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www.advhealthmat.de www.MaterialsViews.com wileyonlinelibrary.com 112     C     O     M     M     U     N     I     C     A     T     I     O     N © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  Adv. Health care Mater.  2012, 1, 112–116   Aurélie Jean and George C. Engelmayr Jr.* Anisotropic Collagen Fibrillogenesis Within Microfabricated Scaffolds: Implications For Biomimetic Tissue Engineering  Dr. A. Jean Department of Bioengineering The Pennsylvania State University 223 Hallowell Building, University Park PA 16802, USA Dr. G. C. Engelmayr Jr. Department of Bioengineering The Pennsylvania State University 223 Hallowell Building University Park PA 16802, USA  E-mail: [email protected] DOI: 10.1002/adhm.201100017 Collagen gels nd widespread application as three-dimensional substrates in cell culture assays, [  1  ]  drug delivery, [  2  ]  and tissue engineering. [3  ]  At the macroscale, boundary constraints inu- ence cell-laden collagen gel anisotropy; [  4  ]  at shorter length scales, composites of collagen gels with microfabricated mate- rials [  5–7  ]  raise questions concerning how brillogenesis itself may be inuenced by the geometry of such microstructures. In particular, collagen gel morphology imparted by compartmen- talization within microfabricated materials could impact func- tional performance parameters (e.g., cell mobility, shape, or alignment; [  8–14  ]  drug diffusion; [  2  ]  hierarchical engineered tissue mechanics [  15–17  ]  ) of such composite devices. In biomimetic tissue engineering, [  18  ]  collagen gels have been used for generating functional myocardium from heart cells. [  3  ]  Collagen gels are capable of promoting cell alignment under boundary constraint [  4  ,  10  ]  or cyclic loading, [  19  ]  however they tend to be mechanically inferior to myocardium. [  8  ]  We generated tissue engineered myocardium by cultivating heart cells on an accordion-like honeycomb (ALH) scaffold rendered by laser microablation of poly(glycerol sebacate) (PGS). [  20  ]  The ALH scaffold provided cardio-mimetic anisotropic elastic proper- ties and a capacity to guide preferential cell alignment. Toward enhancing heart cell-mediated contractility, we developed peri- odic nite element simulations for investigating changes in ALH scaffold geometry [  21]  and investigated improving heart cell seeding efciency via Matrigel. [  22  ]  Matrigel, however, did not promote cardiomyocyte elongation. Based on observations of directional collagen brillogenesis in collagen-doped microuidic devices [  23  ]  and that elongated scaffold pores can promote cell-secreted collagen alignment, [  9  ]  we speculated that directional collagen brillogenesis might manifest within ALH pores. [  18  ]  Anisotropic collagen brillogen- esis could potentially overcome the limited heart cell elongation observed in Matrigel-ALH composites. [  22  ]  To elucidate if ALH scaffolds can induce anisotropic col- lagen brillogenesis, the three-dimensional bril organizations within ALH (Figure 1 A) and square diamond (Figure 1B) pores were imaged by confocal reectance microscopy (Figure 1C,D) and compared to collagen gelled unconstrained on glass slides (Figure S1, Supporting Information). ALH scaffolds preferentially oriented brils along the long axis of the pore (Figure 1C,E), with an orientation index OI  ALH  = 17.75 ± 6.55% signicantly higher than that measured for glass slides ( OI  glass  = 1.45 ± 0.40%; p < 0.05). Indeed, neither glass slides nor square diamond scaffolds (Figure 1D,E; OI  square  = 0.26 ± 0.16%) induced preferential bril orientation along the pore long axis. Providing a measure of both the density and homogeneity of the collagen gel, the inter-bril distance distributions were quantied (Figure 1F). The mean interbril distance was 5.06 ± 0.05 µ m for collagen gelled on glass slides; values for the ALH (4.075 ± 0.5 µ m) and square diamond (4.08 ± 0.3 µ m) scaffolds were lower (  p < 0.05). Hence, the organization of brils tended to be denser upon compartmentalization within the pores of ALH and square diamond scaffolds than on glass slides. The entropy value calculated for ALH pores (ε  ALH  = 3.8 ± 0.23) was signicantly lower than that calculated for glass slides (ε  glass  = 4.6 ± 0.10;  p < 0.05), demonstrating that the organization of brils was more ordered in ALH pores. Square diamond pores exhibited an intermediate value ε  square  = 4.18 ± 0.12. To predict the mechanical stiffnesses and anisotropy of ALH scaffold-collagen composites, compare these with native heart muscle, and to investigate the ramications of aniso- tropic collagen brillogenesis in the ALH scaffold, periodic FE simulations [  21  ]  were conducted. FE predicted effective stiff- nesses E  PD  and E  XD  , and anisotropy ratio r  = E  PD  /E  XD  , and Voigt (Equation 4) and Reuss (Equation 5) elastic bounds of the com- posite initially assumed the collagen was isotropic using upper (24.3 kPa [  15  ]  ) and lower (5 kPa [  24  ]  ) bounds of collagen stiffness. The Reuss bound (range 7.3–35.1 kPa) was dictated by the most compliant component of the composite (i.e., the collagen); the Voigt bound (aka the “rule-of-mixtures”; range 265–278 kPa) was dictated by the stiffer component, and therefore varied only slightly with the stiffness of the collagen. By contrast, FE predicted effective stiffnesses E  PD  (range 108–215 kPa) and E  XD  (range 62.2–173 kPa) depended strongly on the stiffness of the collagen and were comparable to values measured by uniaxial tensile testing (Figure S3, Supporting Information). As expected, FE predicted and measured values of E  PD  and E  XD  with 3 mg mL  1  collagen gelled within the pores were higher than those reported for the ALH scaffold itself (E  PD  = 83 kPa and E  XD  = 31 kPa [  20  ]  ). The FE predicted anisotropy ratios r  = 1.2 and r  = 1.7 associated with the upper and lower collagen

