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INNOVATIVE METHODOLOGY

Noninvasive ultrasonic measurement of arterial wall motion in mice

¹Sections of Cardiovascular Sciences and Geriatrics, Department of Medicine, The Methodist DeBakey Heart Center, Baylor College of Medicine, Houston 77030; and ²Indus Instruments, Houston, Texas 77058

Submitted 5 December 2003 ; accepted in final form 13 April 2004

	ABSTRACT

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Despite the extensive use of genetically altered mice to study cardiovascular physiology and pathology, it remains difficult to quantify arterial function noninvasively in vivo. We have developed a noninvasive Doppler method for quantifying vessel wall motion in anesthetized mice. A 20-MHz probe was held by an alligator clip and positioned over the carotid arteries of 16 mice, including six 3- to 5-mo-old wild-type (WT), four 30-mo-old senescent (old), two apolipoprotein E null (ApoE), and four -smooth muscle actin null (-SMA) mice. Doppler signals were obtained simultaneously from both vessel walls and from blood flow. The calculated displacement signals from the near and far walls were subtracted to generate a diameter signal from which the excursion and an augmentation index were calculated. The excursion ranged between 13 µm (in ApoE) and 95 µm (in -SMA). The augmentation index was lowest in the WT mice (0.06) and highest in the old mice (0.29). We conclude that Doppler signal processing may be used to measure vessel wall motion in mice with high spatial and temporal resolution and that diameter signals can replace pressure signals for calculating the augmentation index. This noninvasive method is able to identify and confirm characteristic changes in arterial properties previously associated with age, atherosclerosis, and the absence of vascular tone.

Doppler displacement; arterial mechanics; blood velocity; carotid artery

Although there has been much activity and new developments in the analysis of cardiac function in mice (6, 15, 20), there is a dearth of methods to assess arterial function in mice, and most of these are invasive and are limited to the central arteries (7). These devices include telemetry of ECG and arterial pressure (Data Sciences International; see Ref. 32); implantable blood flow sensors (Transonic Systems; see Ref. 49); fluid-filled and micromanometer-tipped catheters for arterial pressure sensing (Millar Instruments; see Ref. 29); and cardiac pressure-volume catheters (Millar Instruments; see Ref. 8). All of these methods require surgery and cause major perturbations to the systems under study. Moreover, it is difficult and expensive to maintain the implanted instrumentation and sensors in mice.

During the past decade, we and others have developed and employed several noninvasive methods to measure cardiovascular function in anesthetized but intact mice. These include: two-dimensional (2-D) and M-mode echocardiography for evaluating cardiac anatomy and function (20, 27, 45), tail cuff methods for measuring systolic and diastolic blood pressure (39), and Doppler methods for measuring arterial blood flow velocity (12, 15, 26) and aortic pulse wave velocity (13–15) in mice.

In attempting to evaluate vessel compliance in humans, several groups have developed ultrasonic methods to measure vessel diameter (17, 19, 21) and wall thickness (24) noninvasively. These methods use amplitude, phase, or Doppler detection of the echoes from the vessel walls and subtract near and far wall displacement signals to obtain the change in diameter (19, 21) with resolutions approaching 1 µm (17, 24). These methods require either dedicated instruments or significant modifications to commercial imaging systems. We describe here a relatively simple method for quantifying vascular wall motion in mice in which signals are acquired from a modified 20-MHz pulsed Doppler velocimeter (12), and the required Doppler signal processing is performed in a spreadsheet, such as Excel.

	METHODS

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Principle of operation.

The technique for sensing vessel wall motion in mice is adapted from a tissue Doppler displacement method (11) that was developed originally by us for measuring ventricular thickening in pigs (10), dogs (50), and rats (5) and by others for measuring vessel wall motion in humans (17). In this method, the phase of an echo (which is a function of reflector position) is measured repeatedly over time to determine the displacement of a reflector or ensemble of reflectors with respect to the ultrasonic transducer. Short bursts of ultrasound consisting of two to eight cycles of the carrier frequency (f_o) are directed by a transducer to the tissue of interest. The returning echoes are received by the transducer, amplified, and mixed with quadrature signals from a reference oscillator to generate two phase-detected echo signals. The detected echo signals are then sampled by a range-gate pulse delayed from the transmitted burst by an amount corresponding to the echo-return time to generate in-phase (I) and quadrature (Q) Doppler signals from a sample volume (SV) within the tissue of interest. The I and Q Doppler signals can be viewed on an oscilloscope (Fig. 1) as the X and Y coordinates of a vector with amplitude (a) and phase angle () in polar coordinates such that

