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Mechanical properties of rat thoracic and abdominal aortas
ARTICLE IN PRESS
Journal of Biomechanics 41 (2008) 2227–2236 www.elsevier.com/locate/jbiomech www.JBiomech.com
Mechanical properties of rat thoracic and abdominal aortas N. Assoula,b, P. Flaudc, M. Chaouata,d, D. Letourneura,b,, I. Bataillea,b a
INSERM, U698, Bio-inge´nierie Cardiovasculaire, Hoˆpital X. Bichat, 75018 Paris, France b BPC, Institut Galile´e, Universite´ Paris 13, 93430 Villetaneuse, France c Matie`re et Syste`mes Complexes, CNRS UMR 7057, Universite´ Paris 7, 75013 Paris, France d Service de Chirurgie Plastique, Hoˆpital Rothshild, 75012 Paris, France Accepted 16 April 2008
Abstract Mechanical properties of abdominal and thoracic arteries of 2 mm in diameter were determined from adults Wistar rats. A tensile testing instrument was used to obtain stress/strain curves with arteries immersed in physiological buffer at 37 1C. A displacement was applied on all arteries with various frequencies (1–7.5 Hz) and strains (5–60%). From each curve a Young modulus was obtained using a mathematical model based on a nonlinear soft tissue model. No influence of frequency on modulus was evidenced in the tested range. Abdominal aortas, which were found slightly thicker than thoracic aortas, were characterized by a higher modulus. Due to the interest of decellularized biological materials, we also used SDS/Triton treated arteries, and found that the chemical treatment increased modulus of thoracic arteries. Tensile tests were also performed on thoracic aortas in the longitudinal and transversal directions. Longitudinal moduli were found higher than transversal moduli and the difference could be related to the longitudinal orientation of collagen fibers. These data and mathematical model seem useful in the design of new vascular synthetic or biological prostheses for the field of tissue engineering. r 2008 Elsevier Ltd. All rights reserved. Keywords: Mechanical properties; Rat arteries; SDS/Triton treatment; Tensile tests; Young modulus
1. Introduction Most studies concerning biomechanical aorta evaluation deal with compliance calculation by means of pressure/ artery dimensions relationship (Mourlon-Le Grand et al., 1993; Van Gorp et al., 1995; Be´zie et al., 1998; MacWilliams et al., 1998; Zhao et al., 2000; Labat et al., 2001). Although these methods are interesting because pressure and artery diameter may be measured in situ, no correlation between biomechanical properties and rheological law is evidenced. Indeed, no universal value of Young modulus is obtained, mainly because of its dependence to measurement conditions. For example, Young modulus obtained by the use of a tensile testing instrument is given Corresponding author at: INSERM, U698, Bio-inge´nierie Cardiovasculaire, Universite´ Paris 13, 93430 Villetaneuse, France. Tel.: +33 1 49 40 40 90; fax: +33 1 49 40 30 08. E-mail address: [email protected] (D. Letourneur).
0021-9290/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2008.04.017
for two strain conditions (Katsuda et al., 2002), or stress/ stretch curves are directly given (Papadopoulos and Delp, 2003). Mathematical model by curve fitting is also rarely described (Orosz et al., 1999). Information about mechanical behavior of small caliber arteries like rat aortas is interesting to obtain, as a first approach to the design of small artificial arteries. Indeed, cardiovascular diseases constitute the first cause of mortality in the industrialized countries and patients may suffer a vessel wall thickening that causes sudden death or heavy surgical intervention. When the vascular material of the patient becomes insufficient for autologous transplantation, the damaged artery has to be replaced by an artificial vessel. For vessels larger than 6 mm diameter, artificial substitutes provide satisfying results. The problem remains for small calibers due to thrombosis and intimal hyperplasia (Kannan et al., 2005; Kakisis et al., 2005; Salacinski et al., 2001). Indeed, small caliber flexible prostheses presenting a non-thrombogenic internal surface remain to be designed. Among the possible ways, tissue
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engineering is an emerging field to find cell-compatible tubular synthetic or natural matrices as vascular substitutes (Chaouat et al., 2006; L’Heureux et al., 2006). These substitutes are designed to possess similar mechanical properties as native arteries (Salacinski et al., 2001; Laflamme et al., 2006; L’Heureux et al., 2007). In order to facilitate the design of tubular material that would be first implanted in the rat aorta, the main features of the native material have to be known (Zidi and Cheref, 2003). In addition, chemically treated arteries also constitute an interesting biological material for vascular replacement. Both native and treated rat aortas were thus evaluated because of the potential use of treated aortas as vascular scaffolds (Gomes et al., 2001; Allaire et al., 1997; Touat et al., 2006). Treated cadaveric human arteries were envisaged as possible sources but their low availability limited their widespread use (Dahl et al., 2003). From treated porcine aorta, matrix components were selectively removed to obtain two scaffold types, namely elastin and collagen scaffolds. Compared to elastin scaffolds and fresh aorta, aortic collagen scaffolds exhibited lower tensile moduli and strain at rupture (Lu et al., 2004). Porcine treated arteries (Dahl et al., 2003) were also used as a scaffold onto which vascular cells were seeded. In order to develop smalldiameter vascular grafts, dog carotids (internal diameter ¼ 3 mm) were treated and then seeded with host bonemarrow-derived cells (Debes and Fung, 1995). After 8 weeks, the vascular grafts evidenced the regeneration of the three elements of artery, namely endothelium, media and adventitia (Cho et al., 2005). These works emphasized the possible use of chemically treated arteries as biocompatible scaffolds. However, a good knowledge of their physical properties is thus required. This study aims at evaluating the mechanical properties of small-diameter arterial materials immersed in physiological buffer at 37 1C, using a tensile testing instrument and a curve fitting method. Using native and treated rat arteries, we studied the influence of tensile rate on Young moduli by varying the frequency. Arteries are also known to be anisotropic due to smooth muscle cells and matrix orientation. For example, biaxial tensile tests of square pieces of porcine coronaries evidenced artery anisotropy and a marked nonlinear elastic behavior in both directions (Prendergast et al., 2003; Lally et al., 2004). For this reason, tensile tests were carried out here in longitudinal and transversal directions. We also investigated the variation of mechanical properties along the vasculature by comparing Young moduli of thoracic and abdominal arteries. 2. Experimental part 2.1. Artery preparation Rats were adult male Wistar rats (Breeding Center Rene´ Janvier). A total of 30 rats were used of this study. The procedure and the animal care complied with the Principles
of Laboratory Animal Care formulated by the Institute of Laboratory Animal Resources. The studies were carried out under authorization number 006235 of the Ministe`re de l’Agriculture, France. General anesthesia was obtained by intra-peritoneal injection of pentobarbital (0.1 ml/100 g), which allowed a major sedation with spontaneous ventilation. For aorta removal, the abdominal wall was incised, the pericardium was pushed aside, and then aorta leaving the left ventricle and going down along the spinal column was located. For the thoracic arteries, a segment of about 3 cm was cut 2 cm below the aortic arch. For the abdominal arteries, a segment of about 4 cm was centered on the middle of the aorta and was cut. In order to estimate the in vivo strain of the artery, each section was seized between two forceps and measured before and after its removal. The in vivo strain ev was then defined as follows: v ¼
Lbefore Lafter 100. Lafter
(1)
Lbefore and Lafter are respectively the lengths of the sample before and after sampling. Taking into account this in vivo longitudinal strain, the strain values presented in Section 3 will most often be higher than 15%. The in vivo transversal strain being estimated around 7% (Maurice et al., 2005), low strains are presented for transversal assays. The removed arteries were left in a 0.9% NaCl solution (CDM Lavoisier Laboratories) in order to avoid drying. Forceps and scalpels were used to remove periadventitial tissue around the vessel, then a segment of approximately 1.5 cm was cut and placed in culture media (DMEM; Gibco) until tensile tests. A viability test using MTT (3-(4,5-dimethyldiazol-2-yl)-2,5-diphenyl tetrazolium bromide; Sigma) was used to evaluate the cell viability. We found that human vascular cells were functional for 24 h. In our experiments, mechanical tests were all performed within the 6 h after removal from the animals. The chemical treatment protocol was based on previous studies from our laboratory (Allaire et al., 1997) and was slightly modified. Successive baths were performed at 37 1C: 0.3% sodium dodecylsulphate (SDS) overnight bath, Phosphate buffer saline (PBS) for 30 min (repeated twice), 2.5% Triton bath for 30 min (repeated twice), PBS for 3 h (repeated three times), and PBS overnight. 2.2. Measurements The measurement device (Fig. 1A) is intended to test various soft materials and biomaterials in physiological conditions, namely immersed in physiological buffer at 37 1C. The nominal displacement range is 79 mm and the force range is 1 N. The force sensor (FGP instrument: nominal extent 1 N) is linked to the superior jaw while the displacement sensor (Schlumberger: nominal extent 79 mm) is joined to the inferior jaw. Longitudinal and transversal stretching were performed both on native and treated arteries. For longitudinal tests, the arteries were
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Fig. 1. (A) Whole measurement system: (1) driving modulus, (2) jaws, (3) thermostatic bath, (4) displacement sensor, (5) strength sensor. (B) Sample in longitudinal traction. (C) Sample in transversal traction.
