A Model with Dopamine Depletion in Basal Ganglia and Cerebellum Predicts Changes in Thalamocortical Beta Oscillations

Parkinsonism is presented as a motor syndrome characterized by rigidity, tremors, and bradykinesia, with Parkinson's disease (PD) being the predominant cause. The discovery that those motor symptoms result from the death of dopaminergic cells in the substantia nigra led to focus most of parkinsonism research on the basal ganglia (BG). However, recent findings point to an active involvement of the cerebellum in this motor syndrome. Here, we have developed a multiscale computational model of the rodent brain's BG-cerebellar network. Simulations showed that a direct effect of dopamine depletion on the cerebellum must be taken into account to reproduce the alterations of neural activity in parkinsonism, particularly the increased beta oscillations widely reported in PD patients. Moreover, dopamine depletion indirectly impacted spike-time-dependent plasticity at the parallel fiber-Purkinje cell synapses, degrading associative motor learning as observed in parkinsonism. Overall, these results suggest a relevant involvement of cerebellum in parkinsonism associative motor symptoms.

Mesoscale simulations predict the role of synergistic cerebellar plasticity during classical eyeblink conditioning

According to the motor learning theory by Albus and Ito, synaptic depression at the parallel fibre to Purkinje cells synapse (pf-PC) is the main substrate responsible for learning sensorimotor contingencies under climbing fibre control. However, recent experimental evidence challenges this relatively monopolistic view of cerebellar learning. Bidirectional plasticity appears crucial for learning, in which different microzones can undergo opposite changes of synaptic strength (e.g. downbound microzones-more likely depression, upbound microzones-more likely potentiation), and multiple forms of plasticity have been identified, distributed over different cerebellar circuit synapses. Here, we have simulated classical eyeblink conditioning (CEBC) using an advanced spiking cerebellar model embedding downbound and upbound modules that are subject to multiple plasticity rules. Simulations indicate that synaptic plasticity regulates the cascade of precise spiking patterns spreading throughout the cerebellar cortex and cerebellar nuclei. CEBC was supported by plasticity at the pf-PC synapses as well as at the synapses of the molecular layer interneurons (MLIs), but only the combined switch-off of both sites of plasticity compromised learning significantly. By differentially engaging climbing fibre information and related forms of synaptic plasticity, both microzones contributed to generate a well-timed conditioned response, but it was the downbound module that played the major role in this process. The outcomes of our simulations closely align with the behavioural and electrophysiological phenotypes of mutant mice suffering from cell-specific mutations that affect processing of their PC and/or MLI synapses. Our data highlight that a synergy of bidirectional plasticity rules distributed across the cerebellum can facilitate finetuning of adaptive associative behaviours at a high spatiotemporal resolution.

A cerebellum inspired spiking neural network as a multi-model for pattern classification and robotic trajectory prediction

Spiking neural networks were introduced to understand spatiotemporal information processing in neurons and have found their application in pattern encoding, data discrimination, and classification. Bioinspired network architectures are considered for event-driven tasks, and scientists have looked at different theories based on the architecture and functioning. Motor tasks, for example, have networks inspired by cerebellar architecture where the granular layer recodes sparse representations of the mossy fiber (MF) inputs and has more roles in motor learning. Using abstractions from cerebellar connections and learning rules of deep learning network (DLN), patterns were discriminated within datasets, and the same algorithm was used for trajectory optimization. In the current work, a cerebellum-inspired spiking neural network with dynamics of cerebellar neurons and learning mechanisms attributed to the granular layer, Purkinje cell (PC) layer, and cerebellar nuclei interconnected by excitatory and inhibitory synapses was implemented. The model’s pattern discrimination capability was tested for two tasks on standard machine learning (ML) datasets and on following a trajectory of a low-cost sensor-free robotic articulator. Tuned for supervised learning, the pattern classification capability of the cerebellum-inspired network algorithm has produced more generalized models than data-specific precision models on smaller training datasets. The model showed an accuracy of 72%, which was comparable to standard ML algorithms, such as MLP (78%), Dl4jMlpClassifier (64%), RBFNetwork (71.4%), and libSVM-linear (85.7%). The cerebellar model increased the network’s capability and decreased storage, augmenting faster computations. Additionally, the network model could also implicitly reconstruct the trajectory of a 6-degree of freedom (DOF) robotic arm with a low error rate by reconstructing the kinematic parameters. The variability between the actual and predicted trajectory points was noted to be ± 3 cm (while moving to a position in a cuboid space of 25 × 30 × 40 cm). Although a few known learning rules were implemented among known types of plasticity in the cerebellum, the network model showed a generalized processing capability for a range of signals, modulating the data through the interconnected neural populations. In addition to potential use on sensor-free or feed-forward based controllers for robotic arms and as a generalized pattern classification algorithm, this model adds implications to motor learning theory.

