Contribution of elastin and collagen to the inflation response of the pig thoracic aorta: Assessing elastin's role in mechanical homeostasis

Journal of Biomechanics 45 (2012) 2133–2141

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Contribution of elastin and collagen to the inflation response of the pig thoracic aorta: Assessing elastin’s role in mechanical homeostasis M.A. Lillie n, T.E. Armstrong, S.G. Ge´rard, R.E. Shadwick, J.M. Gosline Department of Zoology, University of British Columbia, Vancouver, BC, Canada V6T 1Z4

a r t i c l e i n f o

abstract

Article history: Accepted 24 May 2012

This study was undertaken to understand elastin’s role in the mechanical homeostasis of the arterial wall. The mechanical properties of elastin vary along the aorta, and we hypothesized this maintained a uniform mechanical environment for the elastin, despite regional variation in loading. Elastin’s physiological loading was determined by comparing the inflation response of intact and autoclave purified elastin aortas from the proximal and distal thoracic aorta. Elastin’s stretch and stress depend on collagen recruitment. Collagen recruitment started in the proximal aorta at systolic pressures (13.3 to 14.6 kPa) and in the distal at sub-diastolic pressures (9.3 to 10.6 kPa). In the proximal aorta collagen did not contribute significantly to the stress or stiffness, indicating that elastin determined the vessel properties. In the distal aorta, the circumferential incremental modulus was 70% higher than in the proximal aorta, half of which (37%) was due to a stiffening of the elastin. Compared to the elastin tissue in the proximal aorta, the distal elastin suffered higher physiological circumferential stretch (29%, P ¼ 0.03), circumferential stress (39%, P ¼0.02), and circumferential stiffness (37%, P ¼ 0.006). Elastin’s physiological axial stresses were also higher (67%, P ¼ 0.003). These findings do not support the hypothesis that the loading on elastin is constant along the aorta as we expected from homeostasis. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Aorta Elastin Collagen Mechanical properties Homeostasis

1. Introduction Elastin and collagen fibers in the arterial wall transmit local mechanical loads to the adjacent vascular smooth muscle cells (VSMC), influencing their adaptive responses during growth and remodeling. The VSMC differentiate between static and dynamic cues (Lehoux et al., 2005), and whether they respond more fundamentally to stress or strain (Taber and Humphrey, 2001; Guo and Kassab, 2004; Kim et al., 2009), regulation of at least one of these parameters is presumably central to homeostasis. Wolinsky and Glagov (1967) found the load per lamellar unit in the thoracic aorta was constant across 10 species, suggesting static stress was a controlled parameter. However, Wolinsky’s measurements were made at a single mid-thoracic point. Physiological forces vary along the aorta, in part due to wave reflection and vessel taper (O’Rourke, 1967; McDonald, 1974; Bogren and Buonocore, 1999; Wood et al., 2001; Markl et al., 2004), and this could affect local stresses unless compensated for by local structural adjustments. Both collagen content (Roveri et al., 1980) and R/H, the ratio of inner-radius-to-wall-thickness on which wall stress depends (Purslow, 1983; Lillie and Gosline, 2007), increase along the aorta, but despite these adjustments

n

Corresponding author. Tel.: þ1 604 822 2373; fax: þ 1 604 822 2416. E-mail address: [email protected] (M.A. Lillie).

0021-9290/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2012.05.034

neither physiological stress nor stretch appears constant. Along the pig aorta and coronary tree, static circumferential stretch varies between ly ¼1.2–1.6, and stress between 10 and 150 kPa (Guo and Kassab, 2004). However, these are average values, and load is partitioned unevenly between collagen and elastin. Elastin bears the entire load at low pressures, with collagen recruited around diastolic pressure (Roach and Burton, 1957; Wolinsky and Glagov, 1964). Arterial stretch approximates the stretch of the elastin but not the collagen, and arterial stress represents the stress on neither component. The static and dynamic loading of the individual components remains to be examined. Accordingly, we studied the inflation behavior of intact and autoclave-purified thoracic aortas to determine whether maintaining a regionally constant mechanical environment for elastin was a homeostatic target.

2. Methods 2.1. Tissue purification Descending thoracic aortas from  100-kg pigs from an abattoir were maintained in iced phosphate buffered saline (PBS), and either tested within 48 h of death (‘‘fresh’’) or stored in PBS at –20 1C (‘‘intact’’). Aortas were cleaned of loosely adhering tissue, leaving as much adventitia as possible. The elastic tissue (‘‘elastin’’) was purified by 8 h autoclaving at 103 kPa (Lillie et al., 1994) (see Appendix A1).

