Modeling of diffusion based correlations between heart rate modulations and respiration pattern

The objective of this work is to lay the foundation for the understanding of oxygen dynamics in the lung during respiration, and this effect on pulmonary hemodynamics. We raised the following questions: What is the variation of the oxygen flow rate into pulmonary capillaries during the respiratory cycle? What is the tradeoff between maintaining a constant blood flow rate through the pulmonary system, and, maintaining a constant oxygen saturation level of the blood flowing through the pulmonary system? A three-stage model was developed. The first stage describes the distribution of gas volume in the various generations of the bronchial tree. The second stage describes the oxygen diffusion process from the pulmonary gas in the alveoli into the pulmonary capillaries. The third stage uses the results of the two previous stages to estimate: a) the dynamics of oxygen partial pressure (pO₂) in different lung generations as the respiratory cycle progresses, b) the changes in the overall volume of oxygen available to bind with the hemoglobin during different stages of the respiratory cycle, and c) how the changes in a and b can affect the heart rate. The model was tested under various respiration patterns (FRC, TV, rate).