Research Papers
Decoding imagined speech with delay differential analysis
Authors: Carvalho, V. R., Mendes, E. M. A. M., Fallah, A., Sejnowski, T. J., Comstock, L., Lainscsek, C.
Published: Frontiers in Human Neuroscience, 18, 1398065, 2024
Speech decoding from non-invasive EEG signals can achieve relatively high accuracy (70-80%) for strictly delimited classification tasks, but for more complex tasks non-invasive speech decoding typically yields a 20-50% classification accuracy. However, decoder generalization, or how well algorithms perform objectively across datasets, is complicated by the small size and heterogeneity of existing EEG datasets. Furthermore, the limited availability of open access code hampers a comparison between methods. This study explores the application of a novel non-linear method for signal processing, delay dierential analysis (DDA), to speech decoding. We provide a systematic evaluation of its performance on two public imagined speech decoding datasets relative to all publicly available deep learning methods. The results support DDA as a compelling alternative or complementary approach to deep learning methods for speech decoding. DDA is a fast and efficient time-domain opensource method that fits data using only few strong features and does not require extensive preprocessi
Transcranial Magnetic Stimulation Facilitates Neural Speech Decoding
Authors: Comstock, L. B., Carvalho, V. R., Lainscsek, C., Fallah, A., Sejnowski, T.
Published: iScience, SSRN 4432677, 2024
Transcranial magnetic stimulation (TMS) has been widely used to study the mechanisms that underlie motor output. Yet, the extent to which TMS acts upon the cortical neurons implicated in volitional motor commands and the focal limitations of TMS remain subject to debate. Previous research links TMS to improved subject performance in behavioral tasks, including a bias in phoneme discrimination. Our study replicates this result, which implies a causal relationship between electromagnetic stimulation and psychomotor activity, and tests whether TMS-facilitated psychomotor activity recorded via electroencephalography (EEG) may thus serve as a superior input for neural decoding. First, we illustrate that site-specific TMS elicits a double dissociation in discrimination ability for two phoneme categories. Next, we perform a classification analysis on the EEG signals recorded during TMS and find a dissociation between the stimulation site and decoding accuracy that parallels the behavioral results. We observe weak to moderate evidence for the alternative hypothesis in a Bayesian analysis of group means, with more robust results upon stimulation to a brain region governing multiple phoneme features. Overall, task accuracy was a significant predictor of decoding accuracy for phoneme categories (F(1,135) = 11.51, p < 0.0009) and individual phonemes (F(1,119) = 13.56, p < 0.0003), providing new evidence for a causal link between TMS, neural function, and behavior.
Network-motif delay differential analysis of brain activity during seizures
Authors: Lainscsek, C., Salami, P., Carvalho, V. R., Mendes, E.M.A.M., Fan, M., Cash, S.S., Sejnowski, T.J.
Published: Chaos, 33 (12), 123136, 2023
Delay Differential Analysis (DDA) is a nonlinear method for analyzing time series based on principles from nonlinear dynamical systems. DDA is extended here to incorporate network aspects to improve the dynamical characterization of complex systems. To demonstrate its effectiveness, DDA with network capabilities was first applied to the well-known Rössler system under different parameter regimes and noise conditions. Network-motif DDA, based on cortical regions, was then applied to invasive intracranial electroencephalographic data from drug-resistant epilepsy patients undergoing presurgical monitoring. The directional network motifs between brain areas that emerge from this analysis change dramatically before, during, and after seizures. Neural systems provide a rich source of complex data, arising from varying internal states generated by network interactions.
Transformations that preserve the uniqueness of the differential form for Lorenz-like systems
Authors: Lainscsek, C., Mendes, E.M.A.M., Salgado, G.H.O., Sejnowski, T. J.
