Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

Uncertainty Quantification and Sensitivity Analysis for Non-invasive Model-Based Instantaneous Wave-Free Ratio Prediction

The main objectives of this work are to validate a 1D-0D unsteady solver with a distributed stenosis model for the patient-specific estimation of resting haemodynamic indices and to assess the sensitivity of instantaneous wave-free ratio (iFR) predictions to uncertainties in input parameters. We considered 52 patients with stable coronary artery disease, for which 81 invasive iFR measurements were available. We validated the performance of our solver compared to 3D steady-state and transient results and invasive measurements. Next, we used a polynomial chaos approach to characterise the uncertainty in iFR predictions based on the inputs associated with boundary conditions (coronary flow, compliance and aortic/left ventricular pressures) and vascular geometry (radius). Agreement between iFR and the ratio between cardiac cycle averaged distal and aortic pressure waveforms (restingP d / P a $$ {P}_d/{P}_a $$ ) obtained through 1D-0D and 3D models was satisfactory, with a bias of 0.0-0.005 (±0.016-0.026). The sensitivity analysis showed that iFR estimation is mostly affected by uncertainties in vascular geometry and coronary flow (steady-state parameters). In particular, our 1D-0D method overestimates invasive iFR measurements, with a bias of -0.036 (±0.101), indicating that better flow estimates could significantly improve our modelling pipeline. Conversely, we showed that standard pressure waveforms could be used for simulations, since the impact of uncertainties related to inlet-pressure waveforms on iFR prediction is negligible. Furthermore, while compliance is the most relevant transient parameter, its effect on iFR estimates is negligible compared to that of vascular geometry and flow. Finally, we observed a strong correlation between iFR and restingP d / P a $$ {P}_d/{P}_a $$ , suggesting that steady-state simulations could replace unsteady simulations for iFR prediction.

Listening to heart sounds through the pressure waveform

Non-invasive diagnostic modalities are integral to cardiovascular care; however, current systems primarily measure peripheral pressure, limiting the breadth of cardiovascular prognostication. We report a novel approach for extracting left side heart sounds using a brachial cuff device. The technique leverages brachial cuff device enhanced signal resolution to capture pressure fluctuations generated by cardiohemic system vibrations, the sound pressure waveform. We analyze left heart catheterization data alongside simultaneous brachial cuff device measurements to correlate sound pressure waveform features with left ventricle (LV) contractility. The extracted sound pressure waveform reveals two prominent oscillatory wave packets, termed WP1 and WP2, originating from cardiac structure vibrations associated with LV contractions and relaxation. We demonstrate that WP1 originates from LV contraction during systolic blood ejection through the aortic valve (AV) and is correlated with LV isovolumetric contraction, clinically measured by LV dPdt-max (Pearson-R = 0.65, p < 0.001). Additionally, we show that WP2 comes from LV elongation required for blood flow deceleration at the end of systole, causing AV closure, and is correlated with LV isovolumetric relaxation, measured by LV ndPdt-max (Pearson-R = 0.55, p < 0.001). These findings highlight the value of cuff sound pressure waveforms in providing insights about dynamic coupling of the LV-Aorta complex for non-invasive assessment of LV contractility.

Elastic jump propagation across a blood vessel junction

The theory of small-amplitude waves propagating across a blood vessel junction has been well established with linear analysis. In this study, we consider the propagation of large-amplitude, nonlinear waves (i.e. shocks and rarefactions) through a junction from a parent vessel into two (identical) daughter vessels using a combination of three approaches: numerical computations using a Godunov method with patching across the junction, analysis of a nonlinear Riemann problem in the neighbourhood of the junction and an analytical theory which extends the linear analysis to the following order in amplitude. A unified picture emerges: an abrupt (prescribed) increase in pressure at the inlet to the parent vessel generates a propagating shock wave along the parent vessel which interacts with the junction. For modest driving, this shock wave divides into propagating shock waves along the two daughter vessels and reflects a rarefaction wave back towards the inlet. However, for larger driving the reflected rarefaction wave becomes transcritical, generating an additional shock wave. Just beyond criticality this new shock wave has zero speed, pinned to the junction, but for further increases in driving this additional shock divides into two new propagating shock waves in the daughter vessels.