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wileyonlinelibrary.com112 © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim  Adv. Healthcare Mater. 2012, 1, 112–116

  Aurélie Jean and George C. Engelmayr Jr.*

Anisotropic Collagen Fibrillogenesis Within MicrofabricatedScaffolds: Implications For Biomimetic Tissue Engineering

 Dr. A. JeanDepartment of BioengineeringThe Pennsylvania State University223 Hallowell Building, University ParkPA 16802, USA

Dr. G. C. Engelmayr Jr.Department of BioengineeringThe Pennsylvania State University223 Hallowell BuildingUniversity ParkPA 16802, USA E-mail: [email protected]

DOI: 10.1002/adhm.201100017

Collagen gels find widespread application as three-dimensionalsubstrates in cell culture assays,[ 1 ]  drug delivery,[ 2 ]  and tissueengineering.[ 3 ]  At the macroscale, boundary constraints influ-ence cell-laden collagen gel anisotropy;[ 4 ]  at shorter lengthscales, composites of collagen gels with microfabricated mate-rials[ 5–7 ]  raise questions concerning how fibrillogenesis itselfmay be influenced by the geometry of such microstructures. Inparticular, collagen gel morphology imparted by compartmen-talization within microfabricated materials could impact func-

tional performance parameters (e.g., cell mobility, shape, oralignment;[ 8–14 ] drug diffusion;[ 2 ] hierarchical engineered tissuemechanics[ 15–17 ] ) of such composite devices.

In biomimetic tissue engineering,[ 18 ] collagen gels have beenused for generating functional myocardium from heart cells.[ 3 ] Collagen gels are capable of promoting cell alignment underboundary constraint[ 4 , 10 ] or cyclic loading,[ 19 ] however they tendto be mechanically inferior to myocardium.[ 8 ]  We generatedtissue engineered myocardium by cultivating heart cells on anaccordion-like honeycomb (ALH) scaffold rendered by lasermicroablation of poly(glycerol sebacate) (PGS).[ 20 ]  The ALHscaffold provided cardio-mimetic anisotropic elastic proper-ties and a capacity to guide preferential cell alignment. Towardenhancing heart cell-mediated contractility, we developed peri-

odic finite element simulations for investigating changes inALH scaffold geometry[ 21 ] and investigated improving heart cellseeding efficiency via Matrigel.[ 22 ]  Matrigel, however, did notpromote cardiomyocyte elongation.