Dual STDP processes at Purkinje cells contribute to distinct improvements in accuracy and speed of saccadic eye movements

Saccadic eye-movements play a crucial role in visuo-motor control by allowing rapid foveation onto new targets. However, the neural processes governing saccades adaptation are not fully understood. Saccades, due to the short-time of execution (20-100 ms) and the absence of sensory information for online feedback control, must be controlled in a ballistic manner. Incomplete measurements of the movement trajectory, such as the visual endpoint error, are supposedly used to form internal predictions about the movement kinematics resulting in predictive control. In order to characterize the synaptic and neural circuit mechanisms underlying predictive saccadic control, we have reconstructed the saccadic system in a digital controller embedding a spiking neural network of the cerebellum with spike timing-dependent plasticity (STDP) rules driving parallel fiber-Purkinje cell long-term potentiation and depression (LTP and LTD). This model implements a control policy based on a dual plasticity mechanism, resulting in the identification of the roles of LTP and LTD in regulating the overall quality of saccade kinematics: it turns out that LTD increases the accuracy by decreasing visual error and LTP increases the peak speed. The control policy also required cerebellar PCs to be divided into two subpopulations, characterized by burst or pause responses. To our knowledge, this is the first model that explains in mechanistic terms the visual error and peak speed regulation of ballistic eye movements in forward mode exploiting spike-timing to regulate firing in different populations of the neuronal network. This elementary model of saccades could be extended and applied to other more complex cases in which single jerks are concatenated to compose articulated and coordinated movements.

CerebelluMorphic: Large-Scale Neuromorphic Model and Architecture for Supervised Motor Learning

The cerebellum plays a vital role in motor learning and control with supervised learning capability, while neuromorphic engineering devises diverse approaches to high-performance computation inspired by biological neural systems. This article presents a large-scale cerebellar network model for supervised learning, as well as a cerebellum-inspired neuromorphic architecture to map the cerebellar anatomical structure into the large-scale model. Our multinucleus model and its underpinning architecture contain approximately 3.5 million neurons, upscaling state-of-the-art neuromorphic designs by over 34 times. Besides, the proposed model and architecture incorporate 3411k granule cells, introducing a 284 times increase compared to a previous study including only 12k cells. This large scaling induces more biologically plausible cerebellar divergence/convergence ratios, which results in better mimicking biology. In order to verify the functionality of our proposed model and demonstrate its strong biomimicry, a reconfigurable neuromorphic system is used, on which our developed architecture is realized to replicate cerebellar dynamics during the optokinetic response. In addition, our neuromorphic architecture is used to analyze the dynamical synchronization within the Purkinje cells, revealing the effects of firing rates of mossy fibers on the resonance dynamics of Purkinje cells. Our experiments show that real-time operation can be realized, with a system throughput of up to 4.70 times larger than previous works with high synaptic event rate. These results suggest that the proposed work provides both a theoretical basis and a neuromorphic engineering perspective for brain-inspired computing and the further exploration of cerebellar learning.

Cerebellum involvement in dystonia: insights from a spiking neural network model during associative learning

