Combining respiratory regulation with breathing mechanism: Application to Cheyne-Stokes Respiration

Mathematical modeling approaches for the respiratory system are done on different abstraction/subsystem levels, depending upon the hypothesis and assumptions. Differential equations are used to describe dynamics of such systems. In the literature, various types of models are available. For example, some models describe the regulation of gases, on the other hand, some models link mouth pressure and air flow. Each of these models are complete for that particular subsystem, considering other subsystems of the body are at steady state. However, there are certain deviations, when a problem related to one subsystem is manifested in other subsystems. Cheyne-Stokes Respiration is one of such condition, which might generate from congestive heart failure or obstructive sleep apnea or central sleep apnea and it is reflected in waxing and waning of the tidal volume, possibly with the presence of apnea and hypopnea. These types of breathing patterns are caused by malfunction of the regulation system or cardiovascular system or neural system. In this work, combining models of the regulation system, breathing mechanism and neural system are considered. Using modulation hypothesis, the combined model is capable of generating Cheyne-Stokes Respiration waveforms. A new parameter, similar to modulation index is introduced to achieve different levels of apnea and hypopnea, which can quantify the diseased condition.