INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

A DETAILED UNDERSTANDING of the stress-strain behavior of the heterogeneous walls of human arteries requires experimental data on the multiaxial mechanical response of each of their layers. Despite their significance, such data are not available. One reason for this is the fact that, to date, there is no appropriate method for anatomic separation of intact single-layer tubes.

It is well recognized that vascular tissues respond strongly to their "mechanical environment" [see, for example, the review article by Liu (18)]. Therefore, knowledge of layer-specific mechanics is an essential prerequisite for an accurate understanding of the complex interaction between the mechanical quantities and the associated biological responses.

Traditionally, vascular research has focused on intimal and medial layers, whereas adventitial physiology and pathophysiology has largely been ignored. However, there is growing experimental evidence that the adventitia plays an important role in various vascular processes, such as atherosclerosis (32, 34), hypertensive remodeling (2, 36, 37), and restenosis after balloon angioplasty (1, 25-27, 39). Thus adventitia research has the potential to significantly improve our understanding of vascular physiology and disease (9). In particular, quantification of adventitial mechanics might provide an essential basis for the investigation of arterial remodeling processes. Moreover, it may help to identify more clearly the mechanisms of acute lumen gain of stenotic arteries (for example, wall stretch, plaque redistribution, and plaque fracture) due to dilatational endovascular interventions, such as balloon angioplasty and stent deployment, and stimulate mechanical optimizations of these procedures. Finally, vascular tissue engineering and vascular graft design could benefit from such investigations.

So far, studies on the mechanical response of adventitias are rare. Von Maltzahn et al. (33) reported the bidimensional elastic response of four bovine carotid adventitias and corresponding hyperelastic models. However, the adventitial layer was not tested separately. Its response was calculated from the difference between the response of the whole wall and the response of the media-intima tube that remained after "peeling" the adventitial layer. Demiray and Vito (5) proposed a strain-energy function for the canine aortic adventitia. The strain energy was based on biaxial tests of rectangular patches of the outer vessel wall from (only) one artery. Because "the aortic media was split roughly in two," it is most likely that their specimens consisted of heterogeneous adventitia-media composites. Moreover, they did not prove that the biaxial response was representative for intact adventitial tubes. To avoid the problems of layer separation, Humphrey (12) proposed an approach to determine layer-specific mechanical properties by performing extension-inflation tests on "inverted arteries" (arteries that were turned inside out) in addition to regular testing. This study (12) provided a theoretical framework for this interesting approach, which was based on the assumption of only two mechanically relevant layers (media and adventitia). Unfortunately, corresponding experiments were not published. Fung and co-workers (7, 35, 38) proposed another approach without the dissection of layers. They assumed a two-layer model based on linear elasticity. Consequently, analyses were restricted to the small strain regime. Because arterial walls exhibit nonlinear stress-strain behavior undergoing finite strains, and because for aged arteries the intima may become a third layer of considerable thickness and mechanical strength, this approach is inappropriate for a general description of adventitial mechanics.

None of the above-mentioned studies were based on adventitial tube tests, and none of the studies reported in situ deformations of arteries. Thus these data do not allow stress analyses for in situ conditions. Furthermore, within the unloaded arterial wall, the adventitia may not be at its zero-stress state, i.e., layer-specific residual stresses and associated residual strains may occur (see, for example, Refs. 12, 22, and 29). This information must be considered to determine valid constitutive laws for the adventitia. Yet, this was not done in any of the above-mentioned studies. Moreover, no study investigated the response to high (therapeutic) loads, which occur in dilational endovascular procedures. Finally, all of the studies mentioned investigated animal specimens. However, conclusions from mechanical tests of animal specimens may be inapplicable for human physiology, because significant interspecies differences are typical for the mechanical response of soft tissues.

In the present study, a technique for the separation of intact adventitial tubes suitable for mechanical loading is described. We present residual stretches of human femoral adventitias, which occur in the unloaded arterial wall, and their mechanical responses to extension-inflation tests with a maximum transmural pressure of 100 kPa (750 mmHg). Specific constitutive laws are given. They are based on the theory of finite hyperelasticity, and they use the assumptions of incompressibility and membranelike structures. Adventitial stress analyses based on in situ vessel deformations are presented and their implications for physiology and cardiovascular medicine are discussed.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Specimen Preparation

Axial in situ stretches characterized the in situ configurations of the vessel at the investigated pressure levels (Table 1). However, a complete characterization of the motion of a tube requires the axial and the circumferential stretches and the associated pressures and axial loads. Additionally, the wall thickness and the (outer) radius of the load-free artery are required. Measurements of the former are described in Thickness Measurements, whereas the latter is described in Test Protocol. All these values are required for suitable stress analyses.

