Model-based analysis of mechanisms responsible for sleep-induced carbon dioxide differences

• Published in: Bulletin of mathematical biology 2006-02, Vol.68 (2), p.315-341
• Main Authors: Aittokallio, T, Gyllenberg, M, Polo, O, Toivonen, J, Virkki, A
• Format: Article
• Language: English
• Subjects: Algorithms; Carbon Dioxide - metabolism; Diffusion; Female; Hemoglobins - metabolism; Humans; Kinetics; Lung - metabolism; Mathematical models; Models, Biological; Postmenopause - metabolism; Postmenopause - physiology; Premenopause - metabolism; Premenopause - physiology; Pulmonary Ventilation - physiology; Regional Blood Flow - physiology; Sleep - physiology; Studies
• ISSN: 0092-8240; 1522-9602
• DOI: 10.1007/s11538-005-9059-3

This work describes a comprehensive mathematical model of the human respiratory control system which incorporates the central mechanisms for predicting sleep-induced changes in chemical regulation of ventilation. The model integrates four individual compartments for gas storage and exchange, namely alveolar air, pulmonary blood, tissue capillary blood, body tissues, and gas transport between them. An essential mechanism in the carbon dioxide transport is its dissociation into bicarbonate and acid, where a buffering mechanism through hemoglobin is used to prevent harmfully low pH levels. In the current model, we assume high oxygen levels and consider intracellular hydrogen ion concentration as the principal respiratory control variable. The resulting system of delayed differential equations is solved numerically. With an appropriate choice of key parameters, such as velocity of blood flow and gain of a non-linear controller function, the model provides steady-state results consistent with our experimental observations measured in subjects across sleep onset. Dynamic predictions from the model give new insights into the behaviour of the system in subjects with different buffering capacities and suggest novel hypotheses for future experimental and clinical studies.