Based on observations of directional collagen fibrillogenesisin collagen-doped microfluidic devices[ 23 ]  and that elongatedscaffold pores can promote cell-secreted collagen alignment,[ 9 ] we speculated that directional collagen fibrillogenesis mightmanifest within ALH pores.[ 18 ] Anisotropic collagen fibrillogen-esis could potentially overcome the limited heart cell elongationobserved in Matrigel-ALH composites.[ 22 ] 

To elucidate if ALH scaffolds can induce anisotropic col-lagen fibrillogenesis, the three-dimensional fibril organizationswithin ALH (Figure 1 A) and square diamond (Figure 1B) poreswere imaged by confocal reflectance microscopy (Figure 1C,D)and compared to collagen gelled unconstrained on glassslides (Figure S1, Supporting Information). ALH scaffoldspreferentially oriented fibrils along the long axis of the pore(Figure 1C,E), with an orientation index OI  ALH = 17.75 ± 6.55%significantly higher than that measured for glass slides (OI  glass = 

1.45 ± 0.40%; p < 0.05). Indeed, neither glass slides nor squarediamond scaffolds (Figure 1D,E; OI  square  =  0.26 ±  0.16%)induced preferential fibril orientation along the pore long axis.Providing a measure of both the density and homogeneity ofthe collagen gel, the inter-fibril distance distributions werequantified (Figure 1F). The mean interfibril distance was 5.06 ± 0.05 µ m for collagen gelled on glass slides; values for the ALH(4.075 ± 0.5 µ m) and square diamond (4.08 ± 0.3 µ m) scaffoldswere lower ( p < 0.05). Hence, the organization of fibrils tendedto be denser upon compartmentalization within the pores ofALH and square diamond scaffolds than on glass slides. Theentropy value calculated for ALH pores (ε  ALH = 3.8 ± 0.23) wassignificantly lower than that calculated for glass slides (ε  glass = 4.6 ±  0.10;  p  <  0.05), demonstrating that the organization of

fibrils was more ordered in ALH pores. Square diamond poresexhibited an intermediate value ε  square = 4.18 ± 0.12. 

To predict the mechanical stiffnesses and anisotropy ofALH scaffold-collagen composites, compare these with nativeheart muscle, and to investigate the ramifications of aniso-tropic collagen fibrillogenesis in the ALH scaffold, periodicFE simulations[ 21 ] were conducted. FE predicted effective stiff-nesses E  PD and E  XD , and anisotropy ratio r  = E  PD /E  XD , and Voigt(Equation 4) and Reuss (Equation 5) elastic bounds of the com-posite initially assumed the collagen was isotropic using upper(24.3 kPa[ 15 ] ) and lower (5 kPa[ 24 ] ) bounds of collagen stiffness.The Reuss bound (range 7.3–35.1 kPa) was dictated by the mostcompliant component of the composite (i.e., the collagen); the

Voigt bound (aka the “rule-of-mixtures”; range 265–278 kPa)was dictated by the stiffer component, and therefore variedonly slightly with the stiffness of the collagen. By contrast, FEpredicted effective stiffnesses E  PD  (range 108–215 kPa) andE  XD (range 62.2–173 kPa) depended strongly on the stiffnessof the collagen and were comparable to values measured byuniaxial tensile testing (Figure S3, Supporting Information).As expected, FE predicted and measured values of E  PD and E  XD with 3 mg mL− 1  collagen gelled within the pores were higherthan those reported for the ALH scaffold itself (E  PD =  83 kPaand E  XD  =  31 kPa[ 20 ] ). The FE predicted anisotropy ratios r  = 1.2 and r  =  1.7 associated with the upper and lower collagen

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stiffness bounds, respectively, were significantly lower than thatpredicted for the ALH scaffold without collagen (2.5) [ 21 ] . Rec-ognizing that the collagen within the ALH scaffold was itselfanisotropic (Figure 1), we simulated collagen anisotropy via anorthotropic material model targeting left ventricular stiffnessesin the circumferential (157 kPa) and longitudinal (84 kPa)directions (r  = 1.87)[ 20 ] and solved for the requisite collagen gelstiffnesses in the PD and XD directions. FE simulations pre-dicted collagen gel stiffnesses E 

coll

PD

 = 47.0 kPa and E coll

PD

 = 26.5kPa (r  coll  =  1.77). Finally, comparing the spatial distribution

of equivalent von Mises strain within the collagen matrix forisotropic (Figure 2 A) and orthotropic (Figure 2B) assumptions,orthotropic yielded a more homogeneous strain distribution(range 0.04–0.05) along the central PD axis versus isotropiccollagen gel (range 0.03–0.07). Hence, FE simulations can beused to predict collagen gel properties required to match ALHscaffold-collagen composite stiffnesses and anisotropy to nativeheart muscle. 

