Study of Kidneys Aims to Identify How They Work, Complexities of Blood Pressure

BUFFALO, N.Y. -- By regulating the concentrations of hundreds, or even thousands, of substances in blood plasma and by releasing hormones to regulate blood pressure and other critical functions, the kidneys maintain an organism's chemical balance.

Every day, the kidneys in an average adult filter about 180 liters of fluid, returning much of it to circulation.

Now mathematicians are trying to figure out how aspects of this incredibly complex system work.

E. Bruce Pitman, Ph.D., associate professor of mathematics at the University at Buffalo, and Harold Layton, Ph.D., of Duke University, have developed a mathematical model of the nephron, the main structure in the kidney.

"We hope to develop a new algorithm flexible enough to allow us to study how the kidney takes up specific substances, where they go and how much time it takes," said Pitman.

They are also hoping their work will yield some new findings about hypertension.

According to Pitman, experimental data have shown a discrepancy between the way kidneys in normal rats maintain concentrations of sodium chloride and other chemicals and the way kidneys in hypertensive rats do.

Pitman and Layton, along with physiologist Leon Moore at the State University of New York at Stony Brook, have now identified the regular oscillations in these concentrations in normal rats as a Hopf bifurcation, a mathematical characterization of how changes occur in the behavior of a solution.

"The concentrations change from remaining constant, to small, regular oscillations within the normal range," said Pitman.

But in hypertensive rats, the concentrations of chemicals appear to be irregular and chaotic.

"We tried to find this chaotic behavior in our models and we couldn't, a sign that these oscillations are much more complicated than those in normal rats," Pitman said.

The mathematicians are adjusting their model so that it accommodates these oscillations.

A paper by the team on this subject appeared in the American Journal of Physiology (Vol. 268, 1995, p. F163).