Hemodynamic effects of a dielectric elastomer augmented aorta on aortic wave intensity: An in-vivo study

Dielectric elastomer actuator augmented aorta (DEA) represents a novel approach with high potential for assisting a failing heart. The soft tubular device replaces a section of the aorta and increases its diameter when activated. The hemodynamic interaction between the DEA and the left ventricle (LV) has not been investigated with wave intensity (WI) analysis before. The objective of this study is to investigate the hemodynamic effects of the DEA on the aortic WI pattern. WI was calculated from aortic pressure and flow measured in-vivo in the descending aorta of two pigs implanted with DEAs. The DEAs were tested for different actuation phase shifts (PS). The DEA generated two decompression waves (traveling upstream and downstream of the device) at activation followed by two compression waves at deactivation. Depending on the PS, the end-diastolic pressure (EDP) decreased by 7% (or increased by 5-6%). The average early diastolic pressure augmentation (Pdia¯) increased by 2% (or decreased by 2-3%). The hydraulic work (WH) measured in the aorta decreased by 2% (or increased by 5%). The DEA-generated waves interfered with the LV-generated waves, and the timing of the waves affected the hemodynamic effect of the device. For the best actuation timing the upstream decompression wave arrived just before aortic valve opening and the upstream compression wave arrived just before aortic valve closure leading to a decreased EDP, an increased Pdia¯ and a reduced.WH.

Non-invasive Assessment by B-Mode Ultrasound of Arterial Pulse Wave Intensity and Its Reduction During Ventricular Dysfunction

Arterial pulse waves contain clinically useful information about cardiac performance, arterial stiffness and vessel tone. Here we describe a novel method for non-invasively assessing wave properties, based on measuring changes in blood flow velocity and arterial wall diameter during the cardiac cycle. Velocity and diameter were determined by tracking speckles in successive B-mode images acquired with an ultrafast scanner and plane-wave transmission. Blood speckle was separated from tissue by singular value decomposition and processed to correct biases in ultrasound imaging velocimetry. Results obtained in the rabbit aorta were compared with a conventional analysis based on blood velocity and pressure, employing measurements obtained with a clinical intra-arterial catheter system. This system had a poorer frequency response and greater lags but the pattern of net forward-traveling and backward-traveling waves was consistent between the two methods. Errors in wave speed were also similar in magnitude, and comparable reductions in wave intensity and delays in wave arrival were detected during ventricular dysfunction. The non-invasive method was applied to the carotid artery of a healthy human participant and gave a wave speed and patterns of wave intensity consistent with earlier measurements. The new system may have clinical utility in screening for heart failure.

The physiological effects of cardiac resynchronization therapy on aortic and pulmonary flow and dynamic and static components of systemic impedance

Background

Patients who improve following cardiac resynchronization therapy (CRT) have left ventricular (LV) remodeling and improved cardiac output (CO). Effects on the systemic circulation are unknown.

Objective

To explore the effects of CRT on aortic and pulmonary blood flow and systemic afterload.

Methods

At CRT implant patients underwent a noninvasive assessment of central hemodynamics, including wave intensity analysis (n = 28). This was repeated at 6 months after CRT. A subsample (n = 11) underwent an invasive electrophysiological and hemodynamic assessment immediately following CRT. CRT response was defined as reduction in LV end-systolic volume ≥15% at 6 months.

Results

In CRT responders (75% of those in the noninvasive arm), there was a significant increase in CO (from 3 ± 2 L/min to 4 ± 2 L/min, P = .002) and LV dP/dt_max (from 846 ± 162 mm Hg/s to 958 ± 194 mm Hg/s, P = .001), immediately after CRT in those in the invasive arm. They demonstrated a significant increase in aortic forward compression wave (FCW) both acutely and at follow-up. The relative change in LV dP/dt_max strongly correlated with changes in the aortic FCW (R _s 0.733, P = .025). CRT responders displayed a significant reduction in afterload, and a decrease in systemic vascular resistance and pulse wave velocity acutely; there was a significant decrease in acute pulmonary afterload measured by the pulmonary FCW and forward expansion wave.

Conclusion

Improved cardiac function following CRT is attributable to a combination of changes in the cardiac and cardiovascular system. The relative importance of these 2 mechanisms may then be important for optimizing CRT.