Composite devices comprised of microfabricated materialsand collagen gels offer the prospect of controlled bridging

Figure 2. Predicted spatial distribution of strain (equivalent von Mises) within the ALH pore simulating (A) isotropic versus (B) orthotropic collagen gelfilling the pore. For each simulation a macroscopic strain of 0.1 was prescribed along the PD direction. (C) The orthotropic collagen gel was predictedto yield a more homogeneous strain distribution (range 0.04–0.05) along the central PD axis of the ALH pore compared with an isotropic collagen gel(range 0.03–0.07). Of note, in the isotropic case (E  coll = 10 kPa) the spatial strain distribution pattern was dictated solely by the shape of the ALH pore;by contrast, in the orthotropic case (E coll

PD  / E collXD   =   47. 0 kPa / 26 .5 kPa ) the pattern was further influenced by simulation of PD-aligned collagen. Color

bar and associated numeric values indicate equivalent von Mises strain and apply to all figure panels A–C.

Figure 1. Representative scanning electron microscopy images of ALH (A) and square diamond (B) scaffolds (100× original magnification; scale bars = 1 mm). Confocal reflectance micrographs of collagen fibrils within a representative pore of an ALH (C) and square diamond (D) scaffold (400× originalmagnification; scale bars = 100 µ m). Collagen fibril angular orientation distributions (E) and inter-fibril distance distributions (F) measured by imageanalysis of collagen-filled ALH (top; red) and square diamond pores (bottom; red) compared with collagen gelled unconstrained on a glass slide(blue).

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between the micro-to-nanometer length scales, potentiallyyielding novel in vitro cell culture assays,[ 1 ]  drug deliverysystems,[ 2 ] and engineered tissues.[ 3 ] Hierarchically, engineeredtissues formed by seeding cells onto microfabricated scaffoldsevolve through the structural–mechanical interplay betweenscaffold, cells, and extracellular matrix. Without accounting

for extracellular matrix, we demonstrated that heart cell-seededALH scaffolds could mimic aspects of cardiac anisotropy. [ 20 ] Extracellular collagen structures, however, play importantroles in myocardium.[ 18 ]  We demonstrated three key findingsregarding collagen gelled within the ALH pore versus uncon-strained on a glass slide: 1) increased order of the fibril distri-bution (i.e., decreased entropy; ε  ALH = 3.8 ± 0.23 versus ε  glass = 4.6 ± 0.10; p < 0.05), 2) increased fibril density (i.e., decreasedmean inter-fibril distance; d  ALH  =  4.075 ±  0.5 µ m versusd  glass = 5.06 ± 0.05 µ m; p < 0.05), and 3) increased fibril alignmentalong the reference angle defined by the ALH pore long axis(OI  ALH = 17.75 ± 6.55% versus OI  glass = 1.45 ± 0.40%; p < 0.05).For comparison, Bayan et al. reported entropy values rangingfrom 6.37–6.5 and OI values ranging from 9.45–13.46% in

similar acellular collagen gels.[ 25 ] Of note, Bayan et al. did notdetect significant differences in OI when comparing 1, 2, and3 mg mL− 1 collagen gels. Further, when gelled on a glass slideand compared with the 3 mg mL− 1 gel, we did not detect any dif-ference in the collagen orientation distribution in a 6 mg mL− 1 collagen gel (Figure S4, Supporting Information). Of note,the degree of collagen fibril alignment mediated by the ALHpore geometry alone (OI  =  17.75 ±  6.55%) was less than thatobserved by Bayan et al. in a 3 mg mL− 1 cell laden gel cultivatedfor 12 days (OI  = 30.86 ± 14.76%).[ 25 ] 

