Arterial pulse wave modeling and analysis for vascular-age studies: a review from VascAgeNet.

Arterial pulse waves (PWs) such as blood pressure and photoplethysmogram (PPG) signals contain a wealth of information on the cardiovascular (CV) system that can be exploited to assess vascular age and identify individuals at elevated CV risk. We review the possibilities, limitations, complementarity, and differences of reduced-order, biophysical models of arterial PW propagation, as well as theoretical and empirical methods for analyzing PW signals and extracting clinically relevant information for vascular age assessment. We provide detailed mathematical derivations of these models and theoretical methods, showing how they are related to each other. Finally, we outline directions for future research to realize the potential of modeling and analysis of PW signals for accurate assessment of vascular age in both the clinic and in daily life.

Relationship between fiducial points on the peripheral and central blood pressure waveforms: rate of rise of the central waveform is a determinant of peripheral systolic blood pressure.

Central systolic blood pressure (cSBP, the peak of the central waveform) is usually regarded as the determinant of peripheral systolic blood pressure with amplification of peripheral systolic blood pressure (pSBP) measured with reference to cSBP. However, the earlier portion of the central waveform up to the first systolic shoulder (P1) may be the major determinant of pSBP. We performed in silico simulation studies and examined previously acquired experimental data (n = 131) in which peripheral and central blood pressure waveforms had been acquired both invasively and noninvasively to examine the determinants of pSBP. Measurements were made at baseline and during perturbation of hemodynamics by inotropic and vasoactive drugs. In silico simulations using a central-to-peripheral transfer function demonstrated that pSBP is dependent on P1 and the rate of change (dP/dt) of central pressure up to the time of P1 but not cSBP. In computational simulations, peripheral reflection in the radial artery was closely related to dP/dt, and 97% of the variability in amplification as measured with reference to P1 was explained by dP/dt. In vivo, amplification of pSBP over P1 was correlated with dP/dt (R > 0.75, P < 0.0001 for all data sets), and P1 and dP/dt were independently correlated with pSBP, explaining 90% of the variability in pSBP. We conclude that P1 and dP/dt are major determinants of pSBP and that pSBP and cSBP are, in part, determined by different cardiac, central, and peripheral vascular properties.NEW & NOTEWORTHY Peripheral systolic BP is determined mainly by the first shoulder and the rate of rise of the central systolic blood pressure waveform rather than the peak of this waveform (central systolic BP). Peripheral and central systolic blood pressure are determined by different cardiac and vascular properties.

Estimating central blood pressure from aortic flow: development and assessment of algorithms.

Central blood pressure (cBP) is a highly prognostic cardiovascular (CV) risk factor whose accurate, invasive assessment is costly and carries risks to patients. We developed and assessed novel algorithms for estimating cBP from noninvasive aortic hemodynamic data and a peripheral blood pressure measurement. These algorithms were created using three blood flow models: the two- and three-element Windkessel (0-D) models and a one-dimensional (1-D) model of the thoracic aorta. We tested new and existing methods for estimating CV parameters (left ventricular ejection time, outflow BP, arterial resistance and compliance, pulse wave velocity, and characteristic impedance) required for the cBP algorithms, using virtual (simulated) subjects (n = 19,646) for which reference CV parameters were known exactly. We then tested the cBP algorithms using virtual subjects (n = 4,064), for which reference cBP were available free of measurement error, and clinical datasets containing invasive (n = 10) and noninvasive (n = 171) reference cBP waves across a wide range of CV conditions. The 1-D algorithm outperformed the 0-D algorithms when the aortic vascular geometry was available, achieving central systolic blood pressure (cSBP) errors ≤ 2.1 ± 9.7 mmHg and root-mean-square errors (RMSEs) ≤ 6.4 ± 2.8 mmHg against invasive reference cBP waves (n = 10). When the aortic geometry was unavailable, the three-element 0-D algorithm achieved cSBP errors ≤ 6.0 ± 4.7 mmHg and RMSEs ≤ 5.9 ± 2.4 mmHg against noninvasive reference cBP waves (n = 171), outperforming the two-element 0-D algorithm. All CV parameters were estimated with mean percentage errors ≤ 8.2%, except for the aortic characteristic impedance (≤13.4%), which affected the three-element 0-D algorithm's performance. The freely available algorithms developed in this work enable fast and accurate calculation of the cBP wave and CV parameters in datasets containing noninvasive ultrasound or magnetic resonance imaging data.NEW & NOTEWORTHY First, our proposed methods for CV parameter estimation and a comprehensive set of methods from the literature were tested using in silico and clinical datasets. Second, optimized algorithms for estimating cBP from aortic flow were developed and tested for a wide range of cBP morphologies, including catheter cBP data. Third, a dataset of simulated cBP waves was created using a three-element Windkessel model. Fourth, the Windkessel model dataset and optimized algorithms are freely available.

