## Abstract

With progressing age, large arteries diminish their longitudinal stretch, which in extreme cases results in tortuosity. Increased age is also associated with loss of vessel distensibility. We measured pressure-diameter curves from muscular porcine carotid arteries ex vivo at different longitudinal stretch ratios (λ_{z} = 1.4 and 1.8) and under different vascular smooth muscle (VSM) conditions (fully relaxed, normal VSM tone, and maximally contracted). Distensibility was found to be halved by decreasing longitudinal stretch from λ_{z} = 1.8 to 1.4 at physiological pressures. This counterintuitive observation is possible because highly nonlinear elastic modulus of the artery and anisotropic properties. Furthermore, a significantly larger basal VSM contraction was observed at λ_{z} = 1.8 than 1.4, although this was clearly not related to a myogenic response during inflation. This dependence of VSM tone to longitudinal stretch may have possible implications on the functional characteristics of the arterial wall.

- wall mechanics
- elastic modulus
- tortuosity
- aging
- vascular smooth muscle

in vivo, segments of large arteries are under axial or longitudinal tension imposed by traction exerted by the surrounding tissue. This longitudinal stretching maintains a straight blood vessel geometry. With progressing age, many large arteries diminish their longitudinal stretch ratio (λ_{z}). In its extreme, this results in tortuosity (16, 17, 27). Aging is also associated with loss of vessel distensibility or compliance in arteries (3, 4, 7,29). Either tortuosity or loss of vessel distensibility has been investigated with hypertension (1, 13, 23, 27, 32). However, tortuosity or longitudinal stretch and distensibility have rarely been studied together. This is because the aforementioned studies were performed almost exclusively using noninvasive techniques on live subjects or live animals. Hence, it was impossible to vary axial or longitudinal stretch.

The reduction of longitudinal stretch (of which tortuosity represents an extreme) and the loss of distensibility with aging, be it with or without hypertension, may be of importance in assessing blood vessel wall physiopathology. We hypothesize that a mechanical link between two phenomena might exist.

Furthermore, when exposed to sudden changes in blood pressure, vascular smooth muscle (VSM) cells are stretched circumferentially and their contractile apparatus is activated, leading to an autonomous contraction known as the myogenic response (6, 24, 26, 31,33). Even when pressure is augmented slowly in ex vivo preparation, VSM tone increases as a result of the myogenic mechanism (19). There appear to be various pathways for the translation of the stretching stimulus to the biomechanical response of contraction (30), some related to the opening or activation of Ca^{2+} channels under the deformation of the cell membrane, resulting in increased cellular Ca^{2+}concentration (5, 34). Not all of these pathways are necessarily dependant on the direction of VSM cell deformation. Thus it seems plausible that longitudinal stretching of an artery might also provoke a VSM response if the deformation is large enough, despite the predominantly circumferential orientation of VSM cells (10,21). So far, literature seems to lack reports on the link between longitudinal stretch of the artery and the VSM response. However, if one accepts that VSM tone drives or at least contributes to vascular remodeling (19, 28), then investigation of VSM tone effects induced by longitudinal stretch would appear necessary.

To test for the dependence of VSM tone on longitudinal stretch and for a biomechanical link between longitudinal extension and distensibility, we submitted arteries to inflation testing at different λ_{z} and different VSM activation states.

## MATERIALS AND METHODS

### Experimental Procedures

Eight porcine common carotid arteries were harvested at the local slaughterhouse and transported in flasks containing PBS with Ca^{2+} and Mg^{2+} on ice to the laboratory. Immediately upon arrival, ∼3-cm-long cylindrical segments from the muscular distal section (Fig.1
*A*) were extracted, and the adventitia was carefully removed while segments were submerged in a PBS bath at room temperature.

The arterial segments were mounted on Inox cannulas and set in a bath containing PBS with Ca^{2+}, Mg^{2+}, and glucose (11.1 mM). The bath was placed in an incubator held at 37°C. An external pump and a pressure sensor were connected to the artery to control lumenal pressure. The lumen diameter and wall thickness of the artery were measured with a high-precision ultrasound tracking device (NIUS, Omega Electronics; Biel, Switzerland), which served also as a data acquisition system (Fig. 1
*B*).

