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(Hypertension. 1995;26:15-19.)
© 1995 American Heart Association, Inc.
Articles |
Biaxial Mechanical Properties of Carotid Arteries From Normotensive and Hypertensive Rats
From INSERM Unit 141 and IFR "Circulation Lariboisière" and INSERM Unit 337 (M.E.S.), Paris, France.
Correspondence to Bernard I. Lévy, INSERM U141, 41 Blvd de la Chapelle, 75010 Paris, France.
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Abstract |
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Abstract Hypertension is known to decrease arterial distensibility and volumetric compliance, as reported from pressure-volume experiments and ring and strip studies of human and animal large arteries. However, recent data using noninvasive in vivo recording of vessel diameter suggest that the cross-sectional compliance of large arteries can be unchanged or even increased in hypertensive subjects. The present study was performed to test the hypothesis that differences between volumetric and cross-sectional compliance could be related to differences in biaxial mechanical properties in normotensive and hypertensive rats. In normotensive (Wistar-Kyoto [WKY]) rats and spontaneously hypertensive rats (SHR) we measured the simultaneous changes in length and diameter of in situ isolated carotid arteries submitted to static pressures (50 to 200 mm Hg by steps of 25 mm Hg each). Carotid artery diameters and lengths were determined by video microscopy and computer-assisted image analysis. At low transmural pressure (50 mm Hg), carotid artery diameter was 710±41 µm in WKY rats and 980±31 µm in SHR (P<.01). In response to pressure increases, the carotid diameter increased by 91±6% in WKY rats and by 41±4% in SHR (P<.01). In parallel, the percent increase in carotid length was much larger in WKY rats than in SHR (31±2% versus 7±1%, respectively; P<.01). In WKY rats, longitudinal distensibility causes significantly larger volumetric values than cross-sectional compliance values; in contrast, because of the very small longitudinal distensibility, volumetric and cross-sectional compliances are almost identical in SHR. In conclusion, the present study suggests that biaxial mechanical properties of arteries could play a role in the damping function of the arterial tree and that measurements of cross-sectional compliance should be interpreted cautiously in normotensive and hypertensive rats when compared with volumetric compliance.
Key Words: elasticity • compliance • arterial wall • carotid arteries • rats
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Introduction |
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TopAbstractIntroductionTheoretical ConsiderationsExperimental ProtocolResultsDiscussionReferences |
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Knowledge of the normal mechanical behavior of arteries is necessary to the understanding of the effects of factors such as aging, hypertension, and atherosclerosis and other vascular diseases on the functional properties of the arterial wall.
Despite the large number of mechanical parameters used by investigators, arterial compliance, defined as the change in volume due to a change in transmural pressure (dV/dP), is one of the most-used parameters to quantify mechanical arterial properties clinically. Arterial compliance is determined both by the vessel geometry and by the intrinsic mechanical properties of the wall. Throughout the years, mainly because of technological limitations, compliance calculations were done as a discrete function by measuring the volume change for a given change in pressure and assuming a steady, linear pressure-volume relation. A vast body of literature exists in which values of compliance are reported for different arteries under different physiological and pathological conditions.1 2 3 4 5
New technological developments in ultrasound allow us to measure precisely arterial diameter in vitro6 and in vivo.7 8 9 10 For in vivo measurements, within the operational ranges of blood pressure it is difficult to establish the complete pressure-diameter relation; therefore, it is impossible to accurately compare values of compliance obtained at different levels of pressure. Furthermore, since most of the measurements are done on vessels assumed to be cylindrical, the mechanical properties of the arteries are presented in terms of changes in cross-sectional area per unit of pressure (Cs=dS/dP, where Cs is cross-sectional compliance), rather than in terms of changes in volume per unit of pressure (Cv=dV/dP, where Cv is volumetric compliance). This interpretation of data is important to consider because it assumes that the longitudinal changes of the vessel are null or negligible and do not contribute significantly to the arterial volume changes.
The literature indicates that discrepancies exist between cross-sectional and volumetric compliances among populations of normotensive animals7 11 and in hypertensive patients12 13 and that a change in pressure in arterial preparations is accompanied not only by a change in diameter but also by a significant longitudinal change in the vessel.14 15 16 17 18
Therefore, the aim of the present work was to simultaneously measure diameter and the longitudinal elongation of the rat carotid artery that is due to steady changes of transmural pressures and to calculate the static compliance, either by taking into account the length change (Cv) or by assuming that the length change is negligible (Cs), in normotensive Wistar-Kyoto (WKY) rats and in spontaneously hypertensive rats (SHR). WKY rats and SHR have been compared previously in studies, particularly as concerns their operational ranges of arterial blood pressure.
