Pulse Wave Imaging for Noninvasive and Quantitative Measurement of Arterial Stiffness In Vivo

Abstract

Background

Arterial stiffening is recognized to be associated with increased cardiovascular mortality and to be a major cause of several cardiovascular complications. Pulse wave velocity (PWV) has been widely accepted to be a reliable and robust measure of arterial stiffness. In this article, the novel ultrasound-based pulse wave imaging (PWI) method is hereby proposed for visualization of the pulse wave during its propagation and for calculation of the PWV.

Methods

The PWV is estimated by measuring the spatiotemporal variation of the pulse wave-induced displacement of the arterial wall within the imaged segment. The method is compared to mechanical testing on aortic phantoms in order to evaluate its reliability and accuracy, and in vivo results are presented on normal abdominal aortas (N = 11).

Results

Good agreement was found with mechanical testing on phantoms (r² = 0.92), showing the reliability of the method. In vivo average PWV and Young's modulus were found to be equal to 4.4 ± 0.6m/s and 108 ± 27kPa, respectively.

Conclusions

Reliability and in vivo feasibility of the proposed PWI method were demonstrated in this study. Its simplicity of use and its capability of providing regional PWV render PWI a valuable tool for quantitative assessment of arterial stiffness. The utility of the method in a clinical setting has yet to be established and is part of an ongoing clinical study.

The relationship between arterial stiffness and cardiovascular risk has been repeatedly demonstrated in several reported studies. The stiffness of large arteries has been shown to be an independent predictor of all-cause and cardiovascular mortalities,¹ especially in hypertensive subjects.² More specifically, aortic stiffness has been shown to be a predictor of primary coronary events³ and of fatal stroke⁴ in hypertensive patients, an independent risk factor for recurrent acute coronary events in patients with ischemic heart disease,⁵ or an independent predictor of cardiovascular mortality for patients with end-stage renal disease⁶. Type-2 diabetes has also been shown to be associated with increased stiffness,^7,8,9 and this association is believed to be a major cause for the increased general cardiovascular risk related to diabetes.¹⁰ Connective tissue disorders such as Marfan syndrome are also associated with significant changes in arterial elasticity,^11,12 which can be an interesting indicator of the progression of the disease.¹³ In all these cases, the knowledge of the arterial stiffness represents a valuable interest for diagnosis, prognosis and decision regarding therapy, and follow-up of the patient. Measuring the arterial stiffness has been recently recommended as an additional test for hypertension management in a Task Force study appointed by the European Society of Hypertension and the European Society of Cardiology.¹⁴

The underlying reason for the correlation between arterial stiffness and cardiovascular risk is related to changes in the cardiac work resulting from arterial stiffening, leading eventually to cardiac hypertrophy, alteration of perfusion and of metabolic demand, and increased systolic dysfunction.^15,16

Reliable methods capable of estimating arterial stiffness represent therefore significant clinical interest. Moreover, the existing poor knowledge on the relationship between molecular and other microscopic processes and arterial stiffening is related to the lack of reliable methods for in vivo measurement of arterial mechanical properties.¹⁷ For all aforementioned reasons, there is valuable interest for a noninvasive, simple-to-use method for quantitative measurement of arterial stiffness in vivo.

The most widespread method for aortic stiffness measurement is the estimation of the pulse wave velocity (PWV), which is directly related to arterial stiffness. In a cylindrical elastic tube filled with an incompressible fluid, the PWV is related to the elastic Young's modulus by the modified Moens–Korteweg equation:¹⁸

where E and ν are the aortic wall Young's modulus and Poisson's ratio (ν ≃ 0.5 for soft quasi-incompressible tissues), R is the lumen radius, h is the wall thickness, and ρ is the density of the wall. Measuring the systemic carotid-femoral PWV is currently recognized as the simplest and most robust method to determine arterial stiffness.¹⁹ It consists of measuring the temporal pulse profile at two different locations, typically, at the carotid and femoral arteries in order to obtain a PWV value averaged within the whole aorta. This can be performed either transcutaneously or by using Doppler flow probes.^19,20 By measuring the time delay Δt of the same point in the waveform (e.g., the foot of the wave) and by estimating the arterial distance ΔD between the two measurement locations, the PWV can be simply estimated as PWV = ΔD/Δt. Several commercially available devices have been developed that allow such measurements.¹⁹ Such methods have proved their relevance and their robustness and they are at the core of most clinical studies involving the measurement of arterial stiffness. However, they are associated with significant limitations that cannot be ignored. The most important one is the lack of knowledge of the exact arterial geometry, which in turn yields uncertainty on the distance measurement ΔD and therefore on the PWV estimate. Moreover, assuming a single-longitudinal flow direction between the carotid and the femoral arteries is incorrect and leads generally to an overestimation of ΔD. Fundamental limitations of such methods have been reviewed in details.²¹ For this reason, the quantitative nature of the PWV estimate becomes limited. Another characteristic of such methods is the global nature of the measurement, as the PWV estimate represents an average global velocity of the pulse wave between the two remote measurement locations. It could be interesting in certain cases to also be able to perform a more localized measurement that could give complementary information of diseases affecting regional arterial stiffness or that could investigate differences in the PWV along the aorta.

