Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements.

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.

Long-term pressure monitoring with arterial applanation tonometry: a non-invasive alternative during clinical intervention?

Arterial tonometry is a non-invasive technique for continuous registration of arterial pressure waveforms. This study aims to assess tonometric blood pressure recording (TBP) as an alternative for invasive long-term bedside monitoring. A prospective study was set up where patients undergoing neurosurgical intervention were subjected to both invasive (IBP) and non-invasive (TBP) blood pressure monitoring during the entire procedure. A single-element tonometric pressure transducer was used to better investigate different inherent error sources of TBP measurement. A total of 5.7 hours of combined IBP and TBP were recorded from three patients. Although TBP performed fairly well as an alternative for IBP in steady state scenarios and some short-term variations, it could not detect relevant long-term pressure variations at all times. These findings are discussed in comparison to existing work. Physiological alterations at the site of TBP measurement are highlighted as a potentially important source of artifacts. It is concluded that at this point arterial tonometry remains not enough understood for long-term use during a delicate operative procedure. Physiological changes at the TBP measurement site deserve further investigation before tonometry technology is to be considered as an non-invasive alternative for long-term clinical monitoring.

Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements.

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.

Influence of zero flow pressure on fractional flow reserve.

Fractional flow reserve (FFR) is a commonly used index to assess the functional severity of a coronary artery stenosis. It is conventionally calculated as the ratio of the pressure distal (Pd) and proximal (Pa) to the stenosis (FFR= Pd/Pa). We hypothesize that the presence of a zero flow pressure (Pzf), requires a modification of this equation. Using a dynamic hydraulic bench model of the coronary circulation, which allows one to incorporate an adjustable Pzf, we studied the relation between pressure-derived FFR = Pdo/Pa, flow-derived true FFRQ = Qs/QN (= ratio of flow through a stenosed vessel to flow through a normal vessel), and the corrected pressure-derived FFRc = (Pd-Pzf)/(Pa-Pzf) under physiological aortic pressures (70 mmHg, 90 mmHg, and 110 mmHg). Imposed Pzf values varied between 0 mmHg and 30 mmHg. FFRc was in good agreement with FFRQ, whereas FFR consistently overestimated FFRQ. This overestimation increased when Pzf increased, or when Pa decreased, and could be as high as 56% (Pzf=30 mmHg and Pa =70 mmHg). According to our experimental study, calculating the corrected FFRC instead of FFR, if Pzf is known, provides a physiologically more accurate evaluation of the functional severity of a coronary artery stenosis.