One of the first things people notice about the human brain is its intricate landscape of hills and valleys. These convolutions derive from the cerebral cortex, a two- to four-millimeter-thick mantle of gelatinous tissue packed with neurons sometimes called gray matter that mediates our perceptions, thoughts, emotions and actions. Other large-brained mammals such as whales, dogs and our great ape cousins have a corrugated cortex, too each with its own characteristic pattern of convolutions. But small-brained mammals and other vertebrates have relatively smooth brains. The cortex of large-brained mammals expanded considerably over the course of evolution much more so than the skull. Indeed, the surface area of a flattened human cortex equivalent to that of an extra-large pizza is three times larger than the inner surface of the braincase. Thus, the only way the cortex of humans and other brainy species can fit into the skull is by folding.

This folding is not random, as in a crumpled piece of paper. Rather it exhibits a pattern that is consistent from person to person. How does this folding occur in the first place? And what, if anything, can the resulting topography reveal about brain function? New research indicates that a network of nerve fibers physically pulls the pliable cortex into shape during development and holds it in place throughout life. Disturbances to this network during development or later, as a result of a stroke or injury, can have far-reaching consequences for brain shape and neural communication. These discoveries could therefore lead to new strategies for diagnosing and treating patients with certain mental disorders.

Scientists have pondered the brain's intricate form for centuries. In the early 1800s German physician Franz Joseph Gall proposed that the shape of a person's brain and skull spoke volumes about that individual's intelligence and personality a theory known as phrenology. This influential, albeit scientifically unsupported, idea led to the collection and study of "criminal," "degenerate" and "genius" brains. Then, in the latter part of the 19th century, Swiss anatomist Wilhelm His posited that the brain develops as a sequence of events guided by physical forces. British polymath D'Arcy Thompson built on that foundation, showing that the shapes of many structures, biological and inanimate, result from physical self-organization.

Provocative though they were, these early suppositions eventually faded from view. Phrenology became known as a pseudoscience, and modern genetic theories eclipsed the biomechanical approach to understanding brain structure. Recently, however, evidence from novel brain-imaging techniques, aided by sophisticated computational analyses, has lent fresh support to some of those 19th-century notions.

Hints that His and Thompson were on the right track with their ideas about physical forces shaping biological structures surfaced in 1997. Neurobiologist David Van Essen of Washington University in St. Louis published a hypothesis in Nature in which he suggested that the nerve fibers that link different regions of the cortex, thereby enabling them to communicate with one another, produce small tension forces that pull at this gelatinous tissue. In a human fetus, the cortex starts out smooth and mostly remains that way for the first six months of development. During that time, the newborn neurons send out their spindly fibers, or axons, to hook up with the receptive components, or dendrites, of target neurons in other regions of the cortex. The axons then become tethered to the dendrites. As the cortex expands, the axons grow ever more taught, stretching like rubber bands. Late in the second trimester, while neurons are still emerging, migrating and connecting, the cortex begins to fold. By the time of birth the cortex has more or less completed development and attained its characteristically wrinkled form.

Van Essen argued that two regions that are strongly linked that is, connected via numerous axons are drawn closer together during development by way of the mechanical tension along the tethered axons, producing an outward bulge, or gyrus, between them. A pair of weakly connected regions, in contrast, drifts apart, becoming separated by a valley, or sulcus.

Modern techniques for tracing neural pathways have made it possible to test the hypothesis that the communication system of the cortex is also responsible for shaping the brain. According to a simple mechanical model, if each axon pulls with a small amount of force, the combined force of axons linking strongly connected areas should straighten the axon paths. Using a tool known as retrograde tracing, in which a dye injected in a small area of the cortex is taken up by the endings of axons and transported backward to the parent cell body, it is possible to show which regions send axons to the injection site. Furthermore, the method can reveal both how dense the connections of an area are and what shapes their axon paths take. Our retrograde tracing studies of a large number of neural connections in the rhesus macaque have demonstrated that, as predicted, most connections follow straight or slightly curved paths. Moreover, the denser the connections are, the straighter they tend to run.

