Closed-Loop neuromodulation for clustering neuronal populations

Abstract

Pathological synchronization of neurons is associated with symptoms of movement disorders, such as Parkinson’s disease and essential tremor. High-frequency deep brain stimulation (DBS) suppresses symptoms, presumably through the desynchronization of neurons. Coordinated reset (CR) delivers trains of high-frequency stimuli to different regions in the brain through multiple electrodes and may have more persistent therapeutic effects than conventional DBS. As an alternative to CR, we present a closed-loop control setup that desynchronizes neurons in brain slices by inducing clusters using a single electrode. Our setup uses calcium fluorescence imaging to extract carbachol-induced neuronal oscillations in real time. To determine the appropriate stimulation waveform for inducing clusters in a population of neurons, we calculate the phase of the neuronal populations and then estimate the phase response curve (PRC) of those populations to electrical stimulation. The phase and PRC are then fed into a control algorithm called the input of maximal instantaneous efficiency (IMIE). By using IMIE, the synchrony across the slice is decreased by dividing the population of neurons into subpopulations without suppressing the oscillations locally. The desynchronization effect is persistent 10 s after stimulation is stopped. The IMIE control algorithm may be used as a novel closed-loop DBS approach to suppress the symptoms of Parkinson’s disease and essential tremor by inducing clusters with a single electrode.

NEW & NOTEWORTHY Here, we present a closed-loop controller to desynchronize neurons in brain slices by inducing clusters using a single electrode using calcium imaging feedback. Phase of neurons are estimated in real time, and from the phase response curve stimulation is applied to achieve target phase differences. This method is an alternative to coordinated reset and is a novel therapy that could be used to disrupt synchronous neuronal oscillations thought to be the mechanism underlying Parkinson’s disease.

INTRODUCTION

Pathological synchronization of neuronal populations is proposed to be responsible for the symptoms of Parkinson’s disease (PD) (1–7) and essential tremor (8). The therapeutic effect of deep brain stimulation (DBS) is therefore attributed to the desynchronization of neurons (9–14).

Recent theoretical and experimental studies, using an approach known as coordinated reset (CR), suggest that inducing clusters in neuronal populations—usually done with segmented electrodes—may have more persistent therapeutic effects than full desynchronization with continuous high-frequency DBS (15–17). The mechanism of action of CR is not fully understood, but computational studies suggest that CR changes the synaptic strengths in the neuronal network such that the system is less likely to return back to the synchronized state, as normally occurs shortly after the stimulus is turned off (18).

If the effectiveness of CR is due to the formation of clusters in a neuronal population, an alternative approach that achieves clustered states in a completely different way might be just as effective. A new mathematical algorithm developed by our colleagues, termed input of maximal instantaneous efficiency (IMIE), induces clusters in a population of oscillators with a uniform stimulus (19). IMIE calculates the stimulation to be delivered to a set of synchronized oscillators using the phase of the individual oscillators tracked in real time and the phase response of those oscillators to an external stimulus, known as the phase response curve (PRC). The stimulus is applied at times when the population is most vulnerable to desynchronization into clusters. After desynchronization is achieved, IMIE then maintains the phase difference between the clusters.

In this work, we use IMIE to induce clusters in a population of synchronized neurons in rat hippocampal slices by delivering an electrical stimulus through a single bipolar electrode so that all neurons receive a common stimulation waveform. To model pathological synchronization, we generate spontaneous oscillations through the bath perfusion of a cholinomimetic drug, carbachol. Depending on the concentration, carbachol is known to generate in vitro spontaneous oscillations in a hippocampal slice from theta to gamma bands (20–24). We apply a weak oscillatory electric field across the slice to prevent the oscillation frequency from drifting and to promote synchrony (25). Then, we measure the neuronal activity using calcium imaging. A PRC is estimated by stimulating the slice and measuring the response of the calcium oscillations. Finally, we use IMIE to induce and maintain phase differences between different regions of interest (ROIs) in the slice without suppressing the oscillations locally.

