Extraction of periodic multivariate signals: mapping of voltage-dependent dye fluorescence in the mouse heart

Dimensional reduction of a V1 ring model with simple and complex cells

In this paper, we extend a framework for constructing low-dimensional dynamical systems models of mammalian primary visual cortex to a cortical network model that incorporates the full nonlinear effects of complex cells. The procedure consists of capturing the essential dynamics in a low-dimensional subspace using empirical methods, then recasting the equations in the reduced vector space. Previously, we considered visual cortical network models consisting of only simple cells with nearly linear responses to external stimuli. Here we show that fully nonlinear effects can be incorporated by examining the dimensional reduction of an idealized ring model of V1 with both simple and complex cells. We found it expedient to divide the subspace into four separate neuronal populations: excitatory simple, excitatory complex, inhibitory simple and inhibitory complex. In order to reproduce the fluctuation-driven dynamics in this reduced space, we incorporated (1) white noises with different intensities into individual neuronal populations, and (2) firing rate estimates to capture the probability of firing due to subthreshold fluctuations. With a more accurate, fitted connectivity, our modified dimensional reduced models can reproduce the firing rates, circular variances and modulation ratios observed in the original ring model.

A multivariate, multitaper approach to detecting and estimating harmonic response in cortical optical imaging data

The efficiency and accuracy of cortical maps from optical imaging experiments have been improved using periodic stimulation protocols. The resulting data analysis requires the detection and estimation of periodic information in a multivariate dataset. To date, these analyses have relied on discrete Fourier transform (DFT) sinusoid estimates. Multitaper methods have become common statistical tools in the analysis of univariate time series that can give improved estimates. Here, we extend univariate multitaper harmonic analysis methods to the multivariate, imaging context. Given the hypothesis that a coherent oscillation across many pixels exists within a specified bandwidth, we investigate the problem of its detection and estimation in noisy data by constructing Hotelling's generalized T(2)-test. We then extend the investigation of this problem in two contexts, that of standard canonical variate analysis (CVA) and that of generalized indicator function analysis (GIFA) which is often more robust in extracting a signal in spatially correlated noise. We provide detailed information on the fidelities of the mean estimates found with our methods and comparison with DFT estimates. Our results indicate that GIFA provides particularly good estimates of harmonic signals in spatially correlated noise and is useful for detecting small amplitude harmonic signals in applications such as biological imaging measurements where spatially correlated noise is common. We demonstrate the power of our methods with an optical imaging dataset of the periodic response to a periodically rotating oriented drifting grating stimulus experiment in cat visual cortex.

Optical imaging of electrically evoked visual signals in cats: II. ICA "harmonic filtering" noise reduction

Optical imaging of intrinsic signals (OIS) is a tool for visualizing differential areas in the primary visual cortex devoted to visual functions such as ocular dominance and spatial orientation preferences. The OIS methodology was employed to verify visual cortical response to a retinal vision prosthesis whereby electrical stimulation is applied to the neural retina in order to elicit visual percepts. However, OIS recording is quite susceptible to cardiac and respiratory artifact, and inherent noise related to the measurement process. This complicates the identification of evoked signals using standard ensemble averaging based image processing. We therefore developed an independent component analysis (ICA) "harmonic filtering" technique to improve the signal-to-noise ratio. This technique is capable of reducing noise components, highlighting response signals to visual and electrical stimuli. Particularly, we demonstrated extraction of an ocular dominance map due to corneal stimulation and localized cortical activation due to intravitreal stimulation.