Dystonia is a neurological movement disorder characterized by twisting and repetitive movements or abnormal fixed postures. This complex brain disease has usually been associated with damages to the Basal Ganglia. However, recent studies point out the potential role of the cerebellum. Indeed, motor learning is impaired in dystonic patients, e.g. during eyeblink classical conditioning, a typical cerebellum-driven associative learning protocol, and rodents with local cerebellar damages exhibit dystonic movements. Alterations in the olivocerebellar circuit connectivity have been identified as a potential neural substrate of dystonia. Here, we investigated this hypothesis through simulations of eyeblink conditioning driven by a realistic spiking model of the cerebellum. The pathological model was generated by decreasing the signal transmission from the Inferior Olive to cerebellar cortex, as observed in animal experiments. The model was able to reproduce a reduced acquisition of eyeblink motor responses, with also an unproper timing. Indeed, this pathway is fundamental to drive cerebellar cortical plasticity, which is the basis of cerebellum-driven motor learning. Exploring different levels of damage, the model predicted the possible amount of underlying impairment associated with the misbehavior observed in patients. Simulations of other debated lesions reported in mouse models of dystonia will be run to investigate the cerebellar involvement in different types of dystonia. Indeed, the eyeblink conditioning phenotype could be used to discriminate between them, identifying specific deficits in the generation of motor responses. Future studies will also include simulations of pharmacological or deep brain stimulation treatments targeting the cerebellum, to predict their impact in improving symptoms.

Cerebellum Involvement in Dystonia During Associative Motor Learning: Insights From a Data-Driven Spiking Network Model

Dystonia is a movement disorder characterized by sustained or intermittent muscle contractions causing abnormal, often repetitive movements, postures, or both. Although dystonia is traditionally associated with basal ganglia dysfunction, recent evidence has been pointing to a role of the cerebellum, a brain area involved in motor control and learning. Cerebellar abnormalities have been correlated with dystonia but their potential causative role remains elusive. Here, we simulated the cerebellar input-output relationship with high-resolution computational modeling. We used a data-driven cerebellar Spiking Neural Network and simulated a cerebellum-driven associative learning task, Eye-Blink Classical Conditioning (EBCC), which is characteristically altered in relation to cerebellar lesions in several pathologies. In control simulations, input stimuli entrained characteristic network dynamics and induced synaptic plasticity along task repetitions, causing a progressive spike suppression in Purkinje cells with consequent facilitation of deep cerebellar nuclei cells. These neuronal processes caused a progressive acquisition of eyelid Conditioned Responses (CRs). Then, we modified structural or functional local neural features in the network reproducing alterations reported in dystonic mice. Either reduced olivocerebellar input or aberrant Purkinje cell burst-firing resulted in abnormal learning curves imitating the dysfunctional EBCC motor responses (in terms of CR amount and timing) of dystonic mice. These behavioral deficits might be due to altered temporal processing of sensorimotor information and uncoordinated control of muscle contractions. Conversely, an imbalance of excitatory and inhibitory synaptic densities on Purkinje cells did not reflect into significant EBCC deficit. The present work suggests that only certain types of alterations, including reduced olivocerebellar input and aberrant PC burst-firing, are compatible with the EBCC changes observed in dystonia, indicating that some cerebellar lesions can have a causative role in the pathogenesis of symptoms.

Brain-Inspired Spiking Neural Network Controller for a Neurorobotic Whisker System

It is common for animals to use self-generated movements to actively sense the surrounding environment. For instance, rodents rhythmically move their whiskers to explore the space close to their body. The mouse whisker system has become a standard model for studying active sensing and sensorimotor integration through feedback loops. In this work, we developed a bioinspired spiking neural network model of the sensorimotor peripheral whisker system, modeling trigeminal ganglion, trigeminal nuclei, facial nuclei, and central pattern generator neuronal populations. This network was embedded in a virtual mouse robot, exploiting the Human Brain Project's Neurorobotics Platform, a simulation platform offering a virtual environment to develop and test robots driven by brain-inspired controllers. Eventually, the peripheral whisker system was adequately connected to an adaptive cerebellar network controller. The whole system was able to drive active whisking with learning capability, matching neural correlates of behavior experimentally recorded in mice.

Emergence of associative learning in a neuromorphic inference network

OBJECTIVE

In the theoretical framework of predictive coding and active inference, the brain can be viewed as instantiating a rich generative model of the world that predicts incoming sensory data while continuously updating its parameters via minimization of prediction errors. While this theory has been successfully applied to cognitive processes - by modelling the activity of functional neural networks at a mesoscopic scale - the validity of the approach when modelling neurons as an ensemble of inferring agents, in a biologically plausible architecture, remained to be explored.

APPROACH

We modelled a simplified cerebellar circuit with individual neurons acting as Bayesian agents to simulate the classical delayed eyeblink conditioning protocol. Neurons and synapses adjusted their activity to minimize their prediction error, which was used as the network cost function. This cerebellar network was then implemented in hardware by replicating digital neuronal elements via a low-power microcontroller.

