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(Circulation Research. 1995;77:1008.)
© 1995 American Heart Association, Inc.

Articles

Direct Effects of Smooth Muscle Relaxation and Contraction on In Vivo Human Brachial Artery Elastic Properties

Alan J. Bank, Robert F. Wilson, Spencer H. Kubo, James E. Holte, Thomas J. Dresing, Hongyu Wang

From the Cardiovascular Division, Department of Medicine, and the Department of Biomedical Engineering, University of Minnesota, Minneapolis.

Correspondence to Alan J. Bank, MD, Cardiovascular Division, Department of Medicine, University of Minnesota Medical School, Box 508 UMHC, 420 Delaware St SE, Minneapolis, MN 55455.

	Abstract

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Abstract The direct effect of smooth muscle relaxation on arterial elastic properties is controversial. Studies in animals show both a decrease and an increase in elastic modulus. In human subjects, the contribution of smooth muscle to arterial elastic mechanics has been limited by difficulty in separating the direct effects of a vasodilator drug on the arterial wall from the indirect effects due to reduced blood pressure. The purpose of the present study was to assess the direct contribution of vascular smooth muscle to brachial artery elastic mechanics in normal human subjects in vivo. We measured brachial artery compliance and incremental elastic modulus (E_inc) in eight normal subjects (age, 22 to 51 years) by using intravascular ultrasound. A 3.5F 30-MHz intravascular ultrasound catheter was placed through a sheath into the brachial artery, and intra-arterial pressure, cross-sectional area, and wall thickness were measured simultaneously under baseline conditions and after the administration of intra-arterial nitroglycerin (100 µg) and norepinephrine (1.2 µg). A pressurized cuff surrounding the brachial artery was inflated to reduce transmural brachial artery pressure. Using this technique, we were able to measure the following arterial characteristics for the first time in human subjects in vivo: (1) the effective unstressed arterial radius and (2) the pressure-area, stress-strain, and pressure-E_inc relations over a wide pressure range (0 to 100 mm Hg). Intra-arterial nitroglycerin increased brachial artery area by 22% and intra-arterial norepinephrine decreased brachial artery area by 17% at 100 mm Hg transmural pressure (P<.001 versus baseline). Nitroglycerin produced a significant (P<.01) nonparallel upward shift of the compliance pressure curve compared with baseline, and norepinephrine produced a smaller downward shift of the compliance-pressure curve. Pulse-wave velocity was decreased from 15.1±1.1 m/s at baseline to 13.2±0.7 m/s at 100 mm Hg after the administration of nitroglycerin (P<.05). Nitroglycerin and norepinephrine also significantly shifted the brachial artery stress-strain and E_inc-strain curves in opposite directions. However, nitroglycerin did not significantly change E_inc under isobaric conditions. This study describes and validates a new technique for determining brachial artery elastic properties in vivo over a wide pressure range. At constant pressure, nitroglycerin-induced smooth muscle relaxation increased brachial artery compliance and decreased pulse-wave velocity without significantly altering E_inc.

Key Words: compliance • elastic modulus • brachial artery • smooth muscle • intravascular ultrasound

	Introduction

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The effects of smooth muscle contraction and relaxation on arterial elasticity are controversial. Smooth muscle contraction can increase arterial stiffness by the direct addition of a tensile force to the arterial wall. However, this effect may be offset by the ability of the active smooth muscle to reduce the size of the artery and shift stress bearing from the relatively stiff collagen fibers to the more distensible elastin fibers.¹ A number of studies have been performed to assess the contribution of smooth muscle to arterial elasticity. Dobrin and Rovick² and Barra et al³ showed that norepinephrine decreased arterial incremental elastic modulus (E_inc) under isobaric conditions. In contrast, Peterson et al⁴ found an increase in E_inc with topical and intravenous norepinephrine and a decrease in E_inc with the vasodilator acetylcholine. Similarly, Yano et al⁵ demonstrated an increase in canine aortic distensibility with diltiazem. Human studies have predominantly shown increased compliance in response to vasodilator drugs.^{6 7 8 9} However, systemic administration of these drugs usually decreases blood pressure in concert with conduit vessel smooth muscle relaxation. Thus, the direct effects of the drugs on the arterial wall are difficult to separate from the indirect effects resulting from a lower distending pressure. In addition, most human studies have only studied arterial elastic properties within the pressure range of diastole to systole. Comparison of individuals or groups with significantly different blood pressures is problematic, and assessment of unstressed arterial caliber (which is used to calculate strain and hence E_inc) has not been feasible.

