Mathematical Analysis and Digital Simulation of the Respiratory Control System

A numerical simulation of the lung-blood-brain-tissue gas transport and exchange system. The basic material balance relationships are expressed in set of differential-difference equations containing a number of dependent time delays based on blood flow rate and vascular capacity. Other equations define the chemical details of transport and acid-base buffering, concentration equilibria, and blood flow behavior. A control function is given defining the dependence of ventilation on hydrogen ion concentration in the cerebrospinal fluid and oxygen content at the carotid chemoceptors. A 500-statement FORTRAN program simulates the responses of the system to a variety of forcings, including carbon dioxide inhalation, hypoxia at sea level, altitude hypoxia, and metabolic disturbances in acid-base balance. Both dynamic and steady-state behavior were reasonably realistic. About one minute machine time on a CDC 3400 computer was required for every four minutes of simulation. To the authors' knowledge, this is the first digital solution of a set of differential-difference equations whose time delays are themselves dependent variables.