Abstract 17947: Mathematical Model of Cheyne-Stokes Respirations as an Educational Tool for Understanding Cardiorespiratory Interactions in Heart Failure

Abstract

Background: Patients with heart failure often develop Cheyne-Stokes Respirations (CSR): a breathing pattern characterized by alternating periods of hyperventilation and apnea. The cardio-respiratory interactions that result in CSR are complex and often difficult to understand for students learning cardiovascular physiology. Aims: We developed a mathematical model of CSR where cardiac output (CO), respiratory rate (RR) and arterial CO 2 (pCO 2 ) can be manipulated to evaluate how periodic fluctuations in different physiological variables develop, thus providing a deeper understanding of cardiorespiratory interactions in heart failure. Methods: Our model consisted of 3 coupled differential equations. (1) pCO 2 is directly proportional to metabolic CO 2 production and inversely proportional to alveolar ventilation (V A ). V A depends on RR, alveolar volume, and CO, with the interaction between CO and ventilation calculated by combining Fick’s principle and the Alveolar Gas Equation. (2) Changes in RR are modeled as a Hill function dependent on pCO 2 . (3) Finally, CO depends on pCO 2 , arterial O 2, and RR. The model was propagated forward in time using Euler’s method. A graphical user interface allows users to easily manipulate variables and observe heart lung interactions. Results: Initial values for RR, CO, and PCO 2 resulting in stable, aperiodic breathing were 10 breaths/min, 6 L/Min, and 40 mmHg, respectively. Perturbing any of these values resulted in periodic fluctuations in RR, CO, and pCO 2 (Figure 1). A key insight of the model is that progressive decreases in CO induce more prominent oscillations in RR and pCO 2 and that pCO 2 directly influences CO. Conclusions: Our mathematical model of cardio-respiratory interactions allows users to easily manipulate physiological variables to graphically visualize how changes in CO and respiratory function give rise to CSR. This may enable students to obtain a deeper understanding of cardiovascular physiology.