Abstract 45: A Mathematical Model of Ventilation, Perfusion, and Oxygenation in Low-Flow States

Abstract

Background: Recent investigations underscore the critical importance of ventilation strategies on resuscitation outcomes. In low perfusion states, such as cardiac arrest and traumatic shock, the rise in intrathoracic pressure that accompanies positive-pressure ventilation (PPV) can significantly impede venous return and lead to a decrease in cardiac output. The optimal ventilation strategy in these “low-flow” states remains unclear. Objectives: To create a mathematical model of perfusion and oxygenation to predict the effects of PPV with both normotension and hypotension. Methods: The lung pressure-volume relationship was modeled using a novel formula allowing manipulation of various lung characteristics, including vital capacity, compliance, and the upper and lower inflection points. A separate formula was then derived to predict mean intrathoracic pressure for a given minute ventilation using the pressure-volume formula. The addition of positive end-expiratory pressure was also modeled. Finally, a formula was derived to model oxygen absorbance as a function of alveolar surface area and flow based on ventilation rate and mean intrathoracic pressure. Results: Mathematical models of the lung pressure-volume relationship, mean intrathoracic pressure, and absorbance were successfully derived. Manipulation of vital capacity, compliance, upper and lower inflection points, positive end-expiratory pressure, and minute ventilation allowed prediction of optimal ventilation rate and tidal volume for a normal and an ARDS lung. For a normal lung, optimal values for both mean intrathoracic pressure and absorption were achieved with a ventilation rate of 4 breaths/min. A decrease in the upper inflection point or increase in minute ventilation resulted in faster optimal ventilation rates, although none exceeded 14 breaths/min. Conclusions: A mathematical model of ventilation was successfully created allowing manipulation of multiple variables related to lung compliance and ventilation strategy. This model suggests the use of lower ventilation rates with larger tidal volumes to minimize the hemodynamic effects of PPV and maximize oxygen absorbance.