The excessive oscillatory synchronisation that emerges in neurological disorders, such as Parkinson’s disease and epilepsy (Uhlhaas and Singer, 2006), can be disrupted using direct electrical stimulation (Edwards et al., 2017). Despite its potential, conventional brain stimulation, therapies still rely on continuous open-loop stimulation, leading to excessive stimulation and burdensome side-effects (Kuo et al., 2018). In theory, closed-loop stimulation guided by an efficient control algorithm should provide better outcomes, disrupting the pathological neuronal dynamics with minimal intervention. But, given the complexity of neuronal systems, it is very challenging to foresee what type of control algorithms would be effective. Multiple in silico studies focused on employing closed-loop control methods to desynchronise pathological oscillations in computational models of neurological disorders (Beverlin Ii and Netoff, 2012; Holt et al., 2016; Nabi et al., 2013; Weerasinghe et al., 2021; Witt et al., 2013), but these have not been translated into studies with real neuronal systems to access its viability.

A particularly prevalent method in the field is delayed feedback control (DFC), a technique from chaos theory developed to stabilise/destabilise chaotic systems using minimal perturbations (Pyragas, 1992; Rosenblum and Pikovsky, 2004a). DFC controls the system by applying a feedback signal proportional to the difference between the current oscillation amplitude and the oscillation amplitude from a fixed delay into the past. DFC has been extensively applied in the context of in silico neuroscience, with studies focusing on specific disorders such as Parkinson’s disease (Rosenblum and Pikovsky, 2004b; Vlachos et al., 2016; Popovych et al., 2017; Daneshzand et al., 2018; Popovych and Tass, 2019; Yu et al., 2021) and epilepsy (Zhou et al., 2020). However, there is still controversy in the literature regarding its efficacy and whether it may instead promote synchronisation, depending on the baseline levels of synchrony of the modelled network (Dovzhenok et al., 2013). Thus, it is critical to test the effectiveness of DFC with biological neuronal networks that display synchronised oscillatory firing. Neuronal cultures on microelectrode arrays (MEAs) are a useful testbed for this task: these cultures self-organise into complex interconnected networks with quasiperiodic synchronised bursting, and MEAs enable closed-loop modulation of the neuronal activity, providing concurrent recording and stimulation at multiple points of the population with high spatial and temporal resolution (Obien et al., 2014).

In this work, we implemented, for the first time, the DFC algorithm to disrupt the synchronised oscillatory bursting of biological neuronal populations. The cells were cultured on MEAs and the network activity was monitored and controlled in real time with electrical stimulation. We show that traditional DFC lacks the adaptability to cope with the malleable dynamics of biological networks and may actually impose a new firing periodicity. As an alternative, we developed and implemented an adaptive DFC (aDFC) algorithm that self-tunes to better predict the current oscillation phase and periodicity. We demonstrate that aDFC reduces the synchronisation of the network and efficiently disrupts the baseline oscillation. While doing so, we identified and characterised a new feature of biological neuronal networks: the intrinsic firing dynamics of a network unveils its propensity for neuromodulation. To better understand this relationship, we went back to the in silico neuronal networks and revealed that their controllability can be conditioned by specific parameters of the network architecture, such as the excitatory/inhibitory balance and overall synaptic weights of the network connections. Taking all together, we show that theoretical predictions regarding the efficacy of DFC might be misleading and we present an improved algorithm for closed-loop electrical stimulation. The knowledge gathered while testing these algorithms in vitro was relevant to recognise shortcomings of in silico simulations and may guide the development of better computational neuronal models. Our results revealed fundamental properties and considerations regarding the controllability of neuronal systems.

To assess the potential of DFC as a closed-loop brain stimulation protocol (Figure 1A, top) for suppressing pathological neuronal oscillations, we developed an in vitro setup composed of hippocampal networks cultured on MEAs, a workstation running the control algorithms and specialised hardware (2100MEA-System, Multichannel Systems [MCS]) interfacing both environments at very low latencies (Figure 1A, bottom). Our in vitro setup provides a powerful testbed to analyse DFC algorithms as it incorporates neuronal populations that display synchronous oscillations (here in the form of quasiperiodic network bursts [NB] with periodicities in the seconds range), an acquisition system that measures the population’s extracellular activity at high spatiotemporal resolution enabling the inference of synchrony among neurons, on-demand electrical pulse generators to stimulate the network at high spatiotemporal resolution, and a feedback loop with low actuation latency in the milliseconds range (orders of magnitude below that of the neuronal dynamics under control).

