Nonlinear dynamic modeling of synaptically driven single hippocampal neuron intracellular activity

Higuchi Fractal Dimension as a Method for Assessing Response to Sound Stimuli in Patients with Diffuse Axonal Brain Injury

The aim of the research was to study the fractal dimension of the EEG signal by the Higuchi's method in patients with diffuse axonal injury (DAI) of the brain.

Materials and Methods

The study was performed in 28 patients with DAI of different severity and 13 sex- and age-matched controls. The Higuchi's method of fractal dimension was used to investigate brain response to sound stimuli of different emotional coloring as well as the features of the EEG signal in the resting state.

Results

The EEG data demonstrated the highest values of fractal dimension in patients with DAI in the resting state. The values of fractal dimension in different emotional states considerably differ both in healthy subjects and in those with DAI. An increase in fractal dimension in response to stimuli occurs predominantly at the frequency of the theta rhythm in the control group and the frequency of the alpha rhythm in the patients with severe DAI.

Conclusion

Higuchi fractal dimension can be used as a complementary diagnostic tool that allows differentiating perception of emotionally significant audio information in patients with brain injury.

Nonlinear predictive control for adaptive adjustments of deep brain stimulation parameters in basal ganglia-thalamic network

The efficacy of deep brain stimulation (DBS) for Parkinson's disease (PD) depends in part on the post-operative programming of stimulation parameters. Closed-loop stimulation is one method to realize the frequent adjustment of stimulation parameters. This paper introduced the nonlinear predictive control method into the online adjustment of DBS amplitude and frequency. This approach was tested in a computational model of basal ganglia-thalamic network. The autoregressive Volterra model was used to identify the process model based on physiological data. Simulation results illustrated the efficiency of closed-loop stimulation methods (amplitude adjustment and frequency adjustment) in improving the relay reliability of thalamic neurons compared with the PD state. Besides, compared with the 130Hz constant DBS the closed-loop stimulation methods can significantly reduce the energy consumption. Through the analysis of inter-spike-intervals (ISIs) distribution of basal ganglia neurons, the evoked network activity by the closed-loop frequency adjustment stimulation was closer to the normal state.

Application of Higuchi's fractal dimension from basic to clinical neurophysiology: A review

BACKGROUND AND OBJECTIVE

For more than 20 years, Higuchi's fractal dimension (HFD), as a nonlinear method, has occupied an important place in the analysis of biological signals. The use of HFD has evolved from EEG and single neuron activity analysis to the most recent application in automated assessments of different clinical conditions. Our objective is to provide an updated review of the HFD method applied in basic and clinical neurophysiological research.

METHODS

This article summarizes and critically reviews a broad literature and major findings concerning the applications of HFD for measuring the complexity of neuronal activity during different neurophysiological conditions. The source of information used in this review comes from the PubMed, Scopus, Google Scholar and IEEE Xplore Digital Library databases.

RESULTS

The review process substantiated the significance, advantages and shortcomings of HFD application within all key areas of basic and clinical neurophysiology. Therefore, the paper discusses HFD application alone, combined with other linear or nonlinear measures, or as a part of automated methods for analyzing neurophysiological signals.

CONCLUSIONS

The speed, accuracy and cost of applying the HFD method for research and medical diagnosis make it stand out from the widely used linear methods. However, only a combination of HFD with other nonlinear methods ensures reliable and accurate analysis of a wide range of neurophysiological signals.

An Asynchronous Recurrent Network of Cellular Automaton-Based Neurons and Its Reproduction of Spiking Neural Network Activities

Modeling and implementation approaches for the reproduction of input-output relationships in biological nervous tissues contribute to the development of engineering and clinical applications. However, because of high nonlinearity, the traditional modeling and implementation approaches encounter difficulties in terms of generalization ability (i.e., performance when reproducing an unknown data set) and computational resources (i.e., computation time and circuit elements). To overcome these difficulties, asynchronous cellular automaton-based neuron (ACAN) models, which are described as special kinds of cellular automata that can be implemented as small asynchronous sequential logic circuits have been proposed. This paper presents a novel type of such ACAN and a theoretical analysis of its excitability. This paper also presents a novel network of such neurons, which can mimic input-output relationships of biological and nonlinear ordinary differential equation model neural networks. Numerical analyses confirm that the presented network has a higher generalization ability than other major modeling and implementation approaches. In addition, Field-Programmable Gate Array-implementations confirm that the presented network requires lower computational resources.

