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We present a neural network approach for closed-loop deep brain stimulation (DBS). We cast the problem of finding an optimal neurostimulation strategy as a control problem. In this setting, control policies aim to optimize therapeutic outcomes by tailoring the parameters of a DBS system, typically via electrical stimulation, in real time based on the patient’s ongoing neuronal activity. We approximate the value function offline using a neural network to enable generating controls (stimuli) in real time via the feedback form. The neuronal activity is characterized by a nonlinear, stiff system of differential equations as dictated by the Hodgkin-Huxley model. Our training process leverages the relationship between Pontryagin’s maximum principle and Hamilton-Jacobi-Bellman equations to update the value function estimates simultaneously. Our numerical experiments illustrate the accuracy of our approach for out-of-distribution samples and the robustness to moderate shocks and disturbances in the system.
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Modeling the effect of magnetoelectric nanoparticles on neuronal electrical activity: An analog circuit approach
This paper introduces a physical neuron model that incorporates magnetoelectric nanoparticles (MENPs) as an essential electrical circuit component to wirelessly control local neural activity. Availability of such a model is important as MENPs, due to their magnetoelectric effect, can wirelessly and noninvasively modulate neural activity, which, in turn, has implications for both finding cures for neurological diseases and creating a wireless noninvasive high-resolution brain-machine interface. When placed on a neuronal membrane, MENPs act as magnetic-field-controlled finite-size electric dipoles that generate local electric fields across the membrane in response to magnetic fields, thus allowing to controllably activate local ion channels and locally initiate an action potential. Herein, the neuronal electrical characteristic description is based on ion channel activation and inhibition mechanisms. A MENP-based memristive Hodgkin–Huxley circuit model is extracted by combining the Hodgkin–Huxley model and an equivalent circuit model for a single MENP. In this model, each MENP becomes an integral part of the neuron, thus enabling wireless local control of the neuron’s electric circuit itself. Furthermore, the model is expanded to include multiple MENPs to describe collective effects in neural systems.
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- Award ID(s):
- 2211082
- PAR ID:
- 10522453
- Publisher / Repository:
- Biointerphases
- Date Published:
- Journal Name:
- Biointerphases
- Volume:
- 19
- Issue:
- 3
- ISSN:
- 1934-8630
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin–Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin–Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.more » « less
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Abstract Over the past decade, magnetoelectric nanoparticles (MENPs) have proven effective in generating local electric fields in response to stimulation with a magnetic field. The applications of such nanoparticles are many and varied, with examples of prior research including use for on-demand drug release, wireless modulation and recording of neural activity, and organic dye degradation. This study investigates the potential for organic dye degradation to be used as a rapid and efficient screening tool to detect the magnetoelectric effect of MENPs, and how the results of such a test mirror the antiproliferative effect of said nanoparticles. Trypan blue was selected as an azo dye to test for dye degradation. Vials of the dye were treated with CoFe2O4@BaTiO3 core-shell MENPs of varying characteristics, both with and without concurrent 1-kHz 250-Oe magnetic stimulation. Dye degradation was measured using ultraviolet (UV)-vis spectroscopy. Dye degradation efficacy varied with varying nanoparticle synthesis parameters. As controls, nanoparticles of the same composition, but with an insignificant magnetoelectric effect, were used. SKOV-3 ovarian cancer cells were then treated with the same nanoparticles, and viability was measured with an adenosine triphosphate (ATP) assay. These measurements show a decrease in cell viability up to 60.3% of control (p = 0.0052), which mirrored the efficacy of dye degradation of up to 69.8% (p = 0.0037) in each of the particle variants, demonstrating the value of azo dye degradation as a simple screening test for MENPs, and showing the potential of MENPs used as wirelessly controlled nanodevices to allow targeted electric field-based treatments.more » « less
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Abstract Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control, which employs a dynamical model of the system to find optimal control inputs, has promise for dealing with the nonlinear dynamics, high levels of exogenous noise, and limited information about unmeasured states and parameters that are common in a wide range of neural systems. However, the challenge still remains of selecting the right model, constraining its parameters, and synchronizing to the neural system.Approach. As a proof of principle, we used recent advances in data-driven forecasting to construct a nonlinear machine-learning model of a Hodgkin–Huxley type neuron when only the membrane voltage is observable and there are an unknown number of intrinsic currents.Main Results. We show that this approach is able to learn the dynamics of different neuron types and can be used with model predictive control (MPC) to force the neuron to engage in arbitrary, researcher-defined spiking behaviors.Significance.To the best of our knowledge, this is the first application of nonlinear MPC of a conductance-based model where there is only realistically limited information about unobservable states and parameters.more » « less
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Abstract The ability to finely manipulate spatiotemporal patterns displayed in neuronal populations is critical for understanding and influencing brain functions, sleep cycles, and neurological pathologies. However, such control tasks are challenged not only by the immense scale but also by the lack of real-time state measurements of neurons in the population, which deteriorates the control performance. In this paper, we formulate the control of dynamic structures in an ensemble of neuron oscillators as a tracking problem and propose a principled control technique for designing optimal stimuli that produce desired spatiotemporal patterns in a network of interacting neurons without requiring feedback information. We further reveal an interesting presentation of information encoding and processing in a neuron ensemble in terms of its controllability property. The performance of the presented technique in creating complex spatiotemporal spiking patterns is demonstrated on neural populations described by mathematically ideal and biophysical models, including the Kuramoto and Hodgkin-Huxley models, as well as real-time experiments on Wein bridge oscillators.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1116/5.0199163
