THIS IS A PRE-PRINT (A WORKING PAPER) OF THE FOLLOWING PUBLISHED PAPER: Bishesh Khanal, Marco Lorenzi, Nicholas Ayache, Xavier Pennec. A biophysical model of brain deformation to simulate and analyze longitudinal MRIs of patients with Alzheimer’s disease. NeuroImage, Elsevier, 2016, 134, pp.35-52. We propose a framework for developing a comprehensive biophysical model that could predict and simulate realistic longitudinal MRIs of patients with Alzheimer’s Disease (AD). The framework includes three major building blocks: i) Atrophy generation ii) Brain deformation iii) Realistic MRI generation. Within this framework, this paper focuses on a detailed implementation of the brain deformation block with a carefully designed biomechanics-based tissue loss model. For a given baseline brain MRI, the model yields a deformation field imposing the desired atrophy at each voxel of the brain parenchyma while allowing the CSF to expand as required to globally compensate for the locally prescribed volume loss. Our approach is inspired by biomechanical principles and involves a system of equations similar to Stokes equations in fluid mechanics but with the presence of a non-zero mass source term. We use this model to simulate longitudinal MRIs by prescribing complex patterns of atrophy. We explore the influence of different spatial distributions of atrophy on the image appearance . The proposed framework could help understand the implications of different model assumptions, regularization choices and spatial priors for the detection and measurement of brain atrophy from longitudinal brain MRIs. Keywords: biophysical model, Alzheimer’s disease, simulation of atrophy, longitudinal MRIs simulation, longitudinal modeling
