An ultrasound-based method for determining pulse wave velocity in ...

ARTICLE IN PRESS

Journal of Biomechanics 37 (2004) 1615–1622

An ultrasound-based method for determining pulse wave velocity in superficial arteries Stein Inge Rabbena,*, Nikos Stergiopulosb, Leif Rune Hellevikc, Otto A. Smisetha, Stig Sl^rdahld, Stig Urheima, Bj^rn Angelsend a

Institute for Surgical Research and Department of Cardiology, Rikshospitalet University Hospital, UiO, Oslo 0027, Norway b Laboratory of Hemodynamics and Cardiovascular Technology, EPFL, Lausanne, Switzerland c Sintef Materials Technology, Trondheim, Norway d Department of Circulation and Imaging, NTNU, Trondheim, Norway Accepted 16 December 2003

Abstract In this paper, we present a method for estimating local pulse wave velocity (PWV) solely from ultrasound measurements: the areaflow (QA) method. With the QA method, PWV is estimated as the ratio between change in flow and change in cross-sectional area (PWV ¼ dQ=dA) during the reflection-free period of the cardiac cycle. In four anaesthetized dogs and 21 human subjects (age 23– 74) we measured the carotid flow and cross-sectional area non-invasively by ultrasound. As a reference method we used the Bramwell–Hill (BH) equation which estimates PWV from pulse pressure and cross-sectional area. Additionally, we therefore measured brachial pulse pressure by oscillometry in the human subjects, and central aortic pulse pressure by micro-manometry in the dogs. As predicted by the pressure dependency of arterial stiffness, the estimated PWV decreased when the aortic pressure was lowered in two of the dogs. For the human subjects, the QA and BH estimates were correlated (R ¼ 0:43; po0:05) and agreed on average (mean difference of 0:14 m=s). The PWV by the BH method increased with age (po0:01) whereas the PWV by the QA method tended to increase with age (po0:1). This corresponded to a larger residual variance (residual = deviation of the estimated PWV from the regression line) for the QA method than for the BH method, indicating different precisions for the two methods. This study illustrates that the simple equation PWV ¼ dQ=dA gives estimates correlated to the PWV of the reference method. However, improvements in the basic measurements seem necessary to increase the precision of the method. r 2004 Elsevier Ltd. All rights reserved. Keywords: Pulse wave velocity; Arterial stiffness; Ultrasound; Echo-tracking; Pulsed wave Doppler; Volume flow estimation

1. Introduction The arterial compliance changes in several diseases such as hypertension, diabetes and arteriosclerosis. In treatment of hypertension, it is of interest to know the total systemic compliance as this modulates the load on the heart. A decrease in total systemic compliance increases the systolic and pulse pressures through loss of arterial buffering and early arrival of the reflected pressure wave. Arterial compliance is inversely related to the pulse wave velocity (PWV). Total systemic compliance has therefore been assessed by measuring the transit time of the pressure or flow waves over the *Corresponding author. Tel.: +47-22958137; fax: +47-22958141. E-mail address: [email protected] (S.I. Rabben). 0021-9290/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2003.12.031

entire aorta (Mohiaddin et al., 1993). In arteriosclerosis, however, there are regional differences in mechanical properties. Hence, local measurements of PWV are also of interest. The local PWV can be estimated by the Bramwell– Hill (BH) equation (Frank, 1920; Bramwell and Hill, 1922): sffiffiffiffiffiffiffiffiffiffiffiffi A% PP PWVBH ¼ ; ð1Þ r DA where A% is the time-averaged cross-sectional area of the vessel, DA the difference between systolic and diastolic areas, PP the pulse pressure, and r the blood density. Usually, the brachial pulse pressure is used as a substitute for the local pulse pressure. However, differences between the brachial and local pressures

