Distribution of Lamellar Deformations
Implications for Properties of the Arterial Media
Abstract—Most computations of arterial mechanics treat the wall as a mechanically homogeneous body, but there are no data to support or refute this. To evaluate this assumption, experiments were performed that measured the deformation of 4 elastic lamellae located at 4 equidistant points across the thickness of the media. Data were obtained at 25–mm Hg pressure steps between 0 and 200 mm Hg. To satisfy the constraints of incompressibility in an isovolumetric cylinder, the innermost structures must undergo larger deformations than the outermost structures. This manifests as thinning of the wall. Therefore, each experiment was performed twice: once with a vessel segment in its normal cylindrical configuration, and again with a contiguous vessel segment turned inside-out to form an inverted cylinder. The deformations of individual lamellae obtained in normal and inverted vessel segments were averaged to determine their extensions independent of location. Results showed that the extensibilities of the lamellae were equal at all 4 anatomic locations across the media, suggesting equal stiffnesses of the lamellae. Other studies were performed to examine the distribution of the circumferential retractions of the lamellae that occurs when a vessel is extended longitudinally. Results showed that circumferential retraction also was distributed uniformly across the wall. These findings demonstrate that the elastic lamellae behave uniformly in both the circumferential and longitudinal directions at different locations across the wall thickness. Because of the interlocked structure of the elastin, muscle, and collagen in the media, these findings suggest that although the media is histologically heterogeneous, it acts mechanically as a homogeneous material.
Most quantitative measures of arterial mechanics treat the arterial wall as though it were a homogeneous body. This is exemplified by the computation of wall stress as the product of pressure and radius divided by wall thickness. The very use of the term “wall thickness” suggests that the distending load is borne uniformly across the thickness of the wall. But histological studies show that the arterial wall is not homogeneous.1 2 3 The intima consists of a single layer of endothelial cells and a thin layer of subendothelial connective tissue; these probably offer negligible mechanical strength. Similarly, the adventitia consists largely of collagen and elastic fibers that remain slack until very high pressures and large diameters are achieved.1 Therefore, at low and physiological pressures, the properties of the wall are determined chiefly by the media. The media is composed of elastin and vascular smooth muscle cells and slack collagen, all arranged in a highly organized fashion.3 The media could function as a unit providing uniform mechanical properties.
The purpose of the present study was to compare the mechanical behavior at different locations across the media using the elastic lamellae as markers of local deformations. Elastic lamellae at 4 equidistant locations across the media were studied. With pressurization, these lamellae could undergo equal, or unequal, deformations depending on their respective stiffnesses. This is complicated by the fact that pressurization of a cylinder composed of an incompressible material must undergo greater deformations at the inner circumference than at the outer circumference to maintain constant cross-sectional area. This manifests as thinning of the wall. To account for constant cross-sectional area, deformations of the 4 index elastic lamellae were measured with vessel segments in their normal configuration and also with contiguous vessel segments inverted. The deformations then were averaged to obtain the mean extensibilities of the lamellae independent of their location.
Carotid arteries were obtained from dogs weighing 25 to 30 kg. The animals were treated humanely, with approval by the Institutional Animal Care and Use Committee, and in accordance with federal guidelines (Guide for the Care and Use of Laboratory Animals, NIH Publication 86-23, revised 1985). Small nicks were placed in the vessels to be able to reestablish in situ length after excision. Experimental procedures are summarized diagrammatically in Figure 1⇓. Each artery was rinsed in normal saline, dissected of adherent adventitia, and cut into 2 cylindrical segments. One segment was studied in its normal configuration, and the other was turned inside-out to provide an inverted segment. Each segment was catheterized at both ends with PE-240 polyethylene tubing with flared tips and was secured with silk sutures. The catheterized vessels were mounted in a tissue bath and restored to in situ length. They were immersed in, and filled with, phosphate-buffered Krebs-Ringer dextrose solution4 held at pH 7.4 and 37°C. The vessels were pressurized in 25–mm Hg steps up to 200 mm Hg and then down in similar steps to 0 mm Hg. These stepwise cycles were repeated 3 times to relax the vessels. The lumen was emptied of Krebs-Ringer solution and filled with a dilute suspension of barium sulfate to provide radiographic contrast. The tissue bath then was drained, and a dental x-ray film was placed immediately beneath the artery. A dental x-ray machine with a 64-cm-long collimating tube was aligned over the tissue bath, and radiographs were taken to obtain vessel diameters with the vessel pressurized in 25–mm Hg steps up to 200 mm Hg. Previous calibrations with steel tubes demonstrated that this arrangement provided radiographic images with no more than 3% magnification.5
