Skip to main content

2017 | OriginalPaper | Buchkapitel

Outgrowing Neurological Diseases: Microcircuits, Conduction Delay and Childhood Absence Epilepsy

verfasst von : John Milton, Jianhong Wu, Sue Ann Campbell, Jacques Bélair

Erschienen in: Computational Neurology and Psychiatry

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The study of familial disorders characterized by recurring changes in neurodynamics, such as epileptic seizures, paralysis and headaches, provide opportunities to identify the mechanisms for dynamic changes in the nervous system. Many of these diseases are channelopathies. The computational challenge is to understand how a constantly present molecular defect in an ion channel can give rise to paroxysmal changes in neurodynamics. The most common of these channelopathies is childhood absence epilepsy (CAE). Here we review the dynamical properties of three neural microcircuits thought to be important in epilepsy: counter inhibition, recurrent inhibition and recurrent excitation. Time delays, \(\tau \), are an intrinsic property of these microcircuits since the time for a signal to travel between two neurons depends on the distance between them and the axonal conduction velocity. It is shown that all of these microcircuits can generate multistability provided that \(\tau \) is large enough. The term “multistability” means that there can be the co-existence of two or more attractors. Attention is drawn to the transient dynamics which can be associated with transitions between attractors, such as delay-induced transient oscillations. In this way we link the paroxysmal nature of seizure recurrences in CAE with time-delayed multistable dynamical systems. The tendency of children with CAE to outgrow their epilepsy is linked to developmental changes in axonal myelination which decrease \(\tau \).

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat L. Glass and M. C. Mackey. Pathological conditions resulting from instabilities in physiological control systems. Ann. New York Acad. Sci., 316:214–235, 1979. L. Glass and M. C. Mackey. Pathological conditions resulting from instabilities in physiological control systems. Ann. New York Acad. Sci., 316:214–235, 1979.
2.
Zurück zum Zitat M. C. Mackey and L. Glass. Oscillation and chaos in physiological control systems. Science, 197:287–289, 1977. M. C. Mackey and L. Glass. Oscillation and chaos in physiological control systems. Science, 197:287–289, 1977.
3.
Zurück zum Zitat M. C. Mackey and J. G. Milton. Dynamical diseases. Ann. New York Acad. Sci., 504:16–32, 1987. M. C. Mackey and J. G. Milton. Dynamical diseases. Ann. New York Acad. Sci., 504:16–32, 1987.
4.
Zurück zum Zitat H. O. Lüders. Deep brain stimulation and epilepsy. Martin Dunitz, New York, 2004. H. O. Lüders. Deep brain stimulation and epilepsy. Martin Dunitz, New York, 2004.
5.
Zurück zum Zitat J. Milton and P. Jung. Epilepsy as a dynamic disease. Springer, New York, 2003. J. Milton and P. Jung. Epilepsy as a dynamic disease. Springer, New York, 2003.
6.
Zurück zum Zitat I. Osorio and M. G. Frei. Real-time detection, quantification, warning and control of epileptic seizures: The foundation of a scientific epileptology. Epil. Behav. 16:391–396, 2009. I. Osorio and M. G. Frei. Real-time detection, quantification, warning and control of epileptic seizures: The foundation of a scientific epileptology. Epil. Behav. 16:391–396, 2009.
7.
Zurück zum Zitat I. Osorio, M. G. Frei, S. Sunderam, J. Giftakis, N. C. Bhavaraja, S. F. Schnaffer, and S. B. Wilkinson. Automated seizure abatement in humans using electrical stimulation. Ann. Neurol. 57:258–268, 2005. I. Osorio, M. G. Frei, S. Sunderam, J. Giftakis, N. C. Bhavaraja, S. F. Schnaffer, and S. B. Wilkinson. Automated seizure abatement in humans using electrical stimulation. Ann. Neurol. 57:258–268, 2005.
8.
Zurück zum Zitat I. Osorio, M. G. Frei, and S. B. Wilkinson. Real-time automated detection and quantitative analysis of seizures and short-term prediction of clinical onset. Epilepsia, 39:615–627, 1998. I. Osorio, M. G. Frei, and S. B. Wilkinson. Real-time automated detection and quantitative analysis of seizures and short-term prediction of clinical onset. Epilepsia, 39:615–627, 1998.
9.
Zurück zum Zitat T. S. Salam, J. L. Perez-Velazquez, and R. Genov. Seizure suppression efficacy of closed-loop versus open-loop deep brain stimulation in a rodent model of epilepsy. IEEE Trans. Neural Sys. Rehab. Eng. 24(6): 710-719, 2016. T. S. Salam, J. L. Perez-Velazquez, and R. Genov. Seizure suppression efficacy of closed-loop versus open-loop deep brain stimulation in a rodent model of epilepsy. IEEE Trans. Neural Sys. Rehab. Eng. 24(6): 710-719, 2016.
10.
Zurück zum Zitat G. Milton J, A. R. Quan, and I. Osorio. Nocturnal frontal lobe epilepsy: Metastability in a dynamic disease? In I. Osorio, H. P. Zaveri, M. G. Frei, and S. Arthurs, editors, Epilepsy: The intersection of neurosciences, biology, mathematics, engineering and physics, pages 501–510, New York, 2011. CRC Press. G. Milton J, A. R. Quan, and I. Osorio. Nocturnal frontal lobe epilepsy: Metastability in a dynamic disease? In I. Osorio, H. P. Zaveri, M. G. Frei, and S. Arthurs, editors, Epilepsy: The intersection of neurosciences, biology, mathematics, engineering and physics, pages 501–510, New York, 2011. CRC Press.
11.
Zurück zum Zitat I. Osorio, H. P. Zaveri, M. G. Frei, and S. Arthurs. Epilepsy: The intersection of neurosciences, biology, mathematics, engineering and physics. CRC Press, New York, 2011. I. Osorio, H. P. Zaveri, M. G. Frei, and S. Arthurs. Epilepsy: The intersection of neurosciences, biology, mathematics, engineering and physics. CRC Press, New York, 2011.
12.
Zurück zum Zitat A. Quan, I. Osorio, T. Ohira, and J. Milton. Vulnerability to paroxysmal oscillations in delay neural networks: A basis for nocturnal frontal lobe epilepsy? Chaos, 21:047512, 2011. A. Quan, I. Osorio, T. Ohira, and J. Milton. Vulnerability to paroxysmal oscillations in delay neural networks: A basis for nocturnal frontal lobe epilepsy? Chaos, 21:047512, 2011.
13.
