a fiber-based constitutive model predicts changes in amount and organization of matrix proteins with...

Biomech Model Mechanobiol (2013) 12:497510DOI 10.1007/s10237-012-0420-9

ORIGINAL PAPER

A fiber-based constitutive model predicts changes in amountand organization of matrix proteins with developmentand disease in the mouse aorta

Jeffrey K. Cheng Ivan Stoilov Robert P. Mecham Jessica E. Wagenseil

Received: 7 October 2011 / Accepted: 26 June 2012 / Published online: 12 July 2012 Springer-Verlag 2012

Abstract Decreased elastin in mice (Eln+/) yields afunctioning vascular system with elevated blood pressureand increased arterial stiffness that is morphologically dis-tinct from wild-type mice (WT). Yet, function is retainedenough that there is no appreciable effect on life span andsome mechanical properties are maintained constant. It isnot understood how the mouse modifies the normal devel-opmental process to produce a functioning vascular sys-tem despite a deficiency in elastin. To quantify changesin mechanical properties, we have applied a fiber-basedconstitutive model to mechanical data from the ascendingaorta during postnatal development of WT and Eln+/mice. Results indicate that the fiber-based constitutive modelis capable of distinguishing elastin amounts and identify-ing trends during development. We observe an increase inpredicted circumferential stress contribution from elastinwith age, which correlates with increased elastin amountsfrom protein quantification data. The model also predictschanges in the unloaded collagen fiber orientation withage, which must be verified in future work. In Eln+/mice, elastin amounts are decreased at each age, along with

Electronic supplementary material The online version of thisarticle (doi:10.1007/s10237-012-0420-9) contains supplementarymaterial, which is available to authorized users.

J. K. ChengDepartment of Biomedical Engineering, Washington University,St. Louis, MO, USA

I. Stoilov R. P. MechamDepartment of Cell Biology and Physiology, WashingtonUniversity School of Medicine, St. Louis, MO, USA

J. E. Wagenseil (B)Department of Biomedical Engineering, Saint Louis University,3507 Lindell Blvd., St. Louis 63103, MO, USAe-mail: [email protected]

the predicted circumferential stress contribution of elastin.Collagen amounts in Eln+/ aorta are comparable to WT,but the predicted circumferential stress contribution of colla-gen is increased. This may be due to altered organization orstructure of the collagen fibers. Relating quantifiable changesin arterial mechanics with changes in extracellular matrix(ECM) protein amounts will help in understanding develop-mental remodeling and in producing treatments for humandiseases affecting ECM proteins.

Keywords Constitutive modeling Elastin Developmental remodeling Arteries Arterial mechanics

1 Introduction

Elastin is an important extracellular matrix (ECM) proteinresponsible for providing elasticity to large arteries. It func-tions together with collagen to produce the classic nonlinearbehavior observed in the arteries of vertebrates with closedcirculatory systems (Shadwick 1999). The elasticity of thelarge arteries reduces the work done by the heart in expandingthe arterial wall as the stroke volume is ejected during systole(Greenwald 2007). A major challenge in understanding howelastin and collagen contribute to the functional propertiesof the arterial wall is identifying how their unique materialproperties together influence the ability of the wall to respondto hemodynamic stress.

Mathematical constitutive modeling has been informativein defining the contribution of elastin and collagen to arterialmechanics. Early constitutive models were phenomenolog-ical in nature, treating the arterial wall as a homogeneousmaterial [reviewed in (Vito and Dixon 2003)]. Later effortsfocused on developing constitutive models that were based onthe microstructure of the arterial wall [reviewed in (Holzapfel

123

498 J. K. Cheng et al.

and Ogden 2010). Holzapfel et al. (2000) proposed a consti-tutive model using two families of collagen fibers symmet-rically oriented with respect to the circumferential axis andembedded in an isotropic, elastin matrix. The model waslater extended to include two additional collagen fiber fam-ilies in the circumferential and axial direction (Baek et al.2007). Modified versions of the four-fiber-family model havebeen used to fit mechanical data of arteries from wild-type(WT) (Hansen et al. 2009) and genetically modified micewith alterations in ECM proteins (Gleason et al. 2008; Eberthet al. 2009; Wan et al. 2010). While these models have beensuccessfully applied to mature arteries, they have not yetbeen utilized to study arterial properties during developmentwhere hemodynamics as well as elastin and collagen amountsare changing.

In almost all animals with a closed circulatory system,elastin and collagen production in the artery wall beginswith the onset of pulsatile blood flow and increases dramati-cally until blood pressure stabilizes postnatally. In WT mice,elastin and collagen expression in the aorta begins aroundembryonic day (E) 14, peaks around postnatal day (P) 14, andreturns to low baseline levels by P30 (Kelleher et al. 2004).During this time, pressure and cardiac output increases sig-nificantly before reaching adult values around P30 (Huanget al. 2006; Ishii et al. 2001; Ishiwata et al. 2003; Wiesmannet al. 2000). Therefore, the protein amounts and consequentmechanical properties of the arterial wall change simulta-neously with the applied hemodynamic loads.

This study uses a fiber-based constitutive model to quan-tify changes in the mechanical properties of the aorta inWT and elastin haploinsufficient (Eln+/) mice from birththrough adulthood. Including Eln+/ animals allows usto determine how changing the mechanical behavior of thearterial wall by genetically reducing elastin amount influ-ences the functional contribution of both elastin and col-lagen throughout the developmental time course. Eln+/mice live until adulthood, but have smaller arterial diametersand thinner walls (Wagenseil et al. 2005). These mice alsohave increased lamellar units and increased systemic bloodpressure, similar to human patients with supravalvular aorticstenosis (SVAS) (Li et al. 1997). Despite these changes, thestressstrain behavior of adult Eln+/ arteries is similar toWT (Wagenseil et al. 2005). Collagen levels are not increasedto compensate for reduced elastin in adult Eln+/ arteries(Faury et al. 2003). The unique structural and mechanicaladaptation of Eln+/ arteries suggests that the developingarteries are able to remodel and reach a new cardiovascularset point or homeostatic state that is normal for these ani-mals, preventing the pathological remodeling expected withadult onset disease (Wagenseil and Mecham 2009).

We previously gathered mechanical data for developingWT and Eln+/ aorta, and some of these data were pre-sented in Le et al. 2011). Parameter estimates in this study

were made by fitting the model equations to the complete setof experimental data with constraints on the relative elastinand collagen stress contributions in the circumferential direc-tion. The constraints ensure that elastin contributes at least30 % at low pressures and collagen contributes at least 75 %at high pressures, as shown in different adult arteries fromvarious species (Dobrin and Canfield 1984; Ferruzzi et al.2011; Fonck et al. 2007). The constraints also allow the def-inition of low and high pressure to be defined separatelyfor each age and genotype. As elastin levels decrease from100 to 50 to 35 % of normal in adult mice, the overall shapeof the arterial pressure-diameter curve changes minimally,except that the onset of arterial stiffening occurs earlier inanimals with less elastin, implying that collagen fibers maybe engaged at different pressures in the different genotypes(Hirano et al. 2007).

Our model predictions are compared to data for elastin andcollagen protein amounts during development and in WT ver-sus Eln+/ aorta. Our results show that changes in the con-stitutive model parameter for elastin correlate with changesin elastin amounts through development and in WT versusEln+/ aorta. The model also predicts alterations in colla-gen fiber orientation and mechanical behavior that must beconfirmed in future studies.