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may exist due to wave propagation and reflections (Nichols and O’Rourke, 1998). To avoid the use of pulse pressure, investigators have measured the PWV by estimating the time delay between the diameter waveforms recorded simultaneously at two close positions along the vessel (Benthin et al., 1991; Sindberg Eriksen et al., 1985). Others (Brands et al., 1998) have estimated the PWV from diameter measurements by calculating the ratio of the temporal and the longitudinal diameter gradients during the reflectionfree period of the cardiac cycle. Both these techniques depend on a reliable identification of the foot of the diameter waveforms and a sufficiently high sampling frequency. The aim of this study was to present and evaluate an alternative to these methods. Eq. (1) is based on measurements of area and pressure. Since pressure, flow and cross-sectional area are related by the wave equation (Milnor, 1989; Nichols and O’Rourke, 1998), PWV can also be estimated from area and flow measurements directly (the area-flow (QA) method). The QA method has previously been applied on magnetic resonance data (Vulliemoz et al., 2002). However, the use of the method on ultrasound data has not yet been presented. The evaluation was performed by comparing the QA method with the BH method (Eq. (1)) in four dogs and 21 human subjects. In all cases, the inner diameter of the vessel (and thereby the cross-sectional area) was measured by echo-tracking (Rabben et al., 2002, 2003), and blood flow was estimated from pulsed wave (PW) Doppler measurements of the maximum velocities across the vessel. The flow estimation was based on an extension of Womersley’s theory for pulsatile flow in rigid tubes (Womersley, 1955).

2. Materials and methods 2.1. Estimation of pulse wave velocity (the area-flow method) Propagation of pressure (P) and flow (Q) waves in the arterial system is governed by the wave equation (Milnor, 1989; Nichols and O’Rourke, 1998), with pulse wave velocity sffiffiffiffiffiffiffiffiffiffiffi A% 1 PWV ¼ ; ð2Þ r CA where A% is the time-averaged cross-sectional area of the vessel, r the blood density, and CA ¼ dA=dP the local area compliance of the vessel. Another quantity relating pressure and flow waves in the arterial system is the characteristic impedance which, in absence of reflections, is defined as Zc ¼ dP=dQ: The characteristic

impedance is hence related to compliance, area and flow Zc ¼

dP dA 1 dA ¼ : dA dQ CA dQ

ð3Þ

However, the solution of the wave equation (Milnor, 1989; Nichols and O’Rourke, 1998) shows that the characteristic impedance is also related to compliance through the following expression: rffiffiffiffiffiffiffiffiffiffiffi r 1 Zc ¼ : ð4Þ A% CA By multiplying Eqs. (2) and (4), we get PWV Zc ¼

1 : CA

ð5Þ

If we insert Zc from Eq. (3), we obtain PWVQA ¼

dQ : dA

ð6Þ

The PWV can therefore be obtained from recordings of flow and area, provided that the data contain a reflection-free period during the cardiac cycle. We know that in most individuals the early systolic wave is reflection free. This can be checked by separating the pressure wave into its forward and backward components (Westerhof et al., 1972; Li, 1986). 2.2. Data recordings 2.2.1. Animal data Four mongrel dogs with body weight 2675 kg (mean7SD) were given thiopentone (25 mg=kg b.w.) and morphine 100 mg IV, followed by infusion of morphine (50–100 mg=h) IV and pentobarbital 50 mg IV every hour. The animals were artificially ventilated through a cuffed endotracheal tube using room air with 20–50% oxygen. In two of the dogs, inflatable vascular constrictors were placed around both caval veins, after median sternotomi. In all four dogs, central aortic pressure was measured by a 5F micromanometer-tipped catheter (Model MPC-500, Millar Instruments, Houston, USA) introduced into a femoral artery and positioned in the thoracic aorta near the orifice of the left carotid artery. Pressure data were digitized at 200 Hz by the ultrasound scanner and stored for further analysis together with the simultaneously recorded ultrasound data (see below). Prior to each experiment, a mercury manometer was used to calibrate the pressure transducers. A fluid-filled catheter in the abdominal aorta was used for absolute pressure reference. Recordings were first taken during baseline. In the two dogs with the caval constrictors, we then inflated the constrictors and did recordings after the systolic aortic pressure had decreased to approximately 60 mmHg: The experiments were approved by the Norwegian Experimental Animal Board.

