Linearity of Pulsatile Pressure-Flow Relations in the Embryonic Chick Vascular System

Abstract

The calculation and modeling of vascular input impedance are based on the assumption that pressure and flow are linearly related in the frequency domain. However, this assumption has not been proven for the embryonic circulation. Therefore, we investigated the linearity of pulsatile pressure-flow relations in vivo with acute alterations in cycle length. We simultaneously measured dorsal aortic pressure with a servonull system and flow velocity with a 20-MHz pulsed-Doppler system in stage 24 chick embryos (n=38). Cycle length was acutely altered using thermal probe(s) applied to the sinus venosus. We determined the impedance spectra at several cycle lengths for each embryo and a reference curve from a three-element Windkessel model with the use of nonlinear curve fitting. We then assessed the scatter of experimental impedance along the reference curve as a measure of linearity in the frequency domain. We found that mean vascular resistance did not change after thermal probe applications ( P >.20 for each), indicating that acute alterations in cycle length did not alter peripheral vascular properties. Superpositioned impedance spectra showed minimal scatter along the model impedance from 0 to 6 Hz. Goodness of fit values ( R 2 ) were near unity (.94 to .97) and were similar for all interventions ( P >.07 for Fisher's z , by F test). Above 6 Hz, both modulus and phase spectra exhibited significant scatter ( P <.05, by F test). Experimental impedance spectra tended to have a fluctuation and a phase-zero crossover, indicating significant wave reflection in the embryonic circulation. Thus, the embryonic vascular system can be approximated as a linear system from 0 to 6 Hz, the range in which the majority (96.0±0.18%) of hydraulic energy is dissipated.