A tissue adaptation model based on strain-dependent collagendegradation and contact-guided cell traction

T.A.M. Heck a, W. Wilson a, J. Foolen a, A.C. Cilingir b, K. Ito a, C.C. van Donkelaar a,n

a Orthopaedic Biomechanics, Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlandsb Mechanical Engineering Department, Sakarya University, Sakarya, Turkey

a r t i c l e i n f o

Article history:Accepted 26 November 2014

Keywords:Tension homeostasisTransient and equilibrium tissue adaptationCollagen remodelingFinite element model

a b s t r a c t

Soft biological tissues adapt their collagen network to the mechanical environment. Collagen remodelingand cell traction are both involved in this process. The present study presents a collagen adaptationmodel which includes strain-dependent collagen degradation and contact-guided cell traction. Celltraction is determined by the prevailing collagen structure and is assumed to strive for tensionalhomeostasis. In addition, collagen is assumed to mechanically fail if it is over-strained. Care is taken touse principally measurable and physiologically meaningful relationships. This model is implemented in afibril-reinforced biphasic finite element model for soft hydrated tissues.

The versatility and limitations of the model are demonstrated by corroborating the predictedtransient and equilibrium collagen adaptation under distinct mechanical constraints against experi-mental observations from the literature. These experiments include overloading of pericardium explantsuntil failure, static uniaxial and biaxial loading of cell-seeded gels in vitro and shortening of periosteumexplants. In addition, remodeling under hypothetical conditions is explored to demonstrate howcollagen might adapt to small differences in constraints.

Typical aspects of all essentially different experimental conditions are captured quantitatively orqualitatively. Differences between predictions and experiments as well as new insights that emerge fromthe present simulations are discussed. This model is anticipated to evolve into a mechanistic descriptionof collagen adaptation, which may assist in developing load-regimes for functional tissue engineeredconstructs, or may be employed to improve our understanding of the mechanisms behind physiologicaland pathological collagen remodeling.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

This work presents a numerical model that aims to study theadaptive behavior of soft tissues to mechanical loading. A thor-ough understanding of this adaptation may provide insight inpathological processes, it may assist in optimizing surgical recon-structions of load-bearing soft tissues, and it may serve the tissueengineering of such tissues through optimized mechanical con-ditioning during culture. In addition to these practical purposes, itis the beauty and the robustness of soft tissue adaptation that isintriguing. The resulting variety in macroscopic structural organi-zations of tissues, which are fully adapted to their particularfunction, yet with similar constitution at the microscopic level,fascinates scientists. This fascination for self-regulating biologicalprocesses has been key to Huiskes’ successful career. Studying

fundamental aspects of human joint replacement (Huiskes, 1979),he understood that bone adaptation is one of the governing factorsthat determine implant failure in the long term. By challenginghimself with questions and hypotheses on bone adaptation, hewent from the tissue level down to cell level mechanics. The titleof one of his many publications is: “If bone is the answer, thenwhat is the question?” (Huiskes, 2000). By posing ourselves suchquestions for various processes and tissues, we develop funda-mental understanding of tissue structure and adaptive processes.The present paper is the result of efforts to understand soft fibroustissue adaptation in general. It shows how the interplay betweenexternal loading, tissue properties and cell activity governs suchadaptation process, very similar to bone adaptation theoriesdeveloped by Huiskes et al. (2000b).

Tissues adapt to changing mechanical conditions by continuousremodeling of their collagen network through cell-mediated andmatrix-associated mechanisms. In the short term, cell alignmentdepends on topological patterns (‘contact guidance’) and themaximal principal strain direction (‘strain avoidance’) (Foolen etal., 2012; Mudera et al., 2000; Wang and Grood, 2000). Cell

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jbiomechwww.JBiomech.com

Journal of Biomechanics

http://dx.doi.org/10.1016/j.jbiomech.2014.12.0230021-9290/& 2014 Elsevier Ltd. All rights reserved.

n Correspondence to: Department of Biomedical Engineering, Gem-Z 4.101,Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, TheNetherlands. Tel.: +31 40 2473135.

E-mail address: c.c.v.donkelaar@tue.nl (C.C. van Donkelaar).

Journal of Biomechanics 48 (2015) 823–831

www.sciencedirect.com/science/journal/00219290www.elsevier.com/locate/jbiomechhttp://www.JBiomech.comhttp://www.JBiomech.comhttp://dx.doi.org/10.1016/j.jbiomech.2014.12.023http://dx.doi.org/10.1016/j.jbiomech.2014.12.023http://dx.doi.org/10.1016/j.jbiomech.2014.12.023http://crossmark.crossref.org/dialog/?doi=10.1016/j.jbiomech.2014.12.023&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.jbiomech.2014.12.023&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.jbiomech.2014.12.023&domain=pdfmailto:c.c.v.donkelaar@tue.nlhttp://dx.doi.org/10.1016/j.jbiomech.2014.12.023

traction to the extracellular matrix (ECM) depends on cell shape,size and focal adhesions (Rape et al., 2011). Cells monitor theirmechanical state and adjust traction forces depending on theenvironmental conditions to reach ‘tensional homeostasis’(Brown et al., 1998; Saez et al., 2005; Ghibaudo et al., 2008;Petroll et al., 2004). Cell traction results in alignment of thecollagen network (Stopak and Harris, 1982), which in turnbecomes a topological trigger for cells to orient. The result is acontinuously adapting tissue with an anisotropic angular distribu-tion of cell orientation, coinciding with the anisotropic angularcollagen fibril distribution (Guido and Tranquillo, 1993). Con-straints such as silicone posts spatially restrict tissue contraction,leading to dense anisotropic tissue arrays (Legant et al., 2009a,2009b; Foolen et al., 2012).

In the long term, collagen turnover influences the collagenstructure (Wang et al., 2007). Coll-I, MMP-1 and MMP-2 genes areupregulated with cyclic strain in fibroblasts (Breen, 2000; Yang etal., 2004; Butt and Bishop, 1997; Shelton and Rada, 2007; Yang etal., 2005; He et al., 2004), while coll-II, MMP-3, -9 and -13expression is enhanced in dynamically loaded chondrocytes(Fitzgerald et al., 2006). Thus, mechanical stimulation increasesboth collagen catabolism and anabolism, resulting in an increasedremodeling rate. Collagen orientation is also mechanoregulated.Tensile strain in collagen fibrils modulates their susceptibility toenzymatic degradation (Nabeshima et al., 1996; Ruberti andHallab, 2005; Bhole et al., 2009; Wyatt et al., 2009; Flynn et al.,2010; Zareian et al., 2010; Camp et al., 2011), likely through aswitch in the molecular state that makes it enzyme-resistant whenstrained (Wyatt et al., 2009; Camp et al., 2011). This mechanismpreserves collagen fibrils that are loaded in an appropriate strainrange, and allows degradation of under-strained fibrils.

