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Development of Differential Connectivity Graph for Characterization of Brain Regions Involved in Epilepsy Ladan AMINI Directors: Christian JUTTEN Hamid SOLTANIAN-ZADEH Co-directors: Sophie ACHARD Gholam Ali HOSSEIN-ZADEH GIPSA-lab,

  1. Directed differential connectivity graph (dDCG) DCG calculation IED and non-IED time intervals iEEG recordings of a typical patient for about 14 seconds. Onsets and offsets of IED and non-IED time intervals. Development of Differential Connectivity Graph 16/48

  2. Directed differential connectivity graph (dDCG) DCG calculation Different frequency bands 1 IED and iEEG Coupling DCG non-IED DCG signals computation inference segmentation ∗ Lower frequencies have higher contribution. Wavelet transforms: narrower bands for lower frequencies. well adapted for the analysis of non-stationary EEG signals [Clark et al. , 1995, Senhadji & Wendling, 2002, Adeli et al. , 2003, Indiradevi et al. , 2008, Conlon et al. , 2009] . Development of Differential Connectivity Graph 17/48

  3. Directed differential connectivity graph (dDCG) DCG calculation Coupling computation Wavelet cross-correlation [Whitcher et al. , 2000, Achard et al. , 2006, Ali, 2009] � � cov ( d j w i [ k ] , d j w � j [ k − τ ]) d j w i , d j w ˆ = � ρ j , τ var ( d j w var ( d j w � i [ k ]) � j [ k − τ ]) The maximum MODWT cross-correlation (MMCC) is our formal coupling measure, MODWT: the maximal overlap discrete wavelet transform [Percival, 1995, Whitcher et al. , 2000] . � � � � ρ ( d j w i , d j w τ ∗ ij = arg max τ ( � ˆ j , τ ) � ) ρ max � � d j w i , d j w ρ ( d j w i , d j w j , τ ∗ ˆ = ˆ ij ) j Development of Differential Connectivity Graph 18/48

  4. Directed differential connectivity graph (dDCG) DCG calculation DCG construction Main idea of DCG: if the couplings between signal pair ( i , j ) change significantly ⇒ connection between nodes i and j . Statistically reliable. We use permutation method. Development of Differential Connectivity Graph 19/48

  5. Directed differential connectivity graph (dDCG) DCG calculation DCG construction Main idea of DCG: if the couplings between signal pair ( i , j ) change significantly ⇒ connection between nodes i and j . Statistically reliable. We use permutation method. Development of Differential Connectivity Graph 19/48

  6. Directed differential connectivity graph (dDCG) DCG calculation Permutation 1 number of possible connections C 1 C 1 C 1 IED . . . number of possible connections C 2 C 2 C 2 non-IED N p th permutation original couplings first permutation Development of Differential Connectivity Graph 20/48

  7. Directed differential connectivity graph (dDCG) DCG calculation Permutation 1 number of possible connections C 1 C 1 C 1 IED . . . . . . number of possible connections C 2 C 2 C 2 non-IED N p th permutation original couplings first permutation Multiple yes raw p-value adjusted p-value � α fw ? connection test estimation correction no no connection Development of Differential Connectivity Graph 20/48

  8. Directed differential connectivity graph (dDCG) DCG calculation Summary DCG is a new method for computation of graphs [Amini et al. , 2010 b ] . DCG focuses on connections whose couplings change significantly between two states. in this work, IED/non-IED generalized to other applications Main properties of DCG: Couplings are calculated in different frequency bands using wavelet J frequency bands: J DCGs DCG is statistically reliable, large number of IED and non-IED time intervals and permutation Development of Differential Connectivity Graph 21/48

  9. Directed differential connectivity graph (dDCG) Characterization of dDCG Outline Directed differential connectivity graph (dDCG) 1 Basic idea of DCG DCG calculation Characterization of dDCG Multiple graph analysis Experimental results 2 dDCG Leading IED regions Conclusion and Perspectives 3 Development of Differential Connectivity Graph 22/48

  10. Directed differential connectivity graph (dDCG) Characterization of dDCG Relevance of the nodes of directed DCG (dDCG) dDCG: set of brain regions involved in IED events. Definition: Source: the amount of emitting information > the amount of receiving information Sink: the amount of emitting information < the amount of receiving information Development of Differential Connectivity Graph 23/48

  11. Directed differential connectivity graph (dDCG) Characterization of dDCG Relevance of the nodes of directed DCG (dDCG) dDCG: set of brain regions involved in IED events. Definition: Source: the amount of emitting information > the amount of receiving information Sink: the amount of emitting information < the amount of receiving information Development of Differential Connectivity Graph 23/48

  12. Directed differential connectivity graph (dDCG) Characterization of dDCG Relevance of the nodes of directed DCG (dDCG) dDCG: set of brain regions involved in IED events. Definition: Source: the amount of emitting information > the amount of receiving information Sink: the amount of emitting information < the amount of receiving information Development of Differential Connectivity Graph 23/48

  13. Directed differential connectivity graph (dDCG) Characterization of dDCG Relevance of the nodes of directed DCG (dDCG) dDCG: set of brain regions involved in IED events. Definition: Source: the amount of emitting information > the amount of receiving information Sink: the amount of emitting information < the amount of receiving information assumption: this information is related to IED events source nodes are leading IED regions We aim to define the source nodes of directed DCG Development of Differential Connectivity Graph 23/48

