title: Algorithms for quantitative quasi-static elasticity imaging using force data.
abstract: Quasi-static elasticity imaging can improve diagnosis and detection of diseases that affect the mechanical behavior of tissue. In this methodology, images of the shear modulus of the tissue are reconstructed from the measured displacement field. This is accomplished by seeking the spatial distribution of mechanical properties that minimizes the difference between the predicted and the measured displacement fields, where the former is required to satisfy a finite element approximation to the equations of equilibrium. In the absence of force data, the shear modulus is determined only up to a multiplicative constant. In this manuscript, we address the problem of calibrating quantitative elastic modulus reconstructions created from measurements of quasi-static deformations. We present two methods that utilize the knowledge of the applied force on a portion of the boundary. The first involves rescaling the shear modulus of the original minimization problem to best match the measured force data. This approach is easily implemented but neglects the spatial distribution of tractions. The second involves adding a force-matching term to the original minimization problem and a change of variables wherein we seek the log of the shear modulus. We present numerical results that demonstrate the usefulness of both methods.
authors: Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180, U.S.A.
authors: Mohit
authors: M
authors: Tyagi
authors: Sevan
authors: S
authors: Goenezen
authors: Paul E
authors: PE
authors: Barbone
authors: Assad A
authors: AA
authors: Oberai
mesh_terms: D000465:Algorithms; D001696:Biomechanical Phenomena; D003198:Computer Simulation; D055119:Elastic Modulus; D054459:Elasticity Imaging Techniques / Q000379:methods*
keywords: biomechanical imaging; elasticity imaging; force data; quantitative modulus images