A review of wave mechanics in the pulmonary artery with an emphasis on wave intensity analysis

Efficient uncertainty quantification in a spatially multiscale model of pulmonary arterial and venous hemodynamics

Pulmonary hypertension (PH) is a debilitating disease that alters the structure and function of both the proximal and distal pulmonary vasculature. This alters pressure-flow relationships in the pulmonary arterial and venous trees, though there is a critical knowledge gap in the relationships between proximal and distal hemodynamics in disease. Multiscale computational models enable simulations in both the proximal and distal vasculature. However, model inputs and measured data are inherently uncertain, requiring a full analysis of the sensitivity and uncertainty of the model. Thus, this study quantifies model sensitivity and output uncertainty in a spatially multiscale, pulse-wave propagation model of pulmonary hemodynamics. The model includes fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. We quantify uncertainty in blood pressure, blood flow rate, wave intensity, wall shear stress, and cyclic stretch. The latter two are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal arterial and venous circulations.

Characterization of pulmonary arterial stiffness using cardiac MRI

Pulmonary arterial stiffness (PAS) is a pathologic hallmark of all types of pulmonary hypertension (PH). Cardiac MRI (CMR), a gold-standard imaging modality for the evaluation of pulmonary flow, biventricular morphology and function has been historically reserved for the longitudinal clinical follow-up, PH phenotyping purposes, right ventricular evaluation, and research purposes. Over the last two decades, numerous indices combining invasive catheterization and non-invasive CMR have been utilized to phenotype the character and severity of PAS in different types of PH and to assess its clinically prognostic potential with encouraging results. Many recent studies have demonstrated a strong role of CMR derived PAS markers in predicting long-term clinical outcomes and improving currently gold standard risk assessment provided by the REVEAL calculator. With the utilization of a machine learning strategies, strong diagnostic and prognostic performance of CMR reported in multicenter studies, and ability to detect PH at early stages, the non-invasive assessment of PAS is on verge of routine clinical utilization. In this review, we focus on appraising important CMR studies interrogating PAS over the last 20 years, describing the benefits and limitations of different PAS indices, and their pathophysiologic relevance to pulmonary vascular remodeling. We also discuss the role of CMR and PAS in clinical surveillance and phenotyping of PH, and the long-term future goal to utilize PAS as a biomarker to aid with more targeted therapeutic management.

Efficient Uncertainty Quantification in a Multiscale Model of Pulmonary Arterial and Venous Hemodynamics

Computational hemodynamics models are becoming increasingly useful in the management and prognosis of complex, multiscale pathologies, including those attributed to the development of pulmonary vascular disease. However, diseases like pulmonary hypertension are heterogeneous, and affect both the proximal arteries and veins as well as the microcirculation. Simulation tools and the data used for model calibration are also inherently uncertain, requiring a full analysis of the sensitivity and uncertainty attributed to model inputs and outputs. Thus, this study quantifies model sensitivity and output uncertainty in a multiscale, pulse-wave propagation model of pulmonary hemodynamics. Our pulmonary circuit model consists of fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite the sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. Our analyses provide uncertainty in blood pressure, flow, and wave propagation phenomenon, as well as wall shear stress and cyclic stretch, both of which are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal circulation.

A computational model of contributors to pulmonary hypertensive disease: impacts of whole lung and focal disease distributions

Pulmonary hypertension has multiple etiologies and so can be difficult to diagnose, prognose, and treat. Diagnosis is typically made via invasive hemodynamic measurements in the main pulmonary artery and is based on observed elevation of mean pulmonary artery pressure. This static mean pressure enables diagnosis, but does not easily allow assessment of the severity of pulmonary hypertension, nor the etiology of the disease, which may impact treatment. Assessment of the dynamic properties of pressure and flow data obtained from catheterization potentially allows more meaningful assessment of the strain on the right heart and may help to distinguish between disease phenotypes. However, mechanistic understanding of how the distribution of disease in the lung leading to pulmonary hypertension impacts the dynamics of blood flow in the main pulmonary artery and/or the pulmonary capillaries is lacking. We present a computational model of the pulmonary vasculature, parameterized to characteristic features of pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension to help understand how the two conditions differ in terms of pulmonary vascular response to disease. Our model incorporates key features known to contribute to pulmonary vascular function in health and disease, including anatomical structure and multiple contributions from gravity. The model suggests that dynamic measurements obtained from catheterization potentially distinguish between distal and proximal vasculopathy typical of pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension. However, the model suggests a non-linear relationship between these data and vascular structural changes typical of pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension which may impede analysis of these metrics to distinguish between cohorts.