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The core of the DFC algorithm used (Figure 1B, black) is analogous to implementations reported in the literature (see Methods section for details). After spike detection (Figure 1C, top row), the instantaneous population firing rate is calculated (Figure 1C, middle row) and filtered by a damped oscillator (Figure 1C, bottom row in blue). The resulting signal is a good representation of the oscillatory behaviour of the network, such as that exhibited while the stimulation is turned OFF (Figure 1C, left). The feedback signal (Figure 1C, left, bottom in red) is then created by subtracting the ongoing oscillation from the half-cycle delayed oscillation (Figure 1C, bottom row in grey). This way, when the activity is oscillatory, the actuation signal is maximal at the antiphase of the neuronal oscillation (Figure 1C, left and middle). The obtained feedback signal is linearly translated to stimulation frequency by applying a fixed gain. Since the actuation signal is explicitly dependent on the neuronal oscillation, stimulation is highly activated when synchrony is high (Figure 1C, middle) and decreases as this firing pattern vanishes (Figure 1C, right). Expanding on the DFC algorithm, and to respond to the dynamic nature of biological neuronal systems, we improved canonical DFC to aDFC by adding an extra component that detects the synchronous firing events (Figure 1C, black circles in middle row). This way, aDFC monitors the current periodicity of the neuronal oscillation (T) and updates the delay duration (T/2) and natural frequency of the oscillator (ω) accordingly (Figure 1B, blue and Figure 1—figure supplement 1).

The neuromodulation performance of the control algorithms was analysed in a series of experiments with multiple neuronal populations on MEAs. Each experiment had three stages: 5 min of spontaneous activity pre-stimulation (OFF), 5 min under stimulation (ON), and 5 min of spontaneous activity post-stimulation (OFF). Every network, here defined as a neuronal culture on a given day in vitro, was submitted to three different stimulation algorithms: standard DFC, aDFC, and random stimulation. During random stimulation, the electrical pulses were triggered by a Poisson process with an average frequency identical to that obtained in the preceding aDFC test. In all algorithms, stimulation was provided as monophasic negative voltage pulses at controlled timings. To ensure that the individual pulses had a comparable effect on the different neuronal networks, we chose a single stimulation electrode that triggered a neuronal response measured by neighbouring electrodes and the minimum voltage amplitude that achieved that response (see Methods section).

Adaptive component is required due to the dynamic nature of neuronal populations

Changes in the neuronal dynamics caused by the stimulation protocols can be evaluated using the wavelet transform of the instantaneous network firing rate (Figure 2A and B). This representation evidences how the bursting periodicity of the network changes over time. Consistent inter-burst intervals (i.e. consistent neuronal oscillations) will appear as an horizontal line in the wavelet domain, corresponding to the fundamental frequency of the oscillation. When stimulation was activated, both DFC and aDFC showed clear effects on the neuronal dynamics. DFC stimulation imposed a change to a faster and very consistent oscillation (DFC periods in Figure 2A and C). This happens because DFC initially forces the network to fire in its antiphase, creating a change in the bursting periodicity. Since this change is not monitored to update the controller’s delay, the delayed oscillator (Figure 1C, grey) no longer matches the antiphase of the ongoing oscillation. Therefore, stimulation becomes prejudicial as it is sent in phase with the new oscillation, reinforcing it (DFC period in Figure 2C).

Figure 2

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On the other hand, aDFC disrupts the spontaneous oscillation frequency exhibited by the network, creating a firing regime where there is no predominant oscillation (aDFC periods in Figure 2B and E). In this case, the controller is constantly forcing the network to fire in antiphase and aDFC adapts as the network oscillation changes with the stimulation. To quantify this effect, we calculated the magnitude of the main oscillation by calculating the signal-to-noise ratio (SNR) of the power spectrum density (PSD) of the instantaneous firing rate for the ON and OFF segments (Figure 2D and F).

Network controllability is conditioned by intrinsic population dynamics

The effect of the different stimulation protocols was evaluated using three metrics calculated for the OFF and ON periods: synchrony, firing rate, and oscillation intensity. Synchrony measures the degree of co-activation of multiple electrodes (see Methods); firing rate corresponds to the average number of spikes per electrode per unit of time (not to be confused with the instantaneous network firing rate signal presented in Figure 2C and E); oscillation intensity corresponds to the SNR of the PSD of the instantaneous firing rate signal (Figure 2D and F).