Zurück zum Zitat J. Milton and D. Black. Dynamic diseases in neurology and psychiatry. Chaos, 5:8–13, 1995. J. Milton and D. Black. Dynamic diseases in neurology and psychiatry. Chaos, 5:8–13, 1995.
14.
Zurück zum Zitat J. M. Rommens, M. L. Iannuzzi, B. Kerem, M. L. Drumm, G. Melmer, M. Dean, R. Rozmahel, J. L. Cole, D. Kennedy, and N. Hidaka. Identification of the cystic fibrosis gene: chromosome walking and jumping. Science, 245:1055–1059, 1989. J. M. Rommens, M. L. Iannuzzi, B. Kerem, M. L. Drumm, G. Melmer, M. Dean, R. Rozmahel, J. L. Cole, D. Kennedy, and N. Hidaka. Identification of the cystic fibrosis gene: chromosome walking and jumping. Science, 245:1055–1059, 1989.
15.
Zurück zum Zitat S. Coombes and P. C. Bressloff. Bursting: The genesis of rhythm in the nervous system. World Scientific, New Jersey, 2005. S. Coombes and P. C. Bressloff. Bursting: The genesis of rhythm in the nervous system. World Scientific, New Jersey, 2005.
16.
Zurück zum Zitat G. B. Ermentrout and D. H. Terman. Mathematical Foundations of Neuroscience. Springer, New York, 2010. G. B. Ermentrout and D. H. Terman. Mathematical Foundations of Neuroscience. Springer, New York, 2010.
17.
Zurück zum Zitat W. Gerstner and W. Kistler. Spiking neuron models: single neurons, populations, plasticity. Cambridge University Press, New York, 2006. W. Gerstner and W. Kistler. Spiking neuron models: single neurons, populations, plasticity. Cambridge University Press, New York, 2006.
18.
Zurück zum Zitat E. M. Izhikevich. Dynamical systems in neuroscience: The geometry of excitability and bursting. MIT Press, Cambridge, MA, 2007. E. M. Izhikevich. Dynamical systems in neuroscience: The geometry of excitability and bursting. MIT Press, Cambridge, MA, 2007.
19.
Zurück zum Zitat C. Koch and I. Segev. Methods in Neuronal Modeling: From synapses to networks. MIT Press, Cambridge, Ma, 1989. C. Koch and I. Segev. Methods in Neuronal Modeling: From synapses to networks. MIT Press, Cambridge, Ma, 1989.
20.
Zurück zum Zitat J. Rinzel and G. B. Ermentrout. Analysis of neural excitability and oscillations. In C. Koch and I. Segev, editors, Methods in Neuronal Modeling: From synapses to networks, pages 135–169, Cambridge, MA, 1989. MIT Press. J. Rinzel and G. B. Ermentrout. Analysis of neural excitability and oscillations. In C. Koch and I. Segev, editors, Methods in Neuronal Modeling: From synapses to networks, pages 135–169, Cambridge, MA, 1989. MIT Press.
21.
Zurück zum Zitat J-B. Kim. Channelopathies. Korean J. Pediatr. 57:1–18, 2013. J-B. Kim. Channelopathies. Korean J. Pediatr. 57:1–18, 2013.
22.
Zurück zum Zitat D. M. Kullman and S. G. Waxman. Neurological channelopathies: new insights into disease mechanisms and ion channel function. J. Physiol., 588.11:1823–1827, 2010. D. M. Kullman and S. G. Waxman. Neurological channelopathies: new insights into disease mechanisms and ion channel function. J. Physiol., 588.11:1823–1827, 2010.
23.
Zurück zum Zitat E. Sigel and M. E. Steinman. Structure, function and modulation of GABA\(_{{\rm {a}}}\) receptors. J. Biol. Chem. 287:40224–40231, 2012. E. Sigel and M. E. Steinman. Structure, function and modulation of GABA\(_{{\rm {a}}}\) receptors. J. Biol. Chem. 287:40224–40231, 2012.
24.
Zurück zum Zitat P. Gloor, M. Avoli, and G. Kostopoulos. Thalamo-cortical relationships in generalized epilepsy with bilaterally synchronous spike-and-wave discharge. In M. Avoli, P. Gloor, R. Naquet, and G. Kostopoulos, editors, Generalized Epilepsy: Neurobiological Approaches, pages 190–212, Boston, 1990. Birkhäuser. P. Gloor, M. Avoli, and G. Kostopoulos. Thalamo-cortical relationships in generalized epilepsy with bilaterally synchronous spike-and-wave discharge. In M. Avoli, P. Gloor, R. Naquet, and G. Kostopoulos, editors, Generalized Epilepsy: Neurobiological Approaches, pages 190–212, Boston, 1990. Birkhäuser.
25.
Zurück zum Zitat G. K. Kostopoulos. Spike-and-wave discharges of absence seizures as a transformation of sleep spindles: the continuing development of a hypothesis. Clin. Neurophysiol. 111 (S2):S27–S38, 2000. G. K. Kostopoulos. Spike-and-wave discharges of absence seizures as a transformation of sleep spindles: the continuing development of a hypothesis. Clin. Neurophysiol. 111 (S2):S27–S38, 2000.
26.
Zurück zum Zitat L. Cocito and A. Primavera. Vigabatrin aggravates absences and absence status. Neurology, 51:1519–1520, 1998. L. Cocito and A. Primavera. Vigabatrin aggravates absences and absence status. Neurology, 51:1519–1520, 1998.
27.
Zurück zum Zitat S. Knack, H. M. Hamer, U. Schomberg, W. H. Oertel, and F. Rosenow. Tiagabine-induced absence status in idiopathic generalized nonconvulsive epilepsy. Seizure, 8:314–317, 1999. S. Knack, H. M. Hamer, U. Schomberg, W. H. Oertel, and F. Rosenow. Tiagabine-induced absence status in idiopathic generalized nonconvulsive epilepsy. Seizure, 8:314–317, 1999.
28.
Zurück zum Zitat J. G. Milton. Epilepsy: Multistability in a dynamic disease. In J. Walleczek, editor, Self-organized biological dynamics and nonlinear control, pages 374–386, New York, 2000. Cambridge University Press. J. G. Milton. Epilepsy: Multistability in a dynamic disease. In J. Walleczek, editor, Self-organized biological dynamics and nonlinear control, pages 374–386, New York, 2000. Cambridge University Press.
29.
Zurück zum Zitat G. van Luijtelaar, C. Behr, and M. Avoli. Is there such a thing as “generalized” epilepsy? In H. E. Scharfman and P. S. Buckmaster, editors, Issues in Clinical Epileptology: A View from the Bench, pages 81–91, New York, 2014. Springer. G. van Luijtelaar, C. Behr, and M. Avoli. Is there such a thing as “generalized” epilepsy? In H. E. Scharfman and P. S. Buckmaster, editors, Issues in Clinical Epileptology: A View from the Bench, pages 81–91, New York, 2014. Springer.
