NDLI: A Stabilized B-Splines FEM Formulation for the Solution of an Inverse Elasticity Problem Arising in Medical Imaging

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Carlos, E. Rivas Paul, E. Barbone Assad, A. Oberai
Copyright Year	2008
Abstract	Soft tissue pathologies are often associated with changes in mechanical properties. For example, breast and other tumors usually present as stiff lumps. Imaging the spatial distribution of the mechanical properties of tissues thus reveals information of diagnostic value. Doing so, however, typically requires the solution of an inverse elasticity problem. In this work we consider the inverse elasticity problem for an incompressible material in plane stress, formulated and solved as a constrained optimization problem. We formulate this inverse problem enforcing high order continuity for our variables. Driven by the requirements for the strong and weak solutions to this problem, we assume that our data field (i.e. the measured displacement) is in H2 and our parameter distribution (i.e. the sought shear modulus distribution) is in H1. This high order regularity requirement for the data is incompatible with standard FEM. We solve this problem using a FEM formulation that is novel in two respects. First, we employ quadratic b-splines that enforce C1 continuity in our displacement field, consistent with the variational requirements of the continuous problem. Second, we include Galerkin-least-squares (GLS) stabilization in the iterative optimization formulation. GLS adds consistent stability to the discrete formulation that otherwise violates an ellipticity condition that is satisfied by the continuous problem. Computational examples validate this formulation and demonstrate numerical convergence with mesh refinement.
Starting Page	141
Ending Page	148
Page Count	8
File Format	PDF
ISBN	9780791848739
DOI	10.1115/IMECE2008-66700
e-ISBN	9780791838402
Volume Number	Volume 12: Mechanics of Solids, Structures and Fluids
Conference Proceedings	ASME 2008 International Mechanical Engineering Congress and Exposition
Language	English
Publisher Date	2008-10-31
Publisher Place	Boston, Massachusetts, USA
Access Restriction	Subscribed
Subject Keyword	Stability Shear modulus Biological tissues Elasticity Mechanical properties Finite element methods Displacement Optimization Stress Soft tissues Finite element model Inverse problems Imaging Biomedical imaging B-splines Tumors
Content Type	Text
Resource Type	Article

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