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Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
Bingni W. Brunton, Lise A. Johnson, Jeffrey G. Ojemann, J. Nathan Kutz
TL;DR
Large-scale neural recordings contain coherent activity across space and time, while common methods often analyze these dimensions separately. The paper adapts dynamic mode decomposition to represent neural data with coupled spatial-temporal modes, validates it on motor recordings, and uses it with machine learning to extract sleep spindle networks. The authors report reliable detection of multiple spindle-network patterns in human ECoG recordings.
Problem
Existing approaches commonly analyze spatial or temporal structure separately, while reliable automated identification of sleep-spindle electrode networks remains limited.
Method
The paper adapts dynamic mode decomposition to neural recordings, using spatial modes and temporal dynamics to create a low-dimensional representation of activity across channels and time.
Results
The method was validated on a motor task and reliably detected multiple sleep-spindle network stereotypes, including localized and physically non-adjacent cortical correlations.
Takeaways & Limitations
DMD provides a framework for analyzing coherent spatial-temporal patterns in large-scale neural recordings and exploring sleep spindle networks.
Takeaways & Limitations
For electrode-array data, the economy SVD can restrict the maximum number of DMD modes to the number of channels, which may be too few to capture all temporal dynamics.
Abstract
from arXiv · showhide
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to hours. Such dynamic datasets are characterized by coherent patterns across both space and time, yet existing computational methods are typically restricted to analysis either in space or in time separately. Here we report the adaptation of dynamic mode decomposition (DMD), an algorithm originally developed for the study of fluid physics, to large-scale neuronal recordings. DMD is a modal decomposition algorithm that describes high-dimensional dynamic data using coupled spatial-temporal modes; the resulting analysis combines key features of performing principal components analysis (PCA) in space and power spectral analysis in time. The algorithm scales easily to very large numbers of simultaneously acquired measurements. We validated the DMD approach on sub-dural electrode array recordings from human subjects performing a known motor activation task. Next, we leveraged DMD in combination with machine learning to develop a novel method to extract sleep spindle networks from the same subjects. We suggest that DMD is generally applicable as a powerful method in the analysis and understanding of large-scale recordings of neural activity.
1 Introduction
Large-scale neural recordings contain coherent patterns across space and time, but existing approaches often analyze these dimensions separately. The paper introduces DMD to combine spatial and temporal modal analysis for neural recordings and demonstrates applications to motor mapping and sleep spindle-network extraction.
- Large-scale neural recordings motivate computational methods that can analyze, visualize, and understand high-dimensional brain activity.
- PCA captures spatial variance but is static and often reproduces dynamic neural time-series data poorly.
- Fourier- and EMD-based temporal analyses characterize signal oscillations but typically operate on individual signals rather than coupled spatial-temporal patterns.
- DMD reduces high-dimensional dynamic data into coupled spatial-temporal modes and combines temporal power-spectrum analysis with spatial PCA.
- The authors validated DMD on human sub-dural electrode recordings during movement and combined it with machine learning to detect sleep spindle networks.
- Sleep spindles occurred coincidentally across different electrode groups at different times, motivating network-level analysis of possible anatomical or functional organization.
- DMD is presented as applicable to escalating-scale neuroscience datasets, including fMRI, MEG, electrode-array, and optical recordings.
2 Results
DMD decomposes multichannel neural recordings into coupled spatial-temporal modes, using reduced representations to capture dynamics and reconstruct observed data. Applied to ECoG, it supports frequency-dependent motor mapping and extraction of distinct sleep spindle networks.
- Dynamic mode decomposition: The algorithm forms shifted data matrices, approximates their dynamics with a reduced operator, and obtains modes and eigenvalues through SVD-based eigendecomposition.The reduced operator is computed in the SVD basis rather than by directly decomposing the full high-dimensional operator.
- Dynamic mode decomposition: DMD decomposes high-dimensional recordings into coupled spatial-temporal modes, separating spatial modes from their temporal dynamics.Each DMD mode encodes spatial correlations, while its eigenvalue captures growth or decay and oscillation frequency.
- Low-rank DMD: Truncated DMD retains the r largest singular-value directions; for human ECoG, r = 40 modes captured over 95% of variance in 300 msec windows.Reconstruction error decreased as more modes were included, and its plateau helped inform truncation.
- Augmented data matrix: Because neural recordings often have fewer channels than time samples, time-shifted augmentation increases the effective channel dimension and addresses the resulting rank mismatch.Without augmentation, the maximum number of DMD modes is restricted by the number of channels.