Based on the above experimental findings, various hypotheseswere formulated with regard to cell activity, cell-matrix interac-tion and cell-independent collagen fiber remodeling. Even thoughexperimental data were quantified, the resulting hypotheses arequalitative in nature. To explore whether the individual hypoth-eses, or the combination thereof, would indeed result in thequantitative tissue adaptation seen under a wide variety of well-defined conditions, requires theoretical approaches. Such theore-tical models show that cell traction and contact guidance canqualitatively predict cell alignment and collagen gel compactionin vitro (Barocas and Tranquillo, 1997), while adaptive cell tractionmay control stress and strain homeostasis (Humphrey, 1999). Byassuming that collagen aligns in between the two principal straindirections, equilibrium collagen structures in various tissues arepredicted (Boerboom et al., 2003; Driessen et al., 2003; Wilson etal., 2006), and similar results are obtained starting from themechanical description of individual collagen fibrils (Kuhl andHolzapfel, 2007). After predicting the final tissue structure, thenext step is to predict the transient adaptation process during thetime of tissue development. Such prediction could for instance beused to develop loading conditions that maximize the rate atwhich load-bearing tissues develop their structure, in addition tooptimizing their final mechanical properties at the end of a tissueengineering study. To predict such transient adaptation process,more physically motivated constitutive models have been devel-oped. These include tissue adaptation based on strain-dependentcollagen degeneration (Van Donkelaar and Wilson, 2007) as wellas effects of cell contraction on collagen alignment (Nagel andKelly, 2012; Soares et al., 2012), or combinations thereof(Loerakker et al., 2013; Van Donkelaar et al., 2013).

The present study demonstrates the versatility and limitationsof a model that combines strain-dependent collagen degradation,mechanosensitive collagen turnover and contact-guided cell trac-tion. Predictions for transient and equilibrium collagen adaptation

under distinct mechanical constraints are corroborated againstexperimental observations from the literature.

2. Materials and methods

Collagen remodeling is implemented in a fibril-reinforced finite element (FE)model as two repeating sequential steps. First, tissue deformation and collagenstrains are calculated as the result of both cell traction and externally appliedforces. Second, collagen content and distribution change as a result of strain-dependent collagen degradation and collagen turnover.

2.1. Constitutive model

In a fibril-reinforced biphasic FE model for soft hydrated tissues (Wilson et al.,2004, 2005), the solid contains a fibrillar part representing the collagen networkand a non-fibrillar part representing the ground substance. The total stress σtot isgiven by

σtot ¼ �pnsI�pnf Iþσs ð1Þ

with σs the effective solid stress, p the hydrostatic pressure, I the unit tensor and nsand nf the solid and fluid volume fractions, respectively. The mechanical behavior ofthe non-fibrillar part is described with a compressible neo-Hookean model:

σ¼ K lnðJÞJ

IþGJðB� J2=3IÞ ð2Þ

with σ the Cauchy stress tensor, B the left Cauchy Green deformation tensor, K thebulk modulus, G the shear modulus and J the volumetric deformation. Themechanical behavior of the fibrillar part is defined as

P1 ¼E1 ek1εf ; log �1� �

; εf ; log 400; εf ; log r0

(ð3Þ

with P1 the fibril stress, εf,log the logarithmic fibril strain and E1 and k1 positivematerial constants. This behavior is applied to each fibril, which represents a groupof fibrils in the tissue and is defined by a density, orientation, initial and currentlength. Although collagen is viscoelastic, it is modeled as an elastic materialbecause the process of collagen remodeling occurs over a much longer time-scale(weeks–months) than the viscoelastic effects (min).

This material model is implemented in ABAQUS v6.11 (Hibbitt, Karlsson &Sorensen, Inc., Pawtucket, RI, USA) using the UMAT subroutine. Per integrationpoint of a 2-dimensional mesh, 30 collagen fibrils are included. One fibril obtains arandom orientation, which defines the orientations of the others with interfibrillarangles of 61. Increasing the number of fibrils did not change the result of thesimulations and the minimum angular resolution of fiber orientations that can becomputed with 30 fiber suffices for comparison with experimental data.

2.2. Implementation

The general concept is that collagen content and distribution are changed bystrain-dependent collagen degradation, collagen production and mechanical fail-ure. Collagen turnover rate is regulated by mechanosensitive cell metabolism. Fibrilstrain is changed by contact-guided cell traction, while cells continuously adapttheir traction forces to reach tensional homeostasis.

2.2.1. Collagen turnoverIt is assumed that mechanical stimulation increases both collagen production

and degradation rate (Wang et al., 2007), and that cell metabolism (fmet) increaseswith cell deformation. Given that cells attach to their environment, deformation ofthe cell is assumed to be equal to deformation of the ECM, and is calculated as theratio between the length of the longest (lf,max) and the shortest (lf,min) fibril:

f met ¼lf ;maxlf ;min

ð4Þ

The change in collagen density (dρ) over time is calculated depending on themetabolic rate and the difference between the rates of collagen degradation (dρdegr/dt) and production (dρprod/dt):

dρ¼ f metdρproddt

�dρdegrdt

� �dt

� �f ρ ð5Þ

in which fρ is a density factor, which ensures that collagen self-assembly anddegradation are more pronounced when there are more fibrils to interact with:

f ρ ¼ρfρip

totf ð6Þ

as defined by collagen density (ρip) and the number of collagen fibrils (totf) inintegration point ip.