  14. Directed differential connectivity graph (dDCG) Characterization of dDCG Can we use classic graph measures for source identification? Total degree ( TD ) = sum of outgoing edges - sum of ingoing edges the information carried by each edge is unknown. 3 2 4 7 1 5 6 Development of Differential Connectivity Graph 24/48

  15. Directed differential connectivity graph (dDCG) Characterization of dDCG Can we use classic graph measures for source identification? Total degree ( TD ) = sum of outgoing edges - sum of ingoing edges node 2: TD ( 2 ) = 1 − 2 = − 1 the information carried by each edge is unknown. 3 2 4 7 1 5 6 Development of Differential Connectivity Graph 24/48

  16. Directed differential connectivity graph (dDCG) Characterization of dDCG Global efficiency ( GE ) Definition: How efficient a node communicates with the rest of graph. Measuring GE? 3 2 4 7 1 5 6   3 1 2 3 4 1 2  ∞ ∞ 1 ∞ ∞ ∞ ∞     ∞ ∞ ∞ ∞ ∞ ∞ ∞    L G = 3 3 1 3 1 2 2     2 2 2 2 3 1 1     2 2 2 2 3 3 1 1 1 1 1 2 2 3 Development of Differential Connectivity Graph 25/48

  17. Directed differential connectivity graph (dDCG) Characterization of dDCG Global efficiency ( GE ) Definition: How efficient a node communicates with the rest of graph. Measuring GE? 3 2 4 7 1 5 6   3 1 2 3 4 1 2  ∞ ∞ 1 ∞ ∞ ∞ ∞     ∞ ∞ ∞ ∞ ∞ ∞ ∞    L G = 3 3 1 3 1 2 2     2 2 2 2 3 1 1     2 2 2 2 3 3 1 1 1 1 1 2 2 3 Development of Differential Connectivity Graph 25/48

  18. Directed differential connectivity graph (dDCG) Characterization of dDCG Global efficiency ( GE ) Definition: How efficient a node communicates with the rest of graph. Measuring GE? 3 2 4 7 1 5 6   3 1 2 3 4 1 2  ∞ ∞ 1 ∞ ∞ ∞ ∞     ∞ ∞ ∞ ∞ ∞ ∞ ∞    L G = 3 3 1 3 1 2 2     2 2 2 2 3 1 1     2 2 2 2 3 3 1 1 1 1 1 2 2 3 Development of Differential Connectivity Graph 25/48

  19. Directed differential connectivity graph (dDCG) Characterization of dDCG Global efficiency ( GE ) Definition: How efficient a node communicates with the rest of graph. Measuring GE? 3 2 ℓ 13 = 1 1 ℓ 13 = 2 ⇒ efficiency 13 = 2 4 7 1 1 ℓ 21 = ∞ ⇒ efficiency 21 = ℓ 21 = 0 5 6   3 1 2 3 4 1 2 E glob [ i ] = average j � = i ( 1  ∞ ∞ 1 ∞ ∞ ∞ ∞  ℓ ij )    ∞ ∞ ∞ ∞ ∞ ∞ ∞    L G = 3 3 1 3 1 2 2     2 2 2 2 3 1 1   E glob [ G ] = average i ( E glob [ i ])   2 2 2 2 3 3 1 1 1 1 1 2 2 3 Development of Differential Connectivity Graph 25/48

  20. Directed differential connectivity graph (dDCG) Characterization of dDCG Global efficiency ( GE ) Definition: How efficient a node communicates with the rest of graph. Measuring GE? we count the paths, but their related information are not considered. 3 2 ℓ 13 = 1 1 ℓ 13 = 2 ⇒ efficiency 13 = 2 4 7 1 1 ℓ 21 = ∞ ⇒ efficiency 21 = ℓ 21 = 0 5 6   3 1 2 3 4 1 2 E glob [ i ] = average j � = i ( 1  ∞ ∞ 1 ∞ ∞ ∞ ∞  ℓ ij )    ∞ ∞ ∞ ∞ ∞ ∞ ∞    L G = 3 3 1 3 1 2 2     2 2 2 2 3 1 1   E glob [ G ] = average i ( E glob [ i ])   2 2 2 2 3 3 1 1 1 1 1 2 2 3 Development of Differential Connectivity Graph 25/48

  21. Directed differential connectivity graph (dDCG) Characterization of dDCG Local efficiency ( LE ) Definition: How efficient a node communicates with its neighbors. Measuring LE? 3 2 4 7 1 5 6 Development of Differential Connectivity Graph 26/48

  22. Directed differential connectivity graph (dDCG) Characterization of dDCG Local efficiency ( LE ) Definition: How efficient a node communicates with its neighbors. Measuring LE? 3 2 3 2 4 7 1 4 1 5 6   ∞ 1 2 ∞  ∞ ∞ 1 ∞  L G7 − =   ∞ ∞ ∞ ∞ ∞ ∞ 1 ∞ Development of Differential Connectivity Graph 26/48

