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

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

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

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)

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[...

Improving the Efficiency of Abdominal Aortic Aneurysm Wall Stress Computations

<div><p>An abdominal aortic aneurysm is a pathological dilation of the abdominal aorta, which carries a high mortality rate if ruptured. The most commonly used surrogate marker of rupture risk is the maximal transverse diameter of the aneurysm. More recent studies suggest that wall stress from models of patient-specific aneurysm geometries extracted, for instance, from computed tomography images may be a more accurate predictor of rupture risk and an important factor in AAA size progression. However, quantification of wall stress is typically computationally intensive and time-consuming, mainly due to the nonlinear mechanical behavior of the abdominal aortic aneurysm walls. These difficulties have limited the potential of computational models in clinical practice. To facilitate computation of wall stresses, we propose to use a linear approach that ensures equilibrium of wall stresses in the aneurysms. This proposed linear model approach is easy to implement and eliminates the burden of nonlinear computations. To assess the accuracy of our proposed approach to compute wall stresses, results from idealized and patient-specific model simulations were compared to those obtained using conventional approaches and to those of a hypothetical, reference abdominal aortic aneurysm model. For the reference model, wall mechanical properties and the initial unloaded and unstressed configuration were assumed to be known, and the resulting wall stresses were used as reference for comparison. Our proposed linear approach accurately approximates wall stresses for varying model geometries and wall material properties. Our findings suggest that the proposed linear approach could be used as an effective, efficient, easy-to-use clinical tool to estimate patient-specific wall stresses.</p></div