Adaptive latent state modeling of brain network dynamics with real-time learning rate optimization

Event detection and classification from multimodal time series with application to neural data

The detection of events in time-series data is a common signal-processing problem. When the data can be modeled as a known template signal with an unknown delay in Gaussian noise, detection of the template signal can be done with a traditional matched filter. However, in many applications, the event of interest is represented in multimodal data consisting of both Gaussian and point-process time series. Neuroscience experiments, for example, can simultaneously record multimodal neural signals such as local field potentials (LFPs), which can be modeled as Gaussian, and neuronal spikes, which can be modeled as point processes. Currently, no method exists for event detection from such multimodal data, and as such our objective in this work is to develop a method to meet this need. Here we address this challenge by developing the multimodal event detector (MED) algorithm which simultaneously estimates event times and classes. To do this, we write a multimodal likelihood function for Gaussian and point-process observations and derive the associated maximum likelihood estimator of simultaneous event times and classes. We additionally introduce a cross-modal scaling parameter to account for model mismatch in real datasets. We validate this method in extensive simulations as well as in a neural spike-LFP dataset recorded during an eye-movement task, where the events of interest are eye movements with unknown times and directions. We show that the MED can successfully detect eye movement onset and classify eye movement direction. Further, the MED successfully combines information across data modalities, with multimodal performance exceeding unimodal performance. This method can facilitate applications such as the discovery of latent events in multimodal neural population activity and the development of brain-computer interfaces for naturalistic settings without constrained tasks or prior knowledge of event times.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity

Objective.Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain-machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales.Approach.Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient learning for modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical SID method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and with spiking and local field potential population activity recorded during a naturalistic reach and grasp behavior.Main results.We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson-Gaussian observations, multiscale SID had a much lower training time while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity and behavior.Significance.Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest, such as for online adaptive BMIs to track non-stationary dynamics or for reducing offline training time in neuroscience investigations.

Modeling and dissociation of intrinsic and input-driven neural population dynamics underlying behavior

Neural dynamics can reflect intrinsic dynamics or dynamic inputs, such as sensory inputs or inputs from other brain regions. To avoid misinterpreting temporally structured inputs as intrinsic dynamics, dynamical models of neural activity should account for measured inputs. However, incorporating measured inputs remains elusive in joint dynamical modeling of neural-behavioral data, which is important for studying neural computations of behavior. We first show how training dynamical models of neural activity while considering behavior but not input or input but not behavior may lead to misinterpretations. We then develop an analytical learning method for linear dynamical models that simultaneously accounts for neural activity, behavior, and measured inputs. The method provides the capability to prioritize the learning of intrinsic behaviorally relevant neural dynamics and dissociate them from both other intrinsic dynamics and measured input dynamics. In data from a simulated brain with fixed intrinsic dynamics that performs different tasks, the method correctly finds the same intrinsic dynamics regardless of the task while other methods can be influenced by the task. In neural datasets from three subjects performing two different motor tasks with task instruction sensory inputs, the method reveals low-dimensional intrinsic neural dynamics that are missed by other methods and are more predictive of behavior and/or neural activity. The method also uniquely finds that the intrinsic behaviorally relevant neural dynamics are largely similar across the different subjects and tasks, whereas the overall neural dynamics are not. These input-driven dynamical models of neural-behavioral data can uncover intrinsic dynamics that may otherwise be missed.

Identifying behavioral links to neural dynamics of multifiber photometry recordings in a mouse social behavior network

Distributed hypothalamic-midbrain neural circuits orchestrate complex behavioral responses during social interactions. How population-averaged neural activity measured by multi-fiber photometry (MFP) for calcium fluorescence signals correlates with social behaviors is a fundamental question. We propose a state-space analysis framework to characterize mouse MFP data based on dynamic latent variable models, which include continuous-state linear dynamical system (LDS) and discrete-state hidden semi-Markov model (HSMM). We validate these models on extensive MFP recordings during aggressive and mating behaviors in male-male and male-female interactions, respectively. Our results show that these models are capable of capturing both temporal behavioral structure and associated neural states. Overall, these analysis approaches provide an unbiased strategy to examine neural dynamics underlying social behaviors and reveals mechanistic insights into the relevant networks.

