Neural signatures of indirect pathway activity during subthalamic stimulation in Parkinson's disease

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) produces an electrophysiological signature called evoked resonant neural activity (ERNA); a high-frequency oscillation that has been linked to treatment efficacy. However, the single-neuron and synaptic bases of ERNA are unsubstantiated. This study proposes that ERNA is a subcortical neuronal circuit signature of DBS-mediated engagement of the basal ganglia indirect pathway network. In people with Parkinson's disease, we: (i) showed that each peak of the ERNA waveform is associated with temporally-locked neuronal inhibition in the STN; (ii) characterized the temporal dynamics of ERNA; (iii) identified a putative mesocircuit architecture, embedded with empirically-derived synaptic dynamics, that is necessary for the emergence of ERNA in silico; (iv) localized ERNA to the dorsal STN in electrophysiological and normative anatomical space; (v) used patient-wise hotspot locations to assess spatial relevance of ERNA with respect to DBS outcome; and (vi) characterized the local fiber activation profile associated with the derived group-level ERNA hotspot.

Model-based closed-loop control of thalamic deep brain stimulation

Introduction: Closed-loop control of deep brain stimulation (DBS) is beneficial for effective and automatic treatment of various neurological disorders like Parkinson's disease (PD) and essential tremor (ET). Manual (open-loop) DBS programming solely based on clinical observations relies on neurologists' expertise and patients' experience. Continuous stimulation in open-loop DBS may decrease battery life and cause side effects. On the contrary, a closed-loop DBS system uses a feedback biomarker/signal to track worsening (or improving) of patients' symptoms and offers several advantages compared to the open-loop DBS system. Existing closed-loop DBS control systems do not incorporate physiological mechanisms underlying DBS or symptoms, e.g., how DBS modulates dynamics of synaptic plasticity. Methods: In this work, we propose a computational framework for development of a model-based DBS controller where a neural model can describe the relationship between DBS and neural activity and a polynomial-based approximation can estimate the relationship between neural and behavioral activities. A controller is used in our model in a quasi-real-time manner to find DBS patterns that significantly reduce the worsening of symptoms. By using the proposed computational framework, these DBS patterns can be tested clinically by predicting the effect of DBS before delivering it to the patient. We applied this framework to the problem of finding optimal DBS frequencies for essential tremor given electromyography (EMG) recordings solely. Building on our recent network model of ventral intermediate nuclei (Vim), the main surgical target of the tremor, in response to DBS, we developed neural model simulation in which physiological mechanisms underlying Vim-DBS are linked to symptomatic changes in EMG signals. By using a proportional-integral-derivative (PID) controller, we showed that a closed-loop system can track EMG signals and adjust the stimulation frequency of Vim-DBS so that the power of EMG reaches a desired control target. Results and discussion: We demonstrated that the model-based DBS frequency aligns well with that used in clinical studies. Our model-based closed-loop system is adaptable to different control targets and can potentially be used for different diseases and personalized systems.

Modeling Instantaneous Firing Rate of Deep Brain Stimulation Target Neuronal Ensembles in the Basal Ganglia and Thalamus

OBJECTIVE

Deep brain stimulation (DBS) is an effective treatment for movement disorders, including Parkinson disease and essential tremor. However, the underlying mechanisms of DBS remain elusive. Despite the capability of existing models in interpreting experimental data qualitatively, there are very few unified computational models that quantitatively capture the dynamics of the neuronal activity of varying stimulated nuclei-including subthalamic nucleus (STN), substantia nigra pars reticulata (SNr), and ventral intermediate nucleus (Vim)-across different DBS frequencies.

MATERIALS AND METHODS

Both synthetic and experimental data were used in the model fitting; the synthetic data were generated by an established spiking neuron model that was reported in our previous work, and the experimental data were provided using single-unit microelectrode recordings (MERs) during DBS (microelectrode stimulation). Based on these data, we developed a novel mathematical model to represent the firing rate of neurons receiving DBS, including neurons in STN, SNr, and Vim-across different DBS frequencies. In our model, the DBS pulses were filtered through a synapse model and a nonlinear transfer function to formulate the firing rate variability. For each DBS-targeted nucleus, we fitted a single set of optimal model parameters consistent across varying DBS frequencies.