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Theoretical Considerations |
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A simple analysis shows that any change in length as function of pressure must induce a difference between dS/dP and dV/dP magnitudes. If the cross-sectional area S(P) and the length L(P) are both functions of the transmural pressure P, the change in cross-sectional compliance Cs is
 | (1) |
and the volumetric compliance per unit of artery length is
 | (2) |
where Lmean is the mean artery length. To compare Cs and Cv, Equation 2 can be expressed as
 | (3) |
By substituting Equation 1 into Equation 3, we obtain
 | (4) |
From Equation 4, Cv is equal to Cs only if L(P)=Lmean and dL/dP=0, ie, if L is constant. If one assumes that L increases when P increases, it is expected that for low pressures L(P)<Lmean and, depending on the magnitude of the second part of Equation 4 {[S(P) · dL/dP]/Lmean}, Cv could be lower or higher than Cs. For higher pressures, when L(P)>Lmean, Cv will always be larger than Cs because the second part of Equation 4 is positive.
For different functions of diameter and length, Cv and Cs will be functions of different magnitude and shape. Different variations of diameter and length as functions of pressure can be observed only for anisotropic materials.
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Experimental Protocol |
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Artery Preparation
All rats received humane care in compliance with the "Principles of Laboratory Animal Care" formulated by the National Society of Medical Research and the "Guide for the Care and Use of Laboratory Animals" published by the National Institutes of Health (DHHS Publication No. 80-23, revised 1985). All operative procedures were performed with the use of standard microsurgical techniques under an operating microscope.
Five 12-week-old normotensive WKY control rats and five age-matched SHR were anesthetized with sodium pentobarbital (50 mg/kg IP) and kept at constant body temperature (38°C) with a thermoregulated heating pad (Harvard Apparatus). After anesthesia was administered, the trachea was cannulated and connected to a rodent respirator (model 680, Harvard Apparatus). Arterial blood pressure was then recorded via a right carotid catheter connected to a pressure transducer (P23ID, Statham Gould).
A midsternal thoracotomy was performed, and the root of the left carotid artery was exposed. The upper end of the left carotid artery was catheterized with a 40-cm-long nylon tube (0.6 mm internal diameter) filled with Tyrode's solution mixed with albumin (4%) and Evan's blue dye (0.03%). The presence of protein in flushing and incubating solutions preserved the endothelium and maintained a physiological osmotic pressure gradient across the vessel wall.19 The root of the left carotid artery was dissected, and a removable clamp was positioned at the junction of the aortic arch and the carotid artery. Approximately 25 mm of carotid artery was isolated. The axial markers consisted of two 10-0 nylon adventitial sutures spaced 3 to 4 mm apart. Care was taken to secure the suture in the periadventitial tissue and not to penetrate below the adventitial layer, thereby affecting wall motion only minimally. The distance between the axial markers and the length of the in situ isolated carotid artery (length greater than 10 times radius) was large enough to avoid "end effects" and was short enough to trap a reasonably uniform carotid segment, minimizing taper.15
Protocol and Data Acquisition
The carotid artery was exposed under a binocular microscope
(x160 magnification) (Microcontrol). The microscope was connected to a
charged coupled device video camera (COHU) and a tape recorder
(S-VHS, Braun), allowing the complete experiment to be recorded for
image analysis.
The vessel was subjected to stepwise increases in pressure of 25 mm Hg each, from 50 to 200 mm Hg. After each change, the pressure was maintained for 4 minutes to let the tissue reach its new steady state condition.20
The data were analyzed using a specific software allowing the digitalization and measurements of the recorded images (Microvision Evry). The system measures to precisely within 10 µm the distance between any two points and the surface and perimeter of a given closed figure.
Diameters and distances between the two arterial markers were measured at each level of pressure. The diameter was calculated as the mean of 10 successive measurements along the piece of artery delimited between the two markers. The length was estimated as the mean value of 10 successive measurements of the distance between the two markers.