opened over the whole length. The obtained rectangular samples were maintained on both ends by stuck pieces of paper (Fig. 1B). For transversal tractions, superior and inferior jaws maintain two fine stainless steel hooks (diameter: 0.2 mm, weight: 0.014 g) that are thread through the 3 mm length thoracic artery (Fig. 1C). An acquisition card (Keithley KPCMCIA 16AI/AO) and a computer are connected to the measurement system. A driving and data acquisition software has been locally developed under DOS in PASCAL programming language. The acquisition frequency was fixed to 300 points per second. A single triangular displacement was imposed, which total duration depended on the imposed frequency. Two simultaneous signals were obtained: the imposed triangular displacement signal and a measured force signal (Fig. 2). Two parameters were fixed for the displacement signal: (a) its total duration, which is the reverse of a signal frequency values (between 1 and 7.5 Hz) and (b) its amplitude that corresponds to a maximal strain (between 8% and 57%). Data obtained using the acquisition software arise in two columns, representing respectively force and displacement, both in Volts. These data were converted respectively into Newton and millimeters using a sensor calibration. For a given displacement, several experiments were performed on the same sample, by increasing frequency by steps of 1 Hz. Then, displacement was modified with an increase by steps of 4%, and the same frequency variation protocol was followed. The sample was removed after the last (maximal) displacement.
2.3. Calculations Tensile tests were used to determine rheological behavior of arteries, by exerting a traction force F on a sample. The sample is characterized by its initial length (L0), its width (l0) and its rectangular section (S0). The section S0 is related to the sample’s mass (m) and density (r1.0 g/cm3) (Chuong and Fung, 1986) of the vascular wall as follows: S0 ¼ V 0 =L0
(2)
with V 0 ¼ m=r.
(3)
Consequently, S0 ¼ m=rL0 ,
(4)
however, S0 ¼ l 0 e.
(5)
Finally, the artery thickness is e ¼ m=rL0 l 0 .
(6)
Assuming the non-compressibility of the sample, its volume is considered constant (V ¼ V0).Thus, S ¼ S0 L0 =L ¼ m=rL.
(7)
S is directly obtained from displacement measurement. The actual stress s is given by s ¼ F =S.
(8)
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0.25
1.8 Displacement Strength
0.2
1.4
Strength (N)
1.2 0.15 1 0.8 0.1 0.6 0.4
Displacement (mm)
1.6
0.05
0.2 0
0 0.0
0.1
0.2
0.3
0.4
0.5 0.6 Time (s)
0.7
0.8
0.9
1.0
Fig. 2. Strength (left scale) and displacement (right scale) versus time for one native thoracic rat artery in longitudinal traction (frequency ¼ 1 Hz; strain ¼ 40%).
s is reported as a function of Cauchy strain: l ¼ L=L0 .
then expressed as (9)
Since most biological soft tissues exhibit nonlinear viscoelastic rheological behavior, a model for nonlinear anisotropic viscoelastic tissue was used with quasi-linear viscoelasticity as introduced by Fung (1972), applied to uniaxial fibers (Flaud and Quemada, 1988; Decraemer et al., 1980). The s ¼ f(l) curve gives the rheological law of the material. For a nonlinear soft material model, s expression is (Flaud and Quemada, 1988): Z l l li sðlÞ ¼ E nðli Þ dli , (10) li 1 where s(l) and E represent respectively real stress, and incremental Young moduli, and n(li) represents a distribution function of recruited fibers versus strain. Considering that mechanical properties of arteries are directly linked to the presence of elastin and collagen, n(l) is given by the following formula (Flaud and Quemada, 1988): NnðlÞ ¼ N e dðl 1Þ þ ðN N e Þnc ðlÞ,
(11)
where N represents total activated fiber number, Ne elastin and (NNe) collagen fiber number. nc (l) is the distribution function of collagen recruited fibers. d(l1) is a Dirac and by definition d ¼ 0 if l6¼1, d6¼0 if l ¼ 1 and Rfunction b f ðxÞdðx 1Þ dx ¼ f ð1Þ for ap1pb. The common hya pothesis that all elastin fibers are recruited from the beginning of tensile test leads to a linear s/l relationship concerning elastin. It may also be possible that some collagen fibers take part to the very first part of s/l curves. The total stress is divided into two contributions, one from elastin and the other from collagen. The stress can be
Ne ðN N e Þ ðl 1Þ þ E c sðlÞ ¼ E e N N
Z
l 1
l li nc ðli Þ dli , li (12)
where Ee is the Young modulus of elastin fibers and Ec the Young modulus of collagen fibers. Eq. (12) is equivalent to Ne ðN N e Þ ðl 1Þ þ E c N N Z l Z l l nc ðli Þ dli nc ðli Þ dli . 1 li 1
sðlÞ ¼ E e
Then, Z l dsðlÞ Ne ðN N e Þ 1 ¼ Ee þ Ec nc ðli Þ dli dl N N 1 li 1 þl nc ðlÞ þ nc ð1Þ nc ðlÞ nc ð1Þ . l And finally, dsðlÞ Ne ðN N e Þ ¼ Ee þ Ec dl N N
Z 1
l
1 nc ðli Þ dli . li
(13)
If l-1 then s(l)-Ee(Ne/N)(l1) and ds(l)/dlEe(Ne/N), where Ne represents the number of firstly recruited fibers, namely essentially elastin fibers. All collagen fibers are recruited in a given finite range of l [1, lm], which implies that Z lm nc ðlÞ dl ¼ 1, (14) 1
where lm is the maximum Cauchy strain.
