Vinod Suresh Joseph C. Anderson James B. Grotberg Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109 Ronald B. Hirschl Department of Surgery, University of Michigan, Ann Arbor, MI 48109 A Mathematical Model of Alveolar Gas Exchange in Partial Liquid Ventilation In partial liquid ventilation (PLV), perfluorocarbon (PFC) acts as a diffusion barrier to gas transport in the alveolar space since the diffusivities of oxygen and carbon dioxide in this medium are four orders of magnitude lower than in air. Therefore convection in the PFC layer resulting from the oscillatory motions of the alveolar sac during ventilation can significantly affect gas transport. For example, a typical value of the Pe ´clet number in air ventilation is Pe;0.01, whereas in PLV it is Pe;20. To study the importance of convection, a single terminal alveolar sac is modeled as an oscillating spherical shell with gas, PFC, tissue and capillary blood compartments. Differential equations describ- ing mass conservation within each compartment are derived and solved to obtain time periodic partial pressures. Significant partial pressure gradients in the PFC layer and partial pressure differences between the capillary and gas compartments ~ P C -P g ! are found to exist. Because Pe@1, temporal phase differences are found to exist between P C -P g and the ventilatory cycle that cannot be adequately described by existing non- convective models of gas exchange in PLV. The mass transfer rate is nearly constant throughout the breath when Pe@1, but when Pe!1 nearly 100% of the transport occurs during inspiration. A range of respiratory rates (RR), including those relevant to high frequency oscillation (HFO)1PLV, tidal volumes ~ V T ! and perfusion rates are studied to determine the effect of heterogeneous distributions of ventilation and perfusion on gas exchange. The largest changes in P C O 2 and P C CO 2 occur at normal and low perfusion rates respectively as RR and V T are varied. At a given ventilation rate, a low RR-high V T combination results in higher P C O 2 , lower P C CO 2 and lower ~ P C -P g ! than a high RR-low V T one. @DOI: 10.1115/1.1835352# Keywords: Partial Liquid Ventilation, Liquid Breathing, Perfluorocarbon, Gas Ex- change, Convection 1 Introduction Liquid breathing in mammals using perfluorocarbon ~PFC! was first demonstrated by Clark and Gollan @1#. Since then the concept has led to the development of partial liquid ventilation ~PLV! as a promising alternative to conventional mechanical gas ventilation ~GV! for treating acute respiratory distress syndrome ~ARDS! and acute lung injury ~ALI!. Studies on animal models @2–6# and human trials @7–11# have indicated improvement in gas exchange and lung compliance associated with the use of PLV. Recent studies have examined the effects of PLV on regional ventilation ( V ˙ A ) and blood flow ( Q ˙ ) distribution in the lung in order to understand the mechanisms behind the global changes in gas exchange and lung mechanics. PFC was found to be predomi- nantly distributed in the dependent regions of injured adult sheep lungs undergoing PLV and more gas than PFC was found to be present in the nondependent regions of the lung @6#. Redistribution of blood flow from the dependent to the nondependent regions of the lung was observed during PLV in lambs @12# and pigs @13#. Ventilation-perfusion ( V ˙ A / Q ˙ ) inhomogeneity was found to be higher during PLV compared to GV in healthy piglets @14#. Sig- nificant regions with low V ˙ A / Q ˙ ratios were observed in rabbits with acute lung injury during PLV @15#. Harris et al. @16# com- pared regional distributions of ventilation, blood flow, and ventilation-perfusion ratio in the normal lung of a sheep during PLV and GV. They found that both ventilation and perfusion are shifted from the dependent regions to the nondependent regions of the lung in PLV, leading to a wide distribution of V ˙ A / Q ˙ in differ- ent regions of the lung. In contrast V ˙ A / Q ˙ ratios were close to unity over most of the lung in GV. In order to understand the mechanisms responsible for improved gas exchange in PLV, it is crucial to determine the contribution to gas exchange of regions whose V ˙ A , Q ˙ , and V ˙ A / Q ˙ differ significantly from their normal values in GV. Previous animal studies indicated enhanced arterial-alveolar ( a - A ) partial pressure gradients in PLV as a result of increased shunt fraction and ventilation-perfusion heterogeneity @14#. Van- Lo ¨bensels et al. developed a mathematical model of gas exchange during PLV in lung subunits with a PFC layer that indicated a diffusion limitation could lead to significant ( a - A ) gradients @17#. However they only considered diffusion of respiratory gases through a stagnant layer of PFC in an alveolar sac. In reality the expansion and contraction of the sac during tidal ventilation cre- ates a flow field within the PFC layer contained inside. The im- portance of convective effects on transport can be estimated through the Pe ´clet number, Pe52 p fR 2 / D, where f is the breath- ing frequency in breaths/second, R is the sac radius, and D is the gas diffusivity in the alveolar medium ~air in GV, PFC, in PLV!. Values of Pe@1 indicate that convection plays a significant role in transport while values of Pe!1 indicate that diffusion is the domi- nant transport mechanism. At normal respiratory rates, Pe ;10 23 – 10 22 in GV while it is on the order of 15–50 in PLV. This is a result of the small diffusivities of O 2 and CO 2 in PFC, which are 1000–10,000 times smaller than in air. Thus convective effects play an important role in the transport of respiratory gases Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Divi- sion December 1, 2003; revision received September 8, 2004. Associate Editor: James Moore. 46 Õ Vol. 127, FEBRUARY 2005 Copyright © 2005 by ASME Transactions of the ASME