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Quantitative elasticity imaging, which retrieves elastic modulus maps from tissue, is preferred to qualitative strain imaging for acquiring system- and operator-independent images and longitudinal and multi-site diagnoses.
Quantitative elasticity imaging has already been demonstrated in optical elastography by relating surface-acoustic and shear wave speed to Young’s modulus via a simple algebraic relationship. Such approaches assume largely homogeneous samples and neglect the effect of boundary conditions.
We present a general approach to quantitative elasticity imaging based upon the solution of the inverse elasticity problem using an iterative technique and apply it to compression optical coherence elastography. The inverse problem is one of finding the distribution of Young’s modulus within a sample, that in response to an applied load, and a given displacement and traction boundary conditions, can produce a displacement field matching one measured in experiment. Key to our solution of the inverse elasticity problem is the use of the adjoint equations that allow the very efficient evaluation of the gradient of the objective function to be minimized with respect to the unknown values of Young’s modulus within the sample. Although we present the approach for the case of linear elastic, isotropic, incompressible solids, this method can be employed for arbitrarily complex mechanical models.
We present the details of the method and quantitative elastograms of phantoms and tissues. We demonstrate that by using the inverse approach, we can decouple the artefacts produced by mechanical tissue heterogeneity from the true distribution of Young’s modulus, which are often evident in techniques that employ first-order algebraic relationships.
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