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Table 1 Representative Young moduli of native and treated aortas determined from a, b, c values in longitudinal and transversal directions Traction Longitudinal
Native abdominal aorta Native thoracic aorta Treated thoracic aorta
Transversal
Native thoracic aorta Treated thoracic aorta
a
b
c
Modulus (N/m2)
57.84 107 4.08 107 12.24 107
123.60 107 8.82 107 27.78 107
66.00 107 4.72 107 15.54 107
50.65 104 6.85 104 37.26 104
4.88 107 7.44 107
10.62 107 16.20 107
5.72 107 8.82 107
7.85 104 14.76 104
a, b, c were determined as described in Section 2 for one representative sample in each conditions. Young modulus (E) was determined from the equation: E ¼ ½3al4 þ 2bl3 þ cl2 l1m .
As
Upward Downward Polynomial (Upward)
80
d sðlÞ ðN N e Þ 1 nc ðlÞ ¼ Ec (15) 2 N l dl (nc(1) ¼ 0 because no collagen fiber is yet recruited at l ¼ 1), the following relationship is obtained: 2
d sðlÞ l N . (16) 2 E N N dl c e The expression Ec(NNe)/N corresponds to the effective collagen modulus Ec-eff, which represents the contribution of the collagen to the global modulus.From (14), we deduced Z lm 2 d sðlÞ l ¼ 1. (17) dl2 E c-eff 1 The best fit obtained from our experimental results is a fourth-order polynome:
nc ðlÞ ¼
sðlÞ ¼ ax4 þ bx3 þ cx2 þ dx þ e. Then, Z lm 2 4 d al þ bl3 þ cl2 þ dl þ e 1
dl
2
and finally lm E c-eff ¼ 3al4 þ 2bl3 þ cl2 1 .
Real stress (kN/m2)
2
60 40 20 0 1
1.1
1.2 1.3 Cauchy strain
1.4
1.5
Fig. 3. Real stress versus Cauchy strain of a native thoracic artery in longitudinal traction (frequency ¼ 1 Hz; strain ¼ 40%). The upward curve represents the increase in displacement (gray symbols). The downward represents the decrease (dark symbols) and the black line represents the polynomial fit (y ¼ 4.03E+06x4–1.70E+07x3+2.69E+ 07x2–1.89E+07x+4.98E+06; R2 ¼ 0.9998).
(18)
l E c-eff
¼ 1,
(19)
(20)
Calculated values for a, b, c in various conditions are reported in Table 1. 2.4. Statistics Values are means (7S.D.). Comparison of biomechanical properties between native thoracic and abdominal arteries, native and treated thoracic arteries were made using two-tailed paired Student’s t-tests. po0.05 was considered significant. 3. Results and discussion A device has been adapted to perform mechanical tests on small-diameter vessels (Fig. 1). As compared to a standard traction apparatus, the small size of biological samples (rat aortas with length of less than 1 cm, and 2 mm
diameter) leads to the use of (a) small apparatus (b) sensitive force and displacement sensors and (c) thermostatic water bath at 37 1C. A preliminary study was first carried out to accurately determine the linear relationship between force sensor response (in Volt) and the force (in Newton). The displacement sensor in Volt was then calibrated for displacement in millimeters. It was thus possible to measure force and displacement versus time for each solicitation of the sample. Fig. 2 is an example representing unprocessed data of a native thoracic rat artery submitted in longitudinal traction to a strain of 40% at 1 Hz. The given strain value corresponds to the maximum strain (at the top of the triangle). The force response for rat arteries is not linear, which suggests that Hooke’s law is not applicable for the samples and justifies a nonlinear approach. The displacement was converted to a Cauchy strain and the force was converted into stress as indicated in experimental part. A typical profile of real stress versus Cauchy strain [s ¼ f(l)] is shown in Fig. 3 for a native thoracic rat artery in longitudinal traction at a frequency of 1 Hz and a maximum strain of 40%. The stress/strain relationship is globally nonlinear and explained by the
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multi-components (collagen, elastin, cells, etc.) of the artery. A calculation method was developed which enables to obtain Young modulus by a fourth-order fitting (Fig. 3). From Eq. (2), we deduce that elastin fibers being recruited first, a linear portion would be observed at the beginning of the curves. Indeed, a linear portion may be evidenced in the curves. In this range, a linear fit is as good as the global polynomial fit. We may then suppose that the fibers recruited at the beginning of the tensile test are mainly elastin fibers, without excluding the presence of some collagen fibers. The contribution of these very-first recruited fibers in the global Young modulus may be evaluated by the d parameter in the expression of s(l) (cf. Eq. (18)), as d represents the slope when l-1. The upward and downward curves are not superimposed at a maximum strain of 40% (Fig. 3). This hysteresis decreases with low strains, as shown in Fig. 4, for native thoracic rat arteries in longitudinal traction at a strain of 16%. Considering the in vivo strain, which was estimated at ca. 27%, we investigated if rat arteries can be considered as totally reversible materials in a wide range of strains. Successive identical experiments were performed at high maximal strains (60%) to discriminate between a delayed elasticity or a partial destruction of artery. All upward curves were superimposed (data not shown), which leads to reject the destructive hypothesis. Upward curves that were not affected by a delay phenomenon were thus selected to obtain Young moduli. Arteries were then submitted to various frequencies from 1 to 7.5 Hz for a given maximal strain value (from 8% to 57%). This frequency range was chosen considering the human average value (1 Hz), the physiological frequency in Wistar rats (5 Hz) and a supra-physiological value in rats (7.5 Hz). Fig. 5A represents Young moduli versus maximal strain on the same native thoracic rat artery in longitudinal traction at various frequencies. The curves in Fig. 5A evidenced no influence of the frequency on the Young Upward Downward Polynomial (Upward)
Real stress (kN/m2)
20 16 12 8 4 0 1
1.04
1.08 1.12 Cauchy Strain
1.16
1.2
Fig. 4. Real stress versus Cauchy strain of a native thoracic artery in longitudinal traction (frequency ¼ 1 Hz; strain ¼ 16.2%). The upward curve represents the increase in displacement (gray symbols). The downward represents the decrease (dark symbols), and the black line represents the fit (y ¼ 4.85E+06x4–2.11E+07x3+3.48E+07x2–2.56E+ 07x+7.05E+06; R2 ¼ 0.9999).
