Microstructural Characterization of Vocal Folds toward a Strain-Energy Model of Collagen Remodeling

Acta Biomaterialia xxx (2013) xxx–xxx

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Acta Biomaterialia

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Microstructural characterization of vocal folds toward a strain-energymodel of collagen remodeling

1742-7061/$ - see front matter � 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.actbio.2013.04.044

⇑ Corresponding author. Tel.: +1 (514) 560 6250; fax: +1 (514) 398 7365.E-mail address: [email protected] (H.K. Heris).

Please cite this article in press as: Miri AK et al. Microstructural characterization of vocal folds toward a strain-energy model of collagen remodelinBiomater (2013), http://dx.doi.org/10.1016/j.actbio.2013.04.044

Amir K. Miri a, Hossein K. Heris a,⇑, Umakanta Tripathy b, Paul W. Wiseman b, Luc Mongeau a

a Department of Mechanical Engineering, McGill University, Montreal, QC, Canada H3A 0C3b Physics and Chemistry Departments, McGill University, Montreal, QC, Canada H3A 2T8

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 December 2012Received in revised form 20 April 2013Accepted 25 April 2013Available online xxxx

Keywords:CollagenHelixNonlinear laser scanning microscopyAtomic force microscopyStrain energy function

Collagen fibrils are believed to control the immediate deformation of soft tissues under mechanical load.Most extracellular matrix proteins remain intact during frozen sectioning, which allows them to bescanned using atomic force microscopy (AFM). Collagen fibrils are distinguishable because of their peri-odic roughness wavelength. In the present study, the shape and organization of collagen fibrils in dis-sected porcine vocal folds were quantified using nonlinear laser scanning microscopy data at themicrometer scale and AFM data at the nanometer scale. Rope-shaped collagen fibrils were observed.The geometric characteristics for the fibrils were fed into a hyperelastic model to predict the biomechan-ical response of the tissue. The model simulates the micrometer-scale unlocking behavior of collagenbundles when extended from their unloaded configuration. Force spectroscopy using AFM was used toestimate the stiffness of collagen fibrils (1 ± 0.5 MPa). The presence of rope-shaped fibrils is postulatedto change the slope of the force–deflection response near the onset of nonlinearity. The proposed modelcould ultimately be used to evaluate changes in elasticity of soft tissues that result from the collagenremodeling.

� 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction

The microstructure of biological soft tissues is composed ofextracellular matrix proteins (ECMs) saturated within a fluid med-ium. The ECMs are composed of fibrous proteins, such as collagenand elastin, entangled in saturated interstitial proteins, such asproteoglycans and glycosaminoglycans. The former group consti-tutes the backbone structure of the ECMs, enabling it to withstandexternal forces. The relationship between load and deformation forthe ECM structure is typically highly nonlinear. Vocal fold tissue,the focus of the present study, undergoes simultaneous longitudi-nal extension and self-sustained transverse oscillations along thesagittal plane during phonation [1]. It is hypothesized here thatcharacterization of the tissue microstructure, along with a properstructural model, allows a better prediction of the biomechanicalbehavior of the vocal folds.

Collagen and elastin are two common sources of intrinsic con-trast in nonlinear laser scanning microscopy (NLSM). This methoddoes not require staining or preprocessing and is thus ideal forimaging the ECMs [2]. Second harmonic generation (SHG) has beenused to image noncentrosymmetic structures, particularly collagenfibrils [3,4]. Fibril-forming collagens are highly ordered helical

structures that produce considerable nonlinear light scattering[5]. Two-photon fluorescence (TPF) microscopy has been used toimage fluorophores in many biological organs. Elastin fibers havean intrinsically high cross-section for TPF emission [6]. Collagenand elastin in human vocal folds were imaged in a recent study [7].

Collagen fibrils can be easily distinguished from other ECMs inuntreated biological tissues based on their periodic roughnesswavelength, called D-banding [8]. This parameter is determinedby the spiral-shaped, helical hierarchy of tropocollagens [9]. Unde-tectable with NLSM, D-banding can be detected using high-resolu-tion atomic force microscopy (AFM) images. An AFM study ofdissected tendons, in which D-banding was identified, has revealedthat individual fibrils may be knitted to form a rope [8]. Based on adifferential-geometry model of multistrand ropes [10], Bozec et al.[8] proved that D-banding can be independent of the fibril diame-ter, and this conclusion resolved a shortcoming of previous models[11].

The configuration of ECMs defines the structural entropy thatcontrols the elastic energy of soft tissues [12]. The quantificationof their configuration allows the development of structural modelsthat could predict the biomechanical behavior in situations wheremechanical properties are impossible to measure directly, such asin scar tissue and wound healing. Collagen fibrils appear to deter-mine the elastic response of soft tissues under mechanical load[13]. In one study, a three-dimensional mechanical model of colla-

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2 A.K. Miri et al. / Acta Biomaterialia xxx (2013) xxx–xxx

gen-reinforced materials, in which collagen fibrils are idealized ashelical elastic springs, was created for soft tissues [14]. A probabil-ity function for collagen waviness was introduced and incorpo-rated into a hyperelastic constitutive model of collagen-reinforced soft tissues [15]. The biophysical interactions betweencollagen fibrils and nonfibrous ECMs, which were included in theviscoelastic models (e.g. [13]), are neglected here for the sake ofconciseness.

