Arterial arcades and collaterals regress under hemodynamics-based diameter adaptation: A computational and mathematical analysis

Arterial networks exhibit a wide range of segment radii, largely thought to result from adaptation to wall shear stress (WSS). Segments remodel outward or inward if WSS is higher or lower than a reference value. While this mechanism seems straightforward for arterial trees, real networks contain arcades, collaterals, and loops. We investigated the stability of these looping structures under WSS control using simulation models of small networks and published coronary and cerebral artery data. Adaptation was modeled as changes in segment radius proportional to deviations from reference WSS. A generalized model included other hemodynamic stimuli like flow and velocity. Simulations consistently predicted loop regression due to the loss of one or more segments, both for the WSS model and the generalized model, regardless of initial conditions or model parameters. This loop loss was also observed in networks with heterogeneous adaptation rates or under dynamic conditions. A mathematical analysis confirmed that loop instability is a direct consequence of Kirchhoff's circuit law, leading to unstable equilibria. Thus, loss of loops is an inherent outcome of arterial networks adapting to local hemodynamics. Additional mechanisms, such as communication between connected segments, may be needed to explain the presence of loops in real networks.