RESULTS

Our model accurately reproduced the firing rates observed and calculated from both synthetic and experimental data. The optimal model parameters were consistent across different DBS frequencies.

CONCLUSIONS

The result of our model fitting was in agreement with experimental single-unit MER data during DBS. Reproducing neuronal firing rates of different nuclei of the basal ganglia and thalamus during DBS can be helpful to further understand the mechanisms of DBS and to potentially optimize stimulation parameters based on their actual effects on neuronal activity.

Inferring cognitive state underlying conflict choices in verbal Stroop task using heterogeneous input discriminative-generative decoder model

Objective. The subthalamic nucleus (STN) of the basal ganglia interacts with the medial prefrontal cortex (mPFC) and shapes a control loop, specifically when the brain receives contradictory information from either different sensory systems or conflicting information from sensory inputs and prior knowledge that developed in the brain. Experimental studies demonstrated that significant increases in theta activities (2-8 Hz) in both the STN and mPFC as well as increased phase synchronization between mPFC and STN are prominent features of conflict processing. While these neural features reflect the importance of STN-mPFC circuitry in conflict processing, a low-dimensional representation of the mPFC-STN interaction referred to as a cognitive state, that links neural activities generated by these sub-regions to behavioral signals (e.g. the response time), remains to be identified.Approach. Here, we propose a new model, namely, the heterogeneous input discriminative-generative decoder (HI-DGD) model, to infer a cognitive state underlying decision-making based on neural activities (STN and mPFC) and behavioral signals (individuals' response time) recorded in ten Parkinson's disease (PD) patients while they performed a Stroop task. PD patients may have conflict processing which is quantitatively (may be qualitative in some) different from healthy populations.Main results. Using extensive synthetic and experimental data, we showed that the HI-DGD model can diffuse information from neural and behavioral data simultaneously and estimate cognitive states underlying conflict and non-conflict trials significantly better than traditional methods. Additionally, the HI-DGD model identified which neural features made significant contributions to conflict and non-conflict choices. Interestingly, the estimated features match well with those reported in experimental studies.Significance. Finally, we highlight the capability of the HI-DGD model in estimating a cognitive state from a single trial of observation, which makes it appropriate to be utilized in closed-loop neuromodulation systems.

Robust Removal of Slow Artifactual Dynamics Induced by Deep Brain Stimulation in Local Field Potential Recordings Using SVD-Based Adaptive Filtering

Deep brain stimulation (DBS) is widely used as a treatment option for patients with movement disorders. In addition to its clinical impact, DBS has been utilized in the field of cognitive neuroscience, wherein the answers to several fundamental questions underpinning the mechanisms of neuromodulation in decision making rely on the ways in which a burst of DBS pulses, usually delivered at a clinical frequency, i.e., 130 Hz, perturb participants' choices. It was observed that neural activities recorded during DBS were contaminated with large artifacts, which lasts for a few milliseconds, as well as a low-frequency (slow) signal (~1-2 Hz) that can persist for hundreds of milliseconds. While the focus of most of methods for removing DBS artifacts was on the former, the artifact removal capabilities of the slow signal have not been addressed. In this work, we propose a new method based on combining singular value decomposition (SVD) and normalized adaptive filtering to remove both large (fast) and slow artifacts in local field potentials, recorded during a cognitive task in which bursts of DBS were utilized. Using synthetic data, we show that our proposed algorithm outperforms four commonly used techniques in the literature, namely, (1) normalized least mean square adaptive filtering, (2) optimal FIR Wiener filtering, (3) Gaussian model matching, and (4) moving average. The algorithm's capabilities are further demonstrated by its ability to effectively remove DBS artifacts in local field potentials recorded from the subthalamic nucleus during a verbal Stroop task, highlighting its utility in real-world applications.