The composition of vulnerable plaque and its effect on arterial waveforms

Carotid plaque composition is a key factor of plaque stability and it carries significant prognostic information. The carotid unstable plaques are characterized by a thin fibrous cap (FC) ≤65μm with large lipid core (LC), while stable plaques have a thicker FC and less LC. Identifying the percentage of plaque compositions could help surgeons to make a precise decision for their patients' treatment protocol. This study aims to distinguish between stable and unstable plaque by defining the relationship between plaque composition and arterial waveform non-invasively. An in-vitro arterial system, composed of a Harvard pulsatile flow pump and artificial circulation system, was used to investigate the effect of the plaque compositions on the pulsatile arterial waveforms. Five types of arterial plaques, composed of the LC, FC, Collagen (Col) and Calcium (Ca), were implemented into the artificial carotid artery to represent the diseased arterial system with 30% of blockage. The pulsatile pressure, velocity and arterial wall movement were measured simultaneously at the site proximal to the plaque. Non-invasive wave intensity analysis (Non-WIA) was used to separate the waves into forward and backward components. The correlation between the plaque compositions and the reflected waveforms was quantitatively analysed. The experimental results indicate that the reflected waveforms are strongly correlated with the plaque compositions, where the percentages of the Col are linearly correlated with the amplitude of the backward diameter (correlation coefficient, r = 0.74) and the lipid content has a strong negative correlation with the backward diameter (r = 0.82). A slight weak correlation exists between the reflected waveform and the percentage of Ca. The strong correlation between the compositions of the plaques with the backward waveforms observed in this study demonstrates that the components of the arterial plaques could be distinguished by the arterial waveforms. This finding might lead to a potential novel non-invasive clinical tool to determine the composition of the plaques and distinguish between stable and vulnerable arterial plaques at the early stage.

Mechanisms of gradual pressure drop in angiographically normal left anterior descending and right coronary artery: Insights from wave intensity analysis

BACKGROUND

This study evaluated the mechanism of decline in coronary pressure from the proximal to the distal part of the coronary arteries in the left anterior descending (LAD) versus the right coronary artery (RCA) from the insight of coronary hemodynamics using wave intensity analysis (WIA).

METHODS

Twelve patients with angiographically normal LAD and RCA were prospectively enrolled. Distal coronary pressure, mean aortic pressure, and average peak velocity were measured at 4 different positions: 9, 6, 3, and 0 cm distal from each coronary ostium.

RESULTS

The distal-to-proximal coronary pressure ratio during maximum hyperemia gradually decreased in proportion to the distance from the ostium (0.92±0.03 and 0.98±0.03 at 9 cm distal to the LAD and RCA ostium). WIA showed the dominant forward-traveling compression wave gradually decreased and the backward-traveling suction wave gradually decreased in proportion to the decrease in coronary pressure through the length of the non-diseased LAD but not the RCA.

CONCLUSIONS

The pushing wave and suction wave intensities on WIA were diminished in proportion to the distance from the ostium of the LAD despite the wave intensity not changing across the length of the RCA, which may lead to gradual intracoronary pressure drop in the angiographically normal LAD.

Comparison of arterial wave intensity analysis by pressure-velocity and diameter-velocity methods in a virtual population of adult subjects

Pressure-velocity-based analysis of arterial wave intensity gives clinically relevant information about the performance of the heart and vessels, but its utility is limited because accurate pressure measurements can only be obtained invasively. Diameter-velocity-based wave intensity can be obtained noninvasively using ultrasound; however, due to the nonlinear relationship between blood pressure and arterial diameter, the two wave intensities might give disparate clinical indications. To test the magnitude of the disagreement, we have generated an age-stratified virtual population to investigate how the two dominant nonlinearities viscoelasticity and strain-stiffening cause the two formulations to differ. We found strong agreement between the pressure-velocity and diameter-velocity methods, particularly for the systolic wave energy, the ratio between systolic and diastolic wave heights, and older subjects. The results are promising regarding the introduction of noninvasive wave intensities in the clinic.