The present study was designed to assess the direct effects of alterations in smooth muscle tone on arterial elastic properties in normal human subjects in vivo. We developed a technique that uses intravascular ultrasound to measure brachial artery cross-sectional area and wall thickness and an intra-arterial fluid-filled catheter to measure pressure and infuse vasoactive drugs directly into the brachial artery. Additionally, an external pressure cuff placed over the imaging site was used to reduce transmural brachial artery pressure. This technique permits measurement of brachial artery compliance and E_inc in vivo over a wide range of pressures and in direct response to vasoactive drugs.

	Materials and Methods

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Study Population
Eight normal male subjects (age, 22 to 51 [mean, 37.5±4.4] years) were studied. They were recruited from newspaper advertisements and were free of heart disease, hypertension, diabetes mellitus, vascular disease, and other medical illness as assessed by history, physical examination, routine blood tests, and electrocardiogram. None of the subjects smoked or were taking medications. Mean blood pressure was 118±3/67±3 mm Hg. Body weight was 84.3±1.5 kg, and forearm volume was 1169±44 mL. Written informed consent was obtained from all subjects. The study was approved by the Human Rights in Research Committee.

Intravascular Ultrasound Measurement of Brachial Artery Elastic Properties
The brachial artery was imaged by using a commercially available intravascular ultrasound system (HP Sonos Intravascular Imaging System, Hewlett Packard Co) and a 3.5F monorail catheter with a 30-MHz mechanical rotating transducer (Boston Scientific Corp). This transducer is situated 1.5 cm from the tip of a 140-cm catheter and produces a 360° tomographic image of the blood vessel. The intravascular ultrasound system uses 64 levels of gray scale and a 60-dB dynamic range, which improves differentiation of the blood-tissue interface. Images are obtained at 30 frames per second. Axial resolution is 100 µm, and lateral resolution is 150 µm (manufacturer’s specifications). All images were obtained at a radial depth display setting of 5 mm. Images were optimized by using compression, time-gain compensation, and postprocessing controls to give the blood in the brachial artery lumen a slight degree of reflectivity. Brachial artery cross-sectional images were recorded on VHS videotape for off-line analysis.

The experimental setup is shown in Fig 1. The intravascular ultrasound catheter was placed into the brachial artery through a 4F arterial sheath with side arm. The catheter was advanced through the sheath into the brachial artery to a point at approximately the middle of the upper arm and 5 to 6 cm past the end of the sheath. Adjustments of ultrasound catheter position, gain, and gray scale were made to obtain optimal images and were not changed over the course of a particular study. Intra-arterial pressure was measured through the side arm of the 4F arterial sheath, which was connected to a pressure transducer (model P23XL, Gould Inc) by using high-pressure tubing. Arterial pressure waveforms were recorded on a four-channel chart recorder (Gould Inc). The arterial pressure signal was also converted to a video signal and overlaid onto the intravascular ultrasound video image by using a video mixer (Panasonic). This allowed for a large-scale arterial pressure waveform to be synchronized with the ultrasound image.

View larger version (70K): [in this window] [in a new window]   Figure 1. Experimental setup. Intravascular ultrasound catheter is placed through the arterial sheath and centered under the upper arm cuff. The sheath side arm is used for drug infusion and measurement of intra-arterial pressure. IVUS indicates intravascular ultrasound catheter.

A 12-cm blood pressure cuff was placed around the upper arm so that the intravascular ultrasound catheter was imaging beneath approximately the center of this cuff. The cuff was connected to a compressed air system (model E-10, D.E. Hokanson), which was calibrated to a mercury manometer and used to rapidly inflate the cuff to the desired pressure. Transmural pressure was defined as intra-arterial pressure minus cuff pressure. Thus, transmural brachial artery pressure could be reduced in direct proportion to the pressure in the cuff.

Computer Analysis of Video Images
Cross-sectional video images of the brachial artery were analyzed off-line to determine brachial artery area and wall thickness. Images were replayed by using a VCR with high-quality still/slow capability (model BR-S378U, JVC) and viewed on a standard video monitor. Selected video frames were digitized by using a frame-grabber board (Data Translation). To improve image quality and stability during the frame-grabbing process, the video signal was sent through a time-based corrector (Digital Processing Systems). Digitized images were stored on optical disks and displayed on a Macintosh IIci computer. The software image-analysis package NIH IMAGE 1.52 was used to assist in measurement of lumen area and wall thickness.

Images were digitized for analysis at end diastole and mid diastole for each condition and external cuff pressure. Diastolic images were used because the rate of pressure decline (dP/dt) in diastole is slower than the rate of pressure rise in systole, thus minimizing the small phase lag between pressure and area (33 milliseconds). The lumen–vessel wall border was manually traced, and the lumen cross-sectional area was automatically determined. Brachial artery area was measured and averaged for five consecutive images. These images were obtained during the last 5 seconds of each 10-second interval following a change in cuff pressure to allow the vessel to equilibrate to the new conditions.

