Mathematical Modeling to Understand Plausible Explanations of Hypoxemia in Early COVID-19

ABSTRACT

Rationale The disease caused by the novel coronavirus (COVID-19) can cause severe hypoxemia even at early stages of disease progression, in some cases without dyspnea or extensive loss of aeration. Early reports and case studies generated several theorized mechanisms of pathophysiological alterations. In this study, we used a mathematical model to investigate the relative effects of lung perfusion abnormalities suspected to produce hypoxemia in early COVID-19 (1) intrapulmonary shunt resulting from vascular dysregulation and virus-related alterations to hypoxic pulmonary vasoconstriction, (2) perfusion defects resulting from thrombosis-mediated microembolism, and (3) venous admixture resulting from ventilation-perfusion mismatching throughout the noninjured lung. Our goal was to quantitatively assess whether the proposed mechanisms of hypoxemia in early COVID-19 are physiologically plausible, particularly in terms of how sensitive oxygenation is to each type of alteration. Materials & Methods: A twelve-compartment mathematical model of the lungs was designed to represent distributed ventilation and perfusion in various lung regions partitioned according to aerated vs. injured status, presence or absence of perfusion defect, and three different height levels. Regional vascular resistance was determined for each compartment, followed by calculation of end-capillary oxygen content. Mixed arterial oxygen content was computed by a perfusion-weighted average of compartmental oxygen contents. Arterial oxygen tension and overall shunt fraction for each scenario were then compared to clinical observations from early reports of COVID-19 patients. Results: In the absence of perfusion defects as well as ventilation-perfusion mismatching throughout the noninjured lung, severe hypoxemia resulting from vascular dysregulation alone required not just impairment of hypoxic pulmonary vasoconstrication, but rather extreme vasodilation in the small region of nonaerated lung (70% reduced vascular resistance). Combined with thrombosis-mediated perfusion defects affecting up to 50% of the normally aerated regions, the requirement for vasodilation in the nonaerated regions was reduced. Finally, accounting for moderate levels of venous admixture resulting from ventilationperfusion mismatching throughout the aerated lung (e.g., due to suboptimal perfusion redistribution), required no vasodilation and only moderate extent of perfusion defect. Conclusion: Evidence for each of the lung perfusion abnormalities investigated in this study can be found in the rapidly evolving body of literature emerging from the COVID-19 pandemic. Individually, our model predicts extreme alterations required for any single mechanism to fully explain observations of severe hypoxemia despite minimal lung involvement at early stages of the disease. By contrast, hypoxemia in early COVID-19 may be explained by relatively small alterations in multiple contributing factors.