Synchrony-Division Neural Multiplexing: An Encoding Model

Cortical neurons receive mixed information from the collective spiking activities of primary sensory neurons in response to a sensory stimulus. A recent study demonstrated an abrupt increase or decrease in stimulus intensity and the stimulus intensity itself can be respectively represented by the synchronous and asynchronous spikes of S1 neurons in rats. This evidence capitalized on the ability of an ensemble of homogeneous neurons to multiplex, a coding strategy that was referred to as synchrony-division multiplexing (SDM). Although neural multiplexing can be conceived by distinct functions of individual neurons in a heterogeneous neural ensemble, the extent to which nearly identical neurons in a homogeneous neural ensemble encode multiple features of a mixed stimulus remains unknown. Here, we present a computational framework to provide a system-level understanding on how an ensemble of homogeneous neurons enable SDM. First, we simulate SDM with an ensemble of homogeneous conductance-based model neurons receiving a mixed stimulus comprising slow and fast features. Using feature-estimation techniques, we show that both features of the stimulus can be inferred from the generated spikes. Second, we utilize linear nonlinear (LNL) cascade models and calculate temporal filters and static nonlinearities of differentially synchronized spikes. We demonstrate that these filters and nonlinearities are distinct for synchronous and asynchronous spikes. Finally, we develop an augmented LNL cascade model as an encoding model for the SDM by combining individual LNLs calculated for each type of spike. The augmented LNL model reveals that a homogeneous neural ensemble model can perform two different functions, namely, temporal- and rate-coding, simultaneously.

Adaptive unscented Kalman filter for neuronal state and parameter estimation

Data assimilation techniques for state and parameter estimation are frequently applied in the context of computational neuroscience. In this work, we show how an adaptive variant of the unscented Kalman filter (UKF) performs on the tracking of a conductance-based neuron model. Unlike standard recursive filter implementations, the robust adaptive unscented Kalman filter (RAUKF) jointly estimates the states and parameters of the neuronal model while adjusting noise covariance matrices online based on innovation and residual information. We benchmark the adaptive filter's performance against existing nonlinear Kalman filters and explore the sensitivity of the filter parameters to the system being modelled. To evaluate the robustness of the proposed solution, we simulate practical settings that challenge tracking performance, such as a model mismatch and measurement faults. Compared to standard variants of the Kalman filter the adaptive variant implemented here is more accurate and robust to faults.

Reduced oriens-lacunosum/moleculare cell model identifies biophysical current balances for in vivo theta frequency spiking resonance

Conductance-based models have played an important role in the development of modern neuroscience. These mathematical models are powerful "tools" that enable theoretical explorations in experimentally untenable situations, and can lead to the development of novel hypotheses and predictions. With advances in cell imaging and computational power, multi-compartment models with morphological accuracy are becoming common practice. However, as more biological details are added, they make extensive explorations and analyses more challenging largely due to their huge computational expense. Here, we focus on oriens-lacunosum/moleculare (OLM) cell models. OLM cells can contribute to functionally relevant theta rhythms in the hippocampus by virtue of their ability to express spiking resonance at theta frequencies, but what characteristics underlie this is far from clear. We converted a previously developed detailed multi-compartment OLM cell model into a reduced single compartment model that retained biophysical fidelity with its underlying ion currents. We showed that the reduced OLM cell model can capture complex output that includes spiking resonance in in vivo-like scenarios as previously obtained with the multi-compartment model. Using the reduced model, we were able to greatly expand our in vivo-like scenarios. Applying spike-triggered average analyses, we were able to to determine that it is a combination of hyperpolarization-activated cation and muscarinic type potassium currents that specifically allow OLM cells to exhibit spiking resonance at theta frequencies. Further, we developed a robust Kalman Filtering (KF) method to estimate parameters of the reduced model in real-time. We showed that it may be possible to directly estimate conductance parameters from experiments since this KF method can reliably extract parameter values from model voltage recordings. Overall, our work showcases how the contribution of cellular biophysical current details could be determined and assessed for spiking resonance. As well, our work shows that it may be possible to directly extract these parameters from current clamp voltage recordings.