Modeling arterial pulse waves in healthy aging: a database for in silico evaluation of hemodynamics and pulse wave indexes.

The arterial pulse wave (PW) is a rich source of information on cardiovascular (CV) health. It is widely measured by both consumer and clinical devices. However, the physical determinants of the PW are not yet fully understood, and the development of PW analysis algorithms is limited by a lack of PW data sets containing reference CV measurements. Our aim was to create a database of PWs simulated by a computer to span a range of CV conditions, representative of a sample of healthy adults. The typical CV properties of 25-75 yr olds were identified through a literature review. These were used as inputs to a computational model to simulate PWs for subjects of each age decade. Pressure, flow velocity, luminal area, and photoplethysmographic PWs were simulated at common measurement sites, and PW indexes were extracted. The database, containing PWs from 4,374 virtual subjects, was verified by comparing the simulated PWs and derived indexes with corresponding in vivo data. Good agreement was observed, with well-reproduced age-related changes in hemodynamic parameters and PW morphology. The utility of the database was demonstrated through case studies providing novel hemodynamic insights, in silico assessment of PW algorithms, and pilot data to inform the design of clinical PW algorithm assessments. In conclusion, the publicly available PW database is a valuable resource for understanding CV determinants of PWs and for the development and preclinical assessment of PW analysis algorithms. It is particularly useful because the exact CV properties that generated each PW are known.NEW & NOTEWORTHY First, a comprehensive literature review of changes in cardiovascular properties with age was performed. Second, an approach for simulating pulse waves (PWs) at different ages was designed and verified against in vivo data. Third, a PW database was created, and its utility was illustrated through three case studies investigating the determinants of PW indexes. Fourth, the database and tools for creating the database, analyzing PWs, and replicating the case studies are freely available.

Noninvasive calculation of the aortic blood pressure waveform from the flow velocity waveform: a proof of concept.

Estimation of aortic and left ventricular (LV) pressure usually requires measurements that are difficult to acquire during the imaging required to obtain concurrent LV dimensions essential for determination of LV mechanical properties. We describe a novel method for deriving aortic pressure from the aortic flow velocity. The target pressure waveform is divided into an early systolic upstroke, determined by the water hammer equation, and a diastolic decay equal to that in the peripheral arterial tree, interposed by a late systolic portion described by a second-order polynomial constrained by conditions of continuity and conservation of mean arterial pressure. Pulse wave velocity (PWV, which can be obtained through imaging), mean arterial pressure, diastolic pressure, and diastolic decay are required inputs for the algorithm. The algorithm was tested using 1) pressure data derived theoretically from prespecified flow waveforms and properties of the arterial tree using a single-tube 1-D model of the arterial tree, and 2) experimental data acquired from a pressure/Doppler flow velocity transducer placed in the ascending aorta in 18 patients (mean ± SD: age 63 ± 11 yr, aortic BP 136 ± 23/73 ± 13 mmHg) at the time of cardiac catheterization. For experimental data, PWV was calculated from measured pressures/flows, and mean and diastolic pressures and diastolic decay were taken from measured pressure (i.e., were assumed to be known). Pressure reconstructed from measured flow agreed well with theoretical pressure: mean ± SD root mean square (RMS) error 0.7 ± 0.1 mmHg. Similarly, for experimental data, pressure reconstructed from measured flow agreed well with measured pressure (mean RMS error 2.4 ± 1.0 mmHg). First systolic shoulder and systolic peak pressures were also accurately rendered (mean ± SD difference 1.4 ± 2.0 mmHg for peak systolic pressure). This is the first noninvasive derivation of aortic pressure based on fluid dynamics (flow and wave speed) in the aorta itself.