The three stimulation protocols were repeated multiple times for each network following the OFF-ON-OFF routine. Their effects on a given network are evidenced by normalising the values of each feature to the initial OFF period (before stimulation) across the multiple trials (Figure 3A). This also reveals how the dynamics are recovered once the stimulation is turned OFF. Note that, for the oscillation intensity, this normalisation corresponds to the difference between the ON and OFF periods, since the SNR scale is logarithmic [dB].

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Some networks were consistently driven to distinct regions of the features space with each stimulation protocol (Figure 3B). We refer to these as controllable networks – hypothetically, an ideal controller could lead such networks to any desired reachable state. On the other hand, some networks did not exhibit consistent modulation when stimulated using the different protocols (Figure 3C). We termed these uncontrollable networks. Based on this definition, each network was classified as either controllable or uncontrollable by calculating the multivariate ANOVA (MANOVA) for the ON values of the three metrics (see Methods for details). Networks with low p-values (p<0.05) (i.e. networks with significantly distinct neuromodulation results for the different stimulation protocols) were considered controllable (Figure 3D). Conceptually, controllability of a network is dependent on the assumed stimulation configuration: a network may be controllable with an array of stimulating electrodes, and uncontrollable using a single stimulating electrode.

Having recognised that some networks are controllable, we questioned if there are any common traits that make them more prone to neuromodulation. Even though there may be an indefinite number of hidden variables that influence the controllability of a neuronal population, some of these properties could be translated into specific firing dynamics, which we can access with the MEAs. If that is the case, then we expect the controllable and uncontrollable networks to have distinct fingerprints in their spontaneous firing dynamics. To evaluate this hypothesis, as well as ensure that the uncontrollable networks did not simply result from an ineffective stimulation electrode, we compared the spontaneous firing rate and synchrony during the initial OFF period (before stimulation) for all the experiments performed with all networks. This revealed that, as hypothesised, controllable and uncontrollable networks lie in different regions of the feature space (Figure 3E and Figure 3—figure supplement 1). Furthermore, controllable networks are in the centre, which is associated with intermediate levels of spontaneous firing rate and synchrony. This can be further evidenced by calculating the principal components (using principal components analysis) of the standardised map and projecting the values of each experiment along the principal component. A histogram shows that the experiments performed with controllable networks are in the centre, surrounded by a bimodal distribution of the experiments performed with uncontrollable networks (Figure 3F).

aDFC disrupts oscillations and decreases overall synchrony in controllable networks

The performances of DFC, aDFC, and Poisson stimulation were evaluated by comparing their average effects on the three metrics across all the controllable network (Figure 4), where each datapoint corresponds to the metric’s mean for all the experiments performed with a given network and stimulation protocol. Uncontrollable networks are not considered here as their results are, by definition, not reproducible. We included trials without stimulation for each network as a control group to capture the natural variability of each metric; in these, we calculated the metrics for two consecutive 5 min blocks of spontaneous activity, representing the initial OFF and ON periods.

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The most significant distinction between control algorithms was evidenced at the level of the bursting oscillations (Figure 4A). Both aDFC and random stimulation led to a significant decrease in oscillation intensity (see also Figure 3—figure supplement 2 for a representative wavelet transform under Poisson stimulation). The standard DFC algorithm, on the other hand, led to a significant increase in the oscillations. This increase in magnitude was followed by an increase in the oscillation frequency (Figure 2A, C and D and Figure 3—figure supplement 3). The only stimulation protocol that led to a significant decrease in synchrony was aDFC (Figure 4B) and its effect was significantly different from that of random stimulation. On the other hand, it was also the only method that significantly increased the average firing rate (Figure 4D), even though the average stimulation frequency was similar for the three methods (Figure 4—figure supplement 1).

Controllability is affected by synaptic strength and balance between excitation and inhibition

We then sought to understand whether the controllability subspace found for the neuronal cultures portrayed any fundamental property of these types of systems and what parameters could govern such behaviour. We modelled randomly connected networks of 1000 Izhikevich neurons (Izhikevich, 2003) with different proportions of regular spiking excitatory neurons and fast-spiking inhibitory neurons. We also varied the overall synaptic weight (see Methods for details). Each condition was simulated five times. The simulations were composed of two different periods: spontaneous activity (OFF) and controlled activity (aDFC ON). For each simulation, we computed the overall synchrony and firing rate for the OFF (Figure 5A) and aDFC ON periods (Figure 5B).

