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Am J Physiol Heart Circ Physiol 288: H2940-H2945, 2005. First published February 4, 2005; doi:10.1152/ajpheart.01099.2004
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Thermomechanical behavior of human carotid arteries in the passive state

G. V. Guinea,1 J. M. Atienza,1 M. Elices,1 P. Aragoncillo,2 and K. Hayashi3

1Departamento de Ciencia de Materiales, E. T. S. de Ingenieros de Caminos, Universidad Politécnica de Madrid, and 2Departamento de Patología Cardiaca, Hospital Clínico Universitario San Carlos, Madrid, Spain; and 3Department of Mechanical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan

Submitted 28 October 2004 ; accepted in final form 28 January 2005


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Localized heating or cooling is expanding the clinical procedures used to treat cardiovascular diseases. Advantageous implementation and development of these methods are linked indissolubly to a deeper understanding of the arterial response to combined mechanical and thermal loads. Despite this, the basic thermomechanical behavior of human blood vessels still remains largely unknown, primarily due to the lack of appropriate experimental data. In this work, the influence of temperature on the passive behavior of human carotid arteries was studied in vitro by means of inflation tests. Eleven carotid segments were tested in the range 0–200 mmHg at four different temperatures of 17, 27, 37, and 42°C. The results show that the combined change of temperature and stress has a dramatic effect on the dilatation coefficient of the arterial wall, which is shifted from negative to positive depending on the stress state, whereas the structural stiffness of the arterial wall does not change appreciably in the range of temperatures tested.

blood vessels; inflation tests; thermal dilatation coefficient; mechanical properties; structural stiffness

QUANTITATIVE KNOWLEDGE of the thermomechanical behavior of human arteries is fundamental for a better understanding of the physiology of the cardiovascular system and for the development of treatment methods and techniques for cardiovascular diseases, such as angioplasty, stent, or bypass surgery. Although much has been written on arterial mechanics (see Ref. 9 and the references herein), thermomechanical experiments on human blood vessels are scarce, and in most cases only physiological temperatures (35–37°C) are considered. Nearly all the data available on the combined response of blood vessels to mechanical and thermal loading come from tests on mammalians such as rabbits, pigs, or dogs.

The thermomechanical behavior of arteries, however, is not a secondary issue in cardiovascular research because many cardiac surgical procedures are performed at nonphysiological temperatures; coronary artery bypass surgeries are ordinarily performed in conditions of hypothermia (26–31°C) (13), and hyperthermia over 50°C is routinely used in thermal balloon angioplasty (3, 10, 16, 22).

Still today, a lot of efforts are devoted to understanding the effects of changes in temperature on the final results of the treatments and the quality of life of the patients (13, 16). Also, the influence of temperature on vascular properties is important in situations like organ preservation, because modifications of temperature could affect intrarenal vasodilatation, bypass surgery, and extracorporeal circulation.

In addition, thermomechanical experimental data are needed for the development of appropriate constitutive equations for the arterial wall (9, 18) implemented in numerical models, which are proving to be a useful tool for surgical procedures as well as for other clinical cardiovascular issues such as the assessment of plaque vulnerability (9).

The first study on the effect of temperature on human blood vessels was brought out more than a century ago by C. S. Roy, who showed that unloaded arteries shrink when heated and expand when cooled (17). Roy tested human, cow, and sheep aortas in the passive state in the range of 16–54°C.

Parallel results were reported by Lawton (15), who performed isometric tests on passive dog aortas at 15–40°C and found that arterial elasticity was primarily entropic-like elastomers. Nevertheless, other data suggest that heat-induced contraction of blood vessels is not so apparent; Dobrin and Canfield (2), working on dog carotid arteries at the 33–39°C interval, did not notice a clear influence of temperature on passive behavior. In addition, Kang et al. (10) observed a weak effect of temperature on the multiaxial mechanical behavior of passive bovine coronary arteries in the range of 21–55°C and reported a significant stiffening of the arterial wall only above 60°C.

In a way similar to passive mechanics, the influence of temperature on the active behavior of arteries is still in question. In vivo tests on rabbit mesenteric arteries by Gorisch and Boergen (4) showed no contraction under 75°C, and Deng et al. (1) found that temperatures between 25 and 37°C had a small effect on the shear modulus of rat aortas under multiaxial loading. Herrera et al. (7) reported contradictory effects of temperature on isometric tests performed in the range of 5–37°C, where a rise of temperature induced contraction in rat aortas while relaxing pig renal arteries.

