2. Epilepsy as diseases of the dynamics of neuronal networks: models and predictions Fernando Lopes da Silva University of Amsterdam, The Netherlands Brain Research Unit Low Temperature Laboratory Helsinki University of Technology April 1st, 2008

3. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Basic question: How does the transition from normal brain activity to “epileptic activity” take place? Basic neurophysiology: two different cases, in vivo and in vitro

4. Principles of interictal-ictal transitions and precursors of seizures Case 1: Absence seizures: The occurrence of Spike-and-Wave discharges in the thalamo-cortical system. Case 2: Temporal Lobe Seizures: The occurrence of seizure activity in the hippocampus and associated brain areas.

5. Principles of interictal-ictal transitions and precursors of seizures Case 1: Absence seizures: The occurrence of Spike-and-Wave discharges in the thalamo-cortical system. Case 2: Temporal Lobe Seizures: The occurrence of seizure activity in the hippocampus and associated brain areas.

6. Spontaneous absence: Patient is requested to press a button immediately after a technician did the same.

7.  genetic model.  no neurological defects.  absences are characterized by behavioral arrest and spike-and-wave discharges (SWDs) in the EEG.  pharmacological responses is similar to that of patients with absences. The WAG/Rij rat as a genetic model of absences seizures Typical SWDs start and end abruptly Meeren, Pijn, van Luijtelaar, Coenen and Lopes da Silva, Journal of Neuroscience 2002,22:1480-95

8. VPM VPL 18.4 8.8 29.3 3.1 9.9 Hindpaw UpperLip Nose “FOCUS” SmI Thalamus B. whole seizure 4.9 A. first 500 msec VPM 2.9 8.1 11.7 30.0 4.3 6.1 VPL UpperLip Nose “FOCUS” SmI Thalamus Hindpaw 20-30 40-50 30-40 70-80 50-60 60-70 Association (%) Evolution of absence seizures: a summary Meeren, Pijn, van Luijtelaar, Coenen and Lopes da Silva, J. Neurosci 2002,22:1480-95 Cortico-Cortical. Intra-Thalamic and Cortico-Thalamic relations The solution was to analyze short EEG epochs

9. A cortical “focus” of spike-and- wave discharges New electrophysiological evidence: extra – and intra- cellular observations

10. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions The occurrence of SWD in the local ECoG coincides with rhythmic membrane depolarizations superimposed on a tonic hyperpolarization of this layer IV neuron (filled with neurobiotin) (GAER rat) Polack, Guillemain, Hu, Deransart, Depaulis and Charpier, J. of Neurosci June 2007

11. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Computational model of the thalamo- cortical neuronal networks In order to understand this behaviour of the neuronal networks we need a computational model Suffczynski, Kalitzin, Lopes da Silva,Dynamics of non-convulsive epileptic phenomena modelled by a bistable neuronal network, Neuroscience 126 (2004) 467–484

12. Thalamocortical network © SEIN, 2003 Medical Physics Department Extracellular activity of a RE neuron (yellow) and cortical field potential (green) recorded in the GAERS during a spike and wave discharge downloaded from Crunelli Research Group: www. thalamus.org.uk pyramidal cell GABAergic interneuron thalamic reticular (RE) neuron thalamocortical (TC) neuron In both TC and RE cells burst firing is provided by I T calcium current TC RE IN PY

13. Time evolution of the neuronal membrane potential: Synaptic currents Synaptic conductances are modeled by convolving firing rate frequency with synaptic impulse response Nonlinear GABA-B synaptic response Nonlinearity is realized by a sigmoidal function of the form: Basic equations of the model (1)

14. The model was realized using the Simulink toolbox of Math Works. Simulations were run using the ode3 integration method with a time step of 1 millisecond duration. Postprocessing was done using Matlab.

16. Model scheme © SEIN, 2003 pyramidal cells population thalamocortical cells population interneuronal population thalamic RE cells population external inputs burst generation process Suffczynski, Kalitzin, Lopes da Silva,Dynamics of non- convulsive epileptic phenomena modelled by a bistable neuronal network, Neuroscience 126 (2004) 467–484

17. Example of a bifurcation between two states: “normal” & “seizure” (absence type), both in the model and in EEG real signals.