Fluid-structure interaction in a fully coupled three-dimensional mitral-atrium-pulmonary model

This paper aims to investigate detailed mechanical interactions between the pulmonary haemodynamics and left heart function in pathophysiological situations (e.g. atrial fibrillation and acute mitral regurgitation). This is achieved by developing a complex computational framework for a coupled pulmonary circulation, left atrium and mitral valve model. The left atrium and mitral valve are modelled with physiologically realistic three-dimensional geometries, fibre-reinforced hyperelastic materials and fluid–structure interaction, and the pulmonary vessels are modelled as one-dimensional network ended with structured trees, with specified vessel geometries and wall material properties. This new coupled model reveals some interesting results which could be of diagnostic values. For example, the wave propagation through the pulmonary vasculature can lead to different arrival times for the second systolic flow wave (S2 wave) among the pulmonary veins, forming vortex rings inside the left atrium. In the case of acute mitral regurgitation, the left atrium experiences an increased energy dissipation and pressure elevation. The pulmonary veins can experience increased wave intensities, reversal flow during systole and increased early-diastolic flow wave (D wave), which in turn causes an additional flow wave across the mitral valve (L wave), as well as a reversal flow at the left atrial appendage orifice. In the case of atrial fibrillation, we show that the loss of active contraction is associated with a slower flow inside the left atrial appendage and disappearances of the late-diastole atrial reversal wave (AR wave) and the first systolic wave (S1 wave) in pulmonary veins. The haemodynamic changes along the pulmonary vessel trees on different scales from microscopic vessels to the main pulmonary artery can all be captured in this model. The work promises a potential in quantifying disease progression and medical treatments of various pulmonary diseases such as the pulmonary hypertension due to a left heart dysfunction.

Measurement, Analysis and Interpretation of Pressure/Flow Waves in Blood Vessels

The optimal performance of the cardiovascular system, as well as the break-down of this performance with disease, both involve complex biomechanical interactions between the heart, conduit vascular networks and microvascular beds. ‘Wave analysis’ refers to a group of techniques that provide valuable insight into these interactions by scrutinizing the shape of blood pressure and flow/velocity waveforms. The aim of this review paper is to provide a comprehensive introduction to wave analysis, with a focus on key concepts and practical application rather than mathematical derivations. We begin with an overview of invasive and non-invasive measurement techniques that can be used to obtain the signals required for wave analysis. We then review the most widely used wave analysis techniques—pulse wave analysis, wave separation and wave intensity analysis—and associated methods for estimating local wave speed or characteristic impedance that are required for decomposing waveforms into forward and backward wave components. This is followed by a discussion of the biomechanical phenomena that generate waves and the processes that modulate wave amplitude, both of which are critical for interpreting measured wave patterns. Finally, we provide a brief update on several emerging techniques/concepts in the wave analysis field, namely wave potential and the reservoir-excess pressure approach.

Patients with Fontan circulation have abnormal aortic wave propagation patterns: A wave intensity analysis study

BACKGROUND

Elevated systemic afterload in patients with Fontan circulation may lead to impaired single ventricular function. Wave intensity analysis (WIA) enables evaluation of compression and expansion waves traveling through vasculature. We aimed to investigate the unfavorable wave propagation causing excessive afterload may be an important contributor to the overall single ventricle function and to the limited functional capacity in this patient population.

METHODS

Patients with hypoplastic left heart syndrome (HLHS) (n = 25), single left ventricle (SLV) (n = 24), and normal controls (n = 10) underwent phase-contrast MRI based WIA analysis evaluated in the ascending aorta. Forward compression wave (FCW) representing dP/dt, backward compression wave (BCW) reflecting vascular stiffness, and forward decompression wave (FDW) representing LV relaxation were recorded and indexed to each other.