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M.A. Lillie et al. / Journal of Biomechanics 45 (2012) 2133–2141 lower case to the loaded. Measurements were not taken near vessel ends. The longitudinal stretch at the midpoint of each segment was

2.2. Autoclave-induced changes in tissue dimensions and residual stretches Aortic elastin lies almost exclusively in the media, so we have reported medial stresses and stretches for intact and autoclaved tissue (Fig. 1). Medial dimensions were measured in the autoclaved elastin and back calculated for the tissue before autoclaving, accounting for autoclave-induced changes in inner radius, length, and medial thickness. Rings of intact and elastin tissue, some of which were from inflation tests, were photographed in PBS at 37 1C with a 12 MPix camera. Aortas were assumed circular in cross-section, and inner and outer radii, Ri, Ro, and ring length were determined. The change in inner radius on purification was obtained from aortas not used for inflation as

lrinner ðzÞ ¼

Rintact i Relastin i

ð1Þ

where z is the axial position along the unloaded aorta relative to the first intercostal branch. The thickness of each lamellar unit was measured in histological sections of fresh, intact and elastin samples. Average thickness was determined by counting the number of lamellae per 0.75 mm at 16 locations per section. Circumferential and axial residual stretches of the lamellar elastin, ly res, lz res, were determined following the protocol given by Lillie and Gosline (2006) (see Appendix A.2). 2.3. Inflation tests A grid was painted along each aorta for measurement of local segment length (Fig. 2). The vessel was mounted horizontally in 37 1C PBS. The proximal end was connected to a pressure reservoir and was fixed in position. While untethered distally, each vessel was inflated at least 4 times for preconditioning, and then inflated to 13.3–18.7 kPa pressure, P, taking photographs at 1.3 kPa increments. The distal end was then coupled to a variable-position force transducer. The attachment point was a steel pin centered on a brass conical depression that allowed free torsional rotation of the aorta around its z-axis. Each aorta was inflated at several axial stretches between 1.2 o lz o1.5. At the end of the tests intact vessels were autoclaved and retested, and elastin aortas were cut into rings, photographed for dimensions, and then dried for density measurement. From the photographs of inflated aortas we obtained local segment lengths, L and l, and outer radii (Fig. 2). Upper case symbols refer to the unloaded state, and

Intact

Elastin

l L

lz ¼ lz res

ð2Þ

where lz res is specific for intact or elastin tissue. Medial volume was calculated from the unloaded autoclaved tissue. Assuming constant elastin volume during deformation (Lillie et al., 2010), ri in loaded elastin aortas was calculated as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ri ¼ r o 2 ðRo 2 Ri 2 ÞL=l ð3Þ For intact aortas, the inner radius of unloaded intact tissue was calculated . In loaded intact aortas ri was calculated with using Eq. (1) and associated Relastin i Eq. (3) where Ro represents the outer radius of the entire aorta (including adventitia). We first assumed medial volume remained constant after autoclaving and back-calculated rMAB qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 intact rintact ðRelastin Relastin ÞLelastin =l þ r intact ð4Þ MAB ¼ o i i Values were later corrected for autoclave-induced changes in density (see Section 3). The mid-media radius, rmid, was the average of ri and ro (elastin) or ri and rMAB (intact). The mid-media circumferential stretch ratio was

ly ¼

r mid l Rmid y res

where ly res is specific for intact or elastin tissue. The total experimental (EXP) axial force was F tot ¼ P pr i 2 þ F z , where Fz is the force registered by the force transducer. We assume the average circumferential and axial wall stresses occurred near mid-media. Average stresses were  

sy sy

intact

Pr i rMAB r i

¼

elastin

Pr i r o r i

¼

Ro RMAB Rmid

Rmid Ri

Ri

Media Adventitia Fig. 1. Dimensions of the unloaded intact ring (left) and autoclaved elastin (right). In the intact ring the mid-medial radius, Rmid was the average of Ri and RMAB, the radius at the media-adventitia border. Ri and RMAB were calculated from Eqs. (1) and (4). In elastin rings Rmid was the average of inner and outer radii, Ri and Ro, measured from photographs.