18. Phase portraits of the system under non-epileptic and epileptic conditions

19. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions  One prediction is that for this kind of seizures the transition occurs randomly; What are the predictions of the model of type 1 with respect to the dynamics of absence seizures?

20. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions This prediction was tested by calculating the distributions of durations and of intervals inter-paroxysms.

21. Distribution of Durations either of paroxysmal events or of inter- paroxysmal events © SEIN, 2003 Medical Physics Department Probability of termination in unit time : p Probability of survival of unit time : 1- p Process duration Number of processes Exponential distribution of process durations P(t) = (1-p)(1-p)….(1-p)p 1 - p = e -λ  p = 1 - e -λ P(t) = (1 - e -λ )e -λt e -λ  1 - λ P(t) = λe -λt Termination of a process is random in time with constant probability simple calculation In common language: In math language: λe -λt log time Prediction

22. Distributions of epochs duration © SEIN, 2003 Medical Physics Department Suffczynski P, Lopes da Silva FH, Parra J, Velis DN, Bouwman BM, van Rijn CM, van Hese P, Boon P, Khosravani H, Derchansky M, Carlen P, Kalitzin S. Dynamics of epileptic phenomena determined from statistics of ictal transitions. IEEE Trans Biomed Eng. 2006 Mar;53(3):524-32.

23. Quasi- exponential (a ~ 1) distribution of SWDs in rat (WAG/Rij)

24. Quasi-exponential distribution of duration of 3 Hz paroxysms in a patient with absence non- convulsive seizures during the night

25. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions But …. Does it hold in all similar cases? Not exactly….

26. Gamma distribution of SWDs duration of GAER rats

28. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Thus, what do we have to modify in the model? It is necessary to include a ‘use-dependent parameter’, i.e. a parameter that changes as a seizure progresses.

29. , A value of α=1 indicates that the termination of ictal epochs is consistent with a Poisson process. A value of α>1 indicates that one or more parameters change gradually after seizure initiation, which facilitates a transition back to the normal state. This may be mediated by a GABA dependent process since it is GVG (Vigabatrin) sensitive. Bouwman BM, Suffczynski P, Lopes da Silva FH, Maris E, van Rijn CM. Eur J Neurosci. 2007 May;25(9):2783-90. Serendipity

30. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions The most likely hypothesis is that this effect depends on “use-dependent” changes in the dynamics of GABA receptors. Possible “use-dependent” candidate process:

31. In Conclusion: The absence types of epilepsy seizures follow a bifurcation dynamical scenario: they display jump transitions (Model type 1).

32. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Case 1: Absence seizures: The occurrence of Spike-and-Wave discharges in the thalamo-cortical system. Case 2: Temporal Lobe Seizures: The occurrence of seizure activity in the hippocampus and associated brain areas.

33. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Case 1: Absence seizures: The occurrence of Spike-and-Wave discharges in the thalamo-cortical system. Case 2: Temporal Lobe Seizures: The occurrence of seizure activity in the hippocampus and associated brain areas.

34. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions An example from basic neurophysiology shows what the properties of a pre-ictal state may be.

35. Disinhibition-induced synchronization of CA3 population firing (perfusion with 10 um bicucculine) After 2 min 6 min7.5 min Convol. Gauss 100 ms (black) & 1600 ms (red) Sliding variance index Var(t)=mean((f-F) 2 ) Mean amplitude of action potentials 1st Epileptiform discharge

36. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Cohen et al (2006) experiments show the existence of what may be called a precursor state. These results imply that in this case there exists a pre-ictal state with special properties. The sliding variance index = mean [(f – F) 2 ] starts to change several minutes before the first epileptiform spike is detected.