For each of the eight arteries, pressure-diameter and pressure-wall thickness curves were measured under three VSM states: normal tone VSM, maximally contracted VSM, and fully relaxed VSM. All eight arteries were subjected to λ_{z} = 1.4 and 1.8 for each VSM state. These stretch ratios have been observed to be in the physiological range in preliminary investigations. Measurements with a λ_{z} below 1.25 have proven to be difficult because small movements of the apparatus, such as heating bath circulation, easily perturbed the artery, causing loss of ultrasound tracking. To ensure that the measurements could be performed within a reasonable time with sufficient quality and physiological relevance, the above stated λ_{z} of 1.4 and 1.8 were chosen. The order in which the longitudinal stretch was applied was randomized. In detail, we applied the following protocol:*1*) Arteries were pressurized at 100 mmHg and stretched, and 15 min was allowed for equilibration. *2*) Five preconditioning cycles ranging from 0 to 150 mmHg were performed. Subsequently, pressure was reset to 100 mmHg. *3*) After 15 min, internal diameter, wall thickness, and pressure were recorded over an inflation cycle from 0 to 150 mmHg. *4*) *Steps 1–3* were repeated for the second stretch ratio.

After this, for measurements under maximally contracted VSM, 90 mM KCl was added the bath solution. This concentration of KCl has been shown to give total contraction, be reversible (i.e., allow a return to nearly the initial normal VSM tone state after washout), and provide reproducible results in preliminary studies. *Steps 1–3*were repeated for each of the two stretch ratios. Again, the sequence in which the stretch ratios were applied was randomized.

Finally, to measure the arteries in a fully relaxed VSM state, the bath solution was replaced with a solution containing 100 μM sodium nitroprusside (SNP). This high concentration of SNP has been shown to be sufficient to totally inactivate the VSM irreversibly in preliminary studies. Again, *steps 1–3* were repeated for each of the two stretch ratios in a randomized sequence.

Inflations were performed at a rate of 2.43 ± 0.41 mmHg/s (mean ± SD). All experiments were finished within 10 h of harvesting.

### Analysis

#### Geometry.

To obtain values at precise pressures for comparison and averaging, the pressure-diameter measurements were interpolated using
Equation 1as a fitting function (22), where p is pressure,*d*(p) is internal diameter, and *d*
_{m}, p_{0}, and p_{1} are fit parameters.*d*
_{m} represents the square of the maximal diameter, p_{0} is the pressure at which compliance is maximal, and p_{1} is the pressure at which compliance is equal to 50% of maximal compliance. Assuming that the arterial wall is incompressible, we similarly fit the pressure-wall thickness measurements to the function
Equation 2where *h*(p) is wall thickness and*h*
_{m} is a fit parameter. Measurements of unpressurized arteries (0–10 mmHg) proved to be difficult. Small movements of the apparatus, such as heating bath circulation, easily perturbed the artery. For this reason, we have chosen to only present data acquired at pressures above 10 mmHg. Whenever data at 0 mmHg were not measurable due to fluttering of the arterial wall but required for calculation (i.e., circumferential stretch), *Eqs. 1
* and *
2
* were used for extrapolation. The same was applied to values near 150 mmHg if the ultrasound tracking was lost due to large lateral wall displacement.

Wall thickness was measured at the proximal and distal sides of the arterial wall relative to the ultrasound transducer. The arithmetic mean of these two measurements was used as the wall thickness value in the analysis.

#### Biomechanical properties.

To characterize the relative contraction of VSM under the normal tone as a function of pressure, we defined the basal contraction coefficient (C_{n})
Equation 3where *d*
_{n}(p) is the pressure-diameter curve under normal VSM tone (without drugs) and*d*
_{r}(p) is the pressure-diameter curve obtained under full relaxation after administration of SNP. Similarly, the maximal contraction capacity [C_{max}(p)] was defined using
Equation 4where *d*
_{c}(p) is the pressure-diameter curve obtained under maximal contraction with KCl.