Structural characterization over different length scales alongwith biomechanical studies [9,15,16] has been used to model thebiophysics of soft tissues. From a histological perspective, the hu-man vocal fold may be subdivided into two primary layers: thelamina propria and the vocalis muscle [17]. The ECM structure ofthe lamina propria is dominated by type I and type III collagen fi-brils, with a higher volume fraction of collagen type III [1,18,19].The porcine vocal fold was chosen because it has a structure sim-ilar to that of human vocal folds [18,19].

The goal of the present study is to characterize the contributionof collagen helical hierarchy to the nonlinear elasticity of soft tis-sues using a structural model. The microstructural morphology ofthe ECMs in porcine vocal folds was investigated using NLSM andAFM imaging. A protocol developed by Miri et al. [7] was used toquantify the helical shape of collagen fibrils, and the stiffness ofindividual fibrils was obtained using AFM-based nanoindentation.Assuming idealized elastic, multistrand, rope structures [10], astrain-energy function associated with the unloaded, stress-freeconfiguration of collagen fibrils was formulated. The formulationwas applied for the simulation of the uniaxial tension responseof a representative volume element of the tissue. The effect ofthe rope–fibril volume fraction on the force–deflection responsewas investigated by numerical analysis.

2. Methods and materials

2.1. Nonlinear laser scanning microscopy

Healthy porcine larynges were obtained from a local abattoirimmediately post mortem and immersed in a normal saline solu-tion. The protocol was approved by the Animal Care Committeeof the Faculty of Medicine, McGill University. Three adult porcinevocal folds, labeled samples I, II and III, were used for the opticalsectioning. The inferior vocal folds were dissected from the laryn-ges by cutting along the subglottal wall, the superior vocal foldsand the vocalis muscle [20]. A rectangular area of approximately2 mm � 4 mm was excised with sharp blades from the central re-gion of the vocal folds within the sagittal plane. The thickness ofthe samples was > 2 mm, within the lamina propria. The tissuewas embedded in optimal cutting temperature (OCT) compound(Sakura Finetek, Dublin, OH) with no washing or dehydration. Itwas then sectioned using a cryostat microtome and divided intoequal-thickness layers of 100 lm from the epithelium. Each slicewas placed between two 22 mm � 22 mm cover glasses. The slideswere placed on the NLSM stage for imaging.

A custom-built multimodal, multiphoton microscope wasused to record the images [7]. In this study, SHG and TPF emis-sions were imaged with an excitation wavelength of 1050 nm,in which the laser light was linearly polarized in the horizontalplane. The excitation objective (Carl Zeiss, Toronto, Canada) wasa 63 � 0.9 numerical aperture (NA) water immersion lens witha 2 mm working distance, and the collection objective was a20 � 0.80 NA water immersion lens with a 0.61 mm workingdistance. The two sinusoidal parameters Ho and Ro, correspond-ing respectively to the periodicity and amplitude of fibers andfibrils, were extracted from the NSLM images. The periodicityof selected bundles was determined using Fourier analysis [7].

Please cite this article in press as: Miri AK et al. Microstructural characterizatioBiomater (2013), http://dx.doi.org/10.1016/j.actbio.2013.04.044

The overall fiber orientation with respect to the longitudinalaxis of the vocal folds was then determined. ImageJ (NIH,Bethesda, MD, USA) was used to calculate the area fraction ofcollagen fibrils or elastin fibers in each image by imposing abinary threshold after background subtraction [7].

Multimode NLSM allows comparisons between the organiza-tions of soft tissue components that have intrinsic contrast in theimages. Networks of collagen fibrils and elastin fibers were simul-taneously scanned in the same imaging plane. In a previous studyof human vocal folds, a qualitative colocalization analysis was used[7]. Colocalization analysis involves the determination of howmuch the SHG and TPF signals overlap. A quantitative approachwas used in the present study to remove observer bias. Pearson’scorrelation coefficient, calculated using ImageJ, quantified thecolocalization of the SHG and TPF channels from the intensitycovariance in each pixel [21]. To reduce noise, the backgroundintensity of each image was subtracted using a rolling-ball algo-rithm (ImageJ; NIH, Bethesda, MD, USA). An available randomiza-tion approach [21] was selected to calculate the Pearsoncoefficient and assess its statistical significance. For each pair ofimages, 25 random images were created by translating horizon-tally and/or vertically the TPF image in 5 pixel increments (i.e.�10, �5, 0, 5 and 10 pixels). The scrambled images, with a lengthscale of several micrometers, maintain the characteristic shape ofthe collagen and elastin features. The Pearson coefficient was cal-culated for each artificial pair and compared to that of the originalpair. The cases selected for the analyses had at least 22 randomiza-tions with Pearson coefficients lower than in the original images.About 20% of the images were eliminated using this criterion.

2.2. Atomic force microscopy

In a separate set of experiments, AFM imaging was performedusing a Multimode Nanoscope IIIa microscope (Veeco, Santa Bar-bara, CA), equipped with a NanoScope V controller. The AFMimages were obtained in both the height and the deflection chan-nels using the contact mode at room temperature. Reflective, gold-coated, sharp silicon nitride microcantilevers (MSNL-10, 0.1–0.6 N m�1; Bruker, Camarillo, CA) were used for high-resolutionimaging of sectioned tissue layers in air, at room temperature.Gold-coated silicon nitride microcantilevers (NPG-10, 0.35 N m�1;Bruker, Camarillo, CA) were used for nanoindentation tests on tis-sue samples immersed in a phosphate buffer saline, pH 7.6, to sim-ulate physiological conditions [22].

