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In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities of the forward problem and replace the finite element solution of the incompressible Navier\u2013Stokes equations by a computationally less\u2010expensive reduced\u2010basis approximation. This greatly reduces the cost of simulating the forward problem. We then consider the solution of inverse problems both in the deterministic sense, by solving a least\u2010squares problem, and in the statistical sense, by using a Bayesian framework for quantifying uncertainty. Two inverse problems arising in hemodynamics modeling are considered: (i) a simplified fluid\u2013structure interaction model problem in a portion of a stenosed artery for quantifying the risk of atherosclerosis by identifying the material parameters of the arterial wall on the basis of pressure measurements; (ii) a simplified femoral bypass graft model for robust shape design under uncertain residual flow in the main arterial branch identified from pressure measurements. Copyright \u00a9 2013 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/cnm.2559","type":"journal-article","created":{"date-parts":[[2013,6,25]],"date-time":"2013-06-25T05:08:34Z","timestamp":1372136914000},"page":"741-776","source":"Crossref","is-referenced-by-count":94,"title":["A reduced computational and geometrical framework for inverse problems in hemodynamics"],"prefix":"10.1002","volume":"29","author":[{"given":"Toni","family":"Lassila","sequence":"first","affiliation":[{"name":"Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE) Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL)  Station 8, CH\u20101015 Lausanne Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea","family":"Manzoni","sequence":"additional","affiliation":[{"name":"Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE) Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL)  Station 8, CH\u20101015 Lausanne Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alfio","family":"Quarteroni","sequence":"additional","affiliation":[{"name":"Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE) Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL)  Station 8, CH\u20101015 Lausanne Switzerland"},{"name":"Modellistica e Calcolo Scientifico (MOX), Dipartimento di Matematica \u2018F. 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