Nonlinear modeling of neural population dynamics for hippocampal prostheses

Abstract

Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input-output transformation of spike trains. In this approach, a MIMO model comprises a series of physiologically-plausible multiple-input, single-output (MISO) neuron models that consist of five components each: (1) feedforward Volterra kernels transforming the input spike trains into the synaptic potential, (2) a feedback kernel transforming the output spikes into the spike-triggered afterpotential, (3) a noise term capturing the system uncertainty, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes. It is shown that this model is equivalent to a generalized linear model with a probit link function. To reduce model complexity and avoid overfitting, statistical model selection and cross-validation methods are employed to choose the significant inputs and interactions between inputs. The model is applied successfully to the hippocampal CA3-CA1 population dynamics. Such a model can serve as a computational basis for the development of hippocampal prostheses.

Hippocampal Microcircuits, Functional Connectivity, and Prostheses

“…We have developed a multiple-input, multiple-output (MIMO), point-process, nonlinear dynamical modeling approach for such a task (Song et al 2006(Song et al , 2009a(Song et al , b, 2013(Song et al , 2014Song and Berger 2010). In this approach, the functional connectivity between neurons is represented as the causal relationship between their spiking activities.…”

A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities

“…That is, 1 in the time series corresponds to when the spike is observed at the predefined time interval, and 0 otherwise [36]. The spiking activity of an output neuron depends on not only the current activities of other neurons, but also the spiking histories, which requires a dynamical model to capture a causal relationship [34].…”

“…Here, g (·) is a known probit link function, which can be interpreted as a noisy threshold function that transforms the pre-threshold membrane potential to output spikes [36]. With the probit link function, Equation (2) can be rewritten in the form of the normal cumulative distribution function as follows [34]:…”

“…Noted that the point-process signalsŷ and y are firstly convolved with a Gaussian kernel with standard deviation σ g , and thus smoothed to continuous signals y σ g (t) and y σ g (t) , respectively. The correlation coefficient r is defined as follows [36]:…”

Extraction of Cortical Modularity Patterns for Neural Prosthetics

“…19.1 as a modeling strategy for the nonlinear dynamics underlying spike-train transformations between L2/3 and L5. This was then used to predict L5 output firing patterns from input patterns of L2/3 neural activity, as a representation of multicolumnar firing patterns (Berger et al 2005(Berger et al , 2011Hampson et al 2012a;Song et al 2007Song et al , 2009. In this application, the identification of spatio-temporal pattern transformation from the PFC layer 2/3 to layer 5 in MEA identified columns was formulated by the MIMO model and analyses included extraction of the first-, second-and third-order temporal firing within at least two defined minicolumns on MEAs inserted repetitively on multiple recording sessions in order to extract relevant patterns of minicolumnar activity related to successful image selection during the match phase of the task.…”