Fig 2 shows a representative intravascular ultrasound image of the brachial artery. Arterial wall thickness was measured at a location where a vein ran adjacent to the wall of the brachial artery. This location significantly improved the ability to discern the outer wall of the blood vessel because of the large difference in echo reflectivity of the wall tissue and the blood in the lumen of the adjacent vein. Ten measurements of wall thickness were made and averaged for each of three beats under baseline conditions with zero cuff pressure. Wall thickness for other conditions and cuff pressures was calculated by assuming that the vessel wall was incompressible and hence that wall cross-sectional area remained constant.^{2 10 11}

View larger version (149K): [in this window] [in a new window]   Figure 2. Representative intravascular ultrasound image. The brachial artery and an adjacent vein are labeled. The arrow points to the outer wall of the brachial artery, which was readily visualized because of the contrasting echodensity of the adjacent vein.

Drugs
Norepinephrine (1.2 µg) was administered to assess the effects of smooth muscle contraction on brachial artery elastic properties. This dose was chosen because preliminary studies demonstrated a large vasoconstrictor effect without significant changes in blood pressure or heart rate.

Nitroglycerin (100 µg) was administered with the goal of producing complete smooth muscle relaxation. Preliminary dose-response studies (n=5) showed that this dose was on the flat portion of the dose-response curve, since it increased brachial artery area by only an additional 2.2% compared with a dose of 10 µg (23.7±4.8% for 100 µg versus 21.5±4.5% for 10 µg). Additionally, the dose of 100 µg is similar to that shown by others (50 to 200 µg) to produce maximal or near-maximal coronary artery dilation.¹²

Drugs were administered as 5 mL boluses over 2 seconds by using 21-gauge needles through the side arm of the arterial sheath. This both improved mixing of the drug in the brachial artery and ensured that the drug reached the site of brachial artery area imaging (which was several centimeters upstream from the end of the arterial sheath). During infusions the brachial artery was imaged, and in all cases echo contrast could be seen within the brachial artery lumen.

Protocol
Studies were performed in a room of constant temperature (22°C to 23°C). Subjects were allowed to eat a light breakfast before the study but were required to refrain from caffeinated beverages on the day of the study. First, forearm volume was measured by using a truncated cone formula as previously described.¹³ Next, a 4F arterial sheath was placed into the nondominant brachial artery after sterile preparation of the antecubitum and application of <0.3 cm³ topical lidocaine. The arm was placed in a comfortable position at the patient’s side just above the level of the heart. Subjects rested quietly for 30 minutes. A sterile plastic sleeve was placed over the intravascular ultrasound catheter to maintain sterility during the study. After appropriate catheter preparation, the catheter was placed through the sheath and positioned in the mid brachial artery. Attempts were made to position the catheter coaxial to the long axis of the blood vessel.

For each pressure-area curve under each condition, a standard sequence of events was performed. Initial brachial artery images and arterial pressure waveforms were recorded on videotape. Pressure in the cuff surrounding the mid upper arm was inflated to 10 mm Hg for 10 seconds. Cuff pressure was subsequently increased in 10 mm Hg increments for 10 seconds each until cuff pressure exceeded diastolic pressure. The arm was maintained in the same position throughout the study so that catheter movement would be minimal.

Two baseline sequences were performed 5 minutes apart to assess reproducibility of the technique. Norepinephrine was then infused, and the above sequence was repeated. After the brachial artery area had returned to its baseline area (15 minutes), nitroglycerin was administered, and the same stepwise increase in cuff pressure was performed. Sequential increases in cuff pressure were begun 1 minute after drug administration. To demonstrate that the duration of action of the norepinephrine and nitroglycerin did not significantly wane during the measurements, brachial artery end-diastolic area was measured immediately before and after the cuff inflation sequence. The mean change in brachial artery area after the cuff inflation sequence was 0.28±0.81 mm² for norepinephrine (P=NS) and -0.23±0.51 mm² for nitroglycerin (P=NS).

Curve Fitting and Calculations of Elastic Properties
Transmural pressure versus area data points were plotted and fit by using least-squares regression with the following formula, which was used by Langewouters et al¹⁴ and others^{15 16} to describe pressure-area curves of blood vessels:

(1)

where A is brachial artery area, P is transmural pressure, and a, b, and c are three parameters that characterize each pressure-area curve. Points on the fitted curves for each condition were averaged every 10 mm Hg, and the mean pressure versus area curves for control, norepinephrine-treated, and nitroglycerin-treated vessels were determined. All individual pressure-area data fit this arctangent model with values of P>.96.

