It's that difference between qualitative and quantitative estimations that motivates the use of mathematical models. Dr. Vasilis Marmarelis uses mathematical models to study how changes in blood pressure affect the blood supply to vital organs. Mathematical models are especially useful in making sense of complicated systems. With Dr. Theodore Berger, professor of biomedical engineering and neurobiology at the University of Southern California, Dr. Marmarelis is tackling one of the most complicated systems, the nervous system. In the nervous system, scores of variables influence one another in complicated ways.
Information travels through the nervous system via electrochemical pulses called action potentials.
The pulses are collected and integrated at sites called synapses, located in a bushy, branching network of nerve fibers known as dendrites. Each neuron's response depends not only on which synapses receive pulses from other neurons, but also on the sequence in which those pulses are received. Marmarelis and Berger are focusing their efforts on understanding and modeling the hippocampus, an area of the brain thought to be involved in memory formation and learning. This, in turn, could lead to better ways of treating Alzheimer's disease and other conditions that result in memory loss. In other work, the researchers are exploring applications of mathematical models to sensory systems, such as the auditory and visual systems, in hopes of finding new ways to compensate for the loss of hearing or sight.