  23. Directed differential connectivity graph (dDCG) Characterization of dDCG Local efficiency ( LE ) Definition: How efficient a node communicates with its neighbors. Measuring LE? a node whose LE is high is not necessarily a source amount of information is not considered 3 2 3 2 4 7 1 4 1 5 6   ∞ 1 2 ∞  ∞ ∞ 1 ∞  L G7 − =   ∞ ∞ ∞ ∞ ∞ ∞ 1 ∞ Development of Differential Connectivity Graph 26/48

  24. Directed differential connectivity graph (dDCG) Characterization of dDCG Local information Local information ( LI ): amount of information passes through each node locally. LI [ a ] = � ab ]) − � V a → b MI ( d a [ k ] , d b [ k − τ ∗ V b → a MI ( d a [ k ] , d b [ k − τ ∗ ab ]) 3 2 a 4 1 5 6 Development of Differential Connectivity Graph 27/48

  25. Directed differential connectivity graph (dDCG) Characterization of dDCG Local information Local information ( LI ): amount of information passes through each node locally. LI [ a ] = � ab ]) − � V a → b MI ( d a [ k ] , d b [ k − τ ∗ V b → a MI ( d a [ k ] , d b [ k − τ ∗ ab ]) 3 2 a 4 1 5 6 the greater positive LI values, the greater relevance of node as a source. total degree of a weighted digraph. Development of Differential Connectivity Graph 27/48

  26. Directed differential connectivity graph (dDCG) Characterization of dDCG Local information Advantages of LI over classic measures weighted measure the information carried by each edge Disadvantages of LI local measure computationally heavy Development of Differential Connectivity Graph 28/48

  27. Directed differential connectivity graph (dDCG) Multiple graph analysis Outline Directed differential connectivity graph (dDCG) 1 Basic idea of DCG DCG calculation Characterization of dDCG Multiple graph analysis Experimental results 2 dDCG Leading IED regions Conclusion and Perspectives 3 Development of Differential Connectivity Graph 29/48

  28. Directed differential connectivity graph (dDCG) Multiple graph analysis Multiple graph analysis j = 1 LI 1 [ n ] dDCG estimated Multiple j = 2 iEEG leading Wavelet dDCG graph signals transform IED LI analysis regions LI : [ n ] J j = J dDCG N (#of nodes) One measure value � � LI : [ n ] = LI j = 1 [ n ] , LI j = 2 [ n ] , . . . , LI j = J [ n ] for node n ⇒ at frequency level j a vector of J components How to compare the relevance of two nodes LI : [ n ] and LI : [ n ′ ] ? Development of Differential Connectivity Graph 30/48

  29. Directed differential connectivity graph (dDCG) Multiple graph analysis Multiple graph analysis j = 1 dDCG estimated Multiple j = 2 iEEG leading Wavelet dDCG graph signals transform IED LI analysis regions LI : [ n ] LI : [ n ′ ] J j = J dDCG N (#of nodes) One measure value � � LI : [ n ] = LI j = 1 [ n ] , LI j = 2 [ n ] , . . . , LI j = J [ n ] for node n ⇒ at frequency level j a vector of J components How to compare the relevance of two nodes LI : [ n ] and LI : [ n ′ ] ? Development of Differential Connectivity Graph 30/48

  30. Directed differential connectivity graph (dDCG) Multiple graph analysis How to consider the LI values of all the frequency bands simultaneously? scalarization of LI : [ n ] into a single scalar value: e.g. max � LI : [ n ] � 2 solutions depend on the importance of the frequency bands the preference between different frequency bands is unknown Development of Differential Connectivity Graph 31/48

  31. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization methods (Pareto optimization) Multiple objective functions are optimized simultaneously � � LI j = 1 [ n ] , LI j = 2 [ n ] , . . . , LI j = J [ n ] [Deb, 1999] : max providing a set of optimal solutions: Pareto front = most relevant nodes = leading IED regions Pareto (1848-1923) Pareto optimization: in economics, and social science Development of Differential Connectivity Graph 32/48

  32. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization (MOP) methods j 2 Dominancy A A E C D F B j 1 nodes or points in 2 dimensions: 2 frequency bands j 1 and j 2 the basic concept of MOP: Definition of dominancy LI j [ A ] ≥ LI j [ D ] & ∃ j LI j [ A ] > LI j [ D ] node A dominates node D : ∀ j node C dominates node E We can reject nodes D and E Development of Differential Connectivity Graph 33/48

  33. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization (MOP) methods j 2 Dominancy LI j = j 2 [ A ] A A A E C D F B j 1 LI j = j 1 [ A ] nodes or points in 2 dimensions: 2 frequency bands j 1 and j 2 the basic concept of MOP: Definition of dominancy LI j [ A ] ≥ LI j [ D ] & ∃ j LI j [ A ] > LI j [ D ] node A dominates node D : ∀ j node C dominates node E We can reject nodes D and E Development of Differential Connectivity Graph 33/48

  34. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization (MOP) methods j 2 Dominancy A A E C D D F B j 1 nodes or points in 2 dimensions: 2 frequency bands j 1 and j 2 the basic concept of MOP: Definition of dominancy LI j [ A ] ≥ LI j [ D ] & ∃ j LI j [ A ] > LI j [ D ] node A dominates node D : ∀ j node C dominates node E We can reject nodes D and E Development of Differential Connectivity Graph 33/48

