Yue Mei

Mechanics Based Tomography: A Preliminary Feasibility Study

We present a non-destructive approach to sense inclusion objects embedded in a solid medium remotely from force sensors applied to the medium and boundary displacements that could be measured via a digital image correlation system using a set of cameras. We provide a rationale and strategy to uniquely identify the heterogeneous sample composition based on stiffness (here, shear modulus) maps. The feasibility of this inversion scheme is tested with simulated experiments that could have clinical relevance in diagnostic imaging (e.g., tumor detection) or could be applied to engineering materials. No assumptions are made on the shape or stiffness quantity of the inclusions. We observe that the novel inversion method using solely boundary displacements and force measurements performs well in recovering the heterogeneous material/tissue composition that consists of one and two stiff inclusions embedded in a softer background material. Furthermore, the target shear modulus value for the stiffer inclusion region is underestimated and the inclusion size is overestimated when incomplete boundary displacements on some part of the boundary are utilized. For displacements measured on the entire boundary, the shear modulus reconstruction improves significantly. Additionally, we observe that with increasing number of displacement data sets utilized in solving the inverse problem, the quality of the mapped shear moduli improves. We also analyze the sensitivity of the shear modulus maps on the noise level varied between 0.1% and 5% white Gaussian noise in the boundary displacements, force and corresponding displacement indentation. Finally, a sensitivity analysis of the recovered shear moduli to the depth, stiffness and the shape of the stiff inclusion is performed. We conclude that this approach has potential as a novel imaging modality and refer to it as Mechanics Based Tomography (MBT).

Reduced Boundary Sensitivity and Improved Contrast of the Regularized Inverse Problem Solution in Elasticity

We observe that posing the inverse problem as a constrained minimization problem under regularization leads to boundary dependent solutions. In this paper, we propose a modified objective function and show with 2D examples that our method works well to reduce boundary sensitive solutions. The examples consist of two stiff inclusions embedded in a softer unit square. These inclusions could be representative of tumors, which are in general stiffer than their background tissues, thus could potentially be detected based on their stiffness contrast. We modify the objective function for the displacement correlation term by weighting it with a function that depends on the strain field. In a simplified 1D coupled model, we derive an analytical expression and observe the same trends in the reconstructions as for the 2D model. The analysis in this paper is confined to inclusions of similar size and may not overlap when projected on the horizontal axis. They may, however, vary in position along the vertical axis. Furthermore, our analysis holds for an arbitrary number of inclusions having distinct stiffness values. Finally, to increase the overall contrast of the tumors and simultaneously improve the smoothness, we solve the regularized inverse problem in a posterior step, utilizing a spatially varying regularization factor.

Regularizing Biomechanical Maps for Partially Known Material Properties

We present the solution of the inverse problem for partially known elastic modulus values, e.g., the elastic modulus is known in some small region on the boundary of the domain from measurements. T...

Spatially Weighted Objective Function to Solve the Inverse Elasticity Problem for the Elastic Modulus

We briefly review the iterative solution of the inverse problem in elasticity, which is posed as a constrained optimization method. The objective function minimizes the discrepancy between a measured and a computed displacement field in the L-2 norm and is subject to the static equations of equilibrium in elasticity. We realize that this inverse formulation is sensitive to Dirichlet and Neumann boundary conditions, i.e., sensitive to varying spatial deformations in the region of interest. This problem arises in particular, when solving the inverse problem for more than one inclusion in a homogeneous background, where the inclusions represent diseased tissues such as cysts, benign tumors, malignant tumors, etc. In order to address this issue, we propose to introduce a new formulation of the objective function, where the displacement correlation term is spatially weighted. We refer to this new formulation as the spatially weighted objective function and show that it improves the uniqueness of the inverse problem solution.

Erratum: Mei, Y., et al. Mechanics Based Tomography: A Preliminary Feasibility Study. Sensors 2017, 17, 1075

The authors wish to correct Figures 12 and 14 in their paper published in Sensors [1], doi:10.3390/s17051075, http://www.mdpi.com/1424-8220/17/5/1075[...].