QUANTITATIVE THREE DIMENSIONAL ELASTICITY IMAGING

Neoplastic tissue is typically highly vascularized, contains abnormal concentrations of extracellular proteins (e.g. collagen, proteoglycans) and has a high interstitial fluid pres- sure compared to most normal tissues. These changes result in an overall stiffening typical of most solid tumors. Elasticity Imaging (EI) is a technique which uses imaging systems to measure relative tissue deformation and thus noninvasively infer its mechanical stiffness. Stiffness is recovered from measured deformation by using an appropriate mathematical model and solving an inverse problem. The integration of EI with existing imaging modal- ities can improve their diagnostic and research capabilities. The aim of this work is to develop and evaluate techniques to image and quantify the mechanical properties of soft tissues in three dimensions (3D). To that end, this thesis presents and validates a method by which three dimensional ultrasound images can be used to image and quantify the shear modulus distribution of tissue mimicking phantoms. This work is presented to motivate and justify the use of this elasticity imaging technique in a clinical breast cancer screening study. The imaging methodologies discussed are intended to improve the specificity of mammography practices in general. During the development of these techniques, several issues concerning the accuracy and uniqueness of the result were elucidated. Two new algorithms for 3D EI are designed and characterized in this thesis. The first provides three dimensional motion estimates from ultrasound images of the deforming ma- terial. The novel features include finite element interpolation of the displacement field, inclusion of prior information and the ability to enforce physical constraints. The roles of regularization, mesh resolution and an incompressibility constraint on the accuracy of the measured deformation is quantified. The estimated signal to noise ratio of the measured displacement fields are approximately 1800, 21 and 41 for the axial, lateral and eleva- tional components, respectively. The second algorithm recovers the shear elastic modulus distribution of the deforming material by efficiently solving the three dimensional inverse problem as an optimization problem. This method utilizes finite element interpolations, the adjoint method to evaluate the gradient and a quasi-Newton BFGS method for optimiza- tion. Its novel features include the use of the adjoint method and TVD regularization with piece-wise constant interpolation. A source of non-uniqueness in this inverse problem is identified theoretically, demonstrated computationally, explained physically and overcome practically. Both algorithms were test on ultrasound data of independently characterized tissue mimicking phantoms. The recovered elastic modulus was in all cases within 35% of the reference elastic contrast. Finally, the preliminary application of these techniques to tomosynthesis images showed the feasiblity of imaging an elastic inclusion.

Chondrogenesis and mineralization during in vitro culture of human mesenchymal stem cells on three-dimensional woven scaffolds.

Human mesenchymal stem cells (hMSCs) and three-dimensional (3D) woven poly(ɛ-caprolactone) (PCL) scaffolds are promising tools for skeletal tissue engineering. We hypothesized that in vitro culture duration and medium additives can individually and interactively influence the structure, composition, mechanical, and molecular properties of engineered tissues based on hMSCs and 3D poly(ɛ-caprolactone). Bone marrow hMSCs were suspended in collagen gel, seeded on scaffolds, and cultured for 1, 21, or 45 days under chondrogenic and/or osteogenic conditions. Structure, composition, biomechanics, and gene expression were analyzed. In chondrogenic medium, cartilaginous tissue formed by day 21, and hypertrophic mineralization was observed in the newly formed extracellular matrix at the interface with underlying scaffold by day 45. Glycosaminoglycan, hydroxyproline, and calcium contents, and alkaline phosphatase activity depended on culture duration and medium additives, with significant interactive effects (all p < 0.0001). The 45-day constructs exhibited mechanical properties on the order of magnitude of native articular cartilage (aggregate, Young's, and shear moduli of 0.15, 0.12, and 0.033 MPa, respectively). Gene expression was characteristic of chondrogenesis and endochondral bone formation, with sequential regulation of Sox-9, collagen type II, aggrecan, core binding factor alpha 1 (Cbfα1)/Runx2, bone sialoprotein, bone morphogenetic protein-2, and osteocalcin. In contrast, osteogenic medium produced limited osteogenesis. Long-term culture of hMSC on 3D scaffolds resulted in chondrogenesis and regional mineralization at the interface between soft, newly formed engineered cartilage, and stiffer underlying scaffold. These findings merit consideration when developing grafts for osteochondral defect repair.

Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.

Designing three-dimensional transformation optical media using quasiconformal coordinate transformations.

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasiconformal mapping approach. The generalized quasiconformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional carpet ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices.

Three-dimensional broadband omnidirectional acoustic ground cloak.

The control of sound propagation and reflection has always been the goal of engineers involved in the design of acoustic systems. A recent design approach based on coordinate transformations, which is applicable to many physical systems, together with the development of a new class of engineered materials called metamaterials, has opened the road to the unconstrained control of sound. However, the ideal material parameters prescribed by this methodology are complex and challenging to obtain experimentally, even using metamaterial design approaches. Not surprisingly, experimental demonstration of devices obtained using transformation acoustics is difficult, and has been implemented only in two-dimensional configurations. Here, we demonstrate the design and experimental characterization of an almost perfect three-dimensional, broadband, and, most importantly, omnidirectional acoustic device that renders a region of space three wavelengths in diameter invisible to sound.

Improved delineation of short cortical association fibers and gray/white matter boundary using whole-brain three-dimensional diffusion tensor imaging at submillimeter spatial resolution.