A combination of mechanisms may have contributed tothe anisotropic collagen fibrillogenesis observed herein. Forexample, when 3 mg mL− 1  collagen solution was flowed into

and gelled within the channels of a collagen-doped alginatemicrofluidic device, Gillette et al. observed that a number ofcollagen fibrils appeared to bridge contiguously, in straightlines, from the collagen-doped alginate (i.e., the channel walls)into the collagen gelled within the channel.[ 23 ] Coupled with thepreference for collagen fibril tip growth predicted by diffusionlimited aggregation models by Parkinson et al.,[ 26 ]  the resultsfrom Gillette et al. suggest that collagen fibrils can grow in astraight line from the tips of collagen fibrils exposed at a sur-face into the bulk of a collagen solution. In the present studycollagen solution was gelled in direct contact with the PGSstructural elements of the ALH scaffold. In a previous study,Sales et al. demonstrated that type I collagen can adsorb to aPGS foam scaffold from dilute solutions, reaching a maximum

surface concentration from solutions as dilute 20 µ L mL− 1 col-lagen.[ 27 ]  We thus expect that the surfaces of the PGS strutswere saturated with adsorbed collagen under the conditionstested herein, and that upon exhausting the available PGS strutsurface area, the growing tips of the collagen fibrils would tendto progress outward from the struts into the bulk collagen solu-tion filling the pore. Indeed, proximal to the collagen gel-PGSstrut interfaces, confocal reflectance micrographs qualitativelyrevealed that collagen fibrils were arranged not in parallel, butrather at finite angles or roughly perpendicular to the PGSstruts (Figure 1C,D). In the case of the square diamond pore, inwhich the PGS struts were oriented at opposing angles of ± 45° 

and at equal distances from each other, essentially equal frac-tions of the collagen fibrils were oriented at ± 45° , yielding nosingle preferential angle of alignment (Figure 1E). By contrast,while the PGS struts were likewise oriented at ± 45° in the ALHscaffold, the distances between opposing struts were longeralong the PD versus XD direction, thereby offering a longer

path for extension of collagen fibrils along the PD direction ofthe ALH pore.

We undertook FE simulations to predict what stiffnessesthe collagen matrix would need to manifest in order for theeffective stiffnesses and anisotropy of the ALH-collagen com-posite to match those of native left ventricular myocardium.FE simulations predicted the collagen would need to exhibitE coll

PD   =  47.0 kPa and E coll

XD   =  26.5 kPa (r  coll  =  1.77) in orderfor the composite to reach 157 kPa and 84 kPa ( r  =  1.87).[ 20 ] Simulations suggested two potential routes toward matchingALH-based constructs to left ventricular mechanical proper-ties. In the context of heart cell-seeding, [ 20 , 22 ]  the stiffness ofthe collagen gel would be expected to increase as the gel iscontracted by the seeded cells; a potential limitation, however,could be debonding of the collagen from the PGS scaffoldupon cell-mediated gel contraction. Toward such approaches,we have demonstrated that cells and collagen can be retainedwithin the ALH pore upon stretching the ALH scaffold(Figure S5, Supporting Information). A broad range of cell-seeded collagen gel stiffnesses have been reported rangingfrom ∼ 37 kPa (estimated from Figure 4 of Feng et al. [ 8 ] ) to5.33 ± 1.33 MPa.[ 28 ] These studies suggest simulation predictedcollagen stiffnesses of 26.5–47.0 kPa could be achieved by anappropriate combination of collagen gel concentration, cellseeding density, and cultivation time. An alternative approachcould involve co-varying the ALH scaffold structure (e.g., strutwidth) and PGS curing conditions (i.e., PGS modulus). [ 21 ] 

We demonstrated by FE simulations that two distinct valuesof strut width (w  ) are capable of yielding an anisotropy ratioequal to that of left ventricular myocardium (i.e., r  = 1.87): w  = 20 µ m or w  = 140 µ m.[ 21 ] The 20 µ m strut width would be bothfeasible to microfabricate and provide allowance for increasedcollagen matrix stiffnesses associated with heart cell-mediatedcontraction. As collagen fiber alignment alone is not suf-ficient to explain the high degree of anisotropy observed infibroblast-seeded collagen gels,[ 29 ]  we speculate that the ani-sotropic collagen fibrillogenesis demonstrated herein, whilesignificant, represents only a starting point in understandingthe interplay between pore geometry, collagen morphology,and cell morphology. In future studies, Voronoi tessellation-based models could be useful in coupling collagen gel mor-phology to mechanical behavior.[ 30 ]  Further, the evolution ofcollagen anisotropy demonstrated in the present study maybe extendable to other hydrogels, such as fibrin and Matrigel.Of particular note, Bian et al. demonstrated that muscle cell-laden fibrin-based hydrogels can be spatially patterned intoanisotropic tissue bundles by casting within microfabricatedpoly(dimethysiloxane) molds.[ 31 ]  More broadly, collagen gel-based cell culture assays and drug delivery systems may mani-fest and potentially exploit anisotropic collagen fibrillogenesis,in particular in miniaturized composites of collagen gel andmicrofabricated or microscale materials. For example, in aminiaturized aortic ring assay introduced by Reed et al., 30 µ L

