Feedback-Mediated Dynamics in the Kidney: Mathematical Modeling
Hwayeon Ryu
Department of Mathematics, Duke University
The glomerular filtration rate in the kidney is controlled, in part, by
the tubuloglomerular feedback (TGF) system, which is a negative feedback
loop that mediates oscillations in tubular fluid flow and in fluid NaCl
concentration of the loop of Henle. In this study, we developed a
mathematical model of the TGF system that represents NaCl transport along
a short loop of Henle with compliant walls. A bifurcation analysis of the
TGF model equations was performed by computing parameter boundaries, as
functions of TGF gain and delay, that separate differing model behaviors.
A comparison with a previous model, which represents only the TAL
explicitly and other segments using phenomenological relations, indicates
that explicit representation of the proximal tubule and descending limb of
the loop of Henle lowers the stability of the TGF system. Model
simulations also suggest that the onset of limit-cycle oscillations (LCO)
results in increases in the time-averaged distal NaCl delivery, whereas
distal fluid delivery is not much affected.