Subdivision Shell Elements with Anisotropic Growth

A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow for arbitrary in-plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl

Automated retinal layer segmentation and pre-apoptotic monitoring for three-dimensional optical coherence tomography

The aim of this PhD thesis was to develop segmentation algorithm adapted and optimized to retinal OCT data that will provide objective 3D layer thickness which might be used to improve diagnosis and monitoring of retinal pathologies. Additionally, a 3D stack registration method was produced by modifying an existing algorithm. A related project was to develop a pre-apoptotic retinal monitoring based on the changes in texture parameters of the OCT scans in order to enable treatment before the changes become irreversible; apoptosis refers to the programmed cell death that can occur in retinal tissue and lead to blindness. These issues can be critical for the examination of tissues within the central nervous system. A novel statistical model for segmentation has been created and successfully applied to a large data set. A broad range of future research possibilities into advanced pathologies has been created by the results obtained. A separate model has been created for choroid segmentation located deep in retina, as the appearance of choroid is very different from the top retinal layers. Choroid thickness and structure is an important index of various pathologies (diabetes etc.). As part of the pre-apoptotic monitoring project it was shown that an increase in proportion of apoptotic cells in vitro can be accurately quantified. Moreover, the data obtained indicates a similar increase in neuronal scatter in retinal explants following axotomy (removal of retinas from the eye), suggesting that UHR-OCT can be a novel non-invasive technique for the in vivo assessment of neuronal health. Additionally, an independent project within the computer science department in collaboration with the school of psychology has been successfully carried out, improving analysis of facial dynamics and behaviour transfer between individuals. Also, important improvements to a general signal processing algorithm, dynamic time warping (DTW), have been made, allowing potential application in a broad signal processing field.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Inferring evolutionary histories of pathway regulation from transcriptional profiling data

One of the outstanding challenges in comparative genomics is to interpret the evolutionary importance of regulatory variation between species. Rigorous molecular evolution-based methods to infer evidence for natural selection from expression data are at a premium in the field, and to date, phylogenetic approaches have not been well-suited to address the question in the small sets of taxa profiled in standard surveys of gene expression. We have developed a strategy to infer evolutionary histories from expression profiles by analyzing suites of genes of common function. In a manner conceptually similar to molecular evolution models in which the evolutionary rates of DNA sequence at multiple loci follow a gamma distribution, we modeled expression of the genes of an \emph{a priori}-defined pathway with rates drawn from an inverse gamma distribution. We then developed a fitting strategy to infer the parameters of this distribution from expression measurements, and to identify gene groups whose expression patterns were consistent with evolutionary constraint or rapid evolution in particular species. Simulations confirmed the power and accuracy of our inference method. As an experimental testbed for our approach, we generated and analyzed transcriptional profiles of four \emph{Saccharomyces} yeasts. The results revealed pathways with signatures of constrained and accelerated regulatory evolution in individual yeasts and across the phylogeny, highlighting the prevalence of pathway-level expression change during the divergence of yeast species. We anticipate that our pathway-based phylogenetic approach will be of broad utility in the search to understand the evolutionary relevance of regulatory change.Comment: 30 pages, 12 figures, 2 tables, contact authors for supplementary table

Automated retinal layer segmentation and pre-apoptotic monitoring for three-dimensional optical coherence tomography

The aim of this PhD thesis was to develop segmentation algorithm adapted and optimized to retinal OCT data that will provide objective 3D layer thickness which might be used to improve diagnosis and monitoring of retinal pathologies. Additionally, a 3D stack registration method was produced by modifying an existing algorithm. A related project was to develop a pre-apoptotic retinal monitoring based on the changes in texture parameters of the OCT scans in order to enable treatment before the changes become irreversible; apoptosis refers to the programmed cell death that can occur in retinal tissue and lead to blindness. These issues can be critical for the examination of tissues within the central nervous system. A novel statistical model for segmentation has been created and successfully applied to a large data set. A broad range of future research possibilities into advanced pathologies has been created by the results obtained. A separate model has been created for choroid segmentation located deep in retina, as the appearance of choroid is very different from the top retinal layers. Choroid thickness and structure is an important index of various pathologies (diabetes etc.). As part of the pre-apoptotic monitoring project it was shown that an increase in proportion of apoptotic cells in vitro can be accurately quantified. Moreover, the data obtained indicates a similar increase in neuronal scatter in retinal explants following axotomy (removal of retinas from the eye), suggesting that UHR-OCT can be a novel non-invasive technique for the in vivo assessment of neuronal health. Additionally, an independent project within the computer science department in collaboration with the school of psychology has been successfully carried out, improving analysis of facial dynamics and behaviour transfer between individuals. Also, important improvements to a general signal processing algorithm, dynamic time warping (DTW), have been made, allowing potential application in a broad signal processing field

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Efficient Learning Machines

Computer scienc

Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work