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831824

Whether collagen degradation or synthesis prevails (Eq. (5)) depends on the fiberstrain (εf), because enzymatic collagen degradation is strain dependent (Wyatt et al.,2009). A transition value (εtransition) represents the strain at which degradation andsynthesis occur at equal rates. This is assumed to equal the average between maximal(dρmax/dt) and minimal (dρmin/dt) degradation rates for under-strained and highlystrained collagen fibrils, respectively:

dρproddt

¼ ðdρmax=dtÞþðdρmin=dtÞ2

ð7Þ

Strain-dependent enzymatic collagen degradation is implemented by decreas-ing collagen density according to Wyatt et al. (2009):

dρdegrdt

¼ dρmindt

þðdρmax=dtÞ�ðdρmin=dtÞ1þ10ðεf � εtransition ÞB

ð8Þ

where smoothing factor B accommodates for the fact that one collagen fibril in themodel represents a population of fibrils within þ31 and �31 angles and withvarious strain levels.

In addition, excessive strains may induce fibril damage. Because each fibrildirection represents a population of fibrils, a gradual transition between no damageand full fibril rupture is defined by two strain thresholds (εmin, εmax) and a strainconstant (εc):

f rup ¼

0; εf oεminεf � εminð Þ2

εmax � εminð Þ εc � εminð Þ; εf Zεmin and εf oεc

1� ðεmax � εf Þ2

εmax � εminð Þðεmax � εc Þ; εf Zεc and εf oεmax1; εf Zεmax

8>>>>>><>>>>>>:

ð9Þ

Finally, this mechanical damage is effective through an effect on the localcollagen density (ρip):

ρip ¼ ð1� f rupÞρip ð10Þ

2.2.2. Cell tractionFibril strain is calculated from the deformation tensor F of the solid matrix.

However, cell traction may cause additional fibril strain. This is implemented bypre-stretching the fibrils in the reference configuration, i.e. by changing the initialfibril length. Cell traction is a function of cell alignment (Rape et al., 2011),implemented as an ellipsoidal function with Tmin and Tmax the traction perpendi-cular and parallel to cell alignment. It is assumed that cells may align to any fibril (i)at each location (ip), yet that the number of aligning cells per fibril direction ðαÞscales with the fibril density. These contributions combined give fibril traction Tf:

Tf ¼ ∑totf

i ¼ 1

ρiρip

ðTminTmaxÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðTmin cos ðαi�αf ÞÞ2þðTmax sin ðαi�αf ÞÞ2

q ð11Þwith

Tmin ¼ 1�f cell�1f cellþ1

ð12Þ

Tmax ¼ 1þ f cell�1f cellþ1The traction value of each fibril direction is normalized (τf) to maintain a

constant cell traction force per integration point:

τf ¼Tf

∑totfi ¼ 1Tfð13Þ

Fibril strain (εf) depends on current fibril length (lf) as calculated from tissuedeformation, and on cell traction which increases with cell density (ρcell) andrelates inversely to fibril density (ρf):

εf ¼ 100% lf �1� �þ εf ;0τf ρcell 1ρf

!ð14Þ

with εf,0 the fibril strain induced by cell traction if τf, ρcell and ρf equal 1. Toimplement this cell traction effect, a new initial fibril length (l0,f) is determinedfrom the current fibril length (lf) and the calculated fibril stretch:

l0;f ¼lf

1þðεf =100%Þð15Þ

2.2.3. Cell traction adaptation towards tensional homeostasisCells adjust their traction forces to maintain tensional homeostasis (Brown et

al., 1998; Saez et al., 2005; Ghibaudo et al., 2008; Petroll et al., 2004). This isimplemented by adjusting the maximum cell traction per fibril with an adaptationfactor (fad,f), such that fibril strain is remodeled towards the strain at whichsynthesis and degradation are in equilibrium (εtransition in Eq. (7)). First, the targettraction value (τtarg) at which fibril strain is equal to εtransition is calculated by

rewriting the previous equations to:

τtarg ¼εtransition�100%ðlf �1Þ

εf ;0ρcellð1=ρf Þð16Þ

The adaptation factor at current time (t) then becomes

f ad;f tð Þ ¼f ad;f t�dtð Þ 1� 1� τtargτf

� �kaddt

� �; τtargoτf

f ad;f t�dtð Þ 1þ τtargτf �1� �

kaddt� �

; τtargZτf

8><>: ð17Þ

with kad the adaptation rate, which may range between 1 (complete adaptationtowards τtarg) and 0 (no adaptation) within each time step (dt). The adaptationfactor is limited between maximum value (fad,max) and 0 to prevent fibril compac-tion by cell traction.

2.3. Simulations

To evaluate the versatility of the model, predictions are corroborated againstdistinct in vitro experiments: tissue overloading until failure, static uniaxial andbiaxial loading, and tissue shortening. In addition, remodeling in some hypotheticalcases is predicted to demonstrate how collagen might adapt to small differences inconstraints.

In all simulations, two-dimensional FE meshes with 4-node plane strain porepressure elements (CPE4P) are used. Because the tissues in the experiments arethin, water transport to reach equilibriums is relatively fast (min) compared to thetime constant of the collagen remodeling process (days), as well as to the durationof the experiments (hours to days). For this reason, water transport is assumedinfinitively fast and this is implemented by prescribing zero pore pressurethroughout the mesh. Unless indicated otherwise, initial collagen density equalsone for all fibrils. One hour experimental time equals one time step with dt¼100.All parameters are provided in Table 1.

2.3.1. Tissue overloadingAxially loaded decellularized bovine pericardium strips were subjected to

collagenase, showing that local stresses accelerate collagen fibril degradation(Ellsmere et al., 1999). Simulations with and without collagen fibril rupturing (Eq.(9)) were performed on a rectangular FE mesh (10�4.5 mm; 180 elements). Whileit is constrained along the top edge, constant pressure of 3.4, 36 or 200 kPa wasapplied to the bottom edge using a coupling constraint, representing weights of 1,10 or 60 g, respectively. Initial collagen distribution in pericardium was approxi-mated from Billiar and Sacks (1997). The values for onset (εmin¼8%) and totalcollagen damage (εmax¼30%) (Eq. (9); Table 1) are selectively used for simulatingthis tissue overloading experiment. Literature reports a wide range of collagenfailure strains. The maximum value was chosen based on the strains at whichindividual collagen fibrils yield and break 20% and 30–50%, respectively (Shen et al.,2008). Yet, damage starts before those strains are reached. Human patella tendonsfail at 16% strain (Butler et al., 1978), and in some cases microscopic collagendamage was already observed at 4% strain (Wang, 2006). Therefore, a lowerthreshold for collagen was chosen in this range.