2 Methods

2.1 Experimental data

Mechanical data for mouse ascending aortas were previ-ously gathered using a pressure myograph (Danish Myo-technology). The methods and results for a single inflationcycle at the in vivo length are presented in Le et al.2011). Briefly, male C57BL/6J WT and Eln+/ mice(Li et al. 1998) at approximately postnatal day (P) 3, 7,14, 21, 30, and 60 were used for all studies. The actualranges after P3 were P78, P1415, P2124, P3034, andP6064 (N = 510 for each age and genotype). All pro-tocols were approved by the Institutional Animal Careand Use Committee. Each aorta was excised and storedin physiologic saline solution (PSS) for 03 days beforetesting (Amin et al. 2011). For testing, each aorta wasmounted in the myograph in PSS at 37 C (Wagenseil et al.2005) and subjected to three constant-length inflation cyclesand three constant-pressure axial stretch cycles (Table 1).In the constant-length inflation cycles, the aorta was held at aconstant length and the myograph system was programmedto cyclically inflate the aorta three times step-wise from 0mmHg to a maximum of 90175 mmHg, depending on age,at a rate of 12 mmHg/s. The rate is considerably slower thanthe physiologic loading rate of an adult mouse aorta (about330 mmHg/s for a 40 mmHg pulse pressure at 600 bpm),

123

A fiber-based constitutive model 499

Table 1 Mechanical test protocols for different aged specimens

Age(days)

Average systolicP from (Le et al.2011)

Constant-length inflation protocols Constant-pressureaxial stretch protocols

PL and PH values(mmHg) for parameterfitting

W T Eln+/ Max P(mmHg)

Wait time(s)

Step P(mmHg)

Typical axialstretch

P (mmHg) Typical axialstretch

WT Eln+/

3 31 33 90 8 9 1.1, 1.2, 1.3 20, 40, 60 1.11.3 PL = 9 PL = 9PH = 45 PH = 45

7 46 48 120 8 12 1.1, 1.2, 1.3 25, 50, 75 1.11.3 PL = 12 PL = 12PH = 60 PH = 48

14 57 65 140 9 14 1.1, 1.2, 1.3 30, 60, 90 1.11.3 PL = 14 PL = 14PH = 98 PH = 70

21 84 90 160 10 20 1.1, 1.25, 1.4 40, 80, 120 1.11.4 PL = 20 PL = 20PH = 120 PH = 100

30 99 108 175 12 25 1.1, 1.3, 1.5 50, 100, 150 1.11.5 PL = 25 PL = 25PH = 125 PH = 100

60 112 127 175 12 25 1.1, 1.3, 1.5 50, 100, 150 1.11.5 PL = 25 PL = 25PH = 125 PH = 100

For constant-length inflation cycles, the myograph system (Danish Myotechnology) was programmed to cyclically inflate the aorta three timesfrom 0 mmHg to the maximum (max) pressure (P) in discrete pressure steps. Deflation occurred in a single step over 60 s for all aortas, allowingthe aorta to fully return to the starting dimensions, while minimizing total cycle time. The maximum pressure avoids damage to the aorta fromoverinflation and ranges from 1.5 to 3 times the average systolic pressure for each age (Le et al. 2011). The wait time provides enough time for thesystem to stabilize at each pressure and allows operator intervention if necessary to correct diameter tracking problems. The pressure steps providean overall rate of 12 mmHg/s from a starting pressure of 0 mmHg. The constant-length values were chosen to provide a range of axial stretchratios at and above the in vivo value and were varied for each aorta. Typical values are presented above. The average in vivo axial stretch ratio isapproximately 1.1 for all ages and genotypes (Supplemental Table 1). For constant- pressure axial stretch cycles, the aorta was cyclically lengthenedmanually three times from the same minimum and maximum axial stretches used in the inflation cycles by turning a micrometer attached to oneof the artery mounting rods at a constant rate of approximately 20 m/s. The constant-pressure values were chosen to provide a range of valuesabove and below the physiologic value. PL and PH values were used to constrain the elastin and collagen circumferential stress contributions in theconstitutive model for the low and high pressure regions. Note that the PL values are similar between genotypes, but PH is lower in Eln+/aorta compared with WT at all ages above P3

but soft biologic tissues are generally insensitive to loadingrates over about three orders of magnitude (Fung 1993).In the constant-pressure axial stretch cycles, the aorta wasinflated to a constant pressure and cyclically extended threetimes from near the in vivo stretch ratio to above the in vivostretch ratio by manually turning the micrometer attached toone of the artery mounting rods at a rate of approximately20 m/s. The in vivo stretch ratio (Supplemental Table 1)was determined by measuring the ratio of the in vivo andex vivo lengths of each aorta from the base of the heart tothe innominate artery using images taken before and afterexcision. The constant-pressure and maximum stretch val-ues varied with the age of the mouse. Due to experimen-tal difficulties, some aortas were subjected to more or lessthan six protocols, but parameter fitting was only performedfor aortas subjected to a minimum of five and a maximumof seven loading protocols. Lumen pressure, outer diame-ter, axial force, and calculated axial stretch were recordedfor each protocol at 1 Hz. Axial stretch with respect to theunloaded configuration was calculated based on the distancetraveled by the artery mounting rod. After testing, the aorta

was removed, cut into rings approximately 0.2 mm thicknessand imaged to measure the unloaded dimensions (Supple-mental Table 1). Assuming the aorta acts as an incompress-ible cylinder with no shear, the mean arterial wall stressesin the circumferential ( ) and axial (zz) direction can becalculated from experimentally measured values using therelations:

= Priro ri , (1)

zz = f + Pr2i

(r2o r2i

) , (2)

where P is the internal pressure, f is the measured axialforce, ri is the inner radius, and ro is the outer radius of theinflated aorta. The inner radius was not measured directly butwas calculated by:

ri =r2o

(R2o R2i

z

)

, (3)

123


where Ro and Ri are the inner and outer radii of the unl-oaded aorta and z is the axial stretch as defined inEq. 7.

For an axisymmetric cylinder subjected to nonlinear, largeelastic deformation in the absence of shear, the inflation andextension of the aorta can be described by the deformationgradient (F), right CauchyGreen strain (C), and the Greenstrain tensors (E):

[F] = diag {r , , z}, (4)[C] = diag

{2r ,

2 ,

2z

}, (5)

[E] = diag{

12

(2r 1

),

12

(2 1

),

12

(2z 1

)}, (6)

where i are the stretch ratios in each direction (r = radial, = circumferential, and z = axial)) defined by:

r = r R

, = rR , z =lL

, (7)

and r and R are the radii of the deformed and undeformedconfigurations, and l and L are the axial lengths in thedeformed and undeformed configurations.

2.2 Model equations

This study uses a fiber-based constitutive model, similar tothe four-fiber-family model that has been used to compare thepassive mechanical data from carotid arteries of WT mice togenetically modified mice with alterations in ECM proteins(Gleason et al. 2008; Eberth et al. 2009; Wan et al. 2010).We have reduced the number of collagen fiber families fromfour (circumferential, axial, and symmetrically angled withrespect to the circumferential axis) to two (symmetricallyangled fibers only) to reduce the number of fitted parameters.The motivation for the reduction in parameters is to focus ona set of parameters that will be more directly relatable tophysiologic changes in the aortic wall and to decrease thechance of obtaining non-unique parameter values. The orig-inal fiber-family model considered only two collagen fiberfamilies, although with separate material properties for themedial and adventitial layers (Holzapfel et al. 2000). We havealso included a passive smooth muscle cell (SMC) fiber fam-ily oriented in the circumferential direction that has beenused to model SMC mechanics in human cerebral (Baeket al. 2007) and mouse carotid arteries (Hansen et al. 2009).SMCs have been shown to have a preferential circumferentialorientation in mammalian aortas (Clark and Glagov 1985).We assume that the SMCs are completely passive during themechanical tests, as similar tests on adult mouse arteries afterkilling the SMCs with KCN showed no significant effectson the mechanical behavior (Faury et al. 1999). We assumethat the two collagen fiber families and the SMC fibers are

embedded in an amorphous, isotropic matrix dominated byelastin.