,

,

hsz iintact ¼ pðr F tot2 r 2 Þ , MAB i

ð6Þ

hsz ielastin ¼ pðroF2totr 2 Þ : i

We applied a strain energy function (SEF), from Horny´ et al. (2006) to the response of the intact aorta: 2

2

02

e

2

W H ¼ bðly þ lz þ lr 3Þþ 2c ðeQ 1Þ, Q¼

0 0 c1 y þ c2 02 z þ 2c 3 y z ,

e

e e

ð7Þ 2

where b, c, c1, c2 and c3, are material parameters, e0 i is Green strain, e0i ¼ ðli 1Þ=2, 1 1 and lr is the radial stretch, calculated as lr ¼ ly lz assuming incompressibility. The elastin behavior was modeled with two elastin SEFs. Gundiah et al. (2009) developed a model for the pig thoracic aorta that produced a reasonable fit to its pressure response (Lillie et al., 2010): 2

Ro

ð5Þ

2

2

2

2

W G ¼ c0 ðly þ lz þ lr 3Þþ c1 ðlz 1Þ2 þ c2 ðly 1Þ2 :

ð8Þ

The Rezakhaniha model (Rezakhaniha et al., 2011) was proposed for rabbit carotid:   2 2 2 2 2 W R ¼ c0 ðly þ lz þ lr 3Þþ c1 ly þ 3 , ð9Þ

ly

where c0, c1 and c2 are material constants. Cauchy stresses were calculated using

sy sr ¼ ly @W @ly sz sr ¼ lz @W @lz

ð10Þ

and the boundary conditions sr(ri)¼ –Pi and sr(ro) ¼ –Po ¼ 0. Modeled pressure, P MOD and total axial force, F MOD were calculated using tot  Z ro  Z ro @W dr @W ly @W , F MOD ly lz  ð11Þ r dr þ P pr 2i PMOD ¼ tot ¼ 2p @ly r @lz 2 @ly ri ri Material coefficients were determined using a non-linear least squares Marquardt–Levenberg algorithm to minimize the error e 2 !2 ! 3 EXP 2 N X P MOD P EXP F MOD j j tot j F tot j 4 5 e¼ þ ð12Þ EXP EXP P F tot j¼1 where N is the number of experimental observations for an aorta and the overbar indicates the mean for that aorta. Parameters were based on three sets of randomly generated initial values. All parameters were positive, and convexity was verified for each aorta following Holzapfel et al. (2000). Circumferential, Ey, and axial, Ez, incremental moduli were calculated following Dobrin and Doyle (1970). We assumed the tissue was orthotropic and behaved linearly over small stretches. The deformation of an anisotropic vessel is

Fig. 2. Autoclaved aorta, comprised of elastin tissue only, shown tethered at an axial stretch of lz ¼ 1.34 and inflated to 13.3 kPa pressure. A grid was painted on with aldehyde fuchsin to measure local segment length, l (  10–25 mm long) and outer radius, ro. Up arrow marks the position of the first intercostal branch, designated as z¼ 0 mm. Other branches are not visible. Unloaded vessel length was 156 mm.

D s nyZ hEz y i

Dez ¼

Dhsz i

Dey ¼

Dhsy i

Ez Ey

nyZ DhEsz z i :

ð13a; bÞ

De is the incremental strain, i.e. for length, ‘, De ¼ 2ð‘2 ‘1 Þ=ð‘2 þ ‘1 Þ, where the subscripts represent different load levels. nyz is the incremental Poisson’s ratio for

M.A. Lillie et al. / Journal of Biomechanics 45 (2012) 2133–2141 axially loaded tissues. Eq. (13) neglects radial stresses, causing an estimated 2.1% and 1.5% error in Ey for the proximal and distal elastin, assuming nry ¼ 0.8 (Patel et al., 1969). Evaluating Eq. (13a) when Dez ¼0 yields

Dhs i nyz ¼  z  D sy

ð14Þ

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rings, stretch was ly ¼ L/L0 where L0 is the zero-stress elastin length, and stress was s ¼Fly/A0, where A0 is the cross-sectional area of the undeformed elastin ring segments. Collagen recruitment stretch is illustrated in Fig. 3. In inflation tests, recruitment was determined statistically as the stretch at which the intact modulus exceeded the elastin modulus.

2.4. Collagen recruitment

3. Results

Rings of intact aorta were tested uniaxially in 37 1C PBS with an Instron 5500 tester following Lillie and Gosline (2007) to obtain force, F, and mid-wall length, L, data. The rings were then autoclaved and retested. For paired intact and elastin

3.1. Tissue dimensions and residual stretches

1.6 Elastin

Circumferential Stretch

1.5

Intact

1.4 1.3 1.2

Elastin R/H, residual stretches, and autoclaving-induced changes in dimensions are given in Table 1. Freezing fresh tissue had no effect on lamellar unit thickness (Fig. 4, paired t-test, n¼9(3)) so data were pooled. Lamellar unit thickness was independent of axial position in fresh and intact tissue, as previously reported (Sokolis et al., 2002), but decreased with axial position in elastin (P¼0.02, linear regression, n¼ 9(3)). Autoclaving expanded the lamellar unit thickness by 24% at z¼0 mm and 11% at z¼100 mm, a difference of 13%. This value was confirmed by measurement of fiber packing density (Appendix A2). Stresses and moduli have been adjusted to account for the changes in tissue dimensions and are reported relative to the dimensions of the intact media. 3.2. Inflation tests

1.1 1.0 0.9 0

100

200

300

400

Stress (kPa) Fig. 3. Determination of the stretch at which collagen is first recruited in uniaxial tests. The behavior of each sample was examined as a function of stress before and after autoclaving. The recruitment stretch was the stretch at which the stress difference between intact and elastin tissue reached a maximum and started to decline.