RESULTS

FCW was lowest in HLHS patients (1098 mm⁵/s), and higher in the SLV group (1457 mm5/s), and controls (6457 mm5/s) (P < 0.001). BCW/FCW was increased in HLHS (0.22) and SLV (0.14) groups compared to controls (0.08) (P = 0.003). Peak VO2 correlated with FCW (R = 0.50, P = 0.015), stroke volume (R = 0.72, P < 0.001), and cardiac output (R = 0.44, P = 0.034).

CONCLUSIONS

Patients with HLHS and SLV have unfavorable aortic WIA patterns with increased BCW/FCW ratio indicating increased systemic afterload due to retrograde compression waves. Reduced FCW and systolic MRI indices correlated with peak VO2 suggesting that abnormal systolic wave propagation may play a role in exercise intolerance for Fontan patients.

Flow profile characteristics in Fontan circulation are associated with the single ventricle dilation and function: principal component analysis study

The Fontan circulation is characterized as a nonpulsatile flow propagation without a pressure-generating ventricle. However, flow through the Fontan circulation still exhibits oscillatory waves as a result of pressure changes generated by the systemic single ventricle. Identification of discrete flow patterns through the Fontan circuit may be important to understand single ventricle performance. Ninety-seven patients with Fontan circulation underwent phase-contrast MRI of the right pulmonary artery, yielding subject-specific flow waveforms. Principal component (PC) analysis was performed on preprocessed flow waveforms. Principal components were then correlated with standard MRI indices of function, volume, and aortopulmonary collateral flow. The first principal component (PC) described systolic versus diastolic-dominant flow through the Fontan circulation, accounting for 31.3% of the variance in all waveforms. The first PC correlated with end-diastolic volume (R = 0.34, P = 0.001), and end-systolic volume (R = 0.30, P = 0.003), cardiac index (R = 0.51, P < 0.001), and the amount of aortopulmonary collateral flow (R = 0.25, P = 0.027)-lower ventricular volumes and a smaller volume of collateral flow-were associated with diastolic-dominant cavopulmonary flow. The second PC accounted for 19.5% of variance and described late diastolic acceleration versus deceleration and correlated with ejection fraction-diastolic deceleration was associated with higher ejection fraction. Principal components describing the diastolic flow variations in pulmonary arteries are related to the single ventricle function and volumes. Particularly, diastolic-dominant flow without late acceleration appears to be related to preserved ventricular volume and function, respectively.NEW & NOTEWORTHY The exact physiological significance of flow oscillations of phasic and temporal flow variations in Fontan circulation is unknown. With the use of principal component analysis, we discovered that flow variations in the right pulmonary artery of Fontan patients are related to the single ventricle function and volumes. Particularly, diastolic-dominant flow without late acceleration appears to be related to more ideal ventricular volume and systolic function, respectively.

Influence of image segmentation on one-dimensional fluid dynamics predictions in the mouse pulmonary arteries

Computational fluid dynamics (CFD) models are emerging tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation have made subject-specific modelling of the cardiovascular system a feasible task, which is particularly important in the case of pulmonary hypertension, requiring a combination of invasive and non-invasive procedures for diagnosis. Uncertainty in image segmentation propagates to CFD model predictions, making the quantification of segmentation-induced uncertainty crucial for subject-specific models. This study quantifies the variability of one-dimensional CFD predictions by propagating the uncertainty of network geometry and connectivity to blood pressure and flow predictions. We analyse multiple segmentations of a single, excised mouse lung using different pre-segmentation parameters. A custom algorithm extracts vessel length, vessel radii and network connectivity for each segmented pulmonary network. Probability density functions are computed for vessel radius and length and then sampled to propagate uncertainties to haemodynamic predictions in a fixed network. In addition, we compute the uncertainty of model predictions to changes in network size and connectivity. Results show that variation in network connectivity is a larger contributor to haemodynamic uncertainty than vessel radius and length.