The cross-effect of temperature and vasoconstrictor drugs was studied by Keatinge (12), who found that temperatures under 10°C inhibited the response of bullock ulnar arteries to adrenaline. Toda et al. (19) showed that the contractile response of rabbit aortas to vasoconstrictor drugs reached a maximum between 33 and 37°C.

From the literature presented above, it appears that temperature may influence both the passive and active behavior of arteries, although the detailed conditions where it occurs are still controversial. Further studies are needed to determine and quantify its effects.

The purpose of the present study was twofold: 1) to offer experimental results on the effect of temperature on the passive mechanical behavior of human carotid arteries that can be profitably used for clinical treatment and cardiovascular research, and 2) to provide valuable data to serve as an experimental benchmark for checking and tuning numerical models on human arteries. We present data from 11 inflation tests performed on arteries stretched to in vivo length at temperatures ranging from 17 to 42°C.

Carotid arteries have been characterized by two general parameters that reflect the overall vessel behavior from the mechanical as well as the thermal point of view: the thermal dilatation coefficient ({alpha}) and Hayashi's stiffness parameter ({beta}). Both parameters give useful values that can be directly applicable to clinical procedures and easily used for research purposes. Other structural parameters such as the pressure-strain elastic modulus (16a) or vascular compliance (4a) can be derived from {beta}, as described in Ref. 6.


   MATERIALS AND METHODS
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 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Materials. Healthy common carotid segments of arteries were harvested from eight human donors deceased from causes not related to atherosclerosis. In addition to other exclusion criteria, all the specimens were checked to ensure the absence of visible or tactile calcified plaques or other macroscopic sign of atherosclerosis. Table 1 gives the sex, age, numbers of donors, and numbers of specimens tested. Informed consent was obtained from the next of kin.


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  		Table 1. Donor information

 
The in vivo length of each vessel was marked before excision. Tubular segments 60 mm long were cut out, immediately frozen, and stored at –80°C. Before the mechanical testing, frozen samples were thawed at room temperature (20°C). Tests were conducted between 2 and 10 days after excision.

Histological analysis. Before the testing, a histological analysis was performed on 5-mm edge portions of the samples to determine their structure and condition by light microscopy. Specimens were fixed by immersion in formaldehyde in no-load conditions and embedded in paraffin to obtain the sections. They were then deparaffinized, hydrated, and stained by hematoxylin-eosin and orcein to resolve the elastic fibers.

Mechanical tests. In vitro pressure-diameter tests at fixed (in vivo) length were carried out at four different temperatures (17, 27, 37, and 42°C).

Arterial segments were cannulated at both ends by means of veterinary needles of appropriate diameter. To prevent sliding between the sample and the cannula, the tips of the needles were machined to form a flange.

Two stainless steel fixtures joined the needles to the grips of an electromechanical tensile testing machine (Instron 4411) equipped with a 100N load cell (Instron 2525-806). The lower fixture was designed to permit internal pressurization of the vascular segment through the needle. The experimental device is sketched in Fig. 1.



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  		Fig. 1. Experimental setup. P, pressure; D, diameter.

 
Specimens were enclosed in a PMMA transparent chamber and submerged in PBS solution heated by a thermostatic bath (Unitronic 6320200). The temperature of the vessel was controlled to 0.5°C by a K-type thermocouple located in the chamber and close to the artery (<4 mm).

Once mounted on the holders, each specimen was stabilized at 37°C and stretched to the in vivo length, equal, on average, to 1.13 times the length at rest. The specimen was then brought to the prescribed temperature and stabilized for at least 15 min. Intravascular pressure was then applied via the lower needle and measured with a pressure transducer with 0.2-mbar accuracy (Druck PMP 4000). Proper zero adjustment of the intraluminal pressure was achieved by subtracting the external pressure due to the fluid in the PMMA chamber. The outer diameter of the specimen, measured at the midpoint section, was continuously recorded using an optical extensometer with 1-µm accuracy (Keyence LS-7500).