2.3.2. Uniaxial loadingCollagen adaptation over 72 h in uniaxially constrained fibroblast-populated

collagen gels (Lee et al., 2008) was simulated by fully constraining top and bottomnodes and coupling the horizontal displacement of nodes along the left and rightedges, separately, to simulate polyethylene sidebars. Mean angle and vector lengthof the fibril distribution are calculated for each integration point using a Matlab(Mathworks Inc) toolbox for circular statistics (Berens, 2009), taking into accountthat fibril angles are only unique within 1801.

2.3.3. Biaxial loadingThe arms of fibroblast-seeded cruciform collagen gels were subjected to 20%

static stretch (Hu et al., 2009). At day 0, 3 and 6 the angular collagen distributionwas measured in the center (CT), long arm (LA) and short arm (SA) of the gel. Analignment index (AI), defined as the normalized fraction of fibrils within 201 of thepredominant direction, was calculated to compare time points and experiments. Insimulations, the gel was allowed to remodel for 24 h during which the arms wereconstrained. Subsequently, the short arms were stretched to 1.01 and the long armsto either 1.04 or 1.20 times their initial length for six days.

2.3.4. Tissue shortening and lengtheningEmbryonic periosteum was able to restore its preferred mechanical strain state

within 72 h of culture, when it was shortened by 10% or lengthened by 5% (Foolenet al., 2010). It could not fully recover when shortened by 15%. Simulations wereperformed for length-changes between �15% and þ5%, including only celltraction, only collagen degradation and production, or with a combination thereof.A 50�50 mm square FE mesh (527 elements) was used, representing a central areaof the idealized cylindrical periosteum. Nodal displacements were constrained in

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831 825

all directions at the top and bottom edge and in horizontal direction at the left andright edge. After 72 h of initial remodeling, tissue length was changed bydisplacement of the top edge and the tissue remodeled for another 72 h afterwhich a force-stretch curve was determined. For comparison with experiments, atransition stretch was defined as the stretch at the reaction force equal to the onereached in the unstrained tissue at 0.96 times the in vivo length. Note that the term‘transition stretch’ is copied for this particular simulation from the originalexperimental paper (Foolen et al., 2010), and should not be confused with thetransition strain parameter used in the model (εtransition in Eq. (16); Table 1).

2.3.5. Hypothetical remodeling casesFour hypothetical remodeling cases illustrated possible effects of small changes

applied to a common TE setup. A collagen gel (20�20 mm, 400 elements, top andbottom edges constrained) was allowed to remodel for 72 h, after which the topsurface was sheared, asymmetrically elongated or asymmetrical shortened duringanother 72 h. In a fourth simulation the collagen gel was attached to poles on itsfour corners for 72 h.

3. Results

3.1. Tissue overloading

A two-phase tissue elongation pattern occurs over time for allsimulations (Fig. 1). Only when fibril rupturing is included, time tofailure decreases with increasing applied load to the tissue, similarto the experimental observations.

3.2. Uniaxial loading

Collagen aligns with the loading direction over time, withtypical distributions of density and degree of alignment near theconstrained sites (Fig. 2).

Fig. 1. Elongation-time curves of statically loaded pericardium strips exposed to collagenase, loaded with 1, 10 and 60 g. Experimental curves (dotted; Ellsmere et al., 1999)and results of simulations without (A) and with (B) strain-dependent collagen rupturing.

Table 1Overview of parameters used in the simulations.

Overloading (Ellsmere etal., 1999) n

Uniaxial constraint (Lee etal., 2008) nn

Biaxial constraint (Hu et al.,2009) nn

Shortening & lengthening (Foolen etal., 2010) nnn

Collagengel nn

Material E1 (Pa) 3.0�103 2.5�102 2.5�102 1.0�103 2.5�102k1 37 5.5 5.5 25 5.5Em (Pa) 1�104 10 10 10 10vm 0.4 0.45 0.45 0.45 0.45

Coll.remodeling

dρmax/dt$ 9.0�10�5 1.0�10�2 5.0�10�4 1.5�10�3 1.0�10�3

dρmin/dt$ 4.5�10�5 5.0�10�3 2.5�10�4 7.5�10�4 5.0�10�4

εtransition (%)# 4.0 4.0 4.0 4.0 4.0

B ## 0.5 0.5 0.5 0.5 0.5εmax (%) ### 30 – – – –εmin (%)

### 8.0 – – – –εc (%) 25 – – – –

Celltraction

fcell – 150 150 150 150ρcell – 1.5 1.5 1.5 1.5ε0 (%) – 4.0 4.0 4.0 4.0kad

$ – 5.0�10�4 1.0�10�3 1.0�10�3 1.0�10�4fad,max

$ – 2.0 5.0 2.0 2.0SIm Increments per

hour1 10 1 10

n Material parameters fitted to biaxial loading experiment (Langdon et al., 1999).nn Material parameters fitted to biaxial tensile tests after 72 h of culture under uniaxial constraint (Lee et al., 2008).nnn Material parameters manually adjusted and parameter study is added to evaluate effects (see text).# Derived from Zareian et al. (2010).## Derived from Wyatt et al. (2009).### Derived from Butler et al. (1978), Shen et al. (2008), Wang (2006).$ Adjusted per simulation to match differences in experimental time, tissue type, cell number and collagen density.

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831826

3.3. Biaxial loading

For the 4% strain (λLA¼1.04) simulation, the AI in the central(CT) region remains low and the LA and SA regions increase tolevels comparable with the experiment (Fig. 3). Only the AI in theLA does not stabilize after 3 days. However, simulations with 20%strain show a different pattern, with increased AI in the CT regionand low AI in the LA.

3.4. Tissue shortening and lengthening

During 3 days of remodeling after lengthening or shortening,the transition stretch shifts towards the new tissue length and thestiffness of the tissue changes. With only collagen remodeling andno cell traction (Fig. 4B), the shift in transition stretch is not asapparent as with cell traction included. This importance of celltraction is in agreement with the experimental data (Foolen et al.,2010). Changes in tissue stiffness also concur with experiments.This is the consequence of collagen remodeling (Fig. 4A) in thesimulations, and is strongly influenced by whether or not celltraction occurs in parallel (Fig. 4E). In simulations, the change instiffness is associated with changes in collagen content, butcollagen loss is not observed experimentally.