An in silico study of the effects of cardiovascular aging on carotid flow waveforms and indexes in a virtual population

Cardiovascular aging is strongly associated with increased risk of cardiovascular disease and mortality. Moreover, health and lifestyle factors may accelerate age-induced alterations, such as increased arterial stiffness and wall dilation, beyond chronological age, making the clinical assessment of cardiovascular aging an important prompt for preventative action. Carotid flow waveforms contain information about age-dependent cardiovascular properties, and their ease of measurement via noninvasive Doppler ultrasound (US) makes their analysis a promising tool for the routine assessment of cardiovascular aging. In this work, the impact of different aging processes on carotid waveform morphology and derived indexes is studied in silico, with the aim of establishing the clinical potential of a carotid US-based assessment of cardiovascular aging. One-dimensional (1-D) hemodynamic modeling was employed to generate an age-specific virtual population (VP) of N = 5,160 realistic carotid hemodynamic waveforms. The resulting VP was statistically validated against in vivo aging trends in waveforms and indexes from the literature, and simulated waveforms were studied in relation to age and underlying cardiovascular parameters. In our study, the carotid flow augmentation index (FAI) significantly increased with age (with a median increase of 50% from the youngest to the oldest age group) and was strongly correlated to local arterial stiffening (r = 0.94). The carotid pulsatility index (PI), which showed less pronounced age variation, was inversely correlated with the reflection coefficient at the carotid branching (r = -0.88) and directly correlated with carotid net forward wave energy (r = 0.90), corroborating previous literature where it was linked to increased risk of cerebrovascular damage in the elderly. There was a high correlation between corrected carotid flow time (ccFT) and cardiac output (CO) (r = 0.99), which was not affected by vascular age. This study highlights the potential of carotid waveforms as a valuable tool for the assessment of cardiovascular aging.NEW & NOTEWORTHY An age-specific virtual population was generated based on a 1-D model of the arterial circulation, including newly defined literature-based specific age variations in carotid vessel properties. Simulated carotid flow/velocity waveforms, indexes, and age trends were statistically validated against in vivo data from the literature. A comprehensive study of the impact of aging on carotid flow waveform morphology was performed, and the mechanisms influencing different carotid indexes were elucidated. Notably, flow augmentation index (FAI) was found to be a strong indicator of local carotid stiffness.

Signatures of obstructions and expansions in the arterial frequency response

BACKGROUND AND OBJECTIVE

The blood pressure and flow waveforms carry valuable information about the condition of the cardiovascular system and a patient's health. Waveform analysis in health and pathological conditions can be performed in the time or frequency domains; the information to be emphasised defines the use of either domain. However, physicians are more familiar with the time domain, and the changes in the waveforms due to cardiovascular diseases and ageing are better characterised in such domain. On the other hand, the analysis of the vascular and geometrical variables determining the signatures in the frequency response of local vascular anomalies, such as aneurysms and stenoses, has not been thoroughly explored. This paper aims to characterise the signatures of obstructions (stenoses) and expansions (aneurysms) in the frequency response of tapered arteries.

METHODS

The first step in our methodology was to incorporate the viscous response of the arterial wall into a one-dimensional elastic formulation that solves the governing equations in the frequency domain. As a second step, we imposed a volumetric flow excitation in arteries simulating the aorta with increasing geometry complexity: from straight to tapered arteries with local expansions or obstructions; and we assessed the frequency response.

