Diffusion tensor imaging (DTI) is a quantitative magnetic resonance imaging technique that measures the three-dimensional diffusion of water molecules within tissue through the application of multiple diffusion gradients. This technique is rapidly increasing in popularity for studying white matter properties and structural connectivity in the living human brain. One of the major outcomes derived from the DTI process is known as fractional anisotropy, a continuous measure restricted on the interval (0,1). Motivated from a longitudinal DTI study of multiple sclerosis, we use a beta semiparametric-mixed regression model for the neuroimaging data. This work extends the generalized additive model methodology with beta distribution family and random effects. We describe two estimation methods with penalized splines, which are formalized under a Bayesian inferential perspective. The first one is carried out by Markov chain Monte Carlo (MCMC) simulations while the second one uses a relatively new technique called integrated nested Laplace approximation (INLA). Simulations and the neuroimaging data analysis show that the estimates obtained from both approaches are stable and similar, while the INLA method provides an efficient alternative to the computationally expensive MCMC method.