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This paper describes an inverse reconstruction technique based on a modified Newton Raphson iterative scheme and the finite element method, which has been developed for computing the spatial distribution of Young's modulus from within soft tissues. Computer simulations were conducted to determine the relative merits of reconstructing tissue elasticity using knowledge of (a) known displacement boundary conditions (DBC), and (b) known stress boundary conditions (SBC). The results demonstrated that computing Young's modulus using knowledge of SBC allows accurate quantification of Young's modulus. However, the quality of the images produced using this reconstruction approach was dependent on the Young's modulus distribution assumed at the start of the reconstruction procedure. Computing Young's modulus from known DBC provided relative estimates of tissue elasticity which, despite the disadvantage of not being able to accurately quantify Young's modulus, formed images that were generally superior in quality to those produced using the known SBC, and were not affected by the trial solution. The results of preliminary experiments on phantoms demonstrated that this reconstruction technique is capable in practice of improving the fidelity of tissue elasticity images, reducing the artefacts otherwise present in strain images, and recovering Young's modulus images that possess excellent spatial and contrast resolution.
Doyley et al. (Fri,) studied this question.