After radiograms were obtained in 25–mm Hg pressure steps between 0 and 200 mm Hg, the vessel was removed from the tissue bath and was anastomosed end-to-end to a 6-mm-diameter polyfluorotetraethylene (PTFE) graft (WL Gore). A smooth, symmetrical polypropylene cone, ie, a micropipette tip, was inserted into the PTFE graft. Then the artery was pressurized intraluminally with 150 mm Hg pressure while held at in situ length. Because the artery was connected end-to-end to the PTFE graft, it was possible to slide the cone from the graft into the pressurized artery without damaging the vessel wall. Then, the pressure was reduced to 0 mm Hg, leaving the unpressurized artery stented from within by the cone. The cone was 5 cm long, 2 mm in diameter at its small end, and 5.5 mm in diameter at its large end. Silk sutures were placed around the artery, securing it onto the intraluminal cone. The PTFE graft and a few millimeters of attached artery were cut off and discarded. The vessel held at in situ length by the cone was immersed in 2% buffered glutaraldehyde. After 24 hours, it was embedded in glycomethacrylate. These histologic methods produce small changes in the tissue volume of soft tissues, ie, about an 8% increase in tissue volume.4 After 24 hours, the polypropylene cone was removed from the fixed, embedded vessel, and the artery was cut into 6-μm serial sections. These sections were stained with orcein so the elastic lamellae could be identified. The above described procedures were performed on vessels in both normal and inverted configurations. The radiograms obtained in 25–mm Hg steps between 0 and 200 mm Hg were mounted in 35-mm slide holders and projected to give images with ×300 magnification. The histologic slides were placed in another 35-mm slide projector set beside to the first projector to permit superimposition of the histologic image over the radiographic image. This method identified the histologic sections that corresponded to the dimensions of the fresh vessel recorded by the radiograms at 0, 25, 50, 75, 100, 125, 150, 175, and 200 mm Hg. Transparent rulers also were projected by both slide projectors. The images of the rulers were superimposed to be certain that magnifications were identical.
Each of the 9 histologic slides was projected at ×300 magnification and was drawn on overlapping sheets of white paper. Four elastic lamellae were identified and traced: The internal elastic lamella (L1), a lamella one third of the way across the thickness of the media (L2), a lamella two thirds of the way across the media (L3), and the external elastic lamella (L4) at the media-adventitial margin. The location of L2 and L3 were verified on each projected section by counting the number of lamellae to be certain that the same lamella was traced on successive slides. Note that L1 was the internal elastic lamella, ie, the lamella nearest the intima, in both the normal and inverted sections. Similarly, L4 was the external elastic lamella, ie, the lamella nearest the adventitia, in both normal and inverted sections. L2 and L3 lamellae were similarly defined anatomically. Thus, each lamella was defined by its anatomic location, irrespective of whether the vessel was normal or inverted. Each of the 4 index lamellae was traced twice on paper. First, the actual wrinkled length was traced; this is shown diagrammatically at the bottom of Figure 1⇑. A tracing also was made to estimate the smoothed circumference through the wrinkled lamellae; this is shown as broken curved lines in the bottom drawing of Figure 1⇑. The white sheets of paper containing the drawings of the elastic lamellae were placed on a Sigmagraph model 300 digitizing pad. The computer program used to determine lamellar lengths was a Sigma Scan version 3.90 (Jandel Scientific). The lines describing the lamellae were traced to measure the lengths of the 4 index lamellae on each histologic slide. In this way, it was possible to determine the circumferential length of the 4 index lamellae at diameters corresponding to each pressure between 0 and 200 mm Hg.
Deformations were computed as extension ratios (λθ): where λθ is the circumferential extension ratio, C is the observed length of the elastic lamella in the pressurized vessel, and C0 is the length of the same lamella in an excised, free-floating vessel that was free of externally applied loads.