Thus, to completely characterize the in situ conditions, the following procedure was performed. Loose connective tissue was removed from the vessel surface. Two black-colored straw chips were glued pointwise with cyanoacrylate adhesive gel onto the middle part of the specimens. Both were orientated transversely to the vessel axis and had a separation distance of ~10 mm. They acted as gauge markers for the axial deformation measurements. The vessel was cannulated with hollow Plexiglas connectors at both ends and inserted in the testing machine. The in situ inflation protocol was then repeated ex situ. This means that at each pressure level, the axial stretch was adjusted to the value that was observed during the in situ inflation and kept constant for 10 min. The associated circumferential stretch and axial load were then measured (see Experimental Setup). Consequently, the in situ configuration, i.e., the circumferential and axial stretches, and the associated in situ loading, i.e., pressure and axial load, were completely determined for the considered pressure levels.

The vessel was taken out of the testing machine, its ends were cut off, and the gauge markers were removed. A scaled picture was taken after 30 min in 37 ± 1°C NaCl solution. The adventitia was then pulled off in "turtleneck" fashion from the underlying media-intima shell (Fig. 1A). Generally, the adherence of the adventitia to the media was weak, so that the separation was "atraumatic." The adventitia retracted immediately in the axial direction (indicating residual tensile stresses) and was placed in 37 ± 1°C NaCl solution. After 30 min, another scaled picture was taken (Fig. 1b). The axial residual stretch was calculated as the ratio of the nonseparated vessel length to the adventitial length. Both lengths were determined photogrammetrically from the pictures taken.

View larger version (73K): [in this window] [in a new window]   Fig. 1.   Separation of the adventitia in a "turtleneck" fashion (a). The axial retraction of the adventitia indicates its residual stretch within the arterial wall (b). Knots, which were used for the determination of axial in situ stretches, are circled. The image was taken in a 37°C, 0.9% NaCl solution. The histological section (c) confirmed correct separation of the adventitia along the external elastic lamina except for a minor fragment of the media. One end of it is located at a vas vasorum, which, apparently caused increased layer adherence. Masson's trichrome staining, 5-µm-thick section.

Gauge markers were again attached to the central region of the adventitia. It was cannulated and inserted in the testing machine, where extension-inflation tests were performed (see Test Protocol).

Experimental Setup

View larger version (31K): [in this window] [in a new window]   Fig. 2.   Experimental setup.

Gauge length and outer diameter were measured optically using a PC-based (CPU 586) videoextensometer (model ME 46-350, Messphysik) utilizing a full-image charge-coupled device (CCD) camera. This class 0.5 instrument supports interactive monitor-based selection of the measuring zone and automatically traces the gauge mark and vessel edge recognition during the experiment. The corresponding deformation data are averaged with respect to the measuring zone and sent to the data-processing unit in real time.

Pressure was measured by means of a five-bar class 1 strain-gauge pressure transducer (model TP12, AEP transducers; Modena, Italy) and generated by a metering pump (model µ333, Neuhold, Graz, Austria), which supports external digital control. To reduce pulsations caused by the pump, fluid is fed to the specimen through a transparent and partly filled plastic cylinder. Axial loads were measured by means of a 25 N class 1 strain-gauge load cell (model F1, AEP transducers).

Digital control of the electric drive of the machine and the pump as well as data acquisition of the crosshead position, applied load, and pressure were performed by two external digital controllers (EDC 25/90W, DOLI; Munich, Germany) especially designed for screw-driven tensile testing machines. A PC (CPU 586) linked to the videoprocessing PC and the two external digital controllers processed and stored the data (pressure, load, outer diameter, gauge length, and crosshead position) on-line by means of dedicated software (Application software, Messphysik). The latter provided programming and execution of user-defined test protocols via feedback control. In particular, it allowed cyclic inflation at adjustable constant rates.

The system operates with a crosshead stroke resolution of 0.04 µm, a minimum resolution of 1 mN for the 25-N load cell used and 20 Pa for the five-bar pressure transducer. Dimensional measurements were performed with axial and transverse resolutions better than 1:10⁵ with respect to the camera's field of view. For the experiments, the field of view was adjusted to 18.3 × 12.8 mm by means of appropriate optics. Load and crosshead position measurements were performed at a sampling rate of 50 Hz, and dimensional measurements were performed with a video frame rate of 25 Hz.