3.5. Hypothetical remodeling cases

After the initial remodeling phase, collagen density is highest inthe corners and lowest at the free edges, while fibrils align in the

constrained direction and towards the corners (Fig. 5A). Whensubsequently shear is applied, the fibrils rotate towards the long-est axis of the gel, with a modest increase in collagen density alongthat line (Fig. 5B). Asymmetric lengthening of the gel increasescollagen density and stimulates alignment at the modulated sideof the gel (Fig. 5C), while asymmetric shortening decreases densityand reduces alignment at the modulated side (Fig. 5D). When a gelis constrained at 4 corners, collagen aligns along the edges andtowards the corners, with highest collagen density in the corners.The collagen distribution is isotropic in the center (Fig. 5E).

4. Discussion

This study demonstrates the versatility of a description ofcollagen remodeling including strain-dependent collagen degra-dation, collagen production, contact guided cell traction andmechanical collagen rupture. Typical aspects of essentially differ-ent experimental conditions and with both explants and cell-populated gels are captured qualitatively. These include the typicaltwo-phase elongation curves in the overloading-to-failure experi-ments on mature pericardium by Ellsmere et al. (1999). Thecharacteristic shift of the transition point where failure startswas only predicted correctly when mechanical rupture of collagenwas included in addition to enzymatic degradation, suggestingthat the experimental data cannot be explained by enzymaticcollagen degradation alone. In periosteum explants, the peculiarshift in the transition point of the force–stretch curve in response

Fig. 2. Angular collagen density distribution (A) and the development over time of its characteristics (B) in the middle 10�10 mm area of a 28�28 mm gel, which isconstrained at the top and bottom. Nodes at the left and right edges are tied such that the edges as a whole may move horizontally. Experimental data represent angularcollagen density distribution normalized to the average initial collagen density (Lee et al., 2008). (C–E) Density (left; colors represent densities ranging from 2/3 (dark blue)to 3 times (red) the initial collagen content, and degree of alignment (right; colors represent vector length; lines oriented in fibril direction) after 6 (C), 12 (D) and 72(E) hours. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831 827

to tissue shortening or lengthening is similar between predictionsand experiments (Foolen et al., 2010). Interestingly, tissue fails toshift the transition point beyond 10% shortening in both experi-ments and simulations. Also, cell contraction was the mostefficient to induce this shift, which agrees with the observationthat Cytochalasin-D, which disrupts the actin cytoskeleton, blocksthis effect (Foolen et al., 2010). In TE constructs, collagen adapta-tion under uniaxial loading concurs quantitatively with theexperiments (Lee et al., 2008), both for collagen density as afunction of angular distribution and for the changes over time. Inaddition, lateral compaction occurred, which is also apparent on aphotograph after remodeling (Fig. 1 in Lee et al., 2008). Collagenalignment in the direction between the applied constraints alsoconcurs with other observations in both gels (e.g. Legant et al.,2009a, 2009b) and tissues (e.g. Foolen et al., 2012), and highqualitative resemblance with experiments is observed for thepinned gel simulation (Fig. 5E; experimental data by Legant etal., 2009a, 2009b (not shown)). Simulations of similar gels underbiaxial loading (Hu et al., 2009) match quantitatively as well, butonly when less displacement is applied to the system. Tissuedevelops differently at the experimentally applied strain levels aswill be discussed later.

However, there are also differences that require discussion.First, the collagen network in explants likely contains variations infibril direction and pre-strains. Also crosslinking may be impor-tant, more so in explants than in TE constructs. Such effects mayaffect experimental results such as the failure patterns in thetissue overloading experiments (Ellsmere et al., 1999; Fig. 1) or the

adaptation to tissue shortening (Foolen et al., 2012; Fig. 4). Similarinhomogeneous effects seem to occur after casting TE gels: in theaxisymmetric setup of Hu et al. (2009) anisotropy develops evenbefore stretch is applied to the arms, resulting in a discrepancybetween simulations (AI¼1) and the experiment (AI¼1.25; datanot shown). Such variations in fiber populations are not incorpo-rated into the model, although some effects are accounted for byusing gradual transitions in for instance the equations represent-ing fibril rupture (Eq. (9)). Second, the non-fibrillar matrix,representing the ground substance, does not remodel. Pressuresassociated with compression of the non-fibrillar matrix in themodel may explain why tissues seem to compact less in simula-tions than in for instance the experiments of Lee et al. (2008).Third, tissue growth is not included. Although the tissue is able toadapt appropriately to 5% elongation (Fig. 4B and C), this is not dueto tissue growth. The model assumes that new collagen moleculesattach to existing fibrils and automatically attain the prevailingfibril strain. However, this will result in continuous increase ofcollagen density if a constant strain is applied that exceeds thetransition strain (εtransition in Eq. (8)) (Eq. (5)). To exemplify thiseffect, simulations with 20% strain in the biaxial condition over-predict collagen density in the center and do not stabilize overtime as experimentally observed (Fig. 3D), whereas a physiologi-cally more realistic response prevails in simulations where theapplied static strain remains lower (Fig. 3C). This unnaturalresponse may be solved by combining the present model with atissue growth approach in which newly synthesized collagenassembles to form an unstrained fibril within the present

Fig. 3. Total length of the cruciform FE mesh is 50 mm. The constrained edge of each arm is 15 mm, tapered to 7 mm in the middle of the arm (A). Experimentally (B; Hu etal., 2009) and numerically determined normalized AI’s for the indicated regions in the center (CT), long arm (LA) and short arm (SA) when the long arm is stretched 4% (C) or20% (D) during 3 and 6 days of remodeling.

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831828

geometry, i.e. within the deformed matrix (Van Donkelaar andWilson, 2007, 2012; Khoshgoftar et al., 2014). Fourth, because cellsattach to the ECM, cell deformation is assumed to follow ECMstrain. This is functional, because they sense these strains andbecause maximum cell contraction force relates to cell shape.However, assuming that cell attachment is a static condition is asimplification. Focal adhesions are dynamic and changes in focaladhesion points may change cell strain. Such adaptive behaviorhas not yet been accounted for and may be part of future modelextension. Fifth, selecting parameters is difficult. Optimizing col-lagen remodeling and cell traction parameters per study is argu-able because each study uses different tissues, gels and cellsources. Yet, in order to allow for comparison between thedifferent cases in this study, parameter variations were kept rathersmall (Table 1). To explore the effect of these choices for cell-traction related parameters, a small parameter study is performed.

