Final answer:
The reticular formation is the network within the brainstem responsible for filtering unnecessary sensory stimuli, although it's not directly described in the provided texts. The brainstem, including the thalamus and various nuclei, plays a central role in processing and relaying sensory and motor information.
Step-by-step explanation:
The network of nuclei and nerve fibers that extends the length of the brain stem and functions to filter unnecessary sensory stimuli is known as the reticular formation. This system is not specifically referenced in the provided excerpts, but it is important for the functions mentioned. The brainstem, which includes the midbrain, medulla oblongata, and the pons, connects the rest of the brain with the spinal cord and plays a critical role in motor and sensory signal relay, as well as visceral controls like heart rate and digestion. The thalamus, part of the diencephalon beside the brainstem, acts as a hub for sensory and motor information traveling to and from the cerebrum. It filters sensory information to the cerebral cortex and also influences what stimuli receive attention. Meanwhile, the nuclei in the brain stem, such as the solitary nucleus and dorsal motor nucleus of the vagus nerve, control vital visceral functions.