30.
Zurück zum Zitat G. van Luijtelaar and E. Sitnikova. Global and focal aspects of absence epilepsy: The contribution of genetic models. Neurosci. Biobehav. Rev. 30:983–1003, 2006. G. van Luijtelaar and E. Sitnikova. Global and focal aspects of absence epilepsy: The contribution of genetic models. Neurosci. Biobehav. Rev. 30:983–1003, 2006.
31.
Zurück zum Zitat J. Milton. Insights into seizure propagation from axonal conduction times. In J. Milton and P. Jung, editors, Epilepsy as a dynamic disease, pages 15–23, New York, 2003. Springer. J. Milton. Insights into seizure propagation from axonal conduction times. In J. Milton and P. Jung, editors, Epilepsy as a dynamic disease, pages 15–23, New York, 2003. Springer.
32.
Zurück zum Zitat J. Bancaud. Physiopathogenesis of generalized epilepsies of organic nature (Stereoencephalographic study). In H. Gastaut, H. H. Jasper, J. Bancaud, and A. Waltregny, editors, The Physiopathogenesis of the Epilepsies, pages 158–185, Springfield, Il, 1969. Charles C. Thomas. J. Bancaud. Physiopathogenesis of generalized epilepsies of organic nature (Stereoencephalographic study). In H. Gastaut, H. H. Jasper, J. Bancaud, and A. Waltregny, editors, The Physiopathogenesis of the Epilepsies, pages 158–185, Springfield, Il, 1969. Charles C. Thomas.
33.
Zurück zum Zitat J. Bancaud. Role of the cerebral cortex in (generalized) epilepsy of organic origin. Contribution of stereoelectroencephalographic investigations (S. E. E. G.) to discussion of the centroencephalographic concept. Presse Med. 79:669–673, 1971. J. Bancaud. Role of the cerebral cortex in (generalized) epilepsy of organic origin. Contribution of stereoelectroencephalographic investigations (S. E. E. G.) to discussion of the centroencephalographic concept. Presse Med. 79:669–673, 1971.
34.
Zurück zum Zitat H. K. M. Meeren, J. P. M. Pijn, E. L. J. M. Can Luijtelaar, A. M. L. Coenen, and F. H. Lopes da Silva. Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats. J. Neurosci. 22:1480–1495, 2002. H. K. M. Meeren, J. P. M. Pijn, E. L. J. M. Can Luijtelaar, A. M. L. Coenen, and F. H. Lopes da Silva. Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats. J. Neurosci. 22:1480–1495, 2002.
35.
Zurück zum Zitat D. Gupta, P. Ossenblok, and G. van Luijtelaar. Space-time network connectivity and cortical activations preceding spike wave discharges in human absence epilepsy: a MEG study. Med. Biol. Eng. Comput. 49:555–565, 2011. D. Gupta, P. Ossenblok, and G. van Luijtelaar. Space-time network connectivity and cortical activations preceding spike wave discharges in human absence epilepsy: a MEG study. Med. Biol. Eng. Comput. 49:555–565, 2011.
36.
Zurück zum Zitat J. R. Tenney, H. Fujiwara, P. S. Horn, S. E. Jacobsen, T. A. Glaser, and D. F. Rose. Focal corticothalamic sources during generalized absence seizures: a MEG study. Epilepsy Res. 106:113–122, 2013. J. R. Tenney, H. Fujiwara, P. S. Horn, S. E. Jacobsen, T. A. Glaser, and D. F. Rose. Focal corticothalamic sources during generalized absence seizures: a MEG study. Epilepsy Res. 106:113–122, 2013.
37.
Zurück zum Zitat I. Westmije, P. Ossenblok, B. Gunning, and G. van Luijtelaar. Onset and propagation of spike and slow wave discharges in human absence epilepsy: a MEG study. Epilepsia, 50:2538–2548, 2009. I. Westmije, P. Ossenblok, B. Gunning, and G. van Luijtelaar. Onset and propagation of spike and slow wave discharges in human absence epilepsy: a MEG study. Epilepsia, 50:2538–2548, 2009.
38.
Zurück zum Zitat S. A. Chkhenkeli and J. Milton. Dynamic epileptic systems versus static epileptic foci. In J. Milton and P. Jung, editors, Epilepsy as a dynamic disease, pages 25–36, New York, 2003. Springer. S. A. Chkhenkeli and J. Milton. Dynamic epileptic systems versus static epileptic foci. In J. Milton and P. Jung, editors, Epilepsy as a dynamic disease, pages 25–36, New York, 2003. Springer.
39.
Zurück zum Zitat J. G. Milton, S. A. Chkhenkeli, and V. L. Towle. Brain connectivity and the spread of epileptic seizures. In V. K. Jirsa and A. R. McIntosh, editors, Handbook of Brain Connectivity, pages 478–503, New York, 2007. Springer. J. G. Milton, S. A. Chkhenkeli, and V. L. Towle. Brain connectivity and the spread of epileptic seizures. In V. K. Jirsa and A. R. McIntosh, editors, Handbook of Brain Connectivity, pages 478–503, New York, 2007. Springer.
40.
Zurück zum Zitat M. Abeles, E. Vaadia, and H. Bergman. Firing patterns of single units in the prefrontal cortex and neural network models. Network, 1:13–25, 1990. M. Abeles, E. Vaadia, and H. Bergman. Firing patterns of single units in the prefrontal cortex and neural network models. Network, 1:13–25, 1990.
41.
Zurück zum Zitat P. Lennie. The cost of cortical computation. Current Biol. 13:493–497, 2003. P. Lennie. The cost of cortical computation. Current Biol. 13:493–497, 2003.
42.
Zurück zum Zitat V.B. Kolmanovskii and V.R. Nosov. Stability of functional differential equations, volume 180 of Mathematics in Science and Engineering. Academic Press, London, England, 1986. V.B. Kolmanovskii and V.R. Nosov. Stability of functional differential equations, volume 180 of Mathematics in Science and Engineering. Academic Press, London, England, 1986.
43.
Zurück zum Zitat H. Smith. An introduction to delay differential equations with applications to the life sciences, volume 57. Springer Science & Business Media, 2010. H. Smith. An introduction to delay differential equations with applications to the life sciences, volume 57. Springer Science & Business Media, 2010.
44.