For an incompressible cylinder, the relevant principlestresses can be calculated as:

i i = F2i iW Eii

p(not summed), (8)

where i = r, , or z and p is the Lagrange multiplier. Inflationand extension in the absence of shear require r = r z = z = 0.

The total strain energy function is represented by the sumof the individual structural constituents elastin (e), collagen(c), and SMCs (m):W = W e + W c + W m . (9)Elastin is modeled as an isotropic, neo-Hookean solid:

W e = c12

(I1 3) , (10)

where c1 is a material parameter and the first invariant isI1 = 2r + 2 + 2z .Collagen is modeled as two fiber families with exponentialbehavior:

W c =2

k=1

c24c3

(ec3

(I k4 1

)2 1), (11)

where c2 and c3 are material parameters and I4 is the fourthinvariant for the kth fiber family as defined by

I k4 = C cos2(k

)+ 2C z sin

(k

)cos

(k

)

+Czz sin2(k

). (12)

where represents the angle of the fibers in the unloadedconfiguration with respect to the circumferential direction.It is assumed that the two collagen fiber families are orientedat angles . SMCs are modeled as a single, circumferen-tially oriented fiber family with exponential behavior:

W m = c44c5

(ec5(I41)2 1

), (13)

where c4 and c5 are material properties and I4 is the fourthinvariant, as defined in Eq. 12, for the single SMC fiber familyoriented at = 0.

2.3 Material parameters

The material parameters (c1c5) and unloaded collagen fiberangle () were determined by constrained nonlinear regres-sion to minimize the error between the experimental and pre-dicted circumferential and axial stress values for every datapoint, i , using the fmincon function in Matlab R2010b. Theerror is defined as:

123


error =

(,exp (i) ,pred (i)

)2

(,exp (i)

)2

+

(zz,exp (i) zz,pred (i)

)2

(zz,exp (i)

)2 (15)

The material parameters were constrained to the positivedomain, and was only allowed to vary between 0 and90 with 0 aligning with the circumferential axis. Parame-ter fitting was performed on data for each individual aorta.Multiple initial parameter estimates were randomly gener-ated to ensure a global minimum was found. Additionally,constraints on the relative stress contributions of elastin andcollagen were implemented to ensure physiologically rel-evant contributions from these constituents. It was assumedthat for the circumferential direction, elastin contributes 30 %of the total stress at low pressures and collagen contributes75 % of the total stress at high pressures. Specifically, theconstraints:

e / > 30 % for PL < P < PH, (16) c / > 75 % for P > PH,

were imposed where e is the circumferential stress fromelastin, is the total circumferential stress, c is the cir-cumferential stress from collagen, PL is the maximum pres-sure for the low-pressure region, and PH is the minimumpressure for the high-pressure region. The values of 30 and75 % for the elastin and collagen contributions to the totalcircumferential stress were chosen from a previous studyusing a four-fiber-family model for mouse carotid arteries(Hansen et al. 2009). While the exact percentages and pres-sure limits may vary for different species and artery types, itis well-accepted that elastin and collagen contribute at differ-ent pressure ranges (Dobrin 1997). PL and PH were assumedto bracket the linear region of the pressurediameter curveand were defined as the second derivative of an empiricalequation (Fonck et al. 2007) fitted to the pressurediameterdata for each aorta at the in vivo length:

PL = max(

2dout P

), (17)

PH = min(

2dout P

), where

dout = a + b [

1 exp( P

c

d

)], (18)

where dout is the external diameter, P is the measured pres-sure, and a, b, c, and d are fitted constants. The second deriv-ative was calculated for each discrete pressure step for everyaorta and averaged for each age and genotype. The pressuresteps that corresponded with the maximum and minimumof the average second derivative values were used to obtain

PL and PH, respectively, for each group. The average val-ues (Table 1) were subsequently used to enforce the relativestress contributions when fitting material parameters for eachaorta. To enforce the constraints in Eq. 16, a penalty functionwas included in the final minimization function:

min _error = error+

(penalty (i))2 (19)where penalty(i) is a penalty function applied to each datapoint, i , to enforce the minimum circumferential stress con-tributions of elastin and collagen in the appropriate pressurerange. The penalty function is:

penalty (i) = 0.3 e

for PL < P (i) < PH

and e

< 0.3, (20)

penalty (i)=0.75 c

for P (i)> PH and

c


the samples suspended in Milli-Q ultra pure water and fil-tered using 0.45 m Ultrafree-MC microcentrifuge tubes(Amicon). Hydrolyzed samples were prepared for analysisby derivatization with 6-aminoquinolyl-N-hydroxysuccin-imidyl carbamate using the AccQ-Fluor reagent kit (Waters).

Desmosine quantification was carried out using a compet-itive ELISA according to the methods developed by Rahman2009). Purified desmosine, isodesmosine, rabbit primaryantibody to desmosine/isodesmosine, and desmosine/isodes-mosine conjugated to ovalbumin were provided by Dr. BarryStarcher (University of Texas Health Science Center, Tyler,Texas). Secondary peroxidase labeled goat anti-rabbit IgGantibody and microtiter plates were purchased as part of acommercially available ELISA kit (KPL).

Quantification of hydroxyproline was carried out byreverse phase HPLC. A Beckman HPLC, System Gold,equipped with a Programmable Solvent Module 126, DiodeArray Detector Module 168, and Autosampler 508 was usedin conjunction with a Waters AccQ.Tag 3.9 150 mm C18Reverse phase Silica base analytical HPLC Column run at39 C. Sample detection was at 260 and 275 nm. A modifi-cation of the Waters amino acid analysis method was devel-oped for the simultaneous separation and quantification ofhydroxyproline with other amino acids in the protein hydro-lyzate. Eluent A consisted of 400 ml of Waters 10 elu-ent buffer A, containing 19 % NaAc+ 13 % Triethylaminediluted in 4 l of mQ water (pH 5.13). Eluent B was 100 %Acetonitrile. The column was run at a flow rate of 1 ml/ minstarting with 100 % eluent A followed by eluent B in a seriesof linear gradients as follows: from 1 to 2.5 % beginning at0.5 min, from 2.5 to 5 % beginning at 16 min, from 5 to 9 %at beginning 21 min, from 9 to 17 % beginning at 22 min,and from 17 to 20 % beginning at 32.5 min. At 38 min, eluentA was replaced by water. At 40 min, eluent B was increasedto 60 % over 1 min, and at 43 min, eluent B was loweredto 17 % over 1 min. After 1 additional minute, water wasreplaced with eluent A, and at 45 min, eluent B was reducedto 0 % to re-equilibrate the column until data acquisition at60 min.

2.5 Statistics

A general linear model (GLM) was used to determine theeffects of age, genotype, and interactions between age andgenotype on the fitted material parameters and protein quan-tification data. Comparisons between ages were performedusing ANOVA followed by the Tukeys HSD post-hoc test.Additional comparisons between genotypes at each age wereperformed using two-tailed t tests assuming unequal vari-ance. Averages are presented as mean SD. All analyseswere performed with SPSS software (IBM). P < .05 is con-sidered significant.

