Abstract. Mathematical tumour growth models have started to attract attention from the medical image analysis community in last years. These models can offer several useful tools for clinical oncology besides the conventional tools already proposed such as segmentation and registration. For instance, they could help us better understand the mechanical influence and the diffusion process of gliomas. For the clinical applications, they would provide us tools to identify the invaded areas that are not visible in the MR images in order to better adapt the resection in surgery or the irradiation margins in radiotherapy. As one of the most important goals, they would give us the opportunity to identify from patient images some model parameters that could help characterising the tumour and perhaps predict its future evolution. There has been vast amount of research on tumour growth modelling, mostly in the field of theoretical biology. We review some of the major approaches taken with an emphasis on the models using medical images.
Following these general guidelines, we give the example of a patient specific model that we have previously proposed. On this basis, we detail our recent works to extrapolate tumour infiltration for radiotherapy, quantifying tumour growth and identifying model parameters. Naturally, these works should be seen as steps to the ultimate challenge, which is to build patient-specific tumour models from the clinical observations (basically images) from which we could extract a few insightful parameters (speed of growth, potential place of recurrence, etc.) for decision support systems and knowledge discovery.

Abstract. Understanding and modelling the individual anatomy of the brain and its variability across a population is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. This also raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. As illustrated in Section 1, applications are very important both in neuroscience, to minimise the influence of the anatomical variability in functional group analyses, and in medical imaging, to better drive the adaptation of generic models of the anatomy (atlas) into patient-specific data. Typical examples in the Health-e-Child context are given by tumours growth model which need to be fed with the fibre orientation everywhere in the brain. We present in Section 2 to 4 the methods that we developed in the context of the Health-e-Child project to analyse the morphometry of the cortex from sulcal lines, fibers and surfaces of internal brain structures. One of our specific goal was also to cope with the inherent specificity of paediatric data with the evolution due to growth: Section 5 describes in detail our strategy to analyse the variability both in space and time of the brain maturation across a population.