Mechanical and optical methods for breast cancer imaging

It has been recognized that mechanical and optical properties of tissues can be the indicators to identify and characterize breast tumors. The objective of this study is to develop new mechanical and optical modalities for qualification of the elastic and optical properties of normal and cancerous breast tissues.

First, a mammography-based elastography (called elasto-mammography) is proposed to generate the elastogram of breast tissues based on conventional X-ray mammography. The displacement information is extracted from mammography projections before and after breast compression. With the incorporation of the displacement measurements, an elastography reconstruction algorithm is specially developed to estimate the elastic moduli of heterogeneous breast tissues. Case studies with numerical breast phantoms are conducted to demonstrate the capability of the proposed elasto-mammogrpahy. It is shown that the proposed methodology is stable and robust for characterization of the elastic moduli of breast tissues from the projective displacement measurement.

Second, a nonlinear elastogrpahy is proposed to extend breast material model to nonlinear cases. A three-dimensional (3D) model is developed for heterogeneous breast tissues extracting from real images including fatty tissue, glandular tissue, and tumors. An exponential-form of nonlinear material model is applied. Based on the finite-deformation constitutive law, discretized nonlinear equations are solved for displacement, strain, and stress fields in breast tissues with given tumors under external compression at breast boundaries. We develop a 3D inverse-problem algorithm to reconstruct the material parameters for nonlinear elastic constitutive relation of breast phantoms with tumors. For the first time, a nonlinear adjoint gradient method is introduced to improve the numerical efficiency and enhance the stability of elastogrpahy reconstruction.

Third, encouraged by the success of linear elasto-mammography and nonlinear elastography, a nonlinear elasto-mammography method is proposed. Mammography projections are taken before and after breast compression and displacement information is extracted for reconstruction of nonlinear breast tissue properties. Numerical phantom study is conducted and results show the proposed nonlinear elasto-mammography is potential to identify and characterize breast tumors in clinic.

Finally, we switch from mechanical to optical method for breast cancer imaging. We develop a finite-element-based algorithm to solve the inverse problem of frequent-domain diffusion equation. With the analytical form of gradients, the adjoint method is expanded to complex domain for the reconstruction of optical parameters in diffuse optical tomography. Specific numerical simulation is carried out and compared with phantom experiment. The results show that the adjoint-based algorithm is efficient and robust for reconstructing the optical parameters.