Four aortas were inflated as fresh and then intact aortas. At physiological pressures ly ¼1.2870.03 in both groups, showing no impact of freezing (paired t-test). No torsion was detected during inflation of any untethered or tethered elastin aorta, indicating either an absence of helical elastin fibers or their axial symmetry. The circumferential responses of aortas to pressurization are shown in Fig. 5. We used in situ axial stretches of lz ¼ 1.24 for the proximal segments and 1.37 for the distal, based on Han and Fung (1995). The intact and elastin aortas showed the same behavior at low pressures, but at higher pressures the elastin aortas tended

Table 1 R/H, Residual stretches and effects of autoclaving on tissue dimensions. Values are given as means7 SE where there is no axial trend. z ¼axial position in mm relative to first intercostal branch, n¼ number of samples, N ¼number of aortas, MAB ¼ media-adventitia border, NS ¼ not significant. Parameter (A) R/H in elastin aorta R/H distal/proximal

Value

n(N)

Statistics

1.25 7 0.04

17(17)

P 50.001, t-testa

1.236 7 0.01 1.247 7 0.01 1.246 7 0.008 1.153 7 0.009 1.173 7 0.01 1.1607 0.008 1.243 7 0.005 1.162 7 0.005

9(3) 9(3) 9(3) 9(3) 9(3) 9(3) 27(6) 27(6)

3 groups NS, ANOVA

(B) Residual stretch ratios Waviness index Intact uncut inner Elastin uncut inner Elastin cut inner Intact uncut MAB Elastin uncut outer Elastin cut outer Pooled inner Pooled outer Circumferential residual stretch Intact inner Intact MAB Elastin inner Elastin outer Axial residual stretch Intact Elastin (C) Effects of autoclaving Inner radius ratio, lr inner Eq. (1) Length ratio a

3 groups NS, ANOVA

Inner vs. outer P5 0.001 t-test

79(5) 79(5) 241(9) 241(9)

P 50.001, t-testa P ¼ 0.04, regression P ¼ 0.001, t-testa P 50.001, regression

0.9897 0.002 0.9897 0.002

125(8) 146(8)

P o 0.001, t-testa P o 0.001, t-testa

1.0177 0.002 1.0037 0.009

115(5) 47(5)

P o 0.001, t-testa NS, t-testa

1.0267 0.0016 0.00031zþ 1.013 1.0117 0.003 0.00031zþ 1.002

Two-tailed, single sample t-test to determine whether stretch ratio differs from a value of 1.

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towards higher extension. At 13.3 kPa pressure (horizontal arrows) the stretch at the proximal end of the elastin aorta was not significantly different than the intact (P¼0.18), but it was significantly larger at the distal end (P ¼0.013). The response of the autoclaved elastin in Fig. 5 is not the response of the elastin within the intact aorta when considered as a function of pressure. We assumed the physiological stretch of the elastin within an intact aorta was the stretch of the intact media at P¼13.3 kPa, i.e., ly ¼1.24 70.01 and lz ¼1.24 for the proximal tissue and ly ¼1.31 70.02 and lz ¼1.37 for the distal (Fig. 5 and Table 2). The large open circles identify these stretches on the elastin curves. These are the points at which the physiological loading of the elastin within the intact vessel must be assessed.

18

Lamellar Unit Thickness (μm)

Fresh Intact Elastin 16

14

12

10 -100

-50

0

50

100

150

200

Axial Position (mm)

3.3. Collagen recruitment Collagen recruitment started at systolic stretches in the proximal aorta but at sub-diastolic in the distal (Fig. 11). In inflated aortas collagen was first recruited between 1.25 o ly o1.27

20

20

15

15

Pressure (kPa)

Pressure (kPa)

Fig. 4. Effect of autoclaving on wall thickness. Mean lamellar unit thickness was measured in histological samples of fresh, intact, and autoclaved elastic tissue. Each data point is the average of about 164 lamellae. Lines show linear regression. Lamellar unit thickness was independent of axial position in the fresh and intact tissue, but decreased in the elastin tissue. Autoclaving increased the lamellar thickness by 24% at z¼ 0 mm and by 11% at z¼ 100 mm. This thickening is due to the release of radial residual strains on autoclaving and was taken into account in the calculation of stress and modulus.