Published: Chaos, 33(10): 103122, 2023
Differential equations serve as models for many physical systems. But, are these equations unique? We prove here that when a 3D system of ordinary differential equations for a dynamical system is transformed to the jerk or differential form, the jerk form is preserved in relation to a given variable and, therefore, the transformed system shares the time series of that given variable with the original untransformed system. Multiple algebraically different systems of ordinary differential equations can share the same jerk form. They may also share the same time series of the transformed variable depending on the parameters of the jerk form. Here, we studied 17 algebraically different Lorenz-like systems that share the same functional jerk form. There are groups of these systems that share the jerk parameters and, therefore, also have the same time series of the transformed variable.
Brain network dynamics codify heterogeneity in seizure evolution
Authors: Rungratsameetaweemana, N., Lainscsek, C., Cash, S. S., Garcia, J. O., Sejnowski, T. J., Bansal, K.
Published: Brain Communications, 4 (5), fcac234, 2022
Dynamic functional brain connectivity facilitates adaptive cognition and behaviour. Abnormal alterations within such connectivity could result in disrupted functions observed across various neurological conditions. As one of the most common neurological disorders, epilepsy is defined by the seemingly random occurrence of spontaneous seizures. A central but unresolved question concerns the mechanisms by which extraordinarily diverse propagation dynamics of seizures emerge. Here, we applied a graph-theoretical approach to assess dynamic reconfigurations in the functional brain connectivity before, during and after seizures that display heterogeneous propagation patterns despite sharing similar cortical onsets. We computed time-varying functional brain connectivity networks from human intracranial recordings of 67 seizures (across 14 patients) that had a focal origin—49 of these focal seizures remained focal and 18 underwent a bilateral spread (focal to bilateral tonic-clonic seizures). We utilized functional connectivity networks estimated from interictal periods across patients as control. Our results characterize network features that quantify the underlying functional dynamics associated with the observed heterogeneity of seizure propagation across these two types of focal seizures. Decoding these network features demonstrate that bilateral propagation of seizure activity is an outcome of the imbalance of global integration and segregation in the brain prior to seizure onset. We show that there exist intrinsic network signatures preceding seizure onset that are associated with the extent to which an impending seizure will propagate throughout the brain (i.e. staying within one hemisphere versus spreading transcallosally). Additionally, these features characterize an increase in segregation and a decrease in excitability within the brain network (i.e. high modularity and low spectral radius). Importantly, seizure-type-specific differences in these features emerge several minutes prior to seizure onset, suggesting the potential utility of such measures in intervention strategies. Finally, our results reveal network characteristics after the onset that are unique to the propagation mechanisms of two most common focal seizure subtypes, indicative of distinct reconfiguration processes that may assist termination of each seizure type. Together, our findings provide insights into the relationship between the temporal evolution of seizure activity and the underlying functional connectivity dynamics. These results offer exciting avenues where graph-theoretical measures could potentially guide personalized clinical interventions for epilepsy and other neurological disorders in which extensive heterogeneity is observed across subtypes as well as across and within individual patients.
Dynamical ergodicity DDA reveals causal structure in time series
Authors: Lainscsek, C., Cash, S. S., Sejnowski, T. J. Kurths, J.
Published: Chaos, 31, 103108, 2021
Determining synchronization, causality, and dynamical similarity in highly complex nonlinear systems like brains is challenging. Although distinct, these measures are related by the unknown deterministic structure of the underlying dynamical system. For two systems that are not independent on each other, either because they result from a common process or they are already synchronized, causality measures typically fail. Here, we introduce dynamical ergodicity to assess dynamical similarity between time series and then combine this new measure with cross-dynamical delay differential analysis to estimate causal interactions between time series. We first tested this approach on simulated data from coupled Rössler systems where ground truth was known. We then applied it to intracranial electroencephalographic data from patients with epilepsy and found distinct dynamical states that were highly predictive of epileptic seizures.
Cortical chimera states predict epileptic seizures
Authors: Lainscsek, C., Rungratsameetaweemana, N., Cash, S. S., Sejnowski, T. J.
