The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476-3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10(-6)) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost.

A numerical model based on the nonlinear, one-dimensional (1-D) equations of pressure and flow wave propagation in conduit arteries is tested against a well-defined experimental 1:1 replica of the human arterial tree. The tree consists of 37 silicone branches representing the largest central systemic arteries in the human, including the aorta, carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs. The set-up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow. Terminal branches end in simple resistance models, consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure. The parameters required by the numerical algorithm are directly measured in the in vitro set-up and no data fitting is involved. Comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1-D time-domain formulation to capture the main features of pulse wave propagation measured throughout the system test. As a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation, the experimental set-up generates waveforms at terminal branches with additional non-physiological oscillations. The frequencies of these oscillations are well captured by the 1-D model, even though amplitudes are overestimated. Adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect, suggesting that wall visco-elasticity might play an important role in the experimental results. Nevertheless, average relative root-mean-square errors between simulations and experimental waveforms are smaller than 4% for pressure and 19% for the flow at all 70 locations studied.

The study of wave propagation at different points in the arterial circulation may provide useful information regarding ventriculoarterial interactions. We describe a number of hemodynamic parameters in the carotid, brachial, and radial arteries of normal subjects by using noninvasive techniques and wave-intensity analysis (WIA). Twenty-one normal adult subjects (14 men and 7 women, mean age 44 ± 6 yr) underwent applanation tonometry and pulsed-wave Doppler studies of the right common carotid, brachial, and radial arteries. After ensemble averaging of the pressure and flow-velocity data, local hydraulic work was determined and a pressure-flow velocity loop was used to determine local wave speed. WIA was then applied to determine the magnitude, timings, and energies of individual waves. At all sites, forward-traveling (S) and backward-traveling (R) compression waves were observed in early systole. In mid- and late systole, forward-traveling expansion waves (X and D) were also seen. Wave speed was significantly higher in the brachial (6.97 ± 0.58 m/s) and radial (6.78 ± 0.62 m/s) arteries compared with the carotid artery (5.40 ± 0.34 m/s; P < 0.05). S-wave energy was greatest in the brachial artery (993.5 ± 87.8 mJ/m²), but R-wave energy was greatest in the radial artery (176.9 ± 19.9 mJ/m²). X-wave energy was significantly higher in the brachial and radial arteries (176.4 ± 32.7 and 163.2 ± 30.5 mJ/m², respectively) compared with the carotid artery (41.0 ± 9.4 mJ/m²; P < 0.001). WIA illustrates important differences in wave patterns between peripheral arteries and may provide a method for understanding ventriculo-arterial interactions in the time domain.