Premium
Algorithms for quantitative quasi‐static elasticity imaging using force data
Author(s) -
Tyagi Mohit,
Goenezen Sevan,
Barbone Paul E.,
Oberai Assad A.
Publication year - 2014
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2665
Subject(s) - shear modulus , elasticity (physics) , minification , elastic modulus , modulus , mathematical analysis , finite element method , displacement field , mathematics , shear (geology) , mathematical optimization , algorithm , geometry , physics , materials science , structural engineering , engineering , thermodynamics , composite material
SUMMARY 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. Copyright © 2014 John Wiley & Sons, Ltd.