Exact solutions of the compressible inverse elasticity problem

2007 ◽  
Vol 121 (5) ◽  
pp. 3110-3110
Author(s):  
Paul E. Barbone ◽  
Assad A. Oberai
Keyword(s):  
Exact Solutions ◽  
Elasticity Problem ◽  
Inverse Elasticity

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

2008 ◽  
Author(s):  
Carlos E. Rivas ◽  
Paul E. Barbone ◽  
Assad A. Oberai
Keyword(s):  
Mechanical Properties ◽  
Diagnostic Value ◽  
Incompressible Material ◽  
High Order ◽  
Elasticity Problem ◽  
Parameter Distribution ◽  
Order Continuity ◽  
B Splines ◽  
Inverse Elasticity ◽  
Continuous Problem

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.

scholarly journals Quantitative Compression Optical Coherence Elastography as an Inverse Elasticity Problem

2016 ◽  
Vol 22 (3) ◽  
pp. 277-287 ◽  
Author(s):  
Li Dong ◽  
Philip Wijesinghe ◽  
James T. Dantuono ◽  
David D. Sampson ◽  
Peter R. T. Munro ◽  
...  
Keyword(s):  
Elasticity Problem ◽  
Optical Coherence ◽  
Inverse Elasticity

Quantitative optical coherence elastography as an inverse elasticity problem (Conference Presentation)

2016 ◽  
Author(s):  
Li Dong ◽  
Philip Wijesinghe ◽  
James T. Dantuono ◽  
David D. Sampson ◽  
Peter R. T. Munro ◽  
...  
Keyword(s):  
Elasticity Problem ◽  
Optical Coherence ◽  
Inverse Elasticity
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