#### Elastic properties.

For circumferential stretch, we chose as our reference state the midwall diameter at 0 mmHg pressure with fully relaxed VSM at the corresponding longitudinal extension [*d*
_{mid,r}(0)]. The midwall circumferential stretch (λ_{θ}) was calculated to be
Equation 5where *d*
_{mid} is the mid-wall diameter.
Equation 6The elastic properties of the arterial wall were expressed using the Hudetz elastic modulus (*H*
_{θθ}) (20) as follows
Equation 7where *d*
_{out}(p) = *d*(p) + 2*h*(p) and is the outer diameter. In the following sections, for comparison, H_{θθ} is shown as a function of λ_{θ} instead of pressure.

In addition to the elastic properties, the structural characteristics were assessed by means of the cross-sectional distensibility D(p)
Equation 8where the luminal cross-section area (*A*) = π*r*
^{2} and *r* is the radius. It is noteworthy that the definition of the Hudetz incremental elastic modulus and the definition of distensibility refer only to parameters obtainable by cross-sectional measurements, as commonly available by noninvasive clinical methods.

### Statistics

Mean curves for diameter, Hudetz elastic modulus, and distensibility were calculated for all VSM states (normal tone, maximally contracted, and fully relaxed VSM) at both elongations (λ_{z} = 1.4 and 1.8). Mean curves were also determined for the basal contraction coefficient and for the maximal contraction capacity at both elongations (λ_{z} = 1.4 and 1.8). For these averages, values were taken from the interpolated data at pressures from 10 to 150 mmHg in steps of 10 mmHg and at intervals of 0.05 for λ_{θ}; λ_{θ}varying between 1.05 and 1.5. This stretch ratio range was covered by almost all measurements for the intraluminar pressure range of 10–150 mmHg. All graphs show the calculated SEs. Where appropriate, paired and two-tailed Student *t*-tests were performed, and *P* values of <0.05 were considered significant.

## RESULTS

For each artery, the measured pressure-diameter and pressure-wall thickness data were used to fit *Eqs. 1
* and *
2
*, respectively. An example is shown in Fig.2. *Equations 1
* and *
2
* describe the measured data adequately with*r*
^{2} values of 0.9947 ± 0.0070 and 0.9839 ± 0.0375, respectively (*r*
^{2} values averaged over the entire data set).

The extension of the arteries from λ_{z} = 1.4 to 1.8 significantly decreased the diameter in all three VSM states (*P* < 0.02) over the entire pressure range (Fig.3). No significant change in wall thickness was detected in any of the three VSM states when longitudinal stretch was altered (data not shown). At λ_{z} = 1.4, the diameter under normal tone remained slightly below the fully relaxed diameter, indicating low contraction (Fig. 3
*B*). Indeed, when these differences are studied with the help of the basal contraction coefficient defined in *Eq. 3
*, we found that, under normal VSM tone, the arteries contracted much more when stretched to λ_{z} = 1.8 than when stretched to λ_{z} = 1.4 (*P* < 0.05 for pressures above 20 mmHg; Fig.4
*A*). In contrast, the maximal contraction capacity remained virtually unchanged when the longitudinal stretch was altered (Fig. 4
*B*). For the quasistatic inflation rate applied, no abrupt changes in the basal contraction coefficient were apparent during inflation, indicating the absence of a spontaneous myogenic response.

For a given artery, λ_{θ} depends primarily on pressure and VSM state. λ_{z} is of less importance for circumferential stretch. Figure 5 shows the Hudetz incremental elastic modulus as function of λ_{θ}. For all three VSM states, there was no significant difference between the elastic modulus at λ_{z} = 1.4 and 1.8 except for the fully relaxed VSM at low λ_{θ}. This suggests that elastic properties are little altered by changes in longitudinal stretch. There was a notable difference between the elastic modulus under normal VSM tone; however, this difference was not statistically significant (Fig. 5
*A*). This difference is probably linked to the increase in VSM contraction at λ_{z} = 1.8 for normal VSM tone as shown and discussed in Fig. 4.

