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Sanchez-Bornot J, Sotero RC, Kelso JAS, Şimşek Ö, Coyle D. Solving large-scale MEG/EEG source localisation and functional connectivity problems simultaneously using state-space models. Neuroimage 2024; 285:120458. [PMID: 37993002 DOI: 10.1016/j.neuroimage.2023.120458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Revised: 09/28/2023] [Accepted: 11/14/2023] [Indexed: 11/24/2023] Open
Abstract
State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high computational costs in large-scale analyses. Sparse inverse covariance estimators can mitigate these costs, but at the expense of a trade-off between enforced sparsity and increased estimation bias, necessitating careful assessment in low signal-to-noise ratio (SNR) situations. To address these challenges, we propose a three-fold solution: (1) Introducing multiple penalised state-space (MPSS) models that leverage data-driven regularisation; (2) Developing novel algorithms derived from backpropagation, gradient descent, and alternating least squares to solve MPSS models; (3) Presenting a K-fold cross-validation extension for evaluating regularisation parameters. We validate this MPSS regularisation framework through lower and more complex simulations under varying SNR conditions, including a large-scale synthetic magneto- and electro-encephalography (MEG/EEG) data analysis. In addition, we apply MPSS models to concurrently solve brain source localisation and functional connectivity problems for real event-related MEG/EEG data, encompassing thousands of sources on the cortical surface. The proposed methodology overcomes the limitations of existing approaches, such as constraints to small-scale and region-of-interest analyses. Thus, it may enable a more accurate and detailed exploration of cognitive brain functions.
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Affiliation(s)
- Jose Sanchez-Bornot
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Magee campus, Derry∼Londonderry, United Kingdom.
| | - Roberto C Sotero
- Department of Radiology and Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
| | - J A Scott Kelso
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Magee campus, Derry∼Londonderry, United Kingdom; Human Brain & Behavior laboratory, Center for Complex Systems & Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA
| | - Özgür Şimşek
- Bath Institute for the Augmented Human, University of Bath, Bath, BA2 7AY, United Kingdom
| | - Damien Coyle
- Intelligent Systems Research Centre, School of Computing, Engineering and Intelligent Systems, Ulster University, Magee campus, Derry∼Londonderry, United Kingdom; Bath Institute for the Augmented Human, University of Bath, Bath, BA2 7AY, United Kingdom
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He F, Yang Y. Nonlinear System Identification of Neural Systems from Neurophysiological Signals. Neuroscience 2021; 458:213-228. [PMID: 33309967 PMCID: PMC7925423 DOI: 10.1016/j.neuroscience.2020.12.001] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Revised: 11/30/2020] [Accepted: 12/01/2020] [Indexed: 12/20/2022]
Abstract
The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a certain amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention.
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Affiliation(s)
- Fei He
- Centre for Data Science, Coventry University, Coventry CV1 2JH, UK
| | - Yuan Yang
- Stephenson School of Biomedical Engineering, The University of Oklahoma, Tulsa, OK 74135, USA; Department of Physical Therapy and Human Movement Sciences, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA; Laureate Institute for Brain Research, Tulsa, OK 74136, USA
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Hamid L, Habboush N, Stern P, Japaridze N, Aydin Ü, Wolters CH, Claussen JC, Heute U, Stephani U, Galka A, Siniatchkin M. Source imaging of deep-brain activity using the regional spatiotemporal Kalman filter. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2021; 200:105830. [PMID: 33250282 DOI: 10.1016/j.cmpb.2020.105830] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2020] [Accepted: 10/31/2020] [Indexed: 06/12/2023]
Abstract
BACKGROUND AND OBJECTIVE The human brain displays rich and complex patterns of interaction within and among brain networks that involve both cortical and subcortical brain regions. Due to the limited spatial resolution of surface electroencephalography (EEG), EEG source imaging is used to reconstruct brain sources and investigate their spatial and temporal dynamics. The majority of EEG source imaging methods fail to detect activity from subcortical brain structures. The reconstruction of subcortical sources is a challenging task because the signal from these sources is weakened and mixed with artifacts and other signals from cortical sources. In this proof-of-principle study we present a novel EEG source imaging method, the regional spatiotemporal Kalman filter (RSTKF), that can detect deep brain activity. METHODS The regional spatiotemporal Kalman filter (RSTKF) is a generalization of the spatiotemporal Kalman filter (STKF), which allows for the characterization of different regional dynamics in the brain. It is based on state-space modeling with spatially heterogeneous dynamical noise variances, since models with spatial and temporal homogeneity fail to describe the dynamical complexity of brain activity. First, RSTKF is tested using simulated EEG data from sources in the frontal lobe, putamen, and thalamus. After that, it is applied to non-averaged interictal epileptic spikes from a presurgical epilepsy patient with focal epileptic activity in the amygdalo-hippocampal complex. The results of RSTKF are compared to those of low-resolution brain electromagnetic tomography (LORETA) and of standard STKF. RESULTS Only RSTKF is successful in consistently and accurately localizing the sources in deep brain regions. Additionally, RSTKF shows improved spatial resolution compared to LORETA and STKF. CONCLUSIONS RSTKF is a generalization of STKF that allows for accurate, focal, and consistent localization of sources, especially in the deeper brain areas. In contrast to standard source imaging methods, RSTKF may find application in the localization of the epileptogenic zone in deeper brain structures, such as mesial frontal and temporal lobe epilepsies, especially in EEG recordings for which no reliable averaged spike shape can be obtained due to lack of the necessary number of spikes required to reach a certain signal-to-noise ratio level after averaging.
