In these and other BMSR projects, mathematical models help researchers move from qualitative description to quantitative analysis, explains codirector Dr. Vasilis Marmarelis. For example, in cooperation with researchers at the University of Texas and at Brown University in Rhode Island, Dr. Marmarelis has used models to study how changes in blood pressure affect the blood supply reaching vital organs such as the brain, heart, and kidneys. We would like to know precisely how much of an effect a specific change in blood pressure has. 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.