Mathematical Models of Cheyne-Stokes Breathing in understanding Cardiovascular and Respiratory Disorders

The interaction between the cardiovascular system and the respiratory system is complicated and may be used for the rehabilitation of the carotid artery disease. Periodic breathing is an unusual form of breathing with oscillations in minute ventilations and with repetitive apneas or near apneas. Cheyne-Stokes like breathing during sleep may be associated with obstructive sleep apnea (OSA) in some individuals. Therefore, it was reasoned that stroke patients with periodic breathing in sleep would be susceptible to OSA and for this purpose a mathematical model is established. The basic material is the balance relationships for the lung-blood-tissue gas transport and exchange system have been expressed in a number of dependent time delays. Additional equations were written to define the chemical details of transport and acid-base buffering, concentration equilibria, and blood flow behavior. The result is simulated analytically and compared with the experimental observations. This work may suggest that a proper directed respiration exercise can be used in the treatment of carotid artery disease.