Characterizing the elastic property distribution of soft materials nondestructively

Soft materials have the advantage that their subsurface structure may be imaged utilizing imaging modalities such as ultrasound, magnetic resonance imaging, computed tomography (CT) scans, and optical coherence tomography. In recent decades subsurface displacement fields were successfully measured using these imaging modalities. These displacement fields are of time-harmonic, transient, or quasi-static nature and can be used to solve an inverse problem in elasticity to determine the elastic material property distribution within the region of interest of the soft material. One important application area is in the detection and diagnosis of diseased tissues, such as breast tumors. This can be done as tumors are often stiffer than their background tissue, and based on the stiffness contrast they can be visualized and distinguished from their surrounding healthy tissues. We will present the solution of the inverse problem in finite elasticity for quasi-static displacement fields. Here, the quasi-static displacement fields may be determined by taking a sequence of ultrasound images while slowly compressing the tissue with the ultrasound transducer. From this sequence of ultrasound images one may determine the displacement fields utilizing well-developed cross-correlation techniques. We solve the inverse problem iteratively by posing it as a constrained optimization problem, where the difference between a measured and computed displacement field is minimized in the L-2 norm and in the presence of Tikhonov regularization. The computed displacement field satisfies the constraint, which are the equations of equilibrium and solved using finite element methods for the current estimate of the elastic property distribution. We model the material to be hyperelastic with a strain energy density function of exponential form and two elastic property parameters: the shear modulus describes the linear elastic behavior, whereas the nonlinear elastic property describes the rate at which the material is stiffening at large strains [1]. In addition, we assume that the material is isotropic and incompressible. This method has been tested on hypothetical data and breast tumor patients [2] and proofed to be robust in the presence of noisy displacement data to recover the tumors. However, this method appears to be sensitive to the applied boundary conditions, i.e., the solution of the inverse problem for uniform boundary compression appears to be different than applying a linearly changing boundary compression. Obviously, the solution of the inverse problem lacks uniqueness with respect to changing boundary conditions. We realize that the uniqueness issue here is primarily because of the formulation of the displacement correlation term in the objective function. We provide a new formulation and show that this leads to a “more unique” solution of the inverse problem and improves the overall contrast. REFERENCES [1] Goenezen, S., Barbone, P., and Oberai, A.A., Solution of the nonlinear elasticity imaging inverse problem: the incompressible case. Computer Methods in Applied Mechanics and Engineering. 2011, 200(13–16), 1406–1420. [2] Goenezen, S., Dord, J.F., Sink, Z., Barbone, P., Jiang, J., Hall, T.J., and Oberai, A.A., Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis. IEEE Trans Med Imaging. 2012, 31(8), 1628–1637

OpenQSEI: A MATLAB package for quasi static elasticity imaging

Quasi Static Elasticity Imaging (QSEI) aims to computationally reconstruct the inhomogeneous distribution of the elastic modulus using a measured displacement field. QSEI is a well-established imaging modality used in medical imaging for localizing tissue abnormalities. More recently, QSEI has shown promise in applications of structural health monitoring and materials characterization. Despite the growing usage of QSEI in multiple fields, fully-executable open source packages are not readily available. To address this, OpenQSEI is developed using a MATLAB platform and shared in an online community setting for continual algorithmic improvement. In this article, we describe the mathematical background of QSEI and demonstrate the basic functionalities of OpenQSEI with examples