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2.2.2. Human data A total of 23 adults (age 23–74) were included in the comparison study after giving their informed consent. Ultrasound data were recorded as described below, while systolic and diastolic pressures of the right brachial artery were recorded oscillometrically every third minute during the examination (Scholar II / 507E Series, Criticare Systems, Waukesha, USA and Critikon Dinamap 1846 SXP, Tampa, Florida, USA). The examinations were started after 10 min of rest in a sitting position. We excluded 2 of the 23 subjects because of poor image quality. 2.2.3. Ultrasound recordings A System FiVe ultrasound scanner (GE Vingmed Ultrasound, Horten, Norway) with a 10 MHz linear array probe was used for recording ultrasound data. The recordings were performed on the left common carotid artery, 3–5 cm proximal to the bifurcation of the internal and external carotid arteries. First, we recorded ultrasound RF data for the extraction of the inner vessel diameter: 3–5 cardiac cycles in humans (dogs: 5–10). When necessary, we steered the RF M-line perpendicular to the artery. Subsequently, we recorded 8–10 (dogs: 10–20) cardiac cycles of PW Doppler data for extraction of blood velocities. To obtain maximum velocities across the vessel, the sample volume of the PW Doppler was made large enough to cover the central portion of the vessel’s cross-section. In all recordings, the steering of the Doppler line was 30 ; and the angle correction was 45–60 : In the human subjects, the criterion for proper alignment of the image plane relative to the artery was visible intima layers at both anterior and posterior vessel walls. In the dogs, the intima layer could not be seen, and therefore the image plane giving the largest vessel diameter was used. 2.3. Data postprocessing 2.3.1. Cross-sectional area estimation The inner diameter of the vessel was tracked from ultrasound RF data (Rabben et al., 2002, 2003). To obtain smooth diameter waveforms, we averaged several cardiac cycles. By assuming axis-symmetric geometry, the cross-sectional area was estimated from the diameter measurements. 2.3.2. Blood flow estimation When the PW sample volume covers the central portion of the vessel, the PW Doppler technique measures the maximum velocities across the vessel. However, the velocity profiles are neither parabolic nor flat. To estimate volume flow, we therefore applied an extension of Womersley’s theory for pulsatile flow in rigid tubes (Womersley, 1955). The flow estimation procedure is presented below.

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Let us assume that the blood vessel is a rigid circular tube with radius R: If the tube is filled with fluid of density r and viscosity m; and vðr; tÞ is the longitudinal velocity of the fluid at a distance r from the center axis of the tube, the equation of motion becomes @2 v 1 @v 1 @v 1 @p  ¼ ; þ @r2 r @r n @t m @z

ð7Þ

where n ¼ m=r is the kinematic viscosity. Eq. (7) is solvable if we assume that @v=@r approaches zero when r-0; i.e. the velocity profiles are axis-symmetric. In a rigid vessel, there will be no blood motion in the radial direction, and the pressure gradient @p=@z will be constant over the cross-section of the vessel. By letting r-0 in Eq. (7), and applying L’Hopital’s rule on the second term, we obtain   1 @p @2 v  1 @v ¼ 2 2   : ð8Þ m @z @r n @t  r¼0