Recent emergence of human connectome imaging has led to a high demand on angular and spatial resolutions for diffusion magnetic resonance imaging (MRI). While there have been significant growths in high angular resolution diffusion imaging, the improvement in spatial resolution is still limited due to a number of technical challenges, such as the low signal-to-noise ratio and high motion artifacts. As a result, the benefit of a high spatial resolution in the whole-brain connectome imaging has not been fully evaluated in vivo. In this brief report, the impact of spatial resolution was assessed in a newly acquired whole-brain three-dimensional diffusion tensor imaging data set with an isotropic spatial resolution of 0.85 mm. It was found that the delineation of short cortical association fibers is drastically improved as well as the definition of fiber pathway endings into the gray/white matter boundary-both of which will help construct a more accurate structural map of the human brain connectome.

Comparison of contrast enhanced three dimensional echocardiography with MIBI gated SPECT for the evaluation of left ventricular function

Background. In clinical practice and in clinical trials, echocardiography and scintigraphy are used the most for the evaluation of global left ejection fraction (LVEF) and left ventricular (LV) volumes. Actually, poor quality imaging and geometrical assumptions are the main limitations of LVEF measured by echocardiography. Contrast agents and 3D echocardiography are new methods that may alleviate these potential limitations. Methods. Therefore we sought to examine the accuracy of contrast 3D echocardiography for the evaluation of LV volumes and LVEF relative to MIBI gated SPECT as an independent reference. In 43 patients addressed for chest pain, contrast 3D echocardiography (RT3DE) and MIBI gated SPECT were prospectively performed on the same day. The accuracy and the variability of LV volumes and LVEF measurements were evaluated. Results. Due to good endocardial delineation, LV volumes and LVEF measurements by contrast RT3DE were feasible in 99% of the patients. The mean LV end-diastolic volume (LVEDV) of the group by scintigraphy was 143 65 mL and was underestimated by triplane contrast RT3DE (128 60 mL; p < 0.001) and less by full-volume contrast RT3DE (132 62 mL; p < 0.001). Limits of agreement with scintigraphy were similar for triplane andfull-volume, modalities with the best results for full-volume. Results were similar for calculation of LV end-systolic volume (LVESV). The mean LVEF was 44 16% with scintigraphy and was not significantly different with both triplane contrast RT3DE (45 15%) and full-volume contrast RT3DE (45 15%). There was an excellent correlation between two different observers for LVEDV, LVESV and LVEF measurements and inter observer agreement was also good for both contrast RT3DE techniques. Conclusion. Contrast RT3DE allows an accurate assessment of LVEF compared to the LVEF measured by SPECT, and shows low variability between observers. Although RT3DE triplane provides accurate evaluation of left ventricular function, RT3DE full-volume is superior to triplane modality in patients with suspected coronary artery disease. © 2009 Cosyns et al; licensee BioMed Central Ltd.

Details of an integrated approach to three-dimensional dynamic fluid structure interaction

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. Numerical modelling of dynamic fluid-structure interaction (DFSI) involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge and until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. A single, finite volume unstructured mesh (FV-UM) spatial discretisation method has been employed on a single mesh for the entire domain. The Navier Stokes equations for fluid flow are solved using a SIMPLE type procedure and the Newmark b algorithm is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics and mesh movement is achieved using a spring based mesh procedure for dynamic mesh movement. In the paper we describe a number of additional computation issues for the efficient and accurate modelling of three-dimensional, dynamic fluid-structure interaction problems.

Three-dimensional simulation of the influence of convection on dendritic solidification

Bulk and interdendritic flow during solidification alters the microstructure development, potentially leading to the formation of defects. In this paper, a 3D numerical model is presented for the simulation of dendritic growth in the presence of fluid flow in both liquid and semi-solid zones during solidification. The dendritic growth was solved by the combination of a stochastic nucleation approach with a finite difference solution of the solute diffusion equation and. a projection method solution of the Navier-Stokes equations. The technique was applied first to simulate the growth of a single dendrite in 2D and 3D in an isothermal environment with forced fluid flow. Significant differences were found in the evolution of dendritic morphology when comparing the 2D and 3D results. In 3D the upstream arm has a faster growth velocity due to easier flow around the perpendicular arms. This also promotes secondary arm formation on the upstream arm. The effect of fluid flow on columnar dendritic growth and micro-segregation in constrained solidification conditions is then simulated. For constrained growth, 2D simulations lead to even greater inaccuracies as compared to 3D.

Exploring the Red Sea seasonal ecosystem functioning using a three-dimensional biophysical model

The Red Sea exhibits complex hydrodynamic and biogeochemical dynamics, which vary both in time and space. These dynamics have been explored through the development and application of a 3-D ecosystem model. The simulation system comprises two off-line coupled submodels: the MIT General Circulation Model (MITgcm) and the European Regional Seas Ecosystem Model (ERSEM), both adapted for the Red Sea. The results from an annual simulation under climatological forcing are presented. Simulation results are in good agreement with satellite and in situ data illustrating the role of the physical processes in determining the evolution and variability of the Red Sea ecosystem. The model was able to reproduce the main features of the Red Sea ecosystem functioning, including the exchange with the Gulf of Aden, which is a major driving mechanism for the whole Red Sea ecosystem and the winter overturning taking place in the north. Some model limitations, mainly related to the dynamics of the extended reef system located in the southern part of the Red Sea, which is not currently represented in the model, still need to be addressed.