Minor impact of constraint from perivascular flow probes on wave intensity analysis

Perivascular flow probes are considered the gold-standard for measuring volumetric blood flow in animal studies. Although flow probes are generally placed non-constrictively around the vessel of interest, pressure-elevating interventions performed during an experiment may lead to vessel expansion and some probe-vessel impingement, particularly in highly compliant vessels such as adult sheep aorta or major pulmonary arteries in fetus lambs. This study assessed to what extent such mild flow probe constraint may impact on wave intensity analysis. We also investigated whether errors arising from flow probe constraint could explain apparent pressure reflection indices (R_p > 1) that have been observed in fetus lamb pulmonary arteries under some experimental conditions. These questions were investigated with one-dimensional models of an adult sheep aorta and fetus lamb pulmonary artery, with a virtual flow probe incorporated as a non-linear external constraint term in the vessel constitutive equation. Model-derived flow and pressure were subjected to standard analysis procedures that would be applied experimentally (correcting for apparent velocity lags and calculating wave speed via the PU-loop method). For the adult sheep model, simulations covering a wide range of haemodynamic conditions revealed a mostly minor effect (<10%) of probe constraint on the intensity and pressure effects of the three major waves (forward compression wave, forward decompression wave, backward compression wave). Moreover, flow probe constraint had essentially no impact on R_p in the fetus lamb model, suggesting that such constraint is unlikely to be responsible for an observed R_p > 1. Mild flow probe constraint is likely to have little impact on wave intensity analysis.

Alterations in Carotid Parameters in ApoE-/- Mice Treated with a High-Fat Diet: A Micro-ultrasound Analysis

Information on the common carotid artery and cerebral microcirculation can be obtained by micro-ultrasound (µUS). The aim of the study described here was to investigate high-fat diet-induced alterations in vascular parameters in ApoE-/- mice. Twenty-two ApoE-/- male mice were examined by µUS and divided into the standard diet (ApoE-/-_SD) and high-fat diet (ApoE-/-_HF) groups. The µUS examination was repeated after 4 mo (T₁). Carotid stiffness, reflection magnitude and reflection index were measured; the amplitudes of the first (W₁) and second (W₂) local maxima, the local minimum (W_b) and the reflection index (RI_WIA = W_b/W₁) were assessed with wave intensity analysis. At T₁, ApoE-/-_HF mice had increased carotid stiffness (1.48 [0.36] vs. 1.88 [0.51]) and reflection magnitude (0.89 [0.07] vs. 0.94 [0.07]) values. Longitudinal comparisons highlighted increases in carotid stiffness for ApoE-/-_HF mice (from 1.37 [0.25] to 1.88 [0.51] m/s) but not for ApoE-/-_SD mice (from 1.40 [0.62] to 1.48 [0.36] m/s). ApoE-/-_HF mice exhibited carotid artery stiffening and increased wave reflections.

Intra-aortic Balloon Counterpulsation for High-Risk Percutaneous Coronary Intervention: Defining Coronary Responders

The effect of intra-aortic balloon counterpulsation (IABC) varies, and it is unknown whether this is due to a heterogeneous coronary physiological response. This study aimed to characterise the coronary and left ventricular (LV) effects of IABC and define responders in terms of their invasive physiology. Twenty-seven patients (LVEF 31 ± 9%) underwent coronary pressure and Doppler flow measurements in the target vessel and acquisition of LV pressure volume loops after IABC supported PCI, with and without IABC assistance. Through coronary wave intensity analysis, perfusion efficiency (PE) was calculated as the proportion of total wave energy comprised of accelerating waves, with responders defined as those with an increase in PE with IABC. The myocardial supply/demand ratio was defined as the ratio between coronary flow and LV pressure volume area (PVA). Responders (44.4%) were more likely to have undergone complex PCI (p = 0.03) with a higher pre-PCI disease burden (p = 0.02) and had lower unassisted mean arterial (87.4 ± 11.0 vs. 77.8 ± 11.6 mmHg, p = 0.04) and distal coronary pressures (88.0 ± 11.0 vs. 71.6 ± 12.4 mmHg, p < 0.001). There was no effect overall of IABC on the myocardial supply/demand ratio (p = 0.34). IABC has minimal effect on demand, but there is marked heterogeneity in the coronary response to IABC, with the greatest response observed in those patients with the most disordered autoregulation.

Changes in contractility determine coronary haemodynamics in dyssynchronous left ventricular heart failure, not vice versa

BACKGROUND

Biventricular pacing has been shown to increase both cardiac contractility and coronary flow acutely but the causal relationship is unclear. We hypothesised that changes in coronary flow are secondary to changes in cardiac contractility. We sought to examine this relationship by modulating coronary flow and cardiac contractility.