Unsupervised learning of stationary and switching dynamical system models from Poisson observations

Objective. Investigating neural population dynamics underlying behavior requires learning accurate models of the recorded spiking activity, which can be modeled with a Poisson observation distribution. Switching dynamical system models can offer both explanatory power and interpretability by piecing together successive regimes of simpler dynamics to capture more complex ones. However, in many cases, reliable regime labels are not available, thus demanding accurate unsupervised learning methods for Poisson observations. Existing learning methods, however, rely on inference of latent states in neural activity using the Laplace approximation, which may not capture the broader properties of densities and may lead to inaccurate learning. Thus, there is a need for new inference methods that can enable accurate model learning.Approach. To achieve accurate model learning, we derive a novel inference method based on deterministic sampling for Poisson observations called the Poisson Cubature Filter (PCF) and embed it in an unsupervised learning framework. This method takes a minimum mean squared error approach to estimation. Terms that are difficult to find analytically for Poisson observations are approximated in a novel way with deterministic sampling based on numerical integration and cubature rules.Main results. PCF enabled accurate unsupervised learning in both stationary and switching dynamical systems and largely outperformed prior Laplace approximation-based learning methods in both simulations and motor cortical spiking data recorded during a reaching task. These improvements were larger for smaller data sizes, showing that PCF-based learning was more data efficient and enabled more reliable regime identification. In experimental data and unsupervised with respect to behavior, PCF-based learning uncovered interpretable behavior-relevant regimes unlike prior learning methods.Significance. The developed unsupervised learning methods for switching dynamical systems can accurately uncover latent regimes and states in population spiking activity, with important applications in both basic neuroscience and neurotechnology.

Post-stimulus encoding of decision confidence in EEG: toward a brain-computer interface for decision making

Objective.When making decisions, humans can evaluate how likely they are to be correct. If this subjective confidence could be reliably decoded from brain activity, it would be possible to build a brain-computer interface (BCI) that improves decision performance by automatically providing more information to the user if needed based on their confidence. But this possibility depends on whether confidence can be decoded right after stimulus presentation and before the response so that a corrective action can be taken in time. Although prior work has shown that decision confidence is represented in brain signals, it is unclear if the representation is stimulus-locked or response-locked, and whether stimulus-locked pre-response decoding is sufficiently accurate for enabling such a BCI.Approach.We investigate the neural correlates of confidence by collecting high-density electroencephalography (EEG) during a perceptual decision task with realistic stimuli. Importantly, we design our task to include a post-stimulus gap that prevents the confounding of stimulus-locked activity by response-locked activity and vice versa, and then compare with a task without this gap.Main results.We perform event-related potential and source-localization analyses. Our analyses suggest that the neural correlates of confidence are stimulus-locked, and that an absence of a post-stimulus gap could cause these correlates to incorrectly appear as response-locked. By preventing response-locked activity from confounding stimulus-locked activity, we then show that confidence can be reliably decoded from single-trial stimulus-locked pre-response EEG alone. We also identify a high-performance classification algorithm by comparing a battery of algorithms. Lastly, we design a simulated BCI framework to show that the EEG classification is accurate enough to build a BCI and that the decoded confidence could be used to improve decision making performance particularly when the task difficulty and cost of errors are high.Significance.Our results show feasibility of non-invasive EEG-based BCIs to improve human decision making.

State-space Model Based Inverse Reinforcement Learning for Reward Function Estimation in Brain-machine Interfaces

The use of reinforcement learning (RL) in brain machine interfaces (BMIs) is considered to be a promising method for neural decoding. One key component of RL-based BMIs is the reward signal, which is used to guide decoders to update the parameters. However, designing effective and efficient rewards can be challenging, especially for complex tasks. Inverse reinforcement learning (IRL) is a method that has been proposed to estimate the internal reward function from subjects' neural activity. However, multi-channel neural activity, which may encode many sources of information, builds a large dimensions of state-action space, making it difficult to directly apply IRL methods in BMI systems. In this paper, we propose a state-space model based inverse Q-learning (SSM-IQL) method to improve the performance of the existing IRL method. The state-space model is designed to extract hidden brain state from high-dimensional neural activity. We tested the proposed method on real data collected from rats during a two-lever discrimination task. Preliminary results show that SSM-IQL provides a more accurate and stable estimation of the internal reward function than the traditional IQL algorithm. This suggests that the use of state-space model in IRL method has potential to improve the design of RL-based BMIs.