Results are expressed as mean±SEM. Repeated-measures ANOVA with one grouping factor (the strain of rats) and one within factor (pressure) were used to test for significant differences between groups. For comparison of values obtained in both strains at each level of pressure, we used the Bonferroni test, with probability values adjusted according to the number of comparisons.
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Results |
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Fig 1 shows a sequence of video images of the carotid artery recorded at different levels of transmural pressure from 50 to 200 mm Hg. Changes in diameter and length were measured in such video images for each rat.
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Fig 2 shows the carotid diameter measured as a function of transmural pressure for the WKY rat group and SHR group. The carotid diameter measured at 75 mm Hg was significantly smaller in WKY rats than in SHR (750±33 versus 1091±27 µm, P<.001), suggesting markedly higher values for unstressed arterial volume in SHR than in WKY rats. In both strains, diameter increased quickly for pressures ranging from 75 to 125 mm Hg and reached a roughly asymptotic curve for pressure values greater than 150 mm Hg. Further increases in pressure had very little effect on diameter. Carotid diameter was significantly larger in SHR than in WKY rats for the whole range of pressure (P<.001) and at each level of pressure except 200 mm Hg, at which carotid diameters were roughly identical between the two groups of rats.
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To compare the mechanical behavior of the vessel as a function of transmural pressure, relative changes in diameter and length were plotted versus carotid pressure (Fig 3A and 3B). Relative changes in longitude and radius were significantly greater in WKY rats than in SHR (P<.001), indicating a stiffer carotid artery in SHR than in WKY rats.
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Fig 4A and 4B show the diameter and length changes (
D
and L, respectively, expressed in millimeters) as a function of
pressure. D and L were significantly larger in WKY rats than in
SHR (P<.001). In the WKY rat group, D had a clear
maximum value between transmural pressures of 75 and 100 mm Hg,
whereas the maximum value of L occurred between 100 and 125 mm Hg.
In contrast, in SHR, the maximum values of D and L were observed
at the same level of pressure (100 to 125 mm Hg), suggesting a more
isotropic material in the artery of SHR than in WKY rats.
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Cv and Cs were calculated according to Equations 1 and 2, respectively. Fig 5 shows the results for both groups plotted as a function of pressure. In WKY rats, Cv was significantly greater than Cs (P<.01); also, Cv reached a significantly greater maximum value for pressure than Cs did (P<.05). In contrast, we did not have evidence of any significant difference between Cv and Cs in the SHR group. Both parameters reached their respective maximum values at the same level of transmural pressure.
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Discussion |
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In the clinical field, Cv, defined as the change of volume of the vessel due to a change of transmural pressure, was for many years the parameter most often used to compare the mechanical properties of vessels acting under different conditions and to evaluate the influence of different diseases or drugs on these mechanical properties. Over the last few years, development of new ultrasonic devices has allowed for accurate and noninvasive measurement of vessel diameter. As a result of the use of these technologies, investigators evaluate the change in cross-sectional area that is due to changes in transmural pressure as an index of stiffness, assuming no changes in vessel length and a cylindrical vessel shape. In recent experimental and clinical studies with ultrasound methods it has been reported that cross-sectional compliance and distensibility are similar in normotensive and hypertensive animals versus patients.7 21 Indeed, radial artery cross-sectional compliance in hypertensive patients has been shown to be paradoxically increased compared with that in normotensive control subjects at the same blood pressure level. Furthermore, a recent clinical study by Laurent et al21 demonstrated that the cross-sectional mechanical properties of the carotid arterial wall were similar at the same transmural pressure among normotensive subjects and hypertensive patients.
Our present results agree with previous observations of changes in length as a function of transmural pressure.14 Our results also corroborate those of Patel et al15 and L'Italien et al,22 who also demonstrated that arteries were stiffer in the longitudinal versus the circumferential direction at physiological length. The latter group used a noncontact method (video-motion analyzer) and reported periodic longitudinal distension of in vivo normotensive rat abdominal aorta and carotid artery, which were in synchrony with the observed circumferential motion. The longitudinal displacements were approximately 30% of the circumferential one. Upon excision, Patel et al15 observed that the longitudinal modulus markedly decreased, thus affirming the restrictive role of the stress component due to traction, previously described by Patel and Fry,17 who also measured simultaneous biaxial displacement by use of an in situ model. In those experiments, as in our own work, the arteries studied were kept in situ, and care was taken to minimally dissect the vessel. However, we cannot exclude the possibility that the longitudinal displacement observed in the present study, as in several previous experiments, could be due to the vessel exposure and dissection and may not exist under real physiological conditions.
