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Mathematicians Seek Better Way To Map Human Brain

Two mathematicians are working on a mathematical way to map the convoluted surface of the human brain so that neuroscientists can compare different brains.

Drs. Ken Stephenson and Charles Collins of the University of Tennessee have been awarded a three-year NSF Focused Research Group grant to investigate new mathematical techniques for producing a two-dimensional representation of the cerebral cortex.

"With continuing advances in imaging technologies, neuroscientists are gathering increasingly detailed data on the structure and functional organization of the cortex," Stephenson said. "But it's difficult to compare brain topology across different human subjects because of individual differences in cortical folding."

He said the brain can't be pictured in three dimensions because there is always some surface that can't be seen. Standard three-dimensional renderings hide much of the surface on the far side or, worse, buried in the deep folds.

"Our hope is that by flattening the image we can do the kinds of mapping that will let neurologists compare brain structures and the locations that govern different functions," he said.

The mathematicians are using a technique called circle-packing, in which a mesh describing the 3-D surface is rendered in the plane by using a configuration of circles with a corresponding pattern of tangencies.

The results approximate what is called a "conformal" flat map, and the object of the research is to develop the algorithms for computing these flat maps. Mathematicians and neuroscientists at Florida State University and the University of Minnesota are collaborating in the study. - By Bill Dockery

Related website:

Circle Packing

[Contact: Bill Dockery]






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