modulus. This result confirms a previous study on arteries (Bauer et al., 1982). To evaluate the time dependence of artery rheological properties, traction rates were calculated and Young moduli were reported in Fig. 5B for different strains. It is noticeable that moduli did not depend on traction rate. Concerning the upward curves, this result means that in the studied frequency range, the rheological behavior of artery during the systolic load is purely elastic. This behavior is in agreement with a model of recruited elastic fibers as described by Fung and used in this study (see Section 2). On the other hand, the strain has an important influence on Young moduli. Indeed, biological components that constitute arteries are known to have different mechanical properties. For example, collagen modulus is higher than elastin modulus (Lu et al., 2004; Prendergast et al., 2003; Shewry et al., 2003). The increase in modulus versus maximum strain could be related to an increase in recruited collagen fibers. This is representative of the nonlinear character of a multi-component material (Zhou and Fung, 1997; Zhang et al., 2007). In addition, rupture was never reached at the maximal tested strain of 60% although this strain largely exceeds the longitudinal stretching measured in vivo (27%). Longitudinal tensile tests were also performed on rat abdominal and thoracic arteries to study the influence of artery location, namely above or below the separation to suprarenal arteries. The average Young moduli of thoracic and abdominal samples are represented at a rat physiological frequency of 5 Hz as a function of maximal strain (Fig. 6). Young modulus of abdominal arteries is higher than the one of thoracic arteries. The change of artery structure from thorax to abdomen is accompanied by change of mechanical properties in a way that could be rather unexpected. Indeed, beyond the thorax, the blood flow divides between both suprarenal and the abdominal arteries and the thoracic artery is subjected to a greater blood flow. This result was already reported by others (Guo and Kassab, 2003), who noticed that aorta wall thickness linearly decreases as blood pressure increases. In agreement with these observations, we calculated a mean aorta thickness for fresh abdominal arteries (638 mm7182) that was greater than the mean thickness of fresh thoracic arteries (537 mm7121). Treated animal or human tissues have been proposed as vascular scaffolds (Dahl et al., 2003; Cho et al., 2005; Allaire et al., 1997). A long-term function of the treated valve matrix was also evidenced (Dohmen et al., 2006; Erdbrugger et al., 2006). Fig. 7 represents Young modulus versus strain for various samples of native and SDS/Triton treated thoracic arteries in longitudinal traction at a frequency of 5 Hz. The Young moduli of the treated samples above 16% strain are significantly higher than those of the native samples. This result can be explained by the influence of the chemical treatment applied to the SDS/Triton treated artery. The same effect was found in pig carotids, in which a Young modulus increase of 54% was observed after treatment (Roy et al., 2005).
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Young Modulus (MN/m2)
2.0 1Hz 2Hz 3Hz 4Hz 5Hz 6Hz 7.5Hz
1.6 1.2 0.8 0.4 0.0
10
5
15
20
30 35 Strain (%)
25
40
45
50
55
60
Strain (%)
Young Modulus (MN/m2)
2.0
57 53
1.6
49 1.2
45 36
0.8
32 16
0.4
8 0.0 2
0
4
6
8
Rate of elongation (s
10
-1)
Fig. 5. (A) Young moduli versus maximal strain at different frequencies of a native thoracic artery in longitudinal traction. (B) Young moduli versus strain rate at different strains of a native thoracic artery.
1.6 Young modulus (MN/m2)
Native thoracic-longitudinal mode Native abdominal-longitudinal mode
1.2
0.8
∗∗
∗∗ ∗∗
∗
∗∗
∗∗
0.4
0.0 15
20
25
30
35
40
Strain (%) Fig. 6. Average Young modulus versus strain of native thoracic (K) and native abdominal (m) rat arteries in longitudinal traction at 5 Hz. Values are means7S.D. of six thoracic and three abdominal native arteries. * and ** corresponded to po0.05 and po0.01, respectively.
The increase of modulus may be due to a partial denaturation of collagen accompanied by a loss in elasticity, and thus an increase of stiffness. Arteries are known to be anisotropic materials because of extracellular matrix fibers and orientation of vascular cells. Collagen fibers are longitudinally aligned whereas
smooth muscle cells are radial. Taking this anisotropy into account, transversal tractions were also performed on normal and SDS/Triton treated thoracic arteries with strains between 8% and 36% (Fig. 8). Young moduli of native and treated samples appear quite similar in transversal assays. In contrast to longitudinal tractions
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Young modulus (MN/m2)
1.6 ∗
Treated thoracic-longitudinal mode
1.2 0.8
Table 2 Average Young moduli of native and treated arteries submitted to a frequency of 5 Hz and 20% strain
∗
Native thoracic-longitudinal mode
∗
∗
Traction
Samples
Modulus (N/m2)
Longitudinal
Native abdominal aortas Native thoracic aortas Treated thoracic aortas
59.0712.0 104 10.077.5 104 31.0715.0 104
Transversal
Native thoracic aortas Treated thoracic aortas
6.674.7 104 18.074.1 104
∗∗
0.4 0.0
20
15
25
30
35
40
Strain (%)
Values are mean7S.D. obtained from 18 rat aortas. Fig. 7. Young modulus versus strain of native (K) and treated (J) thoracic rat arteries in longitudinal traction at 5 Hz. Values are means7S.D. of three treated and five native thoracic arteries. * and ** corresponded to po0.05 and po0.01, respectively.
Young modulus [MN/m2]
1.6 Native thoracic-transversal mode Treated thoracic-transversal mode
1.2
0.8
0.4
∗
∗∗
∗
4. Conclusion
0.0 5
10
15
20
25
20%). In the rat physiological conditions, we could conclude that (i) the modulus of the treated arteries is higher than that of native arteries, (ii) the Young moduli for the longitudinal strains are higher than in transversal traction because of the geometrical structure of an aorta. In addition, we can also noticed that the Young modulus of abdominal arteries with a value of 59.0712.0 104 N/m2 in longitudinal traction is the highest.
30
35
40
Strain [%]
Fig. 8. Young modulus versus strain of native (E) and treated (B) thoracic rat arteries in transversal traction at 5 Hz. Values are means7S.D. of three native and three treated thoracic arteries. * and ** corresponded to po0.05 and po0.01, respectively.
where normal and treated artery moduli are different for strains beyond 16%, they tend to merge up in transversal tractions. Knowing the radial smooth muscle cell orientation, decellularization would be expected to have heavy consequences in the transversal direction. In fact, it is possible that the apparent transversal similarity between normal and treated arteries hides two antagonistic effects: a loss of radial contraction forces, given by the smooth muscle cells in living artery, but also a matrix stiffening as noted in longitudinal stretching. Only longitudinal modulus increases after chemical treatment because of the longitudinal orientation of collagen fibers, which have a major role in artery Young modulus. This behavior will require further investigations such as the seeding of cells on treated scaffolds. Young moduli for representative samples were determined at 5 Hz and 20% strain and corresponding coefficients a, b, and c from Eq. (20) are given in Table 1, for normal and treated arteries in both longitudinal and transversal modes. For comparison purposes, average Young moduli (n ¼ 18 samples) are presented in Table 2 for normal and treated thoracic arteries in longitudinal and transversal traction in physiological conditions (frequency of 5 Hz and maximal strain of
We have determined the Young moduli of thoracic and abdominal rat arteries. Longitudinal and transverse tractions were also compared for native and SDS/Triton treated thoracic arteries. Our results showed a variation of the mechanical properties according to the type of arteries and conditions of traction. This study corresponds to the first stage on the mechanical evaluation of new smalldiameter vascular prostheses (Chaouat et al., 2006) made of biologically compatible hydrogels (Autissier et al., 2007; Thebaud et al., 2007). These results will be used to design new vascular prostheses with appropriate mechanical properties. Conflict of interest For the manuscript entitled ‘‘Mechanical properties of rat thoracic and abdominal aortas’’ to be published in the Journal of Biomechanics, the authors N. Assoul, P. Flaud, M. Chaouat, D. Letourneur, and I. Bataille declare no conflict of interest. Acknowledgments This work was supported by Inserm, University Paris 7 and University Paris 13. We gratefully thank J.P. Guglielmi, J.L. Counord, and H. Del-Gallo (MSC, CNRS-University Paris 7) for the experimental device and their helpful discussions concerning encountered technical problems, A. Abdallian (LAGA, University Paris 13) for his help in the calculation part and L. Louedec (Inserm U 698) for animal care.
