An anisotropic model for tissue growth and remodeling during early development of cerebral aneurysms

This paper presents a constitutive model for predicting the time-dependent response of growing aneurysms during their early development, with particular regards to cerebral aneurysms. The adaptive process is interpreted as the result of two competitive mechanisms: a change in the reference length of collagen fibers and a change in the collagen fiber density. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the growth regime by means of a suitably developed constitutive framework based on the multiplicative decomposition of the deformation gradient into elastic and inelastic components defined for the fibers. Rate equations ruling the time evolution of the fiber reference length and of the fiber density are introduced. The constitutive parameters for the passive behavior of cerebral arterial walls are identified by fitting experimental results taken from the literature. Two representative numerical examples are presented to illustrate the capability of the model of simulating the time evolution of saccular as well as fusiform aneurysms to a perturbation of the homeostatic (physiologic) state. A simplified geometrical model is used for the two examples. The results have shown that the two mechanisms, the change in fiber reference length and the fiber density change, have opposite effects on the stability of the tissue growth. Unstable growth is obtained even for a small perturbation of the reference state in the cases in which the mechanism affecting the fiber density is not sufficiently strong.