Zurück zum Zitat G. Stépán. Retarded Dynamical Systems: Stability and Characteristic Functions, volume 210 of Pitman Research Notes in Mathematics. Longman Group, Essex, 1989. G. Stépán. Retarded Dynamical Systems: Stability and Characteristic Functions, volume 210 of Pitman Research Notes in Mathematics. Longman Group, Essex, 1989.
45.
Zurück zum Zitat O. Diekmann, S. A. van Gils, S.M. Verduyn Lunel, and H.-O. Walther. Delay Equations. Springer-Verlag, New York, 1995. O. Diekmann, S. A. van Gils, S.M. Verduyn Lunel, and H.-O. Walther. Delay Equations. Springer-Verlag, New York, 1995.
46.
Zurück zum Zitat J.K. Hale and S.M. Verduyn-Lunel. Introduction to Functional Differential Equations. Springer Verlag, New York, 1993. J.K. Hale and S.M. Verduyn-Lunel. Introduction to Functional Differential Equations. Springer Verlag, New York, 1993.
47.
Zurück zum Zitat F. H. Lopes da Silva, W. Blanes, S. Kalitizin, J. Parra Gomez, P. Suffczynski, and F. J. Velis. Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia, 44 (suppl. 12):72–83, 2002. F. H. Lopes da Silva, W. Blanes, S. Kalitizin, J. Parra Gomez, P. Suffczynski, and F. J. Velis. Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia, 44 (suppl. 12):72–83, 2002.
48.
Zurück zum Zitat C. M. Florez, R. J. McGinn, V. Lukankin, I. Marwa, S. Sugumar, J. Dian, L. N. Hazrati, P. L. Carlen, and L. Zhang. In vitro recordings of human neocortical oscillations. Cerebral Cortex, 25:578–597, 2015. C. M. Florez, R. J. McGinn, V. Lukankin, I. Marwa, S. Sugumar, J. Dian, L. N. Hazrati, P. L. Carlen, and L. Zhang. In vitro recordings of human neocortical oscillations. Cerebral Cortex, 25:578–597, 2015.
49.
Zurück zum Zitat A. Destexhe. Spike-and-wave oscillations based on the properties of GABA\(_{\rm {B}}\) receptors. J. Neurosci. 18:9099–9111, 1998. A. Destexhe. Spike-and-wave oscillations based on the properties of GABA\(_{\rm {B}}\) receptors. J. Neurosci. 18:9099–9111, 1998.
50.
Zurück zum Zitat A. Destexhe. Corticothalamic feedback: A key to explain absence seizures. In I. Soltesz and K. Staley, editors, Computational Neuroscience in Epilepsy, pages 184–214, San Diego, 2008. Academic Press. A. Destexhe. Corticothalamic feedback: A key to explain absence seizures. In I. Soltesz and K. Staley, editors, Computational Neuroscience in Epilepsy, pages 184–214, San Diego, 2008. Academic Press.
51.
Zurück zum Zitat A. B. Holt and T. I. Netoff. Computational modeling of epilepsy for an experimental neurologist. Exp. Neurol. 244:75–86, 2013. A. B. Holt and T. I. Netoff. Computational modeling of epilepsy for an experimental neurologist. Exp. Neurol. 244:75–86, 2013.
52.
Zurück zum Zitat W. W. Lytton. Computer modeling of epilepsy. Nat. Rev. Neurosci. 9:626–637, 2008. W. W. Lytton. Computer modeling of epilepsy. Nat. Rev. Neurosci. 9:626–637, 2008.
53.
Zurück zum Zitat I. Soltesz and K. Staley. Computational Neuroscience in Epilepsy. Academic Press, San Diego, 2008. I. Soltesz and K. Staley. Computational Neuroscience in Epilepsy. Academic Press, San Diego, 2008.
54.
Zurück zum Zitat G. Baier and J. Milton. Dynamic diseases of the brain. In D. Jaeger and R. Jung, editors, Encyclopedia of Computational Neuroscience, pages 1051–1061, New York, 2015. Springer. G. Baier and J. Milton. Dynamic diseases of the brain. In D. Jaeger and R. Jung, editors, Encyclopedia of Computational Neuroscience, pages 1051–1061, New York, 2015. Springer.
55.
Zurück zum Zitat L. Glass. Dynamical disease: challenges for nonlinear dynamics and medicine. Chaos, 25:097603, 2015. L. Glass. Dynamical disease: challenges for nonlinear dynamics and medicine. Chaos, 25:097603, 2015.
56.
Zurück zum Zitat C. Foley and M. C. Mackey. Mathematical model for G-CSF administration after chemotherapy. J. Theoret. Biol. 19:25–52, 2009. C. Foley and M. C. Mackey. Mathematical model for G-CSF administration after chemotherapy. J. Theoret. Biol. 19:25–52, 2009.
57.
Zurück zum Zitat M. C. Mackey. Periodic auto-immune hemolytic anemia: An induced dynamical disease. Bull. Math. Biol. 41:829–834, 1979. M. C. Mackey. Periodic auto-immune hemolytic anemia: An induced dynamical disease. Bull. Math. Biol. 41:829–834, 1979.
58.
Zurück zum Zitat J. S. Orr, J. Kirk, K. G. Gary, and J. R. Anderson. A study of the interdependence of red cell and bone marrow stem cell populations. Brit. J. Haematol. 15:23–34, 1968. J. S. Orr, J. Kirk, K. G. Gary, and J. R. Anderson. A study of the interdependence of red cell and bone marrow stem cell populations. Brit. J. Haematol. 15:23–34, 1968.
59.
Zurück zum Zitat J. Milton, P. Naik, C. Chan, and S. A. Campbell. Indecision in neural decision making models. Math. Model. Nat. Phenom. 5:125–145, 2010. J. Milton, P. Naik, C. Chan, and S. A. Campbell. Indecision in neural decision making models. Math. Model. Nat. Phenom. 5:125–145, 2010.
60.
Zurück zum Zitat K. Pakdaman, C. Grotta-Ragazzo, and C. P. Malta. Transient regime duration in continuous time neural networks with delay. Phys. Rev. E, 58:3623–3627, 1998. K. Pakdaman, C. Grotta-Ragazzo, and C. P. Malta. Transient regime duration in continuous time neural networks with delay. Phys. Rev. E, 58:3623–3627, 1998.
61.
Zurück zum Zitat K. Pakdaman, C. Grotta-Ragazzo, C. P. Malta, O. Arino, and J. F. Vibert. Effect of delay on the boundary of the basin of attraction in a system of two neurons. Neural Netw. 11:509–519, 1998. K. Pakdaman, C. Grotta-Ragazzo, C. P. Malta, O. Arino, and J. F. Vibert. Effect of delay on the boundary of the basin of attraction in a system of two neurons. Neural Netw. 11:509–519, 1998.