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Journal of Biomechanics 41 (2008) 2227–2236 www.elsevier.com/locate/jbiomech www.JBiomech.com
Mechanical properties of rat thoracic and abdominal aortas N. Assoula,b, P. Flaudc, M. Chaouata,d, D. Letourneura,b,, I. Bataillea,b a
INSERM, U698, Bio-inge´nierie Cardiovasculaire, Hoˆpital X. Bichat, 75018 Paris, France b BPC, Institut Galile´e, Universite´ Paris 13, 93430 Villetaneuse, France c Matie`re et Syste`mes Complexes, CNRS UMR 7057, Universite´ Paris 7, 75013 Paris, France d Service de Chirurgie Plastique, Hoˆpital Rothshild, 75012 Paris, France Accepted 16 April 2008
Abstract Mechanical properties of abdominal and thoracic arteries of 2 mm in diameter were determined from adults Wistar rats. A tensile testing instrument was used to obtain stress/strain curves with arteries immersed in physiological buffer at 37 1C. A displacement was applied on all arteries with various frequencies (1–7.5 Hz) and strains (5–60%). From each curve a Young modulus was obtained using a mathematical model based on a nonlinear soft tissue model. No influence of frequency on modulus was evidenced in the tested range. Abdominal aortas, which were found slightly thicker than thoracic aortas, were characterized by a higher modulus. Due to the interest of decellularized biological materials, we also used SDS/Triton treated arteries, and found that the chemical treatment increased modulus of thoracic arteries. Tensile tests were also performed on thoracic aortas in the longitudinal and transversal directions. Longitudinal moduli were found higher than transversal moduli and the difference could be related to the longitudinal orientation of collagen fibers. These data and mathematical model seem useful in the design of new vascular synthetic or biological prostheses for the field of tissue engineering. r 2008 Elsevier Ltd. All rights reserved. Keywords: Mechanical properties; Rat arteries; SDS/Triton treatment; Tensile tests; Young modulus
1. Introduction Most studies concerning biomechanical aorta evaluation deal with compliance calculation by means of pressure/ artery dimensions relationship (Mourlon-Le Grand et al., 1993; Van Gorp et al., 1995; Be´zie et al., 1998; MacWilliams et al., 1998; Zhao et al., 2000; Labat et al., 2001). Although these methods are interesting because pressure and artery diameter may be measured in situ, no correlation between biomechanical properties and rheological law is evidenced. Indeed, no universal value of Young modulus is obtained, mainly because of its dependence to measurement conditions. For example, Young modulus obtained by the use of a tensile testing instrument is given Corresponding author at: INSERM, U698, Bio-inge´nierie Cardiovasculaire, Universite´ Paris 13, 93430 Villetaneuse, France. Tel.: +33 1 49 40 40 90; fax: +33 1 49 40 30 08. E-mail address: [email protected] (D. Letourneur).
0021-9290/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2008.04.017
for two strain conditions (Katsuda et al., 2002), or stress/ stretch curves are directly given (Papadopoulos and Delp, 2003). Mathematical model by curve fitting is also rarely described (Orosz et al., 1999). Information about mechanical behavior of small caliber arteries like rat aortas is interesting to obtain, as a first approach to the design of small artificial arteries. Indeed, cardiovascular diseases constitute the first cause of mortality in the industrialized countries and patients may suffer a vessel wall thickening that causes sudden death or heavy surgical intervention. When the vascular material of the patient becomes insufficient for autologous transplantation, the damaged artery has to be replaced by an artificial vessel. For vessels larger than 6 mm diameter, artificial substitutes provide satisfying results. The problem remains for small calibers due to thrombosis and intimal hyperplasia (Kannan et al., 2005; Kakisis et al., 2005; Salacinski et al., 2001). Indeed, small caliber flexible prostheses presenting a non-thrombogenic internal surface remain to be designed. Among the possible ways, tissue
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engineering is an emerging field to find cell-compatible tubular synthetic or natural matrices as vascular substitutes (Chaouat et al., 2006; L’Heureux et al., 2006). These substitutes are designed to possess similar mechanical properties as native arteries (Salacinski et al., 2001; Laflamme et al., 2006; L’Heureux et al., 2007). In order to facilitate the design of tubular material that would be first implanted in the rat aorta, the main features of the native material have to be known (Zidi and Cheref, 2003). In addition, chemically treated arteries also constitute an interesting biological material for vascular replacement. Both native and treated rat aortas were thus evaluated because of the potential use of treated aortas as vascular scaffolds (Gomes et al., 2001; Allaire et al., 1997; Touat et al., 2006). Treated cadaveric human arteries were envisaged as possible sources but their low availability limited their widespread use (Dahl et al., 2003). From treated porcine aorta, matrix components were selectively removed to obtain two scaffold types, namely elastin and collagen scaffolds. Compared to elastin scaffolds and fresh aorta, aortic collagen scaffolds exhibited lower tensile moduli and strain at rupture (Lu et al., 2004). Porcine treated arteries (Dahl et al., 2003) were also used as a scaffold onto which vascular cells were seeded. In order to develop smalldiameter vascular grafts, dog carotids (internal diameter ¼ 3 mm) were treated and then seeded with host bonemarrow-derived cells (Debes and Fung, 1995). After 8 weeks, the vascular grafts evidenced the regeneration of the three elements of artery, namely endothelium, media and adventitia (Cho et al., 2005). These works emphasized the possible use of chemically treated arteries as biocompatible scaffolds. However, a good knowledge of their physical properties is thus required. This study aims at evaluating the mechanical properties of small-diameter arterial materials immersed in physiological buffer at 37 1C, using a tensile testing instrument and a curve fitting method. Using native and treated rat arteries, we studied the influence of tensile rate on Young moduli by varying the frequency. Arteries are also known to be anisotropic due to smooth muscle cells and matrix orientation. For example, biaxial tensile tests of square pieces of porcine coronaries evidenced artery anisotropy and a marked nonlinear elastic behavior in both directions (Prendergast et al., 2003; Lally et al., 2004). For this reason, tensile tests were carried out here in longitudinal and transversal directions. We also investigated the variation of mechanical properties along the vasculature by comparing Young moduli of thoracic and abdominal arteries. 2. Experimental part 2.1. Artery preparation Rats were adult male Wistar rats (Breeding Center Rene´ Janvier). A total of 30 rats were used of this study. The procedure and the animal care complied with the Principles
of Laboratory Animal Care formulated by the Institute of Laboratory Animal Resources. The studies were carried out under authorization number 006235 of the Ministe`re de l’Agriculture, France. General anesthesia was obtained by intra-peritoneal injection of pentobarbital (0.1 ml/100 g), which allowed a major sedation with spontaneous ventilation. For aorta removal, the abdominal wall was incised, the pericardium was pushed aside, and then aorta leaving the left ventricle and going down along the spinal column was located. For the thoracic arteries, a segment of about 3 cm was cut 2 cm below the aortic arch. For the abdominal arteries, a segment of about 4 cm was centered on the middle of the aorta and was cut. In order to estimate the in vivo strain of the artery, each section was seized between two forceps and measured before and after its removal. The in vivo strain ev was then defined as follows: v ¼
Lbefore Lafter 100. Lafter
(1)
Lbefore and Lafter are respectively the lengths of the sample before and after sampling. Taking into account this in vivo longitudinal strain, the strain values presented in Section 3 will most often be higher than 15%. The in vivo transversal strain being estimated around 7% (Maurice et al., 2005), low strains are presented for transversal assays. The removed arteries were left in a 0.9% NaCl solution (CDM Lavoisier Laboratories) in order to avoid drying. Forceps and scalpels were used to remove periadventitial tissue around the vessel, then a segment of approximately 1.5 cm was cut and placed in culture media (DMEM; Gibco) until tensile tests. A viability test using MTT (3-(4,5-dimethyldiazol-2-yl)-2,5-diphenyl tetrazolium bromide; Sigma) was used to evaluate the cell viability. We found that human vascular cells were functional for 24 h. In our experiments, mechanical tests were all performed within the 6 h after removal from the animals. The chemical treatment protocol was based on previous studies from our laboratory (Allaire et al., 1997) and was slightly modified. Successive baths were performed at 37 1C: 0.3% sodium dodecylsulphate (SDS) overnight bath, Phosphate buffer saline (PBS) for 30 min (repeated twice), 2.5% Triton bath for 30 min (repeated twice), PBS for 3 h (repeated three times), and PBS overnight. 2.2. Measurements The measurement device (Fig. 1A) is intended to test various soft materials and biomaterials in physiological conditions, namely immersed in physiological buffer at 37 1C. The nominal displacement range is 79 mm and the force range is 1 N. The force sensor (FGP instrument: nominal extent 1 N) is linked to the superior jaw while the displacement sensor (Schlumberger: nominal extent 79 mm) is joined to the inferior jaw. Longitudinal and transversal stretching were performed both on native and treated arteries. For longitudinal tests, the arteries were
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Fig. 1. (A) Whole measurement system: (1) driving modulus, (2) jaws, (3) thermostatic bath, (4) displacement sensor, (5) strength sensor. (B) Sample in longitudinal traction. (C) Sample in transversal traction.