MAIN RESULTS

Persistent changes of synaptic strength - that mirrored neurophysiological observations - emerged via local (neurocentric) prediction error minimization, leading to the expression of associative learning. The same paradigm was effectively emulated in low-power hardware showing remarkably efficient performance compared to conventional neuromorphic architectures.

SIGNIFICANCE

These findings show that: i) an ensemble of free energy minimizing neurons - organized in a biological plausible architecture - can recapitulate functional self-organization observed in nature, such as associative plasticity, and ii) a neuromorphic network of inference units can learn unsupervised tasks without embedding predefined learning rules in the circuit, thus providing a potential avenue to a novel form of brain-inspired artificial intelligence.

Cortico-Cerebellar Hyper-Connections and Reduced Purkinje Cells Behind Abnormal Eyeblink Conditioning in a Computational Model of Autism Spectrum Disorder

Empirical evidence suggests that children with autism spectrum disorder (ASD) show abnormal behavior during delay eyeblink conditioning. They show a higher conditioned response learning rate and earlier peak latency of the conditioned response signal. The neuronal mechanisms underlying this autistic behavioral phenotype are still unclear. Here, we use a physiologically constrained spiking neuron model of the cerebellar-cortical system to investigate which features are critical to explaining atypical learning in ASD. Significantly, the computer simulations run with the model suggest that the higher conditioned responses learning rate mainly depends on the reduced number of Purkinje cells. In contrast, the earlier peak latency mainly depends on the hyper-connections of the cerebellum with sensory and motor cortex. Notably, the model has been validated by reproducing the behavioral data collected from studies with real children. Overall, this article is a starting point to understanding the link between the behavioral and neurobiological basis in ASD learning. At the end of the paper, we discuss how this knowledge could be critical for devising new treatments.

Cerebellar adaptive mechanisms explain the optimal control of saccadic eye movements

Cerebellar synaptic plasticity is vital for adaptability and fine tuning of goal-directed movements. The perceived sensory errors between desired and actual movement outcomes are commonly considered to induce plasticity in the cerebellar synapses, with an objective to improve desirability of the executed movements. In rapid goal-directed eye movements called saccades, the only available sensory feedback is the direction of reaching error information received only at end of the movement. Moreover, this sensory error dependent plasticity can only improve the accuracy of the movements, while ignoring other essential characteristics such as reaching in minimum-time. In this work we propose a rate based, cerebellum inspired adaptive filter model to address refinement of both accuracy and movement-time of saccades. We use optimal control approach in conjunction with information constraints posed by the cerebellum to derive bio-plausible supervised plasticity rules. We implement and validate this bio-inspired scheme on a humanoid robot. We found out that, separate plasticity mechanisms in the model cerebellum separately control accuracy and movement-time. These plasticity mechanisms ensure that optimal saccades are produced by just receiving the direction of end reaching error as an evaluative signal. Furthermore, the model emulates encoding in the cerebellum of movement kinematics as observed in biological experiments.

How the Cerebellum and Prefrontal Cortex Cooperate During Trace Eyeblinking Conditioning

Several data have demonstrated that during the widely used experimental paradigm for studying associative learning, trace eye blinking conditioning (TEBC), there is a strong interaction between cerebellum and medial prefrontal cortex (mPFC). Despite this evidence, the neural mechanisms underlying this interaction are still not clear. Here, we propose a neurophysiologically plausible computational model to address this issue. The model is constrained on the basis of two critical anatomo-physiological features: (i) the cerebello-cortical organization through two circuits, respectively, targeting M1 and mPFC; (ii) the different timing in the plasticity mechanisms of these parallel circuits produced by the granule cells time sensitivity according to which different subpopulations are active at different moments during conditioned stimuli. The computer simulations run with the model suggest that these features are critical to understand how the cooperation between cerebellum and mPFC supports motor areas during TEBC. In particular, a greater trace interval produces greater plasticity changes at the slow path synapses involving mPFC with respect to plasticity changes at the fast path involving M1. As a consequence, the greater is the trace interval, the stronger is the mPFC involvement. The model has been validated by reproducing data collected through recent real mice experiments.