The deflection sensitivity of the piezoelectric transducer wasmeasured by probing the hard surface of the glass substrates. Thisprocedure could have affected the curvature of the probe tip, andthus the tip radius was determined via scanning electron micros-copy, as shown in Fig. 1a. The sphericity of the head of the conicaltip was obtained using a regression, and was found to have a 75 nmradius. The spring constant of the tips was measured using a ther-mal tuning method [23]. Most cantilevers remain linear up to acantilever deflection of 100 nm, as observed in deflection sensitiv-ity curves. The forces measured in the present study were less than�10 nN and the cantilever deflections were less than �30 nm.Hence, nonlinear effects were negligible. The optimal cantileverstiffness for a sample can be determined from the assumptions ofHertz contact theory [24]. An effective stiffness value of�0.3 N m�1 was calculated for nanoindentation testing of collagenfibrils in hydrated conditions [22].

Thin sections of three porcine vocal folds with thicknesses of 7–10 lm were prepared using a procedure similar to that used for theNLSM. The nanoindentation was performed on collagen fibrils. Theforce–volume mode produced a map of load–displacement forcecurves in a 20 point � 20 point grid over the surface of the samples,each of which had an area of 20 lm � 20 lm. A rate of two

n of vocal folds toward a strain-energy model of collagen remodeling. Acta


Fig. 1. (a) Typical force–deflection curve obtained by AFM-based nanoindentation. Scanning electron microscopy was used to characterize the AFM tip. Scale bar is 5 lm. (b)A typical AFM image of the porcine vocal fold superficial layer in which brighter regions are at greater height. Scale bar is 1 lm. (c) A typical stress–stretch curve of vocal foldtissue samples. The sample, shown with a speckle pattern, was subjected to uniaxial sinusoidal tension at 1 Hz. (d) A dual-mode NLSM image of porcine vocal fold laminapropria, in the sagittal plane. (e) Anatomy of porcine hemilarynx. The vocal fold tissue is between the thyroid and arytenoid cartilages. The location of sample excision forimaging is shown.

A.K. Miri et al. / Acta Biomaterialia xxx (2013) xxx–xxx 3

indentation cycles per second was applied, yielding a set of 400indentation curves. The force–volume mode, with a threshold of6 nN, yielded unloading force curves, which were used to esti-mate the elastic tensile modulus as described by Oliver and Pharr[24]. A distribution of the 400 elastic moduli in the selected areawas obtained. In addition to zero-stiffness points that correspondto pore spaces, contributions of the tissue-tip adhesion were sig-nificant at some points. The corresponding data were then disre-garded in the final analysis. The data were imported into MATLAB(The MathWorks, Natick, MA) to obtain the histogram. The valuesof the elastic moduli associated with data population (i.e. theamplitude of the Gaussian fits) were extracted and the maximumvalue was considered to be the elastic modulus of one single col-lagen fibril.


3. Results

Fig. 1 shows an overview of the experimental approach. Fig. 1eshows the location of the vocal fold in a porcine hemilarynx andthe area where the samples were harvested. The average stressvs. stretch, obtained from uniaxial traction testing of the entire vo-cal fold [20], is shown in Fig. 1c. The strong nonlinearity of thestress–stretch curve can be associated with interactions betweencollagen fibrils and other ECMs for large deformations [12].Fig. 1d shows the merged distributions of elastin (red) and collagen(green) networks obtained from a single NLSM imaging acquisi-tion. The collagen fibrils have a characteristic wavy structure whilethe elastin network is interwoven like a basket. The AFM image,Fig. 1b, illustrates the nanoscale features of the ECMs, highlighting




a higher fibers’ effective size (e.g. the diameter) relative to otherECMs of the vocal fold [18,19]. The nanoindentation curve, ob-tained from AFM, and the scanning electron microscopy image ofthe AFM tip used are shown in Fig. 1a.

Selected images of 100 lm � 100 lm regions in the 1st (�0–100 lm depth), 4th (�300–400 lm depth) and 7th (�600–700 lm depth) layers of sample I are shown in Fig. 2. The left col-umn shows the distribution of straight elastin fibers and the rightcolumn shows the bundles of crimp-shaped collagen fibrils. Varia-tions in the collagen and elastin networks with depth are apparent.Highly distributed within the first layer, the elastin network dimin-ishes at greater depths (i.e. closer to the muscle), as seen in the 7th

Fig. 2. Selected images of TPF (red) and SHG (green) channels for the 1st (a,b), the 4th1050 nm. The TPF (red) and SHG (green) channels were recorded at wavelengths of 600/5bar is 20 lm.


layer. The variation is not an optical sectioning artifact because theimaging was done on separate tissue slices. Fig. 2 also shows thatthe collagen fibrils are primarily oriented along the longitudinalaxis of the vocal fold (i.e. the horizontal axis in the images).

The averaged area fractions and associated standard deviationsare shown along with Pearson’s correlation coefficients in Fig. 3.The correlation coefficients support the observation that collagenand elastin are more entangled in the first three layers. The peri-odic, sinusoidal structure of collagen bundles is shown in Fig. 4.Two randomly selected positions for each layer were imaged withNLSM. Ten bundles were selected in each image to calculate theaverage values of the overall orientation, the wave periodicity

(c,d) and the 7th (e,f) 100 lm layers in sample I. The excitation wavelength was0 and 525/50 nm. The pixel resolution of (a) and (b) are twice the other images. Scale



Fig. 4. Depth distribution of the mean collagen sinusoidal parameters and its standard deviation, at two random locations in each of three porcine vocal fold samples, basedon the Fourier series regression. Vertical dashed lines indicate separate tissue slices. The depth coordinate was placed in the coronal plane, the epithelium toward the vocalismuscle. Solid red line, sample I; dashed blue line, sample II; dotted black line, sample III.

