Screening and diagnosis are mainstays of clinical medicine. However, with greater clinical imaging data being available, more complex questions need addressing. For example, in cardiology, the size of abdominal aortic aneurysm (AAA) does not account entirely for its risk of rupture, although rupture is a condition with high mortality. More accurate methods of risk stratification are needed based on the image data. In oncology, screening of cancer high-throughput/high-content microscopy images can give insight into drug efficacy or identify potential safety risks of drugs on other critical systems within the body. In order to fully utilise all the available information, it is necessary to incorporate a wide variety of mathematical skills. Knowledge of texture analysis and segmentation based on PDE models needs to be incorporated into statistical learning algorithms to allow diagnosis. Real time image analysis using shape constrained methods needs to be performed on thousands if not millions of microscopy images and then combined with data from systems level scans such as PET images. Here, the development of computationally efficient optimisation methods that do not require heavy hardware machinery will be essential for the translation of developed analysis tools to clinical practice.
In cardiology, textural analysis of aneurysm CT images (CTTA) measures heterogeneity (kurtosis, skewness, entropy) within standard CT images. Greater heterogeneity in tumours corresponds with adverse pathological features such as hypoxia and neovascularisation, and predicts reduced survival. Building on promising pilot data (TexRAD software) , we will measure CTTA in AAA, assessing its association with annual expansion and rupture. We will also apply textural analysis to CT images of atherosclerosis of the carotid and coronary arteries in subjects at risk of stroke and heart attack. In addition to measuring heterogeneity, whether the spatial relationship of the various components of atherosclerosis (calcium, thrombus, arterial wall) is important in determining clinical events is unknown. Using methodology from applied mathematics for texture analysis , and incorporating recent statistical texture analysis approaches , such features can be incorporated into learning algorithms. These will be investigated using a 2500 patient database of CT images, both contrast and non-contrast, where a mathematically robust and efficient means of extracting these features and expressing the results is essential to answer this question.
In oncology, screening of microscopy data requires automatic image based feature recognition and incorporation into statistical classification and clustering algorithms. Of particular importance, is the ability to do this on high-throughput/high-content imaging in almost real time. This is a necessity if the current techniques used for pre-clinical drug efficacy are to be extended to clinical efficacy in a patient specific manner. Suites of possible compounds can be tested against individual tumour samples to help inform the best treatment options. However, such efficacy will require not only a change in the perception of personalised medicine, but also a change in the idea of personalised risk. Being able to also apply such screening techniques to facilitate personalised safety considerations (to understand the individual risks of cardiac events from oncology drugs for example), also re- quire related analytical tools. While, of course, incorporating such technology into routine clinical usage is well beyond the lifetime of this post-doc position, these initial tools are something that could profoundly change whether such technology is even a viable consideration. Using high-throughput imaging data will allow us to use similar tools to those investigated in the CTTA analysis on these microscopy imaging data sets.
Of course, in oncology, incorporating a number of modalities together is of vital importance from microscopy images at one level to PET and MRI images at the other end of the spectrum. This raises a number of mathe- matical issues about how to extract the relevant information and how to combine it meaningfully in an overall statistical model. This is especially important in diseases such as breast cancer where both mammography data is combined with histological samples, and jointly modelling such data for clinical diagnosis is paramount.
This project would appeal to a candidate with a physics or statistical background.
 Rajani, N.K., Joshi, N.V., Elkhawad, M., Melville, A., Chowdhury, M., Ganeshan, B., Boyle, J., Newby, D.E. and Rudd, J.H. CT textural analysis of abdominal aortic aneurysms as a biomarker for aneurysm growth. The Lancet, 383, p.S87, 2014.
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