Errors in estimation of the input signal for integrate-and-fire neuronal models

Reconstruction of the input signal of the leaky integrate-and-fire neuronal model from its interspike intervals

Extracting the input signal of a neuron by analyzing its spike output is an important step toward understanding how external information is coded into discrete events of action potentials and how this information is exchanged between different neurons in the nervous system. Most of the existing methods analyze this decoding problem in a stochastic framework and use probabilistic metrics such as maximum-likelihood method to determine the parameters of the input signal assuming a leaky and integrate-and-fire (LIF) model. In this article, the input signal of the LIF model is considered as a combination of orthogonal basis functions. The coefficients of the basis functions are found by minimizing the norm of the observed spikes and those generated by the estimated signal. This approach gives rise to the deterministic reconstruction of the input signal and results in a simple matrix identity through which the coefficients of the basis functions and therefore the neuronal stimulus can be identified. The inherent noise of the neuron is considered as an additional factor in the membrane potential and is treated as the disturbance in the reconstruction algorithm. The performance of the proposed scheme is evaluated by numerical simulations, and it is shown that input signals with different characteristics can be well recovered by this algorithm.

Measuring input synchrony in the Ornstein-Uhlenbeck neuronal model through input parameter estimation

We present a method of estimating the input parameters and through them, the input synchrony, of a stochastic leaky integrate-and-fire neuronal model based on the Ornstein-Uhlenbeck process when it is driven by time-dependent sinusoidal input signal and noise. By driving the neuron using sinusoidal inputs, we simulate the effects of periodic synchrony on the membrane voltage and the firing of the neuron, where the peaks of the sine wave represent volleys of synchronised input spikes. Our estimation methods allow us to measure the degree of synchrony driving the neuron in terms of the input sine wave parameters, using the output spikes of the model and the membrane potential. In particular, by estimating the frequency of the synchronous input volleys and averaging the estimates of the level of input activity at corresponding intervals of the input signal, we obtain fairly accurate estimates of the baseline and peak activity of the input, which in turn define the degrees of synchrony. The same procedure is also successfully applied in estimating the baseline and peak activity of the noise. This article is part of a Special Issue entitled Neural Coding 2012.

How Sample Paths of Leaky Integrate-and-Fire Models Are Influenced by the Presence of a Firing Threshold

Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t1 and of a diffusion process conditioned to cross the boundary for the first time at t1. This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences.

Estimating input parameters from intracellular recordings in the Feller neuronal model

We study the estimation of the input parameters in a Feller neuronal model from a trajectory of the membrane potential sampled at discrete times. These input parameters are identified with the drift and the infinitesimal variance of the underlying stochastic diffusion process with multiplicative noise. The state space of the process is restricted from below by an inaccessible boundary. Further, the model is characterized by the presence of an absorbing threshold, the first hitting of which determines the length of each trajectory and which constrains the state space from above. We compare, both in the presence and in the absence of the absorbing threshold, the efficiency of different known estimators. In addition, we propose an estimator for the drift term, which is proved to be more efficient than the others, at least in the explored range of the parameters. The presence of the threshold makes the estimates of the drift term biased, and two methods to correct it are proposed.

Effect of stimulation on the input parameters of stochastic leaky integrate-and-fire neuronal model

The Ornstein-Uhlenbeck neuronal model is specified by two types of parameters. One type corresponds to the properties of the neuronal membrane, whereas the second type (local average rate of the membrane depolarization and its variability) corresponds to the input of the neuron. In this article, we estimate the parameters of the second type from an intracellular record during neuronal firing caused by stimulation (audio signal). We compare the obtained estimates with those from the spontaneous part of the record. As predicted from the model construction, the values of the input parameters are larger for the periods when neuron is stimulated than for the spontaneous ones. Finally, the firing regimen of the model is checked. It is confirmed that the neuron is in the suprathreshold regimen during the stimulation.