This page provides informations on the lectures and schedule of the Summer school.

Lectures
  • George-Henri Cottet (LJK Grenoble) :
  • Level-Set methods and applications in image processing and fluid-structure interaction

    • Introduction to level-set methods. Geometrical notions
    • Diffusion PDE for image processing
    • Anisotropic diffusion and level-set methods
    • Anisotropic diffusion and neural networks
    • Level-Set methods and complex fluids mechanics
    • Level-Set modeling of biological tissues

  • Slides in PDF.
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  • Dirk Drasdo (Projet Bang, Inria) :
  • Towards the systems biology of multi-cellular tissues: Single-cell-based models and beyond.

    • 1. Overview and fundamentals
    • 2. Monolayers: dense phenotypes
    • 3. Cellular automaton
    • 4. Multi-cellular spheroids
    • 5. Liver regeneration

  • Slides in PDF (coming soon).
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  • Marc Lavielle (Univ. Paris Sud, Orsay) :
  • Mixed effects models in pharmacokinetics-pharmacodynamics.

    Mathematical modelling in medicine consists in developping physiological models which describe as accurately as possible studied phenomena. When measured data coming from various patients are available, and we want to explain these data with a model, we have to take into account studied biological phenomena as well as every sources which induce variability in the data : observational errors and variability between subjects. When considered model is parametric, it means we consider that parameters can change from one patient to another. The so called "population" approach then consists in defining a probabilistic model which describes these fluctuations as random around a "mean" population parameter. Such mixed effects models are nowadays widely used in pharmacokinetics to describe e.g. time evolution of drug concentration in a body or viral dynamics to explain variability in the response to the same anti-VIH treatment.

    In the lecture, we will present these mixed effects models as well as some of the tools dedicated to their analysis. In particular, parameter estimation of these models is difficult when the model is not linear and described by a system of ODE. The SAEM (Stochastic Approximation of EM) algorithm is a stochastical algorithm which allows to compute the maximum likelihood estimation (MLE) without any approximation of the model, under rather general hypotheses. Some model selection and validation tools will also be presented, either graphical or numerical, based on an estimation of the likelihood of the model.

  • Slides in PDF.
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  • Nikos Paragios (Ecole Centrale Paris) :
  • Biomedical Image Analysis: State of the Art, Challenges and Perspectives

    Computational visual perception consists of understanding the environment through visual information processing. Biomedical image analysis is a similar task with to automatically interpret images of biological nature towards computer aided assisted diagnosis and intervention. The aim of this class will be to discuss the mathematical concepts behind such a process. In simple words, image perception consists of using a mathematical model to describe the task of interest, then associating this model with the available observations through an objective function to be minimized and last solving computationally for the optimal set of parameters with respect to the considered parametric model.

    This class will present the main mathematical components in the field and the corresponding applications challenged in biomedical image analysis. In particular, we will study continuous / PDE-based and discrete optimization methods with applications to:

    • 1. Image enhancement, noise removal and compression
    • 2. Image grouping, unsupervised clustering and model-free segmentation
    • 3. Prior knowledge, manifold-constrained and manifold enhanced image segmentation
    • 4. Optical flow and Deformable Registration using continuous and discrete optimization methods
    • 5. Machine learning and supervised classification with applications to computer aided diagnosis
    • 6. Clinical aplications

  • Slides in PDF.
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Schedule




  Monday Tuesday Wednesday Thursday Friday
9.00-10.30 Paragios I Drasdo I Drasdo IV Lavielle IV Cottet V
10.30-11.00 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
11.00-12.30 Paragios II Cottet I Drasdo V Lavielle V Zubelli
12.30-14.00 Lunch Lunch Lunch Lunch Lunch
14.00-15.15 Paragios III Drasdo II Lavielle I Cottet III Project Session
15.15-15.45 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break
15.45-17.00 Paragios IV Cottet II Lavielle II Cottet IV Project Session
17.00-17.15   Break Break Break  
17.15-18.30   Drasdo III Lavielle III Ribba  
19.30 Dinner Dinner Dinner Bouillabaisse Dinner