This study reveals that εtransition (Eq. (8)), εf,0 (Eq. (14)) and fad,max(Eq. (17)) together determine tissue compaction, but they do notinfluence the time to reach equilibrium. Thus, the residual forcethat is produced under a given strain condition is hardly changedby any of these parameters, but the stress that is generated maychange significantly. This may be relevant when comparingsimulations with experimentally determined stress rather thanforce. The time that it takes to reach equilibrium is dominated bykad (Eq. (17)). Another effect involving numerical-experimentalcomparison relates to methods for calculation of parameters. Forinstance, the transition stretch in the shortening study (Fig. 4) wasfor practical reasons determined by Foolen et al. (2010) as thetissue length where 1/8th of the tissue stiffness was obtained.Because stress–strain curves are non-linear, this definition cannotbe copied exactly in simulations. The present study uses analternative strain-based definition of the transition-stretch,

Fig. 4. Reaction force–stretch curves (A, C and E) and transition stretch against applied stretch (B, D and F) after 72 h of remodeling at the applied stretch level, for sets ofsimulations with only collagen remodeling (A and B), both collagen remodeling and cell traction adaptation (C and D), and only cell traction adaptation included (E and F).For comparison, the experimental data (Foolen et al., 2010) are indicated in grey diamonds (B, D and F).

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831 829

whereas other numerical studies used force- or stress-basedparameters (Loerakker et al., 2013; Nagel and Kelly, 2012). Thismay explain why the results of the present study compare betterto the experimental data than the result of other studies. Finally,

boundary conditions may differ between experiments and simula-tions, for instance due to experimental inaccuracies. The set ofsimulations with small changes in constraints shows that this mayhave significant effects on the collagen network (Fig. 5). Thisinsight is important for the design of TE experiments and theinterpretation of variability in experimental datasets.

Some of the presented simulations provide new scientificinsight and hypotheses that may be explored in the future. Forinstance, tissue response to mechanical overloading without fibrilrupturing resulted in curves with characteristics that were notseen experimentally (Fig. 1). Thus, fibril rupturing is postulated tooccur throughout lengthening, which suggests significant varia-bility in fibril pre-strain. Also, simulations propose that the shift intransition stretch after tissue shortening results from cell-traction,while the observed change in tissue stiffness develops due tocollagen remodeling (Fig. 4). From these simulations it is furtherhypothesized that failure to fully adapt to 15% shortening may becaused by the maximal cell-traction force.

In conclusion, this manuscript presents the versatility of amodel that describes the collagen remodeling process by strain-dependent collagen degradation, collagen production, contact-guided cell traction and mechanical fibril rupture. Care was takento use principally measurable parameters in physiologically mean-ingful equations. This is expected to make translation of experi-mental data to model input easier, stimulating furtherdevelopment towards a mechanistic model of collagen adaptation.The model is anticipated to improve our understanding of themechanisms behind physiological and pathological collagen remo-deling, and to assist in developing load-bearing TE constructs.

References

Barocas, V.H., Tranquillo, R.T., 1997. An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar networkdeformation, fibril alignment, and cell contact guidance. J. Biomech. Eng. 119(2), 137–145.

Berens, P. Circstat, 2009. A MATLAB toolbox for circular statistics. J. Stat. Softw. 31 (10).Bhole, A.P., Flynn, B.P., Liles, M., Saeidi, N., Dimarzio, C.A., Ruberti, J.W., 2009.

Mechanical strain enhances survivability of collagen micronetworks in thepresence of collagenase: implications for load-bearing matrix growth andstability. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 367 (1902), 3339–3362.

Billiar, K.L., Sacks, M.S., 1997. A method to quantify the fiber kinematics of planartissues under biaxial stretch. J. Biomech. 30 (7), 753–756.

Boerboom, R.A., Driessen, N.J.B., Bouten, C.V.C., Huyghe, J.M., Baaijens, F.P.T., 2003.Finite element model of mechanically induced collagen fiber synthesis anddegradation in the aortic valve. Ann. Biomed. Eng. 31 (9), 1040–1053.

Breen, E.C., 2000. Mechanical strain increases type I collagen expression inpulmonary fibroblasts in vitro. J. Appl. Physiol. 88, 203–209.

Brown, R.A., Prajapati, R., McGrouther, D.A., Yannas, I.V., Eastwood, M., 1998.Tensional homeostasis in dermal fibroblasts: mechanical responses to mechan-ical loading in three-dimensional substrates. J. Cell. Physiol. 175 (3), 323–332.

Butler, D.L., Grood, E.S., Noyes, F.R., Zernicke, R.F., 1978. Biomechanics of ligamentsand tendons. Exerc. Sport Sci. Rev. 6, 125–181.

Butt, R.P., Bishop, J.E., 1997. Mechanical load enhances the stimulatory effect ofserum growth factors on cardiac fibroblast procollagen synthesis. J. Mol. Cell.Cardiol. 29 (4), 1141–1151.

Camp, R.J., Liles, M., Beale, J., Saeidi, N., Flynn, B.P., Moore, E., Murthy, S.K., Ruberti, J.W., 2011. Molecular mechanochemistry: low force switch slows enzymaticcleavage of human type I collagen monomer. J. Am. Chem. Soc. 133 (11),4073–4078.

Driessen, N.J.B., Boerboom, R.a., Huyghe, J.M., Bouten, C.V.C., Baaijens, F.P.T., 2003.Computational analyses of mechanically induced collagen fiber remodeling inthe aortic heart valve. J. Biomech. Eng. 125 (4), 549–557.

Ellsmere, J.C., Khanna, R.A., Lee, J.M., 1999. Mechanical loading of bovine pericar-dium accelerates enzymatic degradation. Biomaterials 20 (12), 1143–1150.

Fitzgerald, J.B., Jin, M., Grodzinsky, A.J., 2006. Shear and compression differentiallyregulate clusters of functionally related temporal transcription patterns incartilage tissue. J. Biol. Chem. 281 (34), 24095–24103.

Flynn, B.P., Bhole, A.P., Saeidi, N., Liles, M., Dimarzio, C.A., Ruberti, J.W., 2010.Mechanical strain stabilizes reconstituted collagen fibrils against enzymaticdegradation by mammalian collagenase matrix metalloproteinase 8 (MMP-8).PLoS One 5 (8)e12337.