Variances of measurements were determined for a relaxed typical specimen at 13.3 kPa and at its in situ length; values of pressure, load, outer diameter, and gauge length had SDs (n = 1,000) of 12.6 Pa, 1.7 mN, 2.4 µm, and 8.1 µm, respectively.

Proper zero adjustment of the pressure was achieved first by opening the valves at the pressure cylinder and at the upper tensile shaft, which is a hollow and transparent plastic tube, and then equating the fluid level within the tensile shaft with that of the tissue bath (see Fig. 2). The pressure was then set to zero, and the valves were closed to measure the "transmural" pressure. Proper zero adjustment of the axial load was achieved by fixing the specimen to the upper shaft and then submerging it and the upper shaft to a marked level. The axial load was then set to zero, and afterward the specimen was fixed at the lower shaft. After the specimen was positioned at the marked level again, the axial load was measured correctly. Bias errors of load measurements come from 1) varying buoyancy forces due to changing positions of the upper shaft and 2) elevation of the fluid level in the upper shaft during inflation. These errors were small (<50 mN), and the results could easily be corrected by means of elementary calculations, which take into account 1) buoyancy forces per unit shaft length and the (known) shaft position and 2) the gas volume in the hollow shaft as a function of the applied pressure.

Before each experiment, the videoextensometer was calibrated by means of a specially designed standard.

Test Protocol

Adventitias were inserted in the testing machine and allowed to equilibrate for 30 min in a 37 ± 1°C, 0.9% NaCl solution. They were then subjected to a series of four cyclic inflation tests for each load domain. Each test was associated with a particular initial axial stretch, which was adjusted before the specimen was inflated.

The initial axial stretches used refer to the difference between the load-free gauge length and the in situ gauge length at 13.3 kPa. [The latter is the product of the load-free gauge length and the (known) axial in situ stretch at 13.3 kPa.] In the first, second, and third tests, the gauge length of the specimen was extended by 50%, 100%, and 150%, respectively, of that particular difference. Occasionally, a fourth test with an axial stretch of 75% of the difference was performed. This protocol aimed to ensure that the experimental "paths" cover the in situ strains. We will refer to these tests as "50%," "100%," "150%," and "75%" tests. If the axial load exceeded 3 N during the "150%" test, the test was stopped and a "125%" test was performed instead.

Finally, the "100%" test was repeated to check for changes of the mechanical behavior during a test series. For some vessels, tube tests of nonseparated specimens were also performed. Those results are not reported in this study but will be published elsewhere.

The specimen was inflated cyclically five times for each single test. Preliminary tests showed that three cycles were enough for proper preconditioning of adventitial specimens. Tests were performed first in the physiological domain and then in the high-pressure domain. Constant inflation rates of 16.5 kPa/min (125 mmHg/min) and 25 kPa/min (190 mmHg/min) were used for the physiological and the high-pressure domain, respectively. The unloaded (referential) outer diameters and radii, respectively, were measured after both the 33 and 100 kPa test series at load-free conditions. All tests were finished within 24 h from autopsy.

The total length of a specimen was kept constant for each individual test. However, due to "end effects" and possible arterial nonuniformity, the axial gauge length and consequently the axial stretch varied significantly. The experimental "paths" of a representative experiment are shown in Fig. 3. These observations demonstrate that for a correct determination of vessel deformation, dimensional measurements must be restricted to the central (gauge) region of a specimen. Remarkably, there are some excellent studies on arterial mechanics, for example, Refs. 29 and 33, which did not exclude end effects.

View larger version (14K): [in this window] [in a new window]   Fig. 3.   Cyclic extension-inflation tests of a preconditioned adventitial specimen (specimen VI, "33-kPa" domain) appear as characteristic experimental "paths" in the deformation plane (circumferential vs. axial stretch). Each of the curves was associated with an initial axial stretch, which is specified by the labels "50%," "75%," "100%," and "150%" (see METHODS for details). Note that there are variations of axial stretches of the gauge region, although the total specimen length was kept constant. All plots show small hystereses.

