A mechanism for the generation of harmonics in oscillations mediated by tubuloglomerular feedback

In the thick ascending limb (TAL), oscillations in tubular flow are converted into oscillations in NaCl concentration; these oscillations are sensed by the macula densa (MD). In a mathematical model of oscillations mediated by tubuloglomerular feedback, we have previously shown that nonlinear NaCl transport characteristics of the TAL generate harmonics of a flow oscillation’s fundamental frequency. In the present study we used elementary mathematics to elucidate the principles of the mechanism by which these harmonics are generated. A sinusoidal flow oscillation entering the TAL generates harmonics in two stages. The first stage is the transformation of that oscillation into a non‐sinusoidal TAL fluid transit time oscillation; that transit time is the principal determinant of NaCl concentration at the MD. The second stage is the transformation of any sinusoidal frequency component of that transit time oscillation into an infinite series of harmonics by nonlinear transepithelial NaCl transport along the TAL. The key prediction of this study is that a periodic TAL tubular flow oscillation will continuously give rise to a series of harmonics in the resulting oscillation in NaCl concentration alongside the MD.