The sculpting power of neural connections is particularly evident in the shape differences between language regions in the left and right hemispheres of the human brain [see "Specializations of the Human Brain," by Norman Geschwind; Scientific American, September 1979]. Take, for instance, the form of the Sylvian fissure a prominent sulcus that separates the frontal and posterior language regions. The fissure on the left side of the brain is quite a bit shallower than the one on the right. The asymmetry seems to be related to the anatomy of a large fiber bundle called the arcuate fascicle, which travels around the fissure to connect the frontal and posterior language regions. Based on this observation and the fact that the left hemisphere is predominantly responsible for language in most people, we postulated in a paper published in 2006 that the arcuate fascicle on the left is denser than the one on the right. A number of imaging studies of the human brain have confirmed this asymmetrical fiber density. In theory, then, the larger fiber bundle should have a greater pulling strength and therefore be straighter than the bundle on the right side. This hypothesis has yet to be tested, however.

Mechanical forces shape more than just the large-scale features of the cerebral cortex. They also have an effect on its layered structure. The cortex is made of horizontal tiers of cells, stacked up as in a multilayered cake. Most areas have six layers, and individual layers in those areas vary in thickness and composition. For example, the regions of the cortex that govern the primary senses have a thick layer 4, and the region that controls voluntary motor functions has a thick layer 5. Meanwhile the association areas of the cortex which underlie thinking and memory, among other things have a thick layer 3.

Such variations in laminar structure have been used to divide the cortex into specialized areas for more than 100 years, most famously by German anatomist Korbinian Brodmann, who created a map of the cortex that is still in use today. Folding changes the relative thickness of the layers, as would happen if one were to bend a stack of sponges. In the gyri, the top layers of the cortex are stretched and thinner, whereas in the sulci, the top layers are compressed and thicker. The relations are reversed in the deep layers of the cortex.

Based on these observations, some scientists had suggested that whereas the shapes of layers and neurons change as they are stretched or compressed, the total area of the cortex and the number of neurons it comprises are the same. If so, thick regions (such as the deep layers of gyri) should contain fewer neurons than thin regions of the cortex. This isometric model, as it is known, assumes that during development neurons first migrate to the cortex and then the cortex folds. For an analogy, imagine folding a bag of rice. The shape of the bag changes, but its capacity and the number of grains are the same before and after folding.

Our investigations into the density of neurons in areas of the prefrontal cortex in rhesus macaques reveal that the isometric model is wrong, though. Using estimates based on representative samples of frontal cortex, we determined that the deep layers of gyri are just as densely populated with neurons as the deep layers of sulci. And because the deep layers of gyri are thicker, there are actually more neurons under a unit area in gyri than in sulci.

Our discovery hinted that the physical forces that mold the gyri and sulci also influence neuronal migration. Developmental studies in humans have bolstered this suggestion. Rather than occurring sequentially, the migration of neurons to the cortex and the folding of the cortex partially overlap in time. Consequently, as the cortex folds, the resulting stretching and compressing of layers may well affect the passage of newly born neurons that migrate into the cortex late in development, which in turn would affect the composition of the cortex.

Moreover, the shapes of individual neurons differ depending on where in the cortex they reside. Neurons situated in the deep layers of gyri, for example, are squeezed from the sides and appear elongated. In contrast, neurons located in the deep layers of sulci are stretched and look flattened. The shapes of these cells are consistent with having been modified by mechanical forces as the cortex folded. It will be an intriguing challenge to figure out whether such systematic differences in the shapes of neurons in gyri and sulci also affect their function.

Our computer simulations suggest that they do: for example, because the cortical sheet is much thicker in the gyri than in the sulci, signals impinging on the dendrites of neurons at the bottom of a gyrus must travel a longer distance to the cell body than do signals impinging on the dendrites of neurons at the bottom of a sulci. Researchers can test the effect of these physical differences on the function of neurons by recording the activity of individual neurons across the undulating cortical landscape work that, to our knowledge, has yet to be undertaken.

To fully understand the relation between form and function, scientists will need to look at an abundance of brains. The good news is that now that we can observe the living human brain using noninvasive imaging techniques, such as structural magnetic resonance imaging, and reconstruct it in three dimensions on computers, we are able to collect images of a great many brains far more than are featured in any of the classical collections of brains obtained after death. Re searchers are systematically studying these extensive databases using sophisticated computer programs to analyze brain shape. One of the key findings from this research is that clear differences exist between the cortical folds of healthy people and those of patients with mental diseases that start in development, when neurons, connections and convolutions form. The mechanical relation between fiber connections and convolutions may explain these deviations from the norm.

Research into this potential link is still in its early phases. But over the past couple of years, several research teams have reported that the brains of schizophrenic patients exhibit reduced cortical folding overall relative to the brains of normal people. The findings are controversial, because the location and type of the folding aberrations vary considerably from person to person. We can say with certainty, however, that brain shape generally differs between schizophrenics and healthy people. Experts have often attributed schizophrenia to a perturbed neurochemical balance. The new work suggests that there is additionally a flaw in the circuitry of the brain's communication system, although the nature of the flaw remains unknown.

