A full picture of longitudinal relaxation in complex heterogeneous environments like white matter brain tissue remains elusive. In tissue, successive approximations, from the solvation layer model to the two pool model, have highlighted how longitudinal magnetization evolution depends on both inter-compartmental exchange and spin-lattice relaxation. In white matter, however, these models fail to capture the behaviour of the two distinct aqueous pools, myelin water and intra/extra-cellular water. A challenge with testing more comprehensive multi-pool models lies in directly observing all pools, both aqueous and non-aqueous. In this work, we advance these efforts by integrating three main experimental and analytical elements: direct observation of the longitudinal relaxation of both the aqueous and the non-aqueous protons in white matter, a wide range of different initial conditions, and application of an analysis pipeline which includes lineshape, CPMG, and fitting of a four pool model. An eigenvector interpretation of the four pool model highlights how longitudinal relaxation in white matter depends on initial conditions. We find that a single set of model parameters is able to describe the entire range of relaxation behaviour observed in all the separable aqueous and non-aqueous pools in experiments involving six different initial conditions. Understanding of the nature and connectedness of the tissue components is crucial in the design and interpretation of many MRI measurements, especially those based on magnetization transfer and longitudinal relaxation. In particular, the dependency of relaxation behaviour on initial conditions is likely the basis for understanding method-dependent discrepancies in in vivo T.