62.
Zurück zum Zitat C. Beaulieu, Z. Kisvarday, P. Somoygi, M. Cynader, and A. Cowey. Quantitative distribution of GABA-immunoresponsive and -immunonegative neurons and synapses in the monkey striate cortex (area 17). Cerebral Cortex, 2:295–309, 1992. C. Beaulieu, Z. Kisvarday, P. Somoygi, M. Cynader, and A. Cowey. Quantitative distribution of GABA-immunoresponsive and -immunonegative neurons and synapses in the monkey striate cortex (area 17). Cerebral Cortex, 2:295–309, 1992.
63.
Zurück zum Zitat J. G. Milton. Epilepsy as a dynamic disease: A tutorial of the past with an eye to the future. Epil. Beh. 18:33–44, 2010. J. G. Milton. Epilepsy as a dynamic disease: A tutorial of the past with an eye to the future. Epil. Beh. 18:33–44, 2010.
64.
Zurück zum Zitat I. Osorio, M. G. Frei, D. Sornette, J. Milton, and Y-C. Lai. Epileptic seizures: Quakes of the brain? Phys. Rev. E, 82:021919, 2010. I. Osorio, M. G. Frei, D. Sornette, J. Milton, and Y-C. Lai. Epileptic seizures: Quakes of the brain? Phys. Rev. E, 82:021919, 2010.
65.
Zurück zum Zitat G. A. Worrell, C. A. Stephen, S. D. Cranstoun, B. Litt, and J. Echauz. Evidence for self-organized criticality in human epileptic hippocampus. NeuroReport, 13:2017–2021, 2010. G. A. Worrell, C. A. Stephen, S. D. Cranstoun, B. Litt, and J. Echauz. Evidence for self-organized criticality in human epileptic hippocampus. NeuroReport, 13:2017–2021, 2010.
66.
Zurück zum Zitat M. Stead, M. Bower, B. H. Brinkmann, K. Lee, W. R. Marsh, F. B. Meyer, B. Litt, J. Van Gompel, and G. A. Worrell. Microseizures and the spatiotemporal scales of human partial epilepsy. Brain, 133:2789–2797, 2010. M. Stead, M. Bower, B. H. Brinkmann, K. Lee, W. R. Marsh, F. B. Meyer, B. Litt, J. Van Gompel, and G. A. Worrell. Microseizures and the spatiotemporal scales of human partial epilepsy. Brain, 133:2789–2797, 2010.
67.
Zurück zum Zitat J. Milton. Neuronal avalanches, epileptic quakes and other transient forms of neurodynamics. Eur. J. Neurosci. 36:2156–2163, 2012. J. Milton. Neuronal avalanches, epileptic quakes and other transient forms of neurodynamics. Eur. J. Neurosci. 36:2156–2163, 2012.
68.
Zurück zum Zitat W. Horsthemke and R. Lefever. Noise-induced transitions: Theory and applications in physics, chemistry and biology. Springer, New York, 1984. W. Horsthemke and R. Lefever. Noise-induced transitions: Theory and applications in physics, chemistry and biology. Springer, New York, 1984.
69.
Zurück zum Zitat P. Milanowski and P. Suffcznski. Seizures start without a common signature of critical transitions. Int. J. Neural Sys. 26: 1650053, 2016. P. Milanowski and P. Suffcznski. Seizures start without a common signature of critical transitions. Int. J. Neural Sys. 26: 1650053, 2016.
70.
Zurück zum Zitat D. A. Williams. A study of thalamic and cortical rhythms in Petit Mal. Brain, 76:50–59, 1953. D. A. Williams. A study of thalamic and cortical rhythms in Petit Mal. Brain, 76:50–59, 1953.
71.
Zurück zum Zitat M. Steriade. The GABAergic reticular nucleus: a preferential target of corticothalamic projections. Proc. Natl. Acad. Sci. USA, 98:3625–3627, 2001. M. Steriade. The GABAergic reticular nucleus: a preferential target of corticothalamic projections. Proc. Natl. Acad. Sci. USA, 98:3625–3627, 2001.
72.
Zurück zum Zitat M. Steriade and D. Contreras. Relations between cortical and cellular events during transition from sleep patterns to paroxysmal activity. J. Neurosci. 15:623–642, 1995. M. Steriade and D. Contreras. Relations between cortical and cellular events during transition from sleep patterns to paroxysmal activity. J. Neurosci. 15:623–642, 1995.
73.
Zurück zum Zitat M. J. Gallagher. How deactivating an inhibitor causes absence epilepsy: Validation of a noble lie. Epilepsy Curr. 13:38–41, 2013. M. J. Gallagher. How deactivating an inhibitor causes absence epilepsy: Validation of a noble lie. Epilepsy Curr. 13:38–41, 2013.
74.
Zurück zum Zitat E. G. Jones. The Thalamus. Plenum Press, New York, 1985. E. G. Jones. The Thalamus. Plenum Press, New York, 1985.
75.
Zurück zum Zitat C. Ajmone-Marsan. The thalamus. Data on its functional anatomy and on some aspects of thalamo-cortical organization. Arch. Italiennes Biol. 103:847–882, 1965. C. Ajmone-Marsan. The thalamus. Data on its functional anatomy and on some aspects of thalamo-cortical organization. Arch. Italiennes Biol. 103:847–882, 1965.
76.
Zurück zum Zitat Y. Choe. The role of temporal parameters in a thalamocortical model of analogy. IEEE Trans. Neural Netw. 15:1071–1082, 2004. Y. Choe. The role of temporal parameters in a thalamocortical model of analogy. IEEE Trans. Neural Netw. 15:1071–1082, 2004.
77.
Zurück zum Zitat T. Tsumoto, O. D. Creutzfield, and C. R. Legendy. Functional organization of the corticofugal system from visual cortex to lateral geniculate nucleus in the cat. Exp. Brain Res. 32:345–364, 1978. T. Tsumoto, O. D. Creutzfield, and C. R. Legendy. Functional organization of the corticofugal system from visual cortex to lateral geniculate nucleus in the cat. Exp. Brain Res. 32:345–364, 1978.
78.
Zurück zum Zitat C. E. Landisman, M. A. Long, M. Beierlein, M. R. Deans, D. L. Paul, and B. W. Connors. Electrical synapses in the thalamic reticular nucleus. J. Neurosci. 22:1002–1009, 2002. C. E. Landisman, M. A. Long, M. Beierlein, M. R. Deans, D. L. Paul, and B. W. Connors. Electrical synapses in the thalamic reticular nucleus. J. Neurosci. 22:1002–1009, 2002.
79.