Ultrasound-based methods have been proposed for the measurement of local arterial stiffness, in contrast with the global arterial stiffness obtained on large regions by the aforementioned methods. They consist of measuring the diameter changes of the aorta at a chosen location in a cross-sectional view, and in evaluating a stiffness parameter by using the additional measurement of the blood pressure. Several parameters, e.g., arterial distensibility, arterial compliance, elastic modulus, volume elastic modulus, Young's elastic modulus, which are all related to the mechanical stiffness of the artery, have previously been proposed and reviewed.^18,22 The main limitation of those parameters is that, unlike the PWV methods, their estimation requires arterial pressure measurement. Pressure can only be invasively assessed in deep-seated vessels for on-site measurement via catheterization. Noninvasive assessment of pressure can also be performed at peripheral arteries by tonometry, but differences of pressure profiles along the arterial tree lead to increased measurement inaccuracy.²²

In this context, this study presents a simple-to-use, totally noninvasive, ultrasound radio-frequency-based speckle tracking method for imaging of the pulse wave and for regional and quantitative assessment of the PWV. Pulse wave imaging (PWI) is a recent imaging technique developed by our group that uses cross-correlation in order to image the pulse wave during its propagation and to estimate the PWV within the imaged segment.²³ It is based on the estimation of 1D radial incremental displacements of the arterial wall in a longitudinal view. The spatiotemporal variations of the displacement allow us to visualize the pulse wave propagation and to estimate the PWV regionally within the field-of-view of the image. The method has been tested in both healthy and diseased mice in vivo.^24,25 First, preliminary PWI measurements obtained in human subjects in vivo have been presented in a very limited sample size²⁶ (five subjects, one measurement per subject), in order to illustrate the feasibility of performing such measurements. The purpose of the present study is to assess the reliability and the reproducibility of the method and to evaluate its capability of estimating PWV and stiffness values in a group of healthy subjects. This study addresses these issues, namely (i) the validation of the method using aortic phantoms, whose stiffness is measured by mechanical testing and (ii) the applicability on human subjects by performing in vivo measurement on healthy subjects, estimating therefore the PWV and, by using the measurement of geometrical dimensions of the aorta, the elastic modulus of the aortic wall.

Methods

Phantom study: validation of the method

Phantom preparation: In order to evaluate the accuracy of the PWI method, experiments were performed on aortic phantoms whose mechanical properties were also measured by mechanical testing. Five polyacrylamide phantoms with different concentrations (20, 25, 30, 35, and 40% polyacrylamide) were prepared. Before gel polymerization, 2% agar powder was added to generate scatterers, and the liquid mixture was poured inside a cylindrical mold. The same mixture was also used in order to prepare samples for mechanical testing. Aortic phantoms had an inner diameter of 9.7mm and a wall thickness of 2mm to closely model the human aorta.

Experimental protocol: Experiments were performed in a water bath (Figure 1). The pulsatile flow was generated by using a peristaltic pump (Manostat Varistaltic, Barrington, IL) and the pulse frequency was set to ~2Hz. A linear array (f = 10MHz) was used for imaging using a clinical ultrasound system (Sonix RP; Ultrasonix Medical, Burnaby, British Columbia, Canada). The sampling frequency was equal to 20MHz, the depth to 40mm, the width to 38mm, and the line density to 16 beams for a full sector. The frame rate was equal to 446Hz. The incremental axial displacement of the aortic wall was calculated by using a 1D cross-correlation method between two consecutive frames.²⁵ This displacement u(z,t) was estimated all along the wall vs. time, allowing to obtain its spatiotemporal profile, where t is the time and z is the distance from the most proximal side (in this case, the inlet of the phantom). The PWV was then calculated from the slope of u(z,t) by tracking the foot of the wave. Ten measurements were performed for each phantom.

Figure 1. Schematic of the experimental protocol used for phantom experiments. The pulsatile flow is generated by a peristaltic pump, and the aortic phantom is imaged in a water bath.

