In this thesis, two fundamental concepts of nuclear magnetic resonance (NMR) were studied and combined in order to develop new solutions to practical problems. These concepts were: the use of pulsed magnetic field gradients for imaging and diffusion measurements, and the relaxation properties of a spin system. Chapter 2 describes how three-dimensional, diffusion-sensitising gradients were used in NMR experiments carried out on a system where long-lived singlet order was populated, allowing relaxation decay constants of the order of minutes to be achieved; this resulted in a new pulse sequence dubbed SADTI (Singlet-Assisted Diffusion Tensor Imaging) used in experiments where the structural characterization of model systems was possible by tracking diffusion of singlet bearing molecules in 3D for a time that is currently not achievable using routine diffusion NMR and magnetic resonance imaging (MRI) techniques. Chapter 3 presents the successful application of selective magnetic field gradients to reduce the duration of singlet order decay constant measurement, from 2.5 hours to less than 8 minutes. Finally, chapter 4 describes the first stages of the application of SADTI pulse sequence to real samples: these consisted of human tissue cultivated on porous polycaprolactone scaffolds; the goal of this study was to verify if SADTI can help in monitoring cell growth on artificial supports, by detecting changes in the diffusion pattern of a molecular probe of choice in which the specimen is immersed. These changes would reflect structural variations occurred within the cultivated scaffold, due to the cells infiltrating the pores and thus modifying the degree of restriction molecular diffusion is subject to. In order to provide the theoretical foundations to these studies, the concept and use of pulsed gradients in imaging and diffusion NMR, the description and measurement of molecular diffusion in free and restricted conditions, and the basic theory behind relaxation properties of the spin systems used, are presented in Chapter 1.