Zurück zum Zitat S-C. Lee, S. L. Patrick, K. A. Richardson, and B. W. Connors. Two functionally distinct networks of gap junction-coupled inhibitory neurons in the thalamic reticular nucleus. J. Neurosci. 34:12182–13170, 2014. S-C. Lee, S. L. Patrick, K. A. Richardson, and B. W. Connors. Two functionally distinct networks of gap junction-coupled inhibitory neurons in the thalamic reticular nucleus. J. Neurosci. 34:12182–13170, 2014.
80.
Zurück zum Zitat J. G. Milton. Dynamics of small neural populations. American Mathematical Society, Providence, RI, 1996. J. G. Milton. Dynamics of small neural populations. American Mathematical Society, Providence, RI, 1996.
81.
Zurück zum Zitat J. T. Paz and J. R. Huguenard. Microcircuits and their interactions in epilepsy: is the focus out of focus? Nat. Neurosci. 18:351–359, 2015. J. T. Paz and J. R. Huguenard. Microcircuits and their interactions in epilepsy: is the focus out of focus? Nat. Neurosci. 18:351–359, 2015.
82.
Zurück zum Zitat O. Sporns and R. Kötter. Motifs in brain networks. PLoS Biol. 2:e369, 2004. O. Sporns and R. Kötter. Motifs in brain networks. PLoS Biol. 2:e369, 2004.
83.
Zurück zum Zitat J. T. Paz, A. S. Bryant, K. Peng, L. Fenno, O. Yizhar, W. N. Frankel, K. Deisseroth, and J. R. Huguenard. A new mode of corticothalamic transmission revealed in the Gria4(-/-) model of absence epilepsy. Nat. Neurosci. 14:1167–1173, 2011. J. T. Paz, A. S. Bryant, K. Peng, L. Fenno, O. Yizhar, W. N. Frankel, K. Deisseroth, and J. R. Huguenard. A new mode of corticothalamic transmission revealed in the Gria4(-/-) model of absence epilepsy. Nat. Neurosci. 14:1167–1173, 2011.
84.
Zurück zum Zitat A. M. Large, N. W. Vogles, S. Mielo, and A-M. M. Oswald. Balanced feedfoward inhibition and dominant recurrent inhibition in olfactory cortex. Proc. Natl. Acad. Sci. USA, 113:2276–2281, 2016. A. M. Large, N. W. Vogles, S. Mielo, and A-M. M. Oswald. Balanced feedfoward inhibition and dominant recurrent inhibition in olfactory cortex. Proc. Natl. Acad. Sci. USA, 113:2276–2281, 2016.
85.
Zurück zum Zitat S.A. Campbell. Stability and bifurcation of a simple neural network with multiple time delays. In S. Ruan, G.S.K. Wolkowicz, and J. Wu, editors, Fields Inst. Commun, volume 21, pages 65–79. AMS, 1999. S.A. Campbell. Stability and bifurcation of a simple neural network with multiple time delays. In S. Ruan, G.S.K. Wolkowicz, and J. Wu, editors, Fields Inst. Commun, volume 21, pages 65–79. AMS, 1999.
86.
Zurück zum Zitat A. Payeur, L. Maler, and A. Longtin. Oscillatory-like behavior in feedforward neuronal networks. Phys. Rev. E, 92:012703, 2015. A. Payeur, L. Maler, and A. Longtin. Oscillatory-like behavior in feedforward neuronal networks. Phys. Rev. E, 92:012703, 2015.
87.
Zurück zum Zitat J. Foss, A. Longtin, B. Mensour, and J. Milton. Multistability and delayed recurrent feedback. Phys. Rev. Lett. 76:708–711, 1996. J. Foss, A. Longtin, B. Mensour, and J. Milton. Multistability and delayed recurrent feedback. Phys. Rev. Lett. 76:708–711, 1996.
88.
Zurück zum Zitat K. D. Graber and D. A. Prince. A critical period for prevention of post-traumatic neocortical hyperexcitability in rats. Ann. Neurol. 55:860–870, 2004. K. D. Graber and D. A. Prince. A critical period for prevention of post-traumatic neocortical hyperexcitability in rats. Ann. Neurol. 55:860–870, 2004.
89.
Zurück zum Zitat A. R. Houweling, M. M. Bazhenov, I. Timofeev, M. Steraide, and T. J. Sejnowski. Homeostatic synaptic plasticity can explain post-traumatic epileptogenesis in chronically isolated neocortex. Cerebral Cortex, 15:834–845, 2005. A. R. Houweling, M. M. Bazhenov, I. Timofeev, M. Steraide, and T. J. Sejnowski. Homeostatic synaptic plasticity can explain post-traumatic epileptogenesis in chronically isolated neocortex. Cerebral Cortex, 15:834–845, 2005.
90.
Zurück zum Zitat K. L. Babcock and R. M. Westervelt. Dynamics of simple electronic networks. Physica D, 28:305–316, 1987. K. L. Babcock and R. M. Westervelt. Dynamics of simple electronic networks. Physica D, 28:305–316, 1987.
91.
Zurück zum Zitat N. Azmy, E. Boussard, J. F. Vibert, and K. Pakdaman. Single neuron with recurrent excitation: Effect of the transmission delay. Neural Netw. 9:797–818, 1996. N. Azmy, E. Boussard, J. F. Vibert, and K. Pakdaman. Single neuron with recurrent excitation: Effect of the transmission delay. Neural Netw. 9:797–818, 1996.
92.
Zurück zum Zitat O. Diez Martinez and J. P. Segundo. Behavior of a single neuron in a recurrent excitatory loop. Biol. Cybern. 47:33–41, 1983. O. Diez Martinez and J. P. Segundo. Behavior of a single neuron in a recurrent excitatory loop. Biol. Cybern. 47:33–41, 1983.
93.
Zurück zum Zitat K. Pakdaman, J-F. Vibert, E. Boussard, and N. Azmy. Single neuron with recurrent excitation: Effect of the transmission delay. Neural Netw. 9:797–818, 1996. K. Pakdaman, J-F. Vibert, E. Boussard, and N. Azmy. Single neuron with recurrent excitation: Effect of the transmission delay. Neural Netw. 9:797–818, 1996.
94.
Zurück zum Zitat K. Pakdaman, F. Alvarez, J. P. Segundo, O. Diez-Martinez, and J-F. Vibert. Adaptation prevents discharge saturation in models of single neurons with recurrent excitation. Int. J. Mod. Simul. 22:260–265, 2002. K. Pakdaman, F. Alvarez, J. P. Segundo, O. Diez-Martinez, and J-F. Vibert. Adaptation prevents discharge saturation in models of single neurons with recurrent excitation. Int. J. Mod. Simul. 22:260–265, 2002.