Inferring stimulation induced short-term synaptic plasticity dynamics using novel dual optimization algorithm

Experimental evidence in both human and animal studies demonstrated that deep brain stimulation (DBS) can induce short-term synaptic plasticity (STP) in the stimulated nucleus. Given that DBS-induced STP may be connected to the therapeutic effects of DBS, we sought to develop a computational predictive model that infers the dynamics of STP in response to DBS at different frequencies. Existing methods for estimating STP–either model-based or model-free approaches–require access to pre-synaptic spiking activity. However, in the context of DBS, extracellular stimulation (e.g. DBS) can be used to elicit presynaptic activations directly. We present a model-based approach that integrates multiple individual frequencies of DBS-like electrical stimulation as pre-synaptic spikes and infers parameters of the Tsodyks-Markram (TM) model from post-synaptic currents of the stimulated nucleus. By distinguishing between the steady-state and transient responses of the TM model, we develop a novel dual optimization algorithm that infers the model parameters in two steps. First, the TM model parameters are calculated by integrating multiple frequencies of stimulation to estimate the steady state response of post-synaptic current through a closed-form analytical solution. The results of this step are utilized as the initial values for the second step in which a non-derivative optimization algorithm is used to track the transient response of the post-synaptic potential across different individual frequencies of stimulation. Moreover, in order to confirm the applicability of the method, we applied our algorithm–as a proof of concept–to empirical data recorded from acute rodent brain slices of the subthalamic nucleus (STN) during DBS-like stimulation to infer dynamics of STP for inhibitory synaptic inputs.

Modeling and Reproducing Textile Sensor Noise: Implications for Textile-Compatible Signal Processing Algorithms

Smart textiles provide an opportunity to simultaneously record various electrophysiological signals from the human body, such as ECG, in a non-invasive and continuous manner. Accurate processing of ECG signals recorded using textile sensors is challenging due to the very low signal-to-noise ratio (SNR). Signal processing algorithms that can extract ECG signal out of textile-based electrode recordings, despite low SNR are needed. Presently, there are no textile ECG datasets available to develop, test and validate these algorithms. In this paper we attempted to model textile ECG signals by adding the textile sensor noise to open access ECG signals. We employed the linear predictive coding method to model different features of this noise. By approximating the linear predictive coding residual signals using Kernel Density Estimation, an artificial textile ECG noise signal was generated by filtering the residual signal with the linear predictive coding coefficients. The obtained textile sensor noise was added to the MIT-BIH Arrhythmia Database (MITDB), thus creating Textile-like ECG dataset consisting of 108 channels (30 min each). Furthermore, a Python code for generating textile-like ECG signals with variable SNR was also made available online. Finally, to provide a benchmark for the performance of R-peak detection algorithms on textile ECG, the five common R-peak detection algorithms: Pan & Tompkins, improved Pan & Tompkins (in Biosppy), Hamilton, Engelse, and Khamis, were tested on textile-like MITDB. This work provides an approach to generating noisy textile ECG signals, and facilitating the development, testing, and evaluation of signal processing algorithms for textile ECGs.

A theoretical framework for the site-specific and frequency-dependent neuronal effects of deep brain stimulation

BACKGROUND

Deep brain stimulation is an established therapy for several neurological disorders; however, its effects on neuronal activity vary across brain regions and depend on stimulation settings. Understanding these variable responses can aid in the development of physiologically-informed stimulation paradigms in existing or prospective indications.

OBJECTIVE

Provide experimental and computational insights into the brain-region-specific and frequency-dependent effects of extracellular stimulation on neuronal activity.

METHODS

In patients with movement disorders, single-neuron recordings were acquired from the subthalamic nucleus, substantia nigra pars reticulata, ventral intermediate nucleus, or reticular thalamus during microstimulation across various frequencies (1-100 Hz) to assess single-pulse and frequency-response functions. Moreover, a biophysically-realistic computational framework was developed which generated postsynaptic responses under the assumption that electrical stimuli simultaneously activated all convergent presynaptic inputs to stimulation target neurons. The framework took into consideration the relative distributions of excitatory/inhibitory afferent inputs to model site-specific responses, which were in turn embedded within a model of short-term synaptic plasticity to account for stimulation frequency-dependence.