Published: Chaos, 29, 121106, 2019
A chimera state is a spatiotemporal pattern of broken symmetry, where synchrony (coherent state) and asynchrony (incoherent state) coexist. Here, we report chimera states in electrocorticography recordings preceding, by several hours, each of seven seizures in one patient with epilepsy. Before the seizures, the onset channels are not synchronized, while the remaining channels are synchronized. During the seizures, this pattern of behavior flips and the nononset channels show a more asynchronous behavior. At a seizure onset, synchrony can be observed that might facilitate termination.
Delay differential analysis for dynamical sleep spindle detection
Authors: Sampson, A. L., Lainscsek, C., Gonzalez, C.E., Ulbert, I., Devinsky, O., Fabo, D., Madsen, J. R., Halgren, E., Cash S. S., Sejnowski, T. J.
Published: Journal of Neuroscience Methods, 316, 12-21, 2019
Background: Sleep spindles are involved in memory consolidation and other cognitive functions. Numerous automated methods for detection of spindles have been proposed; most of these rely on spectral analysis in some form. However, none of these approaches are ideal, and novel approaches to the problem could provide additional insights. New method: Here, we apply delay differential analysis (DDA), a time-domain technique based on nonlinear dynamics to detect sleep spindles in human intracranial sleep data, including laminar electrode, stereoelectroencephalogram (sEEG), and electrocorticogram (ECoG) recordings. Results: We show that this approach is computationally fast, generalizable, requires minimal preprocessing, and provides excellent agreement with human scoring. Comparison with existing methods: We compared the method with established methods on a set of intracranial recordings and this method provided the highest agreement with human expert scoring when evaluated with F1 score while being the second-fastest to run. We also compared the results on the DREAMS surface EEG data, where the method produced a higher average F1 score than all other tested methods except the automated detections published with the DREAMS data. Further, in addition to being a fast and reliable method for spindle detection, DDA also provides a novel characterization of spindle activity based on nonlinear dynamical content of the data. Conclusions: This additional, non-frequency-based perspective could prove particularly useful for certain atypical spindles, or identifying spindles of different types.
Nonlinear dynamics underlying sensory processing dysfunction in schizophrenia
Authors: Lainscsek, C., Sampson, A.L., Kim, R., Thomas, M.L., Man, K., Lainscsek, X., COGS Investigators, Swerdlow, N.R., Braff, D.L., Sejnowski, T. J., Light, G.A.
Published: Proc Natl Acad Sci U S A., 116(9), 3847-3852, 2019
Natural systems, including the brain, often seem chaotic, since they are typically driven by complex nonlinear dynamical processes. Disruption in the fluid coordination of multiple brain regions contributes to impairments in information processing and the constellation of symptoms observed in neuropsychiatric disorders. Schizophrenia (SZ), one of the most debilitating mental illnesses, is thought to arise, in part, from such a network dysfunction, leading to impaired auditory information processing as well as cognitive and psychosocial deficits. Current approaches to neurophysiologic biomarker analyses predominantly rely on linear methods and may, therefore, fail to capture the wealth of information contained in whole EEG signals, including nonlinear dynamics. In this study, delay differential analysis (DDA), a nonlinear method based on embedding theory from theoretical physics, was applied to EEG recordings from 877 SZ patients and 753 nonpsychiatric comparison subjects (NCSs) who underwent mismatch negativity (MMN) testing via their participation in the Consortium on the Genetics of Schizophrenia (COGS-2) study. DDA revealed significant nonlinear dynamical architecture related to auditory information processing in both groups. Importantly, significant DDA changes preceded those observed with traditional linear methods. Marked abnormalities in both linear and nonlinear features were detected in SZ patients. These results illustrate the benefits of nonlinear analysis of brain signals and underscore the need for future studies to investigate the relationship between D
Delay Differential Analysis of Seizures in Multichannel Electrocorticography Data
Authors: Lainscsek, C., Weyhenmeyer, J., Cash, S. S., Sejnowski, T. J.