95.
Zurück zum Zitat Y. Chen and J. Wu. Slowly oscillating periodic solutions for a delayed frustrated network of two neurons. J. Math. Anal. Appl. 259:188–208, 2001. Y. Chen and J. Wu. Slowly oscillating periodic solutions for a delayed frustrated network of two neurons. J. Math. Anal. Appl. 259:188–208, 2001.
96.
Zurück zum Zitat J. Foss, F. Moss, and J. Milton. Noise, multistability and delayed recurrent loops. Phys. Rev. E, 55:4536–4543, 1997. J. Foss, F. Moss, and J. Milton. Noise, multistability and delayed recurrent loops. Phys. Rev. E, 55:4536–4543, 1997.
97.
Zurück zum Zitat J. Foss and J. Milton. Multistability in recurrent neural loops arising from delay. J. Neurophysiol. 84:975–985, 2000. J. Foss and J. Milton. Multistability in recurrent neural loops arising from delay. J. Neurophysiol. 84:975–985, 2000.
98.
Zurück zum Zitat M. C. Mackey and U. an der Heiden. The dynamics of recurrent inhibition. J. Math. Biol. 19:211–225, 1984. M. C. Mackey and U. an der Heiden. The dynamics of recurrent inhibition. J. Math. Biol. 19:211–225, 1984.
99.
Zurück zum Zitat L. H. A. Monteiro, A. Pellizari Filho, J. G. Chaui-Berlinck, and J. R. C. Piquiera. Oscillation death in a two-neuron network with delay in a self-connection. J. Biol. Sci. 15:49–61, 2007. L. H. A. Monteiro, A. Pellizari Filho, J. G. Chaui-Berlinck, and J. R. C. Piquiera. Oscillation death in a two-neuron network with delay in a self-connection. J. Biol. Sci. 15:49–61, 2007.
100.
Zurück zum Zitat R. E. Plant. A Fitzhugh differential-difference equation modeling recurrent neural feedback. SIAM J. Appl. Math. 40:150–162, 1981. R. E. Plant. A Fitzhugh differential-difference equation modeling recurrent neural feedback. SIAM J. Appl. Math. 40:150–162, 1981.
101.
Zurück zum Zitat H.R. Wilson and J.D. Cowan. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12(1):1, 1972. H.R. Wilson and J.D. Cowan. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12(1):1, 1972.
102.
Zurück zum Zitat J. Ma and J. Wu. Multistability in spiking neuron models of delayed recurrent inhibitory loops. Neural Comp. 19:2124–2148, 2007. J. Ma and J. Wu. Multistability in spiking neuron models of delayed recurrent inhibitory loops. Neural Comp. 19:2124–2148, 2007.
103.
Zurück zum Zitat J. Bélair and S.A. Campbell. Stability and bifurcations of equilibria in a multiple-delayed differential equation. SIAM J. Appl. Math. 54(5):1402–1424, 1994. J. Bélair and S.A. Campbell. Stability and bifurcations of equilibria in a multiple-delayed differential equation. SIAM J. Appl. Math. 54(5):1402–1424, 1994.
104.
Zurück zum Zitat J. Guckenheimer and P.J. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York, 1983. J. Guckenheimer and P.J. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York, 1983.
105.
Zurück zum Zitat Y.A. Kuznetsov. Elements of Applied Bifurcation Theory, volume 112 of Applied Mathematical Sciences. Springer-Verlag, Berlin/New York, 1995. Y.A. Kuznetsov. Elements of Applied Bifurcation Theory, volume 112 of Applied Mathematical Sciences. Springer-Verlag, Berlin/New York, 1995.
106.
Zurück zum Zitat S.A. Campbell, J. Bélair, T. Ohira, and J. Milton. Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback. J. Dyn. Diff. Eqns. 7(1):213–236, 1995. S.A. Campbell, J. Bélair, T. Ohira, and J. Milton. Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback. J. Dyn. Diff. Eqns. 7(1):213–236, 1995.
107.
Zurück zum Zitat L. P. Shayer and S.A. Campbell. Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays. SIAM J. Appl. Math. 61(2):673–700, 2000. L. P. Shayer and S.A. Campbell. Stability, bifurcation, and multistability in a system of two coupled neurons with multiple time delays. SIAM J. Appl. Math. 61(2):673–700, 2000.
108.
Zurück zum Zitat G. Fan, S.A. Campbell, G.S.K. Wolkowicz, and H. Zhu. The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons. J. Dyn. Diff. Eqns. 25(1):193–216, 2013. G. Fan, S.A. Campbell, G.S.K. Wolkowicz, and H. Zhu. The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons. J. Dyn. Diff. Eqns. 25(1):193–216, 2013.
109.
Zurück zum Zitat J. Ma and J. Wu. Patterns, memory and periodicity in two-neuron recurrent inhibitory loops. Math. Model. Nat. Phenom. 5:67–99, 2010. J. Ma and J. Wu. Patterns, memory and periodicity in two-neuron recurrent inhibitory loops. Math. Model. Nat. Phenom. 5:67–99, 2010.
110.
Zurück zum Zitat M. Timme and F. Wolf. The simplest problem in the collective dynamics of neural networks: Is synchrony stable? Nonlinearity, 21:1579–1599, 2008. M. Timme and F. Wolf. The simplest problem in the collective dynamics of neural networks: Is synchrony stable? Nonlinearity, 21:1579–1599, 2008.
111.
Zurück zum Zitat H. T. Chugani, M. E. Phelps, and J. C. Mazziotta. Positron emission tomography study of human brain function development. Ann. Neurol., 22:487–497, 1987. H. T. Chugani, M. E. Phelps, and J. C. Mazziotta. Positron emission tomography study of human brain function development. Ann. Neurol., 22:487–497, 1987.
112.
Zurück zum Zitat P. R. Huttenlocher. Developmental changes of aging. Brain Res. 163:195–205, 1979. P. R. Huttenlocher. Developmental changes of aging. Brain Res. 163:195–205, 1979.
113.
Zurück zum Zitat P. R. Huttenlocher and A. S. Dabholkar. Regional differences in synaptogenesis in human cerebral cortex. J. Comp. Neurol., 387:167–178, 1997. P. R. Huttenlocher and A. S. Dabholkar. Regional differences in synaptogenesis in human cerebral cortex. J. Comp. Neurol., 387:167–178, 1997.
114.
