A third data set augments the formalization of callosal shape with direct measurements of neuropsychological function on a simple test battery. The following discussion is a small part of a far more extensive investigation reported in detail by Bookstein and colleagues (2002).

For this application, callosal "outlines" were actually digitized as chains of three-dimensional points that lay on the local axis of symmetry of appropriate anatomical cross sections. These points were then slipped to minimize net bending energy, as discussed earlier, and finally projected onto a common synthetic "midsagittal plane" for analysis. The resulting curves incorporate one true landmark (rostrum, a good three-dimensional point) along with 39 semilandmarks; after Procrustes fitting, there are 40 x 2 = 80 shape coordinates. This geometry was recorded for 30 adult males from the Seattle area who had been diagnosed with either fetal alcohol syndrome or fetal alcohol effects (Institute of Medicine, 1996). The neuropsychological battery here, extracted from a much larger protocol of 260 tests over 6 hours, included five measures of reaction time in each of three experimental conditions (simple, choice, and interhemi-spheric transfer) combining laterality of visual stimulus with laterality or contralaterality of motor response. (This does not constitute a proper battery for testing callosal function per se, as the total allocated time was only 4 minutes, corresponding to only 48 separate experimental stimuli.)

Analysis here is by the method of partial least squares (PLS), which is a singular-value decomposition of the covariance matrix between the callosal shape coordinates and the ranks of the 15 neuropsychological measures, followed by interpretation of the singular vectors as coefficients of linear combinations of the two blocks. PLS can be thought of as a combination of regression analysis and factor analysis; it extracts profiles of behavior that optimally covary with dimensions of shape and also produces scores (latent variables) characterizing the study's subjects on these paired dimensions. For a didactic explanation of the matrix algebra underlying this method, along with an explanation of its differences from canonical correlations analysis and structural equations modeling, see Bookstein and colleagues (1996).

The cross-modality signal relating callosal shape to these functional measures was dominated by the uniform term introduced above, which accounts for almost 60% of the cross-block covariance signal in this data set. (This is unlike the situation in the first example, in which the uniform term contributed no useful information to the descriptive task, the group discrimination.) A single uniform shear correlated 0.40 (Figure 4.13, left panel; p @ 0.03) with a profile of behavior emphasizing leftside reaction time, and RT standard deviation, in the simple experimental condition (press a button with the hand on the side that the visual stimulus is on). The more complex conditions contribute essentially nothing to this structure-behavior covariance: Squared direction cosines of the first singular vector total 0.88 for the five measures in the first experimental condition versus 0.09 for the second and only 0.03 for the third. This is the case even though the first principal component of the three sets of five reaction time measures weights the three almost equally (0.32, 0.34, 0.34).

The callosal shape correlated with greater reaction times (poor performance) is somewhat thinned in the splenium, as shown at upper center in Figure 4.13, and a bit attenuated. The size of these arches, set down point by point in the left panel, is not correlated either with this feature of shape or with the corresponding profile of performance deficit. (The unit of this size measure is millimeters, and the nearest simply phrased measure is callosal length.) A suitable test for the scientific content of this analysis might examine the distribution of the extent to which covariation with callosal shape is concentrated in the first (simple) subtest only; the corresponding tail probability is p @ 0.008. There is no significant signal in the relation of callosal shape to either of the other subtests.

The deficit in reaction time speed in this simple condition does not correlate with full-scale IQ (right panel)

in this sample, nor does the relation differ between subjects with (x) and without (+) the facial stigmata that differentiate fetal alcohol syndrome from fetal alcohol effects. This independence of the teratogenesis from both the facial features and the IQ deficits according to which patients qualify for social services bears directly on public policies regarding treatment of people who are diagnosed with prenatal alcohol damage (Bookstein et al., 2002).

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