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Low percentages of excitatory neurons and weak synaptic weights within the network led to sparse and chaotic activity (region 1 in Figure 5A–C). In this scenario, the controller is sporadically activated due to fluctuations of neuronal activity, creating brief moments of synchronisation (Figure 5C, top). High percentages of excitatory neurons and strong synaptic weights led to highly ordered network dynamics with strong bursting activity (region 3 in Figure 5A–C). Here, the controller could not disrupt the dominating spontaneous activity (Figure 5C, bottom). However, in the transition between these two network states, there was a parameter subspace that generated intermediate baseline levels of firing rate and synchrony (region 2 in Figure 5A–C). In parallel to what was found in vitro, the networks were controllable in this intermediate region (see also Figure 5—figure supplement 1). Here, aDFC could desynchronise the network shortly after activating the stimulation (Figure 5C, middle). Thus, among the multiple possible parameters governing network controllability, the excitatory/inhibitory balance and overall network connectivity strength could explain the separation into controllable and uncontrollable networks seen in vitro.

aDFC can promote transitions to stable asynchronous states

The majority of the in vitro cultures had monostable dynamics, presenting a very consistent firing pattern over time (e.g. OFF periods of Figure 2). In these networks, even though aDFC reduced neuronal synchronisation (Figure 4C) and disrupted baseline oscillatory activity (Figure 2B, E and F and Figure 4A), it generally did so by creating sparser bursting with no particular periodicity. In monostable networks, aDFC did not promote a phase transition to a stable asynchronous state (AS) as opposed to what is typically seen in DFC computational studies (Rosenblum and Pikovsky, 2004a; Vlachos et al., 2016; Popovych et al., 2017; Daneshzand et al., 2018; Popovych and Tass, 2019; Yu et al., 2021; Zhou et al., 2020).

We also found a less common type of networks that had multi-stable dynamics, spontaneously transitioning between different firing regimes. Multi-stable networks were particularly interesting when they presented sporadic transitions to an AS as it showed that these networks could autonomously sustain asynchronous activity, even if only for short periods of time (Figure 6). The different stable states were identified using unsupervised clustering on the values of firing rate and synchrony calculated over a sliding window (Figure 6A and B). A given state was considered asynchronous if its average synchrony was below 0.5 and the mean firing rate was below the average of that network. The obtained clusters correlate with the different regimes seen in the frequency domain (Figure 6C).

Figure 6

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To evaluate the effectiveness of each stimulation protocol in promoting transitions to AS, we compared the percentage of time spent in AS during the OFF and ON periods in multi-stable networks (Figure 6). Since our experimental protocol was composed of 5 min blocks (OFF-ON-OFF), the desynchronising effect of the closed-loop stimulation was only clear for networks that spontaneously exhibited rare and brief (considerably less than 5 min) AS. This way, a significant increase in the time spent in AS during the ON periods was most likely caused by the closed-loop stimulation. Out of all the networks tested, one presented the required criteria to evaluate this effect (Figure 7A and B).

Figure 7

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aDFC consistently promoted desynchronisation in all the trials performed with this network, leading to a considerable increase of time spent in AS (Figure 7C and D). DFC stimulation, on the other hand, tended to impose a new bursting periodicity (as already reported), sometimes interrupted by transitions to AS (Figure 7E and F). However, the percentage of time spent in AS during DFC stimulation is within the range of spontaneous transitions and thus cannot be directly attributed to DFC. Random Poisson stimulation with identical stimulation frequency promoted sparser bursting with some transitions to AS, but these are also within the range of spontaneous transitions (Figure 7G and H). This means that the precisely timed stimuli determined by aDFC are causing the transitions to the AS. Also, the random Poisson stimulation, being an open-loop protocol, does not stop once the desired AS is achieved, which could be a significant drawback in a clinical setting.

Controlling brain activity is a long-standing goal in neuroengineering and holds great potential for multiple clinical applications. This is a challenging problem because neuronal systems have complex dynamics, virtually impossible to fully observe, and the space of actions available to an external controller is highly restricted. Most of these constraints are circumvented in computational studies, allowing researchers to explore solutions in a highly controlled environment. However, under such simplified conditions, these solutions may converge to algorithms that fail when applied to biological neuronal populations. It is, therefore, important to assess the performance of such algorithms with simple biological neuronal systems before moving to in vivo trials. In this work, we tested, for the first time, the efficacy of conventional DFC in an in vitro setting and reported that it promoted a new bursting frequency, instead of ablating it. This is in line with the claim that linear DFC could lead to synchronisation if the delay deviated substantially from the half-period (Pyragas, 2006). This was shown in silico by testing different delays with the same network. Here, however, the deviation from the half-period delay was caused by the fact that DFC stimulation induced a faster periodicity, while the delay was kept constant. The neuronal dynamics aligned with the non-adaptive controller to the point that almost all activity was confined to stimulus responses (Figure 4—figure supplement 1). This was not predicted by computational studies, possibly because the simple in silico networks used were not as dynamic as biological ones and, therefore, could not sustain different synchronisation periodicities.