600

800

1000

1200

1400

1600

1800

0 40 80 120 160

diam

eter

(m)

pressure (mmHg)

P30 WTP30 Eln+/-

Fig. 1 Representative pressure versus diameter curves for a singleinflation cycle at the in vivo length of P30 aortas from WT and Eln+/mice (Le et al. 2011). Arrows indicate PL and PH as determined fromthe second derivative of an empirical equation fit to the data for eachaorta (Eqs. 17 19). PL values are similar between genotypes, but PH islower in Eln+/ aorta compared with WT. PL and PH were averagedfor each age and genotype and used for constraining elastin and collagencontributions in the circumferential direction for the constitutive model.Axial contributions and SMC contributions were not constrained in themodel

3 Results

A pressurediameter plot of representative P30 WT andEln+/ aortas at the in vivo length shows the differencein mechanical behavior between the two genotypes (Fig. 1).Eln+/ aortas have significantly smaller diameters at mostpressures. Arrows indicate the inflection points, PL and PH,used to define the pressure limits for the constraints on elas-tin and collagen contributions in the model. PL is similarbetween genotypes for all ages, while PH is 1225 mmHglower in Eln+/ aorta than WT for all ages above P3(Table 1). PL and PH values were determined from the sec-ond derivative of an empirical equation (Eqs. 1719) fitted tothe pressurediameter data of each aorta at the in vivo length.The penalty constraints enforce a minimum 30 % contribu-tion of elastin toward the total circumferential stress in thelow- to mid-pressure range (between PL and PH) and a mini-mum 75 % contribution of collagen at high pressures (greaterthan PH).

The experimental data and modeling results for all sixmechanical testing protocols for representative P30 WT andEln+/ aortas are shown in Fig. 2. Similar plots for all agesare shown in Supplemental Figs 14. Overall, the predictedpressure values follow the experimental pressures and seemto fit better at the older ages. The predicted force values oftenunderestimate the experimental forces at the lowest and high-est diameter values and also seem to fit better at the older ages.The underestimation of forces at high circumferential stretchvalues was also observed in the original two fiber-familymodel (Holzapfel et al. 2000) and may be a consequence of

123


8001000

12001400

11.05

1.11.15

1.2-5

05

1015

20

outer diam (um)axial stretchaxi

al fo

rce

(mN)

600 80010001200

14001600

11.05

1.11.15

1.20

50

100

150

200

outer diam (m)axial stretch

pres

sure

(mmH

g)

exp datapred data

a bP30 WT

8001000

12001400

11.05

1.11.15

1.20

50

100

150

200

outer diam (um)axial stretch

pres

sure

(mmH

g)

exp datapred data

5001000

15002000

11.05

1.11.15

1.2-5

05

1015

20

outer diam (um)axial stretch

axi

al fo

rce

(mN)

c dP30 WT P30 Eln+/- exp datapred data

exp datapred data

P30 Eln+/-

Fig. 2 Experimental data (exp data) and model predictions (pred data)for the three constant-length inflation and three constant-pressure axialstretch mechanical test protocols for the same representative P30 aortasas Fig. 1 for WT (a, c) and Eln+/ (b, d) mice. Panels a and b show

pressure versus outer diameter (diam) and axial stretch ratio, while pan-els c and d show axial force versus outer diameter and axial stretch ratio.Representative graphs for all ages are shown in Supplemental Figs 14

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80

50

100

150

200

250

300

circ stretch

circ

stre

ss (k

Pa)

circ

stre

ss (k

Pa)

exptotalelastincollagenSMC

a

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.80

50

100

150

200

250

300

circ stretch

bP30 WTexptotalelastincollagenSMC

P30 Eln+/-

Fig. 3 Circumferential (circ) stress versus circumferential stretch ratiofor the inflation cycle at the in vivo length for the same representativeP30 aortas as Fig. 1 for WT (a) and Eln+/ (b) mice. Experimentalstress (exp) and total predicted stress (total), as well as the predictedstress contributions of each constituent (elastin, collagen, and SMCs),

are shown. The elastin contribution is slightly lower, while the collagencontribution is higher in Eln+/ aorta compared with WT. The pre-dicted SMC contribution is minimal in both genotypes. Representativegraphs for all ages are shown in Supplemental Figs 56

assuming isotropic elastin behavior or not including an indi-vidual family of collagen fibers oriented in the axial direction.

A plot of the predicted circumferential stresses for thesame aortas as Fig. 2 against circumferential stretch for theinflation protocol at the in vivo length shows the contribu-tions from individual artery constituents (elastin, collagen,and SMCs) compared with the total predicted and experi-mental stresses (Fig. 3). At the in vivo length, the aorta is

stretched axially, decreasing the diameter compared with theunloaded state, so the starting circumferential stretch ratiocan be


0E+02E-44E-46E-48E-41E-3

c4 (SMC)

012345

c5 (SMC)

05

101520253035

P03 P07 P14 P21 P30 P60

P03 P07 P14 P21 P30 P60

P03 P07 P14 P21 P30 P60

P03 P07 P14 P21 P30 P60

kPa

kPa

kPa

c1 (Elastin)

020406080

100

P03 P07 P14 P21 P30 P60

P03 P07 P14 P21 P30 P60

P03 P07 P14 P21 P30 P60

c2 (Collagen)

0

0.5

1

1.5

2c3 (Collagen)

010203040506070

deg

a

00.20.40.60.8

1Rsqg

d

fe

c

bWTEln+/-

WTEln+/-

WTEln+/-

WTEln+/-

WTEln+/-

WTEln+/-

WTEln+/-

*

*

*

*

(Collagen)*

*

Fig. 4 Average predicted parameter (af) and R2 (g) values for theconstitutive model. Parameters were determined for individual WTand Eln+/ aortas via constrained nonlinear least squares regressionand then averaged for each age and genotype. Parameters for eachindividual aorta are provided in Supplemental Table 1. For clarity,

significant differences between ages are not shown, but are discussedin the text. The parameters c1, c2, and are significantly affected byage (P < .001). P < .05 between WT and Eln+/. N = 5 10 foreach age and genotype. Mean SD

hence low stretch. At higher pressures and stretches, whenthe anisotropic, nonlinear collagen begins to contribute anenforced minimum of 75 % to the total circumferential stress,the model usually matches the experimental stresses within10 %. Predicted circumferential stress values for the SMCsare near zero, showing that as modeled, they do not contributeto the passive mechanical behavior of the mouse aorta. Wechose to focus on the circumferential stress behavior at the invivo length, because that is the most physiologically relevantloading configuration. However, predicted axial stress contri-butions for each constituent can also be compared. Graphs ofthe axial stress versus axial stretch ratio for the axial stretchprotocols at different constant pressures show similar behav-ior to the circumferential direction (not shown). SMCs do notcontribute to the axial stress, because they are assumed to beoriented in the circumferential direction. Elastin contributeslinearly and is isotropic, so the axial behavior is identical

to the circumferential behavior. Collagen contributes non-linearly, and although the minimum contribution was notconstrained, the model predicts that collagen contributes6080 % of the total axial stress at the higher axial stretchratios.

