The activity of the diaphragm and external intercostal muscles is regulated by the in the brain.

The answer is medulla and pons. There is a respiratory center in both regions of the brain stem. The dorsal and ventral respiratory groups of nerves emanate from medulla while the pontine respiratory group from the pons.
The dorsal and ventral respiratory groups stimulate the intercoastal and phrenic nerves of the diaphragm. The pontine regulate the rhythm and depth of breath