Methodology of Recurrent Laguerre-Volterra Network for Modeling Nonlinear Dynamic Systems

A Laguerre-Volterra network model based on ant colony optimization applied to evaluate EMG-force relationship in the muscle fatigue state

With the accuracy and convenience improvement of electromyographic (EMG) acquired by wearable devices, EMG is gradually used to evaluate muscle force signal, a non-invasive evaluation method. However, the relationship between EMG and force is a complex nonlinear relationship, even which will change with different movements and different muscle states. Therefore, it is difficult to evaluate this nonlinear EMG-force relationship, especially when the muscle state gradually transits from non-fatigue to deep fatigue. For more accurate values of force in human fatigue state, this paper proposes a dual-input Laguerre-Volterra network (LVN) model based on ant colony optimization. First, the changes in 19 EMG features are discussed with increasing fatigue. We also consider two non-Gaussian features: kurtosis and negentropy in the 19 features. Later, 11 EMG fatigue features are picked out according to the fatigue test. Then, the preprocessed EMG and a composite signal of the 11 fatigue features are simultaneously input into the LVN model. Subsequently, the ant colony optimization algorithm is selected to train the model parameters. At the same time, a penalty term that we defined is introduced into the model cost function to adjust the weight of each feature adaptively. Finally, some experiments prove that the LVN model could quick fit the accurate force signal in five fatigue stages, such as non-fatigue, slight fatigue, mild fatigue, severe fatigue, and extreme fatigue. This LVN model can quickly transform EMG into strength signal in real time, which is suitable for people to observe muscle strength by a wearable device and makes it easy to detect the muscle current state. This model has good stability and can remain effective for a long time with training once, which provides convenience for the users of wearable devices.

Time-Series Modeling and Forecasting of Cerebral Pressure-Flow Physiology: A Scoping Systematic Review of the Human and Animal Literature

The modeling and forecasting of cerebral pressure-flow dynamics in the time-frequency domain have promising implications for veterinary and human life sciences research, enhancing clinical care by predicting cerebral blood flow (CBF)/perfusion, nutrient delivery, and intracranial pressure (ICP)/compliance behavior in advance. Despite its potential, the literature lacks coherence regarding the optimal model type, structure, data streams, and performance. This systematic scoping review comprehensively examines the current landscape of cerebral physiological time-series modeling and forecasting. It focuses on temporally resolved cerebral pressure-flow and oxygen delivery data streams obtained from invasive/non-invasive cerebral sensors. A thorough search of databases identified 88 studies for evaluation, covering diverse cerebral physiologic signals from healthy volunteers, patients with various conditions, and animal subjects. Methodologies range from traditional statistical time-series analysis to innovative machine learning algorithms. A total of 30 studies in healthy cohorts and 23 studies in patient cohorts with traumatic brain injury (TBI) concentrated on modeling CBFv and predicting ICP, respectively. Animal studies exclusively analyzed CBF/CBFv. Of the 88 studies, 65 predominantly used traditional statistical time-series analysis, with transfer function analysis (TFA), wavelet analysis, and autoregressive (AR) models being prominent. Among machine learning algorithms, support vector machine (SVM) was widely utilized, and decision trees showed promise, especially in ICP prediction. Nonlinear models and multi-input models were prevalent, emphasizing the significance of multivariate modeling and forecasting. This review clarifies knowledge gaps and sets the stage for future research to advance cerebral physiologic signal analysis, benefiting neurocritical care applications.

A new particle filter algorithm filtering motion artifact noise for clean electrocardiogram signals in wearable health monitoring system

With the evolution of wearable systems, more and more people tend to wear wearable devices for health monitoring during sports. However, a large amount of motion artifact noise is introduced at this time, which is difficult to filter out due to its stochasticity. The amplitude and characteristics of motion artifact noise vary with changes in motion intensity. In order to filter out the motion artifact noise, the paperproposes a new particle algorithm, which can detect the intensity of the motion artifact for adaptive filtering, especiallysuitable for wearable health monitoring systems. In this algorithm, variational mode decomposition was first introduced to analyze the noisy electrocardiogram (ECG) signal in order to find the clean components. Then, the Laguerre estimation technique was applied to obtain an accurate ECG polar model. Taking this model as the state equation, a particle filter algorithm was defined to filter out the motion artifact noise. In the particle filter algorithm, we defined a parameter γ whose values were obtained from the six-axis data of motion sensor MPU6050 in our wearable device. This parameter γ could reflect the current noise levels and adaptively update the particle weights. Finally, some exercise experiments proved that the parameter γ could map the motion artifacts in real time and also demonstrated the superiority of the algorithm in terms of signal-to-noise ratio improvement and error reduction compared to other algorithms. The new particle filter algorithm proposed in this paper combines the six-axis data (three-axis accelerometer and three-axis gyroscope) with the ECG signal to effectively eliminate a large amount of motion artifact noise, thus solving the problem of excess noise from wearable devices when people are exercising, allowing them to accurately obtain real-time ECG health information.

