Abstract—Assessment of the rupture risk of plaque is commonly made via imaging of the lumen reduction. However it is known that this is an imperfect criterion and that other features, such as plaque stiffness, may be more relevant. Magnetic Resonance Elastography (MRE) estimates the stiffness of tissues using inversion algorithms applied to the displacement of the tissue, measured in response to the induction of a shear wave from an external actuator. An idealised diseased vessel, embedded in an arbitrary tissue, was created to simulate the application of MRE to atherosclerotic plaque. The behaviour of shear waves propagating through an atherosclerotic plaque with development of the stenosis and lipid pool size was investigated. There is a local increase in wave displacement and decrease in wavelength, through a plaque containing a lipid pool compared to a purely fibrotic plaque. The amplitude of the wave through the lipid increases with lipid pool volume. This suggests that shear waves used in MRE may be able to differentiate between lipid pool sizes within an atherosclerotic plaque. The behaviour of shear waves through relatively large and small lipid pools needs further investigation. Experimental validation of the technique is required. Index Terms—Atherosclerosis, finite element analysis, magnetic resonance elastography, plaque rupture, shear waves. I. INTRODUCTION ardiovascular disease (CVD) is the leading cause of death in the world (29%) and in the UK (38%) [1]. CVD is the broad title for a wide range of afflictions, including stroke and coronary heart disease, the majority of which are caused by atherosclerosis. The most severe symptoms of atherosclerosis are a Manuscript received March 5th, 2011; revised April 4th, 2011. This work was supported by the Engineering and Physical Science Research Council. L. E. J. Thomas-Seale is with Medical Physics, University of Edinburgh, Chancellor’s Building, 49 Little France Crescent, Edinburgh, EH16 4SB, UK (phone: +44 131 2426307; e-mail: L.E.J.Thomas@sms.ed.ac.uk). P. Pankaj is with the School of Engineering, University of Edinburgh, Alexander Graham Bell Building, The King’s Buildings, Edinburgh EH9 3JL, UK (e-mail: Pankaj@ed.ac.uk). N. Roberts is with the Clinical Research Imaging Centre, University of Edinburgh, 47 Little France Crescent, Edinburgh, EH16 4SB, UK (e-mail: Neil.Roberts@ed.ac.uk). P. Hoskins is with Medical Physics, University of Edinburgh, Chancellor’s Building, 49 Little France Crescent, Edinburgh, EH16 4SB, UK (email: P.Hoskins@ed.ac.uk) consequence of plaque rupture and the restriction of blood flow. The decision to surgically intervene is dependent on the percent stenosis, the ratio of the minimum diameter of the stenosed artery to an equivalent healthy section, measured by ultrasound or angiography. It is generally accepted that a carotid endarterectomy is beneficial for symptomatic carotid stenosis between 70-99% [2]. However studies have demonstrated that this is an imperfect criterion. The European Carotid Surgery Trail (ESCT) found that the absolute increase in benefit of surgery, for stenosis greater than 80%, was only 11.6% [3]. This translates to nine surgical interventions to allow one patient to be stroke free after 3 years [3]. The risk of plaque rupture is a trade off between the intrinsic properties of the plaque against the forces, from the blood, acting upon it [4]. It has been established that unstable plaques which are likely to rupture have the similar morphology of a thin fibrous cap and a large lipid core [5]. In these instances the lipid core is of such a low stiffness that the external forces are primarily supported by the fibrous cap and when its strength is exceeded, the plaque ruptures [5]. However composition is difficult to assess using imaging and the composition alone is not sufficient information to determine the strength of a plaque since the properties of the lipid and fibrous cap can vary [6], [7]. Magnetic Resonance Elastography (MRE) is an elasticity imaging technique, which utilizes the temporal and spatial resolution of MRI to quantitatively measure the displacement within a tissue in response to the excitation of harmonic propagating waves [8]. Phase contrast MRI measures low frequency shear waves in the region of 50- 1000Hz [9]. These waves are induced in the desired tissue using external actuation, of which a range of methods may be employed [10], [11], [12]. The displacement data is then inverted into mechanical properties by a process known as wave inversion, of which again there are a range of techniques [9]. MRE has the potential to non-invasively assess the stiffness of an atherosclerotic plaque and hence provide an indication of the risk of rupture. To date there is extremely limited literature available on the application of MRE to arteries; to identify wall stiffness [13], [14], [15], [16] and stenosis size using reflected and transmitted waves [13]. There has been no research published involving MRE analysis of plaque stiffness. Computational Modelling of Magnetic Resonance Elastography Shear Wave Behaviour through Atherosclerotic Plaque with Disease Development Lauren E. J. Thomas-Seale, Pankaj Pankaj, Neil Roberts and Peter R. Hoskins C Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K. ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2011