Frank's Windkessel model described the hemodynamics of the arterial system in terms of resistance and compliance. It explained aortic pressure decay in diastole, but fell short in systole. Therefore characteristic impedance was introduced as a third element of the Windkessel model. Characteristic impedance links the lumped Windkessel to transmission phenomena (e.g., wave travel). Windkessels are used as hydraulic load for isolated hearts and in studies of the entire circulation. Furthermore, they are used to estimate total arterial compliance from pressure and flow; several of these methods are reviewed. Windkessels describe the general features of the input impedance, with physiologically interpretable parameters. Since it is a lumped model it is not suitable for the assessment of spatially distributed phenomena and aspects of wave travel, but it is a simple and fairly accurate approximation of ventricular afterload.

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Right ventricular (RV) afterload is commonly defined as pulmonary vascular resistance, but this does not reflect the afterload to pulsatile flow. The purpose of this study was to quantify RV afterload more completely in patients with and without pulmonary hypertension (PH) using a three-element windkessel model. The model consists of peripheral resistance (R), pulmonary arterial compliance (C), and characteristic impedance (Z). Using pulmonary artery pressure from right-heart catheterization and pulmonary artery flow from MRI velocity quantification, we estimated the windkessel parameters in patients with chronic thromboembolic PH (CTEPH; n = 10) and idiopathic pulmonary arterial hypertension (IPAH; n = 9). Patients suspected of PH but in whom PH was not found served as controls (NONPH; n = 10). R and Z were significantly lower and C significantly higher in the NONPH group than in both the CTEPH and IPAH groups (P < 0.001). R and Z were significantly lower in the CTEPH group than in the IPAH group (P < 0.05). The parameters R and C of all patients obeyed the relationship C = 0.75/R (R(2) = 0.77), equivalent to a similar RC time in all patients. Mean pulmonary artery pressure P and C fitted well to C = 69.7/P (i.e., similar pressure dependence in all patients). Our results show that differences in RV afterload among groups with different forms of PH can be quantified with a windkessel model. Furthermore, the data suggest that the RC time and the elastic properties of the large pulmonary arteries remain unchanged in PH.

During therapy for PH, R and C remain inversely related. Therefore, changes in both R and C better explain changes in cardiac index than either of them alone. Not only resistance but also compliance plays a prominent role in PH especially in an early stage of the disease.

Purpose:To investigate whether an existing method for correction of phase offset errors in phase-contrast velocity quantification is applicable for assessment of main pulmonary artery flow with an MR scanner equipped with a highpower gradient system. Materials and Methods:The correction method consists of fitting a surface through the time average of stationary pixels of velocity-encoded phase images, and subtracting this surface from the velocity images. Pixels are regarded as stationary if their time standard deviation falls into the lowest percentile. Flow was measured in the main pulmonary artery of 15 subjects. Each measurement was repeated on a stationary phantom. The phase offset error in the phantom was used as a reference. Correction was applied with varying polynomial surface orders (0 -5) and stationarity percentiles (5-50%). The optimal surface order and stationarity percentile were determined by comparing the fitted surface with the phantom.Results: Using a first-order surface and a (noncritical) 25% percentile, the correction method significantly reduced the phase offset error from 1.1 to 0.35 cm/second (RMS), which is equivalent to a reduction from 11% to 3.3% of mean volume flow. Phase error correction strongly affected stroke volume (range -11 to 26%). Conclusion:The method significantly reduces phase offset errors in pulmonary artery flow.Key Words: phase-contrast velocity quantification; phase offset error; phase error correction; eddy-current-induced fields; stroke volume; pulmonary blood flow J. Magn. Reson. Imaging 2005;22:73-79.