Foolen, J., Deshpande, V.S., Kanters, F.M.W., Baaijens, F.P.T., 2012. The influence ofmatrix integrity on stress-fiber remodeling in 3D. Biomaterials 33 (30),7508–7518.

Fig. 5. Collagen density distribution (left; density values range linearly from 2/3(dark blue) to 2 times (red) the initial collagen density) and fibril orientation (right;values for vector length indicated in insert (E)) after the initial remodeling phase(A) and after the second remodeling phase in which tissue was loaded by shearingthe top surface (B), elongating (C) or shortening (D) the right side, or pinning at thecorners (E). (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831830

http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref1http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref1http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref1http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref1http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref2http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref3http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref3http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref3http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref3http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref4http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref4http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref5http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref5http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref5http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref6http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref6http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref7http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref7http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref7http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref8http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref8http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref9http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref9http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref9http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref10http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref10http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref10http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref10http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref11http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref11http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref11http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref12http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref12http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref13http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref13http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref13http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref14http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref14http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref14http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref14http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref15http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref15http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref15

Foolen, J., van Donkelaar, C.C., Soekhradj-Soechit, S., Ito, K., 2010. European Societyof Biomechanics S.M. Perren Award 2010: an adaptation mechanism for fibroustissue to sustained shortening. J. Biomech. 43 (16), 3168–3176.

Ghibaudo, M., Saez, A., Trichet, L., Xayaphoummine, A., Browaeys, J., Silberzan, P.,Buguin, A., Ladoux, B., 2008. Traction forces and rigidity sensing regulate cellfunctions. Soft Matter 4 (9), 1836–1843.

Guido, S., Tranquillo, R.T., 1993. A methodology for the systematic and quantitativestudy of cell contact guidance in oriented collagen gels. Correlation of fibroblastorientation and gel birefringence. J. Cell Sci. 105, 317–331.

He, Y., Macarak, E.J., Korostoff, J.M., Howard, P.S., 2004. Compression and tension:differential effects on matrix accumulation by periodontal ligament fibroblastsin vitro. Connect. Tissue Res. 45 (1), 28–39.

Hu, J.-J., Humphrey, J.D., Yeh, A.T., 2009. Characterization of engineered tissuedevelopment under biaxial stretch using nonlinear optical microscopy. TissueEng. Part A 15 (7), 1553–1564.

Huiskes, R., 1979. Some Fundamental Aspects of Human Joint Replacement—Analyses of Stresses and Heat Conduction in Bone-prosthesis Structure.Eindhoven University of Technology (Ph.D. Thesis).

Huiskes, R., 2000. If bone is the answer, then what is the question? J. Anat. 197 (2),145–156.

Huiskes, R., Ruimerman, R., Van Lenthe, G.H., Janssen, J.D., 2000b. Effects ofmechanical forces on maintenance and adaptation of form in trabecular bone.Nature 405, 704–706.

Humphrey, J.D., 1999. Remodeling of a collagenous tissue at fixed lengths. J.Biomech. Eng. 121, 591–597.

Khoshgoftar, M., Wilson, W., Ito, K., van Donkelaar, C.C., 2014. Influence ofextracellular matrix temporal deposition on the swelling and mechanicalproperties of TE cartilage. Tissue Eng. Part A 20 (9-10), 1476–1485.

Kuhl, E., Holzapfel, G.a., 2007. A continuum model for remodeling in livingstructures. J. Mater. Sci. 42 (21), 8811–8823.

Langdon, S.E., Chernecky, R., Pereira, C.A., Abdulla, D., Lee, J.M., 1999. Biaxialmechanical/structural effects of equibiaxial strain during crosslinking of bovinepericardial xenograft materials. Biomaterials 20 (2), 137–153.

Lee, E.J., Holmes, J.W., Costa, K.D., 2008. Remodeling of engineered tissue anisotropyin response to altered loading conditions. Ann. Biomed. Eng. 36 (8), 1322–1334.

Legant, W.R., Pathak, A., Yang, M.T., Deshpande, V.S., McMeeking, R.M., Chen, C.S.,2009a. Microfabricated tissue gauges to measure and manipulate forces from3D microtissues. Proc. Natl. Acad. Sci. U.S.A. 106 (25), 10097–10102.

Legant, W.R., Pathak, A., Yang, M.T., Deshpande, V.S., McMeeking, R.M., Chen, C.S.,2009b. Microfabricated tissue gauges to measure and manipulate forces from3D microtissues. PNAS 106 (25), 10097–10102.

Loerakker, S., Obbink-Huizer, C., Baaijens, F.P., 2013. A physically motivatedconstitutive model for cell-mediated compaction and collagen remodeling insoft tissues. Biomech. Model. Mechanobiol. , http://dx.doi.org/10.1007/s10237-013-0549-1.

Mudera, V.C., Pleass, R., Eastwood, M., Tarnuzzer, R., Schultz, G., Khaw, P.,McGrouther, D.a., Brown, R.a., 2000. Molecular responses of human dermalfibroblasts to dual cues: contact guidance and mechanical load. Cell Motil.Cytoskeleton 45 (1), 1–9.

Nabeshima, Y., Grood, E.S., Sakurai, A., Herman, J.H., 1996. Uniaxial tension inhibitstendon collagen degradation by collagenase in vitro. J. Orthop. Res.: officialpublication of the Orthopaedic Research Society 14 (1), 123–130.

Nagel, T., Kelly, D.J., 2012. Remodelling of collagen fibre transition stretch andangular distribution in soft biological tissues and cell-seeded hydrogels.Biomech. Model. Mechanobiol. 11 (3-4), 325–339.

Petroll, W.M., Vishwanath, M., Ma, L., 2004. Corneal fibroblasts respond rapidly tochanges in local mechanical stress. Invest. Ophthalmol. Vis. Sci. 45 (10),3466–3474.

Rape, A.D., Guo, W.-H., Wang, Y.-L., 2011. The regulation of traction force in relationto cell shape and focal adhesions. Biomaterials 32 (8), 2043–2051.