Predictive neuromodulation of cingulo-frontal neural dynamics in major depressive disorder using a brain-computer interface system: A simulation study

Introduction

Deep brain stimulation (DBS) is a promising therapy for treatment-resistant major depressive disorder (MDD). MDD involves the dysfunction of a brain network that can exhibit complex nonlinear neural dynamics in multiple frequency bands. However, current open-loop and responsive DBS methods cannot track the complex multiband neural dynamics in MDD, leading to imprecise regulation of symptoms, variable treatment effects among patients, and high battery power consumption.

Methods

Here, we develop a closed-loop brain-computer interface (BCI) system of predictive neuromodulation for treating MDD. We first use a biophysically plausible ventral anterior cingulate cortex (vACC)-dorsolateral prefrontal cortex (dlPFC) neural mass model of MDD to simulate nonlinear and multiband neural dynamics in response to DBS. We then use offline system identification to build a dynamic model that predicts the DBS effect on neural activity. We next use the offline identified model to design an online BCI system of predictive neuromodulation. The online BCI system consists of a dynamic brain state estimator and a model predictive controller. The brain state estimator estimates the MDD brain state from the history of neural activity and previously delivered DBS patterns. The predictive controller takes the estimated MDD brain state as the feedback signal and optimally adjusts DBS to regulate the MDD neural dynamics to therapeutic targets. We use the vACC-dlPFC neural mass model as a simulation testbed to test the BCI system and compare it with state-of-the-art open-loop and responsive DBS treatments of MDD.

Results

We demonstrate that our dynamic model accurately predicts nonlinear and multiband neural activity. Consequently, the predictive neuromodulation system accurately regulates the neural dynamics in MDD, resulting in significantly smaller control errors and lower DBS battery power consumption than open-loop and responsive DBS.

Discussion

Our results have implications for developing future precisely-tailored clinical closed-loop DBS treatments for MDD.

Modeling and inference methods for switching regime-dependent dynamical systems with multiscale neural observations

Objective.Realizing neurotechnologies that enable long-term neural recordings across multiple spatial-temporal scales during naturalistic behaviors requires new modeling and inference methods that can simultaneously address two challenges. First, the methods should aggregate information across all activity scales from multiple recording sources such as spiking and field potentials. Second, the methods should detect changes in the regimes of behavior and/or neural dynamics during naturalistic scenarios and long-term recordings. Prior regime detection methods are developed for a single scale of activity rather than multiscale activity, and prior multiscale methods have not considered regime switching and are for stationary cases.Approach.Here, we address both challenges by developing a switching multiscale dynamical system model and the associated filtering and smoothing methods. This model describes the encoding of an unobserved brain state in multiscale spike-field activity. It also allows for regime-switching dynamics using an unobserved regime state that dictates the dynamical and encoding parameters at every time-step. We also design the associated switching multiscale inference methods that estimate both the unobserved regime and brain states from simultaneous spike-field activity.Main results.We validate the methods in both extensive numerical simulations and prefrontal spike-field data recorded in a monkey performing saccades for fluid rewards. We show that these methods can successfully combine the spiking and field potential observations to simultaneously track the regime and brain states accurately. Doing so, these methods lead to better state estimation compared with single-scale switching methods or stationary multiscale methods. Also, for single-scale linear Gaussian observations, the new switching smoother can better generalize to diverse system settings compared to prior switching smoothers.Significance.These modeling and inference methods effectively incorporate both regime-detection and multiscale observations. As such, they could facilitate investigation of latent switching neural population dynamics and improve future brain-machine interfaces by enabling inference in naturalistic scenarios where regime-dependent multiscale activity and behavior arise.