Implementation of an Advanced Frequency-Based Hebbian Spike Timing Dependent Plasticity

The brain is provided with an enormous computing capability and exploits neural plasticity to store and elaborate complex information. One of the multiple mechanisms that neural circuits express is the Spike-timing-dependent plasticity (STDP), a form of long-term synaptic plasticity exploiting the time relationship between pre- and post-synaptic action potentials (i.e., neuron spikes). It has been found that in certain cases, for instance at the input stage of the cerebellum, between mossy fibers and granular neurons, the plasticity is not only driven by the timing of the spikes, but also by the oscillation frequency of the inputs. This complex behaviour has been implemented in this work, where we developed a novel form of advanced synaptic plasticity model to be used in a well-established neural network simulator (NEST). The subsequent tests proved the proper functioning of the plasticity and its range of applicability, demonstrating the possibility to adopt it in noisy and variable conditions, similar to the biological settings.

Monitor-Based Spiking Recurrent Network for the Representation of Complex Dynamic Patterns

Neural networks are powerful computation tools for mimicking the human brain to solve realistic problems. Since spiking neural networks are a type of brain-inspired network, called the novel spiking system, Monitor-based Spiking Recurrent network (MbSRN), is derived to learn and represent patterns in this paper. This network provides a computational framework for memorizing the targets using a simple dynamic model that maintains biological plasticity. Based on a recurrent reservoir, the MbSRN presents a mechanism called a ‘monitor’ to track the components of the state space in the training stage online and to self-sustain the complex dynamics in the testing stage. The network firing spikes are optimized to represent the target dynamics according to the accumulation of the membrane potentials of the units. Stability analysis of the monitor conducted by limiting the coefficient penalty in the loss function verifies that our network has good anti-interference performance under neuron loss and noise. The results of solving some realistic tasks show that the MbSRN not only achieves a high goodness-of-fit of the target patterns but also maintains good spiking efficiency and storage capacity.

The Concept of Transmission Coefficient Among Different Cerebellar Layers: A Computational Tool for Analyzing Motor Learning

High-fidelity regulation of information transmission among cerebellar layers is mainly provided by synaptic plasticity. Therefore, determining the regulatory foundations of synaptic plasticity in the cerebellum and translating them to behavioral output are of great importance. To date, many experimental studies have been carried out in order to clarify the effect of synaptic defects, while targeting a specific signaling pathway in the cerebellar function. However, the contradictory results of these studies at the behavioral level further add to the ambiguity of the problem. Information transmission through firing rate changes in populations of interconnected neurons is one of the most widely accepted principles of neural coding. In this study, while considering the efficacy of synaptic interactions among the cerebellar layers, we propose a firing rate model to realize the concept of transmission coefficient. Thereafter, using a computational approach, we test the effect of different values of transmission coefficient on the gain adaptation of a cerebellar-dependent motor learning task. In conformity with the behavioral data, the proposed model can accurately predict that disruption in different forms of synaptic plasticity does not have the same effect on motor learning. Specifically, impairment in training mechanisms, like in the train-induced LTD in parallel fiber-Purkinje cell synapses, has a significant negative impact on all aspects of learning, including memory formation, transfer, and consolidation, although it does not disrupt basic motor performance. In this regard, the overinduction of parallel fiber-molecular layer interneuron LTP could not prevent motor learning impairment, despite its vital role in preserving the robustness of basic motor performance. In contrast, impairment in plasticity induced by interneurons and background activity of climbing fibers is partly compensable through overinduction of train-induced parallel fiber-Purkinje cell LTD. Additionally, blockade of climbing fiber signaling to the cerebellar cortex, referred to as olivary system lesion, shows the most destructive effect on both motor learning and basic motor performance. Overall, the obtained results from the proposed computational framework are used to provide a map from procedural motor memory formation in the cerebellum. Certainly, the generalization of this concept to other multi-layered networks of the brain requires more physiological and computational researches.

