Final answer:
The vestibular nuclei in the medulla receive impulses from the inner ear's equilibrium apparatus and are key to maintaining balance by influencing the muscle tone of postural muscles.
Step-by-step explanation:
The important nuclei of the indirect (multineural) system that receive impulses from the equilibrium apparatus of the inner ear and assist in maintaining balance by regulating the muscle tone of postural muscles are the vestibular nuclei. These nuclei are located in the medulla and play a crucial role in the processing of equilibrium information. When the vestibular system, which includes the utricle, saccule, and semicircular canals, detects head movement, it sends signals via the vestibulocochlear nerve (CN VIII) to the vestibular nuclei. From there, neurons project axons to various targets, including the spinal cord, to initiate reflexes involved in maintaining posture and balance. Additionally, connections between the vestibular nuclei and the oculomotor, trochlear, and abducens nuclei underpin the vestibulo-ocular reflex (VOR), which serves to stabilize visual images during movement.