r¼0

The pressure gradient in Eq. (7) may now be substituted by Eq. (8). If we assume harmonic solutions, vðr; tÞ ¼ V ðr; oÞejot ; the following expression describes the blood velocities: 1 V 00 ðr; oÞ þ V 0 ðr; oÞ þ l2 V ðr; oÞ r 00 ð9Þ ¼ 2V ð0; oÞ þ l2 V ð0; oÞ; where the prime denotes differentiation with respect to radius r; and l2 ¼ j3 o=n: The homogeneous part of Eq. (9) is a Bessel equation with the solution Vh ðr; oÞ ¼ c0 J0 ðlrÞ; where J0 is the Bessel function of first kind order zero. A particular solution of Eq. (9) is given by Vp ðr; oÞ ¼ ð2=l2 ÞV 00 ð0; oÞ þ V ð0; oÞ; and a general solution of Eq. (9) is therefore given as V ðr; oÞ ¼ Vh ðr; oÞ þ Vp ðr; oÞ ¼ c0 ðJ0 ðlrÞ  1Þ þ V ð0; oÞ:

ð10Þ

Here we have used the fact that V ð0; oÞ ¼ c0 l2 =2; which can be verified by solving the differentiated homogeneous solution Vh00 ðr; oÞ for r ¼ 0: Because we require that the velocities are zero at the vessel boundary, V ðR; oÞ ¼ 0; Eq. (10) becomes 00

J0 ðaj3=2 r=RÞ  J0 ðaj3=2 Þ ; ð11Þ 1  J0 ðaj3=2 Þ pffiffiffiffiffiffiffiffi where a ¼ R o=n is the Womersley number. From Eq. (11) we may estimate velocity profiles across the vessel by knowing only the velocities at the center axis vð0; tÞ; the time-averaged vessel radius R; and the kinematic viscosity n: Integration of Eq. (11) over the vessel radius yields the volume flow 1  F10 ðaÞ QðoÞ ¼ V ð0; oÞpR2 ð12Þ 1  1=J0 ðaj3=2 Þ V ðr; oÞ ¼ V ð0; oÞ

with the Womersley function defined as F10 ðaÞ ¼ 2J1 ðaj3=2 Þ=ðaj3=2 J0 ðaj3=2 ÞÞ; where J1 is the Bessel function

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of first kind order one. The time-varying volume flow may now be estimated by applying the Fourier transform to the center axis velocities vð0; tÞ; by applying Eq. (12) on each harmonic of the center axis velocities, and by applying the inverse Fourier transform to the results of Eq. (12). In this study, the center axis velocities were assumed identical to the maximum velocities of the PW Doppler spectra. To obtain maximum velocities, the automatic tracing algorithm of the System FiVe ultrasound scanner was used. Since the PW Doppler spectrum has a limited frequency (velocity) resolution and high variance, we needed to average several cardiac cycles to obtain smooth velocity waveforms. After the averaging, the velocity waveform was filtered by (a zero phase-distortion) low-pass Butterworth filter with a 3 dB cutoff frequency of 20 Hz; a transition band of 20 Hz; and a stop band attenuation of at least 50 dB: In the flow calculations, the blood density r was set to 1060 kg=m3 ; and blood viscosity m was set to 0:0035 Pa s: 2.4. Comparison study The PWV calculated by the QA method (Eq. (6)) were compared to PWV calculated by the BH equation (Eq. (1)). The correlation coefficient (Pearson’s R) was calculated and tested for significance. The agreement between the two methods was assessed by plotting the difference of the two methods against the mean of the two methods, and calculating the limits of agreement as the mean difference 7 two standard deviations (SD) of the differences (Bland and Altman, 1986).

techniques (Fig. 1A). From the maximum velocities and the time-averaged cross-sectional area, blood flow was calculated by applying Eq. (12) (Fig. 1B). Note that the flow, calculated by applying Eq. (12) (solid line), is considerably lower than the flow calculated by assuming a flat velocity profile (dashed line). Finally, the PWV was found as the slope of the straight portion of the area-flow loop (Fig. 1C). In all subjects included in this study, we found a linear relation between area and flow during early systole indicating a reflection-free period. Table 1 lists pressure parameters and PWV estimates at baseline and during vena cava constriction in two of the dog experiments (dog #3 and #4). The vena cava constriction decreased the mean arterial pressure and pulse pressure. Discrepancies were observed between the QA method and the BH method, but for both methods, the PWV estimates decreased during vena cava constriction. Fig. 2A shows PWV in 21 human subjects (open diamonds) and four dogs (filled triangles), estimated by the QA method plotted against PWV estimated by the BH method. The data points are scattered around the identity line. For the human subjects, the methods correlated significantly: PWVQA ¼ 0:48PWVBH þ 3:07 (R ¼ 0:43; po0:05). In Fig. 2B, the difference between the two methods is plotted against the average of the

