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.

Extraction of the average and differential dynamical response in stimulus-locked experimental data.

In optical imaging experiments of primary visual cortex, visual stimuli evoke a complicated dynamics. Typically, any stimulus with sufficient contrast evokes a response. Much of the response is the same regardless of which stimulus is presented. For instance, when oriented drifting gratings are presented to the visual system, over 90% of the response is the same from orientation to orientation. Small differences may be seen, however, between the responses to different orientations. A problem in the analysis of optical measurements of the response to stimulus in cortical tissue is the distinction of the 'global' or 'non-specific' response from the 'differential' or 'stimulus-specific' response. This problem arises whenever the signal of interest is the difference in response to various stimuli and is evident in many kinds of uni- and multivariate data. To this end, we present enhancements to a frequency-based method that we previously introduced called the periodic stacking method. These enhancements allow us to separately estimate the dynamics of both the average signal across all stimuli (the 'global' response) and deviations from the average amongst the various stimuli (the 'stimulus-specific' response) evoked in response to a set of stimuli. We also discuss improvements in the signal-to-noise ratio, relative to standard trial averaging methods, that result from the data-adaptive smoothing in our method.

Spatiotemporal analysis of optical imaging data.

Previous methods for analyzing optical imaging data have relied heavily on temporal averaging. However, response dynamics are rich sources of information. Here, we develop and present a method that combines principal component analysis and multitaper harmonic analysis to extract the statistically significant spatial and temporal response from optical imaging data. We apply the method to both simulated data and experimental optical imaging data from the cat primary visual cortex.

A population study of integrate-and-fire-or-burst neurons.

Any realistic model of the neuronal pathway from the retina to the visual cortex (V1) must account for the bursting behavior of neurons in the lateral geniculate nucleus (LGN). A robust but minimal model, the integrate-and-fire-or-burst (IFB) model, has recently been proposed for individual LGN neurons. Based on this, we derive a dynamic population model and study a population of such LGN cells. This population model, the first simulation of its kind evolving in a two-dimensional phase space, is used to study the behavior of bursting populations in response to diverse stimulus conditions.

Long-lived localized field configurations in small lattices: application to oscillons

Long-lived localized field configurations such as breathers, oscillons, or more complex objects naturally arise in the context of a wide range of nonlinear models in different numbers of spatial dimensions. We present a numerical method, which we call the adiabatic damping method, designed to study such configurations in small lattices. Using three-dimensional oscillons in straight phi(4) models as an example, we show that the method accurately (to one part in 10(5) or better) reproduces results obtained with static or dynamically expanding lattices, dramatically cutting down in integration time. We further present results for two-dimensional oscillons, whose lifetimes would be prohibitively long to study with conventional methods.