METHODS

Contractility and lusitropy were altered by varying the location of pacing in 8 patients. Coronary autoregulation was transiently disabled with intracoronary adenosine. Simultaneous coronary flow velocity, coronary pressure and left ventricular pressure data were measured in the different pacing settings with and without hyperaemia and wave intensity analysis performed.

RESULTS

Multisite pacing was effective at altering left ventricular contractility and lusitropy (pos. dp/dtmax -13% to +10% and neg. dp/dtmax -15% to +17% compared to baseline). Intracoronary adenosine decreased microvascular resistance (362.5 mm Hg/s/m to 156.7 mm Hg/s/m, p < 0.001) and increased LAD flow velocity (22 cm/s vs 45 cm/s, p < 0.001) but did not acutely change contractility or lusitropy. The magnitude of the dominant accelerating wave, the Backward Expansion Wave, was proportional to the degree of contractility as well as lusitropy (r = 0.47, p < 0.01 and r = -0.50, p < 0.01). Perfusion efficiency (the proportion of accelerating waves) increased at hyperaemia (76% rest vs 81% hyperaemia, p = 0.04). Perfusion efficiency correlated with contractility and lusitropy at rest (r = 0.43 & -0.50 respectively, p = 0.01) and hyperaemia (r = 0.59 & -0.6, p < 0.01).

CONCLUSIONS

Acutely increasing coronary flow with adenosine in patients with systolic heart failure does not increase contractility. Changes in coronary flow with biventricular pacing are likely to be a consequence of enhanced cardiac contractility from resynchronization and not vice versa.

Non-invasive coronary wave intensity analysis

Wave intensity analysis is calculated from simultaneously acquired measures of pressure and flow. Its mathematical computation produces a profile that provides quantitative information on the energy exchange driving blood flow acceleration and deceleration. Within the coronary circulation it has proven most useful in describing the wave that originates from the myocardium and that is responsible for driving the majority of coronary flow, labelled the backward decompression wave. Whilst this wave has demonstrated valuable insights into the pathogenic processes of a number of disease states, its measurement is hampered by its invasive necessity. However, recent work has used transthoracic echocardiography and an established measures of central aortic pressure to produce coronary flow velocity and pressure waveforms respectively. This has allowed a non-invasive measure of coronary wave intensity analysis, and in particular the backward decompression wave, to be calculated. It is anticipated that this will allow this tool to become more applicable and widespread, ultimately moving it from the research to the clinical domain.

Common Carotid Artery Diameter, Blood Flow Velocity and Wave Intensity Responses at Rest and during Exercise in Young Healthy Humans: A Reproducibility Study

The aim of this study was to assess the reproducibility of non-invasive, ultrasound-derived wave intensity (WI) in humans at the common carotid artery. Common carotid artery diameter and blood velocity of 12 healthy young participants were recorded at rest and during mild cycling, to assess peak diameter, change in diameter, peak velocity, change in velocity, time derivatives, non-invasive wave speed and WI. Diameter, velocity and WI parameters were fairly reproducible. Diameter variables exhibited higher reproducibility than corresponding velocity variables (intra-class correlation coefficient [ICC] = 0.79 vs. 0.73) and lower dispersion (coefficient of variation [CV] = 5% vs. 9%). Wave speed had fair reproducibility (ICC = 0.6, CV = 16%). WI energy variables exhibited higher reproducibility than corresponding peaks (ICC = 0.78 vs. 0.74) and lower dispersion (CV = 16% vs. 18%). The majority of variables had higher ICCs and lower CVs during exercise. We conclude that non-invasive WI analysis is reliable both at rest and during exercise.