The experimental and modeled responses of elastin aortas to inflation over all axial stretches are shown in Fig. 6. The Rezakhaniha model did not fit the data and was not used further. The global fit of the Gundiah model was good for the P–ly data, but moderate for the Ftot–ly response. The material coefficients were  20–40% higher in the distal tissue (P¼0.01 t-test on aggregate, Table 3) indicating distal elastin was stiffer than proximal. The intact and elastin aortas withstood the same circumferential stress at low pressures, but at higher pressures the elastin aortas tended towards lower stress (Fig. 7). These differences were greater in the distal tissue than the proximal. The experimental physiological stress was greater in the distal tissue than the proximal, as highlighted by the ovals. This difference is augmented in the modeled response: the predicted stress values underestimated the experimental values by 12% in the proximal tissue but overestimated them by 4% in the distal. The experimental data offer the more conservative basis for statistically comparing the physiological responses of the proximal and distal tissue. The physiological incremental moduli were greater in the distal tissue than the proximal, as highlighted by the circles in Fig. 8. The axial responses of tethered aortas to inflation are shown in Figs. 9 and 10. The modeled axial stress response was too flat for elastin. In the distal aorta at physiological stretches the intact tissue was much stiffer than the elastin, but there was little difference in the proximal aorta (Fig. 10). The axial modulus for elastin was independent of position. To identify possible homeostatic targets, we determined whether any aspect of elastin’s physiological mechanical environment was the same in the proximal and distal aorta. Compared to the elastin tissue in the proximal aorta, the elastin within the distal intact aorta suffered higher circumferential (29%) and axial (54%) stretches, and higher circumferential (39%) and axial (67%) stresses (Table 4). The elastin within the distal intact aorta had a 37% higher circumferential incremental modulus but there was no difference in axial modulus. All of these parameters increased in the intact tissue (Table 4).

10

5

0 0.9

Proximal Intact λz=1.24 Elastin λz=1.24

1.0 1.1 1.2 1.3 1.4 Circumferential Stretch λθ

1.5

10

5

0 0.9

Distal Intact λz=1.37 Elastin λz=1.37

1.0

1.1

1.2

1.3

1.4

1.5

Circumferential Stretch λθ

Fig. 5. Impact of autoclaving and of tissue location on circumferential response to inflation. Values are mean 7 SE for intact and autoclaved elastin aortas. Left panel shows proximal tissue at a mean axial stretch of lz ¼ 1.24. Right panel shows distal tissue at a mean axial stretch of lz ¼1.37. Intact aortas were tested up to 18.6 kPa and elastin aortas to 13.3. At a pressure of 13.3 kPa (horizontal arrows) the stretch in the elastin aorta was not significantly different than in the intact aorta at the proximal end (P¼ 0.18) but it was significantly larger at the distal end (P¼ 0.013). The circumferential stretch of the intact aorta at 13.3 kPa is the mid-physiological stretch of the elastin within the intact aorta. The large circles identify these stretches in the elastin data. These are the points at which the physiological loading of the elastin within the intact vessel must be assessed.

M.A. Lillie et al. / Journal of Biomechanics 45 (2012) 2133–2141

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Table 2 Response of intact aortas, purified elastin aortas, and elastin within an intact aorta to inflation to 13.3 kPa pressure. Elastin within an intact aorta was assumed to have the same stretches as the intact aortic media and developed the stresses and moduli of purified elastin at those stretches. EXP, experimental data; MOD values predicted by SEFs. Tissue Intact EXP EXP MOD MOD Elastin EXP EXP MOD MOD

z (mm)

ly

lz

sy (kPa)

sz (kPa)

Ey (MPa)

Ez (MPa)

173 95 7 3

1.24 7 0.01 1.31 7 0.02

1.24 7 0.01 1.37 7 0.01

1547 8 2157 12 1437 8 2267 28

135 7 12 296 7 32 143 7 12 285 7 28

0.827 0.08 1.397 0.10

0.827 0.15 2.87 0.7

174 99 7 5

1.28 7 0.02 1.40 7 0.02

1.25 7 0.01 1.37 7 0.01

1747 11 2587 21 1537 6 2757 19

129 7 8 217 7 21 107 7 7 202 7 197

0.877 0.06 1.047 0.10

0.757 0.13 0.777 0.08

1.24 1.31

1.24 1.37

1487 8 1907 15 1317 5 1977 15

121 7 8 200 7 19 106 7 6 201 7 19

0.707 0.04 0.957 0.06

0.687 0.14 0.697 0.06

Elastin within intact EXP 174 EXP 99 7 5 MOD MOD

Pressure (kPa)

15

10

significantly to the circumferential load. Distal elastin carried 67% (P ¼0.02) of the axial load, 68% (P¼0.001) of the circumferential stiffness, and 24% (P¼0.004) of the axial stiffness.

