Three- and four-element Windkessel models: Assessment of their fitting performance in a large cohort of healthy middle-aged individuals

Abstract

Lumped-parameter models are used to estimate the global arterial properties by fitting the model to measured (aortic) pressure and flow. Different model configurations coexist, and it is still an open question as to which model optimally reflects the arterial tree and leads to correct estimates of arterial properties. An assessment was made of the performance of (a) the three-element Windkessel model (WK3) consisting of vascular resistance R, total arterial compliance C, and characteristic impedance Z_c; (b) a four-element model with an inertance element L placed in parallel with Z_c (WK4-p); and (c) a four-element model with L placed in series with Z_c (WK4-s). Models were fitted to data measured non-invasively in 2404 healthy subjects, aged between 35 and 55 years. It was found that model performance segregated into two groups. In a group containing 20 per cent of the dataset (characterized by low blood pressure and wave reflection) the WK4-p model outperformed the other models, with model behaviour as envisioned by its promoters. In these cases, the WK3 and WK4-s models led to increased overestimation of total arterial compliance and underestimation of characteristic impedance. However, in about 80 per cent of the cases, the WK4-p model showed a behaviour that was very similar to that of the WK3 and WK4-s models. Here, the WK4-s model yielded the best quality of fit, although model parameters reached physically impossible values for L in about 12 per cent of all cases. The debate about which lumped-parameter model is the better approximation of the arterial tree is therefore still not fully resolved.