Time Domain Method to Identify Simultaneously Parameters of the Windkessel Model Applied to the Pulmonary Circulation

Abstract

Lumped models are frequently used to provide a satisfactory description of the hemodynamic properties of the pulmonary vasculature. The purpose of this study is to describe a method to identify simultaneously the parameters values of windkessel models components. The following equation was used to obtain R1 (characteristic resistance), R2 (peripheral resistance), C (total compliance) and L (inertance): [formula: see text] where ki are the following functions of L, R1, R2 and C: [formula: see text] To assess the accuracy of the method, estimates of R1, R2, and C were compared to characteristic impedance Rc, vascular resistance PVR and pulmonary arterial compliance Cd respectively computed from referenced methods. Comparison between R1 and Rc, PVR and R1 + R2, C and Cd were obtained in 5 anaesthetised pigs during basal conditions and after endotoxin-shock. The results indicate that in both conditions, comparisons evidenced highly significant correlations between values computed by the different approaches (p < 0.0001). Although our method yielded to consistently lower values than values provided by referenced methods, the results were concordant with respect to the expected response of pulmonary vasculature to endotoxin insult. We conclude that our method of identification is suitable for the assessment of lumped parameters windkessel model estimates. The main interest is that actual resistance and compliance values can be obtained easily and simultaneously by a global method approach.

Effective arterial elastance as an index of pulmonary vascular load

“…Systolic ejection interval (t s) was measured from the foot of the pulmonary arterial pressure wave to its incisura, and the diastolic interval was t d ϭ T Ϫ ts, where T is the cardiac length. Pairs of pressure and flow data for each beat were analyzed, and the three elements of the model were simultaneously calculated by using an original analytic procedure, as described previously (12).…”

“…1. The three elements of the model are calculated using an analytic procedure (12,14). Details of this analysis are provided in the APPENDIX.…”

“…Wave reflections play an important role and should be taken into account in pulmonary hypertension resulting from several pathological conditions, like pulmonary embolism and septic shock (1,2,5,14). In this way, the pulmonary arterial impedance spectrum, which is defined in the frequency domain, provides a more precise and complete description of the pulmonary vascular load (12,17). However, because of its complexity, this approach is difficult to use in clinical practice and to link with data obtained in the time domain.…”

Assessment of ventricular contractility and ventricular-arterial coupling with a model-based sensor

“…Moreover, using the pulmonary resistance (R pulin ) to characterize the RV afterload, there is no need to evaluate the arterial elastance using the parameters of the windkessel model, which has the main drawback of needing accurate pressure and flow waveforms [34] usually obtained via added manoeuvres and/or extensive signal conditioning. Equally, the windkessel model has its own limitation in representing an active, regulated non-linear system by a linear model.…”

Effects of U-46619 on Pulmonary Hemodynamics Before and After Administration of BM-573, a Novel Thromboxane A2 Inhibitor

“…Finally, an inductance L is added to allow positive phases angles between flow and pressure waves and accounts for the inertial properties of the blood and for the viscous resistive properties of the vessels wall (Grant & Paradowski, 1987). The four elements of the model were simultaneously identified by using an original analytic procedure previously described (Lambermont et al, 1998).…”