RESULTS

We demonstrated microstimulation-evoked excitatory neuronal responses in thalamic structures (which have predominantly excitatory inputs) and inhibitory responses in basal ganglia structures (predominantly inhibitory inputs); however, higher stimulation frequencies led to a loss of site-specificity and convergence towards neuronal suppression. The model confirmed that site-specific responses could be simulated by accounting for local neuroanatomical/microcircuit properties, while suppression of neuronal activity during high-frequency stimulation was mediated by short-term synaptic depression.

CONCLUSIONS

Brain-region-specific and frequency-dependant neuronal responses could be simulated by considering neuroanatomical (local microcircuitry) and neurophysiological (short-term plasticity) properties.

Modeling and Reconstructing Textile Sensor Noise: Implications for Wearable Technology

Wearable sensors enable the simultaneous recording of several electrophysiological signals from the human body in a non-invasive and continuous manner. Textile sensors are garnering substantial interest in the wearable technology because they can be knitted directly into the daily-used objects like underwear, bra, dress, etc. However, accurate processing of signals recorded by textile sensors is extremely challenging due to the very low signal-to-noise ratio (SNR). Systematic classification of textile sensor noise (TSN) is necessary to: (i) identify different types of noise and their statistical characteristics, (ii) explore how each type of noise influences the electrophysiological signal, (iii) develop optimal textile-specific electronics that suppress TSN, and (iv) reproduce TSN and create large dataset of textile sensors to validate various machine learning and signal processing algorithms. In this paper, we develop a novel technique to classify textile sensor artifacts in ECG signals. By simultaneously recording signals from the waist (textile sensors) and chest (gel electrode), we extract TSN by removing the chest ECG signal from the recorded textile data. We classify TSN based on its morphological and statistical features in two main categories, namely, slow and fast. Linear prediction coding (LPC) is utilized to model each class of TSN by auto-regression coefficients and residues. The residual signal can be approximated by Gaussian distribution which enables reproducing slow and fast artifacts that not only preserve the similar morphological features but also fulfill the statistical properties of TSN. By reproducing TSN and adding them to clean ECG signals, we create a textile-like ECG signal which can be used to develop and validate different signal processing algorithms.

Necessary Conditions for Reliable Propagation of Slowly Time-Varying Firing Rate

Reliable propagation of slow-modulations of the firing rate across multiple layers of a feedforward network (FFN) has proven difficult to capture in spiking neural models. In this paper, we explore necessary conditions for reliable and stable propagation of time-varying asynchronous spikes whose instantaneous rate of changes-in fairly short time windows [20-100] msec-represents information of slow fluctuations of the stimulus. Specifically, we study the effect of network size, level of background synaptic noise, and the variability of synaptic delays in an FFN with all-to-all connectivity. We show that network size and the level of background synaptic noise, together with the strength of synapses, are substantial factors enabling the propagation of asynchronous spikes in deep layers of an FFN. In contrast, the variability of synaptic delays has a minor effect on signal propagation.

Multichannel ECG recording from waist using textile sensors

BACKGROUND

The development of wearable health monitoring systems is garnering tremendous interest in research, technology and commercial applications. Their ability of providing unique capabilities in continuous, real-time, and non-invasive tracking of the physiological markers of users can provide insights into the performance and health of individuals. Electrocardiogram (ECG) signals are of particular interest, as cardiovascular disease is the leading cause of death globally. Monitoring heart health and its conditions such as ventricular disturbances and arrhythmias can be achieved through evaluating various features of ECG such as R-peaks, QRS complex, T-wave, and P-wave. Despite recent advances in biosensors for wearable applications, most of the currently available solutions rely solely on a single system attached to the body, limiting the ability to obtain reliable and multi-location biosignals. However, in engineering systems, sensor fusion, which is the optimal integration and processing of data from multiple sensors, has been a common theme and should be considered for wearables. In recent years, due to an increase in the availability and variety of different types of sensors, the possibility of achieving sensor fusion in wearable systems has become more attainable. Sensor fusion in multi-sensing systems results in significant enhancements of information inferences compared to those from systems with a sole sensor. One step towards the development of sensor fusion for wearable health monitoring systems is the accessibility to multiple reliable electrophysiological signals, which can be recorded continuously.