Distensibility is depicted in Fig. 6. In the case of normal tone (Fig. 6
*A*) and fully relaxed (Fig.6
*C*) VSM, the distensibility of the vessel was initially larger for λ_{z} = 1.4 compared with λ_{z} = 1.8. The rapid loss of distensibility during inflation for λ_{z} = 1.4 quickly reversed the situation (∼25–30 mmHg). At pressures above 40 mmHg, the arteries displayed a significantly higher distensibility at λ_{z} = 1.8 than at 1.4 (*P* < 0.05) when under normal VSM tone or when fully relaxed. The distensibility at physiological pressures ∼90 mmHg at λ_{z} = 1.8 was approximately two times higher than at λ_{z} = 1.4. Under maximally contracted VSM (Fig. 6
*B*), the distensibility was slightly higher at λ_{z} = 1.8; this difference, however, was only significant between 50 and 70 mmHg (*P* < 0.05).

## DISCUSSION

Loss of vessel distensibility and longitudinal tethering are well-documented effects related to aging and hypertension. Furthermore, the development of VSM tone and myogenic mechanism are often assumed to be dependant on the level of circumferential stretch but not on longitudinal stretch. To investigate a possible biomechanical connection between longitudinal stretch and distensibility as well as development of VSM tone, we subjected eight muscular porcine carotid arteries to in vitro inflation testing at two different elongations: λ_{z} = 1.4 and 1.8. To simultaneously study VSM tone, the tests were conducted in absence of drugs (normal tone), under maximally contracted VSM (KCl), and fully relaxed VSM (SNP). From pressure-diameter and pressure-wall thickness curves, we calculated the basal contraction coefficient, maximal contraction capacity, elastic modulus, and cross-sectional distensibility.

Elongating the arteries altered their geometrical configuration to the point that the lumen diameters were significantly reduced, irrespectively of the VSM state (normal tone, maximally contracted, or fully relaxed VSM). The pressure-diameter curves appeared to be shifted in parallel or in proportion to the longitudinal stretch for both the fully relaxed and maximally contracted VSM state. In the case of λ_{z} = 1.4, the pressure-diameter curve under normal VSM tone remained close to the fully relaxed VSM curve, indicating a low contraction. At λ_{z} = 1.8, the pressure-diameter curve under normal VSM tone was shifted further below the fully relaxed VSM curve, indicating an increase in VSM tone. We thus concluded that longitudinal stretching affects normal VSM tone, the level of basal contraction being significantly increased when longitudinal stretch is increased. In contrast, the maximal contraction capacity measured under exposure to KCl was the same at both λ_{z}. Thus the potential of the artery to adjust its diameter relative to the passive state remains the same, regardless of the longitudinal stretch. Longitudinal stretch did not alter the total midwall stress at maximal contraction with KCl (data not shown). Under normal tone VSM, there were no sudden changes in the basal contraction coefficient while the arteries underwent slow inflation, which we interpret as an absence of spontaneous myogenic response (30). Furthermore, the sequence with which the vessels were exposed to the respective elongations was randomized. Thus we assume that when we increase longitudinal stretch we are observing a change in basal VSM tone as result of the changed geometry of the extracellular matrix surrounding the VSM cells (10) and not as a result of inflation and stretch history. We do not know what the precise mechanism responsible for this basal VSM tone augmentation after longitudinal stretching is. One possible explanation might be that the VSM cell membrane is deformed by the matrix it is attached to when the vessel is axially stretched. This deformation might open Ca^{2+} channels to the inside of the cells or release cell internal Ca^{2+} depots near the membrane surface, providing more Ca^{2+}. This would allow the VSM contractile apparatus to elevate its contraction (11, 12, 25).