The circumferential retraction that accompanies longitudinal extension was studied. Carotid arteries were excised from dogs and permitted to retract. Then they were subjected to the procedures illustrated in Figure 2⇓. Each vessel was transected into 4 segments 2 cm in length. Each segment was cannulated at both ends with polyethylene tubing with flared tips to prevent slippage that was secured with silk sutures. Each vessel was mounted in a tissue bath and extended and secured at a predetermined length. Lengths were described as extension ratios (λZ): where λZ is the longitudinal extension ratio, L is the extended length, and L0 is the original length before extension. The segments were extended to no extension (λZ=1.0), 10% extension (λZ=1.1), 30% extension (λZ=1.3), or 50% extension (λZ=1.5). The tissue bath was filled with buffered Krebs-Ringer solution. After 60 minutes, the bath was drained and refilled with 2% buffered glutaraldehyde to fix the vessel segments. Twenty-four hours later, the fixed vessels were embedded in glycomethacrylate. Each vessel was sectioned into rings and stained with orcein so the elastic lamellae could be identified. The sections obtained were projected at ×300 magnification, and the 4 index lamellae (L1, L2, L3, and L4) were drawn. The circumferential lengths of the lamellae were measured using the Sigmagraph model 300 digitizing pad and Jandel Sigma Scan version 3.90 system. This entire experiment was performed twice: once with the vessels mounted in their normal cylindrical configuration, and also with the vessels turned inside-out to form inverted cylinders. Lamellar lengths were used to determine the circumferential retraction that accompanied longitudinal extension.
Figure 3⇓ presents data for 1 artery. The data shown are wrinkle ratios for the 4 index lamellae plotted as a function of pressure. The wrinkle ratios were computed as the smoothed length of the elastic lamellae divided by the wrinkled length of the same lamellae. Wrinkle ratios are inversely related to the “waviness index” described by Wolinsky and Glagov1 but here were determined by direct measurement of the lengths of individual lamellae. At low pressures and small vessel diameters, the lamellae were highly corrugated and were longer than the smoothed curves; therefore, the wrinkle ratios were <1.0. At high pressures and large diameters, the lamellae were stretched so that the smoothed and wrinkled lengths were equal. At these dimensions, the wrinkle ratios were 1.0. Remarkably, the transition between low wrinkle ratios and 1.0 occurred at 25 to 50 mm Hg. This means that only at very low pressures are the elastic properties of intact arteries determined by unwrinkling of the retracted elastic lamellae. At pressures of 25 to 50 mm Hg and above, true stretching of elastic lamellae occurs so that the lamellae exert true resistance to extension.
Figure 4⇓ shows the lengths of the four lamellae normalized by their original lengths. These were computed as circumferential extension ratios (Equation 1) using the dimensions of the lamellae in the free floating vessel segments as the original length (C0). The top panel of Figure 4⇓ shows extension ratios for the vessel in its normal configuration, ie, with the intima facing inward. These data show that the deformations were not equal, in that L1>L2>L3>L4. Such a distribution of deformations is to be expected for any cylindrical structure that remains isovolumetric or is compressible; the inner circumference must increase in size proportionately more than the outer circumference, causing the wall to become thinner. This must occur for the cross-sectional area of the wall to remain constant.
Data obtained for the inverted vessel then were used to compute extension ratios in the inverted vessel (Figure 4⇑, bottom). These deformations are L4>L3>L2>L1, opposite that seen in the normal configuration (Figure 4⇑, top). The data shown in Figure 4⇑ mean that either (1) the lamellae in the 4 regions of the wall are nonuniform in their properties, or (2) their unequal deformations resulted merely from incompressibility and the requirement to maintain constant cross-sectional area.6 7 To resolve this, deformations of each individual lamella were averaged; ie, the deformation of L1 in the normal configuration was added to the deformation of L1 measured in the inverted vessel. The sum of these deformations at each pressure then was divided by 2 to obtain the average. This was done for all 4 index lamellae.
One may then predict 1 of 2 results:
(1) If the properties of the lamellae are nonuniform, then one may expect a divergence or separation of the averaged lamellar deformation curves.
(2) Alternatively, if the properties of the lamellae are uniform, then one may expect the averaged lamellar deformations to fall along a single curve.
The answer is given in Figure 5⇓, which shows averaged deformation curves for L1, L2, L3, and L4 for the normal and inverted vessel segments for 1 artery. It is clear that when wall incompressibility is accounted for, the lamellae exhibit identical extensibilities across the thickness of the media.
Figure 6⇓ shows data for a second, entirely separate artery. Again, the averaged deformation curves for L1, L2, L3, and L4 for this second artery lie on a single curve. Thus, both arteries studied by these histometric methods exhibit uniform extensibilities of the elastic lamellae across the thickness of the media.
Figure 7⇓ summarizes circumferential extension ratios (λθ) (Equation 1) for 11 arteries plotted against longitudinal extension ratios (λZ). Data are shown for the normal configuration (top panel), the inverted configuration (middle panel), and their average (bottom panel). The data show that as the vessels were extended to progressively greater lengths (increasing λZ), the lamellae retracted to decreasing circumferences, ie, to decreasing λθ. Comparison of the circumferential extension ratios (λθ) of the 4 lamellae at each longitudinal extension (λZ) using analysis of variance demonstrated no statistical differences among the 4 lamellae.