All the specimens were mechanically preconditioned before final testing to remove initial stress-relaxation effects and to obtain a stable response. Transmural pressure, i.e., the pressure difference between the inside and the outside of the vessel, was cycled from 0 to 200 mmHg at a loading rate of 3 mmHg/s until stable and reproducible pressure-diameter hysteresis loops were formed. All the arteries tested achieved a stable response before 10 cycles. After being preconditioned, each specimen was then subjected to a new pressurizing cycle between 0 and 200 mmHg at 3 mmHg/s while pressure and external diameter were continuously monitored. Only the ascending branch of the inflation test was used for the analysis, because all the carotid segments displayed similar behavior with a small hysteresis loop.

Test temperatures were sequentially applied on every specimen starting at the lowest level (17°C). The average total test duration per sample (tests at the four temperatures) was 120 min. To check reproducibility, some samples previously tested at the four temperatures (17, 27, 37, and 42°C) were tested once again at 27°C. Because that no appreciable differences were observed between pressure-diameter curves of the two tests at 27°C, it was concluded that pressure-diameter tests of carotid arteries were not affected by the duration of the test.

Thermomechanical analysis. The effect of temperature on the mechanical properties of the carotid arteries was evaluated through pressure-diameter curves measured at different temperatures. Nevertheless, to facilitate data analysis and discussion of the results, two simple "global" parameters were computed from the experimental curves: the thermal dilatation coefficient {alpha} and Hayashi’s {beta} stiffness parameter.

{alpha} measures the change in size caused by temperature. Positive values of {alpha} correspond to substances that expand when heated, whereas negative ones indicate that the material shrinks as the temperature increases. The fractional variation in diameter of a vessel is (in first order) proportional to the temperature increment ({Delta}T) and given by

(1)
where D is the vessel diameter. Integration of Eq. 1 yields

(2)
where the reference diameter (DRef) is the diameter at the reference temperature (TRef). Equation 2 can be transformed to

(3)
by setting D* = DRefe–{alpha}TRef, and {alpha} is readily obtained from experimental data by direct fitting of Eq. 3.

The structural stiffness of the arterial wall has been characterized by the so-called stiffness structural parameter {beta}, introduced by Hayashi and co-workers (5). They proposed an exponential equation to describe the pressure-diameter relationship in the physiological range, which is given by

(4)
where Ps is the standard pressure, recommended to be equal to 100 mmHg (6), and Ds is the vessel diameter at Ps. {beta} values have been found to increase gradually with age and arterial diseases such as atherosclerosis (8).


   RESULTS
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Histological analysis. The carotid artery is an elastic artery, with a large number of elastic fibres mingled with smooth muscles. Figure 2 shows one of the images obtained from the specimens, where no atherosclerotic symptoms are revealed. The average thickness of the media was 226 µm.



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  		Fig. 2. Cross section of a carotid artery.

 
Pressure-diameter curves. The variation of the outer specimen diameter with transmural pressure (i.e., intraluminal pressure minus outer pressure) and temperature in human carotid arteries is illustrated in Fig. 3. Results from different donors and specimens were homogenized before being averaged by dividing the diameter in given conditions [D(P,T)] by that at zero pressure and 37°C [D(0,37)]. The standard error is also indicated in Fig. 3. Figure 3 shows that at high enough pressures, arterial diameter increases when the temperature is raised. Conversely, at low pressure levels, larger diameters correspond to lower temperatures.



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  		Fig. 3. Curves of pressure versus mean diameter ratio at different temperatures (T) in human carotid arteries. Diameter ratios are computed for each specimen by dividing the actual outer diameter at a given pressure and temperature [D(P,T)] by that corresponding to zero pressure and 37°C [D(0,37)]. Mean values and standard errors are shown for the 0- to 200-mmHg pressure interval.

 
The behavior described above is demonstrated in Fig. 4, which is deduced from the data shown in Fig. 3 and shows the change in diameter as a function of temperature at two given pressure levels. It becomes clear from Fig. 4 that arterial diameter decreases with increasing temperature for the lowest level, P = 0 mmHg, whereas at P = 100 mmHg (which is frequently taken as the reference physiological pressure) arterial diameter expands with temperature. The fit of Eq. 3 to the arterial diameters for the two pressure levels gives thermal dilatation coefficients that differ in sign, as shown in Fig. 4.



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  		Fig. 4. Variation with temperature of the mean diameter ratio from Fig. 3 at P = 0 and 100 mmHg. Mean values ± standard error are shown.

