Jordi Alastruey

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.

A Systematic Comparison between 1-D and 3-D Hemodynamics in Compliant Arterial Models

We present a systematic comparison of computational hemodynamics in arteries between a one-dimensional (1-D) and a three-dimensional (3-D) formulation with deformable vessel walls. The simulations were performed using a series of idealized compliant arterial models representing the common carotid artery, thoracic aorta, aortic bifurcation, and full aorta from the arch to the iliac bifurcation. The formulations share identical inflow and outflow boundary conditions and have compatible material laws. We also present an iterative algorithm to select the parameters for the outflow boundary conditions by using the 1-D theory to achieve a desired systolic and diastolic pressure at a particular vessel. This 1-D/3-D framework can be used to efficiently determine material and boundary condition parameters for 3-D subject-specific arterial models with deformable vessel walls. Finally, we explore the impact of different anatomical features and hemodynamic conditions on the numerical predictions. The results show good agreement between the two formulations, especially during the diastolic phase of the cycle.

Attenuation of Wave Reflection by Wave Entrapment Creates a “Horizon Effect” in the Human Aorta

Wave reflection is thought to be important in the augmentation of blood pressure. However, identification of distal reflections sites remains unclear. One possible explanation for this is that wave reflection is predominately determined by an amalgamation of multiple proximal small reflections rather than large discrete reflections originating from the distal peripheries. In 19 subjects (age, 35–73 years), sensor-tipped intra-arterial wires were used to measure pressure and Doppler velocity at 10-cm intervals along the aorta, starting at the aortic root. Incident and reflected waves were identified and timings and magnitudes quantified using wave intensity analysis. Mean wave speed increased along the length of the aorta (proximal, 6.8±0.9 m/s; distal, 10.7±1.5 m/s). The incident wave was tracked moving along the aorta, taking 55±4 ms to travel from the aortic root to the distal aorta. However, the timing to the refection site distance did not differ between proximal and distal aortic measurement sites (proximal aorta, 48±5 ms versus distal aorta, 42±4 ms; P=0.3). We performed a second analysis using aortic waveforms in a nonlinear model of pulse-wave propagation. This demonstrated very similar results to those observed in vivo and also an exponential attenuation in reflection magnitude. There is no single dominant refection site in or near the distal aorta. Rather, there are multiple reflection sites along the aorta, for which the contributions are attenuated with distance. We hypothesize that rereflection of reflected waves leads to wave entrapment, preventing distal waves being seen in the proximal aorta.

Theoretical models for coronary vascular biomechanics: Progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Separation of the reservoir and wave pressure and velocity from measurements at an arbitrary location in arteries

Previous studies based on measurements made in the ascending aorta have demonstrated that it can be useful to separate the arterial pressure P into a reservoir pressure P generated by the windkessel effect and a wave pressure p generated by the arterial waves: P=P + p. The separation in these studies was relatively straightforward since the flow into the arterial system was measured. In this study the idea is extended to measurements of pressure and velocity at sites distal to the aortic root where flow into the arterial system is not known. P is calculated from P at an arbitrary location in a large artery by fitting the pressure fall-off in diastole to an exponential function and assuming that p is proportional to the flow into the arterial system. A local reservoir velocity Ū that is proportional to P is also defined. The separation algorithm is applied to in vivo human and canine data and to numerical data generated using a one-dimensional model of pulse wave propagation in the larger conduit arteries. The results show that the proposed algorithm is reasonably robust, allowing for the separation of the measured pressure and velocity into reservoir and wave pressures and velocities. Application to data measured simultaneously in the aorta of the dog shows that the reservoir pressure is fairly uniform along the aorta, a test of self-consistency of the assumptions leading to the algorithm. Application to data generated with a validated numerical model indicates that the parameters derived by fitting the pressure data are close to the known values which were used to generate the numerical data. Finally, application to data measured in the human thoracic aorta indicates the potential usefulness of the separation.

A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling

Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

Arterial reservoir-excess pressure and ventricular work.

This study is based on the hypothesis that the pressure within the arterial network can be usefully decomposed as the sum of a reservoir pressure and an excess pressure. The reservoir pressure waveform is defined to be the same in each vessel but delayed by the wave travel time from the root of the aorta. Using calculus of variations and mass conservation, which relates the flow and rates of change of pressure in the vessels, we show that the reservoir pressure waveform minimises the ventricular hydraulic work for any physiologically or clinically reasonable ejection waveform and arterial properties, i.e. vessel compliances and terminal resistances. We conclude that the excess pressure determines the excess work done by the ventricle, which may have clinically important implications.

Coronary and Microvascular Physiology During Intra-Aortic Balloon Counterpulsation