Wave intensity analysis and its application to the coronary circulation

Wave intensity analysis (WIA) is a technique developed from the field of gas dynamics that is now being applied to assess cardiovascular physiology. It allows quantification of the forces acting to alter flow and pressure within a fluid system, and as such it is highly insightful in ascribing cause to dynamic blood pressure or velocity changes. When co-incident waves arrive at the same spatial location they exert either counteracting or summative effects on flow and pressure. WIA however allows waves of different origins to be measured uninfluenced by other simultaneously arriving waves. It therefore has found particular applicability within the coronary circulation where both proximal (aortic) and distal (myocardial) ends of the coronary artery can markedly influence blood flow. Using these concepts, a repeating pattern of 6 waves has been consistently identified within the coronary arteries, 3 originating proximally and 3 distally. Each has been associated with a particular part of the cardiac cycle. The most clinically relevant wave to date is the backward decompression wave, which causes the marked increase in coronary flow velocity observed at the start of the diastole. It has been proposed that this wave is generated by the elastic re-expansion of the intra-myocardial blood vessels that are compressed during systolic contraction. Particularly by quantifying this wave, WIA has been used to provide mechanistic and prognostic insight into a number of conditions including aortic stenosis, left ventricular hypertrophy, coronary artery disease and heart failure. It has proven itself to be highly sensitive and as such a number of novel research directions are encouraged where further insights would be beneficial.

A method to implement the reservoir-wave hypothesis using phase-contrast magnetic resonance imaging

The reservoir-wave hypothesis states that the blood pressure waveform can be usefully divided into a “reservoir pressure” related to the global compliance and resistance of the arterial system, and an “excess pressure” that depends on local conditions. The formulation of the reservoir-wave hypothesis applied to the area waveform is shown, and the analysis is applied to area and velocity data from high-resolution phase-contrast cardiovascular magnetic resonance (CMR) imaging. A validation study shows the success of the principle, with the method producing largely robust and physically reasonable parameters, and the linear relationship between flow and wave pressure seen in the traditional pressure formulation is retained. The method was successfully tested on a cohort of 20 subjects (age range: 20–74 years; 17 males).

This paper:

•

Demonstrates the feasibility of deriving reservoir data non-invasively from CMR.

•

Includes a validation cohort (CMR data).

•

Suggests clinical applications of the method.

Wave intensity analysis in mice: age-related changes in WIA peaks and correlation with cardiac indexes

Mouse models are increasingly employed in the comprehension of cardiovascular disease. Wave Intensity Analysis (WIA) can provide information about the interaction between the vascular and the cardiac system. We investigate age-associated changes in WIA-derived parameters in mice and correlate them with biomarkers of cardiac function. Sixteen wild-type male mice were imaged with high-resolution ultrasound (US) at 8 weeks (T ₀) and 25 weeks (T ₁) of age. Carotid pulse wave velocity (PWV) was calculated from US images using the diameter-velocity loop and employed to evaluate WIA. Amplitudes of the first (W ₁) and the second (W ₂) local maxima, local minimum (W _b) and the reflection index (RI = W _b/W ₁) were assessed. Cardiac output (CO), ejection fraction (EF), fractional shortening (FS) and stroke volume (SV) were evaluated; longitudinal, radial and circumferential strain and strain rate values (LS, LSR, RS, RSR, CS, CSR) were obtained through strain analysis. W ₁ (T ₀: 4.42e-07 ± 2.32e-07 m²/s; T ₁: 2.21e-07 ± 9.77 m²/s), W ₂ (T ₀: 2.45e-08 ± 9.63e-09 m²/s; T ₁: 1.78e-08 ± 7.82 m²/s), W _b (T ₀: -8.75e-08 ± 5.45e-08 m²/s; T ₁: -4.28e-08 ± 2.22e-08 m²/s), CO (T ₀: 19.27 ± 4.33 ml/min; T ₁: 16.71 ± 2.88 ml/min), LS (T ₀: 17.55 ± 3.67%; T ₁: 15.05 ± 2.89%), LSR (T ₀: 6.02 ± 1.39 s^-1; T ₁: 5.02 ± 1.25 s^-1), CS (T ₀: 27.5 ± 5.18%; T ₁: 22.66 ± 3.09%) and CSR (T ₀: 10.03 ± 2.55 s^-1; T ₁: 7.50 ± 1.84 s^-1) significantly reduced with age. W ₁ was significantly correlated with CO (R = 0.58), EF (R = 0.72), LS (R = 0.65), LSR (R = 0.89), CS (R = 0.61), CSR (R = 0.70) at T ₀; correlations were lost at T ₁. The decrease in W ₁ and W ₂ suggests a cardiac performance reduction, while that in W_b, considering unchanged RI, might indicate a wave energy decrease. The loss of correlation between WIA-derived and cardiac parameters might reflect an alteration in cardiovascular interaction.

