A Finite Element Mesh Aggregating Approach to Multiple-Source Reconstruction in Bioluminescence Tomography

A finite element mesh aggregating approach is presented to reconstruct images of multiple internal bioluminescence sources. Rather than assuming independence between mesh nodes, the proposed reconstruction strategy exploits spatial structure of nodes and aggregation feature of density distribution on the finite element mesh to adaptively determine the number of sources and to improve the quality of reconstructed images. With the proposed strategy integrated in the regularization-based reconstruction process, reconstruction algorithms need no a priori knowledge of source number; even more importantly, they can automatically reconstruct multiple sources that differ greatly in density or power

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

Improvements in the robustness and accuracy of bioluminescence tomographic reconstructions of distributed sources within small animals

High quality three-dimensional bioluminescence tomographic (BLT) images, if available, would constitute a major advance and provide much more useful information than the two-dimensional bioluminescence images that are frequently used today. To-date, high quality BLT images have not been available, largely because of the poor quality of the data being input into the reconstruction process. Many significant confounds are not routinely corrected for and the noise in this data is unnecessarily large and poorly distributed. Moreover, many of the design choices affecting image quality are not well considered, including choices regarding the number and type of filters used when making multispectral measurements and choices regarding the frequency and uniformity of the sampling of both the range and domain of the BLT inverse problem. Finally, progress in BLT image quality is difficult to gauge owing to a lack of realistic gold-standard references that engage the full complexity and uncertainty within a small animal BLT imaging experiment. Within this dissertation, I address all of these issues. I develop a Cerenkov-based gold-standard wherein a Positron Emission Tomography (PET) image can be used to gauge improvements in the accuracy of BLT reconstruction algorithms. In the process of creating this reference, I discover and describe corrections for several confounds that if left uncorrected would introduce artifacts into the BLT images. This includes corrections for the angle of the animal’s skin surface relative to the camera, for the height of each point on the skin surface relative to the focal plane, and for the variation in bioluminescence intensity as a function of luciferin concentration over time. Once applied, I go on to derive equations and algorithms that when employed are able to minimize the noise in the final images under the constraints of a multispectral BLT data acquisition. These equations and algorithms allow for an optimal choice of filters to be made and for the acquisition time to be optimally distributed among those filtered measurements. These optimizations make use of Barrett’s and Moore-Penrose pseudoinverse matrices which also come into play in a paradigm I describe that can be used to guide choices regarding sampling of the domain and range

Reconstruction d’image en fluorescence par tomographie optique diffuse pour imagerie moléculaire sur petit animal avec lumière proche infrarouge en régime continu

