olfactory nerve. n. Any of numerous olfactory filaments in the olfactory portion of the nasal mucosa that enter the olfactory bulb, where they terminate in synaptic contact with mitral cells, tufted cells, and granule cells. Also called first cranial nerve.he fibers pass into the skull and form synapses with the dendrites of the mitral cells. The area in which the olfactory nerves arise is situated in the most superior part of the mucous membrane that covers the superior nasal concha.