Designing and Validating a Robust Adaptive Neuromodulation Algorithm for Closed-Loop Control of Brain States

OBJECTIVE

Neuromodulation systems that use closed-loop brain stimulation to control brain states can provide new therapies for brain disorders. To date, closed-loop brain stimulation has largely used linear time-invariant controllers. However, nonlinear time-varying brain network dynamics and external disturbances can appear during real-time stimulation, collectively leading to real-time model uncertainty. Real-time model uncertainty can degrade the performance or even cause instability of time-invariant controllers. Three problems need to be resolved to enable accurate and stable control under model uncertainty. First, an adaptive controller is needed to track the model uncertainty. Second, the adaptive controller additionally needs to be robust to noise and disturbances. Third, theoretical analyses of stability and robustness are needed as prerequisites for stable operation of the controller in practical applications.

APPROACH

We develop a robust adaptive neuromodulation algorithm that solves the above three problems. First, we develop a state-space brain network model that explicitly includes nonlinear terms of real-time model uncertainty and design an adaptive controller to track and cancel the model uncertainty. Second, to improve the robustness of the adaptive controller, we design two linear filters to increase steady-state control accuracy and reduce sensitivity to high-frequency noise and disturbances. Third, we conduct theoretical analyses to prove the stability of the neuromodulation algorithm and establish a trade-off between stability and robustness, which we further use to optimize the algorithm design. Finally, we validate the algorithm using comprehensive Monte Carlo simulations that span a broad range of model nonlinearity, uncertainty, and complexity.

MAIN RESULTS

The robust adaptive neuromodulation algorithm accurately tracks various types of target brain state trajectories, enables stable and robust control, and significantly outperforms state-of-the-art neuromodulation algorithms.

SIGNIFICANCE

Our algorithm has implications for future designs of precise, stable, and robust closed-loop brain stimulation systems to treat brain disorders and facilitate brain functions.

EEG-Based Spectral Analysis Showing Brainwave Changes Related to Modulating Progressive Fatigue During a Prolonged Intermittent Motor Task

Repeatedly performing a submaximal motor task for a prolonged period of time leads to muscle fatigue comprising a central and peripheral component, which demands a gradually increasing effort. However, the brain contribution to the enhancement of effort to cope with progressing fatigue lacks a complete understanding. The intermittent motor tasks (IMTs) closely resemble many activities of daily living (ADL), thus remaining physiologically relevant to study fatigue. The scope of this study is therefore to investigate the EEG-based brain activation patterns in healthy subjects performing IMT until self-perceived exhaustion. Fourteen participants (median age 51.5 years; age range 26−72 years; 6 males) repeated elbow flexion contractions at 40% maximum voluntary contraction by following visual cues displayed on an oscilloscope screen until subjective exhaustion. Each contraction lasted ≈5 s with a 2-s rest between trials. The force, EEG, and surface EMG (from elbow joint muscles) data were simultaneously collected. After preprocessing, we selected a subset of trials at the beginning, middle, and end of the study session representing brain activities germane to mild, moderate, and severe fatigue conditions, respectively, to compare and contrast the changes in the EEG time-frequency (TF) characteristics across the conditions. The outcome of channel- and source-level TF analyses reveals that the theta, alpha, and beta power spectral densities vary in proportion to fatigue levels in cortical motor areas. We observed a statistically significant change in the band-specific spectral power in relation to the graded fatigue from both the steady- and post-contraction EEG data. The findings would enhance our understanding on the etiology and physiology of voluntary motor-action-related fatigue and provide pointers to counteract the perception of muscle weakness and lack of motor endurance associated with ADL. The study outcome would help rationalize why certain patients experience exacerbated fatigue while carrying out mundane tasks, evaluate how clinical conditions such as neurological disorders and cancer treatment alter neural mechanisms underlying fatigue in future studies, and develop therapeutic strategies for restoring the patients' ability to participate in ADL by mitigating the central and muscle fatigue.