Rezakhaniha SEF Prox Rezakhaniha SEF Distal Gundiah SEF Prox Gundiah SEF Distal Data Prox λz=1.28 Data Distal λz=1.30

4. Discussion

5

Total Axial Force (N)

0 8 6 4 2 0 0.9

1.0

1.1

1.2

1.3

1.4

Circumferential Stretch λθ Fig. 6. Fit of models to the elastin pressure and force data. The fit of the Gundiah model was good for the pressure response and moderate for the force response. The large circles show the mid-physiological stretches. The Rezakhaniha model did not predict the response.

(13.3  14.6 kPa pressure) at the proximal end and between 1.16 o ly o1.20 (9.3  10.6 kPa pressure) in the distal. In uniaxial tests recruitment occurred at progressively lower stretches along the aorta. The data in Table 2 were used to calculate the fractional contribution of elastin and collagen to the total aortic response at physiological pressure (Table 5). Collagen did not contribute significantly to either the load or incremental stiffness in the proximal aorta. In the distal aorta, collagen did not contribute

It is generally accepted that the arterial mechanical environment is regulated according to mechanical homeostasis (Humphrey, 2008). While the stress and strain distributions appear to be homogenized across the wall, the homeostatic targets that determine the mechanical environment along the arterial tree are unknown. The current study was undertaken to understand elastin’s role in homeostasis. We studied elastin at two aortic locations to establish whether its physiological stretch, stress or stiffness was conserved. The physiological values for these parameters for elastin were isolated by assuming the collagen and elastin operate in parallel. Elastin’s physiological stretch was taken as the stretch of the intact media at physiological pressure. Elastin’s physiological stress and stiffness were the stress and stiffness of purified elastin aortas inflated to the physiological stretch. We believe this is the first study to determine the physiological loading of arterial elastin or quantify the load partitioning between collagen and elastin. The combined properties of collagen and elastin were obtained by inflating intact aortas. Contributions from other wall components were considered negligible. We referred all parameters to the intact medial dimensions so we could assign any observed differences in behavior between intact and elastin aortas to collagen mechanics and not geometry. Although inflations were performed in vitro and axial stretches were based on literature values, the responses we obtained for ly, Ey, Ez and nyz agreed with values measured in situ (Table 6). The properties of elastin alone were obtained from inflated autoclaved aortas. Behaviors of autoclaved elastin and of the elastin within the intact aorta were indistinguishable (Figs. 5 and 7). Autoclaving pig thoracic aorta, therefore, neither alters the elastin measurably nor removes a significant elastic component in series with the VSMC (Davis, 1993; Roy et al., 2008). We used two approaches to analyze the data. The preferred method is to deduce stress and stiffness from constitutive relationships. The Gundiah model provided a good global fit to the elastin pressure response, although it overestimated the regional differences in physiological stress. The alternate is to

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Table 3 Material coefficients for SEF. r2 ¼ the coefficient of determination for the fit to the P–ly response (P) and the Ftot–ly response (F). Location (n)

Coefficients

(A) Intact Proximal (9) Distal (10) (B) Elastin Gundiah Proximal (9) Distal (16) Dist/Prox* (C) Elastin Rezakhaniha Proximal (9) Distal (16) n

b (kPa)

c (kPa)

c1

c2

c3

87 3 77 3

2427 57 1657 34

1.1 7 0.2 1.1 7 0.1

0.94 70.2 1. 4 7 0.2

0.137 0.02 0.137 0.03

c0 (kPa)

c1 (kPa)

c2 (kPa)

217 4 237 4 11%

127 2 187 2 46%

19 7 3 24 7 1 28%

c0 (kPa)

c1 (kPa)

397 2 497 4

137 2 197 3

r2 P

r2 F

0.93 0.96

0.83 0.95

0.96 0.97

0.90 0.91

0.83 0.80

0.34 0.39

P ¼0.01 for the aggregate increase in coefficient values for the Gundiah model.

