Computational models for the study of heart-lung interactions in mammals

The operation and regulation of the lungs and the heart are closely related. This is evident when examining the anatomy within the thorax cavity, in the brainstem and in the aortic and carotid arteries where chemoreceptors and baroreceptors, which provide feedback affecting the regulation of both organs, are concentrated. This is also evident in phenomena such as respiratory sinus arrhythmia where the heart rate increases during inspiration and decreases during expiration, in other types of synchronization between the heart and the lungs known as cardioventilatory coupling and in the association between heart failure and sleep apnea where breathing is interrupted periodically by periods of no-breathing. The full implication and physiological significance of the cardiorespiratory coupling under normal, pathological, or extreme physiological conditions are still unknown and are subject to ongoing investigation both experimentally and theoretically using mathematical models. This article reviews mathematical models that take heart-lung interactions into account. The main ideas behind low dimensional, phenomenological models for the study of the heart-lung synchronization and sleep apnea are described first. Higher dimensions, physiology-based models are described next. These models can vary widely in detail and scope and are characterized by the way the heart-lung interaction is taken into account: via gas exchange, via the central nervous system, via the mechanical interactions, and via time delays. The article emphasizes the need for the integration of the different sources of heart-lung coupling as well as the different mathematical approaches.