opened over the whole length. The obtained rectangular samples were maintained on both ends by stuck pieces of paper (Fig. 1B). For transversal tractions, superior and inferior jaws maintain two fine stainless steel hooks (diameter: 0.2 mm, weight: 0.014 g) that are thread through the 3 mm length thoracic artery (Fig. 1C). An acquisition card (Keithley KPCMCIA 16AI/AO) and a computer are connected to the measurement system. A driving and data acquisition software has been locally developed under DOS in PASCAL programming language. The acquisition frequency was fixed to 300 points per second. A single triangular displacement was imposed, which total duration depended on the imposed frequency. Two simultaneous signals were obtained: the imposed triangular displacement signal and a measured force signal (Fig. 2). Two parameters were fixed for the displacement signal: (a) its total duration, which is the reverse of a signal frequency values (between 1 and 7.5 Hz) and (b) its amplitude that corresponds to a maximal strain (between 8% and 57%). Data obtained using the acquisition software arise in two columns, representing respectively force and displacement, both in Volts. These data were converted respectively into Newton and millimeters using a sensor calibration. For a given displacement, several experiments were performed on the same sample, by increasing frequency by steps of 1 Hz. Then, displacement was modified with an increase by steps of 4%, and the same frequency variation protocol was followed. The sample was removed after the last (maximal) displacement.
2.3. Calculations Tensile tests were used to determine rheological behavior of arteries, by exerting a traction force F on a sample. The sample is characterized by its initial length (L0), its width (l0) and its rectangular section (S0). The section S0 is related to the sample’s mass (m) and density (r1.0 g/cm3) (Chuong and Fung, 1986) of the vascular wall as follows: S0 ¼ V 0 =L0
(2)
with V 0 ¼ m=r.
(3)
Consequently, S0 ¼ m=rL0 ,
(4)
however, S0 ¼ l 0 e.
(5)
Finally, the artery thickness is e ¼ m=rL0 l 0 .
(6)
Assuming the non-compressibility of the sample, its volume is considered constant (V ¼ V0).Thus, S ¼ S0 L0 =L ¼ m=rL.
(7)
S is directly obtained from displacement measurement. The actual stress s is given by s ¼ F =S.
(8)
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0.25
1.8 Displacement Strength
0.2
1.4
Strength (N)
1.2 0.15 1 0.8 0.1 0.6 0.4
Displacement (mm)
1.6
0.05
0.2 0
0 0.0
0.1
0.2
0.3
0.4
0.5 0.6 Time (s)
0.7
0.8
0.9
1.0
Fig. 2. Strength (left scale) and displacement (right scale) versus time for one native thoracic rat artery in longitudinal traction (frequency ¼ 1 Hz; strain ¼ 40%).
s is reported as a function of Cauchy strain: l ¼ L=L0 .
then expressed as (9)
Since most biological soft tissues exhibit nonlinear viscoelastic rheological behavior, a model for nonlinear anisotropic viscoelastic tissue was used with quasi-linear viscoelasticity as introduced by Fung (1972), applied to uniaxial fibers (Flaud and Quemada, 1988; Decraemer et al., 1980). The s ¼ f(l) curve gives the rheological law of the material. For a nonlinear soft material model, s expression is (Flaud and Quemada, 1988): Z l l li sðlÞ ¼ E nðli Þ dli , (10) li 1 where s(l) and E represent respectively real stress, and incremental Young moduli, and n(li) represents a distribution function of recruited fibers versus strain. Considering that mechanical properties of arteries are directly linked to the presence of elastin and collagen, n(l) is given by the following formula (Flaud and Quemada, 1988): NnðlÞ ¼ N e dðl 1Þ þ ðN N e Þnc ðlÞ,
(11)
where N represents total activated fiber number, Ne elastin and (NNe) collagen fiber number. nc (l) is the distribution function of collagen recruited fibers. d(l1) is a Dirac and by definition d ¼ 0 if l6¼1, d6¼0 if l ¼ 1 and Rfunction b f ðxÞdðx 1Þ dx ¼ f ð1Þ for ap1pb. The common hya pothesis that all elastin fibers are recruited from the beginning of tensile test leads to a linear s/l relationship concerning elastin. It may also be possible that some collagen fibers take part to the very first part of s/l curves. The total stress is divided into two contributions, one from elastin and the other from collagen. The stress can be
Ne ðN N e Þ ðl 1Þ þ E c sðlÞ ¼ E e N N
Z
l 1
l li nc ðli Þ dli , li (12)
where Ee is the Young modulus of elastin fibers and Ec the Young modulus of collagen fibers. Eq. (12) is equivalent to Ne ðN N e Þ ðl 1Þ þ E c N N Z l Z l l nc ðli Þ dli nc ðli Þ dli . 1 li 1
sðlÞ ¼ E e
Then, Z l dsðlÞ Ne ðN N e Þ 1 ¼ Ee þ Ec nc ðli Þ dli dl N N 1 li 1 þl nc ðlÞ þ nc ð1Þ nc ðlÞ nc ð1Þ . l And finally, dsðlÞ Ne ðN N e Þ ¼ Ee þ Ec dl N N
Z 1
l
1 nc ðli Þ dli . li
(13)
If l-1 then s(l)-Ee(Ne/N)(l1) and ds(l)/dlEe(Ne/N), where Ne represents the number of firstly recruited fibers, namely essentially elastin fibers. All collagen fibers are recruited in a given finite range of l [1, lm], which implies that Z lm nc ðlÞ dl ¼ 1, (14) 1
where lm is the maximum Cauchy strain.
