Final answer:
The medulla oblongata and the carotid body are the most likely integrators in the given model, controlling the breathing rate and heart rate as part of the brainstem's function.
Step-by-step explanation:
The components in the model that are most likely the integrators for the control of breathing would be the medulla oblongata and the carotid body. The medulla oblongata contains the dorsal respiratory group (DRG) and the ventral respiratory group (VRG) which are involved in maintaining and regulating the breathing rhythm. The carotid body acts as a sensor detecting blood concentrations of oxygen and relays this information to the respiratory centers in the medulla.
The diaphragm, on the other hand, acts as the primary muscle for respiration, and it represents the output of the control system rather than the integrator. The diaphragm contracts in response to signals from the respiratory centers, leading to inspiration, and relaxes for expiration.
The brainstem, which includes the medulla oblongata, plays a crucial role in several autonomic functions such as breathing and heart rate, making it an integral part of the control system for respiratory and cardiovascular regulation.