Published: Neural Computation, 29, 3181-3218, 2017
High-density electrocorticogram (ECoG) electrodes are capable of recording neurophysiological data with high temporal resolution with wide spatial coverage. These recordings are a window to understanding how the human brain processes information and subsequently behaves in healthy and pathologic states. Here, we describe and implement delay differential analysis (DDA) for the characterization of ECoG data obtained from human patients with intractable epilepsy. DDA is a timedomain analysis framework based on embedding theory in nonlinear dynamics that reveals the nonlinear invariant properties of an unknown dynamical system. The DDA embedding serves as a low-dimensional nonlinear dynamical basis onto which the data are mapped. This greatly reduces the risk of overfitting and improves the method's ability to fitclasses of data. Since the basis is built on the dynamical structure of the data, preprocessing of the data (e.g., filtering) is not necessary. We performed a large-scale search for a DDA model that best fit ECoG recordings using a genetic algorithm to qualitatively discriminate between different cortical states and epileptic events for a set of 13 patients. A single DDA model with only three polynomial terms was identified. Singular value decomposition across the feature space of the model revealed both global and local dynamics that could differentiate electrographic and electroclinical seizures and provided insights into highly localized seizure onsets and diffuse seizure terminations. Other common ECoG features such as interictal periods, artifacts, and exogenous stimuli were also analyzed with DDA. This novel framework for signal processing of seizure information demonstrates an ability to reveal unique characteristics of the underlying dynamics of the seizure and may be useful in better understanding, detecting, and maybe even predicting seizures.
Analytical Derivation of Nonlinear Spectral Effects and 1/f Scaling Artifact in Signal Processing of Real-World Data.
Authors: Lainscsek, C., Muller , L. E., Sampson, A. L., Sejnowski, T. J.
Published: Neural Computation, 29(7), 2004-2020, 2017
In estimating the frequency spectrum of real-world time series data, we must violate the assumption of infnite-length, orthogonal components in the Fourier basis. While it is widely known that care must be taken with discretely sampled data to avoid aliasing of high frequencies, less attention is given to the infuence of low frequencies with period below the sampling time window. Here, we derive an analytic expression for the side-lobe attenuation of signal components in the frequency domain representation. This expression allows us to detail the infuence of individual frequency components throughout the spectrum. The frst consequence is that the presence of low-frequency components introduces a 1/fα component across the power spectrum, with a scaling exponent of α ≈ −2. This scaling artifact could be composed of diffuse low-frequency components, which can render it diffcult to detect a priori. Further, treatment of the signal with standard digital signal processing techniques cannot easily remove this scaling component. While several theoretical models have been introduced to explain the ubiquitous 1/fα scaling component in neuroscientifc data, we conjecture here that some experimental observations could be the result of such data analysis procedures.
Bringing order to the neurophysiological chaos underlying sensory processing dysfunction in schizophrenia
Authors: Lainscsek, C., Sampson, A., The COGS Investigators, T., Light, G. A., Sejnowski,T. J.