Ruberti, J.W., Hallab, N.J., 2005. Strain-controlled enzymatic cleavage of collagen inloaded matrix. Biochem. Biophys. Res. Commun. 336 (2), 483–489.

Saez, A., Buguin, A., Silberzan, P., Ladoux, B., 2005. Is the mechanical activity ofepithelial cells controlled by deformations or forces? Biophys. J. 89 (6),L52–L54.

Shelton, L., Rada, J.S., 2007. Effects of cyclic mechanical stretch on extracellularmatrix synthesis by human scleral fibroblasts. Exp. Eye Res. 84 (2), 314–322.

Shen, Z.L., Dodge, M.R., Kahn, H., Ballarini, R., Eppell, S.J., 2008. Stress–strainexperiments on individual collagen fibrils. Biophys. J. 95, 3956–3963.

Soares, a.L.F., Oomens, C.W.J., Baaijens, F.P.T., 2012. A computational model todescribe the collagen orientation in statically cultured engineered tissues.Comput. Methods Biomech. Biomed. Eng. 0 (0), 1–12.

Stopak, D., Harris, A.K., 1982. Connective tissue morphogenesis by fibroblasttraction. Dev. Biol. 90 (2), 383–398.

Van Donkelaar, C.C., Wilson, W., 2012. Mechanics of chondrocyte hypertrophy.Biomech. Model. Mechanobiol. 11 (5), 655–664.

Van Donkelaar C.C., Heck T.A.M., Wilson W., Foolen J., Ito K., 2013. Versatility of acollagen adaptation model that includes strain-dependent degeneration andcell traction. In: Proceedings of the ASME 2013 Summer BioengineeringConference (SBC2013-14214), Sunriver, OR, USA.

Van Donkelaar, C.C., Wilson, W., 2007. A new versatile mechanistic collagenremodeling algorithm. In: Proceedings of the ASME 2007 Summer Bioengineer-ing Conference Keystone, Colorado, USA.

Wang, J.H., Grood, E.S., 2000. The strain magnitude and contact guidance determineorientation response of fibroblasts to cyclic substrate strains. Connect. TissueRes. 41 (1), 29–36.

Wang, J.H.-C., 2006. Review mechanobiology of tendon. J. Biomech. 39, 1563–1582.Wang, J.H., Thampatty, B.P., Lin, J.-S., Im, H.-J., 2007. Mechanoregulation of gene

expression in fibroblasts. Gene 391 (1-2), 1–15.Wilson, W., Driessen, N.J.B., van Donkelaar, C.C., Ito, K., 2006. Prediction of collagen

orientation in articular cartilage by a collagen remodeling algorithm. Osteoar-thritis Cartilage/OARS, Osteoarthritis Research Society 14 (11), 1196–1202.

Wilson, W., van Donkelaar, C.C., van Rietbergen, B., Huiskes, R., 2005. A fibril-reinforced poroviscoelastic swelling model for articular cartilage. J. Biomech. 38(6), 1195–1204.

Wilson, W., van Donkelaar, C.C., van Rietbergen, B., Ito, K., Huiskes, R., 2004.Stresses in the local collagen network of articular cartilage: a poroviscoelasticfibril-reinforced finite element study. J. Biomech. 37 (3), 357–366.

Wyatt, K.E., Bourne, J.W., Torzili, P.A., 2009. Deformation-dependent enzymemechanokinetic cleavage of type I collagen. J. Biomech. Eng. 131 (5), 051004.

Yang, G., Crawford, R.C., Wang, J.H.-C., 2004. Proliferation and collagen productionof human patellar tendon fibroblasts in response to cyclic uniaxial stretching inserum-free conditions. J. Biomech. 37 (10), 1543–1550.

Yang, G., Im, H.-J., Wang, J.H.-C., 2005. Repetitive mechanical stretching modulatesIL-1beta induced COX-2, MMP-1 expression, and PGE2 production in humanpatellar tendon fibroblasts. Gene 363, 166–172.

Zareian, R., Church, K.P., Saeidi, N., Flynn, B.P., Beale, J.W., Ruberti, J.W., 2010.Probing collagen/enzyme mechanochemistry in native tissue with dynamic,enzyme-induced creep. Langmuir 26 (12), 9917–9926.

T.A.M. Heck et al. / Journal of Biomechanics 48 (2015) 823–831 831

http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref16http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref16http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref16http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref17http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref17http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref17http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref18http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref18http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref18http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref19http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref19http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref19http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref20http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref20http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref20http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref21http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref21http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref21http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref22http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref22http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref23http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref23http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref23http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref24http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref24http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref25http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref25http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref25http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref26http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref26http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref27http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref27http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref27http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref28http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref28http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref29http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref29http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref29http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref30http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref30http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref30http://dx.doi.org/10.1007/s10237-013-0549-1http://dx.doi.org/10.1007/s10237-013-0549-1http://dx.doi.org/10.1007/s10237-013-0549-1http://dx.doi.org/10.1007/s10237-013-0549-1http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref32http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref32http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref32http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref32http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref33http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref33http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref33http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref34http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref34http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref34http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref35http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref35http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref35http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref36http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref36http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref37http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref37http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref38http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref38http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref38http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref39http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref39http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref40http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref40http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref41http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref41http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref41http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref42http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref42http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref43http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref43http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref44http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref44http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref44http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref45http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref46http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref46http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref47http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref47http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref47http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref48http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref48http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref48http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref49http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref49http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref49http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref50http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref50http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref51http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref51http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref51http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref52http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref52http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref52http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref53http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref53http://refhub.elsevier.com/S0021-9290(14)00677-0/sbref53

A tissue adaptation model based on strain-dependent collagen degradation and contact-guided cell tractionIntroductionMaterials and methodsConstitutive modelImplementationCollagen turnoverCell tractionCell traction adaptation towards tensional homeostasis

SimulationsTissue overloadingUniaxial loadingBiaxial loadingTissue shortening and lengtheningHypothetical remodeling cases

ResultsTissue overloadingUniaxial loadingBiaxial loadingTissue shortening and lengtheningHypothetical remodeling cases

DiscussionReferences