RESULTS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that are distinguishable from a health condition. The signatures of obstruction and expansions differ; the obstructions increase the magnitude of fundamental frequency and work as a close boundary condition. On the other hand, the expansions diminish the fundamental frequency and work as an open boundary condition. Furthermore, such signatures correlate to the distance between the artery's inlet and the anomaly's starting point and have the potential to pinpoint abnormalities non-invasively.

CONCLUSIONS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that have the potential to detect and follow up on the development of vascular abnormalities. For the latter purpose, constant monitoring may be required; despite this not being a common clinical practice, the new wearable technology offers the possibility of continuous monitoring of biophysical markers such as the pressure waveform.

The effect of cardiac properties on arterial pulse waves: An in-silico study

This study investigated the effects of cardiac properties variability on arterial pulse wave morphology using blood flow modelling and pulse wave analysis. A lumped-parameter model of the left part of the heart was coupled to a one-dimensional model of the arterial network and validated using reference pulse waveforms in turn verified by comparison with in vivo measurements. A sensitivity analysis was performed to assess the effects of variations in cardiac parameters on central and peripheral pulse waveforms. Results showed that left ventricle contractility, stroke volume, cardiac cycle duration, and heart valves impairment are determinants of central waveforms morphology, pulse pressure and its amplification. Contractility of the left atrium has negligible effects on arterial pulse waves. Results also suggested that it might be possible to infer left ventricular dysfunction by analysing the timing of the dicrotic notch and cardiac function by analysing PPG signals. This study has identified cardiac properties that may be extracted from in vivo central and peripheral pulse waves to assess cardiac function.

A noninvasive method of estimating patient-specific left ventricular pressure waveform

BACKGROUND AND OBJECTIVE

The left ventricular pressure waveform is indispensable for the construction of the pressure strain loop when investigating coronary artery disease (CAD) patients. In previous studies by others, exclusion of CAD patients has not allowed a reliable estimation of the left ventricular pressure waveform from the pressure strain loop of these patients. To remedy this, we propose a patient-specific noninvasive method for the estimation of left ventricular pressure.

METHODS

A simplified systemic circulation model consisting primarily of a single fiber model and a 1D simulation of the arterial tree was used. Sensitivity analysis based on the Morris method was performed to select a subset of the important parameters. Following this, the important parameter subset and the set of all the parameters were identified in the model using the pressure waveform of a peripheral artery as input, in a two-step process. In addition, the left ventricular pressure waveform was estimated using the set of all parameters.

RESULTS

Reducing the size of the parameter subset significantly decreases the computational cost of parameter optimization in the first step and greatly simplifies the identification of the full parameter set in the second step. Comparison with the reference left ventricular pressure waveform from CAD patients, showed that the proposed method provides a good estimate of the reference left ventricular pressure waveform. The correlation coefficients between the estimated and reference were r = 0.907, r = 0.904 and r = 0.780 for systolic blood pressure, pulse pressure and mean blood pressure, respectively.

CONCLUSIONS

This work may provide a convenient surrogate for the estimation of the left ventricular pressure waveform.

Computational modelling and application of mechanical waves to detect arterial network anomalies: Diagnosis of common carotid stenosis

BACKGROUND AND OBJECTIVE

This paper proposes a novel strategy to localize anomalies in the arterial network based on its response to controlled transient waves. The idea is borrowed from system identification theories in which wave reflections can render significant information about a target system. Cardiovascular system studies often focus on the waves originating from the heart pulsations, which are of low bandwidth and, hence, can hardly carry information about the arteries with the desired resolution.

METHODS

Our strategy uses a relatively higher bandwidth transient signal to characterize healthy and unhealthy arterial networks through a frequency response function (FRF). We tested our novel approach on data simulated using a one-dimensional cardiovascular model that produced pulse waves in the larger arteries of the arterial network. Specifically, we excited the blood flow from the brachial artery with a relatively high bandwidth flow disturbance and collected the subsequent pressure waveform at peripheral positions. To better differentiate FRFs of healthy and unhealthy networks, we used a FRF that removes the effects of heart pulsations.

