An energy-based model of areas tiling the cortex and its fast computation

Each human cerebral cortex is a highly folded unique map. In order to combine the surface-based cortex data among subjects, we have developed an energy-based model of areas tiling human cerebral cortex across individuals. This model assumes that the cortical map in each individual subject is a sample from a single underlying probability distribution, allowing for higher localization accuracy of structural and functional features of the human brain. We update parameters using Markov Chain Monte Carlo (MCMC) and Gibbs sampling for this hierarchical Bayesian model. However, this procedure is very computationally costly in practice. To address this issue, in this work we have applied several approximation methods including biharmonic matrix approximation (BHA) and sparse sampling for faster Gibbs sampling. We use time, jumping distance, instability and Kullback–Leibler divergence as our comparison metric for efficiency and accuracy. We find out sparse, close, close-sparse mixed and BHA are promising approximation methods to make the model practical at different phases.