The fitted parameters for each individual aorta are shownin Supplemental Table 1. The average fitted material param-eters and R2 values are shown in Fig. 4. The average materialparameters for elastin, c1, and two of the parameters for colla-gen, c2 and , are significantly affected by age (P < .001).For elastin, the parameter c1 increases between successiveages from P3 to P21 in WT (P < .02) and from P7 to P21and P30 to P60 in Eln+/ aorta (P < .02). The parameter c1approximately quadruples in both genotypes from P3 to P21.For collagen, the parameter c2 increases between successiveages from P7 to P21 in WT (P < .004) and from P14 to P21 inEln+/ aorta (P < .002). The parameter c2 approximately

123


triples in both genotypes from P3 to P21. From P30 to P60,c2 decreases 40 % in WT aorta (P < .02). The unloadedcollagen fiber angle, , decreases in angle, toward a morecircumferential orientation, with age, and the effect is morepronounced in Eln+/ than in WT aorta. For example, inP3 Eln+/ aorta is significantly different between every ageafter P7 (P < .0007), while in P3 WT aorta is only signif-icantly different between P14 and P60 (P < .04). Overall, decreases from 50 at P3 to 43 at P60 in WT aorta andfrom 60 at P3 to 43 at P60 in Eln+/ aorta. The averageR2 value is 0.69 0.11 for all ages, showing a reasonablefit of the model to the experimental data. As suggested bySupplemental Figs 14, the average R2 value is 20 % lowerfor P3 and P7 (average = 0.58 0.17) than the older ages(average = 0.72 .07) (P < .001), indicating that modifica-tions to the model assumptions may be necessary to providea better fit at the younger ages.

In comparing material parameters across genotypes, theelastin parameter, c1, for Eln+/ aorta is 3040 % less thanWT beginning at P7 and continuing through P21 (P < .002).One of the collagen parameters, c2, is 30 % lower in Eln+/aorta compared with WT at P14 (P < .002). The unloadedcollagen fiber angle, , is 1520 % higher in Eln+/ aortacompared with WT at P3 and P21 (P < .002). We found sig-nificant interactions between age and genotype for the elas-tin parameter, c1, and the unloaded collagen fiber angle, (P < .03). Similar trends in parameter values, including dif-ferences between genotypes and ages, were observed whenthe model was fit to mechanical data from the left commoncarotid artery of WT and Eln+/ mice from P3 to P60.

The circumferential stress calculated from the mechan-ical data at the average systolic arterial blood pressure foreach age and genotype (Le et al. 2011) is similar in WTand Eln+/ aorta for most ages, until P60 when circumfer-ential stress in the Eln+/ aorta is 30 % higher than WT(P < .001) (Fig. 5a). This behavior is also observed inthe total predicted circumferential stress from the model(Fig. 5b). The 25 % increase in total predicted circumfer-ential stress in P60 Eln+/ aorta (P < .001) is due to a30 % increase in the predicted collagen stress contributioncompared with WT (P < .001). Interestingly, the predictedcircumferential stress contribution of elastin is higher, loweror the same in Eln+/ and WT aorta depending on the age.At P3, the predicted contribution of elastin is increased 35 %in Eln+/ aorta compared with WT (P = .04), and at P7,the predicted contribution of elastin is increased 30 % inWT compared with Eln+/ aorta (P = .003). There areno significant differences in the predicted circumferentialstress contribution of elastin at any of the older ages. Thecalculated and predicted axial stresses for the same loadingconditions show similar behavior (not shown). A plot of thecircumferential stress contributions from elastin and colla-gen as a ratio of the total circumferential stress reveals a

0

50

100

150

200

250

300

0 10 20 30 40 50 60

exp

circ

stre

ss (k

Pa)

postnatal age (days)

a

0

50

100

150

200

250

300

0 10 20 30 40 50 60


b

WTEln+/-

WT, total

WT, elastinWT, collagen

Eln+/-, total

Eln+/-, elastinEln+/-, collagen

*

*

pred

circ

stre

ss (k

Pa)

*

*

*

Fig. 5 Average experimental (exp) (a) (Le et al. 2011) and predicted(pred) (b) circumferential (circ) stress in WT and Eln+/ aorta at thein vivo length and average systolic pressure for each age and genotype.Systolic pressures are found in Table 1. Note that the predicted stressincreases with age, but is similar in WT and Eln+/ aorta at most ages.The large increase in predicted circumferential stress for Eln+/ aortacompared with WT at P60 comes from an increase in the predicted col-lagen stress contribution. For panel a, = P < .05 between WT andEln+/. For panel b, = P < .05 between WT and Eln+/ at P3and P7 for the elastin stress and at P60 for the collagen and total stress.N = 5 10 for each age and genotype. Mean SD

1525 % lower contribution from elastin and 10 % highercontribution of collagen in Eln+/ aorta compared to WT(Fig. 6). The difference is significant at P7 and P14 (P < .01)and becomes insignificant at P21, only to diverge again andbecome significant at P30 and P60 (P < .001). Similarbehavior is seen for the axial stress contributions of elastinand collagen as a ratio of the total axial stress (not shown).

Quantification of total desmosine, a cross-link specificto mature elastin, is presented in Fig. 7a. Desmosineamounts are significantly affected by age in both genotypes(P < .001). There are increases in desmosine amounts foreach successive age from P3 to P21 in WT aorta (P < .03)and between P7 and P30 in Eln+/ aorta (P < .05).Desmosine amounts increase 16-fold in WT aorta and 12-fold in Eln+/ aorta between P3 and P30. Desmosineamounts are reduced 3050 % in Eln+/ aorta compared

123


0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

pred

circ

stre

ss ra

tio


WT, collagenWT, elastin Eln+/-, elastin

Eln+/-, collagen

*

**

**

*

*

*

Fig. 6 Mean predicted (pred) circumferential (circ) stress contribu-tions from elastin and collagen as a ratio of the total circumferentialstress for WT and Eln+/ aorta at the in vivo length and average sys-tolic pressure for each age and genotype. Systolic pressures are foundin Table 1. Predicted stress contributions from the SMCs are negligible.Note that Eln+/ aorta is predicted to have lower elastin and highercollagen circumferential stress ratio contributions. Error bars are omit-ted for clarity. = P < .05 between WT and Eln+/. N = 5 10for each age and genotype

0

0.2

0.4

0.6

0.8

1

1.2

1.4

P03 P07 P14 P21 P30 P60

P03 P07 P14 P21 P30 P60

Desmosinea

0

5

10

15

20

25

Hydroxyprolineb

mol

mol

**

*

*

WTEln+/-

WTEln+/-

Fig. 7 Mean values for total desmosine (a), an elastin specific cross-link, and hydroxyproline (b), an amino acid abundant in collagen, perascending aortic segment for each age and genotype. For clarity, signif-icant differences between ages are not shown, but are discussed in thetext. Desmosine and hydroxyproline amounts are significantly affectedby age (P < .001). = P < .05 between WT and Eln+/. N = 56for each age and genotype. Mean SD

with WT at P21 and older (P < .05). P21 coincides withthe age where elastin gene expression begins declining inthe WT mouse aorta (Kelleher et al. 2004). Quantificationof total hydroxyproline, an amino acid abundant in collagen,

is shown in Fig. 7b. Hydroxyproline amounts are signifi-cantly affected by age in both genotypes (P < .001). Thereare increases in hydroxyproline amounts between successiveages from P7 to P30 in WT aorta (P < .05) and from P3 toP14 and P21 to P30 in Eln+/ aorta (P < .05). Hydroxy-proline amounts increase 14-fold in both genotypes fromP3 to P30. Between P30 and P60, hydroxyproline amountsdecrease 30 % in the WT aorta (P < .01). At P21, there is50 % less hydroxyproline in Eln+/ aorta compared withWT (P < .001), but there are no significant differencesbetween genotypes at any other age. We found significantinteractions between age and genotype for desmosine andhydroxyproline amounts (P < .001). Along with desmo-sine and hydroxyproline amounts, the size of the aorta willincrease with age. Using the in vivo length, unloaded diam-eter, and unloaded thickness of the aorta for each age andgenotype (Le et al. 2011), we calculated the approximatewall volume of the aorta. Normalizing the desmosine andhydroxyproline values by the wall volume does not changethe observed trends in Fig. 7.