Published: Society for Neuroscience, 2015
There is compelling evidence that sensory processing impairments contribute to the cognitive and psychosocial dysfunction affecting the majority of schizophrenia (SZ) patients. An informative probe for sensory processing dysfunction in neuropsychiatric disorders is event-related potentials (ERPs) time-locked to presentations of deviant stimuli interspersed in a train of standard tones, which elicits a response complex dominated by two peaks, labeled mismatch negativity (MMN) and P3a positivity. Conventional approaches to electrocephalogram (EEG) analysis do not access the full wealth of information contained in the ERPs. We have used a new method to analyze EEG data based on nonlinear data analysis that extracts the dynamical structure of the data, which allows for classification of raw data in nearly real time and is highly generalizable across patients. Delay Differential Analysis (DDA) is a time domain classification framework based on embeddings in chaos theory (Lainscsek and Sejnowski, 2015). An embedding reveals the nonlinear invariant properties of an unknown dynamical system (here the brain) from a single time series (here EEG data). The embedding in DDA serves as a low-dimensional nonlinear functional basis onto which the data are mapped. Since the basis is built on the dynamical structure of the data, preprocessing of the data (such as filtering) is not necessary. DDA yields a small number of features (around 4), far fewer than traditional spectral techniques, which greatly reduces the risk of overfitting. We applied DDA to EEG data segments from 1630 subjects (normal control subjects n=753, SZ n=877) who underwent MMN testing as part of a Consortium on the Genetics of Schizophrenia (COGS-2) study. Receiver operating characteristic (ROC) curves were used to evaluate the extent to which DDA and traditional ERP components differentiated the 2 groups. The results of the present study show that DDA improved the differentiation of SZ from NCS (area under the ROC curve was 0.80) relative to conventional ERP analysis (area under the ROC curve was 0.75). Perfect discrimination occurs with the area under the ROC curve is 1. In conclusion, DDA is a powerful technique that capitalizes on information contained in entire EEG signal, revealing hidden information about nonlinear couplings that are not apparent in conventional ERP analyses. Moreover, DDA does not require data cleaning, extensive data processing or computational demands for rapid analysis of EEG results.
Delay differential analysis: a framework for multimodal non-linear classification of Parkinson's disease
Authors: Hernandez, M.E., Weyhenmeyer, J., Lainscsek, C., Sejnowski, T. J., Poizner, H.
Published: Society for Neuroscience 2015, 2015
Parkinson's disease (PD) is the second most prevalent neurodegenerative disorder in the world, yet has no standard diagnostic test. PD is known to lead to marked alterations in cortico-thalamo-basal ganglia activity and subsequent movements, which may provide a biomarker for PD diagnosis. DDA is a time domain analysis framework based on embedding theory in non-linear dynamics. An embedding reveals the nonlinear invariant properties of an unknown dynamical system (here the brain) from a single time series (EEG or behavioral signals). The DDA embedding serves as a lowdimensional nonlinear functional basis onto which the data are mapped. The combination of behavioral and neurological observations gives rise to a multimodal analysis framework that will improve the understanding and classification of neurological disease. We demonstrate how 750 ms of multimodal data can be used to improve DDA classification performance of PD after an unexpected perturbation of a virtual target during reach to grasp movements. We found that the anteroposterior hand position and hand aperture, in particular, provide improved classification performance in comparison to clean EEG data, as evaluated by the area under the ROC curve (AROC), (AROC increases from 0.71 to 0.81 with the addition of behavioral data). Thus, multimodal DDA may provide a tool for aiding the clinician in the diagnosis of PD and allow for earlier intervention with disease modifying therapeutics.
Delay differential analysis: a framework for the analysis of large-scale epileptic electrocorticography recordings
Authors: Weyhenmeyer, J., Lainscsek, C., Cash, S. S., Sejnowski, T. J.
Published: Society for Neuroscience, 2015
High density electrocorticogram (ECoG) electrodes are capable of recording neurophysiological data with high temporal and reasonable spatial resolution. Such recordings are a window to understanding how the human brain processes information and subsequently behaves in healthy and pathologic states. At present, many of the computational methods utilized in the analysis of ECoG recordings are strictly linear, require significant pre-processing, and fail to provide high-level information with respect to the state of the neurological system. In the following study, we describe and implement delay differential analysis (DDA) for the characterization of ECoG data obtained from human patients with intractable epilepsy. DDA is a time domain analysis framework based on embedding theory in nonlinear dynamics. An embedding reveals the nonlinear invariant properties of an unknown dynamical system (here the brain) from a single time series (ECoG signals). The DDA embedding serves as a low-dimensional nonlinear functional basis onto which the data are mapped. Since the basis is built on the dynamical structure of the data, preprocessing of the data, e.g. filtering, is not necessary. DDA yields a low number of features (four or less), far fewer than traditional spectral techniques. This greatly reduces the risk of overfitting and improves the method's ability to fit classes of data. One single three term DDA is shown to qualitatively discriminate between different neurologic states and epileptic events for a set of 13 patients from the raw ECoG data. Singular value computation across the feature space is shown to delineate global and local dynamics. The global and local dynamics differentiate electrographic and electroclinical seizures while also providing insight into a highly localized seizure onset and diffuse seizure termination. Thus, DDA is shown as a new form of computational analysis for ECoG data obtained from the epileptic patient.