- Sensorimotor maps: Movement produced decreased 8–32 Hz DMD magnitudes and increased 76–100 Hz magnitudes over sensorimotor cortex, with separable tongue and hand foci.Hand-movement foci were more dorsal than tongue-movement sites.
3 Discussion
The discussion presents DMD as a spatial-temporal dimensionality-reduction framework for large-scale neural recordings, validated through motor mapping and sleep spindle-network analysis. It emphasizes scalable analyses of dynamic neural patterns and potential extensions to incomplete measurements and varied recording modalities.
- Core contribution: DMD decomposes large-scale neural recordings into a low-dimensional representation capturing coherent patterns across space and multiple temporal frequencies.The approach provides modes and a data-driven linear model for how dynamically important modes evolve over time.
- Validation: Motor-task validation identified selective and separable sensorimotor-cortex regions associated with movement.
- Sleep spindle networks: The spindle-network method detected correlated electrode groups, including localized and physically non-adjacent cortical patterns, across two subjects.These networks were discovered independently of explicit behavior and may represent functionally connected cortical areas.
- Sleep spindle networks: Automated spindle-network identification supports analyses of event duration, frequency, relative timing, and relationships with sleep or pre-epileptic events across many subjects.The computation scales favorably as electrode-array channel counts increase.
- Future directions: DMD extensions that exploit data sparsity may broaden analysis to incomplete measurements with improved robustness.
- Future directions: The authors propose applying spatial-temporal DMD to ECoG, MEG, functional MRI, calcium imaging, LFP, and spike-rate measurements.
4.1 Collection and preprocessing of ECoG recordings
The study used long-term ECoG recordings from two epilepsy patients with sub-dural electrode arrays. Signals were acquired clinically, then filtered and normalized differently for motor mapping and sleep-spindle extraction.
- Participants and recordings: Data came from two female patients undergoing long-term ECoG monitoring before surgical treatment for intractable epilepsy.
- Participants and recordings: Sub-dural platinum electrode arrays had 2.3 mm exposed surfaces and 1 cm spacing.
- Signal acquisition: ECoG signals were recorded at 500 or 2000 Hz using a clinical monitoring system with an approximately 0.1 Hz high-pass filter.
- Preprocessing: Motor-mapping recordings were high-pass filtered above 6 Hz, downsampled to 100 samples/sec, and lasted approximately 4 minutes.
- Preprocessing: For each sleep epoch, electrode traces were z-scored relative to amplitude in the 5–50 Hz range to reduce variable K-complex amplitude effects.
4.2 Sensorimotor mapping
Sensorimotor mapping divided recordings into baseline, tongue-movement, and hand-movement trials, then applied DMD to the middle 2 seconds of each trial across all channels.
- Trial design: Trials were divided into baseline, tongue-movement, and hand-movement conditions for sensorimotor mapping.
- Analysis window: The analysis used the middle 2 seconds of each trial, from 500 to 2500 msec after instruction onset.
- DMD analysis: Each 2-second, all-channel recording window was decomposed by DMD.
4.3 Spindle network extraction
Spindle networks were extracted by detecting DMD modes with excess 11–17 Hz power and clustering the detected modes into stereotyped network types.
- Spindle detection: 300 msec ECoG windows, shifted by 100 msec, were decomposed with DMD to detect modes associated with spindle activity.The DMD spectrum was examined for increased power in the 11–17 Hz spindle band.
- Spindle detection: A robust 1/f^α fit established the expected spectrum, excluding frequencies below 18 Hz and above 57 Hz and rejecting windows with presumptive epileptiform activity.The fit used cumulative DMD spectra for each recording epoch and rejected sporadic electrical-noise outliers.
- Spindle detection: A DMD mode qualified as part of a spindle network only when its power exceeded the upper 99% confidence interval of the 1/f^α fit.Significant spindle-band power also had to persist across three consecutive overlapping windows.
- Network clustering: Qualifying DMD modes from every window were collected into a library and clustered into distinct spindle-network types.The clustering grouped recurring spatial patterns across the recording.
- Network clustering: The clustering used unit-normalized absolute DMD modes projected into r-dimensional principal-components space before Gaussian-mixture modeling.The projections were formed from the first r principal components of |L|.
- Network clustering: The number of clusters was selected by minimizing BIC while varying r from 3–15 and k from 2–10.BIC was used to compare model descriptions with different parameter counts while penalizing overfitting.