Elastography Method for Reconstruction of Nonlinear Breast Tissue Properties

Elastography is developed as a quantitative approach to imaging linear elastic properties of tissues to detect suspicious tumors. In this paper a nonlinear elastography method is introduced for reconstruction of complex breast tissue properties. The elastic parameters are estimated by optimally minimizing the difference between the computed forces and experimental measures. A nonlinear adjoint method is derived to calculate the gradient of the objective function, which significantly enhances the numerical efficiency and stability. Simulations are conducted on a three-dimensional heterogeneous breast phantom extracting from real imaging including fatty tissue, glandular tissue, and tumors. An exponential-form of nonlinear material model is applied. The effect of noise is taken into account. Results demonstrate that the proposed nonlinear method opens the door toward nonlinear elastography and provides guidelines for future development and clinical application in breast cancer study

Viscoelastic modulus reconstruction using time harmonic vibrations

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.Comment: 15 page

Non-identifiability of the Rayleigh damping material model in magnetic resonance elastography

Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Magnetic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, μIμI and ρIρI. Results show the non-identifiability of the RD model at a single input frequency based on a structural analysis with a series of supporting experimental phantom results. The estimated real shear modulus values (μRμR) were substantially correct in characterising various material types and correlated well with the expected stiffness contrast of the physical phantoms. However, estimated RD parameters displayed consistent poor reconstruction accuracy leading to unpredictable trends in parameter behaviour. To overcome this issue, two alternative approaches were developed: (1) simultaneous multi-frequency inversion; and (2) parametric-based reconstruction. Overall, the RD model estimates the real shear shear modulus (μRμR) well, but identifying damping parameters (μIμI and ρIρI) is not possible without an alternative approach

On an inverse problem from magnetic resonance elastic imaging

The imaging problem of elastography is an inverse problem. The nature of an inverse problem is that it is ill-conditioned. We consider properties of the mathematical map which describes how the elastic properties of the tissue being reconstructed vary with the field measured by magnetic resonance imaging (MRI). This map is a nonlinear mapping, and our interest is in proving certain conditioning and regularity results for this operator which occurs implicitly in this problem of imaging in elastography. In this treatment we consider the tissue to be linearly elastic, isotropic, and spatially heterogeneous. We determine the conditioning of this problem of function reconstruction, in particular for the stiffness function. We further examine the conditioning when determining both stiffness and density. We examine the Frechet derivative of the nonlinear mapping, which enables us to describe the properties of how the field affects the individual maps to the stiffness and density functions. We illustrate how use of the implicit function theorem can considerably simplify the analysis of Frechet differentiability and regularity properties of this underlying operator. We present new results which show that the stiffness map is mildly ill-posed, whereas the density map suffers from medium ill-conditioning. Computational work has been done previously to study the sensitivity of these maps, but our work here is analytical. The validity of the Newton-Kantorovich and optimization methods for the computational solution of this inverse problem is directly linked to the Frechet differentiability of the appropriate nonlinear operator, which we justify

Biomechanical properties of breast tissue, a state-of-the-art review

This paper reviews the existing literature on the tests used to determine the mechanical properties of women breast tissues (fat, glandular and tumour tissue) as well as the different values of these properties. The knowledge of the mechanical properties of breast tissue is important for cancer detection, study and planning of surgical procedures such as surgical breast reconstruction using pre-surgical methods and improving the interpretation of clinical tests. Based on the data collected from the analysed studies, some important conclusions were achieved: (1) the Young’s modulus of breast tissues is highly dependent on the tissue preload compression level, and (2) the results of these studies clearly indicate a wide variation in moduli not only among different types of tissue but also within each type of tissue. These differences were most evident in normal fat and fibroglandular tissues

Strain elastography with ultrasound computer tomography: a simulation study based on biomechanical models

Ultrasound computer tomography (USCT) is a promising modality for breast cancer diagnosis which images the reflectivity, sound speed and attenuation of tissue. Elastic properties of breast tissue, however, cannot directly be imaged although they have shown to be applicable as a discriminator between different tissue types. In this work we propose a novel approach combining USCT with the principles of strain elastography. Socalled USCT-SE makes use of imaging the breast in two deformation states, estimating the deformation field based on reconstructed images and thereby allows localizing and distinguishing soft and hard masses. We use a biomechanical model of the breast to realistically simulate both deformation states of the breast. The analysis of the strain is performed by estimating the deformation field from the deformed to the undeformed image by a non-rigid registration. In two experiments the non-rigid registration is applied to ground truth sound speed images and simulated SAFT images. Results of the strain analysis show that for both cases soft and hard lesions can be distinguished visually in the elastograms. This paper provides a first approach to obtain mechanical information based on external mechanical excitation of breast tissue in a USCT system