Abstract
The visual interpretation of intracranial EEG (iEEG) is the standard method used in complex epilepsy surgery cases to map the regions of seizure onset targeted for resection. Still, visual iEEG analysis is labor-intensive and biased due to interpreter dependency. Multivariate parametric functional connectivity measures using adaptive autoregressive (AR) modeling of the iEEG signals based on the Kalman filter algorithm have been used successfully to localize the electrographic seizure onsets. Due to their high computational cost, these methods have been applied to a limited number of iEEG time-series (<60). The aim of this study was to test two Kalman filter implementations, a well-known multivariate adaptive AR model (Arnold et al. 1998) and a simplified, computationally efficient derivation of it, for their potential application to connectivity analysis of high-dimensional (up to 192 channels) iEEG data. When used on simulated seizures together with a multivariate connectivity estimator, the partial directed coherence, the two AR models were compared for their ability to reconstitute the designed seizure signal connections from noisy data. Next, focal seizures from iEEG recordings (73–113 channels) in three patients rendered seizure-free after surgery were mapped with the outdegree, a graph-theory index of outward directed connectivity. Simulation results indicated high levels of mapping accuracy for the two models in the presence of low-to-moderate noise cross-correlation. Accordingly, both AR models correctly mapped the real seizure onset to the resection volume. This study supports the possibility of conducting fully data-driven multivariate connectivity estimations on high-dimensional iEEG datasets using the Kalman filter approach.
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References
Andrzejak RG, David O, Gnatkovsky V et al (2015) Localization of epileptogenic zone on pre-surgical intracranial EEG recordings: toward a validation of quantitative signal analysis approaches. Brain Topogr 28:832–837
Arnold M, Miltner WH, Witte H, Bauer R, Braun C (1998) Adaptive AR modeling of nonstationary time series by means of Kalman filtering. IEEE Trans Biomed Eng 45:553–562
Astolfi L, Cincotti F, Mattia D et al (2008) Tracking the time-varying cortical connectivity patterns by adaptive multivariate estimators. IEEE Trans Biomed Eng 55:902–913
Baccalá LA, Sameshima K (2001) Partial directed coherence: a new concept in neural structure determination. Biol Cybern 84:463–474
Baccalá LA, de Brito CS, Takahashi DY, Sameshima K (2013) Unified asymptotic theory for all partial directed coherence forms. Philos Trans A Math Phys Eng Sci 371:20120158
Bishara AJ, Hittner JB (2012) Testing the significance of a correlation with nonnormal data: comparison of pearson, spearman, transformation, and resampling approaches. Psychol Methods 17:399–417
Blinowska KJ (2011) Review of the methods of determination of directed connectivity from multichannel data. Med Biol Eng Comput 49:521–529
Brodbeck V, Spinelli L, Lascano AM et al (2011) Electroencephalographic source imaging: a prospective study of 152 operated epileptic patients. Brain 134:2887–2897
Bulacio JC, Jehi L, Wong C et al (2012) Long-term seizure outcome after resective surgery in patients evaluated with intracranial electrodes. Epilepsia 53:1722–1730
Carrette E, Vonck K, De Herdt V et al (2010) Predictive factors for outcome of invasive video-EEG monitoring and subsequent resective surgery in patients with refractory epilepsy. Clin Neurol Neurosurg 112:118–126
Ding M, Bressler SL, Yang W, Liang H (2000) Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment. Biol Cybern 83:35–45
Enatsu R, Jin K, Elwan S, Kubota Y et al (2012) Correlations between ictal propagation and response to electrical cortical stimulation: a cortico-cortical evoked potential study. Epilepsy Res 101:76–87
Englot DJ, Modi B, Mishra AM, DeSalvo M, Hyder F, Blumenfeld H (2009) Cortical deactivation induced by subcortical network dysfunction in limbic seizures. J Neurosci 29:13006–13018
Florin E, Gross J, Pfeifer J, Fink GR, Timmermann L (2011) Reliability of multivariate causality measures for neural data. J Neurosci Methods 198:344–358
Granger CWJ (1969) Investigating causal relations by econometric models and crossspectral methods. Econometrica 37:424–438
He B, Dai Y, Astolfi L, Babiloni F, Yuan H, Yang L (2011) eConnectome: a MATLAB toolbox for mapping and imaging of brain functional connectivity. J Neurosci Methods 195:261–269
Jiménez-Jiménez D, Nekkare R, Flores L et al (2015) Prognostic value of intracranial seizure onset patterns for surgical outcome of the treatment of epilepsy. Clin Neurophysiol 126:257–267
