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1 Molecular Pharmacology, Physiology, and Biotechnology, Brown University, Providence, RI, USA
2 Physics, Danish Technical University, Lyngby, Denmark
3 Biomedical Engineering, SUNY Stony Brook, Stony Brook, NY, USA
4 Medical Physiology, University of Copenhagen, Copenhagen, Denmark
* To whom correspondence should be addressed. E-mail: marsh{at}ash.biomed.brown.edu.
We developed a model of tubuloglomerular feedback (TGF) and the myogenic mechanism in afferent arterioles to understand how the two mechanisms are coupled. This paper presents the model. The tubular model predicts pressure, flow, and NaCl concentration as functions of time and tubular length in a compliant tubule that reabsorbs NaCl and water; boundary conditions are glomerular filtration rate (GFR), a nonlinear outflow resistance, and initial NaCl concentration. The glomerular model calculates GFR from a change in protein concentration using estimates of capillary hydrostatic pressure, tubular hydrostatic pressure, and plasma flow rate. The arteriolar model predicts fraction of open K channels, intracellular C
concentration, (Ci), PD, rate of actin--myosin cross bridge formation, force of contraction, and length of elastic elements, and was solved for two arteriolar segments, identical except for the strength of TGF input, with a third, fixed resistance segment representing pre-arteriolar vessels. The two arteriolar segments are electrically coupled. The arteriolar, glomerular, and tubular models are linked; TGF modulates arteriolar circumference which determines vascular resistance and glomerular capillary pressure. The model couples TGF input to voltage gated C channels. It predicts autoregulation of GFR and renal blood flow, matches experimental measures of tubular pressure and macula densa NaCl concentration, and predicts TGF--induced oscillations and a faster smaller vasomotor oscillation. There are nonlinear interactions between TGF and the myogenic mechanism, and these include the modulation of the frequency and amplitude of the myogenic oscillation by TGF. The prediction of modulation is confirmed in a companion study.
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