Fig. 3. Depth distribution of the mean area fraction and its standard deviation for the recorded data, at two random locations in each of three samples, for TPF (red) and SHG(green) channels. Vertical dashed lines indicate separate tissue slices. The depth coordinate was placed in the coronal plane, the epithelium toward the vocalis muscle. Solidred line, TPF area fraction; dashed blue line, SHG area fraction; dotted black line, Pearson correlation coefficient.


and the wave amplitude of the collagen fibrils, as described inSection 2.1.

Four thin slices were extracted from each AFM sample, at100 lm intervals of 0–400 lm depth. Height- and deflection-mode


images were recorded at three randomly chosen regions per sam-ple. The collagen fibrils were identified from D-banding. Carefulexamination of the bundles led to the identification of two distinctcollagen distribution patterns, as shown in the first layer of one se-



Fig. 5. Selected images of single fibrils (a) and rope-like fibrils (b) imaged by AFM, at a depth of 0–100 lm. Scale bar is 1 lm. The ply radius, R, and the helical angle, u, areshown in the right image.

Fig. 6. Distributions of data population vs. indentation modulus E from nanoin-dentation of a vocal fold tissue sample; blue curve for the first fit corresponding tononcollagenous ECMs; red curve for the second fit associated with collagen fibrilstype III; green curve as the third fit associated with collagen fibrils type I; black barsfor the indentation moduli. A combination of the second and third Gaussiandistributions was considered as the stiffness of collagen fibrils.


lected sample (Fig. 5). The left column (Fig. 5a) shows freely dis-tributed single collagen fibrils, which are less integrated than otherECM biopolymers. These were observed in all samples. The rightcolumn (Fig. 5b) shows rope-shaped collagen fibrils, with theirnotable helical angle and ply radius, found mostly near the epithe-lium, at depths of 0–200 lm. Nanoindentation was also performedon several fibril-like objects by the AFM and the map of the elasticmodulus was calculated. A regression of the normal Gaussian dis-tribution with the moduli yielded three major peaks in most cases,one of which is presented in Fig. 6. Based on the range of collagenmodulus in the literature [22], the first peak was attributed to non-collagenous ECMs, including elastin, while two higher peaks wereassociated with the collagen fibrils. The normal probability func-tion was defined as:

PðEÞ ¼ 11ffiffiffiffiffiffiffi2pp exp �ðE� NÞ2

212

!ð1Þ

with N and 1 indicating the mean and the standard deviation of theindentation modulus E. Using this approach, the indentation moduliof the collagen fibrils were obtained. Two data sets were averagedto obtain one range of moduli for vocal fold samples. The overall re-sults were found to vary between 0.5 and 1.5 MPa.


4. Theoretical model

4.1. A hyperelastic model of collagen-reinforced composites

From an engineering perspective, soft tissues are compositestructures composed of elastin and collagen fibers immersed in hy-drated gel-like proteoglycans. Disregarding the effects of viscosity,the tissue hyperelastic model is based on the definition of thestrain-energy function [15], i.e. the Helmholtz free energy whenthe tissue is subjected to isothermal deformation. In vitro experi-ments in constant-temperature media are commonly performedfor soft tissues [20,25]. The strain-energy density function, W, de-notes the elastic energy stored in the deformed tissue per unit vol-ume [26]. It is a function of

W ¼ Wðk1; k2; k3Þ; ð2Þ

where each variable, ki, represents the principal stretch along theith global coordinate (Fig. 7a). By analogy with engineered fiber-reinforced composites, nonfibrous ECMs supply the matrix phaseand fibrous ECMs constitute the reinforcing fibers. An additive for-mulation [26], which assumes affine deformation of all compo-nents, expresses the strain-energy function as:

W ¼ ð1� /f ÞWm þ /f Wf ; ð3Þ

in which Wm denotes the isotropic energy of the nonfibrous pro-teins, and Wf denotes the anisotropic energy of the fibrous proteins,which occupy a volume fraction /f .

In vocal fold tissue, the elastin network is generally distributedalong random directions (Figs. 1c and 2). Any possible variation inmodel parameters along the thickness direction is neglected herebecause the loading is planar along the sagittal plane [20]. Thus,the anisotropic energy, Wf in Eq. (3), was expanded as:

W ¼ ð1� /f ÞWm þ /f ð/cWc þ ð1� /cÞWeÞ; ð4Þ

where Wc denotes the direction-dependent strain-energy functionstored by collagen fibrils occupying a volume fraction /c , and We

denotes the strain-energy contributed to the elastin fibers. In un-loaded tissue samples, collagen fibrils formed a wavy structurewith regular sinusoidal characteristics. Collagen fibrils of vocalfolds seem to be predominantly oriented along the anterior–pos-terior direction [7]. An anisotropy vector, a, and the associatedprobability density function, POðh;/Þ, were thus introduced, whereh and / are the azimuthal and circumferential angles (Fig. 7a). Thecollagen strain-energy function is expressed in spherical coordi-nates as:



(b)

(a)

Fig. 7. (a) Schematic representation of an area of interest imaged by NLSM and a selected single helical fibril with its regression function. (b) Schematic of a four-strand rope model.