Thickness Measurements

Total wall thickness. Before testing, a ring 3 mm in height was cut off the end of an arterial specimen. A scaled picture was taken after 30 min in 0.9% NaCl solution at 37 ± 1°C. The total wall thickness was measured photogrammetrically at four positions and averaged. Additionally, the adventitial wall thickness was measured. However, this was not the unloaded adventitial thickness, because the adventitia is stretched within the wall structure. Unloaded adventitial thickness was calculated based on the assumption of incompressibility (see Theoretical Framework).

Adventitial wall thickness. After the 100 kPa test series was completed, the ring-shaped gauge region of the adventitial specimen was cut radially, thereby producing a strip. The average thickness of this strip was measured by means of the videoextensometer. Therefore, a setup was designed for backlight contour detection. The moisturized strip was placed in air within an opaque chamber on a plate of known thickness (1 mm), so that its lateral side was in-plane with that of the plate. Furthermore, its lateral side was oriented to the CCD camera (field of view, 15.1 × 10.6 mm), and it was illuminated from behind by an appropriate light source. Surplus fluid was carefully removed by means of paper towels.

Histology

Theoretical Framework

Whole wall stresses. The average circumferential and axial Cauchy stresses and _zz (true stresses) of a loaded tube can be calculated by means of global equilibrium equations (6, 12)

(1a)

and

(1b)

where p is the transmural pressure, L is the axial load, r is the outer radius, and h is the wall thickness of the loaded tube, respectively. The outer radius r of the loaded tube may be expressed as r = R, where R is the outer radius of the associated load-free (referential) tube and denotes the circumferential stretch. An expression for the wall thickness h of the loaded tube can be derived by assuming incompressibility (no volume change) of the cylindrical shell, that is

(2)

where Z is the length of the load-free (referential) tube, z is the length of the loaded tube, and H is the wall thickness of the load-free tube, respectively. They are related by the equation z = _zZ, where _z denotes the axial stretch. By substituting these relations into global equilibrium equations (Eq. 1), they can be expressed as functions of the measured quantities p, L, , and _z

(3a)

(3b)

These functions contain the unloaded (referential) wall thickness H and the unloaded (referential) outer radius R as constants, which have to be determined experimentally. The functions can be used to calculate the average stresses of the total wall and the separated adventitia.

Adventitial stresses. For the adventitial layer as part of the intact wall composite, these equations are not applicable. The reason for this is that the portions of the transmural pressure p and the axial load L carried by that layer are not known. To determine the stresses in configurations of interest, it is necessary to identify a constitutive stress-strain relation for the adventitial layer. It allows the calculation of adventitial stresses in the layer as functions of the stretches and _z and a set of (constant) constitutive parameters, denoted as {c_i}, where i{1, ..., n} and n is the number of constitutive parameters. The constitutive parameters have to be evaluated from extension-inflation data of separated adventitial tube specimens (see Regression Analysis). These relations may be expressed in compact form as

(4a)

and

(4b)

According to the theory of finite hyperelasticity (10, 21), constitutive stress-strain relations may be determined as derivatives of an appropriate strain-energy function  = (, _z, c_i) as follows

(5a)

and

(5b)

Thus the stress-strain response of specimens can be expressed completely by a set {c_i} of constitutive parameters together with the associated strain-energy function .

Adventitial pressure load. Equation 1a relates the transmural pressure p to the circumferential Cauchy stress . The constitutive relation (Eq. 4a) for the circumferential stress substituted into Eq. 1a provides a relation that can be solved for the pressure p. Consequently, p is given as a function of the stretches and _z and the set {c_i} of constitutive parameters

(6)

Regression Analysis

Reasonably good fits were obtained with a four-parametric Fung-type exponential strain-energy function (6)

(7a)

where

(7b)

Herein, C, c, c_z, and c_zz are constitutive parameters and E = (  1)/2 and E_zz = (  1)/2 are the components of the Green-Lagrange strain tensor in the circumferential and axial directions, respectively.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Geometry and Kinematics

View larger version (16K): [in this window] [in a new window]   Fig. 4.   Adventitial kinematics is determined by a deformation of the separated load-free adventitia (outer radius R, length Z, and thickness H) into its associated (deformed) configuration within the load-free entire wall (, , ). Circumferential and axial residual stretches (and stresses) govern this deformation process. Second, loading of the entire wall, i.e., axial tethering and transmural pressure, causes circumferential and axial in situ stretches, which lead to the final loaded configuration (outer radius r, length z, and thickness h). Note that the load-free separated adventitia is not stress free because there are (small) in-layer residual stresses (for more details about residual stresses and strains, see the DISCUSSION).

