On the Complexity of Human Neuroanatomy at the Millimeter Morphome Scale: Developing Codes and Characterizing Entropy Indexed to Spatial Scale

In this work we devise a strategy for discrete coding of anatomical form as described by a Bayesian prior model, quantifying the entropy of this representation as a function of code rate (number of bits), and its relationship geometric accuracy at clinically relevant scales. We study the shape of subcortical gray matter structures in the human brain through diffeomorphic transformations that relate them to a template, using data from the Alzheimer's Disease Neuroimaging Initiative to train a multivariate Gaussian prior model. We find that the at 1 mm accuracy all subcortical structures can be described with less than 35 bits, and at 1.5 mm error all structures can be described with less than 12 bits. This work represents a first step towards quantifying the amount of information ordering a neuroimaging study can provide about disease status.