Jouny CC, Adamolekun B, Franaszczuk PJ, Bergey GK (2007) Intrinsic ictal dynamics at the seizure focus: effects of secondary generalization revealed by complexity measures. Epilepsia 48:297–304
Kalman RE (1960) A new approach to linear filtering and prediction theory. J Basic Eng 82:34–45
Kalman RE, Bucy RS (1961) New results on linear filtering and prediction theory. J Basic Eng 83:95–108
Kasess CH (2002) Estimation of time-variant multivariate autoregressive models using Kalman filtering, dissertation, Graz University of Technology, Graz
Korzeniewska A, Mańczak M, Kamiński M, Blinowska KJ, Kasicki S (2003) Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method. J Neurosci Methods 125:195–207
Korzeniewska A, Cervenka MC, Jouny CC et al (2014) Ictal propagation of high frequency activity is recapitulated in interictal recordings: effective connectivity of epileptogenic networks recorded with intracranial EEG. Neuroimage 101:96–113
Leonardi N, Van De Ville D (2015) On spurious and real fluctuations of dynamic functional connectivity during rest. Neuroimage 104:430–436
Lie OV, Papanastassiou AM, Cavazos JE, Szabó ÁC (2015) Influence of intracranial electrode density and spatial configuration on interictal spike localization: a case study. J Clin Neurophysiol 32:e30–e40
Milde T, Leistritz L, Astolfi L et al (2010) A new Kalman filter approach for the estimation of high-dimensional time-variant multivariate AR models and its application in analysis of laser-evoked brain potentials. Neuroimage 50:960–969
Moeller F, Muthuraman M, Stephani U, Deuschl G, Raethjen J, Siniatchkin M (2013) Representation and propagation of epileptic activity in absences and generalized photoparoxysmal responses. Hum Brain Mapp 34:1896–1909
Molenaar PC, Beltz AM, Gates KM, Wilson SJ (2016) State space modeling of time-varying contemporaneous and lagged relations in connectivity maps. Neuroimage 125:791–802
Morrell MJ, RNS System in Epilepsy Study Group (2011) Responsive cortical stimulation for the treatment of medically intractable partial epilepsy. Neurology 77:1295–1304
Mullen T, Acar ZA, Worrell G, Makeig S (2011) Modeling cortical source dynamics and interactions during seizure. Conf Proc IEEE Eng Med Biol Soc 2011:1411–1414
Omidvarnia AH, Mesbah M, Khlif MS, O’Toole JM, Colditz PB, Boashash B (2011) Kalman filter-based time-varying cortical connectivity analysis of newborn EEG. Conf Proc IEEE Eng Med Biol Soc 2011:1423–1426
Plomp G, Quairiaux C, Michel CM, Astolfi L (2014) The physiological plausibility of time-varying Granger-causal modeling: normalization and weighting by spectral power. Neuroimage 97:16–206
Plomp G, Astolfi L, Coito A, Michel CM (2015) Spectrally weighted Granger-causal modeling: motivation and applications to data from animal models and epileptic patients. Conf Proc IEEE Eng Med Biol Soc 2015:5392–5395
Rosenow F, Lüders H (2001) Presurgical evaluation of epilepsy. Brain 124:1683–1700
Schlögl A (2000) The electroencephalogram and the adaptive autoregressive model: theory and applications. Shaker Verlag, Aachen
Schlögl A, Supp G (2006) Analyzing event-related EEG data with multivariate autoregressive parameters. Prog Brain Res 159:135–147
Sinha N, Dauwels J, Wang Y, Cash SS, Taylor PN (2014) An in silico approach for pre-surgical evaluation of an epileptic cortex. Conf Proc IEEE Eng Med Biol Soc 2014:4884–4887
Sommerlade L, Thiel M, Platt B et al (2012) Inference of Granger causal time-dependent influences in noisy multivariate time series. J Neurosci Methods 203:173–185
Stufflebeam SM, Liu H, Sepulcre J, Tanaka N, Buckner RL, Madsen JR (2011) Localization of focal epileptic discharges using functional connectivity magnetic resonance imaging. J Neurosurg 114:1693–1697
Toppi J, Babiloni F, Vecchiato G et al (2012) Towards the time varying estimation of complex brain connectivity networks by means of a General Linear Kalman Filter approach. Conf Proc IEEE Eng Med Biol Soc 2012:6192–6195
van Dellen E, Douw L, Baayen JC et al (2009) Long-term effects of temporal lobe epilepsy on local neural networks: a graph theoretical analysis of corticography recordings. PLoS One 4:e8081
van Mierlo P, Carrette E, Hallez H et al (2011) Accurate epileptogenic focus localization through time-variant functional connectivity analysis of intracranial electroencephalographic signals. Neuroimage 56:1122–1133
van Mierlo P, Carrette E, Hallez H et al (2013) Ictal-onset localization through connectivity analysis of intracranial EEG signals in patients with refractory epilepsy. Epilepsia 54:1409–1418