Table 1 Hemodynamic parameters before (baseline) and during vena cava constriction (vcc) in dog 3 and 4: P% ¼ time-averaged pressure: PP = pulse pressure. PWV = pulse wave velocity. Subscripts QA and BH denote area-flow and Bramwell–Hill, respectively Parameter

#3

#4

Baseline

3. Results Fig. 1 illustrates the QA method applied on data from a young human subject. The maximum velocities and inner vessel diameter were measured by ultrasound

P% PP PWVQA PWVBH

106.6 22.7 3.78 5.64

60 0

(A)

0.2

0.4 0.6 Time [s]

20 0.8

3

20 10

136.6 22.7 8.86 6.77

55.0 11.0 4.30 4.65

mmHg mmHg m/s m/s

15 10 5 0 0.2

0 0

(B)

47.7 8.6 2.01 2.85

vcc

20

30

Flow [cm /s]

100

Flow [cm3/s]

0.52

Velocity [cm/s]

Diameter [cm]

140

Baseline

25

40 0.6 0.56

vcc

Units

0.2

0.4 Time [s]

0.6

0.8

(C)

0.225

0.25 0.275 Area [cm2 ]

0.3

Fig. 1. Illustration of the QA method. Panel A: Measurements of the vessel diameter (—) and maximum velocities (- - -) from the left common carotid artery of a young human subject. Panel B: Flow calculated from maximum velocities and time-averaged diameter by applying Eq. (12) (—) and by assuming a flat velocity profile (- - -). Panel C: Flow versus cross-sectional area. The slope of the straight portion (thick solid line) of the loop corresponds to the reflection-free period of the cardiac cycle and equals the PWV.

ARTICLE IN PRESS S.I. Rabben et al. / Journal of Biomechanics 37 (2004) 1615–1622

4

14

y = 0.48x + 3.07 R = 0.43

12

PWVQA [m/s]

Difference (QA - BH) [m/s]

16

10 8

3 2 1 0

-1

6

-2

4

-3

2

-4

1

2

3

(A)

4 5 6 7 PWVBH [m/s]

8

9

10

Difference (QAflat - BH) [m/s]

14 y = 0.55x + 3.69 R = 0.39

12

4 (B)

16 PWVQAflat [m/s]

1619

10 8

6 Average of QA and BH [m/s]

8

4 3 2 1 0

-1

6

-2

4

-3

2

-4

1

2

3

(C)

4 5 6 7 PWVBH [m/s]

8

9

10

4 (D)

6 8 Average of QAflat and BH [m/s]

9

9

8

8 PWVBH [m/s]

PWVQA [m/s]

Fig. 2. Subplot A: PWV by the QA method (Eq. (6)) plotted against PWV by the BH method (Eq. (1)). The open diamonds represent the human observations, and the filled triangles represent the dog observations. The regression equation and line (thick solid) are from the human subjects. The dotted line represents the identity relation. In two of the dogs we repeated recordings during vena cava constrictions. The thin solid lines connecting filled triangles indicate which points that belong to the same dog (baseline and vena cava constriction). Subplot B: The difference between the two methods plotted against the average of the two methods (human subjects). The dotted line is the mean difference, and the dashed lines represent the mean difference 7 two times SD. Subplots C and D correspond to subplots A and B, respectively, assuming a flat velocity profile.

7 6 5 y = 0.03x + 4.81 R = 0.37 (p