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1Department of Clinical Pharmacology, Faculty of Medicine, St. Mary's Hospital; and 2Physiological Flow Studies Group, Department of Bioengineering, Imperial College, London, United Kingdom
Submitted 15 August 2003 ; accepted in final form 1 February 2005
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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hemodynamics; wave transmission; ultrasound; tonometry
An individual forward-traveling wavefront, generated by the heart at the beginning of cardiac systole, initiates flow and increases pressure in the arteries (25). Although most of the wave energy in this initial compression wave travels distally into smaller arteries, some is reflected back toward the heart at sites of impedance mismatch. These include focal sites such as bifurcations, but nonfocal arterial taper may also contribute to reflection phenomena (39). These reflected waves can be re-reflected as has been demonstrated in vitro (19). At the end of systole, deceleration of left ventricular contraction results in reductions in both pressure and flow in the ascending aorta mediated by a forward-traveling expansion wave (34).
Interactions between forward- and backward-traveling waves result in complex patterns of blood flow and pressure change at different points in the arterial circulation. Analysis of forward- and backward-traveling wave energy therefore provides information regarding ventriculoarterial interaction (8, 10, 35).
The study of arterial waves has classically used vascular impedance theory that considers the observed pressure and flow waveforms to be the superposition of sinusoidal wave trains at the fundamental and harmonic frequencies (26). This method, based on Fourier theory, assumes a linear relationship between pressure and flow in a one-dimensional system at steady state (32). An alternative approach uses the method of characteristics, which considers the measured waveforms as the summation of successive incremental wave fronts. The method assumes neither periodicity nor linearity but does assume waves to be one dimensional in character (33). This has resulted in the development of wave-intensity analysis (WIA) as a novel mathematical tool to describe arterial wave power and energy.
Wave intensity is a term analogous to acoustic intensity and is defined as power transported by the wave fronts per unit area. Changes in pressure and flow velocity are used to determine wave intensity, and the method also allows local wave speed to be determined. Furthermore, with the use of the local wave speed determined from a pressure-flow velocity loop (18), WIA allows the separation of forward- and backward-traveling waves. By referring to the concomitant changes in pressure, compression and expansion can be described (9). Compression and expansion waves have opposite effects on pressure and flow velocity (Table 1).
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With the advent of applanation tonometry and pulsed-wave Doppler, it is now possible to measure both arterial pressure (13, 15, 16, 21, 25) and flow velocity (4, 37) noninvasively and reproducibly in superficial peripheral arteries. The aim of this study is to describe wave intensity and energy patterns in the carotid, brachial and radial arteries of normal human subjects by using noninvasive methods.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Data acquisition.
All the methods used for this study have been described fully in a previous work (43). In brief, subjects were examined while lying supine on a couch in a quiet, temperature-controlled room after a 
10-min rest period. At least three measures of left arm brachial artery systolic (SBP) and diastolic blood pressure (DBP) were then acquired during the study by using a validated, semiautomated blood pressure monitor (Omron HEM-705CP, Hoofddorp, The Netherlands) (31). Mean arterial blood pressure (MAP) was calculated from the standard formula MAP = DBP + (SBP – DBP)/3 (41).
To standardize the protocol, data from the common carotid, brachial, and radial arteries on the right side were collected in the same sequence in all patients. At each site the pressure data were collected first, followed by the velocity data before progressing to the next artery. For each artery, the time taken to acquire both pressure and velocity data was 5 min.
Applanation tonometry was used to record arterial pressure waveforms from the three arteries by using a high-fidelity strain gauge-tipped pencil probe (2). The areas of maximum pulsation were identified by palpation for each of the three arteries, and the tonometer (SPT 301, Millar Instruments, Houston, TX) was then applied to these sites. Over a period of at least 20 cardiac cycles, the signal was amplified (TCB-500 preamplifier, Millar Instruments), digitized at 200 Hz, and transferred to the hard drive of a personal computer (PC) for further analysis. A simultaneous single-lead ECG was also recorded.
To acquire flow-velocity data from the three arteries, the common carotid, brachial, and radial arteries on the right side were imaged using a 7.5- to 10-MHz linear-array transducer and HDI5000 ultrasound machine (ATL-Philips, Bothell, WA). At all sites, B-mode ultrasound was used to ensure correct positioning of the transducer, and pulsed-wave Doppler ultrasound, with a fundamental frequency of 6 MHz, was used to insonate the arterial lumen while ensuring that the ultrasound beam was positioned at 60° incident to the direction of the central luminal blood flow (45). The pulsed Doppler velocity waveform and a simultaneous single-lead ECG trace were acquired continuously for 20 cardiac cycles. A peak velocity waveform was generated using a well-described, online tracing algorithm (36, 38), digitized at a frequency of 200 Hz, and then transferred to a PC hard drive. At each site, the flow-velocity data were acquired within 5 min of the corresponding pressure data.