(1)

(2)

and

(3)

The phase of an echo is related to the target distance (d) by

(4)

where the wavelength () = c/f_o = 78 µm at an ultrasonic f_o = 20 MHz with a speed of sound (c) = 1,560 m/s (11). If the target moves, the change in phase () is related to the change in position or displacement (d) by

(5)

where is the angle between the direction of motion and the direction of the sound beam. If both sides are divided by the time interval required for the motion (t), Eq. 5 becomes the familiar Doppler equation relating the Doppler angular frequency (_d = /t = 2f_d) to the target velocity (v = d/t)

(6)

This general approach to measuring tissue displacement with ultrasound has been validated by ourselves (10, 11) and others (17, 40) and found to be an accurate measure of the relative motion of myocardial and arterial walls. However, because of the ambiguity at every 2 in the measurement of phase, the absolute position of reflectors cannot be determined, and only the relative position or displacement during a short time interval can be measured. In our original implementation in which the displacements were large, we used a bandpass filter (1 Hz to 4 kHz) on the I and Q signals and employed a 1-bit digitizer, resulting in a minimum measurable phase change of /2 or a displacement of 9.5 µm at f_o = 20 MHz and a measurable velocity range of 40 µm/s to 16 cm/s. The application in mice required an improved system able to measure lower displacements and velocities.

View larger version (22K): [in this window] [in a new window]   Fig. 1. A: ECG and the in-phase (I) and quadrature (Q) Doppler signals recorded from the carotid artery near wall of an apolipoprotein E (ApoE) null mouse along with position (or displacement) and velocity calculated from the arctangent of Q/I and its first derivative. B: plot of Q vs. I for 250 ms showing how the phase () of an echo and its first derivative () are calculated and related to reflector position and velocity. f, Frequency; t, time.

We used a dual-gate pulsed Doppler instrument made by coupling two synchronized 20-MHz pulsed Doppler modules (similar to those available from Indus Instruments, Crystal Biotech, or Valpey Fisher) with the wall filters removed to extend the Doppler bandwidth down to the direct current (DC) or 0 Hz. To reduce the size of the SV, the 20-MHz transmitted burst length was reduced from eight to two cycles (0.1 µs). In addition, the bandwidth was increased to 10 MHz, and the cut-off frequency of the phase detector low-pass output filters was increased to 5 MHz. The result is a two-gate pulsed Doppler with audio bandwidths from 0 to 31.25 kHz and independently adjustable range gates or SVs that can be placed anywhere along the sound beam, as shown in Fig. 2, to record wall displacement and/or blood velocity.

View larger version (30K): [in this window] [in a new window]   Fig. 2. Doppler probe held in a clip holder and positioned at an angle over the carotid artery of an anesthetized mouse. Multiple sample volumes [2 are shown here (SV1 and SV2)] are positioned along the beam to measure wall motion and blood velocity. In some of the experiments, the probe was oriented perpendicular to the artery, the SVs were placed over the near and far artery walls, and a second probe was placed at an angle and used to record blood velocity from the lumen.

The I and Q Doppler signals from each module were connected to the 12-bit analog-to-digital converter of a Doppler Signal Processing Workstation (Indus Instruments). During experiments, Doppler signals from blood flow were processed by a fast-Fourier transform (FFT) in real time and displayed on a monitor for use in positioning the probe over the vessel of interest. When the probe and range gates had been properly positioned, the desired signals were collected for 2-s intervals and stored for later analysis. Blood flow signals were processed by the FFT, and the spectral peak or envelope representing the maximum Doppler frequency within the SV was calculated and displayed as the centerline blood velocity waveform. Next, the velocity waveform, the ECG, and the I and Q signals from the wall motion channel(s) were exported in an ASCII text file for importation in an Excel spreadsheet.

During analysis in Excel, the I and Q Doppler signals from each wall motion channel were plotted against each other, as shown in Fig. 1, and offsets were added as needed to position the center of the loops or arcs at the origin. Next, the arctangent(Q/I) = was calculated, de-aliased to account for ambiguity at 2, angle corrected by cos(), and converted to displacement (Eq. 4) for display with the ECG, velocity, and other signals, as shown in Fig. 1. Displacement of the near and far walls was subtracted to obtain the diameter signal. Cardiac cycles with respiratory artifacts and motion were eliminated, and the maximum (max) and minimum (min) diameter were measured and averaged over the remaining cardiac cycles. The augmentation index (AI) for diameter was calculated using the method described by Murgo et al. (33) and Reddy et al. (38) for pressure signals. Briefly the inflection (inf) in the upstroke of diameter was identified as a local minimum in the first derivative (velocity in Figs. 1 and 3) and marked on each cycle along with max and min values, as shown in Fig. 3. AI was then calculated as (max – inf)/(max – min) and the diameter change as max – min.