Impact of pulmonary endarterectomy on pulmonary arterial wave propagation and reservoir function

High wave speed and large wave reflection in the pulmonary artery have previously been reported in patients with chronic thromboembolic pulmonary hypertension (CTEPH). We assessed the impact of pulmonary endarterectomy (PEA) on pulmonary arterial wave propagation and reservoir function in patients with CTEPH. Right heart catheterization was performed using a combined pressure and Doppler flow sensor-tipped guidewire to obtain simultaneous pressure and flow velocity measurements in the pulmonary artery in eight patients with CTEPH before and 3 mo after PEA. Wave intensity and reservoir-excess pressure analyses were then performed. Following PEA, mean pulmonary arterial pressure (PAPm; ∼49 vs. ∼32 mmHg), pulmonary vascular resistance (PVR; ∼11.1 vs. ∼5.1 Wood units), and wave speed (∼16.5 vs. ∼8.1 m/s), i.e., local arterial stiffness, markedly decreased. The changes in the intensity of the reflected arterial wave and wave reflection index (pre: ∼28%; post: ∼22%) were small, and patients post-PEA with and without residual pulmonary hypertension (i.e., PAPm ≥ 25 mmHg) had similar wave reflection index (∼20 vs. ∼23%). The reservoir and excess pressure decreased post-PEA, and the changes were associated with improved right ventricular afterload, function, and size. In conclusion, although PVR and arterial stiffness decreased substantially following PEA, large wave reflection persisted, even in patients without residual pulmonary hypertension, indicating lack of improvement in vascular impedance mismatch. This may continue to affect the optimal ventriculoarterial interaction, and further studies are warranted to determine whether this contributes to persistent symptoms in some patients.NEW & NOTEWORTHY We performed wave intensity analysis in the pulmonary artery in patients with chronic thromboembolic pulmonary hypertension before and 3 mo after pulmonary endarterectomy. Despite substantial reduction in pulmonary arterial pressures, vascular resistance, and arterial stiffness, large pulmonary arterial wave reflection persisted 3 mo postsurgery, even in patients without residual pulmonary hypertension, suggestive of lack of improvement in vascular impedance mismatch.

Aldosterone Induces Vascular Damage

Primary aldosteronism (PA) is hemodynamically independently associated with arterial wall stiffness as assessed by pulse wave velocity (PWV) compared with essential hypertension. Arterial wave reflection parameters derived from pulse wave analysis, such as forward and backward wave amplitudes (Pf and Pb), are promising vascular markers to predict cardiovascular outcomes in addition to PWV. These vascular parameters have never been studied in patients with PA before. In study part A, we prospectively enrolled 67 patients with PA and 132 patients with essential hypertension. In study part B, another 54 patients with PA were enrolled. Heart-carotid PWV was measured, and carotid pressure waveforms were recorded to calculate Pf, Pb, and augmentation index at baseline (part A and B) and 6 months after treatment (part B). The results showed that the patients with PA had significantly higher Pf (P=0.001), Pb (P=0.01), and PWV (P=0.021) than the patients with essential hypertension. In univariate correlation analysis, both log Pf and Pb were significantly correlated with age, office blood pressure, serum potassium level, log PWV, and the presence of PA. However, only Pb was significantly correlated with log plasma renin activity and log aldosterone to renin ratio. In multivariate analysis, log Pf was significantly correlated with the presence of PA (P=0.001), male sex, age, and mean arterial blood pressure. Pb was significantly correlated with the presence of PA (P=0.031), age, and mean arterial pressure. Six months after treatment, Pf and Pb decreased significantly. In conclusion, the patients with PA had significantly increased wave reflections compared with the patients with essential hypertension. Our results provide clinical evidence of aldosterone-related extensive vascular dysfunction of the arterial system.

Pulmonary Vascular Dynamics

The pulmonary circulation carries deoxygenated blood from the systemic veins through the pulmonary arteries to be oxygenated in the capillaries that line the walls of the pulmonary alveoli. The pulmonary circulation carries the cardiac output with a relatively low driving pressure, and so differs considerably in structure and function from the systemic circulation to maintain a low-resistance vascular system. The pulmonary circulation is often considered to be a quasi-static system in both experimental and computational studies of pulmonary perfusion and its matching to ventilation (air flow) for exchange. However, the system is highly dynamic, with cardiac output and regional perfusion changing with posture, exercise, and over time. Here we review this dynamic system, with a focus on understanding the physiology of pulmonary vascular dynamics across spatial and temporal scales, and the changes to these dynamics that are reflective of disease. © 2019 American Physiological Society. Compr Physiol 9:1081-1100, 2019.

