Distance versus dispersion measure relations are constructed for Galactic radio pulsars in small solid angle intervals. The calculations are based on some basic criteria, as well as using the independent distance measurements of well examined pulsars for the first Galactic quadrant, including Galactic central directions. Values of average free electron density for these regions are derived from the fits to distance versus dispersion measure relations and checked for consistency and smoothness. The effects of plasma in the Galactic arms and within the central parts of the Galactic bulge region are also compared and discussed. Our adopted distances for the radio pulsars are compared with the ones given in some other models. Some basic results on distributions of the radio pulsars and the plasma are presented.