View larger version (23K): [in this window] [in a new window]   Fig. 3. Blood velocity, near and far artery wall motion, and net diameter change and velocity are shown from a normal wild-type mouse. The net diameter change is calculated by subtracting far and near wall motion, and wall velocity is calculated as the derivative of diameter change. For determination of augmentation index, the inflection point on the diameter signal (inf) is measured at the local minimum of velocity during the increase in diameter from minimum (min) to maximum (max).

All studies were approved by the Animal Care and Use Committee of Baylor College of Medicine. Sixteen mice consisting of six wild-type (WT), two apolipoprotein E null (ApoE), four -smooth muscle actin null (-SMA), and four 30-mo-old senescent (old) were anesthetized with halothane gas using a sealed chamber. The characteristics of the mice, which were selected based on our prior experience (13, 15, 38) to provide a variety of vascular phenotypes, are shown in Table 1. After induction, each mouse was placed on a temperature-controlled board (15), its four limbs were coated with conductive paste, and each limb was taped with the mouse supine to the ECG electrodes on the board. A cone was placed over the nose for maintenance of anesthesia. The board was connected via ribbon cables to an ECG amplifier and a temperature controller, and board temperature was maintained at 37 ± 2°C throughout the experimental protocol (15). The neck was shaved and coated with acoustic coupling gel, and a 2-mm-diameter 20-MHz Doppler probe, focused at 3 mm, was held by hand over the neck to obtain a blood flow signal from the proximal right common carotid artery. After the vessel was located, the probe was placed in an alligator clip mounted on a stand, oriented at 60° to the artery, and positioned manually to maximize the amplitude of the Doppler blood velocity signal. Care was taken to ensure that the probe did not touch the skin surface. With one range-gated SV positioned at the center of the vessel to record the blood velocity signal, the second SV was adjusted proximally to obtain a signal from the near vessel wall. The wall signal was optimized by adjusting the SV depth to maximize the size and circularity of the loops seen on an X-Y oscilloscope display of the Doppler I and Q signals. Next, fine adjustments were made in the SV and probe positions to maximize both blood velocity and wall motion signals. Next, 2 s of signals (ECG, blood velocity I and Q, and wall displacement I and Q) were digitized and stored for later analysis. After near-wall measurements, the displacement SV was repositioned over the far vessel wall, and the measurements were repeated. Blood velocity was included in each record for timing of waveforms and to verify that the probe was properly positioned over the center of the artery. In one mouse, the probe was mounted vertically over the carotid artery, the two SVs were positioned over the near and far vessel walls to sense displacement, and the SV from a second probe held at 45° was positioned at the center of the vessel to sense blood flow velocity.

	RESULTS

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View larger version (14K): [in this window] [in a new window]   Fig. 4. Carotid artery augmentation index vs. net diameter pulsations for wild-type (WT), old, -smooth muscle actin null (-SMA), and ApoE mice.

View larger version (13K): [in this window] [in a new window]   Fig. 5. Representative carotid artery diameter signals from the 4 types of mice used. Differences in magnitude, wave shape, and heart rate are shown.

View larger version (20K): [in this window] [in a new window]   Fig. 6. Noninvasive diameter signals from the carotid artery, the abdominal aorta, and the iliac artery of a WT mouse. The R-wave of each ECG was aligned at the first beat to show the relative timing of the diameter signals.

	DISCUSSION

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For this method to work reliably, the SV must be long enough in the beam direction that the wall echo remains in the SV throughout the cardiac cycle and short enough to resolve the echoes from the front vessel wall, luminal blood flow, and the back vessel wall. The carotid artery of an adult mouse is 400–600 µm in diameter (12), but the diameter could be smaller in younger mice or in mutant mice. On the basis of the 100-µs burst and sample gate lengths, a wavelength () in tissues at 20 MHz of 78 µm, and the finite bandwidths of the transducer and electronic filters in the signal path, the effective SV length is estimated to be 250 µm. This estimate is in reasonable agreement with the measured SV length of 300 µm at 6 dB down given that the 39-µm movement of the wire will extend the apparent measured SV slightly. Thus the technique should be able to measure displacements as high as 200 µm from vessel walls separated by 400 µm.

