Pressure-flow relations in dog arteries

Exponential taper in arteries: an exact solution of its effect on blood flow velocity waveforms and impedance

The dimensions and wall elasticity commonly taper along the length of mammalian arteries. The effects of taper on flow velocity waveforms can be included by either of two methods; to theoretically divide the artery into short sections wherein the properties are assumed constant (the approximate solution); or to find an exact solution incorporating the effects of taper. In this paper, an exact solution to the resulting, and previously unsolved nonlinear Ricatti equation for the impedance, is obtained by a process of substitutions. This solution is utilised to develop an exact expression for the flow velocity in the artery. The transmission line equations are then combined into a single integral expression for the entire artery and an exact solution to this is evaluated. This is the first solution to simultaneously account for both geometric and elastic taper, and it has been validated by comparing simulations of flow in the aorta of a dog to those using an infinitesimal approximate solution. The Pulsatility Index of the approximate solution requires at least 10 segments to converge to within 5% of that using the exact solution. The exact solution thus accurately accounts for the effects of exponential taper, and may be used to improve existing arterial models, which use the less accurate and more computationally cumbersome approximate solution.

A noninvasive method to estimate arterial impedance by means of assessment of local diameter change and the local center-line blood flow velocity using ultrasound

Vascular impedance is defined as the ratio between the frequency components of the local blood pressure waveform and those of the local blood volume flow waveform. Assessment of vascular impedance is, for example, important to study heart load and distal vascular bed vasomotricity. However, only a few studies on vascular impedance have been performed in humans because pulsatile pressure and volume flow waveforms, simultaneously recorded at the same location, are difficult to obtain noninvasively. The noninvasive assessment of arterial impedance as described in this study is based on the replacement of the pressure waveform by the distension (change in diameter) waveform and the volume flow waveform by the center-line blood flow velocity waveform. Both waveforms can simultaneously and accurately be assessed by means of pulsed ultrasound. It will be shown that, depending on the Womersley number, the volume flow waveform may be replaced by the center-line blood flow velocity waveform for a given frequency range and that the pressure waveform may be replaced by the distension waveform for a wide frequency range. The validation of the proposed ultrasound method was performed through an in vitro study in a flow model with a distensible tube terminated with a hydraulic load (modified windkessel model). It is shown that, in vitro, the proposed method gives the same results as the local spectral pressure-flow relationship.

Computer simulation of the mechanically-assisted failing canine circulation

A model of the cardiovascular system is presented. The model includes representations of the left and right ventricles, a nonlinear multielement model of the aorta and its main branches, and lumped models of the systemic veins and the pulmonary circulation. A simulation of the intra-aortic balloon pump and representations of physiological compensatory mechanisms are also incorporated in the model. Parameters of the left ventricular model were set to simulate either the normal or failing canine circulation. Pressure and flow waveforms throughout the circulation as well as ventricular pressure and volume were calculated for the normal, failing, and assisted failing circulation. Cardiac oxygen supply and consumption were calculated from the model. They were used as direct indices of cardiac energy supply and utilization to assess the effects of cardiac assistance.

The measurement of afterload, vascular input impedance, and power distribution in aorto-femoral bypass

The effects of aorto-femoral bypass grafts on the vascular input impedance, and the ratio of pulsatile to total power were studied in eight dogs. Unilateral ileo-femoral stenosis was simulated and comparisons were made between the input impedance and power distribution in healthy and simulated disease situations. Input impedance magnitude spectra and phase were displayed graphically and it was shown that the presence of the simulated disease increases the ratio of pulsatile to total power as measured in the abdominal aorta from 7.5 to 14.8% (p less than 0.05). This suggests that the presence of the stenosis creates an impedance mismatch thus causing reflected waves to propagate proximally towards the heart. It was concluded that the way in which the heart transfers fluid power into the arterial bed was compromised by the presence of the ileo-femoral partial stenoses. It is further suggested that the system described in the paper makes it possible to quantitatively assess afterload, vascular input impedance and cardiovascular power distribution as a quasi-real time diagnostic procedure.

The relationship between the longitudinal pressure gradient and the blood flow velocity in the canine superior vena cava

In the superior vena cava of anaesthetized open chest dogs the axial pressure gradient (delta P) was measured simultaneously with the blood flow velocity (V) under a variety of preload conditions. Both delta P and V curves showed distinct systolic and diastolic waves. Peak delta P ranged between 26 and 93 P/cm (0.2-0.7 mm Hg/cm) and V varied between 0.095 and 0.19 m/s. Peak systolic delta P, but not peak diastolic delta P was significantly linearly correlated to respectively peak systolic V and peak diastolic V. The shape of delta P and V curves corresponded fairly well but variations of delta P preceded the variations of V. Both the shape correspondence and the phase lag between delta P and V were evaluated by means of the normalized cross-correlation technique. During volume expansion the shape correspondence improved and the phase lag decreased. It is concluded that the transient vena caval blood velocity variations are directly related to the pulsatile axial pressure gradient.

Per-operative haemodynamic assessment of lower limb arterial surgery. Part 1: Hydraulic impedance measurement

Hydraulic impedance measurements have been made during surgery on 32 patients undergoing reconstructive arterial surgery. The reconstructive procedures included aorto-iliac, femoro-popliteal and axillo-femoral bypass, and extended deep femoral angioplasty. It was found that in aorto-iliac reconstruction the phase curves provide the means of assessing success, but that in other cases the impedance measurements though showing a similar trend are unable unequivocally to differentiate between success or failure.