37. Bear, Connors, Paradiso, Neuroscience 1996 Temporal lobe

38. Many factors affect network stability Loss of connections Dormant Cells Feedback Inhibition Feedforward Inhibition Sprouting Excitation Modulatory input Acetylcholine Noradrenaline Inhibitory inter neurons Inhibitory inter neurons Pyramidal neurons Synaptic strength (plasticity,LTP, LTD) Output Ephaptic interactions Gap-ju n ctions Input Intrinsic Currents Apoptosis necrosis of specific cells X Input

39. Neuronal models and the routes to seizures The 2nd case: a simplified model of a Hippocampal network: “Epileptic fast activities can be explained by a model of impaired GABAergic dendritic inhibition” F. Wendling, F. Bartolomei, J.J. Bellanger and P. Chauvel. European Journal of Neuroscience 2002

40. Detail of the model: interaction between different types of inhibitory interneurons and principal (pyramidal) cells. Fast slow

41. Hippocampal EEG pre- ictal and transition to ictal Simulated EEG

42. Hippocampal Neuronal Population Model Fast IN Slow IN

43. Simulated EEG Slow dendritic inhibition B Fast somatic inhibition G

44. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Theoretically we may consider that the transition to an epileptic seizure can occur according to 2 models: 1.Bi- (or multi-stable) systems where jumps between two or more pre-existing attractors can take place, caused by stochastic fluctuations (noise) of any input – Case 1. 2.Parametric alteration, or deformation, that may be caused by an internal change of conditions or an external stimulus (sensory in reflex epilepsies) - Case 2.

45. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions The main question in cases of the second type is how to detect the special properties of the pre-ictal state. Many analytical methods have been proposed. Some of these are based on recording spontaneous neuronal activities. Here I will consider only those methods that use a probe – i.e. a given stimulation protocol - in order to estimate changes in the excitability state of the neuronal networks that may be characteristic of this pre-ictal state.

46. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions With respect to Case 2 we have to note that some seizures, even of the Absence type, may be triggered by an appropriate external stimulus, namely by way of intermittent light stimulation. For example Intermittent light stimulation can be used as a probe to assess the changes in excitability state of the networks.

48. Magnetoencephalography (MEG) at the Free University in Amsterdam Whole-head CTF system 151 MEG sensors Axial gradiometers –3rd order –5 cm baseline

50. IPS (10 Hz), EO, 9 yr, F 123456789101112

51. Mean correlation distance Phase coherency index Theoretical background (Stiliyan Kalitzin) X - sequence of phases; A - sequence of weights X1X2 X3 d(X2,X3) Parra, Kalitzin, Iriarte, Blanes, Velis and Lopes da Silva, Gamma-band phase clustering and photosensitivity: Is there an underlying mechanism common to photosensitive epilepsy and visual perception? Brain. 2003 May;126(Pt 5):1164-72.

52. A B A: Phase coherency analyses – PCI;,B: Amplitude analyses PPR & Absence seizure follows a period of IPS IVD,10Hz stim, EO Hz MEG sensors We found that the most reactive frequency band was the gamma band. PCIPCI PCIPCI

53. Distribution over the scalp of Phase clustering index (PCI) in the gamma frequency band Gamma oscillations and seizures

54. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions This finding led us to investigate whether PCI of EEG signals in other cases, namely of patients with mesial temporal lobe epilepsy could also have a predictive value using another kind of probe.

55. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Implantation layout and electrode bundles: subdural reeds and Intracerebral electrodes aimed at the head of the hippocampus and the midportion of the body of the hippocampus. Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728. Direct intra-cerebral electrical stimulation using a carrier frequency modulation probe

56. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Bilateral electrical stimulation [20 Hz, 800 μA, duration 5 sec] stimulated electrodes are HCL K4 and HCL K5 on the left hippocampus, and HCR H4 and HCR H5 on the right. Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728. The relative phase clustering index (rPCI) is computed for all signals and all stimulated epochs

57. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Statistics of the interictal rPCI values for 18 Traces of 6 patients; grouped according to whether the electrodes were at the Site of Seizure Onset (SOS) or near to it, or not (non-SOS). Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728.