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of collagen solution was gelled within and supported by anylon mesh ring (3 mm inside diameter) comprised of ∼ 50 µ mdiameter fibers arranged in a square lattice (∼ 125 ×  125 µ minside pore dimensions).[ 1 ] As such systems are further mini-aturized for high throughput screening, collagen morphologyinduced by the system boundaries could potentially impact

the directionality of capillary sprouting; similar phenomenacould potentially be exploited in microfluidic collagen gelsmimicking human microvascular networks.[ 32 ]  In the contextof drug delivery, De Paoli et al. have reported on the effects ofoscillating magnetic fields on drug release from magnetic col-lagen gels (i.e., collagen gels containing iron oxide particles ofup to 3 µ m diameter).[ 33 ] In magnetic collagen gels, structuralchanges within the gel associated with oscillating magneticfields were demonstrated to impact drug release kinetics; sim-ilar effects could potentially be mediated by collagen gelationwithin the compartments of microfabricated drug deliverydevices.[ 34 ]  In concert with auxiliary biophysical and bio-chemical regulators, compartmentalizing collagen gels withinmicrofabricated materials represents a promising strategy forcontrolling collagen fibril anisotropy and associated functionalperformance parameters in advanced cell culture assay, drugdelivery, and tissue engineering applications.

Experimental Section

PGS Scaffold–Collagen Gel Composite Preparation : The ALH andsquare diamond scaffolds (5 mm × 5 mm) were fabricated by 213 nmlaser microablation (LSX-213; CETAC Technologies, Inc., Omaha, NE)of 250 µ m thick PGS cured under vacuum (< 50 mTorr) for 7.5 h at160 ° C.[ 22 , 35 ]  The ALH and square diamond scaffolds each compriseda periodic tessellation of unit cells with a strut width of 50 µ m and astrut length (inside the pore) of 200 µ m (Figure 1A,B). The long axis of

the ALH pore was defined as the preferred direction (PD) and the shortaxis the cross-preferred direction (XD). Collagen gel was prepared on iceby adding 100 µ L of 10X phosphate buffered saline (PBS) to 800 µ L of3 mg mL− 1 bovine dermal collagen solution (Sigma, St. Louis, MO). Thesolution was neutralized to pH 7.2–7.6 by 75 µ L of 0.1 M  NaOH and300 µ L was pipetted onto a glass microscope slide (VWR, West Chester,PA) or the scaffold, coverslipped, and then incubated for 1 h in a CO 2 incubator at 37 ° C. Specimens were then imaged immediately withoutfixation.

Confocal Reflectance Imaging  : The collagen fibrils were imaged usinga confocal microscope (FluoView 1000; Olympus America, Center Valley,PA) in reflectance mode (488 nm) (Figure 1C,D).[ 36 ] The interval between z -stack images corresponded to the ( x  ,y ) plane resolution (i.e, 0.621 µ mper pixel for 40X objective and 512 × 512 pixel image). Images were firstsegmented batch-wise via a custom automated algorithm implementedin Matlab [ 37 ]  (Figure S1, Supporting Information). The algorithmcomprised: RGB to grayscale conversion, a median filter, local adaptivethresholding to yield binary images, morphological opening with a1 pixel sized structural element.

Image Analysis of Collagen Fibril Organization : The morphology ofthe collagen fibrils was analyzed from confocal micrographs basedon set theory for image analysis using custom code written in Matlaband Python.[ 38 ]  Measures were averaged over the entire  z -stack (i.e.,∼ 50–70 images) and over ∼ 10 pores (or locations for the glass slide).The size (i.e., interfibril distance) distribution of the inter-fibril spaceswas computed by opening granulometry with a disk D  of diameter d  on complementary binary images. Opening granulometry consisted ofmorphologically opening the set of pixels in each image correspondingto the inter-fibril spaces using a sequence of increasing larger structural

elements (i.e., disks D of diameter d  ). At each value of d, the probabilityP  of one point (i.e., one pixel in the discretized image) belonging to theopened set was calculated (O (d  )) (Equation 1) (Figure S2, SupportingInformation).[ 39 ]  The opening operation included an erosion (Θ ) withD (d  ) following by a dilation (⊕) with an identical D (d  ), removing alldisconnected groups of pixels with a size less than d  .

