State Estimation with Model Reduction and Shape Variability. Application to biomedical problems

We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of spatial domain. This situation arises typically biomedical context where inverse are posed on certain organs or portions body which inevitably involve morphological variations. If one wants provide fast reconstruction methods, algorithms must take into account geometric variability. analyze method allows this variability without needing any priori knowledge parametrization geometrical For this, we rely morphometric techniques involving Multidimensional Scaling, couple them with make use reduced model spaces pre-computed database geometries. prove potential synthetic test problem inspired from blood flows quantities medical interest Doppler ultrasound imaging.