Brachial artery cross-sectional compliance (C) was calculated as the first derivative or instantaneous slope of the pressure versus area curves:

(2)

Circumferential wall stress () was calculated as follows:

(3)

where P is transmural pressure, r_m is midwall radius, and h is wall thickness. Brachial artery inner radius (r_i) was calculated as follows:

(4)

where the brachial artery cross-section was assued to be circular. This assumption was reasonable, since the ratio of the major to the minor axis of 50 randomly selected images under all three experimental conditions was 1.065±0.005.

Circumferential strain () was calculated as follows:

(5)

where r_o is the effective unstressed midwall radius (the midwall radius at 0 mm Hg transmural pressure) under baseline conditions.

E_inc was calculated as follows:

(6)

This method of calculating E_inc is similar to that used by a number of investigators^{2 17 18} and is based on the assumption that the arterial wall is isotropic.

Pulse-wave velocity (PWV) was calculated by using the Moens-Korteweg equation¹⁹ :

(7)

where d is blood density (1.055 g/mL).

Statistics
Curves generated at baseline and after drug administration were compared by ANOVA with two repeated variables (drug and pressure). When the ANOVA interaction term demonstrated a nonparallel shift in curves, we performed post hoc pairwise analysis of the curves at individual pressures with Bonferroni correction for multiple comparisons. Statistical significance was accepted at P<.05. Interobserver and intraobserver area and wall thickness variability and reproducibility of pressure-area and r_o measurements were analyzed by the Bland and Altman technique²⁰ and presented as mean±SD. All other data are presented as mean±SEM.

	Results

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Measurement Variability and Reproducibility
Brachial artery cross-sectional area intraobserver (A.J.B.) and interobserver (A.J.B. and H.W.) variability were assessed by measuring randomly selected intravascular ultrasound images from each individual under baseline conditions, after vasodilation, and after vasoconstriction. The mean difference between two blinded measurements (n=30) made by the same individual was 0.009±0.11 mm² (P=NS). The mean difference between blinded measurements made by two different individuals (n=30) was 0.33±0.45 mm² (P=NS). Similar assessment of wall thickness intraobserver and interobserver variability (n=18) demonstrated mean differences of 0.0009±0.0033 and 0.0002±0.0093 mm, respectively (P=NS). Plots of the average area or wall thickness versus the difference in area or wall thickness (not shown) showed no relation between the difference and the mean, except for interobserver area measurements, where the difference tended to get greater as area increased. All measurements in this study were made by a single observer. Reproducibility of the brachial artery pressure-area relation and r_o measurement was assessed in 10 individuals under baseline conditions 5 minutes apart. As shown in Fig 3, the pressure-area curves were similar over a wide pressure range. The mean difference between repeated area measurements in the same individual at equivalent pressures was 0.048±1.14 mm² (P=NS). The mean difference between repeated r_o determinations was 0.056±0.084 mm (P=NS).

View larger version (20K): [in this window] [in a new window]   Figure 3. Reproducibility of brachial artery area-pressure curves in 10 normal individuals. Measurements were made 5 minutes apart under baseline conditions.

Effects of Drugs on Brachial Artery Area and Compliance
Fig 4 demonstrates brachial artery images for an individual at three different transmural pressures under each of the conditions. Brachial artery cross-sectional area increased with increasing pressure and with decreasing smooth muscle tone. There were no significant changes in systemic arterial pressure with drug infusions (nitroglycerin, 122±4/71±2 to 119±4/71±1 mm Hg; norepinephrine, 123±5/68±1 to 123±5/69±2 mm Hg). Compared with baseline, both nitroglycerin and norepinephrine shifted the pressure-area curves (Fig 5) in a nonparallel fashion (P<.001). The overall differences between the two curves compared with the baseline curve were highly significant (P<.0001). At 100 mm Hg transmural pressure, nitroglycerin increased brachial artery area by 4.4 mm² (22%), and norepinephrine decreased brachial artery area by 3.3 mm² (17%).

View larger version (107K): [in this window] [in a new window]   Figure 4. Brachial artery intravascular ultrasound images from one individual under three different transmural pressures and levels of smooth muscle tone. Arterial cross-sectional area increased with increasing pressure and decreasing smooth muscle tone. NTG indicates nitroglycerin; NE, norepinephrine.

