Mathematical Model for the Quantification of Pulmonary and Intrapulmonary Arteriovenous Anastomoses Blood Flow

Abstract Background and Objectives: Accurately quantifying blood flow through a shunt vessel is vitally important, because shunt prevents gas exchange and can provide a pathway for emboli to bypass the pulmonary microcirculation. Some current techniques allow only an approximate estimate of the pulmonary shunt and present technical-evaluation difficulties that can compromise the result. To overcome the technical-evaluation problems and obtain an accurate detection of the pulmonary blood flow (Q p ) and intrapulmonary arteriovenous anastomoses (Q IPAVA ), it is necessary to find and isolate the fundamental parameters of gas exchange associated with chemical-physical laws that regulate them, develop a specific algebraic-analytical model and subsequently validate it by entering some experimental data. Methods: Elaboration of nine literal equations designed similarly to physics formulas of universal application. Some experimental data were entered to validate them. Results: Q p and Q IPAVA were detected at rest, moderate (50% of VO 2max ) and heavy exercise (≥90% of VO 2max ) both in normoxia (FIO 2 = 0.2093) and acute hypoxia (FIO 2 = 0.125). In normoxia under heavy exercise, Q p decreased slightly (97.56% of Q t ), and Q IPAVA represented 2.44% of Q t . Instead, in hypoxia at heavy exercise, Q p decreased significantly (85.25% of Q t ), and Q IPAVA increased significantly (14.75% of Q t ). It was possible to demonstrate a negative contribution of Q IPAVA directly to gas exchange efficiency and identify incorrect Q t measurements. Conclusions: These equations are precise and of universal application. They describe the real phenomenon of gas exchange for each individual. Q p differs significantly from Q t under some physiological conditions already in healthy subjects. The use of this model will allow research a general advance in the understanding of this critical biological function and in clinical practice a precise and early detection of the pathology.