Final answer:
The neuronal circuit that enables us to continue breathing while asleep is a reflex circuit, controlled by the respiratory centers in the brainstem, particularly the pneumotaxic center in the pons.
Step-by-step explanation:
The type of neuronal circuit that ensures we continue to breathe while asleep is a reflex circuit. Unconscious control of breathing is generally governed by the respiratory centers in the medulla and pons of the brainstem, which operate automatically without the need for cognitive thought. Specifically, the pneumotaxic center, a network of neurons within the pons, plays a crucial role by inhibiting the activity of the neurons in the dorsal respiratory group (DRG), ultimately controlling the rate of breathing during quiet breathing, or eupnea
This is a key component of the autonomic nervous system, which remains active even during unconscious states like sleep.