Mean in situ stretches of the nonseparated vessels subject to the adjusted pressure levels are given in Table 1. Interestingly, the circumferential in situ stretches were extremely small (<5%). This suggests that reactive forces of the vessel surroundings, which occur due to radial expansion of the inflated artery, play an inferior role. The axial in situ stretches were in reasonable agreement with axial retractions of 20-25%, as reported for human femoral arteries (age > 35 yr) (17). Note that significant circumferential and axial residual stretches were observed after the adventitias were dissected from the intima/media tube (see Table 2). Typically, the adventitias were compressed in the circumferential direction, which was indicated by a mean circumferential residual stretch /R of 0.96, and extended axially, indicated by a mean axial residual stretch /Z of 1.09. Remarkably, it was observed that residual stretches hardly changed after 100 kPa of pressurization. Circumferential stretches decreased <1%, and axial stretches decreased ~1.5% (mean values). This means that high-pressure loading of the separated adventitia caused only minimal permanent (plastic) deformations. The stretches of the adventitia under in situ conditions result from multiplications (/R) (r/) = r/R and (/Z) (z/) = z/Z. Mean values at 13.3 kPa were 0.96 for the circumferential direction and 1.19 for the axial direction.

The outer radii R and the thicknesses H of the separated load-free adventitias are shown in Table 2, with mean values 4.26 ± 0.53 and 0.41 ± 0.09 mm (means ± SD), respectively. The mean diameter-to-thickness ratio of 22.7 for the adventitias justifies the thin-wall approach adopted.

Load-Deformation Behavior

View larger version (50K): [in this window] [in a new window]   Fig. 5.   Representative mechanical responses of a preconditioned adventitia (specimen VI) subjected to cyclic pressurization in the 33 kPa domain (A-C) and the 100 kPa domain (D-F). Circumferential stretches (A and D), axial stretches (B and E), and axial loads (C and F) are plotted against pressure for inflation tests with various initial axial stretches specified by the labels "50%," "75%," "100%," "125%," and "150%" (see METHODS for details). Positions of the first loading cycles are indicated by arrows for the 100% tests. Note the small hysteresis of each curve.

Remarkably, also in the 100 kPa domain, the adventitias still exhibited nearly elastic behavior (Fig. 5, D-F), and no signs of material damage were observed. In this domain, the highest circumferential stresses were between 1.1 and 2.1 MPa, and the highest axial stresses were between 0.8 and 1.2 MPa, which means that the ultimate tensile strengths of the investigated adventitias were beyond these ranges.

Constitutive Relations

In Table 3, correlation coefficients for circumferential and axial stresses that measure the agreement between experimental and model stresses are also given. The mean correlation coefficients are 0.99 for the circumferential direction and 0.98 for the axial direction in both domains, which indicates a good performance of the model used. Strain-energy functions with additional polynomial terms and associated constitutive parameters did not lead to significantly better correlations.

To compare the constitutive behavior of the adventitias in the 33 kPa domain, the circumferential stresses are plotted in Fig. 6 against the equibiaxial stretch . Equibiaxial stretching denotes a fictitious deformation with equal stretches in the circumferential and axial directions. The plots show considerable interspecimen variance. In particular, the equibiaxial stretch at 500 kPa varies between 1.014 and 1.125. Similar plots may be obtained for axial stresses. The corresponding curves of the 100 kPa domain did not show large deviations: at 500 kPa of circumferential stress, there was a mean difference between the equibiaxial stretches of ~0.001. Remarkably, for 5 of 11 specimens, the equibiaxial stretch after pressurization with 100 kPa was smaller, i.e., high-pressure loading might have caused material hardening of these adventitias. This phenomenon could be explained by successive recruitment of collagenous fibers in the outer adventitial layers, which are initially less organized than those in the inner layers (see Fig. 1c). The fiber recruitment might overcompensate for potential softening due to damage of the inner layers.

View larger version (27K): [in this window] [in a new window]   Fig. 6.   Comparison of the mechanical behavior of the adventitial specimens I-XI modeled in the 33 kPa domain. Circumferential stresses were computed for hypothetical (nonphysiological) equibiaxial stretches .

Stress Analysis

View larger version (21K): [in this window] [in a new window]   Fig. 7.   In situ circumferential (A) and axial stresses (B) of specimens I-VII subjected to transmural pressure. Values are means ± SD.

