|
The world’s first professor of morphometrics, Fred Bookstein was inspired to apply math to medicine when his nephew suffered his first psychotic episode. He later collaborated with artist Jim Cogswell to create beeswax-and-wire sculptures (right) of the deformed grids he uses to study schizophrenia. |
On my first day of graduate school at Princeton University in 1979, an older student warned that I would encounter a lot of strange characters in the mathematics department. The strangest of all, he said, was a phantomlike figure known as Nash. In the weeks that followed, I occasionally caught sight of Nash shuffling down the hall in a shabby coat and bright red sneakers or sitting in the cafeteria by himself, staring off into space. But I felt his presence most from the nonsensical messages he wrote on blackboards at night. These often took the form of mathematical equations, but they had as much to do with mathematics as a cat walking across the piano has to do with music.
One day, as a group of students gathered to chat with a professor after a class, someone asked about this mystery man. Lowering his voice, the professor told us that Nash had once been John Nash, the brightest light in the greatest group of students that ever studied math at Princeton. In the late 1940s and 1950s, John Nash had made discoveries that his peers still use every day—the Nash equilibrium, the Nash embedding theorem—even as they averted their eyes from the man himself. But then, somewhere along the line, he lost his grip on reality. He began to believe he was receiving messages from outer space and that there were great and hidden conspiracies against him.
Now, four decades after John Nash was lost to mathematics, mathematics itself may hold the key to treating schizophrenia, the mental illness that held his mind hostage. A new way of analyzing shapes, called morphometrics, may allow doctors to tell what changes occur in the brains of schizophrenics before they lose contact with reality. Morphometrics is also providing clues to the development of fetal alcohol syndrome and Alzheimer’s disease and is improving the ability of brain surgeons to map out the routes they will take to perform delicate operations. In the study of the brain, the shape of things to come is, quite literally, shape.
 |
 |
Fred Bookstein, a statistician at the University of Michigan, has spent more than two decades turning morphometrics into a quantitative science. The basic idea, he says, dates back to the sixteenthcentury and the work of the German artist Albrecht Dürer. Inspired, perhaps, by the recent discovery of perspective geometry, Dürer tried laying grid lines over the faces in his portraits. By moving the lines, while keeping the features of the face in the same position relative to the grid, he could transform the face any way he wanted, turning a bluff forehead into a sloping one, a weak chin into a lantern jaw.
Bookstein’s modern variations on Dürer’s theme—four little fun house faces—peer down from a bulletin board outside his office. One is a photograph of Bookstein looking like a dour version of Billy Crystal; the other three are “not-Freds”—computer-generated caricatures of the first photograph. To make the caricatures, Bookstein first scanned his photograph into his computer. Then he attached a grid to 13 “landmarks” on the face, such as the top of the forehead and the tips of the ears. When he was done, he simply moved a few of the landmark points around, thus forcing the grid to warp and bend as if a thin metal plate were attached to it. Engineers, it turns out, have used such “thin-plate splines” for years. But it was Bookstein who realized that these composite images are a perfect way to represent changes in what morphometricians call “shape space”—and to detect shape differences both large and small.
Schizophrenics may hear voices, hallucinate, or suffer from delusions of grandeur, yet the disease usually sneaks up on them.
 |
 |
 |
Move a few landmark points here or there and a picture of Fred Bookstein becomes A “not-Fred” (left and right). The picture in the middle is the real Fred, but the one on the left, Bookstein says, “is the Fred my mother had in mind.”
Shape is a surprisingly elusive concept. True, humans have an extraordinary capacity for picking out subtle differences in shape. Otherwise it would be impossible to identify a friend in a crowded subway station or to quickly distinguish between a fashionable skirt and one that is hopelessly passé. But describing differences in shape invariably turns out to be problematic. Consider the hippocampus, a region of the brain involved in long-term memory formation. To Bookstein, it resembles a “scroll, a partially unwrapped Torah.” To another neuroscientist I spoke with, it “basically looks like a teaspoon.” And to the anatomists who named it, it resembled a seahorse (hippocampus means “sea horse” in Latin).
Modern science needs to describe shapes more precisely than this. “Morphometrics gives you a language for talking about shapes,” says Jim Rohlf of the State University of New York at Stony Brook. Rohlf is the author of the most widely used collection of computer programs for morphometric analysis. “You can say this shape is like that shape, except that it’s expanded here and compressed there.” Even so, Rohlf says, morphometrics is about more than pretty pictures. It also has a core of statistical theory, which explains why thin-plate splines are the best way to represent differences in shape space.
Hidden in Bookstein’s desk is a not-Fred that demonstrates, better than the others, what a difference a subtle change in shape can make. While the not-Freds on the bulletin board outside his office look like big lovable galoots, this one is downright spooky. Instead of a silly grin, he has flat, faintly sneering lips; instead of a bulbous, pear-shaped face, he has a broad nose and disconcertingly wide-set eyes. Bookstein keeps the picture around, perhaps, as a reminder of the slim distance separating the normal from the abnormal. To an outsider, it’s also an eerie echo of the event that has fueled Bookstein’s personal drive to apply morphometrics to schizophrenia.
In 1980, driven by “voices in his head,” one of Bookstein’s nephews came home from college and tried to kill his own parents. Fortunately, he was diagnosed as a schizophrenic and medicated in time to avert a tragedy. But his treatment was long and slow, and even today he has no memory of what happened in certain years of his life.
His nephew’s story, Bookstein would later learn, was surprisingly typical. Though schizophrenics are not especially prone to violence, many of them hear voices, hallucinate, or suffer from delusions of grandeur or persecution or both. One recovered schizophrenic calls her experience with mental hospitals a “revolving door,” and many others can’t socialize with other people, even between psychotic episodes. It’s estimated that about 10 percent of schizophrenics commit suicide. And yet, for all its dramatic symptoms, schizophrenia usually sneaks up on its victims. No single cause of schizophrenia has been identified, and most schizophrenics don’t have their first “psychotic break” until their late teens or early twenties. Moreover, the shape of schizophrenic brains doesn’t vary from normal in any consistent way—at least to the naked eye.
Enter morphometrics. About five years ago, prodded by the memory of his nephew’s misfortune, Bookstein studied the brain scans of 14 schizophrenics and 14 nonschizophrenic volunteers, or “controls,” that had been gathered together by his colleague John DeQuardo. He labeled 13 landmark points each of the brains, converted the landmark points into shapes, and averaged them. 
The National Institute of Mental Health site is a good starting place for learning about schizophrenia on the Web: www.nimh.nih.gov/publicat/schizoph.html.
The Morphometrics homepage, maintained by Jim Rohlf, is a good place for finding out about morphometrics and contains links to a glossary, a directory of researchers, and meeting announcements: life.bio.sunysb.edu/morph.