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Affiliation(s)
- Laith Hamid
- Department of Medical Psychology and Medical Sociology, University of Kiel, D-24113 Kiel, Germany.
| | - Nawar Habboush
- Department of Medical Psychology and Medical Sociology, University of Kiel, D-24113 Kiel, Germany
| | - Philipp Stern
- Institute of Theoretical Physics and Astrophysics, University of Kiel, D-24098 Kiel, Germany
| | - Natia Japaridze
- Department of Neuropediatrics, University of Kiel, D-24098 Kiel, Germany
| | - Ümit Aydin
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, D-48149 Münster, Germany; Multimodal Functional Imaging Lab, Department of Physics and PERFORM Centre, Concordia University, Montreal, Canada
| | - Carsten H Wolters
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, D-48149 Münster, Germany
| | - Jens Christian Claussen
- Institute of Theoretical Physics and Astrophysics, University of Kiel, D-24098 Kiel, Germany; Institute for Neuro- and Bioinformatics, University of Lübeck, D-23562 Lübeck, Germany; Mathematics EAS, Aston University, Aston Triangle, Birmingham B3 7ET, United Kingdom
| | - Ulrich Heute
- Digital Signal Processing and System Theory Group, Faculty of Engineering, University of Kiel, D-24143 Kiel, Germany
| | - Ulrich Stephani
- Department of Neuropediatrics, University of Kiel, D-24098 Kiel, Germany
| | - Andreas Galka
- Department of Medical Psychology and Medical Sociology, University of Kiel, D-24113 Kiel, Germany
| | - Michael Siniatchkin
- Department of Medical Psychology and Medical Sociology, University of Kiel, D-24113 Kiel, Germany; Department of Child and Adolescent Psychiatry and Psychotherapy, Evangelisches Klinikum Bethel gGmbH, D-33617 Bielefeld, Germany
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Lagos-Álvarez B, Padilla L, Mateu J, Ferreira G. A Kalman filter method for estimation and prediction of space–time data with an autoregressive structure. J Stat Plan Inference 2019. [DOI: 10.1016/j.jspi.2019.03.005] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Giraldo-Suarez E, Martinez-Vargas JD, Castellanos-Dominguez G. Reconstruction of Neural Activity from EEG Data Using Dynamic Spatiotemporal Constraints. Int J Neural Syst 2016; 26:1650026. [PMID: 27354190 DOI: 10.1142/s012906571650026x] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We present a novel iterative regularized algorithm (IRA) for neural activity reconstruction that explicitly includes spatiotemporal constraints, performing a trade-off between space and time resolutions. For improving the spatial accuracy provided by electroencephalography (EEG) signals, we explore a basis set that describes the smooth, localized areas of potentially active brain regions. In turn, we enhance the time resolution by adding the Markovian assumption for brain activity estimation at each time period. Moreover, to deal with applications that have either distributed or localized neural activity, the spatiotemporal constraints are expressed through [Formula: see text] and [Formula: see text] norms, respectively. For the purpose of validation, we estimate the neural reconstruction performance in time and space separately. Experimental testing is carried out on artificial data, simulating stationary and non-stationary EEG signals. Also, validation is accomplished on two real-world databases, one holding Evoked Potentials and another with EEG data of focal epilepsy. Moreover, responses of functional magnetic resonance imaging for the former EEG data have been measured in advance, allowing to contrast our findings. Obtained results show that the [Formula: see text]-based IRA produces a spatial resolution that is comparable to the one achieved by some widely used sparse-based estimators of brain activity. At the same time, the [Formula: see text]-based IRA outperforms other similar smooth solutions, providing a spatial resolution that is lower than the sparse [Formula: see text]-based solution. As a result, the proposed IRA is a promising method for improving the accuracy of brain activity reconstruction.