Patient-specific non-invasive estimation of the aortic blood pressure waveform by ultrasound and tonometry.

BACKGROUND AND OBJECTIVE: Aortic blood pressure (ABP) is a more effective prognostic indicator of cardiovascular disease than peripheral blood pressure. A highly accurate algorithm for non-invasively deriving the ABP wave, based on ultrasonic measurement of aortic flow combined with peripheral pulse wave measurements, has been proposed elsewhere. However, it has remained at the proof-of-concept stage because it requires a priori knowledge of the ABP waveform to calculate aortic pulse wave velocity (PWV). The objective of this study is to transform this proof-of-concept algorithm into a clinically feasible technique. METHODS: We used the Bramwell-Hill equation to non-invasively calculate aortic PWV which was then used to reconstruct the ABP waveform from non-invasively determined aortic blood flow velocity, aortic diameter, and radial pressure. The two aortic variables were acquired by an ultrasound system from 90 subjects, followed by recordings of radial pressure using a SphygmoCor device. The ABPs estimated by the new algorithm were compared with reference values obtained by cardiac catheterization (invasive validation, 8 subjects aged 62.3 ± 12.7 years) and a SphygmoCor device (non-invasive validation, 82 subjects aged 45.0 ± 17.8 years). RESULTS: In the invasive comparison, there was good agreement between the estimated and directly measured pressures: the mean error in systolic blood pressure (SBP) was 1.4 ± 0.8 mmHg; diastolic blood pressure (DBP), 0.9 ± 0.8 mmHg; mean blood pressure (MBP), 1.8 ± 1.2 mmHg and pulse pressure (PP), 1.4 ± 1.1 mmHg. In the non-invasive comparison, the estimated and directly measured pressures also agreed well: the errors being: SBP, 2.0 ± 1.4 mmHg; DBP, 0.8 ± 0.1 mmHg; MBP, 0.1 ± 0.1 mmHg and PP, 2.3 ± 1.6 mmHg. The significance of the differences in mean errors between calculated and reference values for SBP, DBP, MBP and PP were assessed by paired t-tests. The agreement between the reference methods and those obtained by applying the new approach was also expressed by correlation and Bland-Altman plots. CONCLUSION: The new method proposed here can accurately estimate ABP, allowing this important variable to be obtained non-invasively, using standard, well validated measurement techniques. It thus has the potential to relocate ABP estimation from a research environment to more routine use in the cardiac clinic. SHORT ABSTRACT: A highly accurate algorithm for non-invasively deriving the ABP wave has been proposed elsewhere. However, it has remained at the proof-of-concept stage because it requires a priori knowledge of the ABP waveform to calculate aortic pulse wave velocity (PWV). This study aims to transform this proof-of-concept algorithm into a clinically feasible technique. We used the Bramwell-Hill equation to non-invasively calculate aortic PWV which was then used to reconstruct the ABP waveform. The ABPs estimated by the new algorithm were compared with reference values obtained by cardiac catheterization or a SphygmoCor device. The results showed that there was good agreement between the estimated and directly measured pressures. The new method proposed can accurately estimate ABP, allowing this important variable to be obtained non-invasively, using standard, well validated measurement techniques. It thus has the potential to relocate ABP estimation from a research environment to more routine use in the cardiac clinic.

