title: New equations for the dose under pulsative/periodic conditions in the design of coated stents.
abstract: The notion of dose that comes from the biologists has been introduced by Delfour et al. (2005 SIAM J. Appl. Math. 65(3):858-881) in the context of coated stents to control restenosis. Assuming a stationary velocity profile of the blood flow in the lumen, it leads to a time-independent equation for the dose that considerably simplifies the analysis and the design problem. Under stable conditions the blood flow is pulsative, that is the velocity field can be assumed to be periodic. So it is necessary to justify the replacement of the periodic field by its time average over the pulsation period. In this paper, firstly we introduce the new unfolded dose and its equations without a priori constraint on the size of the period. So it can be used in biochemical problems where the period is large compared to the time constants of the system. Secondly, we show that, as the period goes to zero, the velocity field can be replaced by its average over the period. Numerical tests on a one-dimensional example are included to illustrate the theory.
authors.affiliation: Centre de Recherches Mathématiques and Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Quebec, Canada. delfour@crm.umontreal.ca
authors.forename: Michel C
authors.initials: MC
authors.lastname: Delfour
authors.forename: André
authors.initials: A
authors.lastname: Garon
mesh_terms: D000465:Algorithms; D001698:Biomedical Engineering; D001783:Blood Flow Velocity; D003198:Computer Simulation; D003324:Coronary Artery Disease / Q000628:therapy; D054855:Drug-Eluting Stents / Q000706:statistics & numerical data; D018056:Hemorheology; D006801:Humans; D008955:Models, Cardiovascular; D011474:Prosthesis Design; D011673:Pulsatile Flow