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Table 1 Representative Young moduli of native and treated aortas determined from a, b, c values in longitudinal and transversal directions Traction Longitudinal
Native abdominal aorta Native thoracic aorta Treated thoracic aorta
Transversal
Native thoracic aorta Treated thoracic aorta
a
b
c
Modulus (N/m2)
57.84 107 4.08 107 12.24 107
123.60 107 8.82 107 27.78 107
66.00 107 4.72 107 15.54 107
50.65 104 6.85 104 37.26 104
4.88 107 7.44 107
10.62 107 16.20 107
5.72 107 8.82 107
7.85 104 14.76 104
a, b, c were determined as described in Section 2 for one representative sample in each conditions. Young modulus (E) was determined from the equation: E ¼ ½3al4 þ 2bl3 þ cl2 l1m .
As
Upward Downward Polynomial (Upward)
80
d sðlÞ ðN N e Þ 1 nc ðlÞ ¼ Ec (15) 2 N l dl (nc(1) ¼ 0 because no collagen fiber is yet recruited at l ¼ 1), the following relationship is obtained: 2
d sðlÞ l N . (16) 2 E N N dl c e The expression Ec(NNe)/N corresponds to the effective collagen modulus Ec-eff, which represents the contribution of the collagen to the global modulus.From (14), we deduced Z lm 2 d sðlÞ l ¼ 1. (17) dl2 E c-eff 1 The best fit obtained from our experimental results is a fourth-order polynome:
nc ðlÞ ¼
sðlÞ ¼ ax4 þ bx3 þ cx2 þ dx þ e. Then, Z lm 2 4 d al þ bl3 þ cl2 þ dl þ e 1
dl
2
and finally lm E c-eff ¼ 3al4 þ 2bl3 þ cl2 1 .
Real stress (kN/m2)
2
60 40 20 0 1
1.1
1.2 1.3 Cauchy strain
1.4
1.5
Fig. 3. Real stress versus Cauchy strain of a native thoracic artery in longitudinal traction (frequency ¼ 1 Hz; strain ¼ 40%). The upward curve represents the increase in displacement (gray symbols). The downward represents the decrease (dark symbols) and the black line represents the polynomial fit (y ¼ 4.03E+06x4–1.70E+07x3+2.69E+ 07x2–1.89E+07x+4.98E+06; R2 ¼ 0.9998).
(18)
l E c-eff
¼ 1,
(19)
(20)
Calculated values for a, b, c in various conditions are reported in Table 1. 2.4. Statistics Values are means (7S.D.). Comparison of biomechanical properties between native thoracic and abdominal arteries, native and treated thoracic arteries were made using two-tailed paired Student’s t-tests. po0.05 was considered significant. 3. Results and discussion A device has been adapted to perform mechanical tests on small-diameter vessels (Fig. 1). As compared to a standard traction apparatus, the small size of biological samples (rat aortas with length of less than 1 cm, and 2 mm
diameter) leads to the use of (a) small apparatus (b) sensitive force and displacement sensors and (c) thermostatic water bath at 37 1C. A preliminary study was first carried out to accurately determine the linear relationship between force sensor response (in Volt) and the force (in Newton). The displacement sensor in Volt was then calibrated for displacement in millimeters. It was thus possible to measure force and displacement versus time for each solicitation of the sample. Fig. 2 is an example representing unprocessed data of a native thoracic rat artery submitted in longitudinal traction to a strain of 40% at 1 Hz. The given strain value corresponds to the maximum strain (at the top of the triangle). The force response for rat arteries is not linear, which suggests that Hooke’s law is not applicable for the samples and justifies a nonlinear approach. The displacement was converted to a Cauchy strain and the force was converted into stress as indicated in experimental part. A typical profile of real stress versus Cauchy strain [s ¼ f(l)] is shown in Fig. 3 for a native thoracic rat artery in longitudinal traction at a frequency of 1 Hz and a maximum strain of 40%. The stress/strain relationship is globally nonlinear and explained by the
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multi-components (collagen, elastin, cells, etc.) of the artery. A calculation method was developed which enables to obtain Young modulus by a fourth-order fitting (Fig. 3). From Eq. (2), we deduce that elastin fibers being recruited first, a linear portion would be observed at the beginning of the curves. Indeed, a linear portion may be evidenced in the curves. In this range, a linear fit is as good as the global polynomial fit. We may then suppose that the fibers recruited at the beginning of the tensile test are mainly elastin fibers, without excluding the presence of some collagen fibers. The contribution of these very-first recruited fibers in the global Young modulus may be evaluated by the d parameter in the expression of s(l) (cf. Eq. (18)), as d represents the slope when l-1. The upward and downward curves are not superimposed at a maximum strain of 40% (Fig. 3). This hysteresis decreases with low strains, as shown in Fig. 4, for native thoracic rat arteries in longitudinal traction at a strain of 16%. Considering the in vivo strain, which was estimated at ca. 27%, we investigated if rat arteries can be considered as totally reversible materials in a wide range of strains. Successive identical experiments were performed at high maximal strains (60%) to discriminate between a delayed elasticity or a partial destruction of artery. All upward curves were superimposed (data not shown), which leads to reject the destructive hypothesis. Upward curves that were not affected by a delay phenomenon were thus selected to obtain Young moduli. Arteries were then submitted to various frequencies from 1 to 7.5 Hz for a given maximal strain value (from 8% to 57%). This frequency range was chosen considering the human average value (1 Hz), the physiological frequency in Wistar rats (5 Hz) and a supra-physiological value in rats (7.5 Hz). Fig. 5A represents Young moduli versus maximal strain on the same native thoracic rat artery in longitudinal traction at various frequencies. The curves in Fig. 5A evidenced no influence of the frequency on the Young Upward Downward Polynomial (Upward)
Real stress (kN/m2)
20 16 12 8 4 0 1
1.04
1.08 1.12 Cauchy Strain
1.16
1.2
Fig. 4. Real stress versus Cauchy strain of a native thoracic artery in longitudinal traction (frequency ¼ 1 Hz; strain ¼ 16.2%). The upward curve represents the increase in displacement (gray symbols). The downward represents the decrease (dark symbols), and the black line represents the fit (y ¼ 4.85E+06x4–2.11E+07x3+3.48E+07x2–2.56E+ 07x+7.05E+06; R2 ¼ 0.9999).