WcðkiÞ ¼Z 2p

0

Z p

0Wfibrilðkf ðki; h;/ÞÞPOðh;/Þ sin /d/dh; ð5Þ

where Wfibril is the energy function of one single fibril, and kf is thestretch along a ðho;/oÞ [15], which depends on the principalstretches and the orientation vector ðho;/oÞ. A bisymmetric uni-modal distribution function was used to describe the anisotropicspatial distribution of collagen fibrils.

The microscale crimp-shaped distribution of collagen fibrils wasmodeled as a planar sinusoidal curve (Fig. 7a). The infinitesimalarc-length, dl, of one single collagen fiber lying along the x-axiswith a length of L, and lying within the yz plane, is expressed as:

dl ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðdx2 þ dy2 þ dz2Þ

q¼ ‘dx; ð6Þ

where ‘ is a random variable, which has a non-normal distributionin the y- and z-directions with a nonzero mean value. A normalGaussian distribution, with a nonzero mean value, was assumedfor the length probability function:

Plð‘Þ ¼1

Xffiffiffiffiffiffiffi2pp exp �ð‘�

�‘Þ2

2X2

!; ð7Þ

in which �‘ and X2 are the mean value and variance, respectively, asestimated from the NLSM images. The integration of Eq. (6) alongthe length of the fibril yields �‘. For a fixed ‘, the effective stretchof the fibril is then obtained as:

�kf ðki; h;/; ‘Þ ¼ kf ðki; h;/Þ � ð‘� 1Þ: ð8Þ

For convenience, WmðkiÞ and WeðkiÞ were modeled using a neo-Hookean material model [26] having shear stiffnesses lm and le.When a representative cubic block of the tissue is subjected to auniaxial extension, k, the Cauchy stress in the direction of loading(i.e. at h ¼ 0 and / ¼ p=2) is obtained from [15]:

r¼2 ð1�/f Þ@Wm

@I1þ/f ð1�/cÞ

@We

@I1

� �k2�1

k

� �

þ/f /ck2Z 2p

0

Z p

0

1kf ðk;h;/Þ

�Z kf ðk;h;/Þ

1

@

@�kfWfibrilð�kf ðk;h;/; ‘ÞÞPlð‘Þd‘

" #POðh;/Þcos2 hsin3 /d/dh;

ð9Þ


where I1ð¼ k2 þ 2=kÞ is strain invariant. The uniaxial traction testdata were obtained from the experiments of a previous, relatedstudy [20]. The measured stress–stretch response of one vocal foldsample is shown in Fig. 1c.

4.2. A rope-shaped model of collagen fibrils

Following the model suggested by Bozec et al. [8] for subfibrillarlength scales, we assumed that collagen fibrils coil around eachother to form a rope-like ply with a right-handed helical shape atthe micrometer length scale. The ply shape might be the result ofan incomplete self-assembly of smaller fibrils. Two distinct typesof fibrils were thus identified, which suggests a strain-energy func-tion of the form:

Wfibrilð�kf Þ ¼ ð1� /plyÞWrodfibrilð�kf Þ þ /plyW

plyfibrilð�kf ;R;uo;nÞ; ð10Þ

in which Wrodfibrilð�kf Þ represents the strain energy function for single

fibrils, considered as elastic rods, and Wplyfibrilð�kf ;R;uo;nÞ represents

the strain energy function for rope-shaped fibrils, with volume frac-tion /ply. A rope is assumed to have n strands, forming a cylinder ofradius, R, with helical angle, uo, which is the complement of thepitch angle (Figs. 5b and 7b). The detailed derivation of the strain-energy function of a single rope-shaped fibril is presented in theAppendix. The strain-energy function Wrod

fibril is then considered tohave a quadratic form, similar to the second part of Wply

fibril, as inEq. (A.7).

4.3. Application to vocal folds lamina propria

Because of its importance for voice production, the laminapropria at a depth of about 0.5 mm [18,19] was the focus ofthis study. The representative element is assumed to be homo-geneous and nonisotropic, with an anisotropy vector in therange 0

�6 ho 6 90

�. The sinusoidal waveform function was

quantified, as shown in Fig. 4, and image analysis was usedto calculate �‘ and X by computing the arc length ofy ¼ Ro sinð2px=HoÞ. The overall orientation, ho, was also imposedwith a probability density function, POðh;/Þ, assuming /o ¼ p=2(i.e. planar loading). A modified von Mises distribution functionwas used:



Table 1Geometrical and mechanical parameters for the collagen fibrils used in the present model for (m = 3) porcine vocal fold tissues, within the depth of 0–0.4 mm.

Parameter /f /c ho E(N.m�2) Kb/t(N.nm2) r(nm) n uo

Mean value & standard deviation 0.601 ± .002 0.875 ± .002 7.51� ± 7.02� 1 � 106 ± 5 � 105 0.97 � 10�9 111 ± 34 8.7 ± 3.8 25.8� ± 12.4

Fig. 8. Distributions of axial stress r vs. axial stretch k for a representative blockmaterial of the tissue, obtained by Eq. (9); dot-dashed black line for a case ofcollagen-free material model, Wfibril ¼ 0; dotted red line for j ¼ 0:05 and/ply ¼ 0:30; dashed blue line for j ¼ 0:05 and /ply ¼ 0:70; solid green line forj ¼ 1:05 and /ply ¼ 0:70. See also Eqs. (10) and (11). The distribution from the free-length probability function in Eq. (6) is also shown using a pink line. The blackarrows show the initiation of the second-order parabolic response.