L’approximation par harmoniques sphériques (SPN) simplifiées de l’équation de transfert radiatif a été proposée comme un modèle fiable de propagation de la lumière dans les tissus biologiques. Cependant, peu de solutions analytiques ont été trouvées pour ce modèle. De telles solutions analytiques sont d’une grande valeur pour valider les solutions numériques des équations SPN, auxquelles il faut recourir dans le cas de tissus avec des géométries courbes complexes. Dans la première partie de cette thèse, des solutions analytiques pour deux géométries courbes sont présentées pour la première fois, à savoir pour la sphère et pour le cylindre. Pour les deux solutions, les conditions aux frontières générales tenant compte du saut d’indice de réfraction à l’interface du tissus et de son milieu environnant, telles qu’applicables à l’optique biomédicale, sont utilisées. Ces solutions sont validées à l’aide de simulations Monte Carlo basées sur un maillage de discrétisation du milieu. Ainsi, ces solutions permettent de valider rapidement un code numérique, par exemple utilisant les différences finies ou les éléments finis, sans nécessiter de longues simulations Monte Carlo. Dans la deuxième partie de cette thèse, la reconstruction itérative pour l’imagerie par tomographie optique diffuse par fluorescence est proposée sur la base d’une fonction objective et de son terme de régularisation de type Lq-Lp. Pour résoudre le problème inverse d’imagerie, la discrétisation du modèle de propagation de la lumière est effectuée en utilisant la méthode des différences finies. La reconstruction est effectuée sur un modèle de souris numérique en utilisant un maillage multi-échelle. Le problème inverse est résolu itérativement en utilisant une méthode d’optimisation. Pour cela, le gradient de la fonction de coût par rapport à la carte de concentration de l’agent fluorescent est nécessaire. Ce gradient est calculé à l’aide d’une méthode adjointe. Des mesures quantitatives utilisées en l’imagerie médicale sont utilisées pour évaluer la performance de l’approche de reconstruction dans différentes conditions. L’approche Lq-Lp montre des performances quantifiées élevées par rapport aux algorithmes traditionnels basés sur des fonction coût de type somme de carrés de différences.Abstract : The simplified spherical harmonics (SPN) approximation to the radiative transfer equation has been proposed as a reliable model of light propagation in biological tissues. However, few analytical solutions have been found for this model. Such analytical solutions are of great value to validate numerical solutions of the SPN equations, which must be resorted to when dealing with media with complex curved geometries. In the first part of this thesis, analytical solutions for two curved geometries are presented for the first time, namely for the sphere and for the cylinder. For both solutions, the general refractiveindex mismatch boundary conditions, as applicable in biomedical optics, are resorted to. These solutions are validated using mesh-based Monte Carlo simulations. So validated, these solutions allow in turn to rapidly validate numerical code, based for example on finite differences or on finite elements, without requiring lengthy Monte Carlo simulations. provide reliable tool for validating numerical simulations. In the second part, iterative reconstruction for fluorescence diffuse optical tomography imaging is proposed based on an Lq-Lp framework for formulating an objective function and its regularization term. To solve the imaging inverse problem, the discretization of the light propagation model is performed using the finite difference method. The framework is used along with a multigrid mesh on a digital mouse model. The inverse problem is solved iteratively using an optimization method. For this, the gradient of the cost function with respect to the fluorescent agent’s concentration map is necessary. This is calculated using an adjoint method. Quantitative metrics resorted to in medical imaging are used to evaluate the performance of the framework under different conditions. The results obtained support this new approach based on an Lq-Lp formulation of cost functions in order to solve the inverse fluorescence problem with high quantified performance

Use of prior information and probabilistic image reconstruction for optical tomographic imaging

Preclinical bioluminescence tomographic reconstruction is underdetermined. This work addresses the use of prior information in bioluminescence tomography to improve image acquisition, reconstruction, and analysis. A structured light surface metrology method was developed to measure surface geometry and enable robust and automatic integration of mirrors into the measurement process. A mouse phantom was imaged and accuracy was measured at 0.2mm with excellent surface coverage. A sparsity-regularised reconstruction algorithm was developed to use instrument noise statistics to automatically determine the stopping point of reconstruction. It was applied to in silico and in simulacra data and successfully reconstructed and resolved two separate luminescent sources within a plastic mouse phantom. A Bayesian framework was constructed that incorporated bioluminescence properties and instrument properties. Distribution expectations and standard deviations were estimated, providing reconstructions and measures of reconstruction uncertainty. The reconstructions showed superior performance when applied to in simulacra data compared to the sparsity-based algorithm. The information content of measurements using different sets of wavelengths was quantified using the Bayesian framework via mutual information and applied to an in silico problem. Significant differences in information content were observed and comparison against a condition number-based approach indicated subtly different results

Novel Harmonic Regularization Approach for Variable Selection in Cox’s Proportional Hazards Model

Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq  (1/2<q<1) regularizations, to select key risk factors in the Cox’s proportional hazards model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL), the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods

Fast Radiative-Transfer-Equation-Based Image Reconstruction Algorithms for Non-Contact Diffuse Optical Tomography Systems

It is well known that the radiative transfer equation (RTE) is the most accurate deterministic light propagation model employed in diffuse optical tomography (DOT). RTE-based algorithms provide more accurate tomographic results than codes that rely on the diffusion equation (DE), which is an approximation to the RTE, in scattering dominant media. However, RTE based DOT (RTE-DOT) has limited utility in practice due to its high computational cost and lack of support for general non-contact imaging systems. In this dissertation, I developed fast reconstruction algorithms for RTE-based DOT (RTE-DOT), which consists of three independent components: an efficient linear solver for forward problems, an improved optimization solver for inverse problem, and the first light propagation model in free space that fully considers the angular dependency, which can provide a suitable measurement operator for RTE-DOT. This algorithm is validated and evaluated with numerical experiments and clinical data. According to these studies, the novel reconstruction algorithm is up to 30 times faster than traditional reconstruction techniques, while achieving comparable reconstruction accuracy