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Affiliation(s)
- E. Giraldo-Suarez
- Department of Electrical Engineering, Universidad Tecnológica de Pereira, Colombia
| | - J. D. Martinez-Vargas
- Signal Processing and Recognition Group, Universidad Nacional de Colombia, Manizales, Colombia
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Abstract
SUMMARYThis paper presents a generalization of the Compressed Extended Kalman Filter (CEKF) by introducing the definition of the compressed operation for Bayesian estimation processes and the definition of the Generalized Compressed Kalman Filter (GCKF). The GCKF extends the original definition of the CEKF, formerly introduced for treating a family of estimation problems, such as the Simultaneous Localization and Mapping (SLAM). The new proposed approach, the GCKF, is capable of treating problems that are more general than those of the original CEKF, such as estimation processes that involve certain stochastic Partial Differential Equation (SPDE) models. In addition to solving the SLAM and multi-agent SLAM problem in an efficient way, the GCKF can be applied to more general cases. As a proof of the capabilities of the new method for solving practical estimation problems, a multi-agent SLAM process is presented in the experimental section of this paper.
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Kuhlmann L, Freestone DR, Manton JH, Heyse B, Vereecke HE, Lipping T, Struys MM, Liley DT. Neural mass model-based tracking of anesthetic brain states. Neuroimage 2016; 133:438-456. [DOI: 10.1016/j.neuroimage.2016.03.039] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Revised: 02/26/2016] [Accepted: 03/18/2016] [Indexed: 01/22/2023] Open
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Habboush N, Hamid L, Japaridze N, Wiegand G, Heute U, Stephani U, Galka A, Siniatchkin M. The choice of the source space and the Laplacian matrix in LORETA and the spatio-temporal Kalman filter EEG inverse methods. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2016; 2015:2745-9. [PMID: 26736860 DOI: 10.1109/embc.2015.7318960] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
The discretization of the brain and the definition of the Laplacian matrix influence the results of methods based on spatial and spatio-temporal smoothness, since the Laplacian operator is used to define the smoothness based on the neighborhood of each grid point. In this paper, the results of low resolution electromagnetic tomography (LORETA) and the spatiotemporal Kalman filter (STKF) are computed using, first, a greymatter source space with the standard definition of the Laplacian matrix and, second, using a whole-brain source space and a modified definition of the Laplacian matrix. Electroencephalographic (EEG) source imaging results of five inter-ictal spikes from a pre-surgical patient with epilepsy are used to validate the two aforementioned approaches. The results using the whole-brain source space and the modified definition of the Laplacian matrix were concentrated in a single source activation, stable, and concordant with the location of the focal cortical dysplasia (FCD) in the patient's brain compared with the results which use a grey-matter grid and the classical definition of the Laplacian matrix. This proof-of-concept study demonstrates a substantial improvement of source localization with both LORETA and STKF and constitutes a basis for further research in a large population of patients with epilepsy.
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Hamid L, Sarabi M, Japaridze N, Wiegand G, Heute U, Stephani U, Galka A, Siniatchkin M. The performance of the spatiotemporal Kalman filter and LORETA in seizure onset localization. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2015; 2015:2741-2744. [PMID: 26736859 DOI: 10.1109/embc.2015.7318959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The assumption of spatial-smoothness is often used to solve the bioelectric inverse problem during electroencephalographic (EEG) source imaging, e.g., in low resolution electromagnetic tomography (LORETA). Since the EEG data show a temporal structure, the combination of the temporal-smoothness and the spatial-smoothness constraints may improve the solution of the EEG inverse problem. This study investigates the performance of the spatiotemporal Kalman filter (STKF) method, which is based on spatial and temporal smoothness, in the localization of a focal seizure's onset and compares its results to those of LORETA. The main finding of the study was that the STKF with an autoregressive model of order two significantly outperformed LORETA in the accuracy and consistency of the localization, provided that the source space consists of a whole-brain volumetric grid. In the future, these promising results will be confirmed using data from more patients and performing statistical analyses on the results. Furthermore, the effects of the temporal smoothness constraint will be studied using different types of focal seizures.
