Interactions between hydrogen protons of water molecules and macromolecules within the myelin sheath surrounding the axons are a major factor influencing the magnetic resonance (MR) contrast in white matter (WM) regions. In past decades, several studies have investigated the underlying effects and reported a wide range of R1 rates for the myelin associated compartments at different field strengths. However, it was also shown that the experimental quantification of the compartment-specific R1 rates is associated with large uncertainties. The current study therefore investigates the longitudinal relaxation rates within the myelin sheath using a molecular dynamic (MD) simulation. For this purpose, a realistic molecular model of the myelin sheath was employed to determine the dipole-dipole induced R1 relaxation rate of the hydrogen protons at clinically relevant field strengths. The results obtained clearly reflect the spatial heterogeneity of R1 with a increased relaxivity of myelin water due to a reduced molecular mobility near the membrane surface. Moreover, the calculated R1 rates for both myelin water and macromolecules are in excellent agreement with experimental findings from the literature at different field strengths.