Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element windkessel models

Abstract

Aortic impedance data of infants, children and adults (age range 0.8-54 yr), previously reported by others, were interpreted by means of three alternative four-element windkessel models: W4P, W4S, and IVW. The W4P and W4S are derived from the three-element windkessel (W3) by connecting an inertance (L) in parallel or in series, respectively, with the aortic characteristic resistance (Rc). In the IVW, L is connected in series with a viscoelastic windkessel (VW). The W4S and IVW (same input impedance) fit the data best. The W4S, however, suffers from the assumption that Rc is part of total peripheral resistance (Rp). The IVW model offers a new paradigm for interpretation of resistive properties in terms of viscous (Rd) properties of vessel wall motion, distinguished from Rp. Results indicated that rapid reduction of Rd/Rp during early development is functional to modulation of decay time constant (taud) of pressure in diastole, such that normalization over heart period (taud/T) is independent of body size. Estimates of total arterial compliance (C) vs. age were fitted by a bell-shaped curve with a maximum at 33 yr. With body weight (BW) factored out by normalization, the C/BW data scattered about a bell-shaped curve centered at 66 mmHg. Inertance was significantly higher in pediatric patients than in adults, in accordance with a lower cross-sectional area of the vasculature, commensurate to a lower aortic flow. Changes of arterial properties appear functional to control the ratio of pulsatile power to active power and keep arterial efficiency as high as 97% in infants and children.

The arterial Windkessel

“…Other investigators have introduced an inertance in series with the characteristic impedance [4,5,7,25,32,57]. This series inertance does not affect the arterial input impedance at low frequencies but at high frequencies.…”

“…The four-element Windkessel has been used by Segers [51,[53][54][55] and Burattini [5]. In practice it turns out that the inertance is very difficult to estimate which is an argument to prefer the three-element Windkessel.…”

Downstream from the Heart Left Ventricle

“…A formal objection may arise as to the notation of the viscoelastic Windkessel (VW) used previously [15,18,27,30] for the viscoelastic variant of Frank's Windkessel. The VEMM notation, introduced here, appears more appropriate to avoid conceptual misunderstanding.…”

“…In an attempt to resolve this shortcoming by means of a model accounting for the viscous, beyond elastic, arterial response disregarded by Sharp et al [17], Burattini and Di Salvia [18] applied one other four-element structure derived from the VEMM by connecting L in series at the input (inertance viscoelastic minimal model, IVEMM, Figure 21.4). Consistently with the reasons set out in Section 21.2.1.1, the IVEMM denomination is introduced here to replace the IVW (inertance viscoelastic Windkessel) denomination used in previous works [18,41,44]. Because the input impedance of the IVEMM has the same generalized expression as that of the W4S (i.e., the ratio of two zeros to one pole), the two models produce identical data fit [18].…”

Using non invasive dynamic parameters of fluid responsiveness in children: there is still much to learn

“…This would negatively impact the accuracy of SVV to predict fluid responsiveness in children. Also, vascular compliance has been shown to be higher in children than in adults, which would again impact the relationship between PPV and SVV [10]. Finally, it is essential to measure changes in cardiac output in order to assess fluid responsiveness [3].…”