METHODS

Brain Slice Preparation

We chose to use rat hippocampal slices to test our closed-loop neuromodulation algorithm because spontaneous oscillations can be generated through the bath perfusion of carbachol and the Schaffer collateral makes it possible for a single electrode to activate a large region of the CA1. All experiments were done in accordance with a protocol approved by the University of Minnesota Institutional Animal Care and Use Committee (IACUC). Brain slices 400-µm thick were prepared from 14- to 21-day-old Long-Evans (L/E) rats using a Vibratome 3000 tissue sectioning system. Slices were incubated in standard artificial cerebrospinal fluid (aCSF) with a composition (in mM) of 124 NaCl, 2 KCl, 2 MgSO₄, 1.25 NaH₂PO₄, 2 CaCl₂, 26 NaHCO₃, and 10 D-glucose (26) at 33°C for at least 1 h. To measure the neuronal activity, Cal-520 AM (AAT Bioquest) calcium indicator with an excitation/emission wavelength at 490/525 nm was used. The dye solution was prepared by dissolving 50 µg of the dye in 48 µL of dimethyl sulfoxide (DMSO) and 1% pluronic acid (27). For staining, 6–8 µL of the dye was dispensed on the surface of the slices in a 2-mL aCSF bath. The slices were then incubated in the dark for 30 min and transferred back into aCSF solution for another hour. The aCSF solution was oxygenated by bubbling 95% O₂ and 5% CO₂ through it for the entire duration of the experiment.

Cell Recordings and Feedback Control

For fluorescence imaging, the slices were transferred to a chamber equipped with a pair of electrodes 6.3-mm apart for generating an oscillating electric field at 6 Hz (see Fig. 1). The electric field was 5–8 mV/mm, which was strong enough to perturb the neurons but not strong enough to generate spontaneous oscillations. Unless reported otherwise, aCSF with 100 µM carbachol was circulated at 0.5–1 mL/min. Images were acquired with an Olympus BX51 WI microscope with a 10× objective and a NeuroCCD-SMQ camera from Redshirt Imaging. Imaging data were digitized by a Little Joe frame grabber and analyzed in real time with in-house-written C code.

Figure 1.

Closed-loop control setup. Calcium imaging data collected with the microscope and camera are analyzed by the computer in real time. The oscillation phase of neurons in each cluster is then calculated, and the appropriate stimulation signal is delivered to the slice with a parallel microelectrode. Two parallel electrodes across the slice generate a weak oscillating electric field at 6 Hz to strengthen the oscillation and prevent drifts in the frequency over the duration of the experiment. Stim, stimulation; DAQ, data acquisition.

Before the control experiment, raw calcium fluorescence data were collected for 40 s and principal component analysis (PCA) was carried out to identify the spatial weighting of pixels whose temporal component had strong oscillations at 5–7 Hz. For each experiment, the first few principal components arise from electrical noise in a range of 12–20 Hz. Therefore, we used fifth to eighth components, where the frequency of interest was dominant. Due to experimental limitations, we tracked the activity of neuronal populations instead of individual neurons. From the area with strongest oscillations at 5–7 Hz, four regions of interest (ROIs) perpendicular to the cell body layer covering CA1, each with a surface area of ∼500 × 200 µm, were selected by hand. The ROIs were treated as phase oscillators similar to individual neurons and represented four clusters to be controlled. Although the number of ROIs is arbitrary, we chose four to be consistent with Matchen and Moehlis (19). The fluorescence light intensity for all pixels were summed over each ROI at each frame. To calculate the phase and amplitude of the oscillations for each ROI in real time, we used a novel sliding discrete-time Fourier transform (DTFT) algorithm called sliding windowed infinite Fourier transform (SWIFT) (28). The SWIFT algorithm predicts the phase and amplitude for the next time point from the current phase and amplitude, which is phase shifted and discounted:

$$X_{t+\Delta t} \left(\omega \right)=e^{-\Delta t/\tau }{e}^{j\omega \Delta t}{X}_t\left(\omega \right)+x_{t+\Delta t}-x_t$$ (1)

where x is calcium fluorescence in time domain, X is Fourier transform of calcium fluorescence data at the central frequency, t is time, Δt is the timestep, ω is the central frequency, j is the imaginary unit, and $e^{-\Delta t/\tau }$ is the window function with $\tau$ being the time constant of the window. We used differentials of the calcium fluorescence data to minimize the effect of the decay in calcium signal on our analysis. In contrast to conventional DTFT methods, SWIFT has advantages that make it suitable for real-time analysis, including good stability and the ability to assign greater weights to more recent samples. Unlike Hilbert transform methods, SWIFT is a causal algorithm.

