Stochastic optimal control of single neuron spike trains

Controlling neural activity: LPV modelling of optogenetically actuated Wilson-Cowan model. J Neural Eng 2024;21:036002. [PMID: 38653250 DOI: 10.1088/1741-2552/ad4212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Objective.This paper aims to bridge the gap between neurophysiology and automatic control methodologies by redefining the Wilson-Cowan (WC) model as a control-oriented linear parameter-varying (LPV) system. A novel approach is presented that allows for the application of a control strategy to modulate and track neural activity.Approach.The WC model is redefined as a control-oriented LPV system in this study. The LPV modelling framework is leveraged to design an LPV controller, which is used to regulate and manipulate neural dynamics.Main results.Promising outcomes, in understanding and controlling neural processes through the synergistic combination of control-oriented modelling and estimation, are obtained in this study. An LPV controller demonstrates to be effective in regulating neural activity.Significance.The presented methodology effectively induces neural patterns, taking into account optogenetic actuation. The combination of control strategies with neurophysiology provides valuable insights into neural dynamics. The proposed approach opens up new possibilities for using control techniques to study and influence brain functions, which can have key implications in neuroscience and medicine. By means of a model-based controller which accounts for non-linearities, noise and uncertainty, neural signals can be induced on brain structures.

State-space optimal feedback control of optogenetically driven neural activity

Objective.The rapid acceleration of tools for recording neuronal populations and targeted optogenetic manipulation has enabled real-time, feedback control of neuronal circuits in the brain. Continuously-graded control of measured neuronal activity poses a wide range of technical challenges, which we address through a combination of optogenetic stimulation and a state-space optimal control framework implemented in the thalamocortical circuit of the awake mouse.Approach.Closed-loop optogenetic control of neurons was performed in real-time via stimulation of channelrhodopsin-2 expressed in the somatosensory thalamus of the head-fixed mouse. A state-space linear dynamical system model structure was used to approximate the light-to-spiking input-output relationship in both single-neuron as well as multi-neuron scenarios when recording from multielectrode arrays. These models were utilized to design state feedback controller gains by way of linear quadratic optimal control and were also used online for estimation of state feedback, where a parameter-adaptive Kalman filter provided robustness to model-mismatch.Main results.This model-based control scheme proved effective for feedback control of single-neuron firing rate in the thalamus of awake animals. Notably, the graded optical actuation utilized here did not synchronize simultaneously recorded neurons, but heterogeneity across the neuronal population resulted in a varied response to stimulation. Simulated multi-output feedback control provided better control of a heterogeneous population and demonstrated how the approach generalizes beyond single-neuron applications.Significance.To our knowledge, this work represents the first experimental application of state space model-based feedback control for optogenetic stimulation. In combination with linear quadratic optimal control, the approaches laid out and tested here should generalize to future problems involving the control of highly complex neural circuits. More generally, feedback control of neuronal circuits opens the door to adaptively interacting with the dynamics underlying sensory, motor, and cognitive signaling, enabling a deeper understanding of circuit function and ultimately the control of function in the face of injury or disease.

Design strategies for dynamic closed-loop optogenetic neurocontrol in vivo

OBJECTIVE

Controlling neural activity enables the possibility of manipulating sensory perception, cognitive processes, and body movement, in addition to providing a powerful framework for functionally disentangling the neural circuits that underlie these complex phenomena. Over the last decade, optogenetic stimulation has become an increasingly important and powerful tool for understanding neural circuit function, owing to the ability to target specific cell types and bidirectionally modulate neural activity. To date, most stimulation has been provided in open-loop or in an on/off closed-loop fashion, where previously-determined stimulation is triggered by an event. Here, we describe and demonstrate a design approach for precise optogenetic control of neuronal firing rate modulation using feedback to guide stimulation continuously.

APPROACH

Using the rodent somatosensory thalamus as an experimental testbed for realizing desired time-varying patterns of firing rate modulation, we utilized a moving average exponential filter to estimate firing rate online from single-unit spiking measured extracellularly. This estimate of instantaneous rate served as feedback for a proportional integral (PI) controller, which was designed during the experiment based on a linear-nonlinear Poisson (LNP) model of the neuronal response to light.

MAIN RESULTS

The LNP model fit during the experiment enabled robust closed-loop control, resulting in good tracking of sinusoidal and non-sinusoidal targets, and rejection of unmeasured disturbances. Closed-loop control also enabled manipulation of trial-to-trial variability.

SIGNIFICANCE

Because neuroscientists are faced with the challenge of dissecting the functions of circuit components, the ability to maintain control of a region of interest in spite of changes in ongoing neural activity will be important for disambiguating function within networks. Closed-loop stimulation strategies are ideal for control that is robust to such changes, and the employment of continuous feedback to adjust stimulation in real-time can improve the quality of data collected using optogenetic manipulation.