Ensemble averaging of the pressure and flow-velocity data. To provide simultaneous representative pressure and flow-velocity waveforms, ensemble averaging of the acquired pressure and flow-velocity data was performed within the Matlab programming environment (Matlab 6.0.0.88 [EC] Release 12, MathWorks, Natick, MA). Six contiguous pressure and flow-velocity waveforms were separated using the fiducial ECG R wave and then ensemble averaged. Ensemble averaging was performed by maximizing the cross-correlation coefficient between each waveform using the first 100 ms of the rapid rise in pressure and flow velocity with a facility for subsequent manual adjustment if necessary.
Calibration of the ensemble-averaged carotid pressure waveform was performed indirectly (43, 44). Previous work (43, 44) has shown that the applanation tonometer may either under or overestimate intra-arterial pressure depending on the force used for applanation. In addition, when MAP alone was used to calibrate the pressure waveforms obtained from our tonometer in vivo, then the waveform pulse pressure differed 13–41% from sphgmomanometry, depending on the patient group studied. We therefore calibrated our tonometer using a pressure phantom.
A pressure phantom was constructed using 1-cm-diameter latex tube placed within a similarly sized Dacron graft. An intravascular pressure catheter (8F SVPC-684A, Millar Instruments) was introduced into the phantom, and the system was filled with saline to achieve a static pressure of 50 mmHg. The high-fidelity strain-gauge tonometer was externally placed 1 cm distal to the catheter and attached to a stand for hands-free measurements. Rapid active filling and passive drainage of the phantom using saline and a syringe achieved variations in pressure. The pressure data from tonometry and invasive catheter measurements were sampled simultaneously at 250 Hz. A series of pressure waveforms was generated over a range of applied applanation pressures. These data confirmed that there was a linear relationship between the intraluminal catheter and tonomety pressures but that the slope of linear regression line increased linearly with an increase in applanation pressure. From these data, appropriate calibration of the tonometer was feasible, thus taking into account the applied force required for applanation.
In vivo, the average applanation force was determined from the six pressure waveform data before ensemble averaging, using the average difference in the measured carotid diastolic pressures (determined by the tonometer) and the brachial DBP (determined by sphygmomanometry). These data were then applied to the pressure data to correct for the applanation force-dependent error (43, 44). A final step matched the ensemble-averaged carotid mean arterial pressure to MAP. Brachial and radial pressure waveforms were ensemble averaged and calibrated directly to the measured brachial SBP and DBP. Whereas the magnitude and morphology of the brachial and radial pressure waveforms are not identical, calibration of the radial pressure waveform using syphgmomanometry-determined brachial SBP and DBP is well established in the literature (12, 14), and the neglect of amplification of the pressure wave between the brachial and radial arteries introduces only a very minor error (24).
Doppler may overestimate peak flow velocities, and errors, particularly at low forward and backward velocities, vary in a nonlinear manner, resulting in distortion of the temporal characteristics of the flow-velocity waveform (34). This may be of particular importance in the brachial, radial, and femoral arteries where flow reversal might typically occur during the cardiac cycle. The nonlinear errors were attributed to the statistical properties of the online velocity waveform-tracing algorithm, and a formula for correction was therefore developed in vitro using a string phantom and shaft encoder. Nonlinear regression analysis, based on a cumulative standard normal probability distribution, was used to determine an appropriate correction. When applied to data in the string phantom that mimicked physiological flow-velocity waveforms, there was a close correlation between the corrected velocities and those determined independently by the shaft encoder (r2 = 0.99, P < 0.0001), and the nonlinear errors were no longer evident.
In vivo, following application of the correction formula determined in the string phantom experiments, six contiguous flow-velocity waveforms were separated in the same manner as the pressure data. Similarly, these data were ensemble averaged after each waveform was aligned using the first 100 ms of the rapid rise in flow velocity as described above to generate a single ensemble-averaged flow-velocity waveform (U).
Hemodynamic calculations.