People diagnosed with autism also exhibit abnormal cortical convolutions. Specifically, some of their sulci appear to be deeper and slightly out of place as compared with those of healthy subjects. In light of this finding, researchers have begun to conceive of autism as a condition that arises from the miswiring of the brain. Studies of brain function support that notion, showing that in autistic people, communication between nearby cortical areas increases, whereas communication between distant areas decreases. As a result, these patients have difficulties ignoring irrelevant things and shifting their attention when it is appropriate to do so.

Mental disorders and learning disabilities can also be associated with aberrations in the composition of the cortical layers. For instance, in the late 1970s neurologist Albert Galaburda of Harvard Medical School found that in dyslexia the pyramidal neurons that form the chief communication system of the cerebral cortex are shifted from their normal position in the layers of the language and auditory areas of the frontal cortex. Schizophrenia, too, may leave imprints on the cortical architecture: some frontal areas of the cortex in affected individuals are aberrant in their neural density. Abnormal distribution of neurons in cortical layers disrupts their pattern of connections, which ultimately impairs the fundamental function of the nervous system in communication. Researchers are just beginning to probe structural abnormalities of the cortex in people with autism, which may further elucidate this puzzling condition.

More studies are needed to ascertain whether other neurological diseases that originate during development also bring about changes in the number and positions of neurons in the cortical layers. Thinking of schizophrenia and autism as disorders that affect neural networks, as opposed to localized parts of the brain, might lead to novel strategies for diagnosis and treatment. For instance, patients who have these conditions might profit from performing tasks that engage different parts of the brain, just as dyslexics benefit from using visual and multimodal aids in learning.

Modern neuroimaging methods have also enabled scientists to test the phrenological notion that cortical convolutions or the amount of gray matter in different brain regions can reveal a person's talents. Here, too, linking form and function is fraught with difficulty. The connection is clearest in people who routinely engage in well-defined coordinated mental and physical exercise.

Professional musicians offer one such example. These individuals, who need to practice extensively, systematically differ from nonmusicians in motor regions of the cortex that are involved in the control of their particular instruments. Still, clear folding patterns that distinguish broader mental talents remain elusive.

We still have much to unravel. For one, we do not yet understand how individual gyri attain their specific size and shape, any more than we understand the developmental underpinnings of variation in ear or nose shape among individuals. Variation is a very complex problem. Computational models that simulate the diversity of physical interactions between neurons during cortical development may throw light on this question in the future. So far, however, the models are very preliminary because of the complexity of the physical interactions and the limited amount of developmental data available.

Scholars are also keen to know more about how the cortex develops. Topping our wish list is a detailed timetable of the formation of the many different connections that make up its extensive communication system. By marking neurons in animals, we will be able to determine when different parts of the cortex develop in the womb, which, in turn, will enable scientists to experimentally modify the development of distinct layers or neurons. Information about the sequence of development will help reveal events that result in abnormal brain morphology and function. The range of neurological diseases with vastly different symptoms such as those seen in schizophrenia, autism, Williams syndrome, childhood epilepsy, and other disorders may be the result of pathology arising at different times in development and variously affecting regions, layers and sets of neurons that happen to be emerging, migrating or connecting when the process goes awry.

To be sure, mechanical forces are not alone in modeling the brain. Comparisons of brain shape have demonstrated that brains of closely related people are more similar to one another than are brains of unrelated people, indicating that genetic programs are at work, too. Perhaps genetic processes control the timing of development of the cortex, and simple physical forces shape the brain as nerve cells are born, migrate and interconnect in a self-organizing fashion. Such a combination may help explain the remarkable regularity of the major convolutions among individuals, as well as the diversity of small convolutions, which differ even in identical twins.

Many of the current concepts about the shape of the brain have come full circle from ideas first proposed more than a century ago, including the notion of a link between brain shape and brain function. Systematic comparisons of brain shape across populations of normal subjects and patients with brain disorders affirm that the landscape of the brain does correlate with mental function and dysfunction.

But even with the advanced imaging methods for measuring brains, experts still cannot recognize the cortex of a genius or a criminal when they see one. New models of cortex folding that combine genetics and physical principles will help us integrate what we know about morphology, development and connectivity so that we may eventually unlock these and other secrets of the brain.