350

300 250 200

1.0

1.2

150 100 Proximal

50 0 0.9

Intact λz=1.24 Elastin λz=1.24

1.0 1.1 1.2 1.3 1.4 Circumferential Stretch λθ

1.5

Circumferential Stress σθ (kPa)

Circumferential Stress σθ (kPa)

350

300 250 200

1.0

1.2

150 100 Distal

50 0 0.9

Intact λz=1.37 Elastin λz=1.37

1.0 1.1 1.2 1.3 1.4 Circumferential Stretch λθ

1.5

Fig. 7. Circumferential stresses in inflated aortas from proximal (left) and distal tissue (right). Symbols show experimental stresses (mean7 SE). Intact aortas were inflated to 18.6 kPa and elastin to 13.3 kPa. At higher stretches (higher pressures) the stresses in the intact aortas tended to exceed those in the elastin aortas, particularly in the distal tissue. Ovals show stresses for the elastin at mid-physiological stretches. Physiological stresses were higher in the distal elastin than in the proximal. Lines show the fit of the models to the data. Around physiological stretches the elastin model underestimates stress in the proximal tissue and overestimates stress in the distal, and this difference in fit will bias any comparison of stresses and moduli deduced from the model. Insets give experimental response without error bars to show the close match of the stresses up to the point of collagen recruitment. Lines in the inset simply connect data points and do not represent a model.

Circumferential Modulus Eθ (MPa)

2.5

2.0

Proximal

Distal

Intact λz=1.24

Intact λz=1.37

Elastin λz=1.24

Elastin λz=1.37

1.5

1.0

0.5

0.0 0.9

1.0

1.1 1.2 1.3 Circumferential Stretch λθ

1.4

1.5

Fig. 8. Circumferential incremental moduli (mean 7 SE) in inflated intact and elastin aortas. Large circles mark the mid-physiological values for the proximal (lower, left circle) and distal elastin (higher, right circle), and indicate that distal tissue operates at a higher incremental modulus.

evaluate mean stresses and incremental moduli. Mean stress ignores residual stresses and stress variation across the wall. Residual stresses (stretches) are positive for elastin, but including them would only augment the already higher distal stresses. Incremental moduli pertain only to the state of strain at which they were determined, which is not an issue in this study where the focus is on physiological loading. Despite their limitations, the two approaches lead to the same conclusions: that the physiological loading of elastin increased along the aorta. All parameters examined save Ez were greater distally (Table 4). Dynamic stretch is determined by the response of the intact aorta to the local pressure pulse, for which we have no data, but unless the dynamic stretch is appropriately modulated, the higher elastin Ey predicts higher dynamic stresses on the distal elastin. Thus in the thoracic aorta homeostasis appears to target neither elastin stretch nor stress, not static and possibly not dynamic. Elastin alone resists deformation at sub-physiological pressures, so it is the first determinant of physiological stretch and stress. Much of the regional difference in elastin’s mechanical environment can be attributed to the 29% higher circumferential stretch in the distal tissue. The primary factor driving this appears to be the relative thinning of the wall, due to both a 25% higher R/H in the distal tissue and a 54% greater axial stretch. The effect of thinning was partially offset by a  28% higher material stiffness of elastin (Table 3). Interestingly, collagen did not contribute to this: collagen was minimally recruited in the proximal aorta (Fig. 11) and did not bear significant stress at

M.A. Lillie et al. / Journal of Biomechanics 45 (2012) 2133–2141

400

Proximal Intact λz=1.24 Elastin λz=1.24

300

Axial Stress σz (kPa)

Axial Stress σz (kPa)

400

200

100

0 0.9

1.0

1.1

1.2

1.3

1.4

1.5

2139

Distal Intact λz=1.37 Elastin λz=1.37

300

200

100

0 0.9

1.0

Circumferential Stretch λθ

1.1

1.2

1.3

1.4

1.5

Circumferential Stretch λθ

Fig. 9. Axial stresses in inflated aortas from proximal (left) and distal tissue (right). Vessels were tethered at an axial stretch of lz ¼ 1.24 in the proximal tissue and 1.37 in the distal. Symbols show experimental data (mean 7 SE). Lines show the fit of the models to the data. Large circles mark the mid-physiological range for the elastin. Stresses were higher in the distal aorta than in the proximal, due in part to the higher axial stretch. In the distal aorta stresses were higher in the intact tissue than in elastin aorta.

4.0 Intact λz=1.24

Distal Intact λz=1.37

Elastin λz=1.24

Elastin λz=1.37

1.4 Circumferential Stretch at Collagen Recruitment

Proximal

Axial Modulus Ez (MPa)

3.0

2.0

1.0

0.0 0.9

1.3

1.2

1.1

Uniaxial Inflation Physiological pressure

1.0 1.0

1.1

1.2

1.3

1.4

1.5

Circumferential Stretch λθ Fig. 10. Axial moduli (mean 7SE) in inflated intact and elastin aortas. Large circles mark the mid-physiological values for the proximal (lower, left circle) and distal elastin (higher, right circle). In the distal tissue at physiological stretch, moduli were higher in the intact tissue than in elastin but at the proximal end intact and elastin moduli were equal. For the elastin aorta, the moduli did not change with position.