Nonlinear dynamical features for improving computational sleep models using Delay Differential Analysis
Authors: LIN, W., Lainscsek, C., Krishnan, G. P., Bazhenov, M., Mednicks, S., Sejnowski, T. J.
Published: Society for Neuroscience, 2015
Cortical network models based on ionic mechanisms have many parameters that must be chosen to match cortical recordings. One measure is comparison of the local field potentials generated by simulations of the model with electrocephalogram (EEG). Here, we use delay differential analysis (DDA), which is a time domain classification framework based on embedding theory in nonlinear dynamics to make the comparison. An embedding reveals the nonlinear invariant properties of an unknown dynamical system (here the brain) from a single time series (here EEG data). The embedding in DDA serves then as a low-dimensional nonlinear functional basis onto which the data are mapped. Since the basis is built on the dynamical structure of the data, preprocessing of the data (such as filtering) is not necessary. DDA yields a low number of features (around 4), far fewer than traditional spectral techniques. This greatly reduces the risk of overfitting. A model that was trained on a single EEG channel from one subject can be applied to a wide range of data from different subjects, channels, and recording systems. In this project, we varied the network's thalamocortical fan-out to simulate networks with different levels of connectivities. Then, we apply DDA to construct a set of non-linear features for the real human sleep EEG data and each network simulation. Finally, the cross correlation between each network simulation and the real sleep data is computed. Our results show that within the connection range we simulated, networks with medium levels of fan-out rate have the highest correlation with real sleep data. This implies that there is an optimum level of connection between the thalamus and the cortex. A too narrow or too broad fanout will disrupt the simulation dynamic from that of real sleep.
Nonlinear dynamical sleep spindle detection using delay differential analysis
Authors: Sampson, A.L., C. Lainscsek, C., Cash, S. S., E. Halgren, E., Sejnowski, T. J.
Published: Society for Neuroscience, 2015
Since nonlinear data analysis works upon the dynamical structure of the data, it allows for classification in near real time of raw data. Here, we use delay differential analysis (DDA), which is a time domain classification framework based on embedding theory. An embedding reveals the nonlinear invariant properties of an unknown dynamical system (here the brain) from a single time series (here electrocephalogram (EEG) data). The embedding in DDA serves as a low-dimensional nonlinear functional basis onto which the data are mapped. Since the basis is built on the dynamical structure of the data, preprocessing of the data is not necessary, and the low dimensionality removes the risk of overfitting. A model that was trained on a single EEG channel from one subject can be applied to a wide range of data from different subjects, channels, and recording systems. Given these desirable properties, DDA is ideally suited to the problem of sleep spindle detection. Sleep spindles are 11-17 Hz oscillations recorded in the EEG during stage 2 sleep. As sleep spindles are thought to arise from the activity of thalamocortical circuitry, they have become a subject of study for their potential roles in memory consolidation and other cognitive functions. In light of their potential importance, a method for reliably identifying spindles in real time is needed. DDA analyses were applied to intracranial recordings from patients with intractable epilepsy and compared to traditional wavelet methods. As a bridge between these two methods, an additional DDA classifier was built on simulated data (noise-diluted harmonics) to detect frequency bands. One single set of DDA parameters can be used for 15 tested recordings. The mean area under the receiver operating characteristic curve is 0.75. DDA is a powerful method for improving the sensitivity of EEG analyses to transitory time series features that does not rely on any post-hoc adjustment of outputs or tailoring to individual subjects.
