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

Abstract

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 (Qp) and intrapulmonary arteriovenous anastomoses (QIPAVA), 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: Qp and QIPAVA were detected at rest, moderate (50% of VO2max) and heavy exercise (≥90% of VO2max) both in normoxia (FIO2= 0.2093) and acute hypoxia (FIO2= 0.125). In normoxia under heavy exercise, Qp decreased slightly (97.56% of Qt), and QIPAVA represented 2.44% of Qt. Instead, in hypoxia at heavy exercise, Qp decreased significantly (85.25% of Qt), and QIPAVA increased significantly (14.75% of Qt). It was possible to demonstrate a negative contribution of QIPAVA directly to gas exchange efficiency and identify incorrect Qt measurements. Conclusions: These equations are precise and of universal application. They describe the real phenomenon of gas exchange for each individual. Qp differs significantly from Qt 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.