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Antelis JM, Minguez J. DYNAMO: concurrent dynamic multi-model source localization method for EEG and/or MEG. J Neurosci Methods 2012; 212:28-42. [PMID: 23022309 DOI: 10.1016/j.jneumeth.2012.09.017] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2012] [Revised: 09/17/2012] [Accepted: 09/17/2012] [Indexed: 10/27/2022]
Abstract
This work presents a new dipolar method to estimate the neural sources from separate or combined EEG and MEG data. The novelty lies in the simultaneous estimation and integration of neural sources from different dynamic models with different parameters, leading to a dynamic multi-model solution for the EEG/MEG source localization problem. The first key aspect of this method is defining the source model as a dipolar dynamic system, which allows for the estimation of the probability distribution of the sources within the Bayesian filter estimation framework. A second important aspect is the consideration of several banks of filters that simultaneously estimate and integrate the neural sources of different models. A third relevant aspect is that the final probability estimate is a result of the probabilistic integration of the neural sources of numerous models. Such characteristics lead to a new approach that does not require a prior definition neither of the number of sources or of the underlying temporal dynamics, allowing for the specification of multiple initial prior estimates. The method was validated by three sensor modalities with simulated data designed to impose difficult estimation situations, and with real EEG data recorded in a feedback error-related potential paradigm. On the basis of these evaluations, the method was able to localize the sources with high accuracy.
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Affiliation(s)
- Javier M Antelis
- Computer Science and Systems Engineering Department I3A, University of Zaragoza, Spain.
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11
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Inverse source imaging methods in recovering distributed brain sources. Biomed Eng Lett 2012. [DOI: 10.1007/s13534-012-0047-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022] Open
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Fukushima M, Yamashita O, Kanemura A, Ishii S, Kawato M, Sato MA. A state-space modeling approach for localization of focal current sources from MEG. IEEE Trans Biomed Eng 2012; 59:1561-71. [PMID: 22394573 DOI: 10.1109/tbme.2012.2189713] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
State-space modeling is a promising approach for current source reconstruction from magnetoencephalography (MEG) because it constrains the spatiotemporal behavior of inverse solutions in a flexible manner. However, state-space model-based source localization research remains underdeveloped; extraction of spatially focal current sources and handling of the high dimensionality of the distributed source model remain problematic. In this study, we propose a novel state-space model-based method that resolves these problems, extending our previous source localization method to include a temporal constraint by state-space modeling. To enable focal current reconstruction, we account for spatially inhomogeneous temporal dynamics by introducing dynamics model parameters that differ for each cortical position. The model parameters and the intensity of the current sources are jointly estimated according to a bayesian framework. We circumvent the high dimensionality of the problem by assuming prior distributions of the model parameters to reduce the sensitivity to unmodeled components, and by adopting variational bayesian inference to reduce the computational cost. Through simulation experiments and application to real MEG data, we have confirmed that our proposed method successfully reconstructs focal current activities, which evolve with their temporal dynamics.
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Affiliation(s)
- Makoto Fukushima
- Graduate School of Information Science, Nara Institute of Science and Technology, Nara 630-0192, Japan.
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Chisci L, Mavino A, Perferi G, Sciandrone M, Anile C, Colicchio G, Fuggetta F. Real-Time Epileptic Seizure Prediction Using AR Models and Support Vector Machines. IEEE Trans Biomed Eng 2010; 57:1124-32. [DOI: 10.1109/tbme.2009.2038990] [Citation(s) in RCA: 173] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Giraldo E, den Dekker AJ, Castellanos-Dominguez G. Estimation of dynamic neural activity using a Kalman filter approach based on physiological models. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2010; 2010:2914-2917. [PMID: 21095984 DOI: 10.1109/iembs.2010.5626281] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
This paper presents a new method to estimate dynamic neural activity from EEG signals. The method is based on a Kalman filter approach, using physiological models that take both spatial and temporal dynamics into account. The filter's performance (in terms of estimation error) is analyzed for the cases of linear and nonlinear models having either time invariant or time varying parameters. The best performance is achieved with a nonlinear model with time-varying parameters.
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Affiliation(s)
- E Giraldo
- Faculty of Electrical and Electronic Engineering, Physics and Computer Science, Technological University of Pereira, Colombia.
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