Long-Lasting Response Changes in Deep Cerebellar Nuclei in vivo Correlate With Low-Frequency Oscillations

The deep cerebellar nuclei (DCN) have been suggested to play a critical role in sensorimotor learning and some forms of long-term synaptic plasticity observed in vitro have been proposed as a possible substrate. However, till now it was not clear whether and how DCN neuron responses manifest long-lasting changes in vivo. Here, we have characterized DCN unit responses to tactile stimulation of the facial area in anesthetized mice and evaluated the changes induced by theta-sensory stimulation (TSS), a 4 Hz stimulation pattern that is known to induce plasticity in the cerebellar cortex in vivo. DCN units responded to tactile stimulation generating bursts and pauses, which reflected combinations of excitatory inputs most likely relayed by mossy fiber collaterals, inhibitory inputs relayed by Purkinje cells, and intrinsic rebound firing. Interestingly, initial bursts and pauses were often followed by stimulus-induced oscillations in the peri-stimulus time histograms (PSTH). TSS induced long-lasting changes in DCN unit responses. Spike-related potentiation and suppression (SR-P and SR-S), either in units initiating the response with bursts or pauses, were correlated with stimulus-induced oscillations. Fitting with resonant functions suggested the existence of peaks in the theta-band (burst SR-P at 9 Hz, pause SR-S at 5 Hz). Optogenetic stimulation of the cerebellar cortex altered stimulus-induced oscillations suggesting that Purkinje cells play a critical role in the circuits controlling DCN oscillations and plasticity. This observation complements those reported before on the granular and molecular layers supporting the generation of multiple distributed plasticities in the cerebellum following naturally patterned sensory entrainment. The unique dependency of DCN plasticity on circuit oscillations discloses a potential relationship between cerebellar learning and activity patterns generated in the cerebellar network.

Proprioceptive Recognition with Artificial Neural Networks Based on Organizations of Spinocerebellar Tract and Cerebellum

Muscle kinematics and kinetics are nonlinearly encoded by proprioceptors, and the changes in muscle length and velocity are integrated into Ia afferent. Besides, proprioceptive signals from multiple muscles are probably mixed in afferent pathways, which all lead to difficulties in proprioceptive recognition for the cerebellum. In this study, the artificial neural networks, whose organizations are biologically based on the spinocerebellar tract and cerebellum, are utilized to decode the proprioceptive signals. Consistent with the controversy of the proprioceptive division in the dorsal spinocerebellar tract, the spinocerebellar tract networks incorporated two distinct inferences, (1) the centralized networks, which mixed Ia, II, and Ib and processed them together; (2) the decentralized networks, which processed Ia, II, and Ib afferents separately. The cerebellar networks were based on the Marr-Albus model to recognize the kinematic states. The networks were trained by a specific movement, and the trained networks were subsequently required to predict kinematic states of six movements. The results demonstrated that the centralized networks, which were more consistent with the physiological findings in recent years, had better recognition accuracy than the decentralized networks, and the networks were still effective even when proprioceptive afferents from multiple muscles were integrated.

Control of a Humanoid NAO Robot by an Adaptive Bioinspired Cerebellar Module in 3D Motion Tasks

A bioinspired adaptive model, developed by means of a spiking neural network made of thousands of artificial neurons, has been leveraged to control a humanoid NAO robot in real time. The learning properties of the system have been challenged in a classic cerebellum-driven paradigm, a perturbed upper limb reaching protocol. The neurophysiological principles used to develop the model succeeded in driving an adaptive motor control protocol with baseline, acquisition, and extinction phases. The spiking neural network model showed learning behaviours similar to the ones experimentally measured with human subjects in the same task in the acquisition phase, while resorted to other strategies in the extinction phase. The model processed in real-time external inputs, encoded as spikes, and the generated spiking activity of its output neurons was decoded, in order to provide the proper correction on the motor actuators. Three bidirectional long-term plasticity rules have been embedded for different connections and with different time scales. The plasticities shaped the firing activity of the output layer neurons of the network. In the perturbed upper limb reaching protocol, the neurorobot successfully learned how to compensate for the external perturbation generating an appropriate correction. Therefore, the spiking cerebellar model was able to reproduce in the robotic platform how biological systems deal with external sources of error, in both ideal and real (noisy) environments.

Complex Dynamics in Simplified Neuronal Models: Reproducing Golgi Cell Electroresponsiveness

Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.

