Logarithmic transformation for high-field BOLD fMRI data.

Parametric statistical analyses of BOLD fMRI data often assume that the data are normally distributed, the variance is independent of the mean, and the effects are additive. We evaluated the fulfilment of these conditions on BOLD fMRI data acquired at 4 T from the whole brain while 15 subjects fixated a spot, looked at a geometrical shape, and copied it using a joystick. We performed a detailed analysis of the data to assess (a) their frequency distribution (i.e. how close it was to a normal distribution), (b) the dependence of the standard deviation (SD) on the mean, and (c) the dependence of the response on the preceding baseline. The data showed a strong departure from normality (being skewed to the right and hyperkurtotic), a strong linear dependence of the SD on the mean, and a proportional response over the baseline. These results suggest the need for a logarithmic transformation. Indeed, the log transformation reduced the skewness and kurtosis of the distribution, stabilized the variance, and made the effect additive, i.e. independent of the baseline. We conclude that high-field BOLD fMRI data need to be log-transformed before parametric statistical analyses are applied.

Figure copying in Williams syndrome and normal subjects.

We evaluated the copying abilities of ten subjects with Williams syndrome (WS; age 6-14 years) and ten normally developing children (age 3-6 years) matched for mental age using the matrices component of the Kaufman Brief Intelligence Test (mKBIT). Each subject copied six figures, including line drawings of closed and open geometrical shapes (alone and in combination), crossed lines, and geometrical shapes made of distinct small, filled circles. Qualitatively, subjects of both groups made comparable copies, although several subjects with WS drew a continuous line when copying figures composed of distinct circles. Quantitatively, the goodness of the copies was assessed by three human observers who rated on an analog scale the similarity of each copy to its visual template. Ratings were converted to a scale from zero (completely different) to 100 (the same) for statistical analyses. We found the following. First, the overall goodness of copies of the templates was very similar between the WS and control groups (WS: mean=46.7, range=0.89-95.4; control: mean=54.5, range=0.89-98.2). Second, there were systematic differences in the goodness of copies between the two groups, depending on the features of the figures. Specifically, the goodness of copies of control subjects was almost the same as that of WS subjects for simple line figures, but was consistently better for composite line figures, and even better for figures in which the shape was made of small, filled circles. Third, there was a significant relation between the goodness of copies (dependent variable) and mental age (mKBIT, independent variable) in both groups, although it was stronger and more highly statistically significant in the control than the WS group. These findings indicate that the principles guiding copying are similar in the two groups and suggest that WS is a case of developmental rather than deviance disorder.

Cerebellar activation during copying geometrical shapes.

We studied functional MRI activation in the cerebellum during copying 9 geometrical shapes (equilateral triangle, isosceles triangle, square, diamond, vertical trapezoid, pentagon, hexagon, circle, and vertical lemniscate). Twenty subjects were imaged during 3 consecutive 45-s periods (rest, visual presentation, and copying). First, there was a positive relation between cerebellar activation and the peak speed of individual movements. This effect was strongest in the lateral and posterior ipsilateral cerebellum but it was also present in the paramedian zones of both cerebellar hemispheres and in the vermis. A finer grain analysis of the relations between the time course of the blood oxygenation level-dependent activation and movement parameters revealed a significant relation to hand position and speed but not to acceleration. Second, there was a significant relation between the intensity of voxel activation during visual presentation and the speed of the upcoming movement. The spatial distribution of these voxels was very similar to that of the voxels activated during copying, indicating that the cerebellum might be involved in motor rehearsal, in addition to its role during movement execution. Finally, a factor analysis of the intensity of activated voxels in the ipsilateral cerebellum during copying (adjusted for the speed effect) extracted 3 shape factors. Factor 1 reflected "roundness," factor 2 "upward pointing," and factor 3 "pointing (up or down) and elongation." These results link cerebellar activation to more global, spatial aspects of copying.