Fred L Bookstein

abstract Procrustes analysis and the thin-plate spline, two new methods for biometrical analysis of curving form, together greatly enhance the power of quantitative studies of callosal shape. This chapter introduces these methods informally and explains why they are more powerful than their predecessors. In a comparison of the brains of chronic schizophrenics with normal brains, a highly localized remodeling of the ventricular boundary of the isthmus in the midsagittal plane distinguishes the groups much more effectively than does the general run of quantitative neuroanatomical differentia for this disease. In another study, the shape of the callosum of healthy elderly males is found to be considerably and reliably different from that of elderly females in the region of the splenium. In a third study, callosal shape is found to be strikingly associated with callosal function in a study of 30 adult males diagnosed with prenatal alcohol damage. In all these studies, statistical significance can be demonstrated rigorously, and shape effects can be localized accurately, even though there are considerably more variables than cases. The combination of Procrustes analysis and thin-plate spline visualization may prove useful in a wide range of epigenetic or syndromal studies of the geometry of this important structure.

Recently, there have been important theoretical and practical advances in morphometrics, the statistics of biological shape and shape change. These developments did not come primarily at the hands of biomedical researchers. Rather, they have arisen since the late 1980s out of advances in probability theory, pattern analysis, and interpolation theory during the preceding decade. Although they have proved quite useful in a variety of prototype biological and biomedical applications, the new methods are not yet well known outside a small expert circle. Most discussions and examples appear in technical journals or conference volumes that are scrutinized far more often by those of us who build tools than by neuroscientists in search of quantitative tools to use. Most accessible, perhaps, are two recent review articles by Bookstein (1998, 1999) and, for the more fred l. bookstein Institute of Anthropology, University of Vienna, Austria; Institute of Gerontology, University of Michigan, Ann Arbor, Michigan.

mathematically oriented, a new graduate text (Dryden andMardia, 1998).

The purpose of this note is to motivate the reader's deeper study of these new methods by pointing to otherwise subtle callosal shape findings that are produced quite straightforwardly with their aid. For an argument introducing and defending a method as unfamiliar as this, the conventional outline of biomedical papers— methods, then results, then discussion—is not particularly helpful. One needs, rather, to explain the methods by the results they produce: to introduce the methods and results at the same time. Hence, my presentation here is in the nature of an informal lecture emphasizing the surprising precision and power of analyses of what is, after all, a rather familiar data resource: outlines of the corpus callosum near the midsagittal plane. I hope thereby to call the new methodology to the attention of a sophisticated professional community who are likely in need of just such a toolkit at this time.

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