To characterize how electrical stimulation modulated the phase of the calcium oscillations, we measured the oscillation period after perturbation (29). The ratio of the measured period to the expected period as a function of the stimulus phase was used to estimate the PRC. We calculated the appropriate stimulation signal for maximizing the phase divergence between the four ROIs using the control IMIE algorithm developed by Matchen and Moehlis (19). Unlike traditional methods for clustering oscillators, IMIE does not require multiple control input sources, as it induces clusters with a common stimulation signal using the phases estimated in real time in combination with a model of how the oscillations respond to perturbation. The controller delivers the stimulation signal to the oscillators to disperse them in phase. IMIE is more energy effective in inducing clusters than regular high-frequency DBS or CR algorithms.

For the case of two oscillators, the IMIE stimulation signal is roughly proportional to $\frac{sin\left(\Delta Z\left(\theta ,t\right)\right)}{\Delta \theta \left(t\right)\sqrt{\Delta \theta \left(t\right)}}$, where $\Delta Z\left(\theta ,t\right)$ is the difference between PRCs and $\Delta \theta \left(t\right)$ is the phase difference between the two oscillators (19). Therefore, the strongest stimulation will be delivered when the oscillators are close in phase but the phase advance difference is maximal.

A schematic representation of the closed-loop setup is shown in Fig. 1. Figure 2 shows a flow chart of the closed-loop experiments. The codes for performing the experiments are available at https://github.com/s110faramarzi/IMIE-Experiments.

Figure 2.

Flow charts of the closed-loop experiment. A: the general experimental protocol. B: flow chart of closed-loop neuromodulation. AMP, amplifier; DG, dendrite gyrus; IMIE stim, maximal instantaneous efficiency stimulation; PCA, principal component analysis; PRC, phase response curve; ROIs, regions of interest; SC, Schaffer collateral; SWIFT, sliding windowed infinite Fourier transform.

RESULTS

To model pathological synchronization, we generated spontaneous oscillations in a hippocampal slice through the bath perfusion of carbachol and the application of a weak oscillatory electric field. Figure 3 illustrates a representative spontaneous oscillation in the CA1 region. To measure neural activity, the slices were stained with Cal-520 AM indicator. To extract oscillations from the fluorescence signal, we performed PCA. Figure 3, B and C show the temporal and spatial components, respectively, of the principal components. We used Thomson’s multitaper analysis of the temporal components to identify those components with a strong oscillation in the 5–7 Hz band with respect to the background; an example is shown in Fig. 3D. To prevent drift in the oscillation frequency, we applied a weak oscillating electric field across the slice at the frequency of the spontaneous oscillation, as shown in the schematic in Fig. 1.

Figure 3.

Extraction of carbachol-induced oscillations with principal component analysis (PCA). To induce spontaneous oscillations, hippocampal brain slices were stained with calcium indicator dye and perfused with artificial cerebrospinal fluid (aCSF) containing carbachol. A: raw fluorescence image showing the cell layers in CA1. B: fifth PCA temporal component of the strongest oscillations at 6 Hz in an arbitrary unit (ABU). C: PCA spatial component, where the brightness of pixels corresponds to the contribution to the temporal component. D: power spectral density of the PCA temporal component showing a peak at 6 Hz from the spontaneous oscillations induced by carbachol.

For the IMIE control algorithm, we needed to extract the phase in real time and measure the PRC of the calcium oscillations to electrical stimulation. The phase was extracted in real time with the SWIFT algorithm, as shown in Fig. 4B. A comparison of the power spectral density (PSD) for the original PCA component (blue) and the component filtered through the SWIFT algorithm (black) is shown in Fig. 4C.

Figure 4.

Phase extraction in real time. A: time evolution of the principal component analysis (PCA) component with the strongest oscillation extracted from the fluorescence data in an arbitrary unit (ABU). B: analytic signal of the PCA component extracted using the SWIFT algorithm. The filtered data around 6.7 Hz (real, blue), the 90^° phase shifted data (imaginary, red), and the instantaneous amplitude (absolute, orange) plotted over time. C: power spectral density (PSD) of the raw PCA component (blue) and the signal filtered through the sliding windowed infinite Fourier transform (SWIFT) algorithm (black).

To estimate the PRCs, pulses with a 0.5–1 mV amplitude and 100 µs width were delivered to the Schaffer collateral at 1–4 Hz through a platinum-iridium parallel bipolar microelectrode, whereas the calcium fluorescence of the CA1 was recorded optically (Fig. 5A). The phase advance induced by the stimulus was measured as the ratio of the oscillation period following the stimulus to the period expected from the oscillation frequency. The PRC is the phase advance as a function of the phase at which the stimulation was delivered. An example of a PRC for the calcium oscillations in response to electrical stimulation is shown in Fig. 5B. To fit a function to the data to estimate the PRC, we repeated the data three times by shifting the data by −2π and 2π each time, and performed a 12th-order polynomial fit so that the fitted PRC is periodic.