  35. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization (MOP) methods j 2 Dominancy A A E E C C D F B j 1 nodes or points in 2 dimensions: 2 frequency bands j 1 and j 2 the basic concept of MOP: Definition of dominancy LI j [ A ] ≥ LI j [ D ] & ∃ j LI j [ A ] > LI j [ D ] node A dominates node D : ∀ j node C dominates node E We can reject nodes D and E Development of Differential Connectivity Graph 33/48

  36. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization methods Pareto front j 2 A A E C C D F F B B j 1 nodes A , C , F , and B : Pareto front there is no node dominating these nodes these nodes do not dominate each other Pareto front: the set of non-dominated nodes Development of Differential Connectivity Graph 34/48

  37. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization methods Pareto front j 2 A A E C C D F F B B j 1 nodes A , C , F , and B : Pareto front there is no node dominating these nodes these nodes do not dominate each other Pareto front: the set of non-dominated nodes Development of Differential Connectivity Graph 34/48

  38. Directed differential connectivity graph (dDCG) Multiple graph analysis Multi-objective optimization methods Estimation of ℓ IED regions Nodes ∈ J -dimensional search space � � LI j = 1 [ n ] , LI j = 2 [ n ] , . . . , LI j = J [ n ] maximize Pareto front or estimated ℓ IED regions: Pareto optimization algorithm (classic) Neighbor-Pareto optimization algorithm (new) Development of Differential Connectivity Graph 35/48

  39. Experimental results Outline Directed differential connectivity graph (dDCG) 1 Basic idea of DCG DCG calculation Characterization of dDCG Multiple graph analysis Experimental results 2 dDCG Leading IED regions Conclusion and Perspectives 3 Development of Differential Connectivity Graph 36/48

  40. Experimental results dDCG Outline Directed differential connectivity graph (dDCG) 1 Basic idea of DCG DCG calculation Characterization of dDCG Multiple graph analysis Experimental results 2 dDCG Leading IED regions Conclusion and Perspectives 3 Development of Differential Connectivity Graph 37/48

  41. Experimental results dDCG Parameters of the patients’ iEEG Parameters of the five patients’ iEEG min max mean 104 111 106 iEEG bipolar channels 4950 6105 5551 possible number of connections 55.44 ≈ 2 × 10 6 samples 42 90 length of data (minutes) 160 614 304 number of IED time intervals 143 200 174 number of non-IED time intervals Development of Differential Connectivity Graph 38/48

  42. Experimental results dDCG Implantation scheme of iEEG electrodes for patient 3 The iEEG recordings are provided by Prof. P . Kahane and his colleagues in Neurology department of Grenoble hospital (CHUG). http://www.diximedical.net Development of Differential Connectivity Graph 39/48

  43. Experimental results dDCG dDCG iEEG recording’s of patient 3 (P3) for two time windows DCG of P3 in 4-8 Hz DCG overlaid on anatomical mesh Development of Differential Connectivity Graph 40/48

  44. Experimental results dDCG dDCG iEEG recording’s of patient 3 (P3) for two time windows DCG of P3 in 4-8 Hz DCG overlaid on anatomical mesh Development of Differential Connectivity Graph 40/48

  45. Experimental results dDCG dDCG iEEG recording’s of patient 3 (P3) for two time windows DCG of P3 in 4-8 Hz DCG overlaid on anatomical mesh Development of Differential Connectivity Graph 40/48

  46. Experimental results Leading IED regions Outline Directed differential connectivity graph (dDCG) 1 Basic idea of DCG DCG calculation Characterization of dDCG Multiple graph analysis Experimental results 2 dDCG Leading IED regions Conclusion and Perspectives 3 Development of Differential Connectivity Graph 41/48

  47. Experimental results Leading IED regions Qualitative comparison between LI and classic measures P1 antHC postHC amyg pHcG mTP global efficiency × × × local efficiency ∗ × × × × × total degree × × local information using Pareto opt × × × visually inspected SOZ × × × × × P2 antHC postHC amyg pHcG global efficiency × local efficiency × × × total degree × × local information using Pareto opt × × × × × visually inspected SOZ P3 antHC postHC pHcG global efficiency × × × local efficiency × × × total degree × × local information using Pareto opt × × visually inspected SOZ × × × antHC postHC amyg entCx mTP an P4 global efficiency × × × × × local efficiency × × × total degree × × × local information using Pareto opt × × × × visually inspected SOZ × × × × × P5 midInsG global efficiency × local efficiency NA total degree × local information using Pareto opt × visually inspected SOZ × amyg: amygdala; ant/post/m: anterior/posterior/mesial; CG: cingulate gyrus; entCx: entorhinal cortex; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not applicable; opt: optimization. Development of Differential Connectivity Graph 42/48

  48. Experimental results Leading IED regions Quantitative comparison between LI and classic measures Definition ( Assumption: vSOZ are ground truth ) TP = No. common regions between ℓ IED regions and vSOZ FN = No. uncommon regions FP = No. ℓ IED regions not included in vSOZ TP Precision = TP + FP TP Sensitivity = TP + FN Development of Differential Connectivity Graph 43/48