Dynamic Redistribution of Plasticity in a Cerebellar Spiking Neural Network Reproducing an Associative Learning Task Perturbed by TMS

During natural learning, synaptic plasticity is thought to evolve dynamically and redistribute within and among subcircuits. This process should emerge in plastic neural networks evolving under behavioral feedback and should involve changes distributed across multiple synaptic sites. In eyeblink classical conditioning (EBCC), the cerebellum learns to predict the precise timing between two stimuli, hence EBCC represents an elementary yet meaningful paradigm to investigate the cerebellar network functioning. We have simulated EBCC mechanisms by reconstructing a realistic cerebellar microcircuit model and embedding multiple plasticity rules imitating those revealed experimentally. The model was tuned to fit experimental EBCC human data, estimating the underlying learning time-constants. Learning started rapidly with plastic changes in the cerebellar cortex followed by slower changes in the deep cerebellar nuclei. This process was characterized by differential development of long-term potentiation and depression at individual synapses, with a progressive accumulation of plasticity distributed over the whole network. The experimental data included two EBCC sessions interleaved by a trans-cranial magnetic stimulation (TMS). The experimental and the model response data were not significantly different in each learning phase, and the model goodness-of-fit was [Formula: see text] for all the experimental conditions. The models fitted on TMS data revealed a slowed down re-acquisition (sessions-2) compared to the control condition ([Formula: see text]). The plasticity parameters characterizing each model significantly differ among conditions, and thus mechanistically explain these response changes. Importantly, the model was able to capture the alteration in EBCC consolidation caused by TMS and showed that TMS affected plasticity at cortical synapses thereby altering the fast learning phase. This, secondarily, also affected plasticity in deep cerebellar nuclei altering learning dynamics in the entire sensory-motor loop. This observation reveals dynamic redistribution of changes over the entire network and suggests how TMS affects local circuit computation and memory processing in the cerebellum.

A Multiple-Plasticity Spiking Neural Network Embedded in a Closed-Loop Control System to Model Cerebellar Pathologies

The cerebellum plays a crucial role in sensorimotor control and cerebellar disorders compromise adaptation and learning of motor responses. However, the link between alterations at network level and cerebellar dysfunction is still unclear. In principle, this understanding would benefit of the development of an artificial system embedding the salient neuronal and plastic properties of the cerebellum and operating in closed-loop. To this aim, we have exploited a realistic spiking computational model of the cerebellum to analyze the network correlates of cerebellar impairment. The model was modified to reproduce three different damages of the cerebellar cortex: (i) a loss of the main output neurons (Purkinje Cells), (ii) a lesion to the main cerebellar afferents (Mossy Fibers), and (iii) a damage to a major mechanism of synaptic plasticity (Long Term Depression). The modified network models were challenged with an Eye-Blink Classical Conditioning test, a standard learning paradigm used to evaluate cerebellar impairment, in which the outcome was compared to reference results obtained in human or animal experiments. In all cases, the model reproduced the partial and delayed conditioning typical of the pathologies, indicating that an intact cerebellar cortex functionality is required to accelerate learning by transferring acquired information to the cerebellar nuclei. Interestingly, depending on the type of lesion, the redistribution of synaptic plasticity and response timing varied greatly generating specific adaptation patterns. Thus, not only the present work extends the generalization capabilities of the cerebellar spiking model to pathological cases, but also predicts how changes at the neuronal level are distributed across the network, making it usable to infer cerebellar circuit alterations occurring in cerebellar pathologies.

Physiology of the cerebellum

The cerebellum is a central brain structure deeply integrated into major loops with the cerebral cortex, brainstem, and spinal cord. The cerebellum shows a complex regional organization consisting of modules with sagittal orientation. The cerebellum takes part in motor control and its lesions cause a movement incoordination syndrome called ataxia. Recent observations also imply involvement of the cerebellum in cognition and executive control, with an impact on pathologies like dyslexia and autism. The cerebellum operates as a forward controller learning to predict the precise timing of correlated events. The physiologic mechanisms of cerebellar functioning are still the object of intense research. The signals entering the cerebellum through the mossy fibers are processed in the granular layer and transmitted to Purkinje cells, while a collateral pathway activates the deep cerebellar nuclei (DCN). Purkinje cells in turn inhibit DCN, so that the cerebellar cortex operates as a side loop controlling the DCN. Learning is now known to occur through synaptic plasticity at multiple synapses in the granular layer, molecular layer, and DCN, extending the original concept of the Motor Learning Theory that predicted a single form of plasticity at the synapse between parallel fibers and Purkinje cells under the supervision of climbing fibers deriving from the inferior olive. Coordination derives from the precise regulation of timing and gain in the different cerebellar modules. The investigation of cerebellar dynamics using advanced physiologic recordings and computational models is now providing new clues on how the cerebellar network performs its internal computations.