Figure 1 shows Doppler I and Q signals and the calculated displacement and velocity of the carotid artery of an ApoE mouse. The total displacement of 13 µm is of a revolution of the Doppler vector. In this method, phase is calculated directly from the I and Q signals (Eq. 3), and the Doppler shift (_d) is calculated from the derivative of phase

(7)

The peak velocity in Fig. 1 is <1 mm/s, and the velocity resolution as estimated by the noise level is on the order of 10 µm/s. The blood velocity in Fig. 2 measured at the same time with the second range gate is 75 cm/s for a dynamic range in velocity of about five orders of magnitude. The noise level on the expanded displacement signal shown in Fig. 2 is still not visible, and resolution of wall displacement is estimated to be <0.1 µm. In practice, when the SV is placed to maximize the echo signal from the near or far carotid artery wall, there is no visible artifact or "noise" from blood echoes. The spatial resolution is thus high enough and the SV short enough to measure artery wall motion without significant contamination or distortion from luminal blood flow.

With Doppler signal processing, it has been shown that improvements in spatial resolution are usually at the cost of velocity or displacement resolution such that shorter and wider bandwidth transmit pulses result in wider bandwidth and less precise Doppler spectra (34). In addition, the frequency-dependent attenuation in tissue that lowers the center frequency of echoes as a function of depth can shift the Doppler spectra (16, 37). Indeed, Rabben et al. (37) and Hoeks et al. (16) have shown, using simulations at 5 MHz, that displacement estimators based on Doppler signal processing can contribute errors or distortions of up to 5%. Although our frequency is higher at 20 MHz, our depth is proportionately lower at 1–4 mm such that errors of a similar magnitude (5%) could be expected during a cardiac cycle. A more significant source of error using our DC-coupled method is the placement of the origin for phase measurements, as shown in Fig. 1. If signal offsets from stationary echoes or case echoes within the probe move the origin from the center of rotation or if the echo amplitude varies during the cardiac cycle, the resulting displacement signal and waveform could be distorted. In this study, we adjusted the range gate position to maximize the wall echo during signal acquisition and adjusted the offsets of the I and Q signals in Excel during analysis to place the origin at the mean radius of curvature of the vector, thereby minimizing distortion.

In previous studies, we have validated the accuracy and fidelity of the Doppler displacement method in vitro using moving phantoms driven by audio speakers (11) and in vivo in pigs (10) and dogs (50) against sonomicrometry and have applied the technology in numerous studies to measure myocardial thickening in rats (5), dogs (3), and humans (2). Even under these extreme conditions where the myocardial tissue compresses, distorts, and shears, as it thickens, the displacement signal was found to agree well with both ultrasound physics and with the reference measurements by sonomicrometry in vivo (10, 50) and optical methods in vitro (11).

The physical situation when measuring artery wall motion in mice is simpler, but, with the total displacement being much smaller, the resolution, precision, and probe stability need to be higher. The alligator clip holders were simple to use and apply and were found to be stable enough to position and hold the probes over the carotid arteries of mice. With proper positioning of the probe, the echo amplitudes from the near and far vessel walls are much higher that those from blood flow within the artery, and we were able to obtain wall motion signals from all mice. The major problem was found to be respiratory motion, which varies in magnitude depending on anatomy, position along the artery, orientation of the probe with respect to the artery, depth of anesthesia, and physiological conditions. In several of the mice, the respiratory motion was large enough to move the artery wall out of the SV during inspiration. However, there were always two to three cardiac cycles during slow expiration that could be analyzed. During this time, the echoes from the artery walls remained in the SV and did not decorrelate during the cardiac cycle such that the loops or arcs on the I-Q display as shown in Fig. 1 were nearly circular in shape.

It was found empirically that, when the probe was placed vertically over the neck of a supine mouse, the near wall of the carotid artery moved much more than the far wall along most of the length of the common carotid artery. When the probe was positioned laterally from the side, both walls moved a similar amount, as shown in Fig. 3. We found in five of the six WT mice that the motion of the far wall was small enough (<10% of near wall motion) that it was not always necessary to subtract far wall motion from near wall motion to calculate the diameter change during the cardiac cycle. Indeed, real-time 2-D ultrasonic images of a mouse carotid artery taken with a VisualSonics Imaging system (on promotional compact disc) show minimal motion of the far wall compared with the near wall during the cardiac cycle but with large translations with respiration.