  49. Experimental results Leading IED regions Quantitative comparison between LI and classic measures Definition ( Assumption: vSOZ are ground truth ) TP = No. common regions between ℓ IED regions and vSOZ FN = No. uncommon regions FP = No. ℓ IED regions not included in vSOZ TP Precision = TP + FP TP Sensitivity = TP + FN Interpretation Precision = 1 if FP = 0; FP � = 0: extra regions are provided. Sensitivity = 1 if FN = 0; FN � = 0: some regions are missed. trade off between FP and FN . Development of Differential Connectivity Graph 43/48

  50. Experimental results Leading IED regions Quantitative comparison between LI and classic measures Definition ( Assumption: vSOZ are ground truth ) TP = No. common regions between ℓ IED regions and vSOZ FN = No. uncommon regions FP = No. ℓ IED regions not included in vSOZ TP Precision = TP + FP TP Sensitivity = TP + FN Interpretation Precision = 1 if FP = 0; FP � = 0: extra regions are provided. Sensitivity = 1 if FN = 0; FN � = 0: some regions are missed. trade off between FP and FN . Remarks antHC postHC pHcG P3 global efficiency × × × LI : more precise and informative local efficiency × × × total degree × × Neighbor-Pareto optimization: relevance local information Pareto × × visually inspected SOZ × × × of ℓ IED regions Development of Differential Connectivity Graph 43/48

  51. Experimental results Leading IED regions Quantitative comparison between LI and classic measures Definition ( Assumption: vSOZ are ground truth ) TP = No. common regions between ℓ IED regions and vSOZ FN = No. uncommon regions FP = No. ℓ IED regions not included in vSOZ TP Precision = TP + FP TP Sensitivity = TP + FN Interpretation Precision = 1 if FP = 0; FP � = 0: extra regions are provided. Sensitivity = 1 if FN = 0; FN � = 0: some regions are missed. trade off between FP and FN . Remarks antHC postHC pHcG P3 global efficiency × × × LI : more precise and informative local efficiency × × × total degree × × Neighbor-Pareto optimization: relevance local information N-Pareto × × × visually inspected SOZ × × × of ℓ IED regions Development of Differential Connectivity Graph 43/48

  52. Experimental results Leading IED regions Comparison between proposed method and other classic methods Methods vSOZ and removed regions: by epileptologists P1 antHC postHC amyg pHcG mTP antsupTG visually inspected SOZ × × × × × removed region × × × × × × electrically stimulated SOZ × eSOZ: by [David et al. , 2008] ℓ IED using LI and Pareto opt × × × P2 antHC postHC amyg pHcG TP visually inspected SOZ × × × × removed region × × × × × electrically stimulated SOZ × × ℓ IED using LI and Pareto opt: ℓ IED using LI and Pareto opt × our method P3 antHC postHC pHcG TP visually inspected SOZ × × × removed region × × × × electrically stimulated SOZ × ℓ IED using LI and Pareto opt × × P4 antHC postHC amyg entCx mTP antCG visually inspected SOZ × × × × × removed region × × × × × electrically stimulated SOZ - ℓ IED using LI and Pareto opt × × × × P5 midInsG visually inspected SOZ × removed region × electrically stimulated SOZ NA ℓ IED using LI and Pareto opt × amyg: amygdala; ant/post/m/sup: anterior/posterior/mesial/superior; CG: cingulate gyrus; entCx: entorhinal cortex; G: gyrus; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not applicable. Development of Differential Connectivity Graph 44/48

  53. Experimental results Leading IED regions Comparison between proposed method and other classic methods Methods vSOZ and removed regions: by epileptologists P1 antHC postHC amyg pHcG mTP antsupTG × × × × × visually inspected SOZ removed region × × × × × × electrically stimulated SOZ × eSOZ: by [David et al. , 2008] ℓ IED using LI and Pareto opt × × × P2 antHC postHC amyg pHcG TP × × × × visually inspected SOZ removed region × × × × × electrically stimulated SOZ × × ℓ IED using LI and Pareto opt: ℓ IED using LI and Pareto opt × our method P3 antHC postHC pHcG TP visually inspected SOZ × × × removed region × × × × electrically stimulated SOZ × ℓ IED using LI and Pareto opt × × P4 antHC postHC amyg entCx mTP antCG visually inspected SOZ × × × × × removed region × × × × × electrically stimulated SOZ - ℓ IED using LI and Pareto opt × × × × P5 midInsG visually inspected SOZ × removed region × electrically stimulated SOZ NA ℓ IED using LI and Pareto opt × amyg: amygdala; ant/post/m/sup: anterior/posterior/mesial/superior; CG: cingulate gyrus; entCx: entorhinal cortex; G: gyrus; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not applicable. Development of Differential Connectivity Graph 44/48