4 Discussion

A fiber-based constitutive model was used to fit mechani-cal data from WT and Eln+/ aortas throughout postnataldevelopment. As modeled, passive SMCs contribute mini-mally to the total circumferential stress in the aortic wall, andthe major contributors are elastin and collagen. The amountof elastin and collagen in each aorta was measured by quan-tifying desmosine and hydroxyproline. The model fits themechanical data from older ages (P14P60) better than fromearlier ages (P3P7), suggesting that the mechanical proper-ties or relative contributions of elastin, collagen, and SMCsmay be different in early postnatal development. The elas-tic lamellae between cell layers are not fully connected andpresumably not fully functional mechanically, until about P7in the mouse aorta (Davis 1995). However, the mechanicalmodel presented here for all time points predicts changesin elastin and collagen stress contributions that are consis-tent with measured changes in protein amounts with age anddisease.

In examining the best fit values of the model parametersover postnatal development, multiple trends are observed.First, there is an increase in the parameters c1 (elastin) and c2(collagen) in WT and Eln+/ aortas up to P21 or P30. Thistrend coincides with desmosine and hydroxyproline amountsin WT and Eln+/ aortas that increase with age up to P21or P30. Desmosine and hydroxyproline amounts are directlyproportional to elastin and collagen amounts, respectively.The changes in model parameters and elastin and collagenamounts with age match elastin and collagen gene expres-sion data for the WT mouse aorta, where expression begins

123


declining around P21 (Kelleher et al. 2004). Interestingly, c1in the Eln+/ aorta continues to increase up to P60, whileEln+/ desmosine levels continue to increase up to P30. Incontrast, there is a clear peak in c1 magnitude and desmosinecontent at P21 for the WT aorta. Although we do not havegene expression data for Eln+/ aorta, it is possible thathigh elastin expression is prolonged past P21 in these micein an attempt to increase total elastin amounts. The collagenparameter, c2, increases significantly up to P21 and decreasesbetween P30 and P60 in both genotypes, approximately mir-roring the changes in hydroxyproline amounts in the aortaswith age. The changes in hydroxyproline amounts with agein Eln+/ aorta are different than in WT with no significantchanges between P14 and P21 or P30 and P60, which mayrepresent an altered timeline of collagen expression to com-pensate for reduced elastin levels. The interactions betweenage and genotype for c1, , desmosine and hydroxyprolineamounts suggest an altered timeline of elastin and collagenorganization, mechanical contribution, and accumulation inthe two genotypes. By P60, when the mice are young adults,Eln+/ mice have approximately half the desmosine andsimilar hydroxyproline to WT mice, consistent with previ-ous data (Faury et al. 2003).

At P60, the average elastin parameter, c1, for WT aortais in the same range as those in previous studies (826 kPa)that modeled the mechanical behavior of adult mouse carotidarteries with a four- fiber-family model (Eberth et al. 2009;Gleason et al. 2008; Hansen et al. 2009; Wan et al. 2010).In all of the studies on mouse arteries, the elastin materialparameter is lower than that found from fitting neo-Hookeanconstitutive models to isolated elastin from pig arteries(70140 kPa) (Gundiah et al. 2009; Watton et al 2009). Theparameter differences may be due to variations between spe-cies or to changes in the elastin mechanical properties uponisolation from the arterial wall (Gundiah et al. 2007). Thecollagen parameters are harder to compare between studiesdue to the different number of collagen fiber families in var-ious studies and the nonlinear mechanical behavior, but ourresults show that in the physiologic range of stretch ratios(1.51.8) (Wagenseil and Mecham 2009), collagen is signif-icantly more stiff than elastin, as expected (Greenwald 2007).

The second trend that is observed from the model predic-tions is that the unloaded collagen fiber angle, , decreaseswith postnatal development. This corresponds to the fibersshifting from a more axial orientation toward a more circum-ferential orientation with age, which increases the ability ofthe fibers to resist the higher blood pressure and bear theincreased circumferential wall stress found in adult arter-ies. The reorientation is more pronounced in Eln+/ thanWT aorta, which indicates remodeling of the collagen fiberorientation over time to adapt to altered mechanical behaviorcaused by reduced elastin levels. The predicted unloaded ori-entation of collagen fibers at 43 in the adult mouse aorta by

the model agrees well with previous measurements of 40 inthe unloaded medial layer of human aorta (Holzapfel 2006).To our knowledge, the reorientation of fibers over postnataldevelopment has not been studied, but the model predictionscan be checked with careful histology or confocal micros-copy. While traditional histological studies of ECM fiber ori-entation have provided limited information, new methods inmultiphoton confocal microscopy can provide greater detailto investigate this in the unloaded and loaded configurations(Ferruzzi et al. 2011; Wan et al. 2010). The combination ofdecreasing c2 after P30 in both genotypes and the continu-ous changes in unloaded collagen fiber angle suggest that thecontinued increase in total stress in the artery wall throughoutdevelopment may be caused by rearrangement and remod-eling of the collagen fibers, rather than changes in collagenamount. This is consistent with the hydroxyproline data forboth genotypes and gene array data for WT aorta (Kelleheret al. 2004) that show limited additional expression or accu-mulation of collagen after P30 in the mouse.

In comparing the model parameters between genotypes,the elastin parameter, c1, for Eln+/ aorta is significantlyreduced compared with WT beginning at P7, the age when theelastic lamellae are complete (Davis 1995), and continuingthrough P21, the age when elastin gene expression beginsdecreasing in the WT aorta (Kelleher et al. 2004). The des-mosine data do not show significant differences in elastinamount between genotypes until P21. Small differences inelastin amounts at the younger ages may have large effectson the mechanical properties and hence significant effects onthe elastin parameter, c1. After P30, the desmosine amountsfor Eln+/ mice are approximately half those of WT mice,but the differences in c1 are no longer significant. There isstill a trend toward reduced c1 in Eln+/ aorta comparedwith WT (P = .06 and .09 for P30 and P60, respectively),and increased samples at these ages may improve the statisti-cal significance. It is possible that varying the elastin contri-bution to the total circumferential stress with age may haveresulted in better agreement between c1 and the desmosinedata. However, the changes in c1 and desmosine amountswith time and between genotypes show that the current, sim-ple model is capable of predicting mechanical differences inthe aortic wall caused by altered elastin amounts with post-natal development and disease. Another notable differencebetween genotypes is the trend in the reduction in collagenparameter, c2, in Eln+/ mice compared with WT at theolder ages (P14P60). While this may seem contradictoryto the similar hydroxyproline amounts between genotypes atmost ages, the change in c2 is accompanied by an increase inthe exponential term, c3, at most ages and slight differencesin , which also characterize collagen in the model. Thenonlinear behavior of the collagen fibers in the model, com-pared with the linear behavior of the elastin matrix, makesit more difficult to equate the collagen parameters to protein

123


amounts. The changes in all of the collagen parameters sug-gest that the mechanical properties and organization of thecollagen fibers may differ between WT and Eln+/ aorta.