The adaptive version, aDFC, effectively disrupted the oscillations and decreased network synchrony. Interestingly, random stimulation, using similar stimulation frequency, was also able to achieve this, although without significantly decreasing synchronisation. Electrical stimulation may be acting as a disrupter of the network dynamics, as it has been proposed for high-frequency deep brain stimulation (Chiken and Nambu, 2016).

We showed that not all networks could be effectively modulated by each stimulation protocol. However, it is important to note that controllability is contingent on the neurostimulation conditions. In particular, the fact that we only used one stimulating electrode may restrict the pool of controllable networks. We did so to follow the principle that DFC should control the system using minimal intervention (Rosenblum and Pikovsky, 2004a). Also, despite the fact that aDFC decreased the synchrony of controllable networks, the neuronal activity was still mostly dominated by synchronous events. These results were far from those obtained in previous in silico studies, where the synchronous events vanish almost completely. We point to two possible causes. First, with our setup, we could only apply excitatory electrical stimulation, much like existing implantable stimulators. For this reason, when the actuation signal (here modulated as a stimulation frequency) was negative, we sent no input to the network. Nonetheless, in theory, using only the positive phase of the actuation signal should still prevent the formation of synchronous events, as it did in our in silico tests. So, it is possible that the limiting factor is the neuronal model itself. The unconstrained growth of our hippocampal cultures may have led to highly interconnected networks whose neurons simply cannot fire asynchronously. This is further supported by the fact that aDFC consistently promoted the AS in a network that could already sustain it autonomously. Again, these considerations are conditioned to the method used, whose main goal was to achieve desynchronisation with minimal intervention. Other methods can achieve network desynchronisation by following approaches that are more aggressive. Namely, it was already shown that continuous stimulation at higher frequencies (10–50 Hz), distributed across multiple electrodes, can prevent network synchronisation (Wagenaar et al., 2005). This is done, however, at the cost of highly increasing the overall network’s firing rate, thus possibly establishing yet another non-physiological state. The goal of avoiding an abnormal prolonged increase in the population’s firing rate is grounded on the understanding that excessive activity is also detrimental in a neuronal circuit. Whether aDFC is more efficient in disrupting pathological oscillations than high-frequency stimulation (HFS) used in current stimulation therapies remains unknown. Nevertheless, as opposed to fixed/continuous HFS, aDFC stimulation adapts to the population oscillation frequency and ceases once the network is desynchronised.

Despite being able to disrupt the baseline oscillation and decreasing synchrony levels, there is still margin to improve the aDFC algorithm by making it self-adaptive in terms of the actuation gain, pulse amplitude, and selection of stimulation electrode(s), all of which were tuned manually before starting the experiments. It remains to be explored whether such an adaptive controller would consistently achieve full desynchronisation in this type of networks.

To conclude, the technological advances made in implantable neurostimulators open the door for the use of algorithms capable of controlling pathological neuronal dynamics. We show that aDFC has the potential to be a promising candidate and believe that the considerations extracted from this in vitro study will support the translation to future in vivo experiments.

The data that support the findings of this study are openly available in ZENODO at the following URL/DOI: https://doi.org/10.5281/zenodo.10138445.

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Author details

1. Domingos Leite de Castro

   1. Neuroengineering and Computational Neuroscience Lab, i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal
   2. Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2539-0311

2. Miguel Aroso

   Neuroengineering and Computational Neuroscience Lab, i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal

   Contribution

   Investigation, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-3118-0185

3. A Pedro Aguiar

   Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

   Contribution

   Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

4. David B Grayden

   Department of Biomedical Engineering, University of Melbourne, Melbourne, Australia

   Contribution

   Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

5. Paulo Aguiar

   Neuroengineering and Computational Neuroscience Lab, i3S - Instituto de Investigação e Inovação em Saúde, Universidade do Porto, Porto, Portugal

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Investigation, Methodology, Project administration, Writing – review and editing

   For correspondence

   pauloaguiar@i3s.up.pt

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4164-5713

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