Slantlet transform-based segmentation and α -shape theory-based 3D visualization and volume calculation methods for MRI brain tumour

Magnetic Resonance Imaging (MRI) being the foremost significant component of medical diagnosis which requires careful, efficient, precise and reliable image analyses for brain tumour detection, segmentation, visualisation and volume calculation. The inherently varying nature of tumour shapes, locations and image intensities make brain tumour detection greatly intricate. Certainly, having a perfect result of brain tumour detection and segmentation is advantageous. Despite several available methods, tumour detection and segmentation are far from being resolved. Meanwhile, the progress of 3D visualisation and volume calculation of brain tumour is very limited due to absence of ground truth. Thus, this study proposes four new methods, namely abnormal MRI slice detection, brain tumour segmentation based on Slantlet Transform (SLT), 3D visualization and volume calculation of brain tumour based on Alpha (α) shape theory. In addition, two new datasets along with ground truth are created to validate the shape and volume of the brain tumour. The methodology involves three main phases. In the first phase, it begins with the cerebral tissue extraction, followed by abnormal block detection and its fine-tuning mechanism, and ends with abnormal slice detection based on the detected abnormal blocks. The second phase involves brain tumour segmentation that covers three processes. The abnormal slice is first decomposed using the SLT, then its significant coefficients are selected using Donoho universal threshold. The resultant image is composed using inverse SLT to obtain the tumour region. Finally, in the third phase, four original ideas are proposed to visualise and calculate the volume of the tumour. The first idea involves the determination of an optimal α value using a new formula. The second idea is to merge all tumour points for all abnormal slices using the α value to form a set of tetrahedrons. The third idea is to select the most relevant tetrahedrons using the α value as the threshold. The fourth idea is to calculate the volume of the tumour based on the selected tetrahedrons. In order to evaluate the performance of the proposed methods, a series of experiments are conducted using three standard datasets which comprise of 4567 MRI slices of 35 patients. The methods are evaluated using standard practices and benchmarked against the best and up-to-date techniques. Based on the experiments, the proposed methods have produced very encouraging results with an accuracy rate of 96% for the abnormality slice detection along with sensitivity and specificity of 99% for brain tumour segmentation. A perfect result for the 3D visualisation and volume calculation of brain tumour is also attained. The admirable features of the results suggest that the proposed methods may constitute a basis for reliable MRI brain tumour diagnosis and treatments

Advances in the Development of Shape Similarity Methods and Their Application in Drug Discovery

Molecular similarity is a key concept in drug discovery. It is based on the assumption that structurally similar molecules frequently have similar properties. Assessment of similarity between small molecules has been highly effective in the discovery and development of various drugs. Especially, two-dimensional (2D) similarity approaches have been quite popular due to their simplicity, accuracy and efficiency. Recently, the focus has been shifted toward the development of methods involving the representation and comparison of three-dimensional (3D) conformation of small molecules. Among the 3D similarity methods, evaluation of shape similarity is now gaining attention for its application not only in virtual screening but also in molecular target prediction, drug repurposing and scaffold hopping. A wide range of methods have been developed to describe molecular shape and to determine the shape similarity between small molecules. The most widely used methods include atom distance-based methods, surface-based approaches such as spherical harmonics and 3D Zernike descriptors, atom-centered Gaussian overlay based representations. Several of these methods demonstrated excellent virtual screening performance not only retrospectively but also prospectively. In addition to methods assessing the similarity between small molecules, shape similarity approaches have been developed to compare shapes of protein structures and binding pockets. Additionally, shape comparisons between atomic models and 3D density maps allowed the fitting of atomic models into cryo-electron microscopy maps. This review aims to summarize the methodological advances in shape similarity assessment highlighting advantages, disadvantages and their application in drug discovery

Topology of complex networks: models and analysis

There is a large variety of real-world phenomena that can be modelled and analysed as networks. Part of this variety is reflected in the diversity of network classes that are used to model these phenomena. However, the differences between network classes are not always taken into account in their analysis. This thesis carefully addresses how to deal with distinct classes of networks in two different contexts. First, the well-known switching model has been used to randomise different classes of networks, and is typically referred to as the switching model. We argue that really we should be talking about a family of switching models. Ignoring the distinction between the switching model with respect to different network classes has lead to biased sampling. Given that the most common use of the switching model is as a null-model, it is critical that it samples without bias. We provide a comprehensive analysis of the switching model with respect to nine classes of networks and prove under which conditions sampling is unbiased for each class. Recently the Curveball algorithm was introduced as a faster approach to network randomisation. We prove that the Curveball algorithm samples without bias; a position that was previously implied, but unproven. Furthermore, we show that the Curveball algorithm provides a flexible framework for network randomisation by introducing five variations with respect to different network classes. We compare the switching models and Curveball algorithms to several other random network models. As a result of our findings, we recommend using the configuration model for multi-graphs with self-loops, the Curveball algorithm for networks without multiple edges or without self-loops and the ordered switching model for directed acyclic networks. Second, we extend the theory of motif analysis to directed acyclic networks. We establish experimentally that there is no difference in the motifs detected by existing motif analysis methods and our customised method. However, we show that there are differences in the detected anti-motifs. Hence, we recommend taking into account the acyclic nature of directed acyclic networks. Network science is a young and active field of research. Most existing network measures originate in statistical mechanics and focus on statistics of local network properties. Such statistics have proven very useful. However, they do not capture the complete structure of a network. In this thesis we present experimental results on two novel network analysis techniques. First, at the local level, we show that the neighbourhood of a node is highly distinctive and has the potential to match unidentified entities across networks. Our motivation is the identification of individuals across dark social networks hidden in recorded networks. Second, we present results of the application of persistent homology to network analysis. This recently introduced technique from topological data analysis offers a new perspective on networks: it describes the mesoscopic structure of a network. Finally, we used persistent homology for a classification problem in pharmaceutical science. This is a novel application of persistent homology. Our analysis shows that this is a promising approach for the classification of lipid formulations