 
The effect of temperature on the shape of the pressure-diameter curve is shown in Fig. 5, where the diameters D(P,T) measured at a given temperature T have been rescaled by dividing them by the diameter at zero-pressure level [D(0,T)]. Mean values were obtained by averaging over all the samples. In this plot, temperature increments are seen to have a softening effect on the mechanical response of the artery, leading to more compliant curves independent of the pressure level.



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  		Fig. 5. Curves of pressure versus mean relative diameter curves at different temperatures in human carotid arteries. Relative diameters are computed for each temperature by dividing D(P,T) by that corresponding to zero pressure [D(0,T)]. Mean values and standard errors in the 0- to 200-mmHg pressure interval are shown.

 
Thermal dilatation coefficient. Values of {alpha} at different pressure levels were computed for all the arteries by least-square fitting of Eq. 3 to diameter-temperature pairs corresponding to the same pressure. The mean values of {alpha} and the standard errors are given in Fig. 6 as a function of pressure.



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  		Fig. 6. Thermal dilatation coefficient ({alpha}) as a function of pressure level for human carotid arteries. Mean values ± standard errors are shown.

 
{alpha} displays negative values from zero pressure up to ~10 mmHg, where an inversion takes place and {alpha} becomes positive. The {alpha} curve increases monotonically with pressure level, although a progressively decreasing slope suggests that it could approach a saturation value close to +10–3 (°C)–1.

Structural stiffness parameter. Figure 7 shows the mean {beta} value and standard error for human carotid arteries as a function of temperature. Individual {beta} values were computed for every specimen at specific temperatures by least-square fitting of Eq. 4 to recorded pressure-diameter curves.



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  		Fig. 7. Variation of Hayashi's stiffness structural parameter ({beta}) with temperature for human carotid arteries. Mean values ± standard errors are shown.

 
Although mean values of {beta} seemed to decrease moderately with temperature, this variation was not statistically significant due to the large experimental scatter. Paired Student's t-test between {beta} values obtained at the two extreme temperatures (17 and 42°C) gave P = 0.3, as shown in Fig. 7.


   DISCUSSION
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
As already stated in the introduction, most data available on the influence of temperature on arterial properties lead to nonconclusive results. This is probably due first to the lack of experimental data on the thermomechanical behavior of blood vessels, most specially on human arteries, and, second, because most controversial results are a result of cross-effects produced by the combined action of stresses, temperature, and the muscular activation state.

In this work, we focused on the influence of temperature on the passive mechanical behavior of human carotid arteries, with all the tests being performed on cryopreserved specimens. By this procedure, we separated the ground behavior of the arterial wall (mainly dictated by elastin and collagen components) from that influenced by the muscular response. Nevertheless, it is worth noting that preliminary results by the authors on living carotid arteries suggest that as long as no stimulation is present, findings reported in this study could also apply to living vessels.

Broadly speaking, temperature seems to have a softening effect on the passive response of carotid arteries when measured by pressure-diameter tests. Figure 3, which shows the mean behavior registered in all the tests, illustrates how higher temperatures shift pressure-diameter curves to the right at large enough values of the pressure, whereas the opposite (a shift to the left) happens for low-pressure values. As a result, pressure-diameter curves become more compliant. This trend is more easily observed in Fig. 5 by the introduction of diameters relative to zero-pressure level at each temperature [D/D(0,T)].

The reverse effect of temperature at high and low pressures gives rise to a pressure-dependent behavior of {alpha}. When a carotid artery is subjected to pressure as low as P = 0 mmHg, its outer diameter shrinks as temperature increases (Fig. 4), and the least-square fitting of (D,T) values to Eq. 3 results in a mean negative {alpha} equal to –0.63 x 10–3 (°C)–1.

However, diameter dependence on temperature reverses above a certain pressure threshold, and the artery dilates noticeably as the pressure level rises. In the case of P = 100 mmHg, the reference physiological pressure, the slope of the diameter versus temperature curve is positive (Fig. 4) and the fit of Eq. 3 to experimental points gives a mean {alpha} of +0.73 x 10–3 (°C)–1.

Figure 6 illustrates the evolution of the mean {alpha} with transmural pressure. Despite the experimental scatter, it is shown that {alpha} increases at a decreasing rate as pressure rises, from a negative value close to –0.7 x 10–3 (°C)–1 for P = 0 mmHg to almost +10–3 (°C)–1 at P = 200 mmHg. The mean {alpha} becomes positive at a pressure threshold of about 10 mmHg and reaches +0.7 x 10–3 (°C)–1 at P = 100 mmHg. Although the data shown in Fig. 6 could suggest {alpha} coming close to a saturation value at high enough pressure levels, this point is still controversial and deserves further research.

