Our research concerns the process by which the mammalian kidney regulates its blood flow in the face of fluctuations of arterial blood pressure. Blood flow to each renal tubule is controlled by an ensemble of two nonlinear systems; one is sensitive to the flow dependent concentration of NaCl in the tubular fluid at a specific tubular site, and the other responds to changes in blood pressure. These two processes interact because they act on a single group of smooth muscle cells in arterioles supplying the renal tubule.
We have developed a mathematical model of pressure, flow, and NaCl concentration in a renal tubule, and of the action of these two regulatory processes on smooth muscle cells of the arteriole. The model successfully simulates experimentally measured oscillations in each of the regulatory systems, and also predicts a nonlinear interaction, whose presence we have confirmed in experimental records of blood flow.
The slower oscillation of the two has been found to change to an irregular fluctuation in animals with high blood pressure. The change is known as a bifurcation, and the change leads to a state with characterists of deterministic chaos. Our goal is to use the model to determine the cause of the bifurcation, which should lead to testable predictions about causality.
Our working hypothesis about the cause of the bifurcation arises from our observation that renal tubules use signal propagation over the walls of arterioles to influence each other. We also found that the strength of this signal propagation was increased several fold in animals with high blood pressure. Renal tubules act in concert with each other to respond to naturally occurring fluctuations in blood pressure. When signal strength increses in high blood pressure, additionl tubules will be recruited to the ensemble of synchronized tubules, including those with different anatomical properties. This recruitment will add an asymmetry to the ensemble which may induce the bifurcation to chaos.
This work is supported by NIH Grant EB003508, D.J. Marsh Principal Investigator.