POðh;/Þ ¼sin2 /

8pI0ðjÞexpðj cosðh� hoÞÞ þ exp ð�j cos ðh� hoÞÞ½

þ exp ðj cos ðhþ hoÞÞ þ expð�j cos ðhþ hoÞÞ�; ð11Þ

where I0ðjÞ is the modified Bessel function, and j is the concentra-tion parameter. Eq. (11) satisfies the normalization condition. Thevolume fraction of fibrous proteins, /f , and the volume fraction ofcollagen, /c , were deduced from histological data [18,19].

The geometric parameters of rope-shaped fibrils were esti-mated from the AFM images (Fig. 5). The helical angles and theply radii were measured in the images, using NanoScope Analysis1.4 (Veeco, Santa Barbara, CA). The data are summarized in Table 1.Volume fraction values, /ply, of 0.30 and 0.70 were assumed in thecalculations. Collagen fibrils play a negligible role for small defor-mation. The strain-energy function related to matrix and elastinis described by a single constant, which was identified from the lin-ear portion of the stress–stretch curves [25]. Assuming equal stiff-ness, the corresponding shear moduli were obtained aslm ¼ le ¼ 15� 103 Pa: Eq. (9) calculates the Cauchy stress of auniform cubic element subjected to uniaxial loading. For a repre-sentative volume element, Eq. (9) was used to calculate stress vs.axial stretch. A script written in MATLAB (The MathWorks, Natick,MA) was used to calculate the stress for two values of the momentof anisotropy, j, and the rope–fibril volume fraction, /ply, as shownin Fig. 8.

5. Discussion

5.1. Spatial distributions of collagen and elastin networks

As illustrated in Fig. 1b and d, NLSM and AFM methods wereused to image vocal fold tissue for the development of a strain en-ergy formulation that considers the collagen helical hierarchy. Thespatial distribution of ECMs in unloaded and untreated tissue slices


defines the stress-free microstructure. The elastin fibers are moreisotropic than collagen fibrils in a planar distribution (i.e. the sag-ittal plane). This observation supports the hypothesis of the isotro-pic contribution of the elastin network to the strain-energyfunction, and it substantiates the poor colocalization of SHG andTPF signals. Comparisons between the fibrous structure seen inFig. 1d and nonfibrous ECMs in Fig. 1b suggest that fibrous proteinsare the dominant structure at the micrometer scale in terms ofmechanical resistance while other ECMs play a more effective roleat smaller scales. The cellular components are not included in thepresent study because of the composition of the lamina propria [1].

The collagen and elastin networks are more organized near thesuperficial layer, as shown in Fig. 2a and b, than in the deep layer ofthe lamina propria, as shown in Fig. 2c and d. In the muscle (Fig. 2eand f), the elastin fibers disappear and the collagen network israther isotropic, consistent with the histological data [18,19]. Hu-man vocal folds have regularly oriented collagen and elastin net-works [7], while the porcine vocal fold lamina propria has amore randomly distributed structure. These differences suggestdistinct mechanical properties. The phonatory function of vocalfolds requires an integrated, unidirectional network of collagenand elastin. A similar waviness seen in Fig. 2 was observed in col-lagen fibrils taken from intact vocal folds fixed in formaldehyde [7],which shows that the crimp shape of the collagen fibrils is notcaused by tissue preparation.

Signal area fractions that represent the layer-wise distributionof collagen and elastin fibers, are shown in Fig. 3. The TPF signalstrength was nearly uniform down to a depth of 0.6 mm, beyondwhich it significantly decreased in the vocal muscle [19]. TheSHG signal has a high magnitude below the epithelium and thenbecomes uniform at varying depths, all the way down to the mus-cle. The collagen within the superficial layer, immediately belowthe epithelium, is oriented parallel to the surface, causing an in-creased SHG signal (Fig. 2b). Fig. 3 confirms the homogeneity ofthe lamina propria in porcine larynges and substantiates the useof a homogeneous model. The human vocal fold lamina propria,in contrast, is multilayered [18,19], which requires more elaboratemodeling.

Insight into the interactions between collagen and elastin net-works is provided by SHG and TPF images (Fig. 3). The Pearson’scorrelation coefficient, in general, ranges from �1 to +1, with +1indicating perfectly correlated objects. A positive number was ex-pected as collagen and elastin fill the entire space, but the correla-tion decreased beyond a depth of �0.4 mm. The Pearson’scoefficient was found to vary between �0.12 and �0.50 for theporcine lamina propria. Qualitative colocalization, based on obser-vation, however, may indicate a lower correlation for porcine tis-sue than for human tissue [7]. This criterion cannot offer arigorous comparison because the fibrous structures are vector-valued, curvilinear objects.

5.2. Structural characterization of collagen fibrils at two length scales

A sinusoidal regression curve (Fig. 7a) was used to extract theperiodicity and orientation of collagen fibrils. The lamina propria(<0.5 mm) has a uniform distribution of parameters with respectto the muscle. For a depth of 400 lm, the measured amplitudeand periodicity were Ro = 3.08 ± 1.01 lm and Ho = 20.62 ± 7.43 lm,respectively. The free length of the fibrils (i.e. after uncurling) was




then computed and used in the simulation. Referring to Fig. 4, thedominant orientation was around 0�, with a lower variance in theregions near the epithelium. The estimated threshold stretch,where the collagen network dominates the stretch–stress re-sponse, was 1.19 ± 0.08. This value was implemented in the free-length probability function shown in Eq. (7) to generate Fig. 8.