Model-Driven Analysis of Eyeblink Classical Conditioning Reveals the Underlying Structure of Cerebellar Plasticity and Neuronal Activity

The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.

Real-Time In Vivo Intraocular Pressure Monitoring using an Optomechanical Implant and an Artificial Neural Network

Optimized glaucoma therapy requires frequent monitoring and timely lowering of elevated intraocular pressure (IOP). A recently developed microscale IOP-monitoring implant, when illuminated with broadband light, reflects a pressure-dependent optical spectrum that is captured and converted to measure IOP. However, its accuracy is limited by background noise and the difficulty of modeling non-linear shifts of the spectra with respect to pressure changes. Using an end-to-end calibration system to train an artificial neural network (ANN) for signal demodulation we improved the speed and accuracy of pressure measurements obtained with an optically probed IOP-monitoring implant and make it suitable for real-time in vivo IOP monitoring. The ANN converts captured optical spectra into corresponding IOP levels. We achieved an IOP-measurement accuracy of ±0.1 mmHg at a measurement rate of 100 Hz, which represents a ten-fold improvement from previously reported values. This technique allowed real-time tracking of artificially induced sub-1 s transient IOP elevations and minor fluctuations induced by the respiratory motion of the rabbits during in vivo monitoring. All in vivo sensor readings paralleled those obtained concurrently using a commercial tonometer and showed consistency within ±2 mmHg. Real-time processing is highly useful for IOP monitoring in clinical settings and home environments and improves the overall practicality of the optical IOP-monitoring approach.

Event- and Time-Driven Techniques Using Parallel CPU-GPU Co-processing for Spiking Neural Networks

Modeling and simulating the neural structures which make up our central neural system is instrumental for deciphering the computational neural cues beneath. Higher levels of biological plausibility usually impose higher levels of complexity in mathematical modeling, from neural to behavioral levels. This paper focuses on overcoming the simulation problems (accuracy and performance) derived from using higher levels of mathematical complexity at a neural level. This study proposes different techniques for simulating neural models that hold incremental levels of mathematical complexity: leaky integrate-and-fire (LIF), adaptive exponential integrate-and-fire (AdEx), and Hodgkin-Huxley (HH) neural models (ranged from low to high neural complexity). The studied techniques are classified into two main families depending on how the neural-model dynamic evaluation is computed: the event-driven or the time-driven families. Whilst event-driven techniques pre-compile and store the neural dynamics within look-up tables, time-driven techniques compute the neural dynamics iteratively during the simulation time. We propose two modifications for the event-driven family: a look-up table recombination to better cope with the incremental neural complexity together with a better handling of the synchronous input activity. Regarding the time-driven family, we propose a modification in computing the neural dynamics: the bi-fixed-step integration method. This method automatically adjusts the simulation step size to better cope with the stiffness of the neural model dynamics running in CPU platforms. One version of this method is also implemented for hybrid CPU-GPU platforms. Finally, we analyze how the performance and accuracy of these modifications evolve with increasing levels of neural complexity. We also demonstrate how the proposed modifications which constitute the main contribution of this study systematically outperform the traditional event- and time-driven techniques under increasing levels of neural complexity.

A Selective Change Driven System for High-Speed Motion Analysis

Vision-based sensing algorithms are computationally-demanding tasks due to the large amount of data acquired and processed. Visual sensors deliver much information, even if data are redundant, and do not give any additional information. A Selective Change Driven (SCD) sensing system is based on a sensor that delivers, ordered by the magnitude of its change, only those pixels that have changed most since the last read-out. This allows the information stream to be adjusted to the computation capabilities. Following this strategy, a new SCD processing architecture for high-speed motion analysis, based on processing pixels instead of full frames, has been developed and implemented into a Field Programmable Gate-Array (FPGA). The programmable device controls the data stream, delivering a new object distance calculation for every new pixel. The acquisition, processing and delivery of a new object distance takes just 1.7 μ s. Obtaining a similar result using a conventional frame-based camera would require a device working at roughly 500 Kfps, which is far from being practical or even feasible. This system, built with the recently-developed 64 × 64 CMOS SCD sensor, shows the potential of the SCD approach when combined with a hardware processing system.

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate “realistic” models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems.