But these findings are also maddeningly inconsistent. Three quarters of the published studies have found enlarged ventricles in schizophrenics; one quarter have not. Three quarters find smaller hippocampi; one quarter do not. “There is a significant overlap between subjects with schizophrenia and controls for every imaging (and neuropathological) parameter,” Oxford psychiatrist Paul Harrison wrote in a review article last year. “For this reason. . . schizophrenia cannot be diagnosed using either a brain scan or a microscope.”
Morphometrics may provide the answer, and it has already won some converts. At Case Western Reserve in Cleveland, Ohio, for instance, psychiatrist Peter Buckley has used Bookstein’s methods to show that the ventricles in male schizophrenic brains differ in shape as well as size from those in brains. But Bookstein still worries that his pilot studies have attracted too little attention. “I find myself, quite to my surprise, as radical at age 51 as I was as a graduate student,” he sighs.
In the meantime, more and more scientists have been finding applications for his techniques in other areas. Marcus runs a discussion list that now has more than 400 subscribers, and Rohlf and Bookstein have given seminars in Vienna, Paris, Tuscany, Taiwan, and elsewhere. Because of its sensitivity to small differences, morphometrics is especially useful in the classification of species. Biologists have used Bookstein’s methods to study a whole bestiary of animals: bats, fishes, midges, mice, coral, shrews, and even pinworms.
More important, perhaps, is that brain surgeons now use the science of shape in the operating room, where they have long fretted over just where to do their cutting. The brain is an exceedingly mysterious, delicate, and malleable organ. Slice the wrong part of it, and your patient might lose her peripheral vision or her ability to do needlepoint or understand English. More and more often, therefore, brain surgeons depend on three-dimensional computer images produced by ct and mri scanners to plan operations and even to see what they are doing during the operation. The volume scans allow them to see the inside structure of the brain with millimeter accuracy and to work through small incisions instead of opening a large piece of the skull.
Still, the new technology poses problems that only sophisticated shape analysis can solve. A part of the brain may appear in stunning detail, but what is its function? That question can be answered by a technique called “brain warping,” in which landmarks in the brain are mapped (by a thin-plate spline or a similar transformation) to corresponding points on a “brain atlas.” This tells the computer exactly how the patient’s brain geometry differs from that of a generic brain and allows the boundaries of functional regions, like the visual cortex, to be identified. When the surgeon enters the operating room, he sees a giant color display on the computer monitor, like a Rand McNally guide to that patient’s brain.
The discovery that has Bookstein most excited nowadays is a possible test for fetal alcohol syndrome, which in some ways lies at the opposite end of the mental illness spectrum from schizophrenia. Fetal alcohol syndrome starts affecting patients’ lives right away, in infancy. It is about half as common as schizophrenia, affecting nearly 1 million Americans, and every bit as hard to diagnose. Many mothers are reluctant to admit they drank heavily during pregnancy. Others can’t care for their babies and give them up for adoption. Then the first people to realize that something is wrong with the child are the adoptive parents, who have no clue about the birth mother’s drinking history. If there were a way to consistently diagnose fetal alcohol syndrome, even without knowing a child had been exposed to alcohol in the womb, many of these unwitting victims could get the specialized help and advocacy they need.
Children with fetal alcohol syndrome have shortened eyelids, a narrow forehead, and a missing philtrum (the fold between the upper lip and the nose). But those with a milder form of the syndrome, known as fetal alcohol effects, may not bear the telltale facial features. “Many of these kids don’t get diagnosed, and then they start acting weirder and weirder,” says Ann Streissguth, a member of the research group that discovered the syndrome in 1973. “Their parents don’t know what’s wrong with them.”
Although people with fetal alcohol syndrome and fetal alcohol effects are rarely retarded (at least according to iq tests) they have trouble tuning out distractions. Often they can’t cope with new situations or tasks. One of Streissguth’s more successful patients got a steady job as a busboy in a restaurant and was doing well until he was asked to substitute for the cashier. “He ended up throwing furniture and had to be taken to the hospital in restraints,” she says. As they move into adulthood, the problems just get worse. Sixty percent of people with fetal alcohol syndrome and fetal alcohol effects drop out of school, get suspended, or get expelled. More than a third go to jail.
Once again, the shape of the corpus callosum may hold an answer. In people with both forms of the syndrome, the callosum is either much wider than normal or much narrower. While an embryo is exposed to alcohol in the womb, Bookstein says, “there’s a process that’s basically out of control.” It’s as if nature were aiming at the correct shape but didn’t have as good aim as usual.
Testing children for early signs of fetal alcohol syndrome or schizophrenia—or tracking the diseases’ development in the brain—is no simple task. mri scans are elaborate, expensive, and somewhat intimidating, and they require special permission from parents. When used on adults, however, Bookstein’s method is already a powerful tool. In a study now being reviewed for publication, Bookstein and Streissguth looked at the results of behavioral tests and brain scans of 45 adult men, 30 of them afflicted with either fetal alcohol syndrome or fetal alcohol effects, the others not. Though neither Bookstein nor Streissguth had ever met the patients, they guessed the correct diagnosis in all but one instance.
In Bookstein’s field, such concrete results are so rare as to seem almost suspect. Most mathematicians take a perverse pride in abstruseness, in their work’s stubborn irrelevance to daily life. “It will be millions of years before we’ll have any understanding,” Hungarian theorist Paul Erdös said. “And even then it won’t be complete understanding, because we’re up against the infinite.” But shape theory, in Bookstein’s hands, is mathematics made flesh: It not only sheds new light on mental illness, it may change a doctor’s diagnosis or his decision on where to cut a living brain.
“When I look back on it, I see [mathematics’] appeal to me as having been primarily aesthetic,” Bookstein says, “and that is not a justification. The justification is that it occasionally makes sense of the world, and does so in quite unexpected ways.” As for schizophrenia, he admits that the disease is so complex and multifaceted that a true diagnostic test for it may be 20 years away. Still, there is a kind of poetic justice to the fact that such a test, when it comes, may be rooted in Bookstein’s work. Like John Nash, Bookstein is an outsider, an autodidact who dared to think “outside the box,” taking on problems that most experts considered unsolvable.
Was it worth it? Bookstein would clearly say yes. But Nash might have thought twice. Had he been given drugs to forestall his schizophrenia, his life would have been immeasurably easier. But then those same drugs might have taken the reckless edge off his mathematical genius. “You would have lost the Nash embedding theorem,” , Bookstein points out, and someone else might have won the 1994 Nobel prize for economics. Is a Nobel prize worth 30 years of madness? For anyone who saw Nash during his long, bleak battle with his own mind, the answer is obvious.