  54. Experimental results Leading IED regions Comparison between proposed method and other classic methods Methods vSOZ and removed regions: by epileptologists P1 antHC postHC amyg pHcG mTP antsupTG × × × × × visually inspected SOZ removed region × × × × × × electrically stimulated SOZ × eSOZ: by [David et al. , 2008] ℓ IED using LI and Pareto opt × × × P2 antHC postHC amyg pHcG TP × × × × visually inspected SOZ × × × × × removed region electrically stimulated SOZ × × ℓ IED using LI and Pareto opt: ℓ IED using LI and Pareto opt × our method P3 antHC postHC pHcG TP visually inspected SOZ × × × × × × × removed region electrically stimulated SOZ × ℓ IED using LI and Pareto opt × × P4 antHC postHC amyg entCx mTP antCG visually inspected SOZ × × × × × removed region × × × × × electrically stimulated SOZ - ℓ IED using LI and Pareto opt × × × × P5 midInsG visually inspected SOZ × removed region × electrically stimulated SOZ NA ℓ IED using LI and Pareto opt × amyg: amygdala; ant/post/m/sup: anterior/posterior/mesial/superior; CG: cingulate gyrus; entCx: entorhinal cortex; G: gyrus; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not applicable. Development of Differential Connectivity Graph 44/48

  55. Experimental results Leading IED regions Comparison between proposed method and other classic methods Methods vSOZ and removed regions: by epileptologists P1 antHC postHC amyg pHcG mTP antsupTG × × × × × visually inspected SOZ removed region × × × × × × electrically stimulated SOZ × eSOZ: by [David et al. , 2008] ℓ IED using LI and Pareto opt × × × P2 antHC postHC amyg pHcG TP × × × × visually inspected SOZ × × × × × removed region electrically stimulated SOZ × × ℓ IED using LI and Pareto opt: ℓ IED using LI and Pareto opt × our method P3 antHC postHC pHcG TP visually inspected SOZ × × × × × × × removed region × electrically stimulated SOZ ℓ IED using LI and Pareto opt × × P4 antHC postHC amyg entCx mTP antCG visually inspected SOZ × × × × × removed region × × × × × electrically stimulated SOZ - ℓ IED using LI and Pareto opt × × × × P5 midInsG visually inspected SOZ × removed region × electrically stimulated SOZ NA ℓ IED using LI and Pareto opt × amyg: amygdala; ant/post/m/sup: anterior/posterior/mesial/superior; CG: cingulate gyrus; entCx: entorhinal cortex; G: gyrus; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not applicable. Development of Differential Connectivity Graph 44/48

  56. Experimental results Leading IED regions Comparison between proposed method and other classic methods Methods vSOZ and removed regions: by epileptologists P1 antHC postHC amyg pHcG mTP antsupTG × × × × × visually inspected SOZ removed region × × × × × × electrically stimulated SOZ × eSOZ: by [David et al. , 2008] ℓ IED using LI and Pareto opt × × × P2 antHC postHC amyg pHcG TP × × × × visually inspected SOZ × × × × × removed region electrically stimulated SOZ × × ℓ IED using LI and Pareto opt: ℓ IED using LI and Pareto opt × our method P3 antHC postHC pHcG TP visually inspected SOZ × × × × × × × removed region × electrically stimulated SOZ ℓ IED using LI and Pareto opt × × P4 antHC postHC amyg entCx mTP antCG visually inspected SOZ × × × × × removed region × × × × × electrically stimulated SOZ - × × × × ℓ IED using LI and Pareto opt P5 midInsG visually inspected SOZ × removed region × electrically stimulated SOZ NA × ℓ IED using LI and Pareto opt amyg: amygdala; ant/post/m/sup: anterior/posterior/mesial/superior; CG: cingulate gyrus; entCx: entorhinal cortex; G: gyrus; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not applicable. Development of Differential Connectivity Graph 44/48

  57. Experimental results Leading IED regions Comparison between proposed method and other classic methods Methods vSOZ and removed regions: by epileptologists P1 antHC postHC amyg pHcG mTP antsupTG × × × × × visually inspected SOZ removed region × × × × × × electrically stimulated SOZ × eSOZ: by [David et al. , 2008] ℓ IED using LI and Pareto opt × × × P2 antHC postHC amyg pHcG TP × × × × visually inspected SOZ × × × × × removed region electrically stimulated SOZ × × ℓ IED using LI and Pareto opt: ℓ IED using LI and Pareto opt × our method P3 antHC postHC pHcG TP visually inspected SOZ × × × × × × × removed region × electrically stimulated SOZ Remarks ℓ IED using LI and Pareto opt × × P4 antHC postHC amyg entCx mTP antCG visually inspected SOZ × × × × × ℓ IED: congruent with vSOZ, removed region × × × × × electrically stimulated SOZ - removed regions, and eSOZ × × × × ℓ IED using LI and Pareto opt P5 midInsG visually inspected SOZ × removed region × ℓ IED: reliable results for electrically stimulated SOZ NA × presurgery evaluations ℓ IED using LI and Pareto opt amyg: amygdala; ant/post/m/sup: anterior/posterior/mesial/superior; CG: cingulate gyrus; entCx: entorhinal cortex; G: gyrus; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not applicable. Development of Differential Connectivity Graph 44/48