Because surface scanning using AFM can suffer from cuttingartifacts, the high-intensity regions of the height-mode imageswere eliminated. The compliance of vocal fold tissue preventedAFM imaging in hydrated conditions; however, tissue dehydrationmay have affected the imaging. The images revealed two types ofcollagen fibrils: single and rope-shaped. Two porcine samples ta-ken from intact vocal folds, and fixed in formaldehyde, were alsoimaged by AFM as control experiments. Similar patterns were ob-served. Insignificant physical integrations between single fibrilsand other ECM macromolecules were observed in the AFM images.The rope-shaped fibrils were better integrated with nonfibrousECMs, a characteristic of type I collagen [12], which suggests thatrope-shaped fibrils may fall into this category. Models based onthe additive decomposition of material elastic energy (Eq. (4)) ap-pear incapable of representing this group of collagen fibrils.

5.3. Biomechanics of collagen-reinforced soft tissues

The technical difficulty involved in in situ measurements neces-sitates a multiscale, structural model that can predict the stiffnessof tissue from that of individual components, such as collagen fi-brils. The AFM-based indentation (Fig. 1a) offers a mechanicalcharacterization tool at the nanometer scale. It was used alongwith statistical analysis to estimate the stiffness of collagen fibrils(Fig. 6). The indentation elastic modulus may be influenced by thesoft microstructure underneath the collagen fibril being indented.However, collagen stiffness values on the order of GPa, which werereported for dehydrated samples [22], seem large for vocal folds.

The present formulation assumes affine deformation betweencollagen fibrils and other ECMs (Eq. (4)). The mechanical resistancecontributed by collagen fibrils is a result of their natural stiffnessand the loose cross-linking between collagen fibrils and otherECMs. Biomechanical aspects of collagen fibrils have been investi-gated following two approaches [27]. One approach involves iso-lating and purifying collagen fibrils, and determining theirstructure and interactions in vitro [28]. The other approach in-cludes measurements of the bulk mechanical properties of collag-enous tissues [20], and predictions of collagen stiffness frommultiscale models. Contrary to these two approaches, AFM-basednanoindentation of fresh tissue samples allows for biomechanicalcharacterization of a single collagen fiber in its naturalconfiguration.

Mechanical testing results (Fig. 1b) show that the stress vs.stretch response is nonlinear for stretch values greater than �1.2.The model shown in Eq. (9) may be used to simulate the behaviorof a tissue representative volume element, e.g., when comparingFig. 8 and Fig. 1b. The initial parts of the curves in Fig. 8 (k < 1.2)belong to collagen-free contributions, highlighting the resistanceof nonfibrous ECMs and elastin. The collagen fibrils uncurl withnegligible resistance to the loading. A comparison between thecurves for different /ply s reveals the region (1.2 < k < 1.4), whereuntwisting the rope-shaped structures has a great influence onthe stiffness (i.e. the tangential modulus). For large stretches where1.4 < k, the collagen fibrils act like unlocked free rods and stress vs.stretch obeys a parabolic relationship. The dispersion of anisot-ropy, j, affects the tissue response in this region. The main contri-bution of the rope structures in the present formulation can beobserved as greater slope changes in the region 1.2 < k < 1.4 for dif-ferent volume fractions of rope-shaped fibrils, /ply. The untwisting


mechanism controls the transition from the linear response to thenonlinear (i.e. parabolic) response at large stretch values.

The proposed model is based on the idea that some of the elasticenergy required to move a fully extended crimped fiber is used tountwist the fibrils. As a strain-energy theory, the model can simu-late the tissue response based on its unloaded configuration. Theformulation further enables the derivation of analytical expres-sions, which can be implemented in a numerical analysis [16] topredict the tissue response for physiologically relevant stressstates. The present model has some limitations. Only the solidmechanics of soft tissues was considered, assuming no interactionsbetween the solid structure and interstitial fluid. The fluid phasemay contribute significantly to the viscoelasticity of the tissue[20]. The evolution of noncollagenous ECMs, particularly elastin fi-bers, when collagen fibrils undergo deformation was also excluded.Finally, the model does not consider fibril cross-linking (i.e. no fi-bril-to-fibril interactions). The mechanisms of ECM remodelingshould be investigated in future experiments.

5.4. Implications to collagen remodeling in wound healing and tissueengineering

In contrast with available constitutive models [13,15,16], theproposed formulation provides a mathematical framework tostudy the biomechanical evolution of soft tissues under remodel-ing or growth. For example, vocal fold scarring that results fromthe surgical removal of vocal fold lesions and voice abuse is a com-mon problem in voice clinics [29]. Long-term consequences ofscarring include tissue remodeling, during which the ECM compo-sition changes over weeks until a mature scar is formed [29]. Col-lagen fibrils undergo helical self-assembly at different length scaleswith significant effects on the biomechanical behavior of thetissue.

Many vocal fold lesions are treated by the injection of tissue-engineering biomaterials [23]. Design and fabrication of injectablebiomaterials has followed a trial-and-error approach without agood understanding of ECM remodeling (e.g. for the vocal fold tis-sue [30]). Interaction of collagen fibrils and tissue engineering scaf-folds affects ECM remodeling and eventual tissue elasticity. Theremodeling process by which the neo-ECM matures into a hetero-geneous and anisotropic structure can affect the mechanical stiff-ness of the tissue [32] in ways that could be modeled using theframework proposed in the present work.

