A mathematical model of tone in the structural remodeling of arterioles

Abstract

Acute changes in microvascular tone affects vessel diameter and thus local tissue perfusion. In the short term such changes does not affect vascular structure. Longstanding changes in tone may however, result in a structural microvascular remodeling. We present a simple mathematical model of a vessel wall containing passive elastic and active contractile elements. The wall is sensitive to circumferential wall stress. If wall stress increases tone will increase and vice versa (a myogenic response). Structurally the vessel responds to longstanding changes in tone with a eutrophic reorganization of the wall material around a lumen of another size. During a simulation the vessel initially attains a steady contracted state. A step change in pressure is followed by an acute adjustment of tone and diameter. This myogenic response leads to a partial normalization of the wall stress, but at another level of tone. If the pressure stimulus is maintained, the vessel slowly remodels until the initial level of tone is reestablished. This process also restores the basal level of wall stress and leads to a normalization of the length of the individual layer within the wall. The results do not depend on the specific shape of the myogenic response. Conclusion: Structural remodeling driven by a change in vascular tone can cause normalization of wall stress, wall strain and tone in a vessel exposed to a sustained change in pressure.