Thus, we may conclude that the circumferential contraction that accompanies longitudinal extension is distributed uniformly across the wall, causing the lamellae to retract uniformly. These data indicate that on a regional basis, both circumferential extensibilities and circumferential retractions of the lamellae with axial extension are distributed uniformly across the thickness of the media.
The present experiments in dog carotid artery examined the deformation of the elastic lamellae as a measure of local deformations. The elastic lamellae were stretched and became load-bearing at 25 to 50 mm Hg (Figure 3⇑). Similar observations were reported previously for the rabbit aorta by Wolinsky and Glagov,1 who used a “waviness index.”
Analysis of lamellar deformations revealed that the circumferential properties of the elastic lamellae are equal in the 4 regions of the media (Figures 5 through 7⇑⇑⇑). No direct measurements could be made of the soft tissue between the elastic lamellae because there are no identifiable markers of deformation. But there are relevant published data. Using semithin light microscopic and ultrathin electron microscopic techniques, Clark and Glagov3 meticulously examined the details of arterial wall structure. They found that in the walls of elastic arteries, the media is composed of musculoelastic fascicles. Each fascicle consists of circumferentially oriented vascular smooth muscle cells and an encompassing network of branching elastic fibers. The fascicles are grouped into cell strips or cell layers, each of which is bracketed by elastic fibers. Bundles of wavy (slack) collagen fibers are interposed between adjacent elastic fiber systems. Thus, the artery wall consists of elastin–muscle cells–elastin–collagen–elastin–muscle cells–elastin… With hypertension, there are increasing numbers of attachments between elastin and the vascular muscle cells.8 All of these observations imply a highly integrated, interlocked anatomic system of elastin and vascular muscle where 1 element, elastin, cannot be extended without extending the other, ie, the attached vascular muscle cells. The collagen fibers were slack and presumably were not substantially load-bearing at low and physiological pressures.3 Enzymatic degradation studies in vitro9 10 and physiological analysis in vivo11 suggest this role of collagen as well. These observations, coupled with the observed uniformity of response of the elastic lamellae across the wall (Figures 5 through 7⇑⇑⇑), suggest that the artery wall behaves mechanically as though it were a homogeneous material, despite its marked histologic heterogeneity.
The connective tissues of the adventitia are not deformed until very high transmural pressures are applied and large diameters are achieved.1 9 10 In fact, dissection between the media and the adventitia permits the outer layer to spring open to a larger circumference.10 Therefore, it is likely that the adventitia bears little or no distending loads at normal physiological pressures and in fact appears to be subjected to compression by its attachments to the smaller media.
The present findings are relevant to some current bioengineering issues. In the present study, deformations were computed using the dimensions of the unloaded free-floating vessel segment as a reference value. Use of a material in the unloaded state as a reference is a common practice in engineering. Using this method, one finds that stresses are distributed nonuniformly across the wall; they are highest at the intima, declining curvilinearly to reach lowest values at the outer margins of the wall.12 13 Blood vessels adapt morphologically and mechanically to increased wall stress.3 14 Therefore, on the basis of previously published stress distributions,12 13 one might have expected greater stiffness and hence lower extensions for L1 than for L2, L2>L3, and L3>L4. This was not found. Instead, the 4 lamellae exhibited identical average deformations (Figures 5⇑ and 6⇑). Some authors suggest that deformations should not be computed with respect to the retracted, unloaded state because the vessels never exist in vivo at these dimensions. Moreover, when fully unloaded, the vessels manifest evidence of residual stresses, ie, residual compression near the intima and residual tension near the outer margin of the media. As a result, when a ring of artery is transected, it springs open to assume a larger radius.15 16 17 18 The authors making these observations suggest that deformations should not be computed with respect to the unloaded state but instead using the dimensions of the vessel at physiological pressures and in situ length as a reference state.17 18 When this is done, the computed distribution of stresses does not decline curvilinearly across the wall12 13 but instead remains constant across the thickness of the wall.19 This is similar to the distribution of extensibilities seen here (Figures 5⇑ and 6⇑). Thus, the present experimental results are consistent with the computation of vessel properties relative to a physiological reference state.
- Received August 31, 1998.
- Revision received September 24, 1998.
- Accepted November 3, 1998.
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