To study the influence of the residual stretches of the adventitias on their stress states, additional stress computations were performed with residual stretches omitted. In general, this leads to a marked stress reduction to about one-half the average wall stresses or even smaller. Dotted-dashed lines with squares illustrate the associated data. This characteristic result was obtained for all specimens except specimen VIII (which is not included in Fig. 7). In the latter case, omission of residual stretches caused an increase of adventitial stresses.

Finally, Fig. 8 shows the normalized adventitial pressure load p_A/p for specimens I-VIII. This is the portion of transmural pressure p_A that is carried by the adventitia divided by transmural pressure p. According to this definition, the normalized adventitial pressure load would be 1.0 if the transmural pressure were carried solely by the adventitia. The normalized adventitial pressure load is about one-fourth to one-third at p = 13.3 kPa and increases at higher pressures up to a mean value of 0.6 at p = 26.7 kPa. Interestingly, this means for specimens I-VIII that pressure loads that exceed the physiological level of 13.3 kPa are carried mainly by the adventitia.

View larger version (11K): [in this window] [in a new window]   Fig. 8.   Transmural pressure p versus the normalized adventitial pressure load pA/p, i.e., the portion of the transmural pressure pA carried by the adventitia divided by the transmural pressure p. The diagram includes data for specimens I-VIII. Values are means ± SD.

The calculated adventitial pressure loads of specimens IX-XI were greater than the transmural pressure, which indicates significant errors in the results (see DISCUSSION). Therefore, these specimens were not included in Figs. 7 and 8.

Statistics

There were significant negative correlations between age and axial in situ stretch (r = 0.69, P = 0.02) and equibiaxial stretch at 500 kPa of circumferential stress (r = 0.65, P = 0.03). This suggests that axial in situ stretches decrease and adventitias stiffen with age. Nonsignificant trends for an age-dependent increase were seen for the circumferential (r = 0.35, P = 0.29) and axial (r = 0.17, P = 0.61) residual stretches.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

A major goal of vessel mechanics is the determination of the mechanical loads and the associated deformations that occur in the arterial wall. Most studies on vessel wall mechanics consider arterial walls as single-layer homogeneous structures. However, arterial walls are heterogeneous three-layered composites (adventitia, media, and intima) with layer-specific histological features. Thus a better understanding of their mechanical function at the tissue level requires layer-specific data. To the knowledge of the authors, this study is the first to report direct measurements of the mechanical responses of human adventitial tubes under physiological and high-pressure (therapeutical) loading conditions. The fundamental prerequisite of this study is a preparation technique that provides a relatively atraumatic method for the separation of intact adventitial tubes from the underlying media-intima cylinders in a turtleneck fashion (Fig. 1a). Histological analyses confirmed correct layer separation through the external elastic membrane (Fig. 1c). According to the experience of the authors, the technique described is much more difficult or may even be impossible for arteries of young experimental animals. Thus, despite the problems of accessibility and significant interspecimen differences, aged human arteries may provide a promising basis for layer-specific mechanical studies. Moreover, in regard to cardiovascular medicine, the material behavior of aged human arteries is of crucial interest.

Residual Stretches

Additionally, we measured the opening angles of adventitial rings (not reported here), which were cut radially, to reveal radial gradients of residual strains (and stresses) within the adventitias. However, because the investigated adventitias exhibited extremely soft behavior at their load-free configurations and because their thicknesses were small, these strains (and the associated stresses) appeared to be negligible compared with the "total-layer" residual stretches.

Constitutive Models

Basically, comparisons with von Maltzahn et al.'s constitutive models are not appropriate, because in this approach residual stretches are not considered and, hence, constitutive formulations are not referred to the load-free state. Von Maltzahn et al.'s models for bovine carotid adventitias are extremely soft. On the basis of these models, we calculated equibiaxial stretches of ~1.8 at a circumferential stress of 500 kPa, whereas for the aged adventitias investigated, these stretches are only ~1.06 (see Fig. 6). Considering these facts and keeping in mind the negative correlation with age (see the Statistics), one may conclude that not only the intima and media but also the adventitia stiffens due to age-related structural changes, i.e., there is an "adventitiosclerosis." The isotropic model of Demiray and Vito (5) for bovine aortic adventitias, which is inappropriate for a general description of adventitial response, yields an equibiaxial stretch of 1.5 at 500 kPa.