Figure 5.

Estimating the phase response curve (PRC) of the calcium oscillation responses to electrical stimulation. A: time evolution of the calcium oscillation phase (blue) and electrical stimulation (orange). B: PRC (blue circles) and a polynomial fit (black curve).

The goal of this study was to cause phase divergence in ROIs through electrical stimulation using information about the phase in real time. IMIE was used to determine the stimulus needed to control the phase difference between oscillatory systems using the phase of each population estimated in real time and their PRCs. The PRC for all ROIs in the CA1 was similar (see Supplemental Fig. S2; Supplemental Figures are available at https://doi.org/10.5281/zenodo.4305003) and we assume it remained unchanged during the experiment. We then divided the CA1 into four regions, as shown in Fig. 6A. Figure 6D shows the phases of the four ROIs over time. The stimulation signal is off for the first 5 s of the experiment to establish a baseline, and as expected, all ROIs are synchronized at the same phase. After baseline is established, the stimulus is applied to the Schaffer collateral, and the phases start to diverge. Figure 6C shows how the phase synchrony between ROIs changes over time. Supplemental Fig. S3 shows another example of the phase evolution including a time window after modulation. Based on comparison of the PSDs of the four CA1 regions before and after application of the control algorithm, as shown in Fig. 6B, desynchronization weakens the peak at 6 Hz. The amplitudes of the individual regions remain the same or decrease slightly with modulation, but the signal-to-noise ratio decreases significantly (see Supplemental Fig. S1) indicating that stimulation adds power to the frequencies close to the oscillation frequency.

Figure 6.

Feedback-controlled desynchronization in neurons. A: the CA1 region is divided into four arbitrary regions of interest (ROIs) within which the phase at 6 Hz is estimated in real time. The layers of CA1 are labeled oriens (Or), pyramidale (Pyr), radiatum (Rad), and lacunosum moleculare (LM). B: power spectral density (PSD) for 5-s periods before (blue) and during (black) closed-loop desynchronization averaged across all four ROIs. The peak at 6 Hz decreases due to desynchronization. C: average phases of the four ROIs at selected times plotted on the unit circle. D: phase of each of the four ROIs over time. E: stimulation (Stim) waveform in mV. The feedback controller is turned on at 5 s. F: average phase difference between the four clusters. Phases diverge within a few seconds after the stimulus is turned on.

We repeated the experiment across 20 slices from nine animals. Figure 7 shows the average phase difference between the four clusters relative to the baseline collected during stimulation. As seen, the average phase difference increases as the control is applied. We performed a Wilcoxon rank-sum test (α = 0.05) and found a significant decrease in synchrony when comparing the power measured premodulation to that measured during the modulation window (P = 8.7 × 10⁻⁵). We also saw a decrease in synchrony in the 10 s window following modulation (P = 9.5 × 10⁻³); this decrease seemed to be more persistent for the trials with the highest desynchronization.

Figure 7.

Control algorithm effectively desynchronizes neurons. The y-axis shows the average phase difference normalized to the premodulation phase difference. Each curve represents a separate experiment. A Wilcoxon rank-sum test (α = 0.05) showed a significant increase in phase difference over the baseline during modulation and postmodulation (P = 8.7 × 10⁻⁵). No significant decrease in phase difference was observed in the window immediately following modulation compared to the modulation window, indicating that desynchronization persists following modulation (P = 9.5 × 10⁻³).

DISCUSSION

Here, we tested a novel closed-loop algorithm as a method to desynchronize neuronal populations rather than suppress them. We analyzed calcium fluorescence data to extract oscillations in hippocampal slices. Then, we used our control algorithm to change the relative phases of the subpopulations in the slice by delivering an electrical stimulus through a single electrode. Stimulation was strong when populations were vulnerable to desynchronization and weak when divergence was achieved or their phase was insensitive to the stimulation.

One way to control synchrony in dynamical systems is to shift them between chaotic and periodic states. Ott and et al. (30) have shown that a chaotic system where oscillators are desynchronized is transformed to a periodic state, where they are synchronized, through stabilization of unstable periodic orbits with an external perturbation. Schiff and et al. (31) have used chaos control techniques to make bursts in brain slices periodic or chaotic, depending on the stimulation time. Using phase resetting curves of neuronal bursters, Neiman and et al. (32) were able to induce clusters with repeated stimuli. Our theoretical studies with Wilson et al. (14) have shown that chaotic desynchronization is achieved with repetitive stimulation at a certain range of stimulus amplitude and frequencies. As an alternative approach, this work estimates the phase of oscillators at the current time to determine the stimulation to shift the system from a fully synchronized state to a splay state, whereas both the starting and target states are periodic.