Multi-Input, Multi-Output Neuronal Mode Network Approach to Modeling the Encoding Dynamics and Functional Connectivity of Neural Systems

This letter proposes a novel method, multi-input, multi-output neuronal mode network (MIMO-NMN), for modeling encoding dynamics and functional connectivity in neural ensembles such as the hippocampus. Compared with conventional approaches such as the Volterra-Wiener model, linear-nonlinear-cascade (LNC) model, and generalized linear model (GLM), the NMN has several advantages in terms of estimation accuracy, model interpretation, and functional connectivity analysis. We point out the limitations of current neural spike modeling methods, especially the estimation biases caused by the imbalanced class problem when the number of zeros is significantly larger than ones in the spike data. We use synthetic data to test the performance of NMN with a comparison of the traditional methods, and the results indicate the NMN approach could reduce the imbalanced class problem and achieve better predictions. Subsequently, we apply the MIMO-NMN method to analyze data from the human hippocampus. The results indicate that the MIMO-NMN method is a promising approach to modeling neural dynamics and analyzing functional connectivity of multi-neuronal data.

Modeling Nonlinear Synaptic Dynamics: A Laguerre-Volterra Network Framework for Improved Computational Efficiency in Large Scale Simulations

Synapses are key components in signal transmission in the brain, often exhibiting complex non-linear dynamics. Yet, they are often crudely modelled as linear exponential equations in large-scale neuron network simulations. Mechanistic models that use detailed channel receptor kinetics more closely replicate the nonlinear dynamics observed at synapses, but use of such models are generally restricted to small scale simulations due to their computational complexity. Previously, we have developed an ``input-output'' (IO) synapse model using the Volterra functional series to estimate nonlinear synaptic dynamics. Here, we present an improvement on the IO synapse model using the extbf{Laguerre-Volterra network (LVN) framework. We demonstrate that utilization of the LVN framework helps reduce memory requirements and improves the simulation speed in comparison to the previous iteration of the IO synapse model. We present results that demonstrate the accuracy, memory efficiency, and speed of the LVN model that can be extended to simulations with large numbers of synapses. Our efforts enable complex nonlinear synaptic dynamics to be modelled in large-scale network models, allowing us to explore how synaptic activity may influence network behavior and affects memory, learning, and neurodegenerative diseases.

Nonlinear Modeling of Neural Interaction for Spike Prediction Using the Staged Point-Process Model

Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than quadratic models, and the modified L-M algorithm also demonstrates fast convergence.

A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics

In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Mechanism-Based and Input-Output Modeling of the Key Neuronal Connections and Signal Transformations in the CA3-CA1 Regions of the Hippocampus

This letter examines the results of input-output (nonparametric) modeling based on the analysis of data generated by a mechanism-based (parametric) model of CA3-CA1 neuronal connections in the hippocampus. The motivation is to obtain biological insight into the interpretation of such input-output (Volterra-equivalent) models estimated from synthetic data. The insights obtained may be subsequently used to interpretat input-output models extracted from actual experimental data. Specifically, we found that a simplified parametric model may serve as a useful tool to study the signal transformations in the hippocampal CA3-CA1 regions. Input-output modeling of model-based synthetic data show that GABAergic interneurons are responsible for regulating neuronal excitation, controlling the precision of spike timing, and maintaining network oscillations, in a manner consistent with previous studies. The input-output model obtained from real data exhibits intriguing similarities with its synthetic-data counterpart, demonstrating the importance of a dynamic resonance in the system/model response around 2 Hz to 3 Hz. Using the input-output model from real data as a guide, we may be able to amend the parametric model by incorporating more mechanisms in order to yield better-matching input-output model. The approach we present can also be applied to the study of other neural systems and pathways.