  58. Experimental results Leading IED regions Comparison between proposed method and other classic methods Methods vSOZ and removed regions: by epileptologists P1 antHC postHC amyg pHcG mTP antsupTG visually inspected SOZ × × × × × removed region × × × × × × electrically stimulated SOZ × eSOZ: by [David et al. , 2008] ℓ IED using LI and Pareto opt × × × P2 antHC postHC amyg pHcG TP visually inspected SOZ × × × × removed region × × × × × electrically stimulated SOZ × × ℓ IED using LI and Pareto opt: ℓ IED using LI and Pareto opt × our method P3 antHC postHC pHcG TP visually inspected SOZ × × × removed region × × × × electrically stimulated SOZ × Remarks ℓ IED using LI and Pareto opt × × P4 antHC postHC amyg entCx mTP antCG visually inspected SOZ × × × × × ℓ IED: congruent with vSOZ, removed region × × × × × electrically stimulated SOZ - removed regions, and eSOZ ℓ IED using LI and Pareto opt × × × × P5 midInsG visually inspected SOZ × removed region × ℓ IED: reliable results for electrically stimulated SOZ NA × presurgery evaluations ℓ IED using LI and Pareto opt amyg: amygdala; ant/post/m/sup: anterior/posterior/mesial/superior; CG: cingulate gyrus; entCx: entorhinal cortex; G: gyrus; HC: hippocampus; Ins: insula; midInsG: middle short gyrus of insula; pHcG: parahippocampal gyrus; T: temporal; TP: temporal pole; NA: not ℓ IED: without using seizures. applicable. Development of Differential Connectivity Graph 44/48

  59. Conclusion and Perspectives Outline Directed differential connectivity graph (dDCG) 1 Basic idea of DCG DCG calculation Characterization of dDCG Multiple graph analysis Experimental results 2 dDCG Leading IED regions Conclusion and Perspectives 3 Development of Differential Connectivity Graph 45/48

  60. Conclusion and Perspectives Conclusion Methodological point of view Development of DCG: identify the reliable discriminated connections between two states [Amini et al. , 2010 b ] Local information [Amini et al. , 2010 a ] Integration of advanced/reliable methods Pareto optimization [Deb, 1999] Permutation [Pollard & van der Laan, 2003] Application point of view ℓ IED regions (based on IEDs) congruent with vSOZ (based on seizures) Development of Differential Connectivity Graph 46/48

  61. Conclusion and Perspectives Perspective Methodological point of view Automatic IED labelling Estimating ℓ IED regions from scalp EEG (noninvasive) General application of DCG Application point of view Using larger number of patients for the relationship ℓ IED/SOZ. Development of Differential Connectivity Graph 47/48

  62. Conclusion and Perspectives List of Related Publications Journals 1 L. Amini, C. Jutten, S. Achard, O. David, P . Kahane, L. Vercueil, L. Minotti, G. A. Hossein-Zadeh, and H. Soltanian-Zade, Comparison Of Five Directed Graph Measures For Identification Of Leading Interictal Epileptic Regions, Physiological Measurements , Physiol. Meas. , vol. 31, pp. 1529-1546, 2010. 2 L. Amini, C. Jutten, S. Achard, O. David, H. Soltanian-Zadeh, G. A. Hossein-Zadeh, P . Kahane, L. Minotti, and L. Vercueil, Directed Differential Connectivity Graph Of Interictal Epileptiform Discharges, accepted in IEEE Trans. Biomed. Eng. . Conferences 1 L. Amini, R. Sameni, C. Jutten, G. A. Hossein-Zadeh, and H. Soltanian-Zadeh, MR Artifact Reduction in the Simultaneous Acquisition of EEG and fMRI of Epileptic Patients, Proc. of 16th European Signal Processing Conference (EUSIPCO), Lausanne, Switzerland , August 25-29, 2008. 2 L. Amini, S. Achard, C. Jutten, G.A. Hossein-Zadeh, and H. Soltanian-Zadeh, Connectivity Analysis of EEG Recordings for Epileptic Patients, The 10th International Conference On Cognitive Neuroscience (ICON X), Bodrum, Turkey , September 1-5, 2008. 3 L. Amini, S. Achard, C. Jutten, H. Soltanian-Zadeh, G. A. Hossein-Zadeh, O. David, and L. Vercueil, Sparse Differential Connectivity Graph of Scalp EEG for Epileptic Patients, Proc. of the 17th European Symposium on Artificial Neural Networks (ESANN), Bruges, Belgium , April 22-24, 2009. 4 L. Amini, C. Jutten, S. Achard, O. David, H. Soltanian-Zadeh, G. A. Hossein-Zadeh, P . Kahane, L. Minotti, and L. Vercueil, Directed Epileptic Network From Scalp And Intracranial EEG Of Epileptic Patients, Proc. of the IEEE International Workshop On Machine Learning For Signal Processing (MLSP), Grenoble, France , September 2-4, 2009. Development of Differential Connectivity Graph 48/48

  63. Appendix Outline Appendix 4 Development of Differential Connectivity Graph 49/48

  64. Appendix Graphs Graph is a set pair of nodes (associated with iEEG bipolar channels or bipolar electrode leads) and edges (or connections). Particular directed graph (digraph): oriented graphs. Development of Differential Connectivity Graph 50/48

  65. Appendix Wavelet transform Wavelet coefficients of a typical iEEG channel in different frequency bands Development of Differential Connectivity Graph 51/48

