Computational Scattering Models for Elastic and Electromagnetic Waves in Particulate Media

Numerical models were developed to simulate the propagation of elastic and electromagnetic waves in an arbitrary, dense dispersion of spherical particles. The scattering interactions were modeled with vector multipole fields using pure-orbital vector spherical harmonics, and solved using the full vector form of the boundary conditions. Multiple scattering was simulated by translating the scattered wave fields from one particle to another with the use of translational addition theorems, summing the multiple-scattering contributions, and recalculating the scattering in an iterative fashion to a convergent solution. The addition theorems were rederived in this work using an integral method, and were shown to be numerically equivalent to previously published theorems. Both ordered and disordered collections of up to 5,000 spherical particles were used to demonstrate the ability of the scattering models to predict the spatial and frequency distributions of the transmitted waves. The results of the models show they are qualitatively correct for many particle configurations and material properties, displaying predictable phenomena such as refractive focusing, mode conversion, and photonic band gaps. However, the elastic wave models failed to converge for specific frequency regions, possibly due to resonance effects. Additionally, comparison of the multiple-scattering simulations with those using only single-particle scattering showed the multiple-scattering computations are quantitatively inaccurate. The inaccuracies arise from nonconvergence of the translational addition theorems, introducing errors into the translated fields, which minimize the multiple-scattering contributions and bias the field amplitudes towards single-scattering contributions. The addition theorems are shown to converge very slowly, and to exhibit plateaus in convergence behavior that can lead to false indications of convergence. The theory and algorithms developed for the models are broad-based, and can accommodate a variety of structures, compositions, and wave modes. The generality of the approach also lends itself to the modeling of static fields and currents. Suggestions are presented for improving and implementing the models, including extension to nonspherical particles, efficiency improvements for the algorithms, and specific applications in a variety of fields

Improved Modeling and Image Generation for Fluorescence Molecular Tomography (FMT) and Positron Emission Tomography (PET)

In this thesis, we aim to improve quantitative medical imaging with advanced image generation algorithms. We focus on two specific imaging modalities: fluorescence molecular tomography (FMT) and positron emission tomography (PET). For FMT, we present a novel photon propagation model for its forward model, and in addition, we propose and investigate a reconstruction algorithm for its inverse problem. In the first part, we develop a novel Neumann-series-based radiative transfer equation (RTE) that incorporates reflection boundary conditions in the model. In addition, we propose a novel reconstruction technique for diffuse optical imaging that incorporates this Neumann-series-based RTE as forward model. The proposed model is assessed using a simulated 3D diffuse optical imaging setup, and the results demonstrate the importance of considering photon reflection at boundaries when performing photon propagation modeling. In the second part, we propose a statistical reconstruction algorithm for FMT. The algorithm is based on sparsity-initialized maximum-likelihood expectation maximization (MLEM), taking into account the Poisson nature of data in FMT and the sparse nature of images. The proposed method is compared with a pure sparse reconstruction method as well as a uniform-initialized MLEM reconstruction method. Results indicate the proposed method is more robust to noise and shows improved qualitative and quantitative performance. For PET, we present an MRI-guided partial volume correction algorithm for brain imaging, aiming to recover qualitative and quantitative loss due to the limited resolution of PET system, while keeping image noise at a low level. The proposed method is based on an iterative deconvolution model with regularization using parallel level sets. A non-smooth optimization algorithm is developed so that the proposed method can be feasibly applied for 3D images and avoid additional blurring caused by conventional smooth optimization process. We evaluate the proposed method using both simulation data and in vivo human data collected from the Baltimore Longitudinal Study of Aging (BLSA). Our proposed method is shown to generate images with reduced noise and improved structure details, as well as increased number of statistically significant voxels in study of aging. Results demonstrate our method has promise to provide superior performance in clinical imaging scenarios

Innovative boundary integral and hybrid methods for diffuse optical imaging

Diffuse Optical Imaging (DOI), the study of the propagation of Near Infra-Red (NIR) light in biological media, is an emerging method in medical imaging. Its state-of-the-art is non-invasive, versatile and reasonably inexpensive. In Diffuse Optical Tomography (DOT), the adaptation of numerical methods such as the Finite Element Method (FEM) and, more recently the Boundary Element Method (BEM), has allowed the treatment of complex problems, even for in vivo functional three-dimensional imaging. This work is the first attempt to combine these two methods in DOT. The BEM-FEM is designed to tackle layered turbid media problems. It focuses on the region of interest by restraining the reconstruction to it. All other regions are treated as piecewise-constant in a surface-integral approach. We validated the model in concentric spheres and found that it compared well with an analytical result. We then performed functional imaging of the neonate’s motor cortex in vivo, in a reconstruction restricted to the brain, both with FEM and BEM-FEM. Another use of the BEM in DOI is also outlined. NIR Spectroscopy (NIRS) devices are particularly used in brain monitoring and Diffuse Optical Cortical Mapping (DOCM). Unfortunately, they are very often accompanied by rudimentary analysis of the data and the 3D appreciation of the problem is missed. The BEM DOCM developed in the current work represents an improvement, especially since a topographical representation of a motor activation in the cortex is clearly reconstructed in vivo. In the interest of computational speed an acceleration technique for the BEM has been developed. The Fast Multipole Method (FMM), which is based on the decomposition of Green’s function on a basis of Bessel and Hankel functions, eases the evaluation of the BEM matrix, along with a faster calculation of the solutions

Multi-modal diffuse optical tomography and bioluminescence tomography system for preclinical imaging

The development, characterisation and testing of a novel all-optical, multi-modal preclinical biomedical imaging system is presented. The system aims to provide a new way of accurately visualising the spatial distribution and activity of molecular structures and processes in small animals by combining 3D bioluminescence tomography (BLT; reconstruction-based 3D imaging of internal bioluminescent reporter distributions), diffuse optical tomography (DOT; reconstruction-based imaging of optical parameter distributions) and optical surface capture techniques. The key principle of the imaging system is to use surface capture results to enhance the accuracy of DOT image reconstruction, and to use the results of both surface capture and DOT to enhance the accuracy of BLT. Presented experiments show that the developed system can reconstruct luminescent source distributions and optical parameters accurately and that small animal imaging is feasible with the system

Light transport in inhomogeneous scattering media : perturbation theory and biomedical application

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Magnetic Hybrid-Materials

Externally tunable properties allow for new applications of suspensions of micro- and nanoparticles in sensors and actuators in technical and medical applications. By means of easy to generate and control magnetic fields, fluids inside of matrices are studied. This monnograph delivers the latest insigths into multi-scale modelling, manufacturing and application of those magnetic hybrid materials

Magnetic Hybrid-Materials

Externally tunable properties allow for new applications of suspensions of micro- and nanoparticles in sensors and actuators in technical and medical applications. By means of easy to generate and control magnetic fields, fluids inside of matrices are studied. This monnograph delivers the latest insigths into multi-scale modelling, manufacturing and application of those magnetic hybrid materials