Mechanical testing: For each phantom, a total of six samples were tested in quasi-static shear tests using an ARES rheometer (TA-Instruments, New Castle, DE). The shear modulus G was measured, and, assuming quasi-incompressibility, the Young's modulus E could be determined as E = 3G. Cylindrical samples (12mm diameter, 3–4mm thick) were tested. Additional details about this mechanical testing protocol have already been reported.²⁷

In vivo study

Experiments were performed on 12 healthy volunteers, among whom one subject was rejected due to poor echographic image. The results reported here are therefore those obtained on 11 healthy subjects (4 females and 7 males), with ages varying between 24 to 36 years (average 28.9 ± 3.3 years old, ± denoting the s.d.). The age range was chosen to be narrow in order to limit the effect of age. The blood pressure was measured by sphygmomanometry in order to ensure that all subjects were normotensive. The study was approved by the Institutional Review Board of Columbia University. The infrarenal abdominal aorta was imaged transabdominally using a phased array (f = 3.3MHz) and the same ultrasound system as for the phantoms. The angle of view was 90°, and the image depth varied between 8 and 11cm depending on the subject. The line density was equal to 32 beams per full sector, so that the frame rate varied between 180 and 260Hz. Ten measurements were performed on each subject at different cardiac cycles and averaged.

Results

Phantom study

As described in the Methods section, the PWV was calculated from the spatiotemporal profile of the incremental displacement u(z,t). An example of the temporal incremental displacement at four different time frames, overlaid onto the B-mode image, is illustrated in Figure 2, clearly showing the propagation of the wavefront.

Figure 2. Successive PWI images (overlaid onto underlying B-mode image), showing the propagation of the pulse wave from left to right. White arrows depict the approximate location of foot of the wave on both upper (corresponding to anterior) and lower (corresponding to posterior) walls. PWI, pulse wave imaging.

The PWV values estimated in the corresponding five phantoms are detailed in Table 1, clearly illustrating an increase of the PWV with the phantom stiffness. The corresponding Young's moduli (Table 1) were calculated using the modified Moens–Korteweg equation. The stiffness values were compared to those obtained by mechanical testing. Figure 3 depicts the Young's modulus values obtained by both methods. The average relative difference between the two methods was found to be equal to 38%, illustrating the relatively good agreement between the results obtained by the two methods, given the distinct experimental protocol for each one. A good correlation was found between the two methods over the phantoms tested (r² = 0.92, Figure 3).

Table 1.

Results found by PWI and mechanical testing for the five phantoms tested, average values and s.d.

Figure 3. Comparison between PWI and mechanical testing. (a) Young's modulus of the five phantoms measured by the two methods and (b) corresponding correlation plot.

In vivo study

Figure 4 illustrates an example of the in vivo PWI images in the abdominal aorta of a human subject, and depicts the corresponding spatiotemporal displacement profile u(z,t), as well as how the PWV is calculated from u(z,t).

Figure 4. In vivo results. (a) Aortic wall displacement at four different frames (delay between two successive frames is 7.7ms) overlaid onto B-mode image, showing clearly the propagation of the wavefront (black arrow) from right to left. For clarity, the displacement is also represented on the surrounding tissue (b) profile of the wall displacement vs. time and distance from inlet, and (c) determination of the pulse wave velocity from the fit of this profile at the foot of the wave. PWV, pulse wave velocity.

Table 2 illustrates the results obtained in all 11 subjects tested. For each one of them, the PWV was calculated by the method described above. Aortic dimensions (diameter and wall thickness) were measured on the B-mode image. The average Young's modulus was calculated from the measured PWV, from the dimensions of the aorta, and by assuming a density of ρ = 1,060kg/m³ and a Poisson's ratio of ν = 0.495. An average value of E = 108kPa and a s.d. of 27kPa were found for the Young's modulus of the human abdominal aorta in vivo.

Table 2.

In vivo PWV values measured in 11 volunteers, and corresponding Young's modulus calculated from equation (1)

Discussion

In this paper, the PWI method was introduced as a noninvasive, ultrasound-based method for imaging of the pulse wave propagation and for quantitative estimation of regional PWV and regional arterial stiffness. Before in vivo human application, the proposed method was compared to mechanical testing in aortic phantoms, which allowed to demonstrate its reliability and to evaluate its accuracy. Good agreement was found with mechanical testing, demonstrating therefore the quantitative value of the proposed method. Despite this good agreement, it is important to mention that PWI was tested on homogeneous, cylindrically shaped phantoms. As a consequence, it cannot be directly compared to physiologic cases, where such assumptions may be limited, but are deemed to be acceptable in most sections of the large arteries.