OBJECTIVES This study sought to identify the effect of coronary autoregulation on myocardial perfusion during intra-aortic balloon pump (IABP) therapy. BACKGROUND IABP is the most commonly used circulatory support device, although its efficacy in certain scenarios has been questioned. The impact of alterations in microvascular function on IABP efficacy has not previously been evaluated in humans. METHODS Thirteen patients with ischemic cardiomyopathy (left ventricular ejection fraction: 34 ± 8%) undergoing percutaneous coronary intervention were recruited. Simultaneous intracoronary pressure and Doppler-flow measurements were undertaken in the target vessel following percutaneous coronary intervention, during unassisted and IABP-assisted conditions. Coronary autoregulation was modulated by the use of intracoronary adenosine, inducing maximal hyperemia. Wave intensity analysis characterized the coronary wave energies associated with balloon counterpulsation. RESULTS Two unique diastolic coronary waves were temporally associated with IABP device use; a forward compression wave and a forward expansion wave caused by inflation and deflation, respectively. During basal conditions, IABP therapy increased distal coronary pressure (82.4 ± 16.1 vs. 88.7 ± 17.8 mm Hg, p = 0.03), as well as microvascular resistance (2.32 ± 0.52 vs. 3.27 ± 0.41 mm Hg cm s(-1), p = 0.001), with no change in average peak velocity (30.6 ± 12.0 vs. 26.6 ± 11.3 cm s(-1), p = 0.59). When autoregulation was disabled, counterpulsation caused an increase in average peak velocity (39.4 ± 10.5 vs. 44.7 ± 17.5 cm s(-1), p = 0.002) that was linearly related with IABP-forward compression wave energy (R(2) = 0.71, p = 0.001). CONCLUSIONS Autoregulation ameliorates the effect of IABP on coronary flow. However, during hyperemia, IABP augments myocardial perfusion, principally due to a diastolic forward compression wave caused by balloon inflation, suggesting IABP would be of greatest benefit when microcirculatory reserve is exhausted.

Dominance of the Forward Compression Wave in Determining Pulsatile Components of Blood Pressure: Similarities Between Inotropic Stimulation and Essential Hypertension

Pulsatile components of blood pressure may arise from forward (ventricular generated) or backward wave travel in the arterial tree. The objective of this study was to determine the relative contributions of forward and backward waves to pulsatility. We used wave intensity and wave separation analysis to determine pulsatile components of blood pressure during inotropic and vasopressor stimulation by dobutamine and norepinephrine in normotensive subjects and compared pulse pressure components in hypertensive (mean±SD, 48.8±11.3 years; 165±26.6/99±14.2 mm Hg) and normotensive subjects (52.2±12.6 years; 120±14.2/71±8.2 mm Hg). Dobutamine (7.5 &mgr;g/kg per minute) increased the forward compression wave generated by the ventricle and increased pulse pressure from 36.8±3.7 to 59.0±3.4 mm Hg (mean±SE) but had no significant effect on mean arterial pressure or the midsystolic backward compression wave. By contrast, norepinephrine (50 ng/kg per minute) had no significant effect on the forward compression wave but increased the midsystolic backward compression wave. Despite this increase in the backward compression wave, and an increase in mean arterial pressure, norepinephrine increased central pulse pressure less than dobutamine (increases of 22.1±3.8 and 7.2±2.8 mm Hg for dobutamine and norepinephrine, respectively; P<0.02). An elevated forward wave component (mean±SE, 50.4±3.4 versus 35.2±1.8 mm Hg, in hypertensive and normotensive subjects, respectively; P<0.001) accounted for approximately two thirds of the total difference in central pulse pressures between hypertensive and normotensive subjects. Increased central pulse pressure during inotropic stimulation and in essential hypertension results primarily from the forward compression wave.Pulsatile components of blood pressure may arise from forward (ventricular generated) or backward wave travel in the arterial tree. The objective of this study was to determine the relative contributions of forward and backward waves to pulsatility. We used wave intensity and wave separation analysis to determine pulsatile components of blood pressure during inotropic and vasopressor stimulation by dobutamine and norepinephrine in normotensive subjects and compared pulse pressure components in hypertensive (mean±SD, 48.8±11.3 years; 165±26.6/99±14.2 mm Hg) and normotensive subjects (52.2±12.6 years; 120±14.2/71±8.2 mm Hg). Dobutamine (7.5 μg/kg per minute) increased the forward compression wave generated by the ventricle and increased pulse pressure from 36.8±3.7 to 59.0±3.4 mm Hg (mean±SE) but had no significant effect on mean arterial pressure or the midsystolic backward compression wave. By contrast, norepinephrine (50 ng/kg per minute) had no significant effect on the forward compression wave but increased the midsystolic backward compression wave. Despite this increase in the backward compression wave, and an increase in mean arterial pressure, norepinephrine increased central pulse pressure less than dobutamine (increases of 22.1±3.8 and 7.2±2.8 mm Hg for dobutamine and norepinephrine, respectively; P <0.02). An elevated forward wave component (mean±SE, 50.4±3.4 versus 35.2±1.8 mm Hg, in hypertensive and normotensive subjects, respectively; P <0.001) accounted for approximately two thirds of the total difference in central pulse pressures between hypertensive and normotensive subjects. Increased central pulse pressure during inotropic stimulation and in essential hypertension results primarily from the forward compression wave. # Novelty and Significance {#article-title-19}

Modelling pulse wave propagation in the rabbit systemic circulation to assess the effects of altered nitric oxide synthesis

Pulse wave propagation in the mature rabbit systemic circulation was simulated using the one-dimensional equations of blood flow in compliant vessels. A corrosion cast of the rabbit circulation was manufactured to obtain arterial lengths and diameters. Pulse wave speeds and inflow and outflow boundary conditions were derived from in vivo data. Numerical results captured the main features of in vivo pressure and velocity pulse waveforms in the aorta, brachiocephalic artery and central ear artery. This model was used to elucidate haemodynamic mechanisms underlying changes in peripheral pulse waveforms observed in vivo after administering drugs that alter nitric oxide synthesis in the endothelial cells lining blood vessels. According to our model, these changes can be explained by single or combined alterations of blood viscosity, peripheral resistance and compliance, and the elasticity of conduit arteries.