Modeling of pulmonary hemodynamics

The pulmonary circulation poses special problems with respect to modeling and understanding its functional hemodynamic behavior. A variety of models have been proposed to elucidate its functional behavior drawing on the analogy of electric transmission lines. Circulatory components that have been proposed include not only linear time invariant but also time variant and nonlinear elements [1]. Since the pulmonary circulation is a low pressure system respiration has an important effect on its hemodynamics. Consequently, respiration has to be taken into accounted when attempting to predict pulmonary hemodynamics. Most models of circulatory dynamics rely on phasor methods which provide useful parameters such as characteristic impedance and compliance. However, these models can describe only the pulmonary circulation during specific phases of the respiratory cycle [2], due to the fact that the driving frequency of the system is considered to be the heart rate. Perturbations due to respiration, which usually occur at a significantly lower frequency, are regarded as noise or as a trend. While the pulmonary circulation may be considered as a system in quasi steady state oscillations, it is subjected to asynchronous pressure pulsations due to cardiodynamics and respiration. As a result phasor based models are inapplicable throughout the respiratory cycle. System parameters that are obtained using these models are inaccurate if respiration effects are ignored and may lead to misinterpretation of its behavior. To gain a better understanding of the pulmonary circulation we propose to model the pulmonary circulation, including respiratory effects, with an hydraulic analog throughout the respiratory cycle. The model is tested on the canine pulmonary circulation under anesthetized open chest conditions. The lumped parameter model proposed here consists of a single compartment. The airway pressure and the right ventricle are considered as two independent power sources. Since the system is connected to two sources of different driving frequencies and the right ventricle is connected via the pulmonary valve the dynamic action of the valve must also be included.