A Comparative Study of Collagen Matrix Density Effect on Endothelial

Sprout Formation Using Experimental and Computational Approaches

AMIR SHAMLOO,1 NEGAR MOHAMMADALIHA,1 SARAH C. HEILSHORN,2 and AMY L. BAUER3

1Center of Excellence in Energy Conversion (CEEC), School of Mechanical Engineering, Sharif University of Technology, P.O.Box 11155-9567, Tehran, Iran; 2Department of Materials Science & Engineering, Stanford University, Stanford, CA 94305,

USA; and 3Los Alamos National Laboratory, Los Alamos, NM 87545, USA

(Received 8 March 2015; accepted 4 August 2015)

Associate Editor Michael Gower oversaw the review of this article.

Abstract—A thorough understanding of determining factorsin angiogenesis is a necessary step to control the developmentof new blood vessels. Extracellular matrix density is knownto have a significant influence on cellular behaviors andconsequently can regulate vessel formation. The utilization ofexperimental platforms in combination with numerical mod-els can be a powerful method to explore the mechanisms ofnew capillary sprout formation. In this study, using anintegrative method, the interplay between the matrix densityand angiogenesis was investigated. Owing the fact that theextracellular matrix density is a global parameter that canaffect other parameters such as pore size, stiffness, cell–matrix adhesion and cross-linking, deeper understanding ofthe most important biomechanical or biochemical propertiesof the ECM causing changes in sprout morphogenesis iscrucial. Here, we implemented both computational andexperimental methods to analyze the mechanisms responsiblefor the influence of ECM density on the sprout formationthat is difficult to be investigated comprehensively using eachof these single methods. For this purpose, we first utilized aninnovative approach to quantify the correspondence of thesimulated collagen fibril density to the collagen density in theexperimental part. Comparing the results of the experimentalstudy and computational model led to some considerableachievements. First, we verified the results of the computa-tional model using the experimental results. Then, wereported parameters such as the ratio of proliferating cellsto migrating cells that was difficult to obtain from exper-imental study. Finally, this integrative system led to gain anunderstanding of the possible mechanisms responsible for theeffect of ECM density on angiogenesis. The results showedthat stable and long sprouts were observed at an intermediatecollagen matrix density of 1.2 and 1.9 mg/ml due to a balancebetween the number of migrating and proliferating cells. As aresult of weaker connections between the cells and matrix, alower collagen matrix density (0.7 mg/ml) led to unstable and

broken sprouts. However, higher matrix density (2.7 mg/ml)suppressed sprout formation due to the high level of matrixentanglement, which inhibited cell migration. This study alsoshowed that extracellular matrix density can influence sproutbranching. Our experimental results support this finding.

Keywords—Endothelial sprout, Matrix density, Microfluidic

device, Cellular Potts Model, Multi-scale model.

INTRODUCTION

The formation of new blood vessels via angiogenesisis a rate-limiting step for normal development andphysiology, as well as numerous pathologic processes,including cancer and ophthalmologic disorders such asmacular degeneration.20 In cancer, the concept of an‘‘angiogenic switch’’, whereby neovascularization bothprecedes and is necessary for tumor progression andmetastasis, was proposed by Folkman and Hanahan.27

The development of tumor angiogenesis is mechanis-tically quite complex, involving vessel growth into aninitially avascular tumor mass,21 the early recruitmentof vasculature from neighboring tissue,30 and thecontribution of circulating endothelial stem cells.3 Gi-ven the anti-cancer therapeutic potential of an angio-genesis blockade, significant efforts have been devotedtoward understanding the molecular mechanismsunderlying blood vessel formation.19,29,60,63 Potentialtherapies for numerous other diseases (e.g., peripheralarterial disease, diabetic wound healing, maculardegeneration, stroke, myocardial infarction) includeeither the prevention or promotion of angiogenesis.Many biochemical factors have been identified thateither deter or encourage blood vessel formation.41

However, very little is known quantitatively about theinterrelationship between the cell and the biochemical

Address correspondence to Amir Shamloo, Center of Excellence

in Energy Conversion (CEEC), School of Mechanical Engineering,

Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iran.

