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This study was performed to assess the temporal evolution of damage within lesions and the normal-appearing white matter, measured using frequent magnetization transfer (MT) MRI, in relapsing-remitting multiple sclerosis (RRMS). The relationship of MT ratio (MTR) changes with measures of lesion burden, and the sample sizes needed to demonstrate a treatment effect on MTR metrics in placebo-controlled MS trials were also investigated. Bimonthly brain conventional and MT MRI scans were acquired from 42 patients with RRMS enrolled in the placebo arm of a 14-month, double-blind trial. Longitudinal MRI changes were evaluated using a random effect linear model accounting for repeated measures, and adjusted for centre effects. The Expanded Disability Status Scale (EDSS) score remained stable over the study period. A weak, but not statistically significant, decrease over time was detected for normal-appearing brain tissue (NABT) average MTR (-0.02% per visit; p = 0.14), and MTR peak height (-0.15 per visit; p = 0.17), while average lesion MTR showed a significant decrease over the study period (-0.07% per visit; p = 0.03). At each visit, all MTR variables were significantly correlated with T2 lesion volume (LV) (average coefficients of correlation ranging from -0.54 to -0.28, and p-values from <0.001 to 0.02). At each visit, NABT average MTR was also significantly correlated with T1-hypointense LV (average coefficient of correlation = -0.57, p < 0.001). The estimation of the sample sizes required to demonstrate a reduction of average lesion MTR (the only parameter with a significant decrease over the follow-up) ranged from 101 to 154 patients to detect a treatment effect of 50% in a 1-year trial with a power of 90%. The steady correlation observed between conventional and MT MRI measures over time supports the hypothesis of axonal degeneration of fibres passing through focal lesions as one of the factors contributing to the overall MS burden.