Determining the cortical target of transcranial magnetic stimulation.

Determining the cortical region that is effectively targeted by TMS to induce a reproducible behavioral effect is a non-trivial problem. In mapping experiments, a grid of coil positions is used to systematically assess the TMS effect on, e.g. muscle responses or error rates. The center-of-mass (CoM) of the response distribution is projected onto the cortex to determine the likely target site, implicitly assuming the existence of a single, contiguous target. The mapping results, however, often contain several local maxima. These could either stem from measurement noise, or hint towards a distributed target region. Critically, the calculation of a CoM, by design, treats multiple maxima as if they were noise. Here, a stringent hierarchical sigmoidal model fitting approach is developed that determines the cortical target(s) from TMS mapping based on electric field calculations. Monte-Carlo simulations are used to assess the significance and the goodness-of-fit of the sigmoidal fits, and to obtain confidence regions around the calculated targets. The approach was applied to mapping data on visual suppression (N=7). In all subjects, we reliably identified two or three neighboring targets commonly contributing to the suppression effect (average distance+/-SD: 7.7+/-2.3 mm). This demonstrates that (i) the assumption of a single CoM is not generally valid and (ii) the combination of TMS mapping with the fitting approach has a cortical resolution of <1 cm. The estimates for the field strength necessary to achieve 50% of the maximal suppression effect vary noticeably across subjects (mean+/-SD: 139+/-24 V/m), indicating inter-individual differences in the susceptibility to TMS.

Contrast discrimination with pulse trains in pink noise.

Detection performance was measured with sinusoidal and pulse-train gratings. Although the 2.09-cycles-per-degree pulse-train, or line, grating contained at least eight harmonics all at equal contrast, it was no more detectable than its most detectable component. The addition of broadband pink noise designed to equalize the detectability of the components of the pulse train made the pulse train approximately a factor of 4 more detectable than any of its components. However, in contrast-discrimination experiments, with a pedestal or masking grating of the same form and phase as the signal and with 15% contrast, the noise did not affect the discrimination performance of the pulse train relative to that obtained with its sinusoidal components. We discuss the implications of these observations for models of early vision, in particular the implications for possible sources of internal noise.

Contrast discrimination with sinusoidal gratings of different spatial frequency.

The detectability of contrast increments was measured as a function of the contrast of a masking or "pedestal" grating at a number of different spatial frequencies ranging from 2 to 16 cycles per degree of visual angle. The pedestal grating always had the same orientation, spatial frequency, and phase as the signal. The shape of the contrast-increment threshold versus pedestal contrast (TvC) functions depends on the performance level used to define the "threshold," but when both axes are normalized by the contrast corresponding to 75% correct detection at each frequency, the TvC functions at a given performance level are identical. Confidence intervals on the slope of the rising part of the TvC functions are so wide that it is not possible with our data to reject Weber's law.

The psychometric function: I. Fitting, sampling, and goodness of fit.

The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (or lapses). We show that failure to account for this can lead to serious biases in estimates of the psychometric function's parameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditional chi2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods.

The psychometric function: II. Bootstrap-based confidence intervals and sampling.

The psychometric function relates an observer's performance to an independent variable, usually a physical quantity of an experimental stimulus. Even if a model is successfully fit to the data and its goodness of fit is acceptable, experimenters require an estimate of the variability of the parameters to assess whether differences across conditions are significant. Accurate estimates of variability are difficult to obtain, however, given the typically small size of psychophysical data sets: Traditional statistical techniques are only asymptotically correct and can be shown to be unreliable in some common situations. Here and in our companion paper (Wichmann & Hill, 2001), we suggest alternative statistical techniques based on Monte Carlo resampling methods. The present paper's principal topic is the estimation of the variability of fitted parameters and derived quantities, such as thresholds and slopes. First, we outline the basic bootstrap procedure and argue in favor of the parametric, as opposed to the nonparametric, bootstrap. Second, we describe how the bootstrap bridging assumption, on which the validity of the procedure depends, can be tested. Third, we show how one's choice of sampling scheme (the placement of sample points on the stimulus axis) strongly affects the reliability of bootstrap confidence intervals, and we make recommendations on how to sample the psychometric function efficiently. Fourth, we show that, under certain circumstances, the (arbitrary) choice of the distribution function can exert an unwanted influence on the size of the bootstrap confidence intervals obtained, and we make recommendations on how to avoid this influence. Finally, we introduce improved confidence intervals (bias corrected and accelerated) that improve on the parametric and percentile-based bootstrap confidence intervals previously used. Software implementing our methods is available.

The contribution of color to visual memory in X-chromosome-linked dichromats.

We used a recognition memory paradigm to assess the visual memory of X-chromosome-linked dichromats for color images of natural scenes. The performance of 17 protanopes and 14 deuteranopes, who lack the second (red-green opponent) subsystem of color vision, but retain the primordial (yellow-blue opponent) subsystem, was compared with that of 36 color normal observers. During the presentation phase, 48 images of natural scenes were displayed on a CRT for durations between 50 and 1000 msec. Each image was followed by a random noise mask. Half of the images were presented in color and half in black and white. In the subsequent query phase, the same 48 images were intermixed with 48 new images and the subjects had to indicate which of the images they had already seen during the presentation phase. We find that the performance of the color normal observers increases with exposure duration. However, they perform 5-10% better for colored than for black and white images, even at exposure durations as short as 50 msec. Surprisingly, performance is not impaired for the dichromats, whose recognition performance is also better for colored than for black and white images. We conclude either that X-chromosome-linked dichromats may be able to compensate for their reduced chromatic information range when viewing complex natural scenes or that the chromatic information in most natural scenes, for the durations tested, is sufficiently represented by the surviving primordial color subsystem.

No role for motion blur in either motion detection or motion-based image segmentation.

The human contrast sensitivity function is bandpass in form for stimuli of low temporal frequency but low pass for flickering or moving stimuli. Because the loss in sensitivity to moving stimuli is large, images moving on the retina have little perceptible high-spatial-frequency content. The loss of high-spatial-frequency content--often referred to as motion blur--provides a potential cue to motion. The amount of motion blur is a function of stimulus velocity but is significant at velocities encountered by the visual system in everyday situations. Our experiments determined the influence of high-spatial-frequency losses induced by motion of this order on motion detection and on motion-based image segmentation. Motion detection and motion-based segmentation tasks were performed with either spectrally low-pass or spectrally broadband stimuli. Performance on these tasks was compared with a condition having no motion but in which form differences mimicked the perceptual loss of high spatial frequencies produced by motion. This allowed the relative salience of motion and motion-induced blur to be determined. Neither image segmentation nor motion detection was sensitive to the high-spatial-frequency content of the stimuli. Thus the change in perceptual form produced in moving stimuli is not normally used as a cue either for motion detection or for motion-based image segmentation in ordinary situations.