As shown in Equation 4, a change in length due to change in transmural pressure can explain the difference in magnitude between Cv and Cs. However, this alone cannot account for the differences in the shape of Cv and Cs curves as a function of pressure and especially for the position of the maximum values for Cv and Cs.
It appears from Fig 4A and 4B and from Equations 1 and 4 that in WKY rats the significant differences between quantitative values of Cs and Cv are related to the great extent of longitudinal changes in the carotid artery dimension when pressure is increased. Furthermore, the shift of the maximum of the Cv-pressure relation to the right versus the Cs-pressure relation could be related to an anisotropic behavior of the carotid wall, evidencing maximal slope of diameter and length changes for different transmural pressures.
It is well established that the arterial wall is anisotropic, ie, that its elastic properties are not equal in all directions.15 18 For example, the canine carotid and femoral arteries are stiffer in the circumferential than in the longitudinal direction, whereas canine and bovine aorta are stiffer longitudinally than circumferentially. There are several reasons for vessel anisotropy. First, there are differences in wall architecture and in load bearing by wall constituents in each direction. For example, in the canine carotid artery, elastin bears loads in both the circumferential and longitudinal directions, whereas collagen and vascular muscle bear loads predominantly in the circumferential direction. Also, arteries in vivo undergo unequal deformations in each direction, and this differentially stretches and stiffens all constituents.
In the present work, a rat preparation was developed, allowing us to evaluate with a high degree of accuracy and reproducibility the diameter and length changes of the carotid artery as a function of transmural pressure. Although the changes in diameter with pressure were much greater than those in length with pressure, our findings clearly indicate that the changes in length cannot be neglected: Length can increase 10% to 15% between the application of 50 to 200 mm Hg pressure. In 1994, L'Italien et al22 reported a 4% in vivo longitudinal displacement in abdominal aorta from normotensive rats submitted to physiological pulse pressure. Our present results in WKY rats are of the same order of magnitude for similar ranges in pressure. Furthermore, in vivo carotid longitudinal compliance is expected to be large enough to accommodate a range of neck extension. Therefore, the values of Cv within the physiological pressure ranges (100 to 140 mm Hg) were significantly larger than those of Cs by approximately 30%. Furthermore, in WKY rats, the anisotropy of the arterial wall was demonstrated on the basis of the differences in the shapes of Cs and Cv relations versus transmural pressure. The maximum compliance values were reached for pressure values greater for volumetric than for cross-sectional compliances, ie, at the point where the maximum change of length occurs.
An important finding of the present study was that WKY rats and SHR differed significantly in terms of anisotropy of the arterial wall. In SHR, the dL/dP practically did not change with transmural pressure, indicating a lack of longitudinal extensibility in hypertensive rats and therefore no significant differences between Cs and Cv values at any given value of transmural pressure. This finding is important to consider, since Coskinas and Price23 showed that the sensitivity of the rat aorta to norepinephrine depends on muscle length and that this relation is not altered in hypertension.
The difference in behavior of arteries from WKY rats and SHR may have important consequences when comparing the compliance-pressure relation of the two strains using an ultrasound echo-tracking technique in which cross-sectional area (and not volume) is measured. These differences may be particularly difficult to understand and to analyze because with the echo-tracking technique in vivo only the operating ranges of the compliance-pressure curves are investigated. From Fig 5 it is clear that when pressure-Cv relations are analyzed, these curves are significantly different in SHR and WKY rats, whereas pressure-Cs curves obtained in WKY rats and SHR at their respective operating pressure values are not markedly different. Following from in vivo experiments, this aspect may be amplified by the increased variability of the determinations and the concomitant changes in vasomotor tone that may affect the degree of anisotropy.
In conclusion, in view of previous observations and our present results, we suggest that the two static mechanical parameters Cv and Cs are both useful but cannot be considered similar because they reflect different mechanical properties of the vessel.
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Acknowledgments |
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This work was supported in part by E.C. Grant (Biomed 1) and a grant from the Societé Française d'Hypertencion.
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References |
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