Using medical imaging for measuring the PWV locally has recently gained significant interest. In particular, regional tracking of the pulse wave in arteries has been proposed by using phase-contrast magnetic resonance imaging,²⁸ B-mode wall tracking²⁹ or tissue Doppler imaging of the arterial wall.³⁰ Similarly, PWI estimates the local wall motion along the imaged segment by using 1D cross-correlation, allowing therefore qualitative visualization of the pulse wave and quantitative estimation of the PWV. As a noninvasive, regional, quantitatively validated, and of simple use, i.e., easily integrable into any ultrasound system, the PWI method carries significant interest for clinical purposes. It could represent a valuable complementary tool to the current gold standard methods for measuring the PWV. It overcomes several of the most significant limitations of the global carotid-to-femoral methods, which are essentially related to the simplification of the arterial tree structure and the lack of knowledge of the true arterial length. PWI provides localized measurements of the average stiffness within the imaged arterial segment (typically 8cm–12cm). This allows measurement of the changes in stiffness along the arterial tree through simple shift in the ultrasound transducer location.

The s.d. calculated over 10 measurements was found to be ~10% of the average value. As a consequence, we propose that the estimated value by the PWI method should be the average taken over 10 consecutive measurements. Whereas this is not an absolute requirement of the method, it allows to increase significantly the reliability of the proposed PWV value. Regarding practical aspects, obtaining 10 measurements does not pose a significant problem, because they are obtained over 10 consecutive cardiac cycles, which results in an acquisition of ~10s. The only limitation would be the need for breathholding during the duration of the acquisition, which could potentially be a problem in some patients. However, this drawback could be easily overcome by performing several separate acquisitions if needed.

In addition to the standard ultrasound-related restrictions such as difficulty in imaging of obese patients due to increased attenuation, PWI has additional limitations that must be considered. The most significant one is that, being a spatiotemporal technique, its accuracy is strongly related to its temporal resolution. Using the in vivo experimental protocol presented in this study, the frame rate is limited to ~500fps (by reducing the beam density to 16), which denotes an upper limit for the PWV estimate to ~10m/s in order to ensure reliability of the measurement. The measurement inaccuracy imposed by frame rate limitations is believed to be the cause of the increasing discrepancy between PWI and mechanical testing in the phantom study as the PWV increases (Figure 2). This limitation could, however, be overcome by using an automated composite imaging technique, which relies on the natural periodicity of the underlying physiology in order to achieve a higher effective frame rate.³¹ This consists of dividing the field-of-view in smaller sectors, hence, increasing the frame rate, and of using the periodicity in order to reconstruct the full view. Another limitation is that, currently, the estimation of the displacement, and therefore the visualization of the wave, are processed offline. Major ongoing development of the method is implementation of real-time processing for direct, on-site visualization of the pulse wave and estimation of the PWV.

As discussed previously, assumption is currently made that the aortic section imaged is homogeneous within the field-of-view, i.e., within an 8–12-cm long segment. The method offers therefore the possibility to obtain PWV values semiregionally, and to perform the measurement at different regions of the arterial tree with relative ease by shifting the transducer location. This could be used to detect abnormal regional changes in stiffness, as well as stiffness differences between different regions in the arterial tree. However, this assumption becomes invalid in the case of cardiovascular conditions that involve strongly localized wall heterogeneity. Examples are abdominal aortic aneurysms or arterial plaques. In such examples, arterial wall mechanical properties can be dramatically altered within a small region that can span from a few millimeters to a few centimeters. As a consequence, the pulse wave propagation pattern can be very complex, as shown in prior animal studies performed on mice with angiotensin II-induced abdominal aortic aneurysms model²⁵ and on mice with calcified aortas.²⁴ A more complete inverse approach must be developed in order to measure the PWV and to infer to the local mechanical properties. Ongoing investigation includes studying pulse wave patterns in such cases by using both analytical and numerical³² (i.e., fluid-structure interaction finite-element simulations) approaches. PWI could therefore represent a particularly valuable opportunity in those examples as a tool for estimation of local vascular mechanical properties.

In conclusion, the capability of imaging the pulse wave and estimating arterial stiffness averaged over the imaged segment was demonstrated. This renders PWI a noninvasive, simple-to-use technique for estimation of regional arterial stiffness. Although the reliability and the reproducibility of the method have been demonstrated in this study on both arterial phantoms and healthy subjects, the utility of the method in a clinical setting has still to be established and is part of an ongoing clinical study.

Disclosure

The authors declared no conflict of interest.