When the predicted circumferential stress is separated intothe contributions of each constituent in the model, reducedpredicted contributions from elastin in Eln+/ aorta arecompensated for by increased predicted contributions fromcollagen that result in a similar total circumferential stress atphysiologic pressure at most ages. It is perhaps the need forthe arteries to achieve a homeostatic stress state that is drivingthe remodeling process and altering the relative contributionof each component. Previous investigators have noted a con-sistency at physiologic pressures in the tension per lamellarunit in mammals (Wolinsky and Glagov 1967), elastic modu-lus in vertebrates (Gibbons and Shadwick 1989), and elasticmodulus in jawless vertebrates and invertebrates (Davisonet al. 1995). Mathematical modeling including turnover of themajor wall constituents also observed a remodeling responsethat returned wall stress toward a homeostatic value (Glea-son and Humphrey 2004). Thus, circumferential wall stressat each age may be an important target for developmentalremodeling.

Constraints were imposed on the model parameters toensure physiologically relevant contributions from the elas-tin and collagen proteins. The contributions were deter-mined from previous reports that elastin contributes mostlyin the low to mid-pressure range (Dobrin and Canfield 1984;Ferruzzi et al. 2011; Fonck et al. 2007) and that collagencontributes mostly in the high pressure range as the fibersare relatively unengaged at physiologic pressures (Green-wald et al. 1997). The constraint values were chosen fromprior modeling of adult mouse carotid arteries (Hansen et al.2009). While the selection of the particular constraint valueswas admittedly arbitrary, we found that varying the elastincontribution from 10 to 40 % and collagen contribution from55 to 85 % of the total circumferential stress did not changethe observed trends in the parameters. Constraints were notapplied to the SMCs or to the axial stress behavior, becausethere are more limited data available to determine the appro-priate constraints, and we wished to impose the least amountof constraints necessary. Inclusion of similar constraints inthe axial direction with 30 % elastin contribution toward thetotal axial stress between PL < P < PH and 75 % colla-gen contribution toward the total axial stress at P > PH,also did not change the observed parameter trends. In addi-tion, an alternate method of constraining the circumferentialstress contributions of elastin and collagen by completelyseparating their contributions to different operating pressureranges produced similar trends in the parameters, indicatingthat separate mechanical contributions of elastin and colla-gen can describe the total stress behavior of the developingmouse aorta. The model predicts minimal contributions to thetotal stress from the SMCs, which is consistent with previous

data for large, elastic arteries. Using Cytochalasin D to dis-solve the SMC actin cytoskeleton or Triton X to remove thecells from the arterial wall has minimal effects on the passivepressurediameter behavior of adult mouse carotid arteries(Corley et al. 2010).

This study is not without limitations. To minimize thenumber of mice required, male mice were used for mechan-ical characterization and female mice were used for pro-tein quantification. Differences between the sexes in therelationship between aortic mechanical behavior and wallconstituents may account for some of the inconsistenciesin correlating model parameters with elastin and collagenamounts. The current model does not explicitly include vol-ume or mass fractions of the wall constituents. While a casecan be made for changes in the material parameters to rep-resent changes in constituent amounts, they are not directlyrelatable to protein amounts. Future studies may involve theuse of volume or mass fraction terms to more accuratelycapture the differences in relative protein amounts; however,this increases the number of fitted parameters and the chanceof obtaining non-unique parameter values. Also, the aorticwall was considered a single homogeneous layer. Histol-ogy results clearly indicate that the aortic wall consists ofthree distinct layers with different structures and composi-tions. This spatial organization is a key difference betweenlarge elastic arteries, muscular arterioles, and thinner capil-laries, and future modeling efforts should consider the spatialarrangement of proteins. Despite having less total elastin, theEln+/ mouse aorta has increased lamellar units (Li et al.1998). This difference in spatial organization of elastin maycontribute to the observed differences in the age trends of theelastin parameter, c1, between the two genotypes. The trans-mural wall stress distribution was not included in the model.Previous work has shown that the residual stresses normal-ize the transmural wall stress, so that the mean wall stressis a reasonable approximation (Chuong and Fung 1986).Similar models without residual stress have proven effectiveat comparing mechanical behavior in mouse arteries withaltered ECM amounts (Eberth et al. 2009; Ferruzzi et al.2011). Unloaded orientation of the collagen fiber families isincluded, but the orientation distribution, as well as any con-siderations about the waviness or unloaded configuration ofindividual collagen fibers, is not included (Fonck et al. 2007).Additionally, there is evidence that the elastin matrix is notcompletely isotropic in the arterial wall (Rezakhaniha et al.2011). Work is ongoing to determine the best strain energyfunctions to describe the ECM proteins. It is also importantto note that all of the parameters were determined from fitsto ex vivo test results. In vivo mechanical behavior may beslightly different due to interactions with surrounding tissue(Liu et al. 2007), but the ex vivo tests allow the applicationof a range of loading protocols for robust error minimizationof the best fit parameters.

123


5 Conclusion

In summary, a fiber-based constitutive model for the mouseaorta is presented that predicts changes in ECM mechanicalproperties and organization in postnatal development and dis-ease. Material parameters were fitted from mechanical dataof WT and Eln+/ aorta from P3 to P60 using constraintsbased on prior literature. The fitted material parameters pre-dict changes in elastin and collagen stress contributions thatare consistent with protein quantification data for both geno-types and previous gene expression data in developing WTaorta. The model also predicts changes in collagen fiberorientation that must be confirmed in future studies. Relat-ing changes in constituent amounts and organization to themechanical behavior of the composite aortic wall may helpunderstand developmental remodeling and guide treatmentsfor human disease.

Acknowledgments This work was supported, in part, by the NIH[Grants RO1 HL074138 (RPM), R00 HL087563 (JEW), R01 HL105314(RPM and JEW), and T32 HL007275 (JKC)].

References

Amin M, Kunkel AG, Le VP, Wagenseil JE (2011) Effect of stor-age duration on the mechanical behavior of mouse carotid artery.J Biomech Eng 133(7):071007. doi:10.1115/1.4004415

Baek S, Valentin A, Humphrey JD (2007) Biochemomechanics of cere-bral vasospasm and its resolution: II. Constitutive relations andmodel simulations. Ann Biomed Eng 35(9): 14981509. doi:10.1007/s10439-007-9322-x

Chuong CJ, Fung YC (1986) On residual stresses in arteries. J BiomechEng 108(2):189192

Clark JM, Glagov S (1985) Transmural organization of the arterialmedia. The lamellar unit revisited. Arteriosclerosis 5(1):1934

Corley B, Le VP, Wagenseil JE (2010) Mechanical contribution ofsmooth muscle cells in large elastic arteries. Paper presented atthe Biomedical Engineering Society Annual Meeting, Austin, TX

Davis EC (1995) Elastic lamina growth in the developing mouse aorta.J Histochem Cytochem 43(11):11151123

Davison IG, Wright GM, DeMont ME (1995) The structure and phys-ical properties of invertebrate and primitive vertebrate arteries.J Exp Biol 198(Pt 10):21852196

Dobrin PB (1997) Chapter 3: physiology and pathophysiology of bloodvessels. In: Sidawy AN, Sumpio BE, DePalma RG (eds) Thebasic science of vascular disease. Futura Publishing, New York pp69105

Dobrin PB, Canfield TR (1984) Elastase, collagenase, and the biaxialelastic properties of dog carotid artery. Am J Physiol 247(1 Pt 2):H124131

Eberth JF, Taucer AI, Wilson E, Humphrey JD (2009) Mechanics ofcarotid arteries in a mouse model of Marfan Syndrome. Ann Bio-med Eng 37(6): 10931104. doi:10.1007/s10439-009-9686-1

Faury G, Maher GM, Li DY, Keating MT, Mecham RP, Boyle WA(1999) Relation between outer and luminal diameter in cannulat-ed arteries. Am J Physiol 277(5 Pt 2):H17451753