Less is often more : applied inverse problems using hp-forward models

To solve an applied inverse problem, a numerical forward model for the problem’s physics is required. Commonly, the finite element method is employed with discretizations consisting of elements with variable size h and polynomial degree p. Solutions to hp-forward models are known to converge exponentially by simultaneously decreasing h and increasing p. On the other hand, applied inverse problems are often ill-posed and their minimization rate exhibits uncertainty. Presently, the behavior of applied inverse problems incorporating hp elements of differing p, h, and geometry is not fully understood. Nonetheless, recent research suggests that employing increasingly higher-order hp-forward models (increasing mesh density and p) decreases reconstruction errors compared to inverse regimes using lower-order hp-forward models (coarser meshes and lower p). However, an affirmative or negative answer to following question has not been provided, “Does the use of higher order hp-forward models in applied inverse problems always result in lower error reconstructions than approaches using lower order hp-forward models?” In this article we aim to reduce the current knowledge gap and answer the open question by conducting extensive numerical investigations in the context of two contemporary applied inverse problems: elasticity imaging and hydraulic tomography – nonlinear inverse problems with a PDE describing the underlying physics. Our results support a negative answer to the question – i.e. decreasing h (increasing mesh density), increasing p, or simultaneously decreasing h and increasing p does not guarantee lower error reconstructions in applied inverse problems. Rather, there is complex balance between the accuracy of the hp-forward model, noise, prior knowledge (regularization), Jacobian accuracy, and ill-conditioning of the Jacobian matrix which ultimately contribute to reconstruction errors. As demonstrated herein, it is often more advantageous to use lower-order hp-forward models than higherorder hp-forward models in applied inverse problems. These realizations and other counterintuitive behavior of applied inverse problems using hp-forward models are described in detail herein

Subjective approach to optimal cross-sectional design of biodegradable magnesium alloy stent undergoing heterogeneous corrosion

Existing biodegradable Magnesium Alloy Stents (MAS) have several drawbacks, such as high restenosis, hasty degradation, and bulky cross-section, that limit their widespread application in a current clinical practice. To find the optimum stent with the smallest possible cross-section and adequate scaffolding ability, a 3D finite element model of 25 MAS stents of different cross-sectional dimensions were analysed while localized corrosion was underway. For the stent geometric design, a generic sine-wave ring of biodegradable magnesium alloy (AZ31) was selected. Previous studies have shown that the long-term performance of MAS was characterized by two key features: Stent Recoil Percent (SRP) and Stent Radial Stiffness (SRS). In this research, the variation with time of these two features during the corrosion phase was monitored for the 25 stents. To find the optimum profile design of the stent subjectively (without using optimization codes and with much less computational costs), radial recoil was limited to 27 % (corresponding to about 10 % probability of in-stent diameter stenosis after an almost complete degradation) and the stent with the highest radial stiffness was selected.The comparison of the recoil performance of 25 stents during the heterogeneous corrosion phase showed that four stents would satisfy the recoil criterion and among these four, the one having a width of 0.161 mm and a thickness of 0.110 mm, showed a 24 % – 49 % higher radial stiffness at the end of the corrosion phase. Accordingly, this stent, which also showed a 23.28 % mass loss, was selected as the optimum choice and it has a thinner cross-sectional profile than commercially available MAS, which leads to a greater deliverability and lower rates of restenosis

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)

Effect of Outflow Tract Banding on Embryonic Cardiac Hemodynamics

We analyzed heart wall motion and blood flow dynamics in chicken embryos using in vivo optical coherence tomography (OCT) imaging and computational fluid dynamics (CFD) embryo-specific modeling. We focused on the heart outflow tract (OFT) region of day 3 embryos, and compared normal (control) conditions to conditions after performing an OFT banding intervention, which alters hemodynamics in the embryonic heart and vasculature. We found that hemodynamics and cardiac wall motion in the OFT are affected by banding in ways that might not be intuitive a priori. In addition to the expected increase in ventricular blood pressure, and increase blood flow velocity and, thus, wall shear stress (WSS) at the band site, the characteristic peristaltic-like motion of the OFT was altered, further affecting flow and WSS. Myocardial contractility, however, was affected only close to the band site due to the physical restriction on wall motion imposed by the band. WSS were heterogeneously distributed in both normal and banded OFTs. Our results show how banding affects cardiac mechanics and can lead, in the future, to a better understanding of mechanisms by which altered blood flow conditions affect cardiac development leading to congenital heart disease

Development of a new microstructure-based constitutive model for healthy and cancerous tissue

1 pageinfo:eu-repo/semantics/publishe