modulus. This result confirms a previous study on arteries (Bauer et al., 1982). To evaluate the time dependence of artery rheological properties, traction rates were calculated and Young moduli were reported in Fig. 5B for different strains. It is noticeable that moduli did not depend on traction rate. Concerning the upward curves, this result means that in the studied frequency range, the rheological behavior of artery during the systolic load is purely elastic. This behavior is in agreement with a model of recruited elastic fibers as described by Fung and used in this study (see Section 2). On the other hand, the strain has an important influence on Young moduli. Indeed, biological components that constitute arteries are known to have different mechanical properties. For example, collagen modulus is higher than elastin modulus (Lu et al., 2004; Prendergast et al., 2003; Shewry et al., 2003). The increase in modulus versus maximum strain could be related to an increase in recruited collagen fibers. This is representative of the nonlinear character of a multi-component material (Zhou and Fung, 1997; Zhang et al., 2007). In addition, rupture was never reached at the maximal tested strain of 60% although this strain largely exceeds the longitudinal stretching measured in vivo (27%). Longitudinal tensile tests were also performed on rat abdominal and thoracic arteries to study the influence of artery location, namely above or below the separation to suprarenal arteries. The average Young moduli of thoracic and abdominal samples are represented at a rat physiological frequency of 5 Hz as a function of maximal strain (Fig. 6). Young modulus of abdominal arteries is higher than the one of thoracic arteries. The change of artery structure from thorax to abdomen is accompanied by change of mechanical properties in a way that could be rather unexpected. Indeed, beyond the thorax, the blood flow divides between both suprarenal and the abdominal arteries and the thoracic artery is subjected to a greater blood flow. This result was already reported by others (Guo and Kassab, 2003), who noticed that aorta wall thickness linearly decreases as blood pressure increases. In agreement with these observations, we calculated a mean aorta thickness for fresh abdominal arteries (638 mm7182) that was greater than the mean thickness of fresh thoracic arteries (537 mm7121). Treated animal or human tissues have been proposed as vascular scaffolds (Dahl et al., 2003; Cho et al., 2005; Allaire et al., 1997). A long-term function of the treated valve matrix was also evidenced (Dohmen et al., 2006; Erdbrugger et al., 2006). Fig. 7 represents Young modulus versus strain for various samples of native and SDS/Triton treated thoracic arteries in longitudinal traction at a frequency of 5 Hz. The Young moduli of the treated samples above 16% strain are significantly higher than those of the native samples. This result can be explained by the influence of the chemical treatment applied to the SDS/Triton treated artery. The same effect was found in pig carotids, in which a Young modulus increase of 54% was observed after treatment (Roy et al., 2005).
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Young Modulus (MN/m2)
2.0 1Hz 2Hz 3Hz 4Hz 5Hz 6Hz 7.5Hz
1.6 1.2 0.8 0.4 0.0
10
5
15
20
30 35 Strain (%)
25
40
45
50
55
60
Strain (%)
Young Modulus (MN/m2)
2.0
57 53
1.6
49 1.2
45 36
0.8
32 16
0.4
8 0.0 2
0
4
6
8
Rate of elongation (s
10
-1)
Fig. 5. (A) Young moduli versus maximal strain at different frequencies of a native thoracic artery in longitudinal traction. (B) Young moduli versus strain rate at different strains of a native thoracic artery.
1.6 Young modulus (MN/m2)
Native thoracic-longitudinal mode Native abdominal-longitudinal mode
1.2
0.8
∗∗
∗∗ ∗∗
∗
∗∗
∗∗
0.4
0.0 15
20
25
30
35
40
Strain (%) Fig. 6. Average Young modulus versus strain of native thoracic (K) and native abdominal (m) rat arteries in longitudinal traction at 5 Hz. Values are means7S.D. of six thoracic and three abdominal native arteries. * and ** corresponded to po0.05 and po0.01, respectively.
The increase of modulus may be due to a partial denaturation of collagen accompanied by a loss in elasticity, and thus an increase of stiffness. Arteries are known to be anisotropic materials because of extracellular matrix fibers and orientation of vascular cells. Collagen fibers are longitudinally aligned whereas
smooth muscle cells are radial. Taking this anisotropy into account, transversal tractions were also performed on normal and SDS/Triton treated thoracic arteries with strains between 8% and 36% (Fig. 8). Young moduli of native and treated samples appear quite similar in transversal assays. In contrast to longitudinal tractions
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Young modulus (MN/m2)
1.6 ∗
Treated thoracic-longitudinal mode
1.2 0.8
Table 2 Average Young moduli of native and treated arteries submitted to a frequency of 5 Hz and 20% strain
∗
Native thoracic-longitudinal mode
∗
∗
Traction
Samples
Modulus (N/m2)
Longitudinal
Native abdominal aortas Native thoracic aortas Treated thoracic aortas
59.0712.0 104 10.077.5 104 31.0715.0 104
Transversal
Native thoracic aortas Treated thoracic aortas
6.674.7 104 18.074.1 104
∗∗
0.4 0.0
20
15
25
30
35
40
Strain (%)
Values are mean7S.D. obtained from 18 rat aortas. Fig. 7. Young modulus versus strain of native (K) and treated (J) thoracic rat arteries in longitudinal traction at 5 Hz. Values are means7S.D. of three treated and five native thoracic arteries. * and ** corresponded to po0.05 and po0.01, respectively.
Young modulus [MN/m2]
1.6 Native thoracic-transversal mode Treated thoracic-transversal mode
1.2
0.8
0.4
∗
∗∗
∗
4. Conclusion
0.0 5
10
15
20
25
20%). In the rat physiological conditions, we could conclude that (i) the modulus of the treated arteries is higher than that of native arteries, (ii) the Young moduli for the longitudinal strains are higher than in transversal traction because of the geometrical structure of an aorta. In addition, we can also noticed that the Young modulus of abdominal arteries with a value of 59.0712.0 104 N/m2 in longitudinal traction is the highest.
30
35
40
Strain [%]
Fig. 8. Young modulus versus strain of native (E) and treated (B) thoracic rat arteries in transversal traction at 5 Hz. Values are means7S.D. of three native and three treated thoracic arteries. * and ** corresponded to po0.05 and po0.01, respectively.
where normal and treated artery moduli are different for strains beyond 16%, they tend to merge up in transversal tractions. Knowing the radial smooth muscle cell orientation, decellularization would be expected to have heavy consequences in the transversal direction. In fact, it is possible that the apparent transversal similarity between normal and treated arteries hides two antagonistic effects: a loss of radial contraction forces, given by the smooth muscle cells in living artery, but also a matrix stiffening as noted in longitudinal stretching. Only longitudinal modulus increases after chemical treatment because of the longitudinal orientation of collagen fibers, which have a major role in artery Young modulus. This behavior will require further investigations such as the seeding of cells on treated scaffolds. Young moduli for representative samples were determined at 5 Hz and 20% strain and corresponding coefficients a, b, and c from Eq. (20) are given in Table 1, for normal and treated arteries in both longitudinal and transversal modes. For comparison purposes, average Young moduli (n ¼ 18 samples) are presented in Table 2 for normal and treated thoracic arteries in longitudinal and transversal traction in physiological conditions (frequency of 5 Hz and maximal strain of
We have determined the Young moduli of thoracic and abdominal rat arteries. Longitudinal and transverse tractions were also compared for native and SDS/Triton treated thoracic arteries. Our results showed a variation of the mechanical properties according to the type of arteries and conditions of traction. This study corresponds to the first stage on the mechanical evaluation of new smalldiameter vascular prostheses (Chaouat et al., 2006) made of biologically compatible hydrogels (Autissier et al., 2007; Thebaud et al., 2007). These results will be used to design new vascular prostheses with appropriate mechanical properties. Conflict of interest For the manuscript entitled ‘‘Mechanical properties of rat thoracic and abdominal aortas’’ to be published in the Journal of Biomechanics, the authors N. Assoul, P. Flaud, M. Chaouat, D. Letourneur, and I. Bataille declare no conflict of interest. Acknowledgments This work was supported by Inserm, University Paris 7 and University Paris 13. We gratefully thank J.P. Guglielmi, J.L. Counord, and H. Del-Gallo (MSC, CNRS-University Paris 7) for the experimental device and their helpful discussions concerning encountered technical problems, A. Abdallian (LAGA, University Paris 13) for his help in the calculation part and L. Louedec (Inserm U 698) for animal care.
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