrn2416|issn=1471-0048|pmc=2739976|pmid=18594562}}

The crisis phenomenon (seizure) exists and shares certain dynamical properties across different scales{{Cite journal|last1=Depannemaecker|first1=Damien|last2=Destexhe|first2=Alain|last3=Jirsa|first3=Viktor|last4=Bernard|first4=Christophe|date=2021-02-22|title=Modeling Seizures: From Single Neurons to Networks|url=https://www.preprints.org/manuscript/202102.0478/v1|doi=10.20944/preprints202102.0478.v1 |doi-access=free }} and different organisms.{{Cite journal|last1=Jirsa|first1=Viktor K.|last2=Stacey|first2=William C.|last3=Quilichini|first3=Pascale P.|last4=Ivanov|first4=Anton I.|last5=Bernard|first5=Christophe|date=2014-06-10|title=On the nature of seizure dynamics|url=https://doi.org/10.1093/brain/awu133|journal=Brain|volume=137|issue=8|pages=2210–2230|doi=10.1093/brain/awu133|issn=1460-2156|pmc=4107736|pmid=24919973}} It is possible to distinguish different approaches: the phenomenological models focus on the dynamics observed, generally reduced to few dimension it facilitates the study from the point of view of the theory of dynamical systems{{Cite journal|last1=Saggio|first1=Maria Luisa|last2=Spiegler|first2=Andreas|last3=Bernard|first3=Christophe|last4=Jirsa|first4=Viktor K.|date=2017-07-25|title=Fast–Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes|journal=The Journal of Mathematical Neuroscience|volume=7|issue=1|pages=7|doi=10.1186/s13408-017-0050-8|issn=2190-8567|pmc=5526832|pmid=28744735 |doi-access=free }} and more mechanistic models that explain the biophysical interactions underlying seizures. It is also possible to use these approaches to model and analyse the interactions between different regions of the brain{{Cite journal|last1=Breakspear|first1=M.|last2=Roberts|first2=J. A.|last3=Terry|first3=J. R.|last4=Rodrigues|first4=S.|last5=Mahant|first5=N.|last6=Robinson|first6=P. A.|date=2005-11-09|title=A Unifying Explanation of Primary Generalized Seizures Through Nonlinear Brain Modeling and Bifurcation Analysis|journal=Cerebral Cortex|volume=16|issue=9|pages=1296–1313|doi=10.1093/cercor/bhj072|pmid=16280462|issn=1460-2199|doi-access=free}} (In this case the notion of network plays an important role{{Cite journal|last1=Terry|first1=John R.|last2=Benjamin|first2=Oscar|last3=Richardson|first3=Mark P.|date=2012|title=Seizure generation: The role of nodes and networks|journal=Epilepsia|language=en|volume=53|issue=9|pages=e166–e169|doi=10.1111/j.1528-1167.2012.03560.x|pmid=22709380|s2cid=25085531|issn=1528-1167|doi-access=free}}) and the transition to ictal state.{{Cite journal|last1=Wendling|first1=Fabrice|last2=Hernandez|first2=Alfredo|last3=Bellanger|first3=Jean-Jacques|last4=Chauvel|first4=Patrick|last5=Bartolomei|first5=Fabrice|date=October 2005|title=Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG|journal=Journal of Clinical Neurophysiology|volume=22|issue=5|pages=343–356|issn=0736-0258|pmc=2443706|pmid=16357638}} These large-scale approaches have the advantage of being able to be related to the recordings made in humans thanks to electroencephalography (EEG). It offers new directions for clinical research, particularly as an additional tool in the treatment of refractory epilepsy {{Cite journal|date=2017-01-15|title=The Virtual Epileptic Patient: Individualized whole-brain models of epilepsy spread|journal=NeuroImage|language=en|volume=145|pages=377–388|doi=10.1016/j.neuroimage.2016.04.049|issn=1053-8119|last1=Jirsa|first1=V.K.|last2=Proix|first2=T.|last3=Perdikis|first3=D.|last4=Woodman|first4=M.M.|last5=Wang|first5=H.|last6=Gonzalez-Martinez|first6=J.|last7=Bernard|first7=C.|last8=Bénar|first8=C.|last9=Guye|first9=M.|last10=Chauvel|first10=P.|last11=Bartolomei|first11=F.|issue=Pt B|pmid=27477535|s2cid=36510741|doi-access=free}}{{Cite journal|last1=Khambhati|first1=Ankit N.|last2=Davis|first2=Kathryn A.|last3=Lucas|first3=Timothy H.|last4=Litt|first4=Brian|last5=Bassett|first5=Danielle S.|date=September 2016|title=Virtual Cortical Resection Reveals Push-Pull Network Control Preceding Seizure Evolution|url=|journal=Neuron|language=en|volume=91|issue=5|pages=1170–1182|doi=10.1016/j.neuron.2016.07.039|pmc=5017915|pmid=27568515}}

Other approaches are to use the models to try to understand the mechanisms underlying these seizures using biophysical descriptions from the neuron scale.{{Cite bioRxiv|last1=Depannemaecker|first1=Damien|last2=Ivanov|first2=Anton|last3=Lillo|first3=Davide|last4=Spek|first4=Len|last5=Bernard|first5=Christophe|last6=Jirsa|first6=Viktor|date=2020-10-23|title=A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level|language=en|biorxiv=10.1101/2020.10.23.352021}}{{Cite journal|last1=Cressman|first1=John R.|last2=Ullah|first2=Ghanim|last3=Ziburkus|first3=Jokubas|last4=Schiff|first4=Steven J.|last5=Barreto|first5=Ernest|date=April 2009|title=The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics|journal=Journal of Computational Neuroscience|language=en|volume=26|issue=2|pages=159–170|doi=10.1007/s10827-008-0132-4|issn=0929-5313|pmc=2704057|pmid=19169801}}{{Cite journal|last1=Destexhe|first1=A.|last2=Bal|first2=T.|last3=McCormick|first3=D. A.|last4=Sejnowski|first4=T. J.|date=1996-09-01|title=Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices|url=https://www.physiology.org/doi/10.1152/jn.1996.76.3.2049|journal=Journal of Neurophysiology|language=en|volume=76|issue=3|pages=2049–2070|doi=10.1152/jn.1996.76.3.2049|pmid=8890314 |issn=0022-3077|url-access=subscription}}{{Cite journal|last1=Almeida|first1=Antônio-Carlos G. De|last2=Rodrigues|first2=Antônio M.|last3=Scorza|first3=Fúlvio A.|last4=Cavalheiro|first4=Esper A.|last5=Teixeira|first5=Hewerson Z.|last6=Duarte|first6=Mário A.|last7=Silveira|first7=Gilcélio A.|last8=Arruda|first8=Emerson Z.|date=2008|title=Mechanistic hypotheses for nonsynaptic epileptiform activity induction and its transition from the interictal to ictal state—Computational simulation|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1528-1167.2008.01686.x|journal=Epilepsia|language=en|volume=49|issue=11|pages=1908–1924|doi=10.1111/j.1528-1167.2008.01686.x|pmid=18513350|s2cid=12024463|issn=1528-1167|url-access=subscription}} This makes it possible to understand the role of homeostasis and to understand the link between physical quantities (such as the concentration of potassium for example) and the pathological dynamics observed.{{citation needed|date=July 2021}}

This area of research has evolved rapidly in recent years and continues to show promise for our understanding and treatment of epilepsies for either for direct clinical application in the case of refractory epilepsy or fundamental research to guide experimental works.{{citation needed|date=July 2021}}