Hydraulic work per unit area was calculated as:
 | (1) |
Local wave speed was calculated using a pressure-flow velocity loop (18). From the conservation of mass and momentum, there is a simple relationship between the changes in pressure and flow velocity that is valid only when a forward-traveling wave is present, and this is summarized in the "waterhammer" equation:
 | (2) |
is the density of blood (1.06 g/cm3), and c is the local wave speed. If the ensemble-averaged pressure and velocity data are plotted as shown in Fig. 1, a pressure-flow velocity loop can be constructed. In the carotid artery there is a linear portion of the loop corresponding to the earliest part (50 ms) of arterial systole. This suggests that during this time there are no reflected waves present at the site of measurement. During this early period of arterial systole, c is equal to the gradient of the line describing the relationship between pressure and flow velocity, and, using Eq. 2, local wave speed can be calculated. At the brachial and radial arteries where earlier reflections may occur, the gradient of the early linear portion of the loop was determined over the first 15 ms of arterial systole.
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The mathematical methods of WIA are described in more detail in previous work (11, 33). The forward and backward components of the measured change in pressure and flow velocity were determined from the following equations derived from the method of characteristics theory:
 | (3) |
 | (4) |
With the integration of the forward- and backward-traveling changes in pressure, the forward- and backward-pressure waveforms were determined, and, from these, maximum forward and backward pressure could be calculated. An integration constant was included arbitrarily in the forward pressure and was taken to be the minimum value of P. The integration constant for U was zero.
Forward and backward wave intensities (I) were calculated as follows:
 | (5) |
Forward wave intensities had a magnitude greater than zero, whereas backward wave intensities had a magnitude less than zero.
Compression waves were defined as occurring during positive changes in pressure and expansion waves during negative changes. The time of onset and offset of each wave was determined manually using electronic crosshairs, and the error in timings was <5 ms. Wave energy was determined by integrating the area under the wave-intensity curve between these two time points. The time of onset of each wave was determined relative to the onset of the first forward compression wave (S). The time of onset of the S wave relative to the fiducial ECG R wave was also determined.
Other groups have normalized wave intensity as the product of the derivatives of P and U with respect to time (dP/dt and dU/dt, respectively) (11, 35). Such an approach allows data acquired at different sampling rates to be compared directly but results in complex units (mmHg·m·s–3), which do not represent wave power per unit area and do not allow wave energy to be easily determined. To compare the results from this study with those from other groups, one should convert watts per squared meter into millimeters of Hg times meter per cubed seconds by multiplying wave intensity values by 300. Previous studies have not separated the waves into their forward- and backward-traveling components and have therefore only reported net wave intensity.
Statistics. The clinical characteristics of the subjects are expressed as means ± SD, whereas all other data, which are derived from ensemble-averaged pressure and flow velocity, are expressed as means ± SE. To assess the significance of differences between arterial sites, two-way ANOVA was used (Excel, Microsoft Office 2000, Microsoft, Redmond, WA). The F-statistic and P values are presented, and P values were considered significant at values <0.05.
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Hydraulic work was significantly higher in the carotid artery (539 ± 27 J/m2) compared with the brachial (315 ± 45 J/m2) and radial (251 ± 46 J/m2) arteries (carotid vs. brachial, F = 24.3, P < 0.001, and carotid vs. radial, F = 38.6, P < 0.001). There was no significant difference in hydraulic work between the brachial and radial arteries (F = 3.5, P = 0.09).
The maximum forward and backward components of pressure and pulse pressure are shown in Table 3. Forward pressure was significantly higher in the brachial artery compared with the carotid artery (F = 163.4, P < 0.001). Taking into account the integration constant in the forward pressure, the forward pulse pressures were significantly higher in both the brachial (F = 253.2, P < 0.001) and radial arteries (F = 6.4, P < 0.05) compared with the carotid artery. Additionally, maximum reflected backward pressures and backward pulse pressures were significantly higher in the brachial (F = 14.7, P < 0.005) and radial arteries (F = 6.9, P < 0.05) compared with the carotid artery.
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Both the S and D waves are generated by the left ventricle of the heart (10, 34). The S wave is generated by myocardial contraction, resulting in the opening of the aortic valve, increased arterial pressure, and acceleration of arterial flow. In this study, we showed that both the S-wave intensity and the forward component of pressure were significantly higher in the brachial artery compared with the carotid artery. A reasonable assumption, bearing in mind the similarity in heart rates during the brachial and carotid studies, is that cardiac contractility remained unchanged during these studies. The differences in wave power between the two sites may therefore have been mediated through differences in arterial wall structure, geometry, and branching. For example, from Eq. 2 it can be seen that as local wave speed increases, the forward component of pressure can be predicted to increase.