Experimental data have also been published for biaxial tests of bovine epicardium (15) and canine epicardium (13, 14). The epicardium may be thought of as a structure similar to the adventitia. However, these studies utilized a type of membrane approach, which, unfortunately, does not allow the calculation of true stresses (Cauchy stresses).

In Situ Stress States

Again, there are no comparable data for adventitial in situ stresses. At least the results of von Maltzahn and colleagues (33) obtained for bovine carotid adventitias, which are assumed to be near the in situ state, and the estimated stresses for bovine epicardium (15) are of the same order of magnitude, between 30 and 600 kPa.

Implications for Vascular Physiology

These novel insights into arterial wall mechanics stimulate the hypothesis that the adventitia plays an essential role for regulatory systems that control vascular remodeling and vessel tone. There is, indeed, a sound histological basis for such a function: in addition to the intimal endothelium, large vessels possess a "second endothelial organ" located in the intima of the vasa vasorum. These endothelial cells may react on elevated mechanical stresses with specific paracrine activity, which could affect the entire vessel wall. Moreover, endothelial cells of venae vasorum are connected to the venous low-pressure system, which could act as an independent pressure reference (having a reference value is a beneficial feature for every measuring system).

One may further hypothesize that adventitial endothelial cells could have a mechanotransductory system that senses tensile stresses (instead of shear stresses, which can be sensed by intimal endothelial cells). This would allow the adventitial endothelial cells to measure the transmural pressure indirectly via the adventitial stress state and then respond to it appropriately. Additionally, in contrast to the intima and media, the adventitia is innervated by the "nervi vasorum," which provide an obvious control structure for vasomotor function [for more details, see, for example, the review by Gutterman (9)].

Beside endothelial cells, further potential candidates for "regulatory cells" are adventitial fibroblasts. There is experimental evidence that these cells may provide a powerful potential source of nitric oxide (16, 40). Remarkably, in this regard, it has also been shown that nitric oxide produced in the adventitia (by fibroblasts that were transduced with recombinant endothelial nitric oxide synthetase) causes effective vessel relaxation (31). Moreover, it has been demonstrated recently that removal of the adventitia alters the response of medial smooth muscle cells to various dilators and constrictive agents (8, 20).

After balloon injury, it has been documented that adventitial fibrocytes undergo phenotypic modulation to myofibroblasts, which proliferate and produce platelet-derived growth factor. Adventitial fibroblasts have been observed to migrate to the media and intima, where they contribute to neointima formation, and they may be responsible for constrictive remodeling (2, 25-27, 34, 39). In recent studies, the morphological changes in the adventitia after balloon angioplasty are summarized as "neoadventitia formation" (4, 19) according to the term "neointima formation" for the intimal changes. The complex neoadventitial response shows that the adventitia is not an inert structure but reacts very actively to the initial mechanical injury.

In summary, the adventitia may play a significant role in controlling vessel structure and function. For a thorough understanding of these processes, it is necessary to clarify the complex interaction between the physical environment of vascular layers and their biological behavior on a quantitative basis. This requires "mechanobiological" models that mathematically link stresses and strains in vascular tissues with the quantities specifying the associated biological response (proliferation, production of extracellular matrix, paracrine activities, etc.). To date, most of the existing models deal only with average wall stresses [see, for example, the study by Rachev and colleagues (23)] or suffer from a lack of appropriate layer-specific experimental data if two-layer models are utilized (28). The layer-specific adventitial data in the present work may be helpful for more appropriate mathematical modeling of vascular remodeling processes. Our data suggest that the adventitia will be a prominent "factor" for such models.

Implications for Balloon Angioplasty

In this context, it is important to specify the term "high-pressure" loading. Femoral arteries, for example, are dilated with balloon inflation pressures of 0.5-1 MPa. Because angioplasty balloons become nearly incompliant at their nominal diameter, they carry the major portion of the pressure load. Therefore, pressure loads of the vessel walls and, in particular, of the adventitias are much smaller than the balloon inflation pressures. The maximum pressure of 100 kPa used in the present study is likely to cover the range of pressure loads that occurs during angioplasty. Additionally, for some specimens (not reported here), we performed inflation even up to 300 kPa, which led to the same characteristic behavior as experiments with 100 kPa. In general, maximum pressures were limited rather by the capabilities of the inflating pump than by the failure strength of the specimens. If, however, the nominal diameter of a balloon is too large, the adventitia faces extremely high pressures, which finally might cause rupture. Because of the pronounced stiffening behavior of the adventitia, the difference between a "safe" and a "dangerous" balloon diameter is only small.