6. Conclusion

The microstructure of porcine vocal fold tissue was visualizedusing NLSM and AFM. The results showed the distribution of colla-gen and elastin networks in label-free fresh tissue slices. The bas-ket-like elastin network and crimp-shaped collagen fibrils wereimaged by NLSM. Colocalization of collagen fibrils and elastin fi-bers was negligible in porcine tissue, unlike in previous studiesof human vocal folds. Collagen fibrils were identified by their sur-face D-banding, and their nanoscale features were mapped by AFM.Two distinct fibril constituents were identified: freely distributedsingle fibrils and rope-shaped fibrils.

The elastic properties of collagen-reinforced soft tissues wereinvestigated using a composite structural model, where the effectof fibril untwisting was included using classical rope mechanics.Nanoindentation with AFM was further applied to estimate the lin-ear modulus of collagen fibrils, which was found to be in the rangeof 0.5–1.5 MPa. A calculation of stress vs. stretch revealed the con-tribution of the collagen helical hierarchy to the nonlinear relationbetween external loading and tissue deformation. This model canpredict the biomechanical behavior of vocal fold tissue, where




assembly of the collagen fibrils factors heavily into the remodelingprocess. The proposed methodology for microstructural character-ization and the strain-energy formulation are applicable to othersoft fibrous tissues.

Acknowledgements

This work was supported by NCDCD grant R01-DC005788 andCanadian Institutes of Health Research (CIHR). P.W.W. acknowl-edges Discovery Grant support from the Natural Sciences and Engi-neering Research Council of Canada (NSERC) and equipmentsupport from the Canadian Foundation for Innovation (CFI). Theauthors would like to express their greatest gratitude to Prof.François Barthelat (Mechanical Engineering Department, McGillUniversity, Montreal) for sharing his atomic force microscope.

Appendix A

Referring to Fig. 7b, a ply is made of n strands of radius r twistedaround each other on a uniform circular cylinder of radius R andinfinite extent (i.e. R=Lo � 0), a physically motivated assumption.Two geometrical constraints were used in a previous study [10]to obtain perfectly bonded strands. The global reference (x, y, z)is used for defining the external loading and a right-handed ortho-normal coordinate frame (e1, e2, e3) is introduced for kinematicalanalysis. In the case of constant curvature and torsion, the para-metric arc-length vector is written as:

r ðsÞ ¼ ðþR sin#;�R sin#; s cos uÞ; ð12Þ

where # ðsÞ ¼ s sinu=R and s represents the arc length and u is thehelical angle or the complement of pitch angle (Fig. 7b). The consis-tency of perfect contact between adjacent strands in a right-handedply is guaranteed [8] by:

d cos2 u� sin u sin2pn� d sin u

� �¼ 0 ð13Þ

2 1� cos2pn� d sinu

� �� þ d2 cos2 u ¼ 2r

R

� �2

: ð14Þ

Eq. (A.2) gives d; a shift parameter, based on known u and Eq. (A.3)yields the helical radius R. The mechanics of the rope model providegoverning equations [10]. When the rope is extended by axial force,Fo, per unit length, the equilibrium equation is then:

2nKb sin3 u cos uþ nKtRs cos 2uþ R2Fo sin u ¼ 0; ð15Þ

where Kb is the bending stiffness and Kt is the torsional stiffness ofeach strand. Also s is the axial torsional strain in each strand andmay be decomposed as [10]:

s ¼ cþ so; ð16Þ

with c being the internal pretwist, also called Love’s twist, lockedduring creation of the rope. The second term is so (� sin 2u=2R),the strand twist (Fig. 7b). Although this model neglects some char-acteristics of deformation in the strands, it is suitable for largedeformation [10,31]. The axial stretch is defined accordingly as�kf ¼ cosu= cosuo [10] with uo as the balanced helical angle. A con-vex and coercive strain-energy function (per strand) is a assumedhere with a quadratic function of the bending/torsion strains, asshown below [31]:

Wplyð�kf ;R;uo;nÞ ¼1

2pr2R2 Kb ð1� �k2f cos2 uoÞ

2

þ 12pr2R2 Kt ð�kf cos uo

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� �k2

f cos2 uo

qþ RcÞ2;

ð17Þ


The formula above expresses the energy of the ply as far as it istwisted. The pretwist, c, is computed by imposing Fo ¼ 0 andu ¼ uo in Eqs. (A.4) and (A.5). To generalize the problem, it is fur-ther assumed that the strand acts like a single fibril when it is com-pletely straightened. Considering �E as the axial stiffness, the strainenergy function is further modified:

Wplyfibrilð�kf ;R;uo;nÞ ¼ Wplyð�kf ;R;uo;nÞHðcos�1 uo � �kf Þ

þ 12

�E ð�kf � cos�1 uoÞ2 Hð�kf � cos�1 uoÞ; ð18Þ

where Hð�Þ is the Heaviside function.

Appendix B. Figures with essential colour discrimination

Certain figures in this article, particularly Figs. 1–8 are difficultto interpret in black and white. The full colour images can be foundin the on-line version, at http://dx.doi.org/10.1016/j.actbio.2013.04.044.

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Microstructural Characterization of Vocal Folds toward a Strain-Energy Model of Collagen Remodeling

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