RESULTS

In this paper, we develop a textile-based multichannel ECG band that has the ability to measure ECG from multiple locations on the waist. As a proof of concept, we demonstrate that ECG signals can be reliably obtained from different locations on the waist where the shape of the QRS complex is nearly comparable with recordings from the chest using traditional gel electrodes. In addition, we develop a probabilistic approach-based on prediction and update strategies-to detect R-peaks from noisy textile data in different statuses, including sitting, standing, and jogging. In this approach, an optimal search method is utilized to detect R-peaks based on the history of the intervals between previously detected R-peaks. We show that the performance of our probabilistic approach in R-peak detection is significantly better than that based on Pan-Tompkins and optimal-threshold methods.

CONCLUSION

A textile-based multichannel ECG band was developed to track the heart rate changes from multiple locations on the waist. We demonstrated that (i) the ECG signal can be detected from different locations on the waist, and (ii) the accuracy of the detected R-peaks from textile sensors was improved by using our proposed probabilistic approach. Despite the limitations of the textile sensors that might compromise the quality of ECG signals, we anticipate that the textile-based multichannel ECG band can be considered as an effective wearable system to facilitate the development of sensor fusion methodology for pervasive and non-invasive health monitoring through continuous tracking of heart rate variability (HRV) from the waist. In addition, from the commercialization point of view, we anticipate that the developed band has the potential to be integrated into garments such as underwear, bras or pants so that individuals can use it on a daily basis.

Simultaneous Bayesian Estimation of Excitatory and Inhibitory Synaptic Conductances by Exploiting Multiple Recorded Trials

Advanced statistical methods have enabled trial-by-trial inference of the underlying excitatory and inhibitory synaptic conductances (SCs) of membrane-potential recordings. Simultaneous inference of both excitatory and inhibitory SCs sheds light on the neural circuits underlying the neural activity and advances our understanding of neural information processing. Conventional Bayesian methods can infer excitatory and inhibitory SCs based on a single trial of observed membrane potential. However, if multiple recorded trials are available, this typically leads to suboptimal estimation because they neglect common statistics (of synaptic inputs (SIs)) across trials. Here, we establish a new expectation maximization (EM) algorithm that improves such single-trial Bayesian methods by exploiting multiple recorded trials to extract common SI statistics across the trials. In this paper, the proposed EM algorithm is embedded in parallel Kalman filters or particle filters for multiple recorded trials to integrate their outputs to iteratively update the common SI statistics. These statistics are then used to infer the excitatory and inhibitory SCs of individual trials. We demonstrate the superior performance of multiple-trial Kalman filtering (MtKF) and particle filtering (MtPF) relative to that of the corresponding single-trial methods. While relative estimation error of excitatory and inhibitory SCs is known to depend on the level of current injection into a cell, our numerical simulations using MtKF show that both excitatory and inhibitory SCs are reliably inferred using an optimal level of current injection. Finally, we validate the robustness and applicability of our technique through simulation studies, and we apply MtKF to in vivo data recorded from the rat barrel cortex.

Regulation of Cortical Dynamic Range by Background Synaptic Noise and Feedforward Inhibition

The cortex encodes a broad range of inputs. This breadth of operation requires sensitivity to weak inputs yet non-saturating responses to strong inputs. If individual pyramidal neurons were to have a narrow dynamic range, as previously claimed, then staggered all-or-none recruitment of those neurons would be necessary for the population to achieve a broad dynamic range. Contrary to this explanation, we show here through dynamic clamp experiments in vitro and computer simulations that pyramidal neurons have a broad dynamic range under the noisy conditions that exist in the intact brain due to background synaptic input. Feedforward inhibition capitalizes on those noise effects to control neuronal gain and thereby regulates the population dynamic range. Importantly, noise allows neurons to be recruited gradually and occludes the staggered recruitment previously attributed to heterogeneous excitation. Feedforward inhibition protects spike timing against the disruptive effects of noise, meaning noise can enable the gain control required for rate coding without compromising the precise spike timing required for temporal coding.

