Modeling the interaction between tubuloglomerular feedback and myogenic mechanisms in the control of glomerular mechanics

Abstract

Introduction: Mechanical stresses and strains exerted on the glomerular cells have emerged as potentially influential factors in the progression of glomerular disease. Renal autoregulation, the feedback process by which the afferent arteriole changes in diameter in response to changes in blood pressure, is assumed to control glomerular mechanical stresses exerted on the glomerular capillaries. However, it is unclear how the two major mechanisms of renal autoregulation, the afferent arteriole myogenic mechanism and tubuloglomerular feedback (TGF), each contribute to the maintenance of glomerular mechanical homeostasis. Methods: In this study, we made a mathematical model of renal autoregulation and combined this model with an anatomically accurate model of glomerular blood flow and filtration, developed previously by us. We parameterized the renal autoregulation model based on data from previous literature, and we found evidence for an increased myogenic mechanism sensitivity when TGF is operant, as has been reported previously. We examined the mechanical effects of each autoregulatory mechanism (the myogenic, TGF and modified myogenic) by simulating blood flow through the glomerular capillary network with and without each mechanism operant. Results: Our model results indicate that the myogenic mechanism plays a central role in maintaining glomerular mechanical homeostasis, by providing the most protection to the glomerular capillaries. However, at higher perfusion pressures, the modulation of the myogenic mechanism sensitivity by TGF is crucial for the maintenance of glomerular mechanical homeostasis. Overall, a loss of renal autoregulation increases mechanical strain by up to twofold in the capillaries branching off the afferent arteriole. This further corroborates our previous simulation studies, that have identified glomerular capillaries nearest to the afferent arteriole as the most prone to mechanical injury in cases of disturbed glomerular hemodynamics. Discussion: Renal autoregulation is a complex process by which multiple feedback mechanisms interact to control blood flow and filtration in the glomerulus. Importantly, our study indicates that another function of renal autoregulation is control of the mechanical stresses on the glomerular cells, which indicates that loss or inhibition of renal autoregulation may have a mechanical effect that may contribute to glomerular injury in diseases such as hypertension or diabetes. This study highlights the utility of mathematical models in integrating data from previous experimental studies, estimating variables that are difficult to measure experimentally (i.e. mechanical stresses in microvascular networks) and testing hypotheses that are historically difficult or impossible to measure.

Keywords: glomerulus; mathematical modeling; myogenic; renal autoregulation; tubuloglomerular feedback.

FIGURE 1

Autoregulation model schematic. Models of the glomerulus and tubule are used to estimate SNGFR and macula densa solute concentration, C_MD. The afferent arteriole model calculates wall tension T_P, and T_P and C_MD are used to calculate the myogenic and TGF tones, denoted S_Myo and S_TGF, respectively. The interaction between S_Myo and S_TGF is denoted by Ψ in the diagram and will be referred to as such throughout this article. References are included to indicate the core references used to construct each model, with the novelty of the glomerulus sub-model accentuated.

FIGURE 2

Tubule model predicts osmolality, fluid velocity and the reabsorbed fluid load on the length of the tubule and at varied pressures. (A) Tubular fluid osmolality (black) and velocity (blue) as a function of length along the tubule in the baseline case. (B) Macula densa osmolality (C_MD) and fluid velocity at the macula densa as a function of perfusion pressure. (C) SNGFR and the reabsorbed fluid load change with altered perfusion pressure. In (B–C), the afferent arteriole and glomerulus models were used to translate perfusion pressure into SNGFR (Figure 1), assuming no feedback (open-loop). The tubule model was then used to compute macula densa osmolality and fluid velocity (B), as well as the reabsorbed fluid load (C).

FIGURE 3

Renal autoregulation model parameterization. Data obtained from literature from Takenaka (Takenaka et al., 1994) and Bell (Bell and Navar, 1982) are represented as points, wherein (A) open circles indicate the control animals, closed circles indicate the animals that received furosemide, open triangles indicate animals that received diltiazem, and (B) open squares indicate animals whose TGF response was manually controlled by placing a wax block in the proximal tubule. Model results are shown as curves, (A) black indicating a passive afferent arteriole, blue indicating only the myogenic mechanism is active, dashed magenta indicates both myogenic and TGF mechanisms are active but do not interact (no Ψ), red indicates that both mechanisms are operant and that the myogenic mechanism sensitivity is modified by the TGF (Ψ). (B) The solid magenta line indicates that the myogenic mechanism is active, but TGF is manually controlled (i.e., tubular fluid concentration is stable, without TGF operant).

FIGURE 4

Myogenic mechanism and TGF signal curves. (A) The myogenic curve (blue) is a function of the afferent arteriole wall tension. The TGF-mediated modification to the myogenic curve, in red, is included to show the difference between the myogenic mechanism with and without TGF operant. (B) The TGF curve is black and is a function of the macula densa osmolality.

FIGURE 5

Steady-state glomerular hemodynamics with each autoregulatory mechanism removed to show the functional results of reduction in autoregulatory efficiency.

FIGURE 6

Model predictions of steady-state, spatially averaged shear stress, hoop stress and CSGFR values generated by a varied perfusion pressure (top row). We model a passive afferent arteriole (black), an afferent arteriole with only the myogenic mechanism operant (blue), the additive TGF and myogenic mechanisms (dashed magenta, no Ψ), and the TGF with a modified myogenic mechanism (red, with Ψ). We then compute the contribution of each autoregulatory mechanism to the maintenance of the mechanical stresses at control values (bottom row). The myogenic mechanism contribution (green) is highest, while TGF (blue) and Ψ (pink) play a smaller role in contributing to the maintenance of glomerular mechanical homeostasis.

FIGURE 7

Transient mechanical stress and strains exerted on each glomerular capillary by a pressure pulse from the rat heartbeat. Each data point corresponds to one of the 320 glomerular capillaries in the network. Transient mechanical stresses include capillary circumferential strain (ε_θ, (A), change in shear stress on the endothelium (Δτ, (B) and the change in CSGFR (ΔCSGFR, (C). The model afferent arteriole parameters are varied to simulate the passive (‘Passive’), and the control condition with Ψ (‘Control’). Two mean perfusion pressures (P_A) were considered, 100 mmHg (black boxes) and 130 mmHg (red boxes), as indicated by the number next to the model condition for each group. Lines in each box indicate the median across all capillaries, the bottom and top of the boxes indicate 75th and 25th percentiles, respectively, and whiskers indicate outliers.

FIGURE 8

Circumferential strain distribution across the glomerular capillary network. Each of the networks above is representative of the network topology of the model glomerulus; each segment represents a capillary segment, with nodes connecting the segments as a representation of points of bifurcation and/or coalescing. Arrows indicate flow direction. The thickness of the capillary, as well as the color (scale bar at right) are proportional to the circumferential strain on that capillary segment. Mean pressure is 130 mmHg. The strain is calculated for the passive case, when both autoregulatory mechanisms are inoperant, and the control case, in which both mechanisms are operant and their interaction Ψ is present.