58. rPCI as function of time preceding a seizure Values of rPCI en route to a seizure combined for all sites rPCI > 0.6 – Seizure occurring 80%; 0.1>rPCI 80%. Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728.

59. Seizure anticipation signal variable Seizure risk assessment seizure anticipation control parameters interictal state seizure state bifurcation point Low riskHigh risk patient control parameters time intervention or warning measurement Pre-ictal Special properties?

60. Counter-stimulation is capable of annihilating the transition to the paroxysmal oscillation Negative stimulus Positive stimulus

61. Is it possible to anticipate the occurrence of epileptic seizures by means of (chronic) ICES in some refractory epileptic syndromes? ? Is it possible to prevent/to abort the occurrence of epileptic seizures by means of (chronic) ICES in refractory epileptic syndromes? Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Questions and Answers

62. Bifurcation dynamical model: jump transition – Case 1. Deformation model: gradual transition – Case 2. In Conclusion: there are 2 main classes of models that may explain the transition to an epileptic seizure

63. Bifurcation dynamical model: jump transition between two (or more) pre-existing attractors – Case 1. Deformation model: gradual transition; in this case brain properties are assumed to change such that a new seizure state – or attractor – is either formed or is made more prominent in the pre-ictal state – Case 2. In Conclusion: there are 2 main classes of models that may explain the transition to an epileptic seizure Both models assume the existence of attractors that correspond to a seizure state

64. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Collaborators from the Department of Medical Physics of the Institute of Epilepsy SEIN (“Meer en Bosch”, Heemstede) and Center of NeuroSciences, University of Amsterdam): Stiliyan Kalitzin, Piotr Suffczynski Jaime Parra. Elan Ohayon Fernando Lopes da Silva Dimitri Velis

65. Details are described in Kalitzin, Parra, Velis, and Lopes da Silva, (2002) Enhancement of Phase Clustering in the EEG/MEG Gamma Frequency Band Anticipates Transitions to Paroxysmal Epileptiform Activity in Epileptic Patients With Known Visual Sensitivity. IEEE Transactions on BioMedical Engineering, 49 (11), 1279-85. Parra, Kalitzin, Iriarte, Blanes, Velis and Lopes da Silva, (2003) Gamma-band phase clustering and photosensitivity: Is there an underlying mechanism common to photosensitive epilepsy and visual perception? Brain, 126(Pt 5):1164-72. Lopes da Silva FH, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN. Dynamical diseases of brain systems: different routes to epileptic seizures. IEEE Trans Biomed Eng. 2003 May;50(5):540-8. Principles of interictal-ictal transitions and precursors of seizures

66. Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, (2005) Electrical brain- stimulation paradigm for estimating the seizure onset site and the time to ictal transition in temporal lobe epilepsy. Clin Neurophysiol, 116(3):718-28. Suffczynski P, Lopes da Silva FH, Parra J, Velis DN, Bouwman BM, van Rijn CM, van Hese P, Boon P, Khosravani H, Derchansky M, Carlen P, Kalitzin S. Dynamics of epileptic phenomena determined from statistics of ictal transitions. IEEE Trans Biomed Eng. 2006 Mar;53(3):524-32. Kalitzin SN, Parra J, Velis DN, Lopes da Silva FH Quantification of unidirectional nonlinear associations between multidimensional signals. IEEE Trans Biomed Eng. 2007 Mar;54(3):454-61. Bouwman BM, Suffczynski P, Lopes da Silva FH, Maris E, van Rijn CM. GABAergic mechanisms in absence epilepsy: a computational model of absence epilepsy simulating spike and wave discharges after vigabatrin in WAG/Rij rats. Eur J Neurosci. 2007 May;25(9):2783-90. Ohayan, EL, Kwan, HC, McIntyre Burnham, W, Suffczynski, P, Lopes da Silva, FH and Kalitzin, S, Adaptable Internittency and autonomous Transitions in Epilepsy and Cognition, Proceedings of the the 1st International Conference on Cognitive Neurodynamics – 2007, Shanghai.

67. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Not only intermittent light stimulation may trigger this kind of epileptic seizures; also other forms of visual stimuli may do the same, such as Pokémon video.

68. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions

70. Parra J, Kalitzin SN, Stroink H, Dekker E, de Wit C, Lopes da Silva FH. Removal of epileptogenic sequences from video material: the role of color. Neurology. 2005; 64(5):787-91. Removal of epileptogenic sequences from video material: the role of color. Neurology. 2005; 64(5):787-91.

71. Finding of a value of α<1 suggests that seizure initiation occurs according to a random- walk process. In this case the distribution has a fast decay followed by a long tail. Inter-ictal epochs Bouwman BM, Suffczynski P, Lopes da Silva FH, Maris E, van Rijn CM. Eur J Neurosci. 2007 May;25(9):2783-90.

72. Principles of interictal-ictal transitions and precursors of seizures  A value of α<1 reveals that the probability of a transition to a seizure is not constant and it is larger immediately after one seizure and thereafter decreases over time.  Such properties are characteristic of a random-walk process.  Because in a random-walk scenario the probability of seizure initiation is highest immediately after termination of the previous seizure, this kind of dynamic results in a grouping of seizures, i.e., in the appearance of clusters of ictal episodes separated by long interictal periods

73. Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions Alternate or 3rd model: autonomous intermittent transitions between 2 (or more) phases without the occurrence of a perturbation neither from the environment or from any change in network properties. This intermittency model must be further analyzed in real cases.

74. Principles of interictal-ictal transitions and precursors of seizures Proceedings of the the 1st International Conference on Cognitive Neurodynamics – 2007, Shanghai. Adaptable Intermittency and Autonomous Transitions in Epilepsy and Cognition Elan Liss Ohayon 1, Hon C. Kwan 2, W. McIntyre Burnham 1,2, Piotr Suffczynski 3, Fernando H. Lopes da Silva 4,5, Stiliyan Kalitzin 5 1University of Toronto Epilepsy Research Program, 2Department of Physiology, Toronto, Canada, 3Institute of Experimental Physics, Warsaw University, Warsaw, Poland, 4Swammerdam Institute for Life Sciences, University of Amsterdam, The Netherlands, 5Dutch Epilepsy Clinics Foundation (SEIN), Heemstede, The Netherlands

75. Transfer between firing rate and membrane potential Transfer function for the burst firing mode Where G B is the maximal firing rate within a burst, variables n inf (V) and m inf (V) are static sigmoidal functions that describe the fractions of neurons that are deinactivated or activated, respectively. Expressions (9) and (10) describe the time delay of I T inactivation. Basic equations of the model (2)

76. Wendling’s model of Hippocampal network

77. Simulated signalsReal EEG signals

78. Cortico-Cortical Associations: Bilaterally Symmetric Sites 1 11 9 7 5 3 13 2 8 6 4 14 12 10 C. 1 3 5 7 9 11 13 2 4 6 8 10 12 14 Cx left Cx right A. B. 1 mV 1 s D. Meeren, Pijn, van Luijtelaar, Coenen and Lopes da Silva, J. Neurosci 2002,22:1480-95

79. A cortical “focus” of spike-and- wave discharges SWDs are initiated in the facial somatosensory cortex in GAERS and propagate to other cortical areas and to the thalamus. Polack, Guillemain, Hu, Deransart, Depaulis and Charpier, J. of Neurosci June 2007

80. Bifurcation diagram © SEIN, 2003 Medical Physics Department only paroxysmal normal and paroxysmal only normal Input Normal activity - steady state Paroxysmal activity - limit cycle Input distribution

81. Occurrence of transition to “epileptic seizure” mode: parameter sensitivity

82. Active observation: stimulation with “carrier frequency” Phase clustering index (PCI) Complex amplitudes Repetitive stimulus S. Kalitzin, J. Parra, D. Velis, F. Lopes da Silva, Enhancement of phase clustering in the EEG/MEG gamma frequency band anticipates transition to paroxysmal epileptiform activity in epileptic patients with known visual sensitivity, IEEE-TBME, v.49, 11 p 1279-1286, 2002