  66. Appendix Wavelet transform c j + 1 [ k ] = h j [ − k ] ∗ c j i [ k ] , j = 0 , . . . , J − 1 i d j + 1 [ k ] = g j [ − k ] ∗ c j i [ k ] , j = 0 , . . . , J − 1 i � h j [ k 2 ] , k even h j + 1 [ k ] = 0 , k odd Development of Differential Connectivity Graph 52/48

  67. Appendix IED and non-IED segment matrices IED and non-IED m = 1 detection . . . L 1 j = 1 . . S 1 . J m T 1 s 1 m im s l im T l m N m M j = X wavelet 1 X . . . L 2 T T x i d j i S 2 N N m T 2 s 2 m im N J wavelet IED and non- iEEG coefficient IED segment signals matrices matrices of level j 0 Development of Differential Connectivity Graph 53/48

  68. Appendix Multiple testing � H n µ 1 n = µ 2 0 : n H n µ 1 n � = µ 2 1 : n µ 1 µ 2 � n − � n t n = � 2 2 ( � n ) + ( � n ) σ 1 σ 2 L 1 L 2 � � � � � � � t n p card ( n p | � > | t n | ) n p [ n ] = N p � a [ i ] = max ( a [ i − 1 ] , 1 − ( 1 − p [ i ]) N c − i + 1 ) 2 ≤ i ≤ N c a [ 1 ] = 1 − ( 1 − p [ 1 ]) N c i = 1 Development of Differential Connectivity Graph 54/48

  69. Appendix Time delay estimation nodes i and j ∈ DCG d j w i and d j w j : wavelet coefficients of signal pair ( i , j ) in frequency band related to j w for the whole selected time for processing. � � d j w i [ k ] , d j w � � � cov j [ k − τ ] d j w i , d j w � ρ � j , τ = var ( d j w var ( d j w � i [ k ]) � j [ k − τ ]) � � �� � � τ ∗ j w d j w i , d j w �� = arg max ( ρ j , τ � ) ij τ Development of Differential Connectivity Graph 55/48

  70. Appendix Reliability of time delay estimation Development of Differential Connectivity Graph 56/48

  71. Appendix Reliability of time delay estimation Jackknife method: For N w = 100 windows of length W = 20 minutes, the time delay τ ∗ j w is ij estimated. W is large enough to include enough number of IEDs. τ ∗ j w ¯ = arg max u (ˆ ( u )) p τ ∗ jw ij ij τ ∗ j w × τ ∗ j w #(¯ > 0 ) / #( edges ) is in the range [ 78 95 ]% for different frequency ij ij bands. Remarks τ ∗ j w can provide reliable estimation of the most probable time lag if: ij significant couplings length of signal pairs are long enough for a proper estimation of CCF τ max is chosen properly. Development of Differential Connectivity Graph 57/48

  72. Appendix Reliability of time delay estimation Jackknife method: Frequency (Hz) 2-4 4-8 8-16 16-32 32-64 τ ∗ j w × τ ∗ j w #(¯ > 0 ) / # (edges) 94/110 74/82 41/43 18/23 8/9 ij ij percentage ( % ) 85 90 95 78 88 Development of Differential Connectivity Graph 58/48

  73. Appendix Choice of τ max in dDCG increase of τ max ⇒ increases the bias & variance (length of overlapped signals) of time delay estimation. decreasing τ max less than the true time delay ⇒ missing the time delay τ max : the smallest value of the maximum physiological constraint. We need to know the range of physiological constraints (IED propagation delay < [ 50 200 ] msec). Development of Differential Connectivity Graph 59/48

  74. Appendix (a) 2-4 Hz, τ max = 100 samples (b) 4-8 Hz, τ max = 100 samples (c) 2-4 Hz, τ max = 16 samples (d) 4-8 Hz, τ max = 16 samples Development of Differential Connectivity Graph 60/48

  75. Appendix Pretest for testing the significance of each edge of DCG The effect of adding a pretest Connections whose couplings are significantly greater than the threshold for both IED and non-IED states are entered the multiple testing. � H n µ l 0 : n ≤ 0.3 H n µ l 1 : n > 0.3 Development of Differential Connectivity Graph 61/48

  76. Appendix Pretest for testing the significance of each edge of DCG Comparison Similarity percentage: the normalized sum of common number of significant or non-significant t-values over number of possible connections. Remarks most of the connections of the DCG have significantly large couplings in both IED and non-IED time intervals DCG is designed to detect the connections whose couplings change significantly between IED and non-IED time intervals Similarity percentage 2-4 4-8 8-16 16-32 32-64 P1 96.83 92.53 94.45 97.65 99.27 P2 100 99.95 99.54 99.69 99.87 Development of Differential Connectivity Graph 62/48

  77. Appendix Different frequency bands Why wavelet transform? Wavelet transforms are well adapted for the analysis of non-stationary EEG signals [Clark et al. , 1995, Senhadji & Wendling, 2002, Adeli et al. , 2003, Yamaguchi, 2003, Indiradevi et al. , 2008, Conlon et al. , 2009] . Provide automatic frequency selection. Narrower bands for lower frequencies. Daubechies mother wavelets are a proper choice for filtering IED signals [Adeli et al. , 2003] . We calculated DCGs for different frequency bands using wavelet transform. Development of Differential Connectivity Graph 63/48

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