View larger version (24K): [in this window] [in a new window]   Figure 5. Mean pressure vs area curves under three experimental conditions: baseline, norepinephrine (NE, 1.2 µg), and nitroglycerin (NTG, 100 µg). NTG significantly increased brachial artery area, and NE significantly decreased brachial artery area over the entire pressure range. *P<.0001 vs baseline.

Mean compliance versus pressure curves are shown in Fig 6. Both drugs produced a nonparallel (P<.001) curve shift that was significant when averaging over all pressures (P<.01). Since the magnitude of the drug effect decreased with increasing pressure and was thus smallest over the normal physiological range of pressures, a separate analysis was performed at transmural pressures of 70, 80, 90, and 100 mm Hg. Comparison of the nitroglycerin versus baseline or norepinephrine curves over this pressure range also demonstrated a nonparallel (P<.001) curve shift with a significant increase in compliance over this pressure range (P<.001). There was no significant difference between the norepinephrine and baseline curves over this pressure range.

View larger version (22K): [in this window] [in a new window]   Figure 6. Mean pressure vs compliance curves at baseline and after intra-arterial norepinephrine (NE) and nitroglycerin (NTG) administration. NTG significantly increased brachial artery compliance (45% to 60%) compared with baseline and NE over the entire pressure range. NE did not significantly decrease compliance, although it tended to shift the pressure-area curve downward, especially at lower transmural pressures. The magnitude of the effect of NTG and NE on brachial artery compliance is more clearly seen in the bottom figure, which shows the data on a smaller vertical scale. *P<.05, NTG vs baseline or NE.

Effects of Drugs on Stress, Strain, E_inc, and Pulse-Wave Velocity
Mean stress versus strain curves are shown in Fig 7. Smooth muscle relaxation produced a large rightward shift in the stress-strain curve, and smooth muscle constriction produced a large leftward shift of the curve (P<.01 for each drug versus baseline). Fig 8 depicts isometric and isobaric E_inc curves. At constant E_inc, strain is significantly higher after nitroglycerin administration and significantly lower after norepinephrine administration compared with baseline conditions (P<.01 for each drug versus baseline). Under isobaric conditions, there was no significant difference among the three curves, although the norepinephrine curve was shifted slightly to the right of the baseline and nitroglycerin curves. Thus, despite increases in compliance of 45% to 65% with nitroglycerin compared with baseline, there was no significant effect of nitroglycerin on isobaric E_inc.

View larger version (21K): [in this window] [in a new window]   Figure 7. Mean stress vs strain curves at baseline and after norepinephrine (NE) and nitroglycerin (NTG) administration. NE significantly shifted the curve leftward, and NTG significantly shifted the curve rightward. *P<.01 vs baseline.

View larger version (19K): [in this window] [in a new window]   Figure 8. Isometric (top) and isobaric (bottom) incremental elastic modulus (Einc) curves under baseline conditions, after norepinephrine (NE) administration, and after nitroglycerin (NTG) administration. NTG decreased and NE increased isometric Einc. Under isobaric conditions, there was no significant change in Einc with alterations in smooth muscle tone. *P<.01 vs baseline.

Fig 9 shows pulse-wave velocity versus transmural pressure curves. Pulse-wave velocity increased directly with transmural pressure for all three conditions. There was no significant difference in pulse-wave velocity between the baseline and norepinephrine curves. Nitroglycerin significantly (P<.05) reduced pulse-wave velocity compared with baseline and norepinephrine-induced conditions.

View larger version (18K): [in this window] [in a new window]   Figure 9. Effects of norepinephrine (NE) and nitroglycerin (NTG) on pulse-wave velocity. NTG significantly reduced pulse-wave velocity over the entire pressure range, whereas NE had no significant effect. *P<.05 vs baseline.

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion References

 
The present study demonstrates that intravascular ultrasound is a useful tool for studying brachial artery elastic mechanics over a wide pressure range in human subjects in vivo. By using this tool in conjunction with intra-arterial drug infusions, we showed that the normal human brachial artery has a large vasodilator and vasoconstrictor reserve. Smooth muscle relaxation with nitroglycerin at constant pressure increased arterial compliance and decreased pulse-wave velocity. Nitroglycerin and norepinephrine significantly shifted the stress-strain and E_inc-strain curves in opposite directions. Although nitroglycerin decreased and norepinephrine increased E_inc under isometric conditions, there was no significant change in E_inc with alterations in smooth muscle tone under isobaric conditions.