The "atypical" (negative) {alpha} found at pressures under 10 mmHg fully agrees with the early findings by Roy (17), who in 1880 first reported this behavior in human blood vessels. He studied length changes in 9.25-cm strips (1 cm in diameter) taken from the human aorta under no internal pressure. Interestingly, the {alpha} that can be deduced from his measurements is equal to –0.7 x 10–3 (°C)–1, a value close to that we have obtained in this work for P = 0 mmHg (see Fig. 4). Other studies on mammalians have reported similar results in unloaded vessels, such as the work by Lawton in 1954 (15) on dog aortas, which indicated the entropic basis of this behavior as primarily dictated by arterial wall composition (elastin and collagen).

Nevertheless, Herrera et al. (7, 8) have shown opposite trends in tests performed on living pig renal arteries and rat aortas (the former contracted when heated whereas the latter expanded), which they explained by the different nature of the vessels (muscular vs. elastic). They put forward the hypothesis that elastic fibers (prevalent in elastic arteries such as the aorta) were responsible for the cooling-induced relaxation, whereas smooth muscle cells largely found in muscular vessels contract due to the increase of intracellular calcium induced by temperature. This explanation, however, cannot be applied to our results because the human common carotid artery is mainly an elastic vessel, as shown in Fig. 2, and, in addition, our specimens were not alive. Consequently, the observed pressure dependence of {alpha} has to be considered as produced by passive constituents of the arterial wall.

In accordance with the results presented in this work, one of the authors discovered a similar behavior in Wistar rats (K. Hayashi, unpublished observations). The thermal expansion of their common carotid artery has been found to be pressure dependent, changing from negative to positive at about P = 120 mmHg. Although both types of artery show an inversion point, the inversion pressure in human carotid arteries is significantly lower than that measured by Hayashi in Wistar rats. One possible reason is the observed strong dependence of {alpha} on the mechanical stress state. Rat arteries were axially stretched up to 1.4 and over (in vivo length for rat carotids), in contrast to the 1.13 elongation ratio for human carotid arteries used in our work, so the combined action of axial stress (due to axial stretching) and circumferential stress (due to pressure) could be responsible for the shifting of the inversion point. In addition, other factors could came into play such as differences in arterial wall composition and the distribution of elastin and collagen.

With regard to arterial stiffness, Fig. 7 shows the values of {beta}, which does not seem to change appreciably within the range of temperature analyzed in this work. {beta}, on average, seems to diminish moderately with temperature and is consistent with the observed increment of compliance of pressure-diameter curves, as deduced from Figs. 3 and 5. Nevertheless, this tendency cannot be taken as statistically significant due to the large scatter of experimental points.

The high {beta} values obtained in our work are comparable with results from other human arteries of elderly patients (11, 14), which have shown that arterial stiffness increases gradually with age, specially above 70 yr (6).

In conclusion, this work demonstrates that the combined effect of temperature and stress has a striking effect on the dilatation coefficient of the human carotid arterial wall, which can shift from negative to positive depending on the stress state. On the other hand, the structural stiffness of carotid arteries seems not to change appreciably within the range of temperatures tested.

As the available data reveal, the combined effect of temperature and stress can dramatically affect arterial properties, and consequently has to be properly taken into account for clinical treatments and when developing constitutive equations for the arterial wall. Further research is required to complement and enlarge the reported thermomechanical data on human arteries.


   GRANTS
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
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REFERENCES
 
The authors gratefully acknowledge financial support for this study provided by Ministerio de Ciencia y Tecnología (Spain) Grant MAT 2003-04906 and by Comunidad de Madrid (Spain) Projects 07N/0001/2002 and GR/MAT/0038/2004.


   FOOTNOTES
 

Address for reprint requests and other correspondence: G. V. Guinea, Departamento de Ciencia de Materiales, E. T. S. de Ingenieros de Caminos, Universidad Politécnica de Madrid, c/ Profesor Aranguren s/n, 28040 Madrid, Spain (E-mail: gguinea{at}mater.upm.es)

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.


   REFERENCES
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
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