Our work was motivated by the preliminary finding that CR methods show more persistent suppression of symptoms than conventional DBS in in vitro (33), non-human primate models of PD (34) and in human patients (15). CR has been proposed to drive the population into clusters, and the timing between the clusters may induce plasticity, resulting in more permanent synaptic changes. However, CR is open-loop and requires multiple electrodes. Here, we induce clusters with a closed-loop neuromodulation setup using a single electrode.

Current closed-loop techniques often use biomarkers, such as increased neuronal discharge in motor cortex (35) or basal ganglia (36–38), for patients with PD or non-human primate models of PD (39, 40). Also, tremor sensed using an accelerometer on the patient’s hand has been used as a biomarker for closed-loop control (41). IMIE, in contrast, uses phase differences in real time as a biomarker for determining the stimulus needed to desynchronize neurons without suppressing the oscillations.

IMIE is generalizable and may be applied to almost any kind of oscillator as long as the phase and PRC are measurable. In the original formulation, IMIE assumed that the neurons are identical and uncoupled and that their phase order cannot change. However, in our experiments, we observed the activities of brain regions rather than of individual neurons. Furthermore, our study allowed the phase order of the ROIs to change. Despite these relaxations, we found that the desynchronization of brain areas achieved with IMIE is similar to that obtained in simulations (19). In the simulations, the average phase difference between four clusters is close to the maximum, $\frac{\pi }{2}$, and the phase difference is maintained to the end of the simulation (19). In the experiments, the average phase difference was far from the maximum, and the clustered state was not maintained for long (see Fig. 6F as an example). The tendency of the system to return to the synchronized state may be due to short-term depression or adaptation.

An interesting finding of our study is that desynchronization persisted beyond the application of IMIE, as seen in Fig. 7. This result might be due to changes in synaptic weights in the neuronal network. Furthermore, for a set of coupled neurons, the clustered state is more stable than the fully desynchronized state. We leave the investigation of the induced clustered states and their effects on plasticity and network connectivity for future work.

We have used a train of pulses to measure the PRC, that may cause adaptation (42). Furthermore, the PRC itself may change during the modulation. Finally, due to the electrical noise in the system, we were unable to obtain PRCs with infinitesimal stimulations, as used in the computational model of the IMIE algorithm. Despite all these relaxations, we have found that IMIE is able to desynchronize neurons; however, IMIE may be further improved by using adaptive control techniques to optimize the stimulation waveform without a priori estimating the PRC. Recently, our laboratory has developed a Bayesian adaptive dual controller that optimizes the stimulus based on the phase of β oscillations (43), and this controller may be combined with our control algorithm. Ideally, a DBS setup needs to be simple and energy efficient. Our approach is a step toward that design goal.

Patients with DBS may suffer from side effects such as undesired changes in movement (44–46) and even mood (47, 48). These side effects may be reduced with closed-loop or adaptive DBS, as the stimulation signal is delivered only when needed.

CONCLUSIONS

In this work, we have introduced a closed-loop control algorithm to induce clusters in brain slices in real time using optical signals and electrical feedback. Unlike in CR methods, here, the clusters are achieved with a single input signal. The simplicity of this closed-loop algorithm allows it to be adopted in a variety of therapeutic applications, such as for the treatment of epilepsy, essential tremor, and depression, where synchronous oscillations may underlie the pathology.

GRANTS

This work was supported by the National Science Foundation (NSF) 1634445, “Collaborative research: Understanding and optimizing dynamic stimulation for improvement of short- and long-term brain function” and the National Institutes of Health (NIH) 5P50NS098573, “Circuit-based deep brain stimulation for Parkinson’s disease” (TIN).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

S.F. and T.I.N. conceived and designed research; performed experiments; analyzed data; interpreted results of experiments; prepared figures; drafted manuscript; edited and revised manuscript; approved final version of manuscript.

ENDNOTE

At the request of the authors, readers are herein alerted to the fact that additional materials related to this manuscript may be found at https://github.com/s110faramarzi/IMIE-Experiments. These materials are not a part of this manuscript and have not undergone peer review by the American Physiological Society (APS). APS and the journal editors take no responsibility for these materials, for the website address, or for any links to or from it.