Effects of Drugs on Arterial Caliber and Compliance
The resting caliber of an artery depends on the balance between passive (pressure-induced) expansion and active contraction.²¹ The present study assessed the role of these two factors on arterial caliber by investigating the brachial artery in vivo over a wide range of both pressures and smooth muscle activity. In the present study, nitroglycerin increased brachial artery area by 22%, and norepinephrine decreased brachial artery area by 17% at 100 mm Hg. Thus, under physiological pressure, the normal brachial artery has considerable tone and a large vasodilator and vasoconstrictor reserve. Arterial caliber was dependent on transmural pressure. Decreasing transmural pressure from 100 to 0 mm Hg produced a mean decrease in baseline arterial area of 30%. The effects of drugs were also dependent on pressure, with the magnitude of vasodilation or vasoconstriction (the difference between the pressure-area curves in Fig 5) increasing in a curvilinear manner with respect to pressure.

The smooth muscle relaxation produced by nitroglycerin increased compliance significantly compared with either baseline or norepinephrine-induced compliance over the entire pressure range studied. Norepinephrine tended to decrease compliance compared with baseline values, although the magnitude of this effect was small, and the effect was predominantly at low transmural pressures. The change in compliance with smooth muscle relaxation varied from 0.004 mm²/mm Hg at 100 mm Hg transmural pressure to 0.140 mm²/mm Hg at 0 mm Hg transmural pressure—a 35-fold difference. Although the absolute change in arterial compliance with smooth muscle relaxation increased markedly with decreasing transmural pressure, the percent change in arterial compliance with nitroglycerin was similar over the entire pressure range and varied between 45% and 65%. These changes are consistent with previous studies using different techniques to assess forearm compliance changes in response to systemic nitrate administration.^{7 8 9 22} In most, but not all,²² studies of the effects of smooth muscle relaxation on arterial compliance, it has been difficult to separate the direct effects of a drug on the arterial wall from the indirect effects of the drug as a result of decreased blood pressure. Our technique avoids this potential problem by infusing drugs intra-arterially at the site used for compliance measurement in doses that do not significantly alter systemic arterial pressure. Even if arterial pressure is altered by infused drugs, this effect can be corrected for by using the external cuff to alter transmural brachial artery pressure.

There are at least four competing factors that determine the effect of a vasoactive drug on arterial compliance. First, and most apparent, is the direct effect of the drug on the arterial wall smooth muscle. The active tension that the smooth muscle can generate is estimated at between 1.5 and 3.0x10⁶ dyne/cm².^{23 24} Loss of this tension as a result of smooth muscle relaxation should thus have a direct effect on increasing vessel compliance. A second factor that would tend to make an artery more compliant after smooth muscle relaxation relates to arterial geometry. If an artery exhibits the same change in radius for a given change in pressure in both the vasodilated and vasoconstricted state, then the artery in the vasodilated state will be more compliant than the identical vasoconstricted vessel, since arteries approximate cylinders and computations of cross-sectional compliance require the radius to be squared. A third factor, which would oppose the effects of the previously mentioned determinants of compliance, is the effect of arterial size on fractional recruitment of collagen. The relation between pressure and area (or stress and strain) in a blood vessel is curvilinear and concave toward the pressure (stress) axis. This is a result of differential load bearing by the distensible elastin and the relatively stiff collagen at different pressure (stress) or area (strain).^{1 25} As smooth muscle is relaxed and arterial caliber increases, one would expect the fractional recruitment of collagen to increase and the vessel to become less compliant. The final factor relates to the interaction or linking between the collagen, elastin, and smooth muscle within the arterial wall. Although a number of models have been proposed for the arrangement (series and parallel) of these three important structures in the arterial media,^{3 26 27} there is as yet no general agreement on a model that fits all the experimental data. Several investigators^{28 29} have proposed that smooth muscle in the arterial wall is in series with collagen and that both are in parallel with elastin. During smooth muscle contraction, the collagen jacket is tensed, making the vessel stiffer. During smooth muscle relaxation, stress is released from the collagen and transferred to the more distensible elastin. The data from the present study are in agreement with this model. For example, if the slopes of the pressure-area curves (the compliances) are examined (Fig 5) at equivalent cross-sectional areas, it is apparent that the vasoconstricted vessel is markedly less compliant than the vasodilated vessel. The magnitude of this difference is much greater than can be explained solely by the addition of smooth muscle tension to the vasoconstricted vessel. A logical, though not the only, explanation is that the fractional recruitment of collagen at the same cross-sectional area is greater for the vasoconstricted vessel than for the vasodilated vessel.