Another potential effect of angioplasty is redistribution, i.e., remodeling of prominent "soft lesions" along the vessel axis due to balloon compression. It is understood that for an effective compression of plaques, the vessel wall must act as a stiff support. According to our data, this support might be provided mainly by the adventitia. Thus redistribution requires a balloon that is large enough to stretch and stiffen the adventitia sufficiently.

It is common practice in interventional medicine to choose the balloon diameter according to the adjacent nonstenotic vessel segment to avoid vessel rupture. Our results support this clinical approach and emphasize the importance of a proper choice of the balloon diameter for a safe and effective procedure.

Another interesting observation of this study is the fact that the (marked) fluid level in the tissue bath (see Fig. 2), which was covered to inhibit evaporation, did not elevate even during high-pressure tests. We estimate that the hydraulic permeability coefficient, which is the ratio of the flow rate per unit area to the pressure gradient, is <5.84 × 10¹⁵ m⁴/Ns, i.e., within the range of articular cartilage. For this estimation, we assumed an adventitial surface area of 30 cm², an adventitial thickness of 0.3 mm, a mean pressure of 50 kPa, and a test duration of 120 min. In addition, we assumed an elevation of 1 mm in the tissue bath with a cross-sectional area of 210 cm². Regarding angioplasty, this means that the potential extrusion of "soft lesion fluids" per unit area (1 cm²) is in the range of 0.01 mm³. Therefore, we conclude that volume reduction of plaques by means of fluid filtration through the adventitia is not likely to be a significant contributor of luminal restoration.

Limitations

The assumption of homogeneity may lead to an underestimation of the stresses in the inner adventitia because the outer parts of the adventitia, which exhibit less organized arrangement of collagen fibers (see Fig. 1c), are likely to be less load bearing.

Similarly, the assumption of incompressibility may also lead to an underestimation of stresses because a stress-induced fluid extrusion, in particular from the looser outer adventitial parts, would be associated with smaller cross sections and thus with higher stresses. However, if there is a fluid exchange during cyclic loading, it must occur very fast because the observed hysteresis is small (see Fig. 5). A material, such as cartilage, with retarded fluid exchange exhibits large hysteresis.

Another limitation of the study is that the contraction states of the arteries investigated were not determined. The vessel tone in vivo, i.e., the contraction of the medial smooth muscle cells, may have been higher than postmortem after vessel inflation. Therefore, the adventitial pressure loads may be smaller than calculated. On the other hand, Cox (3) demonstrated (for canine arteries) that passive and active vessel responses converge at pressures between 150 and 200 mmHg (20.0 and 26.7 kPa), so that the adventitial stress state becomes relatively independent of the medial contraction state. Moreover, the vessel reactivities of the arteries investigated were probably small because they showed significant intimal thicknesses (0.39 mm mean value) and histology revealed fibrosis of the medias.

Results concerning in situ stress states and adventitial pressure loads should be interpreted with caution. These results depend significantly on the measurements of the in situ axial stretches, which are difficult to obtain accurately. Additionally, the whole adventitial deformation occurs within small circumferential and axial stretch ranges of <20% (see Fig. 4). At a pressure of 13.3 kPa, the change of circumferential stress per 1% circumferential stretch is up to 150 kPa, and the representation of experimental data by means of the constitutive models is also afflicted with (small) errors: for example, at a transmural pressure of 13.3 kPa, the mean difference between experimental and calculated pressure loads of the inflated adventitias was 5.5%. These numbers may explain why, for specimens IX-XI, the calculated adventitial pressure loads are physically impossible, i.e., they are larger than the transmural pressure.

Furthermore, the adventitial thickness is a crucial factor for stress calculations. However, reliable thickness measurements of highly deformable thin structures such as adventitias are very difficult, and hence they might be afflicted with errors (see METHODS). Finally, relatively few specimens were investigated (although the number is at least double that considered in previous studies). Turtleneck dissection was practicable only for adventitial tissues from elderly subjects. Consequently, only specimens from this group were investigated, so that in turn conclusions regarding the role of the adventitia in vascular function are restricted to this particular group. Despite these restrictions, however, our data provide a novel, clear, and consistent picture of the in situ mechanics of aged human adventitias.