Using wave intensity analysis to determine local reflection coefficient in flexible tubes

It has been shown that reflected waves affect the shape and magnitude of the arterial pressure waveform, and that reflected waves have physiological and clinical prognostic values. In general the reflection coefficient is defined as the ratio of the energy of the reflected to the incident wave. Since pressure has the units of energy per unit volume, arterial reflection coefficient are traditionally defined as the ratio of reflected to the incident pressure. We demonstrate that this approach maybe prone to inaccuracies when applied locally. One of the main objectives of this work is to examine the possibility of using wave intensity, which has units of energy flux per unit area, to determine the reflection coefficient. We used an in vitro experimental setting with a single inlet tube joined to a second tube with different properties to form a single reflection site. The second tube was long enough to ensure that reflections from its outlet did not obscure the interactions of the initial wave. We generated an approximately half sinusoidal wave at the inlet of the tube and took measurements of pressure and flow along the tube. We calculated the reflection coefficient using wave intensity (R_dI and R_dI^0.5) and wave energy (R_I and R_I^0.5) as well as the measured pressure (R_dP) and compared these results with the reflection coefficient calculated theoretically based on the mechanical properties of the tubes. The experimental results show that the reflection coefficients determined by all the techniques we studied increased or decreased with distance from the reflection site, depending on the type of reflection. In our experiments, R_dP, R_dI^0.5 and R_I^0.5 are the most reliable parameters to measure the mean reflection coefficient, whilst R_dI and R_I provide the best measure of the local reflection coefficient, closest to the reflection site. Additional work with bifurcations, tapered tubes and in vivo experiments are needed to further understand, validate the method and assess its potential clinical use.

In silico coronary wave intensity analysis: application of an integrated one-dimensional and poromechanical model of cardiac perfusion

Coronary wave intensity analysis (cWIA) is a diagnostic technique based on invasive measurement of coronary pressure and velocity waveforms. The theory of WIA allows the forward- and backward-propagating coronary waves to be separated and attributed to their origin and timing, thus serving as a sensitive and specific cardiac functional indicator. In recent years, an increasing number of clinical studies have begun to establish associations between changes in specific waves and various diseases of myocardium and perfusion. These studies are, however, currently confined to a trial-and-error approach and are subject to technological limitations which may confound accurate interpretations. In this work, we have developed a biophysically based cardiac perfusion model which incorporates full ventricular–aortic–coronary coupling. This was achieved by integrating our previous work on one-dimensional modelling of vascular flow and poroelastic perfusion within an active myocardial mechanics framework. Extensive parameterisation was performed, yielding a close agreement with physiological levels of global coronary and myocardial function as well as experimentally observed cumulative wave intensity magnitudes. Results indicate a strong dependence of the backward suction wave on QRS duration and vascular resistance, the forward pushing wave on the rate of myocyte tension development, and the late forward pushing wave on the aortic valve dynamics. These findings are not only consistent with experimental observations, but offer a greater specificity to the wave-originating mechanisms, thus demonstrating the value of the integrated model as a tool for clinical investigation.

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

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.

Wave intensity analysis in air-filled flexible vessels

Wave intensity analysis (WIA) is an analytical technique generally used to investigate the propagation of waves in the cardiovascular system. Despite its increasing usage in the cardiovascular system, to our knowledge WIA has never been applied to the respiratory system. Given the analogies between arteries and airways (i.e. fluid flow in flexible vessels), the aim of this work is to test the applicability of WIA with gas flow instead of liquid flow. The models employed in this study are similar to earlier studies used for arterial investigations. Simultaneous pressure (P) and velocity (U) measurements were initially made in a single tube and then in several flexible tubes connected in series. Wave speed was calculated using the foot-to-foot method (cf), which was used to separate analytically the measured P and U waveforms into their forward and backward components. Further, the data were used to calculate wave intensity, which was also separated into its forward and backward components. Although the measured wave speed was relatively high, the results showed that the onsets and the nature of reflections (compression/expansion) derived with WIA, corresponded well to those anticipated using the theory of waves in liquid-filled elastic tubes. On average the difference between the experimental and theoretical arrival time of reflection was 6.1% and 3.6% for the single vessel and multivessel experiment, respectively. The results suggest that WIA can provide relatively accurate information on reflections in air-filled flexible tubes, warranting further studies to explore the full potential of this technique in the respiratory system.