4D Shape-Preserving Modelling of Bone Growth

From a set of temporally separated scannings of the same anatomical structure we wish to identify and analyze the growth in terms of a metamorphosis. That is, we study the temporal change of shape which may provide an understanding of the biological processes which govern the growth process. We subdivide the growth analysis into growth simulation, growth modelling, and finally the growth analysis. In this paper, we present results of growth simulation of the mandible from 3 scannings of the same patient in the age of 9 months, 21 months, and 7 years. We also present the first growth models and growth analyzes. The ultimative goal is to predict/simulate human growth which would be extremely useful in many surgical procedures

Analyse mathématique et modélisation

Henri Berestycki, directeur d’études Méthodes d’EDP et numériques en finance de marchés (avec Olivier Pironneau, professeur à l’Université Paris-VI) Différents aspects de la modélisation mathématique des marchés financiers ont été présentés. On s’est attaché en particulier à la formulation en termes d’équations aux dérivées partielles (EDP) des problèmes d’évaluation de produits dérivés (options, contrats futurs, etc.) et de techniques de gestion du risque. Les outils d’analyse mathématique d..

Surface-bounded growth modeling applied to human mandibles

From a set of longitudinal three-dimensional scans of the same anatomical structure, we have accurately modeled the temporal shape and size changes using a linear shape model. On a total of 31 computed tomography scans of the mandible from six patients, 14851 semilandmarks are found automatically using shape features and a new algorithm called geometry-constrained diffusion. The semilandmarks are mapped into Procrustes space. Principal component analysis extracts a one-dimensional subspace, which is used to construct a linear growth model. The worst case mean modeling error in a cross validation study is 3.7 mm