Effects of friction and nonlinearities on the separation of arterial waves into their forward and backward components

A computational study of pressure wave reflections in the pulmonary arteries

Experiments using wave intensity analysis suggest that the pulmonary circulation in sheep and dogs is characterized by negative or open-end type wave reflections, that reduce the systolic pressure. Since the pulmonary physiology is similar in most mammals, including humans, we test and verify this hypothesis by using a subject specific one-dimensional model of the human pulmonary circulation and a conventional wave intensity analysis. Using the simulated pressure and velocity, we also analyse the performance of the P-U loop and sum of squares techniques for estimating the local pulse wave velocity in the pulmonary arteries, and then analyse the effects of these methods on linear wave separation in the main pulmonary artery. P-U loops are found to provide much better estimates than the sum of squares technique at proximal locations, but both techniques accumulate progressive error at distal locations away from heart, particularly near junctions. The pulse wave velocity estimated using the sum of squares method also gives rise to an artificial early systolic backward compression wave. Finally, we study the influence of three types of pulmonary hypertension viz. pulmonary arterial hypertension, chronic thromboembolic pulmonary hypertension and pulmonary hypertension associated with hypoxic lung disease. Simulating these conditions by changing the relevant parameters in the model and then applying the wave intensity analysis, we observe that for each group the early systolic backward decompression wave reflected from proximal junctions is maintained, whilst the initial forward compression and the late systolic backward compression waves amplify with increasing pathology and contribute significantly to increases in systolic pressure.

Validity of the local nonlinear arterial flow theory: influence of the upstream and downstream conditions

The "local flow" theory provides a simple way to take into account the nonlinear convective terms associated with blood flow in large arteries. The assumption that blood velocity profiles vary slowly with the longitudinal coordinate allows a simple nonlinear resolution via a mathematical approximation. Although validated in vitro by its authors, this theory still needs to be verified in accordance with the range of variation of the hemodynamical parameters. This constitutes the aim of this work where we assess the validity of two models issued from this theory: the "direct model" using the pressure-gradient as an input for the calculations and the "indirect model" using the centre-line velocity. The assessment of these models is made by comparing their solutions to those of the linear theory using numerical simulations. Our main conclusion is that the indirect model has a wide range of validity while the direct one fails in the presence of a strong reflected wave.

Separation of haemodynamic flow waves measured by MR into forward and backward propagating components

Physiological information on the action of the heart and on the reflection sites in the arterial system can be derived respectively from the forward and the backward propagating pressure or flow wave components. Earlier work on the separation of these components was exclusively based on invasive measurements of pressure or flow. In this study magnetic resonance (MR), which is a non-invasive imaging technique, was used to measure the blood flow waveform simultaneously at multiple positions along a vessel. Linear one dimensional transmission-line theory was used to separate the flow waves into forward and backward propagating components. First results, obtained from the thoracic aorta of five healthy male volunteers, consistently showed a negative reflection with a delay of about 100 ms between the foot of the forward and the foot of the backward propagating flow wave. Our model, consisting of a single vessel segment with constant diameter and wall properties, was validated by the excellent agreement between the vessel area as calculated from the flow data using the law of mass conservation and as directly measured with a different independent MR technique.

Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes

Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive, the task provides a sensitive tool for the examination of the effect of nonlinearities in the arterial system.