David B. Grayden

Yueyang Liu, Artemio Soto-Breceda, Yun Zhao et al.

Objective Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to EEG. However, this approach lacks a reliable method to determine the initial filter conditions and assumes that the distribution of states remains Gaussian. This study presents an alternative, data-driven method to track the states and parameters of neural mass models (NMMs) from EEG recordings using deep learning techniques, specifically an LSTM neural network. Approach An LSTM filter was trained on simulated EEG data generated by a neural mass model using a wide range of parameters. With an appropriately customised loss function, the LSTM filter can learn the behaviour of NMMs. As a result, it can output the state vector and parameters of NMMs given observation data as the input. Main Results Test results using simulated data yielded correlations with R squared of around 0.99 and verified that the method is robust to noise and can be more accurate than a nonlinear Kalman filter when the initial conditions of the Kalman filter are not accurate. As an example of real-world application, the LSTM filter was also applied to real EEG data that included epileptic seizures, and revealed changes in connectivity strength parameters at the beginnings of seizures. Significance Tracking the state vector and parameters of mathematical brain models is of great importance in the area of brain modelling, monitoring, imaging and control. This approach has no need to specify the initial state vector and parameters, which is very difficult to do in practice because many of the variables being estimated cannot be measured directly in physiological experiments. This method may be applied using any neural mass model and, therefore, provides a general, novel, efficient approach to estimate brain model variables that are often difficult to measure.

Jonas F. Haderlein, Andre D. H. Peterson, Parvin Zarei Eskikand et al.

Predicting future system behaviour from past observed behaviour (time series) is fundamental to science and engineering. In computational neuroscience, the prediction of future epileptic seizures from brain activity measurements, using EEG data, remains largely unresolved despite much dedicated research effort. Based on a longitudinal and state-of-the-art data set using intercranial EEG measurements from people with epilepsy, we consider the automated discovery of predictive features (or biomarkers) to forecast seizures in a patient-specific way. To this end, we use the path signature, a recent development in the analysis of data streams, to map from measured time series to seizure prediction. The predictor is based on linear classification, here augmented with sparsity constraints, to discern time series with and without an impending seizure. This approach may be seen as a step towards a generic pattern recognition pipeline where the main advantages are simplicity and ease of customisation, while maintaining forecasting performance on par with modern machine learning. Nevertheless, it turns out that although the path signature method has some powerful theoretical guarantees, appropriate time series statistics can achieve essentially the same results in our context of seizure prediction. This suggests that, due to their inherent complexity and non-stationarity, the brain's dynamics are not identifiable from the available EEG measurement data, and, more concretely, epileptic episode prediction is not reliably achieved using EEG measurement data alone.

Jonas F. Haderlein, Andre D. H. Peterson, Anthony N. Burkitt et al.

Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity. Crucially, this data is subject to measurement errors as well as uncertainties in the underlying system model. As a result, standard signal processing using autoregressive model estimators may be biased. We present a framework for autoregressive modelling that incorporates these uncertainties explicitly via an overparameterised loss function. To optimise this loss, we derive an algorithm that alternates between state and parameter estimation. Our work shows that the procedure is able to successfully denoise time series and successfully reconstruct system parameters. This new paradigm can be used in a multitude of applications in neuroscience such as brain-computer interface data analysis and better understanding of brain dynamics in diseases such as epilepsy.

Johnson Zhou, Joseph West, Krista A. Ehinger et al.

Objective. Electroencephalography (EEG) data is derived by sampling continuous neurological time series signals. In order to prepare EEG signals for machine learning, the signal must be divided into manageable segments. The current naive approach uses arbitrary fixed time slices, which may have limited biological relevance because brain states are not confined to fixed intervals. We investigate whether adaptive segmentation methods are beneficial for machine learning EEG analysis. Approach. We introduce a novel adaptive segmentation method, CTXSEG, that creates variable-length segments based on statistical differences in the EEG data and propose ways to use them with modern machine learning approaches that typically require fixed-length input. We assess CTXSEG using controllable synthetic data generated by our novel signal generator CTXGEN. While our CTXSEG method has general utility, we validate it on a real-world use case by applying it to an EEG seizure detection problem. We compare the performance of CTXSEG with fixed-length segmentation in the preprocessing step of a typical EEG machine learning pipeline for seizure detection. Main results. We found that using CTXSEG to prepare EEG data improves seizure detection performance compared to fixed-length approaches when evaluated using a standardized framework, without modifying the machine learning method, and requires fewer segments. Significance. This work demonstrates that adaptive segmentation with CTXSEG can be readily applied to modern machine learning approaches, with potential to improve performance. It is a promising alternative to fixed-length segmentation for signal preprocessing and should be considered as part of the standard preprocessing repertoire in EEG machine learning applications.

Jing Mu, David B. Grayden, Ying Tan et al.

The steady-state visual evoked potential (SSVEP) is one of the most widely used modalities in brain-computer interfaces (BCIs) due to its many advantages. However, the existence of harmonics and the limited range of responsive frequencies in SSVEP make it challenging to further expand the number of targets without sacrificing other aspects of the interface or putting additional constraints on the system. This paper introduces a novel multi-frequency stimulation method for SSVEP and investigates its potential to effectively and efficiently increase the number of targets presented. The proposed stimulation method, obtained by the superposition of the stimulation signals at different frequencies, is size-efficient, allows single-step target identification, puts no strict constraints on the usable frequency range, can be suited to self-paced BCIs, and does not require specific light sources. In addition to the stimulus frequencies and their harmonics, the evoked SSVEP waveforms include frequencies that are integer linear combinations of the stimulus frequencies. Results of decoding SSVEPs collected from nine subjects using canonical correlation analysis (CCA) with only the frequencies and harmonics as reference, also demonstrate the potential of using such a stimulation paradigm in SSVEP-based BCIs.

Jing Mu, Ying Tan, David B. Grayden et al.

Stimulation methods that utilise more than one stimulation frequency have been developed for steady-state visual evoked potential (SSVEP) brain-computer interfaces (BCIs) with the purpose of increasing the number of targets that can be presented simultaneously. However, there is no unified decoding algorithm that can be used without training for each individual users or cases, and applied to a large class of multi-frequency stimulated SSVEP settings. This paper extends the widely used canonical correlation analysis (CCA) decoder to explicitly accommodate multi-frequency SSVEP by exploiting the interactions between the multiple stimulation frequencies. A concept of order, defined as the sum of absolute value of the coefficients in the linear combination of the input frequencies, was introduced to assist the design of Multi-Frequency CCA (MFCCA). The probability distribution of the order in the resulting SSVEP response was then used to improve decoding accuracy. Results show that, compared to the standard CCA formulation, the proposed MFCCA has a 20% improvement in decoding accuracy on average at order 2, while keeping its generality and training-free characteristics.