Delay Differential Analysis of Time Series
Authors: Lainscsek, C., and Sejnowski, T.J.
Published: Neural Computation, 2015
Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra.These can be efficiently computed with short time windows and are robust to noise.For frequency analysis, this framework is a multivariate extension of discrete Fourier transform(DFT), and for higher - order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations.This method can be applied to short or sparse time series and can be extended to cross- trial and cross - channel spectra if multiple short data segments of the same experiment are available.Together, this time - domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher - order spectra across time compared with frequency - based methods such as the DFT and cross - spectral analysis.
Automatic Sleep Scoring from a Single Electrode Using Delay Differential Equations (Ed.)
Authors: Lainscsek, C., Messager, V., Portman, A., Muir, J.-F., Sejnowski, T. J. Letellier, C., Awrejcewicz, J. (Ed.)
Published: In: In: Applied Non-Linear Dynamical Systems, 371-382, 2014
Sleep scoring is commonly performed from electroencephalogram (EEG), electrooculogram (EOG), and electromyogram (EMG) to produce a socalled hypnogram. A neurologist thus visually encodes each epoch of 30 s into one of the sleep stages (wake, REM sleep, S1, S2, S3, S4). To avoid such a long process (about 3-4 hours) a technique for automatic sleep scoring from the signal of a single EEG electrode located in the C3/A2 area using nonlinear delay differential equations (DDEs) is presented here. Our approach considers brain activity as resulting from a dynamical system whose parameters should vary according to the sleep stages. It is thus shown that there is at least one coefficient that depends on sleep stages and which can be used to construct a hypnogram. The correlation between manual hypnograms and the coefficient evolution is around 80%, that is, about the inter-rater variability. In order to rank sleep quality from the best to the worst, we introduced a global sleep quality index which is used to compare manual and automatic sleep scorings, thus using our ability to state about sleep quality that is the final goal for physicians.
Delay differential analysis of EEG during reaching to grasp virtual objects
Authors: Hernandez, M. E., Weyhenmeyer, J., Lainscsek, C., Sejnowski, T. J., Poizner, H.
Published: Society for Neuroscience Abstracts, 2014
Parkinson's disease (PD) is a costly, chronic, neurodegenerative disorder that affects tens of millions of people worldwide, yet no biomarker has been established to date. PD is known to lead to marked alterations in cortical-basal ganglia activity and is characterized by motor impairments such as bradykinesia, muscle rigidity, resting tremor, and postural instability. Using non-linear Delay Differential Analysis (DDA) for time-domain classification of PD patients on and off dopaminergic therapy (PD-on, PD-off, respectively, n=9) from healthy age-matched controls (CO, n=10), we hypothesize that individual trials of EEG data can be used to classify CO from PD-on/off. Surface EEG activity was recorded from 64- channels in all subjects during a reaching task to grasp rectangular virtual objects with haptic feedback provided. A tone was provided to indicate the start of the trial, and two data sets, one full second prior to the tone (resting state) and half a second after the tone were used for classification (posttone). The virtual object was unexpectedly rotated 90 degrees in the frontal plane on a subset (33%) of trials and two additional data sets of behavioral and EEG data, time-locked to the onset of the object perturbation are considered. Resting state EEG provided a relatively uniform classification performance for CO vs. all PD patients and poorer performance within PD patients. In contrast to resting state, post-tone EEG was shown to provide increased classification performance towards occipital areas, consistent with a PD patient's increased reliance on visual feedback processes during complex motor tasks. Task-related changes in EEG after the onset of the perturbation were also identified that merit further exploration with behavioral changes due to PD. Thus, non-linear features in EEG data may provide a potential biomarker for Parkinson's disease based on single 1 s or 1/2 s trials of EEG data that are sensitive to changes in a virtual grasping movement.
