Glaucoma is the second leading cause of blindness worldwide. Despite active research efforts driven by the importance of diagnosis and treatment of the optic degenerative neuropathy, the relationship between structural and functional changes along the glaucomateous evolution are still not clearly understood. Dynamic changes of the lamina cribrosa (LC) in the presence of intraocular pressure (IOP) were suggested to play a significant role in optic nerve damage, which motivates the proposed research to explore the relationship of changes of the 3D structure of the LC collagen meshwork to clinical diagnosis. We introduce a framework to quantify 3D dynamic morphological changes of the LC under acute IOP changes in a series of swept-source optical coherence tomography (SS-OCT) scans taken under different pressure states. Analysis of SS-OCT images faces challenges due to low signal-to-noise ratio, anisotropic resolution, and observation variability caused by subject and ocular motions. We adapt unbiased diffeomorphic atlas building which serves multiple purposes critical for this analysis. Analysis of deformation fields yields desired global and local information on pressure-induced geometric changes. Deformation variability, estimated with repeated images of a healthy volunteer without IOP elevation, is found to be a magnitude smaller than pressure-induced changes and thus illustrates feasibility of the proposed framework. Results in a clinical study with healthy, glaucoma suspect, and glaucoma subjects demonstrate the potential of the proposed method for non-invasive in vivo analysis of LC dynamics, potentially leading to early prediction and diagnosis of glaucoma.