System identification of point-process neural systems using probability based Volterra kernels

BACKGROUND

Neural information processing involves a series of nonlinear dynamical input/output transformations between the spike trains of neurons/neuronal ensembles. Understanding and quantifying these transformations is critical both for understanding neural physiology such as short-term potentiation and for developing cognitive neural prosthetics.

NEW METHOD

A novel method for estimating Volterra kernels for systems with point-process inputs and outputs is developed based on elementary probability theory. These Probability Based Volterra (PBV) kernels essentially describe the probability of an output spike given q input spikes at various lags t1, t2, …, tq.

RESULTS

The PBV kernels are used to estimate both synthetic systems where ground truth is available and data from the CA3 and CA1 regions rodent hippocampus. The PBV kernels give excellent predictive results in both cases. Furthermore, they are shown to be quite robust to noise and to have good convergence and overfitting properties. Through a slight modification, the PBV kernels are shown to also deal well with correlated point-process inputs.

COMPARISON WITH EXISTING METHODS

The PBV kernels were compared with kernels estimated through least squares estimation (LSE) and through the Laguerre expansion technique (LET). The LSE kernels were shown to fair very poorly with real data due to the large amount of input noise. Although the LET kernels gave the best predictive results in all cases, they require prior parameter estimation. It was shown how the PBV and LET methods can be combined synergistically to maximize performance.

CONCLUSIONS

The PBV kernels provide a novel and intuitive method of characterizing point-process input-output nonlinear systems.

Model-based asessment of an in-vivo predictive relationship from CA1 to CA3 in the rodent hippocampus

Although an anatomical connection from CA1 to CA3 via the Entorhinal Cortex (EC) and through backprojecting interneurons has long been known it exist, it has never been examined quantitatively on the single neuron level, in the in-vivo nonpatholgical, nonperturbed brain. Here, single spike activity was recorded using a multi-electrode array from the CA3 and CA1 areas of the rodent hippocampus (N = 7) during a behavioral task. The predictive power from CA3→CA1 and CA1→CA3 was examined by constructing Multivariate Autoregressive (MVAR) models from recorded neurons in both directions. All nonsignificant inputs and models were identified and removed by means of Monte Carlo simulation methods. It was found that 121/166 (73 %) CA3→CA1 models and 96/145 (66 %) CA1→CA3 models had significant predictive power, thus confirming a predictive 'Granger' causal relationship from CA1 to CA3. This relationship is thought to be caused by a combination of truly causal connections such as the CA1→EC→CA3 pathway and common inputs such as those from the Septum. All MVAR models were then examined in the frequency domain and it was found that CA3 kernels had significantly more power in the theta and beta range than those of CA1, confirming CA3's role as an endogenous hippocampal pacemaker.

Volterra dendritic stimulus processors and biophysical spike generators with intrinsic noise sources

We consider a class of neural circuit models with internal noise sources arising in sensory systems. The basic neuron model in these circuits consists of a dendritic stimulus processor (DSP) cascaded with a biophysical spike generator (BSG). The dendritic stimulus processor is modeled as a set of nonlinear operators that are assumed to have a Volterra series representation. Biophysical point neuron models, such as the Hodgkin-Huxley neuron, are used to model the spike generator. We address the question of how intrinsic noise sources affect the precision in encoding and decoding of sensory stimuli and the functional identification of its sensory circuits. We investigate two intrinsic noise sources arising (i) in the active dendritic trees underlying the DSPs, and (ii) in the ion channels of the BSGs. Noise in dendritic stimulus processing arises from a combined effect of variability in synaptic transmission and dendritic interactions. Channel noise arises in the BSGs due to the fluctuation of the number of the active ion channels. Using a stochastic differential equations formalism we show that encoding with a neuron model consisting of a nonlinear DSP cascaded with a BSG with intrinsic noise sources can be treated as generalized sampling with noisy measurements. For single-input multi-output neural circuit models with feedforward, feedback and cross-feedback DSPs cascaded with BSGs we theoretically analyze the effect of noise sources on stimulus decoding. Building on a key duality property, the effect of noise parameters on the precision of the functional identification of the complete neural circuit with DSP/BSG neuron models is given. We demonstrate through extensive simulations the effects of noise on encoding stimuli with circuits that include neuron models that are akin to those commonly seen in sensory systems, e.g., complex cells in V1.

