A Two-Timescale Reduced-Order Model Coupling Acute Arterial Compliance with Stress- and Shear-Regulated Growth and Remodeling

Arterial growth and remodeling (G\&R) models should distinguish immediate load-induced deformation from slower structural adaptation. A computationally light two-timescale model was therefore developed in which the reference-pressure structural geometry, described by inner radius $R_g$ and wall thickness $H_g$, is separated from the instantaneously loaded geometry $R_i$ and $h$. At every slow G\&R state, a nonlinear scalar equilibrium is solved for pressure-dependent dilation while annular wall area is conserved to represent acute wall incompressibility. The resulting loaded geometry determines circumferential stress and wall shear stress (WSS), whose signed deviations from homeostatic targets are transmitted through separate stress and shear signal channels. Stress signaling regulates wall growth through a lumped growth-factor variable, whereas WSS signaling regulates structural radius. The effective wall-growth and radius-rate parameters were constrained using separate rat aortic-thickness and mesenteric-artery diameter endpoints and were not interpreted as universal validation. For an acute pressure increase from 120 to 180~mmHg, the compliant model predicted an 8.11\% increase in loaded radius and a 6.78\% decrease in loaded thickness; the corresponding stress and WSS changes were $+73.96\%$ and $-20.86\%$. A matched rigid-wall model produced no acute geometric change, $+50\%$ stress, and no WSS change. At day 28, loaded thickness increased by 17.82\% and 19.80\% in staged and sustained high-pressure protocols, respectively, while loaded radius increased by 14.11\% under increased flow. These states remained transient: equilibrium-entry times were 95--242 days under the primary criterion. All 49 acute-parameter combinations yielded physical solutions, although response magnitudes varied substantially. The framework thus adds acute compliance to homeostatic feedback without abandoning reduced-order interpretability, while making the limits of endpoint anchoring and parameter identifiability explicit.