Characterization of biological growth using iterated diffeomorphisms

Mathematical and statistical modeling of biological growth are important problems in medical diagnostics. We study a structured model, called growth by random iterated diffeomorphisms (GRID), that models growth by emphasizing its local nature. The cumulative growth is composed of several smaller deformations; each deformation models an active region by capturing deformation local to that region, and is characterized by a seed and a radial deformation pattern around the seed. The GRID variables - seed locations and radial deformation patterns - are estimated from observed images in two steps: (i) Estimate a cumulative deformation over an observation interval, and (ii) Estimate GRID variables using maximum-likelihood criterion from the estimated cumulative deformation. We demonstrate this framework using MRI image data of a rat´s brain growth