Opioid-induced respiratory depression: a mathematical model for fentanyl

In this paper, respiratory depressant effects of fentanyl are described quantitatively by a mathematical model. The model is an extension of a previous one, which reproduces the human ventilatory control system on a physiological basis. It includes the following: three compartments for gas storage and exchange (lungs, body tissue, and brain tissue); the main mechanisms involved in ventilation control (peripheral chemoreceptors, central chemoreceptors, and the central hypoxic depression); and local blood flow regulation. The effects of fentanyl on the respiratory system include a decrease in peripheral and central chemoreceptor gains on ventilation and a direct inhibition of respiratory neural activity. All parameters in the model were chosen according to the literature. The model is able to reproduce the ventilatory effects of fentanyl in several conditions: 1) constant levels of fentanyl; 2) after a bolus injection; 3) at fixed levels of P_ETCO2; and 4) after artificial ventilation. According to the model, in spontaneously breathing subjects, minute ventilation depends on two opposing actions: fentanyl inhibitory influences, which depress ventilation, reducing oxygen tension and increasing CO₂ tension, and the consequent activation of chemoreceptors, which stimulates ventilation. Simulations of anesthetized patients resuming spontaneous breathing after artificial ventilation demonstrate the risk of prolonged apnea and tissue hypoxemia. A safe transition can be achieved by increasing patient PCO₂ toward the end of artificial ventilation, because an advanced chemoreceptor stimulation is produced, which promptly counteracts fentanyl-induced inhibition at cessation of artificial ventilation.