Zurück zum Zitat N. Barnea-Goraly, V. Menon, M. Eckart, L. Tamm, R. Bammer, A. Karchemskiy, C. C. Dant, and A. L. Reiss. White matter development during childhood and adolescence: A cross-sectional diffusion tensor imaging study. Cerebral Cortex, 15:1848–1854, 2005. N. Barnea-Goraly, V. Menon, M. Eckart, L. Tamm, R. Bammer, A. Karchemskiy, C. C. Dant, and A. L. Reiss. White matter development during childhood and adolescence: A cross-sectional diffusion tensor imaging study. Cerebral Cortex, 15:1848–1854, 2005.
115.
Zurück zum Zitat G. Z. Tau and B. S. Peterson. Normal development of brain circuits. Neuropschopharmacology, 35:147–168, 2010. G. Z. Tau and B. S. Peterson. Normal development of brain circuits. Neuropschopharmacology, 35:147–168, 2010.
116.
Zurück zum Zitat J-S Liang, S-P Lee, B. Pulli, J. W. Chen, S-C Kao, Y-K Tsang, and K. L-C Hsieh. Microstructural changes in absence seizure children: A diffusion tensor magnetic resonance imaging study. Ped. Neonatology 57(4): 318-325, 2016. J-S Liang, S-P Lee, B. Pulli, J. W. Chen, S-C Kao, Y-K Tsang, and K. L-C Hsieh. Microstructural changes in absence seizure children: A diffusion tensor magnetic resonance imaging study. Ped. Neonatology 57(4): 318-325, 2016.
117.
Zurück zum Zitat H. Chahboune, A. M. Mishra, M. N. DeSalvo, L. H. Stocib, M. Purcano, D. Scheinost, X. Papademetris, S. J. Fyson, M. L. Lorincz, V. Crunelli, F. Hyder, and H. Blumenfeld. DTI abnormalities in anterior corpus callosum of rats with spike-wave epilepsy. NeuroImage, 47:459–466, 2009. H. Chahboune, A. M. Mishra, M. N. DeSalvo, L. H. Stocib, M. Purcano, D. Scheinost, X. Papademetris, S. J. Fyson, M. L. Lorincz, V. Crunelli, F. Hyder, and H. Blumenfeld. DTI abnormalities in anterior corpus callosum of rats with spike-wave epilepsy. NeuroImage, 47:459–466, 2009.
118.
Zurück zum Zitat W. A. Hauser, J. F. Annegers, and L. T. Kurland. The incidence of epilepsy in Rochester, Minnesota, 1935–1984. Epilepsia, 34:453–468, 1993. W. A. Hauser, J. F. Annegers, and L. T. Kurland. The incidence of epilepsy in Rochester, Minnesota, 1935–1984. Epilepsia, 34:453–468, 1993.
119.
Zurück zum Zitat P. A. Robinson, C. J. Rennie, and D. L. Rowe. Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys. Rev. E, 65:041924, 2002. P. A. Robinson, C. J. Rennie, and D. L. Rowe. Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys. Rev. E, 65:041924, 2002.
120.
Zurück zum Zitat W. J. Freeman. Neurodynamics: An exploration of mesoscopic brain dynamics. Springer Verlag, London, 2000. W. J. Freeman. Neurodynamics: An exploration of mesoscopic brain dynamics. Springer Verlag, London, 2000.
121.
Zurück zum Zitat W. J. Freeman and M. D. Holmes. Metastability, instability, and state transitions in cortex. Neural Netw. 18:497–504, 2005. W. J. Freeman and M. D. Holmes. Metastability, instability, and state transitions in cortex. Neural Netw. 18:497–504, 2005.
122.
Zurück zum Zitat E. Sitnokova, A. E. Hramov, V. V. Grubov, A. A. Ovchinnkov, and A. A. Koronovsky. On-off intermittency of thalamo-cortical oscillations in the electroencephalogram of rats with genetic predisposition to absence epilepsy. Brain Res., 1436:147–156, 2012. E. Sitnokova, A. E. Hramov, V. V. Grubov, A. A. Ovchinnkov, and A. A. Koronovsky. On-off intermittency of thalamo-cortical oscillations in the electroencephalogram of rats with genetic predisposition to absence epilepsy. Brain Res., 1436:147–156, 2012.
123.
Zurück zum Zitat M. Goodfellow, K. Schindler, and G. Baier. Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model. NeuroImage, 55:920–932, 2011. M. Goodfellow, K. Schindler, and G. Baier. Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model. NeuroImage, 55:920–932, 2011.
124.
Zurück zum Zitat J. Milton and J. Foss. Oscillations and multistability in delayed feedback control. In H. G. Othmer, F. R. Adler, M. A. Lewis, and J. C. Dallon, editors, Case Studies in Mathematical Modeling: Ecology, Physiology and Cell Biology, pages 179–198, Upper Saddle River, NJ, 1997. Prentice Hall. J. Milton and J. Foss. Oscillations and multistability in delayed feedback control. In H. G. Othmer, F. R. Adler, M. A. Lewis, and J. C. Dallon, editors, Case Studies in Mathematical Modeling: Ecology, Physiology and Cell Biology, pages 179–198, Upper Saddle River, NJ, 1997. Prentice Hall.
125.
Zurück zum Zitat G.B. Ermentrout. XPPAUT 5.91 – the differential equations tool. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 2005. G.B. Ermentrout. XPPAUT 5.91 – the differential equations tool. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 2005.
126.
Zurück zum Zitat L.F. Shampine and S. Thompson. Solving DDEs in MATLAB. Appl. Num. Math., 37:441–458, 2001. L.F. Shampine and S. Thompson. Solving DDEs in MATLAB. Appl. Num. Math., 37:441–458, 2001.
127.
Zurück zum Zitat K. Engelborghs, T. Luzyanina, and G. Samaey. DDE-BIFTOOL v. 2.00: a MATLAB package for bifurcation analysis of delay differential equations. Technical Report TW-330, Department of Computer Science, K.U. Leuven, Leuven, Belgium, 2001. K. Engelborghs, T. Luzyanina, and G. Samaey. DDE-BIFTOOL v. 2.00: a MATLAB package for bifurcation analysis of delay differential equations. Technical Report TW-330, Department of Computer Science, K.U. Leuven, Leuven, Belgium, 2001.
128.
Zurück zum Zitat K. Engelborghs, T. Luzyanina, and D. Roose. Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM Trans. Math. Software, 28(1):1–21, 2002. K. Engelborghs, T. Luzyanina, and D. Roose. Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM Trans. Math. Software, 28(1):1–21, 2002.
Metadaten
Titel
Outgrowing Neurological Diseases: Microcircuits, Conduction Delay and Childhood Absence Epilepsy
verfasst von
John Milton
Jianhong Wu
Sue Ann Campbell
Jacques Bélair
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-49959-8_2