The National Science Foundation is supporting research of mathematician Nikos Chrisochoides, a professor at the College of William and Mary, and colleagues to develop computer modeling of human brain to assist neurosurgeons with pre- and intra-operative planning, as the overall morphology of the brain often changes during surgery:
Everything changes after the surgeons open your skull.
Your brain, and the tumor inside it, no longer fully float in their protective bath of cerebrospinal fluid. Gravity comes into play, as does the atmospheric pressure of the operating theater. The brain responds to these foreign forces, the cerebral tissue sagging, rebounding and changing shape. The tumor that the neurosurgeons want to remove also has changed position…
In essence, the William and Mary team provides the surgical team with a dynamic computer model of the patient’s brain. In clinical trials, Chrisochoides says his team can render a new model in six or seven minutes, but hopes to be able to do so in under two minutes.
“We want to help the neurosurgeon make an informed decision of what to cut, where the critical paths are, what areas to avoid,” he said. “I’m neither a neurosurgeon nor a doctor, so the contribution of my research is to make this distillation of objects really, really, really fast.”
Chrisochoides’ lab is dominated by a projection computer monitor whose screen would not look out of place in a small multiplex theater. Chrisochoides handed out 3-D glasses to a small audience that included a colleague from NASA and Andriy Fedorov, a Ph.D. student recently returned from 15 months as the team’s representative at Harvard.
Chrisochoides takes his place at the keyboard and mouse, and the huge monitor displays a parietal slice of a computer mesh brain. A nasty-looking blob clearly indicates the presence of the tumor. The glasses give the audience a striking 3-D effect, showing off the curves of the vector arrows indicating how displacement–represented by color as well as length of the shaft–was acting on the brain.
The process begins with the acquisition of a variety of images before the surgery–images which are otherwise unavailable in the middle of the procedure. Low-resolution intraoperative data allows the tracking of the shift of brain matter and calculates how to change the preoperative images accordingly.
The brain, of course, is an elastic object.
“If you push it,” Chrisochoides said, “it takes energy and then after a while it settles down. We can calculate the place where it settles by solving the partial differential equation. Mathematicians can tell us that there is a solution, but they cannot tell us what the solution is. There’s no such thing for this equation. There’s no analytic solution. So we have to approximate.”
Chrisochoides approximates the geometry of the patient’s brain by tessellating it into triangles in three dimensions, or in other words, generating a mesh representing the brain.