Ethnicity differences in geometric remodelling and myocardial composition in hypertension unveiled by cardiovascular magnetic resonance.

AIMS: Hypertensive patients of African ancestry (Afr-a) have higher incidences of heart failure and worse clinical outcomes than hypertensive patients of European ancestry (Eu-a), yet the underlying mechanisms remain misunderstood. This study investigated right (RV) and left (LV) ventricular remodelling alongside myocardial tissue derangements between Afr-a and Eu-a hypertensives. METHODS AND RESULTS: 63 Afr-a and 47 Eu-a hypertensives underwent multi-parametric cardiovascular magnetic resonance. Biventricular volumes, mass, function, mass/end-diastolic volume (M/V) ratios, T2 and pre-/post-contrast T1 relaxation times, synthetic extracellular volume, and myocardial fibrosis (MF) were measured. 3D shape modelling was implemented to delineate ventricular geometry. LV and RV mass (indexed to body-surface-area) and M/V ratio were significantly greater in Afr-a than Eu-a hypertensives (67.1 ± 21.7 vs. 58.3 ± 16.7 g/m2, 12.6 ± 3.48 vs. 10.7 ± 2.71 g/m2, 0.79 ± 0.21 vs. 0.70 ± 0.14 g/mL, and 0.16 ± 0.04 vs. 0.13 ± 0.03 g/mL, respectively; P < 0.03). Afr-a patients showed greater basal interventricular septum thickness than Eu-a patients, influencing LV hypertrophy and RV cavity changes. This biventricular remodelling was associated with prolonged T2 relaxation time (47.0 ± 2.2 vs. 45.7 ± 2.2 ms, P = 0.005) and higher prevalence (23% vs. 4%, P = 0.001) and extent of MF [2.3 (0.6-14.3) vs. 1.6 (0.9-2.5) % LV mass, P = 0.008] in Afr-a patients. Multivariable linear regression showed that modifiable cardiovascular risk factors and greater end-diastolic volume, but not ethnicity, were independently associated with greater LV mass. CONCLUSION: Afr-a hypertensives had distinctive biventricular remodelling, including increased RV mass, septal thickening and myocardial tissue abnormalities compared with Eu-a hypertensives. From this study, modifiable cardiovascular risk factors and ventricular geometry, but not ethnicity, were independently associated with greater LV myocardial mass.

Novel Pressure Wave Separation Analysis for Cardiovascular Function Assessment Highlights Major Role of Aortic Root.

OBJECTIVE: A novel method was presented to separate the central blood pressure wave (CBPW) into five components with different biophysical and temporal origins. It includes a time-varying emission coefficient ( γ) that quantifies pulse wave generation and reflection at the aortic root. METHODS: The method was applied to normotensive subjects with modulated physiology by inotropic/vasoactive drugs (n = 13), hypertensive subjects (n = 158), and virtual subjects (n = 4,374). RESULTS: γ is directly proportional to aortic flow throughout the cardiac cycle. Mean peak γ increased with increasing pulse pressure (from <30 to >70 mmHg) in the hypertensive (from 1.6 to 2.5, P < 0.001) and in silico (from 1.4 to 2.8, P < 0.001) groups, dobutamine dose (from baseline to 7.5 µg/kg/min) in the normotensive group (from 2.1 to 2.7, P < 0.05), and remained unchanged when peripheral wave reflections were suppressed in silico. This was accompanied by an increase in the percentage contribution of the cardiac-aortic-coupling component of CBPW in systole: from 11% to 23% (P < 0.001) in the hypertensive group, 9% to 21% (P < 0.001) in the in silico group, and 17% to 23% (P < 0.01) in the normotensive group. CONCLUSION: These results suggest that the aortic root is a major reflection site in the systemic arterial network and ventricular-aortic coupling is the main determinant in the elevation of pulsatile pulse pressure. SIGNIFICANCE: Ventricular-aortic coupling is a prime therapeutic target for preventing/treating systolic hypertension.

Hemodynamic Mechanism of the Age-Related Increase in Pulse Pressure in Women.