RESULTS

Results demonstrate the ability of the proposed FRF to detect and follow-up on the development of a common carotid artery (CCA) stenosis. We tested distinct geometrical variations of the stenosis (size, length and position) and observed differences between the FRFs of healthy and unhealthy networks in all cases; such differences were mainly due to geometrical variations determined by the stenosis.

CONCLUSIONS

We have provided a theoretical proof of concept that demonstrates the ability of our novel strategy to detect and track the development of CCA stenosis by using peripheral pressure waves that can be measured non-invasively in clinical practice.

Early Diagnosis of Intracranial Internal Carotid Artery Stenosis Using Extracranial Hemodynamic Indices from Carotid Doppler Ultrasound

Atherosclerotic intracranial internal carotid artery stenosis (IICAS) is a leading cause of strokes. Due to the limitations of major cerebral imaging techniques, the early diagnosis of IICAS remains challenging. Clinical studies have revealed that arterial stenosis may have complicated effects on the blood flow’s velocity from a distance. Therefore, based on a patient-specific one-dimensional hemodynamic model, we quantitatively investigated the effects of IICAS on extracranial internal carotid artery (ICA) flow velocity waveforms to identify sensitive hemodynamic indices for IICAS diagnoses. Classical hemodynamic indices, including the peak systolic velocity (PSV), end-diastolic velocity (EDV), and resistive index (RI), were calculated on the basis of simulations with and without IICAS. In addition, the first harmonic ratio (FHR), which is defined as the ratio between the first harmonic amplitude and the sum of the amplitudes of the 1st−20th order harmonics, was proposed to evaluate flow waveform patterns. To investigate the diagnostic performance of the indices, we included 52 patients with mild-to-moderate IICAS (<70%) in a case−control study and considered 24 patients without stenosis as controls. The simulation analyses revealed that the existence of IICAS dramatically increased the FHR and decreased the PSV and EDV in the same patient. Statistical analyses showed that the average PSV, EDV, and RI were lower in the stenosis group than in the control group; however, there were no significant differences (p > 0.05) between the two groups, except for the PSV of the right ICA (p = 0.011). The FHR was significantly higher in the stenosis group than in the control group (p < 0.001), with superior diagnostic performance. Taken together, the FHR is a promising index for the early diagnosis of IICAS using carotid Doppler ultrasound methods.

A coupling strategy for a first 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

A key factor governing the mechanical performance of the heart is the bidirectional coupling with the vascular system, where alterations in vascular properties modulate the pulsatile load imposed on the heart. Current models of cardiac electromechanics (EM) use simplified 0D representations of the vascular system when coupling to anatomically accurate 3D EM models is considered. However, these ignore important effects related to pulse wave transmission. Accounting for these effects requires 1D models, but a 3D-1D coupling remains challenging. In this work, we propose a novel, stable strategy to couple a 3D cardiac EM model to a 1D model of blood flow in the largest systemic arteries. For the first time, a personalised coupled 3D-1D model of left ventricle and arterial system is built and used in numerical benchmarks to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system's physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our first 3D-1D coupled model is shown to be efficient and robust, with negligible additional computational costs compared to 3D-0D models. We further demonstrate that the calibrated 3D-1D model produces simulated data that match with clinical data under baseline conditions, and that known physiological responses to alterations in vascular resistance and stiffness are correctly replicated. Thus, using our coupled 3D-1D model will be beneficial in modelling studies investigating wave propagation phenomena.

