Evaluation of Natriuretic Control Signals: A Mathematical Modeling Analysis
Authors: Yu Hongtao , Hallow Melissa Karen 
Published: April 2020

The normal kidney quickly matches sodium (Na+) excretion to Na+ intake with minimal change in blood pressure or plasma Na+ concentration, primarily by adjusting tubular reabsorption. However, consensus is lacking on the biophysical signal(s) sensed by tubule cells. Renal perfusion pressure (RPP) and renal interstitial hydrostatic pressure (RIHP) can alter Na+ reabsorption, but pressure does not always increase, and in fact sometimes decreases, with Na+ intake/volume expansion. Renal blood flow (RBF) can alter Na+ reabsorption but is normally tightly autoregulated. Renin may play an important role, but there still must be an earlier biophysical signal that reaches the macula densa (MD) to induce changes in renin. Sympathetic activity may be important, but renal denervation does not eliminate this phenomenon. Atrial natriuretic peptide (ANP) and cortical oxygen delivery (COD) may also play a role. It is difficult to experimentally determine the relative contributions, magnitudes, and ranges of these regulatory mechanisms. Thus, we aimed to couple experimental data with mathematical modeling to assess the role of these potential regulatory signals.A mathematical model of cardiorenal function was used to evaluate possible physiological signals
mediating the natriuretic response and coupled with a published experimental study, in which RIHP, RBF, fractional Na+ excretion (FENA), and
GFR were measured in volume expanded (VE – saline infusion) or hydropenic (HY) anesthetized dogs during incremental renal vein constrictions. While RIHP and RBF usually change in tandem, venous constriction decouples them. RIHP and RBF were first evaluated as possible signals for tubular Na+ reabsorption, alone and in combination. However, they could only partially explain experimentally observed changes in FENA in response to venous constriction in VE and HY. In combination, these two mechanisms reproduced the general trends of decreasing FENA with venous constriction in VE, and increasing FENA with venous constriction in HY. However, the two signals could not explain the much higher FENA observed in VE vs HY, at points where both RIHP and RBF were very similar. This indicates that increased FENA with volume expansion is due to another signal. VE increases atrial stretch and thus ANP, while VE decreases COD through hemodilution. We found that ANP or COD as natriuretic signals alone poorly described the experimental data. However, the combination cases RIHP‐RBF‐ANP or ‐ COD nearly reproduced the changes in FENA with venous constriction in VE vs HY., However, they failed to fully capture the large FENA value at the baseline in VE (Exp.: 5.4% vs. Sim.: 3%). When combined RIHP, RBF, ANP, and COD factors together as the integrated control signal, the model fully reproduced the experimental data, including the large FENA at the baseline.This analysis demonstrates that multiple mechanisms likely act simultaneously to mediate natriuresis, and the relative importance of each depends on conditions (e.g. volume expansion, congestion, etc.). This has implications for how we interpret experimental data and how we understand disease states.