We examined the influence of arterial stiffening and ventricular ejection dynamics on the age-related increase in central pulse pressure. A total of 2033 women aged 18 to 91 years from the Twins UK cohort were studied. Aortic flow and central blood pressure were measured by Doppler sonography and carotid tonometry, respectively. Measured values of central pulse pressure were compared with values predicted from aortic pulse wave velocity and ventricular ejection characteristics. Central pulse pressure at the first shoulder ( P1) increased with age from 29.2±8.0 in those <40 years to 44.2±13.8 mm Hg in those >70 years (means±SD; P<0.001), an increase explained almost entirely by the concomitant increase in aortic pulse wave velocity. Pulse pressure, at the second pressure peak ( P2, usually equal to peak central pulse pressure) increased to a greater extent with age: from 29.1±7.8 mm Hg for those <40 years to 60.2±20.5 mm Hg for those >70 years ( P<0.001). The ratio of P2/P1 closely mirrored the ratio of ejection volume to ejection velocity at corresponding time points, and the proportionately greater increase in P2 compared with P1 was explained by increased ventricular ejection up to the time of P2. This increased from 52.5±13.1 to 59.3±17.8 mL ( P<0.001) in parallel with an age-related increase in stroke volume and body mass index. These results suggest that the age-related change in central pulse wave morphology is driven mainly by an increase in arterial stiffening and altered pattern of ventricular ejection.

Identifying Hemodynamic Determinants of Pulse Pressure: A Combined Numerical and Physiological Approach.

We examined the ability of a simple reduced model comprising a proximal characteristic impedance linked to a Windkessel element to accurately predict central pulse pressure (PP) from aortic blood flow, verified that parameters of the model corresponded to physical properties, and applied the model to examine PP dependence on cardiac and vascular properties. PP obtained from the reduced model was compared with theoretical values obtained in silico and measured values in vivo. Theoretical values were obtained using a distributed multisegment model in a population of virtual (computed) subjects in which cardiovascular properties were varied over the pathophysiological range. In vivo measurements were in normotensive subjects during modulation of physiology with vasoactive drugs and in hypertensive subjects. Central PP derived from the reduced model agreed with theoretical values (mean difference±SD, -0.09±1.96 mm Hg) and with measured values (mean differences -1.95±3.74 and -1.18±3.67 mm Hg for normotensive and hypertensive subjects, respectively). Parameters extracted from the reduced model agreed closely with theoretical and measured physical properties. Central PP was seen to be determined mainly by total arterial compliance (inversely associated with central arterial stiffness) and ventricular dynamics: the blood volume ejected by the ventricle into the aorta up to time of peak pressure and blood flow into the aorta (corresponding to the rate of ventricular ejection) up to this time point. Increased flow and volume accounted for 20.1 mm Hg (52%) of the 39.0 mm Hg difference in PP between the upper and lower tertiles of the hypertensive subjects.

Computational assessment of hemodynamics-based diagnostic tools using a database of virtual subjects: Application to three case studies.

Many physiological indexes and algorithms based on pulse wave analysis have been suggested in order to better assess cardiovascular function. Because these tools are often computed from in-vivo hemodynamic measurements, their validation is time-consuming, challenging, and biased by measurement errors. Recently, a new methodology has been suggested to assess theoretically these computed tools: a database of virtual subjects generated using numerical 1D-0D modeling of arterial hemodynamics. The generated set of simulations encloses a wide selection of healthy cases that could be encountered in a clinical study. We applied this new methodology to three different case studies that demonstrate the potential of our new tool, and illustrated each of them with a clinically relevant example: (i) we assessed the accuracy of indexes estimating pulse wave velocity; (ii) we validated and refined an algorithm that computes central blood pressure; and (iii) we investigated theoretical mechanisms behind the augmentation index. Our database of virtual subjects is a new tool to assist the clinician: it provides insight into the physical mechanisms underlying the correlations observed in clinical practice.