Electronic mail: shamloo@sharif.edu

Annals of Biomedical Engineering (� 2015)

DOI: 10.1007/s10439-015-1416-2

� 2015 Biomedical Engineering Society

and biomechanical environment. Although significantstrides have been made, a comprehensive and multi-scale understanding of the relationships involved inangiogenesis and tumor growth, and thus an effectivecure or treatment, is still a work in progress.

What is known is that blood vessel formation andcohesive vascular network structures require thecoordinated motion of a multitude of cells, favorableenvironmental factors, and successful signal transduc-tion. These complex vascular networks exhibitdynamic behavior including endothelial cell migration,proliferation, elongation, and branching.14 Asendothelial cells migrate into the extracellular matrix(ECM), they undergo cell-type specific specialization,with tip cells forming filopodia to sense and migratetoward chemoattractants such as vascular endothelialgrowth factor (VEGF), while stalk cells proliferate andform vascular tubes.15,23,49 Tip cells express receptorsincluding VEGFR2 and VEGFR3 that are not ex-pressed by stalk cells and that are functionally requiredfor angiogenesis.46,59 These molecular level differencesbetween tip cells and stalk cells result in differentmigration and proliferation rates.23 While observationsat and below the single cell length scale have led toadvancements in our understanding of tissue forma-tion, this process cannot be truly described and studiedwithout observing the systems of collective cell phe-nomena that occur across much larger time and lengthscales. It is this system of cellular communication andinteraction that ultimately results in coordinated cellmotion and cohesive tissue formation.

Recently, several groups have developed in vitromodels of angiogenesis that have produced new in-sights into the mechanisms of coordinated endothelialcell movement.10,12,24,34,38,40,47,51–53,56,57,61,62 Althoughvarious in vitro and in vivo assays have been developedto provide precise insight into the field of angiogene-sis,31,44 microfluidic devices show a considerablepotential for angiogenesis studies because they allowprecise and quantitative control over the extracellularmicroenvironment, thereby enabling direct testing ofhypotheses that cannot be achieved using in vivomodels alone.64 For example, a variety of microfabri-cated culture devices apply quantified concentrationgradients of soluble factors to two-dimensional (2D)monolayer cultures and/or three-dimensional (3D)sprouting morphogenesis cultures of endothelialcells.10,18,51,52 These quantitative in vitro results werevalidated through design of an optimized VEGF-de-livery system for in vivomurine hind leg ischemia,10 butthere remains a need for a high-throughput approachwith the ability to test the simultaneous effects ofbiochemical and biomechanical factors and to explainthe mechanisms behind these effects. Furthermore,Mathematical investigations of angiogenesis have

employed continuous, discrete, and mechanical modelsto describe a variety of dynamics believed to influenceangiogenesis.2,9,13,16,17,36,42,50,58 However, despite clearevidence that the ECM is crucial to cellular behaviorand vascular patterning, most models of angiogenesisneglect the dynamic interaction between endothelialcells and the ECM. Until recently, no single mathe-matical model existed that (a) couples multiple timeand length scales, (b) generates realistic capillarystructures, including branching and anastomoses,without a priori prescribing rules and probabilities tothese events, and (c) considers the complex biochemi-cal and mechanical interactions that occur betweenendothelial cells and the ECM.4,5

Computational techniques can be applied to simu-late a wide range of biological phenomena includingintracellular processes, formation of multi-cellularstructures and distribution of biochemical factorswithin cellular microenvironments.4–6,26,28,32,33,35,45