Control Analysis and Design for Statistical Models of Spiking Networks

A popular approach to characterizing activity in neuronal networks is the use of statistical models that describe neurons in terms of their firing rates (i.e., the number of spikes produced per unit time). The output realization of a statistical model is, in essence, an n-dimensional binary time series, or pattern. While such models are commonly fit to data, they can also be postulated de novo, as a theoretical description of a given spiking network. More generally, they can model any network producing binary events as a function of time. In this paper, we rigorously develop a set of analyses that may be used to assay the controllability of a particular statistical spiking model, the point-process generalized linear model (PPGLM). Our analysis quantifies the ease or difficulty of inducing desired spiking patterns via an extrinsic input signal, thus providing a framework for basic network analysis, as well as for emerging applications such as neurostimulation design.

Minimal time spiking in various ChR2-controlled neuron models

We use conductance based neuron models, and the mathematical modeling of optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of geometric optimal control theory to study singular extremals, and we implement a direct method to compute optimal controls. When the system is too large to theoretically investigate the existence of singular optimal controls, we observe numerically the optimal bang-bang controls.

Algorithmic design of a noise-resistant and efficient closed-loop deep brain stimulation system: A computational approach

Advances in the field of closed-loop neuromodulation call for analysis and modeling approaches capable of confronting challenges related to the complex neuronal response to stimulation and the presence of strong internal and measurement noise in neural recordings. Here we elaborate on the algorithmic aspects of a noise-resistant closed-loop subthalamic nucleus deep brain stimulation system for advanced Parkinson’s disease and treatment-refractory obsessive-compulsive disorder, ensuring remarkable performance in terms of both efficiency and selectivity of stimulation, as well as in terms of computational speed. First, we propose an efficient method drawn from dynamical systems theory, for the reliable assessment of significant nonlinear coupling between beta and high-frequency subthalamic neuronal activity, as a biomarker for feedback control. Further, we present a model-based strategy through which optimal parameters of stimulation for minimum energy desynchronizing control of neuronal activity are being identified. The strategy integrates stochastic modeling and derivative-free optimization of neural dynamics based on quadratic modeling. On the basis of numerical simulations, we demonstrate the potential of the presented modeling approach to identify, at a relatively low computational cost, stimulation settings potentially associated with a significantly higher degree of efficiency and selectivity compared with stimulation settings determined post-operatively. Our data reinforce the hypothesis that model-based control strategies are crucial for the design of novel stimulation protocols at the backstage of clinical applications.

A Review of Control Strategies in Closed-Loop Neuroprosthetic Systems

It has been widely recognized that closed-loop neuroprosthetic systems achieve more favorable outcomes for users then equivalent open-loop devices. Improved performance of tasks, better usability, and greater embodiment have all been reported in systems utilizing some form of feedback. However, the interdisciplinary work on neuroprosthetic systems can lead to miscommunication due to similarities in well-established nomenclature in different fields. Here we present a review of control strategies in existing experimental, investigational and clinical neuroprosthetic systems in order to establish a baseline and promote a common understanding of different feedback modes and closed-loop controllers. The first section provides a brief discussion of feedback control and control theory. The second section reviews the control strategies of recent Brain Machine Interfaces, neuromodulatory implants, neuroprosthetic systems, and assistive neurorobotic devices. The final section examines the different approaches to feedback in current neuroprosthetic and neurorobotic systems.

Performance breakdown in optimal stimulus decoding

OBJECTIVE

One of the primary goals of neuroscience is to understand how neurons encode and process information about their environment. The problem is often approached indirectly by examining the degree to which the neuronal response reflects the stimulus feature of interest.

APPROACH

In this context, the methods of signal estimation and detection theory provide the theoretical limits on the decoding accuracy with which the stimulus can be identified. The Cramér-Rao lower bound on the decoding precision is widely used, since it can be evaluated easily once the mathematical model of the stimulus-response relationship is determined. However, little is known about the behavior of different decoding schemes with respect to the bound if the neuronal population size is limited.

MAIN RESULTS

We show that under broad conditions the optimal decoding displays a threshold-like shift in performance in dependence on the population size. The onset of the threshold determines a critical range where a small increment in size, signal-to-noise ratio or observation time yields a dramatic gain in the decoding precision.

SIGNIFICANCE

We demonstrate the existence of such threshold regions in early auditory and olfactory information coding. We discuss the origin of the threshold effect and its impact on the design of effective coding approaches in terms of relevant population size.