相关论文: Parameter Identification Problem in the Hodgkin an…
We compare six numerical integrators' performance when simulating a regular spiking cortical neuron model whose 74-compartments are equipped with eleven membrane ion channels and Calcium dynamics. Four methods are explicit and two are…
This work proposes a two-dimensional electrophysiological model for describing neuronal responses to external electric stimuli under patch-clamped conditions. Our proposed model successfully captures the key features of the Hodgkin-Huxley…
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference…
In the last fifteen years a debate emerged about the validity of the famous Hodgkin-Huxley model for nerve impulse. Mechanical models have been proposed. This note reviews the experimental properties of the nerve impulse and discusses the…
The Hodgkin-Huxley equations constitute one of the more realistic neuronal models in literature and the most accepted one. It is well known that, depending on the value of the external stimuli current, it exhibits periodic solutions, both…
This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and…
This work explores four nonlinear classical models of neural oscillators, the Hodgkin-Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Nonlinear contraction theory is used to develop observers…
The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish…
The generation and conduction of action potentials represents a fundamental means of communication in the nervous system, and is a metabolically expensive process. In this paper, we investigate the energy efficiency of neural systems in a…
Neuronal models based on the Hodgkin-Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modeled deterministically, experimental recordings show stochastic fluctuations,…
By means of the concepts of factorial moment, return map and NM estimator, we analyze some responses of a HH neuron to various types of spike-train inputs. The corresponding fractal dimensions and values of NM estimators can describe the…
The Hodgkin-Huxley (HH) model is the currently accepted formalism of neuronal excitability. However, the HH model does not capture a number of biophysical behaviors associated with action potentials or propagating nerve impulses. Physical…
The stochastic FitzHugh-Nagumo (FHN) model is a two-dimensional nonlinear stochastic differential equation with additive degenerate noise, whose first component, the only one observed, describes the membrane voltage evolution of a single…
We introduce a method for computing probabilities for spontaneous activity and propagation fail- ure of the action potential in spatially extended, conductance-based neuronal models subject to channel noise, based on statistical properties…
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…
Serotonergic, noradrenergic and dopaminergic brainstem (including midbrain) neurons, often exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz, though dopaminergic and noradrenergic neurons only exhibit such…
We demonstrate that our recently developed theory of electric field wave propagation in anisotropic and inhomogeneous brain tissues, which has been shown to explain a broad range of observed coherent synchronous brain electrical processes,…
Hodgkin-Huxley equations as a monumental breakthrough in biological and physiological theory of the 20th century had been distilled into many simplified models to study, typically FitzHugh-Nagumo equations and Hindmarsh-Rose equations, but…
We construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane potential of the…
We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn-Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the…