Table 4 Regional variation of the experimental loads and stiffness of the intact aorta and of the elastin within the intact aorta at physiological stretches. A significant difference by t-test indicates the loading was greater in the distal aorta than proximal. NS, not significant. Tissue

Parameter

Distal/proximal

Significance

Intact

ly  1 lz  1

1.29 1.54 1.48 2.30 1.70 3.44

P ¼0.03

1.39 1.67 1.37 1.01

P ¼0.02 P ¼0.003 P ¼0.006 NS

sy sz Ey Ez Elastin within intact

sy sz Ey Ez

P ¼0.001 P o0.001 P o0.001 P ¼0.02

-50

0

50 Axial Position (mm)

100

150

Fig. 11. The circumferential stretch at the point of first collagen recruitment decreased along the aorta. Circles show individual recruitment stretches determined in uniaxial tests. In inflation tests collagen was recruited between ly ¼ 1.25 and 1.27 (13.3 and 14.6 kPa) in the proximal aorta and between ly ¼ 1.16 and 1.20 (9.3 and 10.6 kPa) in the distal. The bars without caps show the stretches corresponding to these pressures. Bars with caps show the physiological range of stretches measured by inflation of intact aortas. Collagen recruitment approached systolic in the proximal aorta but sub-diastolic in the distal.

13.3 kPa, even in the distal aorta (Table 5). Mean stress pertains to the static response, and this appears determined by elastin. Collagen did contribute to the incremental stiffness, but only in the distal aorta. Incremental modulus pertains to the dynamic response, and collagen and elastin modulated this equally: Ey was 70% higher in the distal intact aorta compared to proximal, and the elastin alone contributed 37% (Table 4). A stronger incremental stiffness in the distal aorta would counter an augmented pulse pressure (McDonald, 1974). The mechanism by which elastin’s material properties vary is unknown. We have ruled out fiber packing density (Appendix A3), incomplete purification (Appendix A1), and, since Ez does not fall as Ey rises, partitioning of orthogonal fibers. Non-orthogonal fibers, however, could contribute to both Ey and Ez (Hollander et al., 2011), and although lamellar elastin is predominantly

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Table 5 Relative contributions of collagen and elastin in the intact aorta at physiological stretches. Stress and modulus of the elastin within the intact aorta are compared with values in the intact aorta (i.e. elastin plus collagen). A significant difference by t-test indicates a portion of the stress or stiffness was borne by collagen. NS, not significant. Location

Parameter

Elastin/intact

Significance

Proximal

sy sz

0.96 0.90 0.85 0.83

NS NS NS NS

0.88 0.67 0.68 0.24

NS P¼ 0.02 P¼ 0.001 P¼ 0.004

Ey Ez Distal

sy sz Ey Ez

Table 6 Comparison of the response obtained in the current in vitro study of the intact aorta with published studies of the thoracic aorta. Parameter

This study

Previous Ref. study

Species

ly

1.28 7 0.02a 0.64 7 0.05b 1.14 7 0.3b 0.29 7 0.02a 1.70

1.26 0.74 0.99 0.29 1.67

Pig in situ Dog in vivo Dog in vivo Dog in vivo Pig in vitro

Ey (MPa) Ez (MPa)

nyz Dist. Ey/prox. Ey a b

Guo and Kassab (2004) Patel et al. (1969) Patel et al. (1969) Patel et al. (1969) Roveri et al. (1980)

Average of proximal and distal values. Distal aorta based on combined area of media and adventitia.

circumferential (Gundiah et al., 2006; Farand et al., 2007; Timmins et al., 2010) the interlamellar elastic fibers are nonorthogonal (Davis, 1993; O’Connell et al., 2008). If non-orthogonal fibers do contribute, the absence of observed torsion indicates they are axially symmetric. We have treated the media as mechanically homogeneous (Dobrin, 1999; Stergiopulos et al., 2001), but the impact of possible structural and mechanical heterogeneities should be further investigated (Greenwald et al., 1997; Kim et al., 2009; Ning et al., 2010; Timmins et al., 2010). Identifying how and why elastin varies regionally is key to developing structural based elastin SEFs and understanding elastin’s physiological milieu.

Conflict of Interest statement There is no conflict of interest.

Acknowledgments The authors would like to thank Bentley Ge´rard for the excellent technical help. This work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council to J.M.G. and by a Discovery Accelerator Grant from the Natural Sciences and Engineering Research Council to R.E.S.

Appendix A. Supplementary information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech. 2012.05.034.

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