 O (d ) = P ( x 

  ∈(( A

fibrils

)C 

Θ(d ))⊕ D (d ))   (1)

The fibril angular orientation distribution was measured using thefast Fourier transform (FFT),[ 40 ]  which yields the intensity angulardistribution I (θ  ). The angle θ  m  for which the intensity was maximum(m) was identified on I (θ  ) and defined the predominant fibril direction.The FFT-based image analysis used a Matlab program previously usedto quantify cellular F-actin filament orientation.[ 20 ] An orientation indexOI (θ  m ) was calculated from I (θ  ) at θ  m to yield the percentage of fibrilsstrictly oriented in the reference angle direction (herein designated as 0° to correspond with the PD direction of the ALH pore) (Equation 2)[ 25 ] .

 

OI (θ m)  =   100

2

 180

0  I(θ )

cos2 (θ −θ m )

d θ  

180

0  I(θ )d θ 

−1

 

(2)

 

Of note, the orientation index used herein[ 25 ] was distinct from thatused in our previous study.[ 20 ] The entropy (i.e., a measure of disorder)was measured by processing the Hough transform [ 41 ]  using a customMatlab program. The Shannon entropy ε  of the probability distributionp (θ  ) of predominant directions was calculated (Equation 3).[ 25 ] 

ε   = −

 p (θ )

log [ p (θ )]

 

(3)

Statistical differences were determined by two-tailed student t-tests(Matlab) with a p -value < 0.05 considered significant. Values reportedrepresent mean ± standard deviation for n = 6 samples.

Periodic Finite Element Simulations : A multiscale periodic FE methodpreviously applied to the ALH scaffold itself[ 21 ] was used herein to predictthe elastic stiffnesses of the ALH scaffold-collagen gel composite (Z-setsoftware [ 42 ] ). The Young’s modulus and Poisson ratio of the PGS formingthe scaffold struts were specified as 825 kPa and 0.45, respectively. [ 21 ] 

Upper and lower bounds on Young’s modulus (linear elastic isotropicassumptions) of a 3 mg mL− 1 collagen were specified as 24.3 kPa[ 15 ] and5 kPa[ 24 ] and a Poisson ratio of 0.45 was assumed. The elastic stiffnessesof the ALH scaffold-collagen gel composite in the PD (E  PD ) and XD(E  XD ) directions were predicted. An anisotropy ratio r   =  E  PD /E  XD  wascalculated.[ 21 ] In addition, the Voigt (Equation 4) and Reuss (Equation 5)bounds known as the upper (i.e., the rule-of-mixtures) and lower elasticbounds were determined:

 E Voigt

=   E PGS V vPGS   +   E coll V vcoll   (4)

E Reuss=

 V vPGS

E PGS+

V vcoll

E coll

−1

 (5)

 

Simulations were conducted allowing for anisotropic elastic behaviorof the collagen gelled within the ALH pores via an orthotropic material

model in which elastic constants were optimized (augmented Lagrangianmethod) based on the criteria that E  PD and E  XD equaled values measuredpreviously for adult rat left ventricular myocardium in the respectivecircumferential and longitudinal directions.[ 20 ] In the orthotropic materialmodel the collagen gel stiffness in the z (i.e., thickness) direction wasassumed to take an intermediate value (i.e., 10 kPa) between upper[ 15 ] and lower[ 24 ] bounds.

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Acknowledgements

Funding for this work was provided by National Institutes of Health(NIH) Grant 1-R01-HL086521-01A2 (PI Dr. Lisa E. Freed, SubawardPI GCE). This funding was made possible by the American Recovery andReinvestment Act. The authors gratefully acknowledge Dr. Lisa E. Freed(The Charles Stark Draper Laboratories and Massachusetts Institute of

Technology, Cambridge, MA) for helpful discussions in preparing themanuscript and Sarah R. Bass, John L. Dzikiy, and Harshal Sawant fortheir assistance conducting experiments.

Received: November 4, 2011Published online: December 15, 2011