The D wave is an expansion wave generated at the end of systole by a decrease in myocardial shortening rate that results in a reduction in both arterial pressure and flow and contributes to the closure of the aortic valve. We have shown that D-wave intensity differs between the carotid and more peripheral arteries, being highest in the carotid artery and lowest in the radial artery. Importantly, we note that the timing of the wave is the same in all three arteries relative to the S wave, confirming previous work suggesting that the wave is of cardiac origin. The D wave may become smaller in magnitude as it travels distally from the heart due to damping by the arterial wall and therefore contributes less to pressure and flow reduction at the end of systole in the smaller muscular arteries compared with the central elastic arteries, such as the carotid and aorta arteries.
The R wave is a backward-traveling reflection of the S wave. Previous in vivo work using aortic clamping or aortic balloon inflation to increase the local reflections has resulted either in an increase in the R-wave intensity (35) or earlier onset and longer duration of the R wave (17) in the ascending aorta. These changes have been associated with augmentation of pressure or an increase in hydraulic work in the ascending aorta.
We showed that R-wave energy was significantly higher in the radial artery compared with that in the carotid artery and that the peak-reflected backward pressure was significantly higher from the hand and forearm than from the head. By normalizing for the S-wave energy in each artery, it is apparent that there are differences in the amount of reflection at each site. For example 17% of the S-wave energy was reflected as the R wave in the carotid artery compared with 27% in the radial artery. This indicates that there are differences in impedance mismatching between different beds, and the increased reflection from the hand may be related either to the anatomy of the hand circulation or the level of resting vasoconstrictor tone in the hand where circulation largely occurs through the skin.
Our study is the first to describe the presence of midsystolic X waves in peripheral arteries. Previous studies have shown the presence of reflected, backward-traveling expansion waves in the pulmonary arteries during early systole (7) and in the coronary arteries during early diastole (42), and these resulted in a reduction in pressure and an increase in flow velocity. However, the X wave is a forward-traveling expansion wave that contributes to a reduction in both pressure and flow velocity during midsystole. The heart is unlikely to be the source of the X wave. Previous invasive work has not observed X waves in the ascending aorta. Additionally, our data show that the X-wave energy is higher at a more peripheral site (the radial artery) compared with a more central artery (the carotid artery). The X wave may therefore occur after reflection of the R wave from a proximal open-end type reflection site, such as when it travels back toward the heart and meets a bifurcation (7, 27).
The differences in hydraulic work and wave speed between elastic and muscular arteries are representative of differences in their structure and function. Typically, the brain receives 15% of cardiac output (5), and, assuming that the majority of cerebral blood flow travels via the carotid arteries, each carotid artery carries 7% of cardiac output. The brachial artery, however, receives a much smaller proportion of the cardiac output at rest. Estimates from our data suggest that the forearm receives 2% of the cardiac output at rest. Thus one might expect hydraulic work in the carotid artery to be greater than that in the brachial and radial arteries in the resting state.
Wave speed is dependent on the elastic properties of the wall, wall thickness, the luminal radius, the Poisson ratio (the ratio of transverse to longitudinal strain), and the density of blood (1). The distensibility of an artery (
) (defined as 1/A·dA/dP, where A is the cross-sectional area in arterial diastole and dA is the change in cross-sectional area), has a simple relationship to the wave speed (c=1/
). Structural factors that influence arterial distensibility clearly influence the local wave speed. Histological work has described the structural differences between elastic and muscular arteries (3, 6) and recent noninvasive work (40) confirms that the elastic moduli of the brachial and radial arteries are different to that of the common carotid artery.
Potential limitations. The use of noninvasive methods is important to assess arterial hemodynamics in both healthy volunteers and in patient groups, because invasive monitoring is increasingly becoming ethically unacceptable, particularly in our institution. This inevitably introduces potential sources of error. For example, in our study we acquired pressure and flow-velocity data sequentially, whereas in previous invasive studies these data were acquired simultaneously using appropriate catheters. Furthermore, the calibration of the pressure waveform required the use of noninvasively acquired data. However, brachial sphygmomanometry, a tool widely used and accepted in routine clinical practice, provides accurate estimates of brachial blood pressure, provided there is no evidence of calcification of the media of the artery. In this study, direct imaging of the arterial wall was performed in every subject.
A potential source of error was the calibration of the radial pressure directly to the brachial sphygmomanometry pressure. Although this may introduce a small error, this strategy has been applied in a number of previous studies (12, 14).
In conclusion, we have described important differences in wave speed, hydraulic work, and wave patterns among the carotid, brachial, and radial arteries of normal volunteers using noninvasive techniques. Wave transmission in peripheral arteries is a complex interaction of forward- and backward-traveling compression and expansion waves produced by the heart or generated by reflections.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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REFERENCES |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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