Blood vessels are continuously adapting their structures to meet the metabolic demands of the tissue. Usually such an adaptation makes the vessel system more powerful in blood delivery. At the same time, many cardiovascular diseases are also related to irregular vessel adaptation, e.g. the hypertension patients appear to have lower micro-vessel density, smaller vessel lumen size, and larger vessel wall thickness. The wall shear stress and blood pressure play important roles in the adaptation. However, previous models which take into account these effects are not stable without some unknown additional stimulus. Our work shows that the pre-capillary sphincters, which are important in the blood auto-regulation, are also crucial in maintaining the adaptation stability.