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There are four respiratory centres in the brain stem. Two of which are medullary centres (so called because they are situated in the medulla). These are the expiratory centre and the inspiratory centre, which together are called the respiratory rhythm centre.
The Apneustic centre is responsible for additional stimulation of the inspiratory centre. It acts to make inspiration longer, decreasing the respiratory rate.
The pneumotaxic centre has the exact opposite effect and inhibits the inspiratory centre, increasing the respiratory rate, and decreasing tidal volume.
The aortic bodies are present along the aortic arch. These detect a decrease in arterial pO2, increase in arterial CO2, and decrease in arterial pH. If they detect any one of these changes, they stimulate the medullary inspiratory centre to increase the respiratory rate.