Dynamic response of local pulmonary blood flow to alveolar gas tensions: Analysis

It has been reported that left lower lobe pulmonary blood flow (Q̇) and alveolar CO₂ decrease then oscillate in a progressively damped manner when the lobar inspirate is changed from pure O₂ to N₂. This damped oscillatory response of lobar Q̇ is abolished by maintaining lobar CO₂ constant. We set out to develop the simplest mathematical model that can simulate these experimental results by using techniques derived from control theory. Different models were tested. The simplest model that predicts the experimental data incorporates an exponential decrease of lobar Q̇ to local alveolar hypoxia (time constant 3 min) and a damped oscillatory response of lobar Q̇ to local alveolar hypocapnia. The response to hypocapnia has two components: a vasodilator effect possibly related to intracellular [H⁺] and a vasoconstrictor effect possibly related to changes of molar CO₂. Both these components (time constants of 4.8 min) interact with each other by cross-coupled elements (time constants of 4.8 min). This model can be used to forecast results so that its validity can be tested by experiment.