Functional identification of spike-processing neural circuits

We introduce a novel approach for a complete functional identification of biophysical spike-processing neural circuits. The circuits considered accept multidimensional spike trains as their input and comprise a multitude of temporal receptive fields and conductance-based models of action potential generation. Each temporal receptive field describes the spatiotemporal contribution of all synapses between any two neurons and incorporates the (passive) processing carried out by the dendritic tree. The aggregate dendritic current produced by a multitude of temporal receptive fields is encoded into a sequence of action potentials by a spike generator modeled as a nonlinear dynamical system. Our approach builds on the observation that during any experiment, an entire neural circuit, including its receptive fields and biophysical spike generators, is projected onto the space of stimuli used to identify the circuit. Employing the reproducing kernel Hilbert space (RKHS) of trigonometric polynomials to describe input stimuli, we quantitatively describe the relationship between underlying circuit parameters and their projections. We also derive experimental conditions under which these projections converge to the true parameters. In doing so, we achieve the mathematical tractability needed to characterize the biophysical spike generator and identify the multitude of receptive fields. The algorithms obviate the need to repeat experiments in order to compute the neurons' rate of response, rendering our methodology of interest to both experimental and theoretical neuroscientists.

Analog low-power hardware implementation of a Laguerre-Volterra model of intracellular subthreshold neuronal activity

The right level of abstraction for a model mimicking a neural function is often difficult to determine. There are trade-offs between capturing biological complexities on one hand and the scalability and efficiency of the model on the other. In this work, we describe a nonlinear Laguerre-Volterra model of the synaptic temporal integration of input spikes to postsynaptic potentials. This model is then efficiently implemented using analog subthreshold circuits and can serve as a foundation for future large-scale hardware systems that can emulate multi-input multi-output (MIMO) spike transformations in populations of neurons. The normalized mean square error in estimating real data using the circuit implementation of this model is less than 15%. The model components are modular and its parameters are adjustable for modeling temporal integration by neurons in other brain regions. The total power consumption of this nonlinear Laguerre-Volterra system is less than 5nW.

Nonlinear dynamic modeling of neuron action potential threshold during synaptically driven broadband intracellular activity

Activity-dependent variation of neuronal thresholds for action potential (AP) generation is one of the key determinants of spike-train temporal-pattern transformations from presynaptic to postsynaptic spike trains. In this study, we model the nonlinear dynamics of the threshold variation during synaptically driven broadband intracellular activity. First, membrane potentials of single CA1 pyramidal cells were recorded under physiologically plausible broadband stimulation conditions. Second, a method was developed to measure AP thresholds from the continuous recordings of membrane potentials. It involves measuring the turning points of APs by analyzing the third-order derivatives of the membrane potentials. Four stimulation paradigms with different temporal patterns were applied to validate this method by comparing the measured AP turning points and the actual AP thresholds estimated with varying stimulation intensities. Results show that the AP turning points provide consistent measurement of the AP thresholds, except for a constant offset. It indicates that 1) the variation of AP turning points represents the nonlinearities of threshold dynamics; and 2) an optimization of the constant offset is required to achieve accurate spike prediction. Third, a nonlinear dynamical third-order Volterra model was built to describe the relations between the threshold dynamics and the AP activities. Results show that the model can predict threshold accurately based on the preceding APs. Finally, the dynamic threshold model was integrated into a previously developed single neuron model and resulted in a 33% improvement in spike prediction.