Faury G, Pezet M, Knutsen RH, Boyle WA, Heximer SP, McLean SE,Minkes RK, Blumer KJ, Kovacs A, Kelly DP, Li DY, Starcher B,Mecham RP (2003) Developmental adaptation of the mouse car-diovascular system to elastin haploinsufficiency. J Clin Invest112(9):14191428

Ferruzzi J, Collins MJ, Yeh AT, Humphrey JD (2011) Mechanicalassessment of elastin integrity in fibrillin-1-deficient carotid arter-ies: implications for Marfan syndrome. Cardiovasc Res 92(2):287295. doi:10.1093/cvr/cvr195

Fonck E, Prodhom G, Roy S, Augsburger L, Rufenacht DA, Stergiopu-los N (2007) Effect of elastin degradation on carotid wall mechan-ics as assessed by a constituent-based biomechanical model. AmJ Physiol Heart Circ Physiol 292(6): H27542763. doi:01108.2006[pii]10.1152/ajpheart.01108.2006

Fung YC (1993) Biomechanics: mechanical properties of living tissues,2nd edn. Springer, New York

Gibbons CA, Shadwick RE (1989) Functional similarities in themechanical design of the aorta in lower vertebrates and mammals.Experientia 45(1112):10831088

Gleason RL, Dye WW, Wilson E (2008) Quantification of the mechan-ical behavior of carotid arteries from wild-type, dystrophin-defi-cient, and sarcoglycan- knockout mice. J Biomech 41(15): 32133218. doi:10.1016/j.jbiomech.2008.08.012.Quantification

Gleason RL, Humphrey JD (2004) A mixture model of arterial growthand remodeling in hypertension: altered muscle tone and tissueturnover. J Vasc Res 41(4):352363

Greenwald SE (2007) Ageing of the conduit arteries. J Pathol 211(2):157172. doi:10.1002/path.2101

Greenwald SE, Moore JEJr., Rachev A, Kane TP, Meister JJ (1997)Experimental investigation of the distribution of residual strains inthe artery wall. J Biomech Eng 119(4):438444

Gundiah N, Ratcliffe MB, Pruitt LA (2007) Determination of strainenergy function for arterial elastin: Experiments using histologyand mechanical tests. J Biomech 40(3):586594

Gundiah N, Ratcliffe MB, Pruitt LA (2009) The biomechanics of arte-rial elastin. J Mech Behav Biomed Mater 2(3):288296

Hansen L, Wan W, Gleason RL (2009) Microstructurally motivatedconstitutive modeling of mouse arteries cultured under alteredaxial stretch. J Biomech Eng 131(10):101015. doi:10.1115/1.3207013

Hirano E, Knutsen RH, Sugitani H, Ciliberto CH, Mecham RP(2007) Functional rescue of elastin insufficiency in mice by thehuman elastin gene: implications for mouse models of human dis-ease. Circ Res 101(5):523531

Holzapfel GA (2006) Determination of material models for arterialwalls from uniaxial extension tests and histological structure.J Theor Biol 238(2): 290302. doi:S0022-5193(05)00208-0[pii]10.1016/j.jtbi.2005.05.006

Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive frame-work for arterial wall mechanics and a comparative study of mate-rial models. J Elast 61(13):148

Holzapfel GA, Ogden RW (2010) Constitutive modelling of arteries.P R Soc A Math Phy 466(2118):15511596

Huang Y, Guo X, Kassab GS (2006) Axial nonuniformity of geomet-ric and mechanical properties of mouse aorta is increased dur-ing postnatal growth. Am J Physiol Heart Circ Physiol 290(2):H657664

Ishii T, Kuwaki T, Masuda Y, Fukuda Y (2001) Postnatal developmentof blood pressure and baroreflex in mice. Auton Neurosci 94(12):3441

Ishiwata T, Nakazawa M, Pu WT, Tevosian SG, Izumo S (2003) Devel-opmental changes in ventricular diastolic function correlate withchanges in ventricular myoarchitecture in normal mouse embryos.Circ Res 93(9):857865

Kelleher CM, McLean SE, Mecham RP (2004) Vascular extracellularmatrix and aortic development. Curr Top Dev Biol 62:153188

Le VP, Knutsen RH, Mecham RP, Wagenseil JE (2011) Decreased aor-tic diameter and compliance precedes blood pressure increases inpostnatal development of elastin-insufficient mice. Am J Phys-iol Heart Circ Physiol 301(1): H221229. doi:10.1152/ajpheart.00119.2011

123


Li DY, Faury G, Taylor DG, Davis EC, Boyle WA, Mecham RP,Stenzel P, Boak B, Keating MT (1998) Novel arterial pathol-ogy in mice and humans hemizygous for elastin. J Clin Invest102(10):17831787

Li DY, Toland AE, Boak BB, Atkinson DL, Ensing GJ, Morris CA,Keating MT (1997) Elastin point mutations cause an obstructivevascular disease, supravalvular aortic stenosis. Hum Mol Genet6(7):10211028

Liu Y, Dang C, Garcia M, Gregersen H, Kassab GS (2007) Surround-ing tissues affect the passive mechanics of the vessel wall: theoryand experiment. Am J Physiol Heart Circ Physiol 293(6): H32903300. doi:10.1152/ajpheart.00666.2007

Rahman M (2009) An enzyme-linked immunosorbent assay (ELISA) toquantitate desmosine and isodesmosine. In: Stephen F (ed). AustinState University, Texas, United States

Rezakhaniha R, Fonck E, Genoud C, Stergiopulos N (2011) Role ofelastin anisotropy in structural strain energy functions of arte-rial tissue. Biomech Model Mechanobiol 10(4): 599611. doi:10.1007/s10237-010-0259-x

Shadwick RE (1999) Mechanical design in arteries. J Exp Biol 202(Pt23):33053313

Vito RP, Dixon SA (2003) Blood vessel constitutive models-1995-2002. Annu Rev Biomed Eng 5:413439

Wagenseil JE, Mecham RP (2009) Vascular extracellular matrix andarterial mechanics. Physiol Rev 89(3): 957989. doi:10.1152/physrev.00041.2008

Wagenseil JE, Nerurkar NL, Knutsen RH, Okamoto RJ, Li DY,Mecham RP (2005) Effects of elastin haploinsufficiency on themechanical behavior of mouse arteries. Am J Physiol Heart CircPhysiol 289(3): H12091217. doi:10.1152/ajpheart.00046.2005

Wan W, Yanagisawa H, Gleason RLJr. (2010) Biomechanical andmicrostructural properties of common carotid arteries from fib-ulin-5 null mice. Ann Biomed Eng 38(12): 36053617. doi:10.1007/s10439-010-0114-3

Watton PN, Ventikos Y, Holzapfel GA (2009) Modelling the mechani-cal response of elastin for arterial tissue. J Biomech 42(9):13201325

Wiesmann F, Ruff J, Hiller KH, Rommel E, Haase A, Neubauer S(2000) Developmental changes of cardiac function and massassessed with MRI in neonatal, juvenile, and adult mice. Am JPhysiol Heart Circ Physiol 278(2):H652657

Wolinsky H, Glagov S (1967) A lamellar unit of aortic medial structureand function in mammals. Circ Res 20((1):99111

123

A fiber-based constitutive model predicts changes in amount and organization of matrix proteins with development and disease in the mouse aortaAbstract1 Introduction2 Methods2.1 Experimental data2.2 Model equations2.3 Material parameters2.4 Protein quantification2.5 Statistics

3 Results4 Discussion5 ConclusionAcknowledgmentsReferences

a fiber-based constitutive model predicts changes in amount and organization of matrix proteins with...

Documents