Methods similar to the one described here have been applied in the past at lower frequencies to measure diameter changes in humans and animals (17, 18, 37, 47). In humans, the percent change in carotid diameter during the cardiac cycle is reported to be between 5 and 15% (37). In rats, the reported aortic diameter change is 16% (47). In mice, the aortic diameter change is on the order of 12–15% (18). If we estimate the mean carotid diameter to be 400–600 µm, the percent diameter change during the cardiac cycle would be 2–20% in the mice studied here and is in general agreement with accepted values.

Arterial diameter pulsations relative to the pulse pressure have been used in the past to estimate vessel compliance (35). At a given pulse pressure, a more compliant artery undergoes a larger diameter pulsation. The mutant and old mice used here for illustrative purposes were chosen because we and others had found changes in pulse wave velocity (13, 15) and AI (38) in these mice suggestive of alterations in artery compliance and perhaps wall motion. In a previous study, we showed that ApoE mice have similar pressures to control mice but increased pulse wave velocity (13), suggesting an increase in stiffness. In -SMA mice, we had found decreased pulse wave velocity and an inability to increase vascular tone in response to a vasoconstrictor, phenylephrine (15, 42). Our previous studies with senescent mice have shown that old mice have increased pulse pressure and pulse wave velocity (38). Although the number of mice studied here is too small to draw conclusions regarding vascular phenotypes in these groups of mice, the general findings of low-diameter pulsations in ApoE mice and high-diameter pulsations in -SMA mice are in agreement with prior studies.

It has been shown by others that diameter signals can be used to estimate local arterial pulse pressure and waveforms in humans (46). The similarity of diameter signals taken noninvasively to pressure signals taken invasively from mice (38) suggests that diameter signals could replace pressure signals in certain situations where calibration is not needed. These include measurement of arrival times in the determination of pulse wave velocity (Fig. 6; see Refs. 14 and 48) and in the calculation of the AI (Fig. 4 and Refs. 33 and 35). Indeed, the diameter signals taken noninvasively from carotid arteries in mice resemble central pressure signals from humans and larger animals taken invasively using intravascular catheter-tip pressure sensors (33, 35) and noninvasively using tonometry (25). The signals reported here (Fig. 5) also show a remarkable resemblance to carotid diameter signals recorded from humans using similar ultrasound methods (37). In a classic paper (33), Murgo et al. (33) classified the shapes of human central aortic pressure waves based on the AI and wave reflections into types A (AI > 0.12), B (0 < AI < 0.12), and C (AI < 0 with the inflection occurring after the systolic peak). In general, the carotid displacement signals from adult mice resemble the type B pattern, which is associated in humans with 30- to 40-yr-old adults. The diameter signals from old mice and from atherosclerotic (ApoE) mice have higher AI values than normal WT mice, as shown in Fig. 4, and resemble Murgo et al.'s type A pattern seen in older adults. This suggests an earlier arrival of reflections from the periphery in these mice (35), consistent with our earlier findings of increased pulse wave velocity in old (38) and ApoE (13) mice and also consistent with findings in old (25) and atherosclerotic (36) humans.

In conclusion, we have shown that near and far artery wall displacement signals can be obtained noninvasively from intact anesthetized mice using a modified 20-MHz pulsed Doppler velocimeter, with the required signal processing done off-line in Excel. The technique is relatively simple to implement and has the advantage that blood velocity signals can be obtained at the same time from the same or from different probes. The calibration is based on well-understood ultrasound physics, and the generated signals have a precision or noise level on the order of 0.1 µm. The displacement waveforms closely resemble published pressure waveforms from mice and larger animals and can be analyzed in a similar manner in applications, such as calculation of the AI, where absolute calibration is not required. The potential exists to use velocity in place of flow and diameter in place of pressure to noninvasively study central and peripheral arterial mechanics, vascular impedance, and wave reflections in mice and other small animals.

	GRANTS

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This work was supported in part by National Institutes of Health Grants HL-22512 (C. J. Hartley), AG-17899 (G. E. Taffet), HL-52364 (S. Madala), HL-73041 (A. K. Reddy), RR-14799 (C. J. Hartley), and HL-42550 (M. L. Entman) and by a grant to the DeBakey Heart Center from the Hankamer Foundation.

	ACKNOWLEDGMENTS

 
We thank Thuy T. Pham, James A. Brooks, Jennifer S. Pocius, Ross J. Hartley, and Alex Tumang for valuable contributions to this research.

	FOOTNOTES

 

Address for reprint requests and other correspondence: C. J. Hartley, Dept. of Medicine (CVS), Baylor College of Medicine, One Baylor Plaza, Houston, TX 77030 (E-mail: chartley{at}bcm.tmc.edu).

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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