Spring 1995 Mission

The orange and the grapefruit

An orange and grapefruit will help a layman appreciate a brain mapper's need for this complex thing called the "convex hull method of spatial normalization."

Convex hull, developed at the Research Imaging Center (RIC), uses algorithms to "warp" images of human brains and make them ready for scientific comparison. The task is much like fitting a grapefruit inside an orange. No two brains have the exact same size, shape and structure. Identifying the functions of different parts of the brain requires accurate cross-comparison between images taken from hundreds of people.

The outgrowth of work in the '80s by the center's director, Peter T. Fox, MD, convex hull has been honed into computer algorithms by medical physicist J. Hunter Downs III, PhD, an RIC instructor. The brain research community is debating the convex hull method as a possible standard in building an atlas of the brain's functions. Accepting a standard would speed the brain mapping project by letting researchers worldwide compare and share like data.

"I'm a toolmaker," said Dr. Downs, who studied computer science as an undergraduate at The University of Texas at San Antonio and completed his doctorate in medical physics in 1994 at the Health Science Center. "This is a tool designed so the neuroscientists can talk coherently about how the brain functions."

The convex hull concept also has industrial applications where points must be plotted on a curve. For example, engineers who design auto bodies use its principles.

Dr. Fox pioneered the idea for brain imaging in 1985 at Washington University when he took what is called the "bounding box" method a step further. The box describes the boundary drawn around any selected part of the brain image; the image inside then is enlarged or reduced for comparison with like images from other subjects. Dr. Fox began work that would expand the scope beyond warping, or "normalizing," length, width and height. He began exploring a way to normalize curvature as well.

Arriving at the Health Science Center, Dr. Fox described the concept to Dr. Downs and Jack L. Lancaster, PhD, a physicist, professor of radiology and head of the RIC's computer software development team. "I didn't know the mathematical term or the concept of convex hull, but Hunter and Jack sure did. They said, 'That's a convex hull.'"

Here is how it works:

"Use the orange and the grapefruit for an example," Dr. Downs said. "The bounding box is able to stretch the dimensions of the orange to match the size of the grapefruit, but neither the grapefruit nor the orange is quite circular so we need to make them the same shape.

"Convex hull keeps the whole brain image in a three-dimensional space. It is conceived as a way to scale outward from some central point by using the ratios of that distance from the central point to the convex hull surface, which is the outside of the brain," he said.

"For example, you want to scale the orange to be the same size as the grapefruit so you can determine where the seeds lie relative to the different shapes. You take the outer surface of the orange and the central point of the orange and find the lengths in every direction. You do the same thing with the grapefruit. Then you use the ratios of those lengths between the orange and the grapefruit to stretch out the orange to the grapefruit," he said.

Dr. Fox had conceived of several measurements, but computer applications of the convex hull allow for thousands that touch virtually any point on the curved surface.

Convex hull is being used on images of the whole brain and is accurate to within 2 millimeters. The average brain is 180 millimeters long. Dr. Fox and his staff now are developing ways to selectively measure smaller portions of the brain using the same methodology. He expects to sharpen accuracy fourfold to within .04-millimeter of where any given brain function takes place.

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