Kr. Raghavan et Ae. Yagle, FORWARD AND INVERSE PROBLEMS IN ELASTICITY IMAGING OF SOFT-TISSUES, IEEE transactions on nuclear science, 41(4), 1994, pp. 1639-1648
In elasticity imaging, a surface deformation is applied to an object u
sing small pistons, and the resulting induced strains in the interior
of the object are measured using ultrasonic imaging. Two important pro
blems are considered: (1) the forward problem of determining the strai
ns induced by a known deformation of an object with known elasticity;
and (2) the inverse problem of reconstructing elasticity from measured
strains and the equations of equilibrium. The method of finite differ
ences is used to solve the forward problem for a given piston configur
ation; some non-trivial issues arise in determining boundary condition
s. The finite difference equations are then rearranged into a linear s
ystem of equations which formulates the inverse problem; this system c
an be solved for the unknown elasticities. This formulation of the inv
erse problem is completely consistent with the forward problem; this i
s useful for interative methods in which the deformation is adaptively
changed. A comparison between simulated and actual measured results d
emonstrate the feasibility of the proposed procedure.