Electrocardiogram Classification Using Delay Differential Equations
Authors: Lainscsek, C., Sejnowski, T. J.
Published: Chaos, 23, 023132, 2013 PMCID:PMC3710263, 2013
Time series analysis with nonlinear delay differential equations (DDEs) reveals nonlinear as well as spectral properties of the underlying dynamical system. Here, global DDE models were used to analyze 5 min data segments of electrocardiographic (ECG) recordings in order to capture distinguishing features for different heart conditions such as normal heart beat, congestive heart failure, and atrial fibrillation. The number of terms and delays in the model as well as the order of nonlinearity of the model have to be selected that are the most discriminative. The DDE model form that best separates the three classes of data was chosen by exhaustive search up to third order polynomials. Such an approach can provide deep insight into the nature of the data since linear terms of a DDE correspond to the main time-scales in the signal and the nonlinear terms in the DDE are related to nonlinear couplings between the harmonic signal parts. The DDEs were able to detect atrial fibrillation with an accuracy of 72%, congestive heart failure with an accuracy of 88%, and normal heart beat with an accuracy of 97% from 5 min of ECG, a much shorter time interval than required to achieve comparable performance with other methods.
Non-linear Dynamical Analysis of EEG Time Series Distinguishes Patients with Parkinson's Disease From Healthy Individuals
Authors: Lainscsek, C., Hernandez, M.E., Weyhenmeyer, J., Sejnowski, T. J., Poizner, H.
Published: Society for Neuroscience Abstracts, 2013
The pathophysiology of Parkinson’s disease (PD) is known to involve altered patterns of neuronal firing and synchronization in cortical-basal ganglia circuits. One window into the nature of the aberrant temporal dynamics in the cerebral cortex of PD patients can come from analysis of the patients electroencephalography (EEG). Rather than using spectral-based methods, we used data models based on delay differential equations (DDE) as non-linear time-domain classification tools to analyze EEG recordings from PD patients on and off dopaminergic therapy and healthy individuals. Two sets of 50 1-s segments of 64-channel EEG activity were recorded from nine PD patients on and off medication and nine agematched controls. The 64 EEG channels were grouped into 10 clusters covering frontal, central, parietal, and occipital brain regions for analysis. DDE models were fitted to individual trials, and model coefficients and error were used as features for classification.The best models were selected using repeated random sub-sampling validation and classification performance was measured using the area under the ROC curve A0. In a companion paper, we show that DDEs can uncover hidden dynamical structure from short segments of simulated time series of known dynamical systems in high noise regimes. Using the same method for finding the best models, we found here that even short segments of EEG data in PD patients and controls contained dynamical structure, and moreover, that PD patients exhibited a greater dynamic range than controls. DDE model output on the means from one set of 50 trials provided nearly complete separation of PD patients off medication from controls: across brain regions, the area under the receiver-operating characteristic curves, A0, varied from 0.95 to 1.0. For distinguishing PD patients on vs. off medication, classification performance A0 ranged from 0.86 to 1.0 across brain regions. Moreover, the generalizability of the model to the second set of 50 trials was excellent, with A0 ranging from 0.81 to 0.94 across brain regions for controls vs. PD off medication, and from 0.62 to 0.82 for PD on medication vs. off. Finally, model features significantly predicted individual patients' motor severity, as assessed with standard clinical rating scales.
Non-linear Dynamical Classification of Short Time Series of the Rossler System in High Noise Regimes
Authors: Lainscsek, C., Hernandez, M.E., Weyhenmeyer, J., Poizner, H., Sejnowski,T.J.
Published: Society for Neuroscience Abstracts, 2013
Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson's disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to -30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A0 under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.