Subthreshold membrane currents confer distinct tuning properties that enable neurons to encode the integral or derivative of their input

Neurons rely on action potentials, or spikes, to encode information. But spikes can encode different stimulus features in different neurons. We show here through simulations and experiments how neurons encode the integral or derivative of their input based on the distinct tuning properties conferred upon them by subthreshold currents. Slow-activating subthreshold inward (depolarizing) current mediates positive feedback control of subthreshold voltage, sustaining depolarization and allowing the neuron to spike on the basis of its integrated stimulus waveform. Slow-activating subthreshold outward (hyperpolarizing) current mediates negative feedback control of subthreshold voltage, truncating depolarization and forcing the neuron to spike on the basis of its differentiated stimulus waveform. Depending on its direction, slow-activating subthreshold current cooperates or competes with fast-activating inward current during spike initiation. This explanation predicts that sensitivity to the rate of change of stimulus intensity differs qualitatively between integrators and differentiators. This was confirmed experimentally in spinal sensory neurons that naturally behave as specialized integrators or differentiators. Predicted sensitivity to different stimulus features was confirmed by covariance analysis. Integration and differentiation, which are themselves inverse operations, are thus shown to be implemented by the slow feedback mediated by oppositely directed subthreshold currents expressed in different neurons.

Blind Deconvolution of Hodgkin-Huxley neuronal model

Neuron transforms information via a complex interaction between its previous states, its intrinsic properties, and the synaptic input it receives from other neurons. Inferring synaptic input of a neuron only from its membrane potential (output) that contains both sub-threshold and action potentials can effectively elucidate the information processing mechanism of a neuron. The term coined blind deconvolution of Hodgkin-Huxley (HH) neuronal model is defined, for the first time in this paper, to address the problem of reconstructing the hidden dynamics and synaptic input of a single neuron modeled by the HH model as well as estimating its intrinsic parameters only from single trace of noisy membrane potential. The blind deconvolution is accomplished via a recursive algorithm whose iterations contain running an extended Kalman filtering followed by the expectation maximization (EM) algorithm. The accuracy and robustness of the proposed algorithm have been demonstrated by our simulations. The capability of the proposed algorithm makes it particularly useful to understand the neural coding mechanism of a neuron.

Inferring trial-to-trial excitatory and inhibitory synaptic inputs from membrane potential using Gaussian mixture Kalman filtering

Time-varying excitatory and inhibitory synaptic inputs govern activity of neurons and process information in the brain. The importance of trial-to-trial fluctuations of synaptic inputs has recently been investigated in neuroscience. Such fluctuations are ignored in the most conventional techniques because they are removed when trials are averaged during linear regression techniques. Here, we propose a novel recursive algorithm based on Gaussian mixture Kalman filtering (GMKF) for estimating time-varying excitatory and inhibitory synaptic inputs from single trials of noisy membrane potential in current clamp recordings. The KF is followed by an expectation maximization (EM) algorithm to infer the statistical parameters (time-varying mean and variance) of the synaptic inputs in a non-parametric manner. As our proposed algorithm is repeated recursively, the inferred parameters of the mixtures are used to initiate the next iteration. Unlike other recent algorithms, our algorithm does not assume an a priori distribution from which the synaptic inputs are generated. Instead, the algorithm recursively estimates such a distribution by fitting a Gaussian mixture model (GMM). The performance of the proposed algorithms is compared to a previously proposed PF-based algorithm (Paninski et al., 2012) with several illustrative examples, assuming that the distribution of synaptic input is unknown. If noise is small, the performance of our algorithms is similar to that of the previous one. However, if noise is large, they can significantly outperform the previous proposal. These promising results suggest that our algorithm is a robust and efficient technique for estimating time varying excitatory and inhibitory synaptic conductances from single trials of membrane potential recordings.