Whereas the diameter decreased under axial elongation, no significant change in arterial wall thickness was observed. This seemingly peculiar finding can be explained only if the nonisotropic properties of the artery are taken into account. One theoretical way to demonstrate this is to use a strain-energy function to describe the mechanical properties of the artery, such as
Equation 9
as proposed by Chuong and Fung (9). ρ_{0}is the mass density of the wall, *W* is the strain energy per unit mass, *c* and*b*
_{1}–*b*
_{6} are constants, and *E*
_{θ}, *E _{z}
*, and

*E*are Green's strains for the circumferential, longitudinal, and radial directions, respectively. These strains are related to the stretch ratios as follows Equation 10

_{r}*Equation 9*allows us to calculate the energy stored in any deformation of the arterial wall excluding shear and to derive, theoretically, the wall properties and stresses. The constants

*c*and

*b*

_{1}–

*b*

_{6}are material constants. In the experiment described above, only longitudinal stretch is imposed and

*E*

_{θ}and

*E*[corresponding to λ

_{r}_{θ}and the radial stretch ratio (λ

_{r})] are free to vary within the following constraints:

*1*) incompressibility of the arterial wall (λ

_{θ}λ

_{r}λ

_{z}= 1) and

*2*) minimal strain energy represented by

*Eq.9*, which together with boundary conditions leads to

*3*) the equilibrium under applied pressure and longitudinal force. When the constant

*b*

_{4}, combining

*E*

_{θ}and

*E*, is large (i.e., not negligible compared with the others), we can obtain a set of elastic constants of a wall with the following characteristics: increasing

_{z}*E*by stretching longitudinally will require one or both of the remaining principal directions to diminish stretch as imposed by the incompressibility (first condition). With the strong link between

_{z}*E*

_{θ}and

*E*, described by a large value of the parameter

_{z}*b*

_{4}, the energy needed to stretch longitudinally can be minimized largely by reducing

*E*

_{θ}. A reduction in

*E*

_{θ}is essentially equivalent to the reduction of the midwall diameter. As can be seen in Fig. 5, the elastic modulus decreases when midwall circumferential stretch is reduced. This decrease in the elastic modulus makes it possible to augment the cross-sectional distensibility despite the fact that the wall is relatively thicker. A thicker wall would normally mean a less distensible artery; however, in the case presented here, the decrease in the elastic modulus overweighs wall thickening, leading thus to a more distensible vessel. As we have seen from our measurements, the distensibility is in fact almost doubled by longitudinal stretching at physiological operating pressures. However, at low pressures, the geometry and elastic modulus are different, and distensibility appears to be diminished by longitudinal stretching. We see that the influence of geometry and nonlinear elasticity on vessel distensibility are competing factors and therefore distensibility can be either increased or decreased, depending on the load conditions (intraluminar pressure and longitudinal extension).

As shown by various previous investigators, arteries must be considered as nonlinear and anisotropic in their material properties when we wish to model the mechanics of the wall (2, 9, 14, 18,20, 35-38). Indeed, when the organization of the constituents is studied (10), this is to be expected, particularly in the case of the coiled collagen, which begins to take on loads when it reaches higher pressures and is stretched (8,15). We observed that the Hudetz incremental elastic modulus, which considers only the circumferential deformation, is unchanged by the longitudinal elongation over the measured range. Particularly the maximally contracted and fully relaxed VSM states display almost identical elastic properties. Even if stretching increases VSM contraction under normal VSM tone, this is not sufficient to alter the elastic modulus of the arterial wall significantly. The passive components of the wall (i.e., matrix) mask the relatively minor effect of VSM tone on the elastic modulus.

In summary, longitudinal stretch of the muscular porcine carotids affects both VSM tone and distensibility of the vessel. VSM tone is augmented in response to longitudinal stretch with possible implications to vessel wall remodeling. The effects of nonlinearity and anisotropy can explain from a biomechanical standpoint the link between the loss of distensibility and loss of longitudinal stretch of principal conduit arteries, as often observed in hypertensive or aged patients.

## Acknowledgments

The authors thank Gabriela Montorzi and Veronica Gabillara for valuable help in obtaining the samples and materials used and for advice on the drugs used.

## Footnotes

This work was supported by Swiss National Science Foundation Grant 0021-055665.98, a Swiss Federal Institute of Technology, Zurich Lausanne (EPFL) PhD student exchange grant, and the EPFL.

Address for reprint requests and other correspondence: M. Zulliger, LHTC AA-B.026, EPFL, CH-1015 Lausanne, Switzerland (E-mail: martin.zulliger{at}epfl.ch).

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.August 22, 2002;10.1152/ajpheart.00298.2002

- Copyright © 2002 the American Physiological Society