Final answer:
The peripheral parts of the diaphragm are innervated by the phrenic nerve, which originates from the cervical plexus at spinal cord levels C3 to C5, and controls the muscle contractions for breathing.
Step-by-step explanation:
The innervation to the peripheral parts of the diaphragm is primarily supplied by the phrenic nerve. The phrenic nerve, a systemic nerve from the cervical plexus, is connected to the spinal cord at cervical levels 3 to 5. It is responsible for the muscle contractions that drive ventilation, meaning the diaphragm's motor fibers which form part of the phrenic nerve allow for breathing. If these fibers are damaged below the mid-cervical level, ventilation can still occur, preventing spinal cord damage in this region from being immediately fatal.