Models of the human brain, patterned on engineering control theory, may some day help researchers control such neurological diseases as epilepsy, Parkinson’s and migraines, according to a Penn State researcher who is using mathematical models of neuron networks from which more complex brain models emerge.
"The dual concepts of observability and controlability have been considered one of the most important developments in mathematics of the 20th century," said Steven J. Schiff, the Brush Chair Professor of Engineering and director of the Penn State Center for Neural Engineering. "Observability and controlability theorems essentially state that if you can observe and reconstruct a system’s variables, you may be able to optimally control it. Incredibly, these theoretical concepts have been largely absent in the observation and control of complex biological systems."
Those engineering concepts were originally designed for simple linear phenomena, but were later revised to apply to non-linear systems. Such things as robotic navigation, automated aircraft landings, climate models and the human brain all require non-linear models and methods.
"If you want to observe anything that is at all complicated — having more than one part — in nature, you typically only observe one of the parts or a small subset of the many parts," said Schiff, who is also professor of neurosurgery, engineering science and mechanics, and physics, and a faculty member of the Huck Institutes of the Life Sciences. "The best way of doing that is make a model. Not a replica, but a mathematical representation that uses strategies to reconstruct from measurements of one part to the many that we cannot observe."
This type of model-based observability makes it possible today to create weather predictions of unprecedented accuracy and to automatically land an airliner without pilot intervention.
"Brains are much harder than the weather," said Schiff. "In comparison, the weather is a breeze."
There are seven equations that govern weather, but the number of equations for the brain is uncountable, according to Schiff. One of the problems with modeling the brain is that neural networks in the brain are not connected from neighbor to neighbor. Too many pathways exist.
"We make and we have been making models of the brain’s networks for 60 years," Schiff said at the recent annual meeting of the American Association for the Advancement of Science in Boston. “We do that for small pieces of the brain. How retina takes in an image and how the brain decodes that image, or how we generate simple movements are examples of how we try now to embody the equations of motion of those limited pieces. But we never used the control engineer’s trick of fusing those models with our measurements from the brain. This is the key — a good model will synchronize with the system it is coupled to.”
(Image: Photograph by Anne Keiser, National Geographic; model by Yeorgos Lampathakis)