NONLINEAR FILTER PROPERTIES OF THE THICK ASCENDING LIMB

A mathematical model was used to investigate the filter properties of the thick ascending limb (TAL), that is, the response of TAL luminal N aCl concentration to oscillations in tubular fluid flow. For the speci al case of no transtubular NaCl backleak and for spatially homogeneous transport parameters, the model predicts that NaCl concentration in i ntratubular fluid at each location along the TAL depends only on the f luid transit time up the TAL to that location. This exact mathematical result has four important consequences: 1) when a sinusoidal componen t is added to steady-state TAL flow, the NaCl concentration at the mac ula densa (MD) undergoes oscillations that are bounded by a range inte rval envelope with magnitude that decreases as a function of oscillato ry frequency; 2) the frequency response within the range envelope exhi bits nodes at those frequencies where the oscillatory flow has a trans it time to the MD that equals the steady-state fluid transit time (thi s nodal structure arises from the establishment of standing waves in l uminal concentration, relative to the steady-state concentration profi le, along the length of the TAL); 3) for any dynamically changing but positive TAL flow rate, the luminal TAL NaCl concentration profile alo ng the TAL decreases monotonically as a function of TAL length; and 4) sinusoidal oscillations in TAL flow, except at nodal frequencies, res ult in nonsinusoidal oscillations in NaCl concentration at the MD. Num erical calculations that include NaCl backleak exhibit solutions with these same four properties. For parameters in the physiological range, the first few nodes in the frequency response curve are separated by antinodes of significant amplitude, and the nodes arise at frequencies well below the frequency of respiration in rat. Therefore, the nodal structure and nonsinusoidal oscillations should be detectable in exper iments, and they may influence the dynamic behavior of the tubuloglome rular feedback system.