Impact of chronic hypoxia on proximal pulmonary artery wave propagation and mechanical properties in rats

Arterial stiffness and wave reflection are important components of the ventricular afterload. Therefore, we aimed to assess the arterial wave characteristics and mechanical properties of the proximal pulmonary arteries (PAs) in the hypoxic pulmonary hypertensive rat model. After 21 days in normoxic or hypoxic chambers (24 animals/group), animals underwent transthoracic echocardiography and PA catheterization with a dual-tipped pressure and Doppler flow sensor wire. Wave intensity analysis was performed. Artery rings obtained from the pulmonary trunk, right and left PAs, and aorta were subjected to a tensile test to rupture. Collagen and elastin content were determined. In hypoxic rats, proximal PA wall thickness, collagen content, tensile strength per unit collagen, maximal elastic modulus, and wall viscosity increased, whereas the elastin-to-collagen ratio and arterial distensibility decreased. Arterial pulse wave velocity was also increased, and the increase was more prominent in vivo than ex vivo. Wave intensity was similar in hypoxic and normoxic animals with negligible wave reflection. In contrast, the aortic maximal elastic modulus remained unchanged, whereas wall viscosity decreased. In conclusion, there was no evidence of altered arterial wave propagation in proximal PAs of hypoxic rats while the extracellular matrix protein composition was altered and collagen tensile strength increased. This was accompanied by altered mechanical properties in vivo and ex vivo. NEW & NOTEWORTHY In rats exposed to chronic hypoxia, we have shown that pulse wave velocity in the proximal pulmonary arteries increased and pressure dependence of the pulse wave velocity was steeper in vivo than ex vivo leading to a more prominent increase in vivo.

Pulmonary artery wave propagation and reservoir function in conscious man: impact of pulmonary vascular disease, respiration and dynamic stress tests

KEY POINTS

Wave travel plays an important role in cardiovascular physiology. However, many aspects of pulmonary arterial wave behaviour remain unclear. Wave intensity and reservoir-excess pressure analyses were applied in the pulmonary artery in subjects with and without pulmonary hypertension during spontaneous respiration and dynamic stress tests. Arterial wave energy decreased during expiration and Valsalva manoeuvre due to decreased ventricular preload. Wave energy also decreased during handgrip exercise due to increased heart rate. In pulmonary hypertension patients, the asymptotic pressure at which the microvascular flow ceases, the reservoir pressure related to arterial compliance and the excess pressure caused by waves increased. The reservoir and excess pressures decreased during Valsalva manoeuvre but remained unchanged during handgrip exercise. This study provides insights into the influence of pulmonary vascular disease, spontaneous respiration and dynamic stress tests on pulmonary artery wave propagation and reservoir function.

ABSTRACT

Detailed haemodynamic analysis may provide novel insights into the pulmonary circulation. Therefore, wave intensity and reservoir-excess pressure analyses were applied in the pulmonary artery to characterize changes in wave propagation and reservoir function during spontaneous respiration and dynamic stress tests. Right heart catheterization was performed using a pressure and Doppler flow sensor tipped guidewire to obtain simultaneous pressure and flow velocity measurements in the pulmonary artery in control subjects and patients with pulmonary arterial hypertension (PAH) at rest. In controls, recordings were also obtained during Valsalva manoeuvre and handgrip exercise. The asymptotic pressure at which the flow through the microcirculation ceases, the reservoir pressure related to arterial compliance and the excess pressure caused by arterial waves increased in PAH patients compared to controls. The systolic and diastolic rate constants also increased, while the diastolic time constant decreased. The forward compression wave energy decreased by ∼8% in controls and ∼6% in PAH patients during expiration compared to inspiration, while the wave speed remained unchanged throughout the respiratory cycle. Wave energy decreased during Valsalva manoeuvre (by ∼45%) and handgrip exercise (by ∼27%) with unaffected wave speed. Moreover, the reservoir and excess pressures decreased during Valsalva manoeuvre but remained unaltered during handgrip exercise. In conclusion, reservoir-excess pressure analysis applied to the pulmonary artery revealed distinctive differences between controls and PAH patients. Variations in the ventricular preload and afterload influence pulmonary arterial wave propagation as demonstrated by changes in wave energy during spontaneous respiration and dynamic stress tests.