Unstressed Radius and Circumferential Arterial Strain
The present study is the first, to our knowledge, to measure the effective unstressed radius of an artery in human subjects in vivo. The r_o of the brachial artery at baseline is 84% of the radius at 100 mm Hg. Reproducibility studies demonstrated a mean difference between repeated r_o determinations of 3% of baseline r_o. The r_o increases with smooth muscle relaxation and decreases with smooth muscle contraction, demonstrating that smooth muscle tone contributes to arterial caliber even at 0 mm Hg transmural pressure. In order to calculate arterial circumferential strain, a reference radius or diameter is needed. Some investigators have used the mean radius of a vessel over a single cardiac cycle, since it has been difficult to measure the unstressed radius in vivo.¹⁸ Others have used the radius of an artery at some predefined low (but greater than zero) pressure.^{2 3} Most investigators use the same unstressed length or radius for both constricted and relaxed vessels (as was done in the present study), although this practice is not universal.²¹ Dobrin³⁰ argues that this single-reference method of computing strains corresponds to the behavior of arteries in vivo and treats each vessel as a single relaxed artery with superimposed vascular smooth muscle properties.

Smooth Muscle Contribution to Stress-Strain, E_inc, and Pulse-Wave Velocity Curves
A number of in vitro and animal studies of arterial mechanical properties have shown that vascular smooth muscle contraction shifts the stress-strain curve toward the stress axis and that smooth muscle relaxation does the opposite.^{2 3 24 31 32} Our findings are in agreement with these studies, since intra-arterial nitroglycerin and norepinephrine produced curve shifts similar to those found in isolated vessels or animals in vivo.

Most investigators demonstrate an increase in isometric E_inc with smooth muscle contraction and a decrease in isometric E_inc with smooth muscle relaxation in isolated vessels or animals in vivo. The present study confirms these findings in human subjects over a wide pressure range. The effects of alterations in smooth muscle tone on isobaric E_inc are less clear, with studies showing both increases⁴ and decreases^{2 3 21} in blood vessel stiffness after smooth muscle contraction. Isobaric analysis showed no significant effect of smooth muscle tone on E_inc in the present study, although there was a trend for E_inc to be decreased after the administration of norepinephrine. The explanation for the effect of drugs on E_inc is similar to that described above regarding the effects of vasoactive drugs on compliance. However, the geometric considerations are not applicable, since E_inc describes only the stiffness of the arterial wall and is independent of arterial size.

Nitroglycerin produced near-maximal smooth muscle relaxation. The resultant stress-strain curve is thus almost exclusively attributable to collagen and elastin in the arterial wall. Roach and Burton¹ have demonstrated that under very low pressure or stress, the elastic modulus of the arterial wall is equal to the elastic modulus of elastin, since little or no collagen bears stress under this condition. The mean elastic modulus of elastin (the E_inc at zero stress) in the present study was 1.0x10⁶ dyne/cm². This value is consistent with data from a number of other studies that estimate the elastic modulus of elastin to be between 1 and 10x10⁶ dyne/cm².^{28 33 34}

Pulse-wave velocity was calculated by using the Moens-Korteweg equation. Although more complex equations have been derived to calculate wave velocity for a thick-walled tube,¹⁹ the equation used gives a reasonable estimate of pulse-wave velocity, which has been verified in the dog aorta by several investigators.^{35 36} Brachial artery pulse-wave velocity was 15 m/s at 100 mm Hg in the present study. This value is similar though slightly higher than values measured in the human arm using other methods, which have ranged from 9 to 14 m/s.^{22 37 38} Nitroglycerin significantly reduced pulse-wave velocity without altering blood pressure. This finding is of potential clinical importance, since a reduction in pulse wave velocity will delay the return of reflected waves and reduce left ventricular impedance.³⁹

Relation Between Compliance and E_inc
We demonstrated an 45% to 65% improvement in brachial artery compliance with smooth muscle relaxation over a pressure range from 0 to 100 mm Hg. Over this same pressure range, there was no difference in isobaric E_inc with smooth muscle relaxation. This dissociation between compliance and E_inc after smooth muscle relaxation can occur because compliance and E_inc describe different, but related, arterial elastic parameters. Arterial compliance is a measure of an artery’s ability to cushion or buffer pulsatile pressure and is thus dependent on both geometry (vessel lumen size) and stiffness. In contrast, E_inc is independent of geometry and is a measure solely of arterial wall stiffness.⁴⁰ If isobaric smooth muscle relaxation results in no change in E_inc, compliance will increase as a result of geometric changes (an increase in lumen area), as was seen in the present study. If smooth muscle relaxation decreases E_inc, compliance must increase. However, if smooth muscle relaxation increases E_inc, compliance can remain unchanged, increase, or decrease, depending on the magnitude of both the vasodilation and the increase in E_inc.

Methodological Considerations
The brachial artery was chosen for this investigation because it is a muscular artery; therefore, the effects of drugs on arterial caliber should be much greater than on elastic arteries such as the aorta. Also, this artery is readily accessible, relatively straight, and easily compressed by an external cuff.

