Visualising Volumetric Fractals

Fractal images have for many years been a richsource of exploration by those in computer science who also havean interest in graphics. They often served as a way of testing theperformance of new computing hardware and to explore thecapabilities of emerging display technologies. While there havebeen forays by some into 3D geometric fractals, the 3Dequivalents of the Mandelbrot set have been largely ignored. Thisis largely due to the lack of suitable tools for rendering these setsexcept perhaps as isosurfaces, a rather unsatisfactory and limitedrepresentation. The following will illustrate the application ofGPU based raycasting, a now relatively standard approach tovolume rendering, to the representation of volumetric fractals.Leveraging existing software that has been designed for generalvolume visualisation allows the interested 3D fractal explorer tofocus on the mathematical generation of the volume data ratherthan reinventing the entire volume rendering pipeline

Modeling the variability of shapes of a human placenta

While it is well-understood what a normal human placenta should look like, a deviation from the norm can take many possible shapes. In this paper we propose a mechanism for this variability based on the change in the structure of the vascular tree

Statistical shape analysis for bio-structures : local shape modelling, techniques and applications

A Statistical Shape Model (SSM) is a statistical representation of a shape obtained from data to study variation in shapes. Work on shape modelling is constrained by many unsolved problems, for instance, difficulties in modelling local versus global variation. SSM have been successfully applied in medical image applications such as the analysis of brain anatomy. Since brain structure is so complex and varies across subjects, methods to identify morphological variability can be useful for diagnosis and treatment. The main objective of this research is to generate and develop a statistical shape model to analyse local variation in shapes. Within this particular context, this work addresses the question of what are the local elements that need to be identified for effective shape analysis. Here, the proposed method is based on a Point Distribution Model and uses a combination of other well known techniques: Fractal analysis; Markov Chain Monte Carlo methods; and the Curvature Scale Space representation for the problem of contour localisation. Similarly, Diffusion Maps are employed as a spectral shape clustering tool to identify sets of local partitions useful in the shape analysis. Additionally, a novel Hierarchical Shape Analysis method based on the Gaussian and Laplacian pyramids is explained and used to compare the featured Local Shape Model. Experimental results on a number of real contours such as animal, leaf and brain white matter outlines have been shown to demonstrate the effectiveness of the proposed model. These results show that local shape models are efficient in modelling the statistical variation of shape of biological structures. Particularly, the development of this model provides an approach to the analysis of brain images and brain morphometrics. Likewise, the model can be adapted to the problem of content based image retrieval, where global and local shape similarity needs to be measured

A fractal based model of diffusion MRI in cortical grey matter

Diffusion Weighted Magnetic Resonance (DWMR) Imaging is an important tool in diagnostic neuroimaging, but the biophysical basis of the DWMR signal from biological tissue is not entirely understood. Testable, theoretical models relating the DWMR signal to the tissue, therefore, are crucial. This work presents a toy version of such a model of water DWMR signals in brain grey matter. The model is based on biophysical characteristics and all model parameters are directly interpretable as biophysical properties such as diffusion coefficients and membrane permeability allowing comparison to known values. In the model, a computer generated Diffusion Limited Aggregation (DLA) cluster is used to describe the collected membrane morphology of the cells in cortical grey matter. Using credible values for all model parameters model output is compared to experimental DWMR data from normal human grey matter and it is found that this model does reproduce the observed signal. The model is then used for simulating the effect on the DWMR signal of cellular events known to occur in ischemia. These simulations show that a combination of effects is necessary to reproduce the signal changes observed in ischemic tissue and demonstrate that the model has potential for interpreting DWMR signal origins and tissue changes in ischemia. Further studies are required to validate these results and compare them with other modeling approaches. With such models, it is anticipated that sensitivity and specificity of DWMR in tissues can be improved, leading to better understanding of the origins of MR signals in biological tissues, and improved diagnostic capability

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Fractal and multifractal analysis of PET-CT images of metastatic melanoma before and after treatment with ipilimumab

PET/CT with F-18-Fluorodeoxyglucose (FDG) images of patients suffering from metastatic melanoma have been analysed using fractal and multifractal analysis to assess the impact of monoclonal antibody ipilimumab treatment with respect to therapy outcome. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient therapeutic outcome condition. In 20 out-of 24 cases the fractal analysis results match those of the medical records, while 7 cases are considered as special cases because the patients have non-tumour related medical conditions or side effects which affect the results. The decrease in the fractal dimensions with the deterioration of the patient conditions (in terms of disease progression) are attributed to the hierarchical localisation of the tracer which accumulates in the affected lesions and does not spread homogeneously throughout the body. Fractality emerges as a result of the migration patterns which the malignant cells follow for propagating within the body (circulatory system, lymphatic system). Analysis of the multifractal spectrum complements and supports the results of the fractal analysis. In the kinetic Monte Carlo modelling of the metastatic process a small number of malignant cells diffuse throughout a fractal medium representing the blood circulatory network. Along their way the malignant cells engender random metastases (colonies) with a small probability and, as a result, fractal spatial distributions of the metastases are formed similar to the ones observed in the PET/CT images. In conclusion, we propose that fractal and multifractal analysis has potential application in the quantification of the evaluation of PET/CT images to monitor the disease evolution as well as the response to different medical treatments.Comment: 38 pages, 9 figure

Tumour grading and discrimination based on class assignment and quantitative texture analysis techniques

Medical imaging represents the utilisation of technology in biology for the purpose of noninvasively revealing the internal structure of the organs of the human body. It is a way to improve the quality of the patient's life through a more precise and rapid diagnosis, and with limited side-effects, leading to an effective overall treatment procedure. The main objective of this thesis is to propose novel tumour discrimination techniques that cover both micro and macro-scale textures encountered in computed tomography (CI') and digital microscopy (DM) modalities, respectively. Image texture can provide significant information on the (ab)normality of tissue, and this thesis expands this idea to tumour texture grading and classification. The fractal dimension (FO) as a texture measure was applied to contrast enhanced CT lung tumour images in an aim to improve tumour grading accuracy from conventional CI' modality, and quantitative performance analysis showed an accuracy of 83.30% in distinguishing between advanced (aggressive) and early stage (non-aggressive) malignant tumours. A different approach was adopted for subtype discrimination of brain tumour OM images via a set of statistical and model-based texture analysis algorithms. The combined Gaussian Markov random field and run-length matrix texture measures outperformed all other combinations, achieving an overall class assignment classification accuracy of 92.50%. Also two new histopathological multi resolution approaches based on applying the FO as the best bases selection for discrete wavelet packet transform, and when fused with the Gabor filters' energy output improved the accuracy to 91.25% and 95.00%, respectively. While noise is quite common in all medical imaging modalities, the impact of noise on the applied texture measures was assessed as well. The developed lung and brain texture analysis techniques can improve the physician's ability to detect and analyse pathologies leading for a more reliable diagnosis and treatment of disease