In the sixties, Dr Donald Ross designed a surgical solution for young patients with aortic valve disease by using the patients’ own pulmonary valve. The Ross procedure is the only aortic valve replacement technique that can restore long-term survival and preserve quality of life. The main failure mode of the Ross procedure is wall dilatation, potentially leading to valve regurgitation and leakage. Dilatation occurs due to the inability of the pulmonary autograft to adapt to the sudden increase in loading when exposing to aortic pressures. Previous experimental data has shown that a permanent external support wrapped around the artery can prevent the acute dilatation of the arterial wall. However, the textile support leads to stress-shielding phenomena due to the loss of mechanical wall compliance. We present a pragmatic and modular computational framework of arterial growth and remodeling predicting the long-term outcomes of cardiovascular tissue adaptation, with and without textile wrapping. The model integrates mean, systolic and diastolic pressures and assumes the resulting wall stresses to drive the biological remodeling rules. Rather than a single mean pressure or stress deviation from the homeostatic state, we demonstrate that only pulsatile stresses can predict available experimental results. Therefore, we suggest that a biodegradable external support could induce benign remodeling in the Ross procedure. Indeed, a biodegradable textile wrapped around the autograft fulfills the trade-off between prevention of acute dilatation on the one hand and recovery of arterial wall compliance on the other hand. After further validation, the computational framework can set the basis for the development of an actual biodegradable external support for the Ross procedure with optimized polymer mechanical properties and degradation behavior.