A random field model for anisotropic strain energy functions and its application for uncertainty quantification in vascular mechanics

This paper deals with the construction of random field models for spatially-dependent anisotropic strain energy functions indexed by complex geometries. The approach relies on information theory and the principle of maximum entropy, which are invoked in order to construct the family of first-order marginal probability distributions in accordance with fundamental constraints such as polyconvexity, coerciveness and consistency at small strains. We then address the definition of a sampling methodology able to perform on domains that are non-homotopic to a sphere, with the aim to generate the non-Gaussian random fields on non-simplified geometries—such as patient-specific geometries in computational biomechanics. The algorithm is based on the construction of a diffusion field that involves local geometrical features of the manifolds defining domain boundaries. We finally present numerical applications on vascular tissues, including the case of an arterial wall defined by real patient-specific data.