A proof of concept study for machine learning application to stenosis detection

This proof of concept (PoC) assesses the ability of machine learning (ML) classifiers to predict the presence of a stenosis in a three vessel arterial system consisting of the abdominal aorta bifurcating into the two common iliacs. A virtual patient database (VPD) is created using one-dimensional pulse wave propagation model of haemodynamics. Four different machine learning (ML) methods are used to train and test a series of classifiers—both binary and multiclass—to distinguish between healthy and unhealthy virtual patients (VPs) using different combinations of pressure and flow-rate measurements. It is found that the ML classifiers achieve specificities larger than 80% and sensitivities ranging from 50 to 75%. The most balanced classifier also achieves an area under the receiver operative characteristic curve of 0.75, outperforming approximately 20 methods used in clinical practice, and thus placing the method as moderately accurate. Other important observations from this study are that (i) few measurements can provide similar classification accuracies compared to the case when more/all the measurements are used; (ii) some measurements are more informative than others for classification; and (iii) a modification of standard methods can result in detection of not only the presence of stenosis, but also the stenosed vessel.

Graphical Abstract

Machine learning for detection of stenoses and aneurysms: application in a physiologically realistic virtual patient database

This study presents an application of machine learning (ML) methods for detecting the presence of stenoses and aneurysms in the human arterial system. Four major forms of arterial disease-carotid artery stenosis (CAS), subclavian artery stenosis (SAS), peripheral arterial disease (PAD), and abdominal aortic aneurysms (AAA)-are considered. The ML methods are trained and tested on a physiologically realistic virtual patient database (VPD) containing 28,868 healthy subjects, adapted from the authors previous work and augmented to include disease. It is found that the tree-based methods of Random Forest and Gradient Boosting outperform other approaches. The performance of ML methods is quantified through the [Formula: see text] score and computation of sensitivities and specificities. When using six haemodynamic measurements (pressure in the common carotid, brachial, and radial arteries; and flow-rate in the common carotid, brachial, and femoral arteries), it is found that maximum [Formula: see text] scores larger than 0.9 are achieved for CAS and PAD, larger than 0.85 for SAS, and larger than 0.98 for both low- and high-severity AAAs. Corresponding sensitivities and specificities are larger than 90% for CAS and PAD, larger than 85% for SAS, and larger than 98% for both low- and high-severity AAAs. When reducing the number of measurements, performance is degraded by less than 5% when three measurements are used, and less than 10% when only two measurements are used for classification. For AAA, it is shown that [Formula: see text] scores larger than 0.85 and corresponding sensitivities and specificities larger than 85% are achievable when using only a single measurement. The results are encouraging to pursue AAA monitoring and screening through wearable devices which can reliably measure pressure or flow-rates.

Machine Learning-Based Pulse Wave Analysis for Early Detection of Abdominal Aortic Aneurysms Using In Silico Pulse Waves

An abdominal aortic aneurysm (AAA) is usually asymptomatic until rupture, which is associated with extremely high mortality. Consequently, the early detection of AAAs is of paramount importance in reducing mortality; however, most AAAs are detected by medical imaging only incidentally. The aim of this study was to investigate the feasibility of machine learning-based pulse wave (PW) analysis for the early detection of AAAs using a database of in silico PWs. PWs in the large systemic arteries were simulated using one-dimensional blood flow modelling. A database of in silico PWs representative of subjects (aged 55, 65 and 75 years) with different AAA sizes was created by varying the AAA-related parameters with major impacts on PWs—identified by parameter sensitivity analysis—in an existing database of in silico PWs representative of subjects without AAAs. Then, a machine learning architecture for AAA detection was trained and tested using the new in silico PW database. The parameter sensitivity analysis revealed that the AAA maximum diameter and stiffness of the large systemic arteries were the dominant AAA-related biophysical properties considerably influencing the PWs. However, AAA detection by PW indexes was compromised by other non-AAA related cardiovascular parameters. The proposed machine learning model produced a sensitivity of 86.8 % and a specificity of 86.3 % in early detection of AAA from the photoplethysmogram PW signal measured in the digital artery with added random noise. The number of false positive and negative results increased with increasing age and decreasing AAA size, respectively. These findings suggest that machine learning-based PW analysis is a promising approach for AAA screening using PW signals acquired by wearable devices.