This document introduces multivariate functional principal component analysis (mFPCA). mFPCA is a technique that estimates individual trajectories from sparse longitudinal data for multiple processes simultaneously. It models the response of each individual at each time point as the sum of the mean trajectory, individual deviations due to principal modes of variation, and error. mFPCA determines the principal modes of variation in trajectories across individuals and evaluates the association between these modes of variation among different processes. The document provides the mathematical model for mFPCA, representing the response as a function of basis coefficients for the mean and individual deviations, and illustrates its application to modeling trajectories of multiple brain regions.