INSTITUTE OF PHYSICS PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY Phys. Med. Biol. 49 (2004) 2955–2974 PII: S0031-9155(04)77153-5 Evaluation of the adjoint equation based algorithm for elasticity imaging Assad A Oberai 1 , Nachiket H Gokhale 1 , Marvin M Doyley 2 and Jeffrey C Bamber 3 1 Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA 02215, USA 2 Thayer School of Engineering, Dartmouth College, and Department of Radiology, Dartmouth-Hitchcock Medical Center, Lebanon, NH, USA 3 Joint Department of Physics, Royal Marsden Hospital and Institute of Cancer Research, Sutton, Surrey, UK E-mail: oberai@bu.edu Received 3 March 2004 Published 17 June 2004 Online at stacks.iop.org/PMB/49/2955 doi:10.1088/0031-9155/49/13/013 Abstract Recently a new adjoint equation based iterative method was proposed for evaluating the spatial distribution of the elastic modulus of tissue based on the knowledge of its displacement field under a deformation. In this method the original problem was reformulated as a minimization problem, and a gradient- based optimization algorithm was used to solve it. Significant computational savings were realized by utilizing the solution of the adjoint elasticity equations in calculating the gradient. In this paper, we examine the performance of this method with regard to measures which we believe will impact its eventual clinical use. In particular, we evaluate its abilities to (1) resolve geometrically the complex regions of elevated stiffness; (2) to handle noise levels inherent in typical instrumentation; and (3) to generate three-dimensional elasticity images. For our tests we utilize both synthetic and experimental displacement data, and consider both qualitative and quantitative measures of performance. We conclude that the method is robust and accurate, and a good candidate for clinical application because of its computational speed and efficiency. 1. Introduction Elastography is an emerging new imaging technique with applications in detecting breast and other cancers (Ophir et al 1999, Chenevert et al 1998, Bamber et al 2002, Garra et al 1997, Weaver et al 2001, Skovoroda et al 1995, Sumi et al 1995), atherosclerosis (Ryan and Foster 1997, de Korte et al 1997, 1998, 1999, 2000a, 2000b, Cespedes et al 2000), and deep vein 0031-9155/04/132955+20$30.00 © 2004 IOP Publishing Ltd Printed in the UK 2955