Measuring and Modeling the Effect of Audio on Human Focus in Everyday Environments Using Brain-Computer Interface Technology

The goal of this study was to investigate the effect of audio listened to through headphones on subjectively reported human focus levels, and to identify through objective measures the properties that contribute most to increasing and decreasing focus in people within their regular, everyday environment. Participants (N = 62, 18–65 years) performed various tasks on a tablet computer while listening to either no audio (silence), popular audio playlists designed to increase focus (pre-recorded music arranged in a particular sequence of songs), or engineered soundscapes that were personalized to individual listeners (digital audio composed in real-time based on input parameters such as heart rate, time of day, location, etc.). Audio stimuli were delivered to participants through headphones while their brain signals were simultaneously recorded by a portable electroencephalography headband. Participants completed four 1-h long sessions at home during which different audio played continuously in the background. Using brain-computer interface technology for brain decoding and based on an individual’s self-report of their focus, we obtained individual focus levels over time and used this data to analyze the effects of various properties of the sounds contained in the audio content. We found that while participants were working, personalized soundscapes increased their focus significantly above silence (p = 0.008), while music playlists did not have a significant effect. For the young adult demographic (18–36 years), all audio tested was significantly better than silence at producing focus (p = 0.001–0.009). Personalized soundscapes increased focus the most relative to silence, but playlists of pre-recorded songs also increased focus significantly during specific time intervals. Ultimately we found it is possible to accurately predict human focus levels a priori based on physical properties of audio content. We then applied this finding to compare between music genres and revealed that classical music, engineered soundscapes, and natural sounds were the best genres for increasing focus, while pop and hip-hop were the worst. These insights can enable human and artificial intelligence composers to produce increases or decreases in listener focus with high temporal (millisecond) precision. Future research will include real-time adaptation of audio for other functional objectives beyond affecting focus, such as affecting listener enjoyment, drowsiness, stress and memory.

Modeling multiscale causal interactions between spiking and field potential signals during behavior

Objective. Brain recordings exhibit dynamics at multiple spatiotemporal scales, which are measured with spike trains and larger-scale field potential signals. To study neural processes, it is important to identify and model causal interactions not only at a single scale of activity, but also across multiple scales, i.e. between spike trains and field potential signals. Standard causality measures are not directly applicable here because spike trains are binary-valued but field potentials are continuous-valued. It is thus important to develop computational tools to recover multiscale neural causality during behavior, assess their performance on neural datasets, and study whether modeling multiscale causalities can improve the prediction of neural signals beyond what is possible with single-scale causality. Approach. We design a multiscale model-based Granger-like causality method based on directed information and evaluate its success both in realistic biophysical spike-field simulations and in motor cortical datasets from two non-human primates (NHP) performing a motor behavior. To compute multiscale causality, we learn point-process generalized linear models that predict the spike events at a given time based on the history of both spike trains and field potential signals. We also learn linear Gaussian models that predict the field potential signals at a given time based on their own history as well as either the history of binary spike events or that of latent firing rates. Main results. We find that our method reveals the true multiscale causality network structure in biophysical simulations despite the presence of model mismatch. Further, models with the identified multiscale causalities in the NHP neural datasets lead to better prediction of both spike trains and field potential signals compared to just modeling single-scale causalities. Finally, we find that latent firing rates are better predictors of field potential signals compared with the binary spike events in the NHP datasets. Significance. This multiscale causality method can reveal the directed functional interactions across spatiotemporal scales of brain activity to inform basic science investigations and neurotechnologies.

A Robust and Adaptive Control Algorithm for Closed-Loop Brain Stimulation

Developing closed-loop brain stimulation systems can benefit the treatment of neurological and neuropsychiatric disorders and facilitate brain functions. Current designs of closed-loop controllers have used time-invariant linear models of brain activity to devise non-adaptive controllers. However, unmodeled nonlinear dynamics can happen during real-time closed-loop control, leading to nonlinear uncertainty in the brain activity model. Current non-adaptive controllers cannot track the nonlinear model uncertainty and are not robust to noise, both of which can compromise their control performance. Here, within an ℒ₁ adaptive control framework, we develop a new discrete-time robust and adaptive closed-loop control algorithm that addresses a general form of nonlinear model uncertainty. We conduct Monte Carlo simulations to validate the robust and adaptive control algorithm and show that it significantly outperforms existing closed-loop control algorithms. Our results can facilitate future designs of precise and safe closed-loop brain stimulation systems to treat neurological and neuropsychiatric disorders and modulate brain functions.