van Mierlo P, Papadopoulou M, Carrette E et al (2014) Functional brain connectivity from EEG in epilepsy: seizure prediction and epileptogenic focus localization. Prog Neurobiol 121:19–35
Varotto G, Franceschetti S, Spreafico R, Tassi L, Panzica F (2010) Partial directed coherence estimated on stereo-EEG signals in patients with Taylor’s type focal cortical dysplasia. Conf Proc IEEE Eng Med Biol Soc 2010:4646–4649
Varotto G, Tassi L, Franceschetti S, Spreafico R, Panzica F (2012) Epileptogenic networks of type II focal cortical dysplasia: a stereo-EEG study. Neuroimage 61:591–598
Vidaurre C, Sander TH, Schlögl A (2011) BioSig: the free and open source software library for biomedical signal processing. Comput Intell Neurosci 2011:935364
Wang HE, Bénar CG, Quilichini PP, Friston KJ, Jirsa VK, Bernard C (2014) A systematic framework for functional connectivity measures. Front Neurosci 8:405
Wilke C, Ding L, He B (2008) Estimation of time-varying connectivity patterns through the use of an adaptive directed transfer function. IEEE Trans Biomed Eng 55:2557–2564
Wilke C, van Drongelen W, Kohrman M, He B (2009) Identification of epileptogenic foci from causal analysis of ECoG interictal spike activity. Clin Neurophysiol 120(8):1449–1456
Wilke C, van Drongelen W, Kohrman M, He B (2010) Neocortical seizure foci localization by means of a directed transfer function method. Epilepsia 51(4):564–572
Wilke C, Worrell G, He B (2011) Graph analysis of epileptogenic networks in human partial epilepsy. Epilepsia 52(1):84–93
Yaffe RB, Borger P, Megevand P et al (2015) Physiology of functional and effective networks in epilepsy. Clin Neurophysiol 126:227–236
Acknowledgments
This project has received Funding from the University of Texas Health Science Center at San Antonio School of Medicine/Institute for Integration of Medicine and Science Grant No. 158580 (O.L.); and the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 660230 (P.vM.).
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Octavian V. Lie and Pieter van Mierlo have contributed equally to this work.
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10548_2016_527_MOESM1_ESM.eps
Supplementary material 1 (EPS 43840 kb). Colocalization of the seizure-onset estimates based on outdegree and the resection volume (patient 2). a. preictal baseline and EEG seizure onset (arrow) in the 50-channel dataset (upper), and the corresponding outdegree-over-time maps derived from connectivity analyses using m1/iAWPDC (middle) and m2/iAWPDC (lower). Boxed channels fall within the resection volume; b. EEG recording of the same seizure in the full (n=73) channel dataset (upper), and the corresponding outdegree-over-time map using m2/iAWPDC (lower)
10548_2016_527_MOESM2_ESM.eps
Supplementary material 2 (EPS 2370 kb). Dynamic correlation of the outdegree maps estimated based on m1 and m2 (patient 2). Time-matched Pearson correlation of the outdegree values resulting from m1 or m2 application. c- channel, rho- mean Pearson correlation coefficient
10548_2016_527_MOESM3_ESM.eps
Supplementary material 3 (EPS 47184 kb). Colocalization of the seizure-onset estimates based on outdegree and the resection volume (patient 3). a. preictal baseline and EEG seizure onset (arrow) in the 50-channel dataset (upper), and the corresponding outdegree-over-time maps derived from connectivity analyses using m1/iAWPDC (middle) and m2/iAWPDC (lower). Boxed channels fall within the resection volume; b. EEG recording of the same seizure in the full (n=91) channel dataset (upper), and the corresponding outdegree-over-time map using m2/iAWPDC (lower)
10548_2016_527_MOESM4_ESM.eps
Supplementary material 4 (EPS 2585 kb). Dynamic correlation of the outdegree maps estimated based on m1 and m2 (patient 3). Time-matched Pearson correlation of the outdegree values resulting from m1 or m2 application. c- channel, rho- mean Pearson correlation coefficient
10548_2016_527_MOESM5_ESM.eps
Supplementary material 5 (EPS 1675 kb). Functional connectivity analysis of a seizure recorded with high-density iEEG. a. designed signal matrix for a seizure signal involving 80 ictal channels added to random background noise; b. The connectivity matrix of the 192-channel seizure
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Lie, O.V., van Mierlo, P. Seizure-Onset Mapping Based on Time-Variant Multivariate Functional Connectivity Analysis of High-Dimensional Intracranial EEG: A Kalman Filter Approach. Brain Topogr 30, 46–59 (2017). https://doi.org/10.1007/s10548-016-0527-x
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DOI: https://doi.org/10.1007/s10548-016-0527-x