The magnetic particle imaging (MPI) performance of collections of chains of magnetic nanoparticles with Néel and Brownian relaxation mechanisms was studied by carrying out simulations based on the Landau-Lifshitz-Gilbert equation and rotational Brownian dynamics, respectively. The effect of magnetic dipole-dipole interactions within chains on the time-domain average magnetic dipole moment and corresponding dynamic hysteresis loops, harmonic spectra, and point spread functions (PSFs) of the particle chains was evaluated. The results show that interactions within chains lead to 'square-like' dynamic hysteresis loops and enhanced MPI performance, compared to chains of non-interacting nanoparticles. For nanoparticles with the Brownian relaxation mechanism, subjected to a superimposed alternating and ramping magnetic field mimicking the magnetic field in MPI applications, we studied the dependence of x-space MPI performance of particle chains on parameters such as the amplitude of the alternating magnetic field, surface-to-surface separation between nanoparticles, solvent viscosity, and the number of nanoparticles in a chain. The results illustrate that magnetic dipole-dipole interactions within a chain contribute to enhanced MPI performance, and also suggest that there exist optimal values of the above parameters that lead to the best x-space MPI performance, i.e. maximum peak signal intensity and smallest full-width-at-half-maximum in PSFs.