Real-time tracking of neuronal network structure using data assimilation

Abstract

A nonlinear data assimilation technique is applied to determine and track effective connections between ensembles of cultured spinal cord neurons measured with multielectrode arrays. The method is statistical, depending only on confidence intervals, and requiring no form of arbitrary thresholding. In addition, the method updates connection strengths sequentially, enabling real-time tracking of nonstationary networks. The ensemble Kalman filter is used with a generic spiking neuron model to estimate connection strengths as well as other system parameters to deal with model mismatch. The method is validated on noisy synthetic data from Hodgkin-Huxley model neurons before being used to find network connections in the neural culture recordings.

Estimating Time-Varying Applied Current in the Hodgkin-Huxley Model

“…. , N. Parameter tracking of this type has been used in various data assimilation problems; see, e.g., [10][11][12]20]. Here we note that the choice of the standard deviation σ ξ in the drift term of the random walk is important in the accuracy and uncertainty of the resulting parameter estimate.…”

“…for the problem at hand due to the sequential nature of the algorithm's updating scheme, which corrects the model prediction with the available data one point at a time [8,9]. If the time-varying parameter changes more slowly than the system dynamics, it is possible to track the change in the parameter over time using a random walk [10][11][12]. Further, since unknowns are treated as random variables in the Bayesian framework, there is a natural measure of uncertainty in the resulting parameter estimates, which lies in the estimated ensemble covariances of the underlying posterior probability distributions [13,14].…”

Survey and evaluation of neural computation models for bio-integrated systems

“…In [66] it is shown that with use of a finite weighted ensemble, an ensemble Kalman filter (EnKF) is capable of approximating a non-linear system. This method is implemented for the analysis of neural networks in [67]. The validation of this implementation is tested on simulated networks of neurons modeled with Hodgkin-Huxley model and the various parameters of this model are made available in [68].…”

Data Based Reconstruction of Duplex Networks

“…In principle, Eq. (20) indicates that one can maximize L 1 and L 2 with respect to a i j and b i j , respectively, to uncover the connectivity of node i. However, the conventional maximization process leads to equations that cannot be solved because the quantity a i j (b i j ) appears in the exponential term and the values of λ i (or U β i ) are unknown.…”