The elastic parameters measured with this technique are somewhat different from those measured with most in vitro or in vivo techniques. In vitro studies of arterial elastic behavior often assess static elastic properties of arteries.^{14 17} In vivo techniques in humans often involve measurement of dynamic elastic properties throughout the systolic and diastolic phases of a single cardiac cycle over the normal pressure range.^{15 16} We generated compliance and E_inc curves from transmural pressure, area, and wall thickness data acquired in diastole over a number of different cardiac cycles of widely varying transmural pressure. The compliance and E_inc curves depicted in the present study thus demonstrate the dynamic elastic properties of the in vivo human brachial artery at a frequency of 1 Hz (mean heart rate, 63.4±3.6 bpm). Since only diastolic portions of the cardiac cycle were analyzed, this technique assesses the purely elastic behavior of the brachial artery and not the viscous and inertial behavior that is exhibited during the rapid stretch of systole.⁴¹

An important issue regarding the technique used to assess brachial artery elastic mechanics is the precision and reproducibility of arterial cross-sectional area and wall thickness measurements. There is no generally accepted "gold standard" for comparison of brachial artery measurements. Nevertheless, intravascular ultrasound measurements have been shown in a number of studies to correlate well with angiographic and pathological assessments of arterial luminal area^{42 43 44 45 46} and wall thickness.^{46 47 48 49}

In the present study, we assessed baseline reproducibility of our technique by measuring brachial artery area at different transmural pressures on two occasions 5 minutes apart. The pressure-area curves were very similar over the entire pressure range. Wall thickness intraobserver and interobserver measurement variability was reasonable but greater than area variability. Wall thickness measurements were made at a location where a vein ran adjacent to the brachial artery. Since veins have very thin walls, a good approximation of the arterial wall thickness could be obtained by measuring the distance between the arterial blood–intima border and the venous blood–intima border. Using this technique, we obtained a mean wall thickness–to–radius ratio of 0.11. This value is consistent with data obtained in animal studies that have shown wall thickness–to–radius ratios of between 0.11 and 0.15 for large peripheral muscular arteries.²⁰ Even if our wall thickness measurements were inaccurate by as much as 10%, the main findings of the present study would not be significantly changed. Wall thickness was measured under baseline conditions at zero cuff pressure for each individual. All other wall thickness measurements were calculated on the basis of the arterial cross-sectional area and by assuming conservation of wall mass.^{2 10 11} Therefore, although the absolute values would change some, the effects of drugs on arterial elastic properties would be nearly identical.

The technique used to measure arterial elastic properties in the present study requires arterial puncture. It is possible that this procedure altered baseline brachial artery area. We attempted to minimize this potential effect by allowing the subjects to rest quietly for 30 minutes before acquiring baseline data and by measuring brachial artery area and wall thickness at a location 10 cm proximal to the site of arterial puncture.

In the present study, we altered transmural brachial artery pressure by applying external compression to the tissues surrounding the brachial artery. Similar techniques have been used by others to alter arterial transmural pressure.^{22 50} Transmural arterial pressure was defined as intra-arterial pressure minus external cuff pressure. If the cuff pressure was not completely transmitted to the underlying brachial artery, the transmural pressure would be overestimated. We addressed this possibility by producing the same calculated transmural pressure under two different conditions: (1) intra-arterial pressure of 100 mm Hg and cuff pressure of x and (2) intra-arterial pressure of 70 mm Hg and cuff pressure of x-30. If the entire cuff pressure is transmitted to the brachial artery, then these conditions should give similar brachial artery area measurements. The mean difference in brachial artery area under these two conditions was 0.048±0.058 mm² (n=25), which is 0.3% of the mean area.

Conclusions
A new intravascular ultrasound technique for measuring brachial artery elastic properties in human subjects in vivo has been described. With this technique, effective unstressed arterial radius was measured and arterial elastic parameters were determined over a wide range of pressures and smooth muscle tone. At constant pressure, smooth muscle relaxation with intra-arterial nitroglycerin increased brachial artery compliance and decreased pulse-wave velocity without significantly altering E_inc.

	Acknowledgments

 
This study was supported in part by an American Heart Association Grant-in-Aid, a grant-in-aid from the University of Minnesota faculty, program project grant PO1-HL-32427 from the National Institutes of Health, and General Clinical Research Center grant M01-RR-00400. The authors would like to thank Linda K. Tschumperlin, RN, and Kathleen Mullen, RN, for their assistance in performing this study and Thomas S. Rector, PhD, for his assistance with data analysis.

Received February 27, 1995; accepted July 12, 1995.

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