These computational methods, when combined withexperimental verifications, have the potential to helpexplain the mechanisms behind biological processesthat cannot be understood from in vivo or in vitrotechniques alone.8,48 It was shown that maximal cellmigration happens at an intermediate binding level ofthe cells to the matrix, but more compliant matrices aremore favorable for 3D cell movement when keepingthe cell–matrix binding level constant.65 Anothergroup applying both experimental and computationaltechniques to study leukocyte rolling found that inaddition to the ligand surface density the convectiveflux of the bonds and the dissociation rate at the backof a cell’s contact zones determines the rolling velocityof the cells.39 In addition, a recent analysis on neuronalaxon path-finding integrating experiment and simula-tion has found that different mechanisms may beresponsible for neuronal axon path-finding.43 It wasshown that at steeper gradients axon turning is themore possible response of neuronal cells to neu-rotrophic factors whereas at shallower gradients biasedaxonal growth rate towards biochemical gradients is amore probable cause for directional path-finding ofneurons.43

In this study, we have developed experimental andcomputational platforms capable of testing multiplevariables and explaining the interplay between bio-chemical and biomechanical factors in a study of theeffects of matrix density on endothelial sprout mor-phogenesis. Our simulation results were verified on ourexperimental platform. Both computational andexperimental observations illuminated collagen fibrildensity as a critical factor in the morphology andcharacteristics of sprouts within matrices of varyingstiffness. Our studies elucidate the role of collagen fibrildensity as a determinant factor affecting the formation

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of multi-cellular structures from single endothelial cellsduring angiogenesis. Comparing the results fromexperimental and computational methods introducedthe binding affinity between the cells and the collagenfibers as the main factor affecting endothelial sproutformation within collagen matrices of varying densi-ties.

MATERIALS AND METHODS

In Vitro Endothelial Sprouting Assays

Microfluidic devices were fabricated in PDMS(Sylgard 184, Midland, MI) using soft lithography aspreviously described51,52 (Fig. S1). Transparencymasks were generated from CAD files of fluidicchannels using negative photoresist (SU-8). Sharpenedneedles (20 gauge) were used to punch inlets and out-

lets of the cell culture chamber and reagent channels.To form an irreversible seal between the PDMS andthe glass substrate, both surfaces were exposed tooxygen plasma treatment for 2–3 min and broughtimmediately into contact. This microfluidic device en-ables quantifiable measurements of endothelial cellchemotaxis in response to known gradients of solublefactors that remain stable from 1 h to weeks (Fig. 1a).The microfluidic device also enables real-time imagingof cellular dynamics in both 2D and 3D culture mod-els. A stable concentration gradient across the cellculture chamber was generated as shown in Fig. S2.Rheological tests on the collagen/fibronectin matrixsamples were performed using an oscillatory rheometer(Anton-Paar) in parallel-plate geometry.

Adult human dermal microvascular endothelial cells(HMVEC, Lonza, Walkersville, MD) were first grownas monolayer cultures on the surfaces of collagen-

FIGURE 1. The diffusion-based microfluidic gradient generator device (a); Three dimensional monolayer cultures of adult humandermal microvascular endothelial cells (HMVEC) on the surfaces of collagen-coated dextran beads were embedded within collagenI/fibronectin matrices. (b); Collective cell migration and endothelial sprout formation in response to VEGF gradient (c); the equi-librium profile of VEGF concentration within the cell culture chamber; see also Fig. S1 (d); the initial VEGF field in the computationdomain (e); the systems integrated mathematical multi-scale model (f).

A Comparative Study of Collagen Matrix Density Effect

coated dextran beads (Cytodex, GE, d ~ 170 lm) toform endothelial sprouts (Figs. 1b, 1c). These beadswere then suspended within a 3D matrix containing rattail collagen Type I (BD Biosciences) and fibronectin(final concentration of 5 lg/ml, 10% total volumetricmixture) and consequently cultured inside themicrofluidic device (~20 beads/device) that generatedprecise and stable VEGF gradients (Fig. 1d).Endothelial Growth Medium-2MV (EGM-2MV) sup-plemented with various concentrations of VEGF(VEGF-A isoform VEGF (165), R&D Systems, Min-neapolis, MN) was continuously supplied to the sourcereagent channel, while EGM-2MV with no VEGF wassupplied to the sink reagent channel. The injection flowrate was 40 nl/min. Upon VEGF stimulation, ECsunderwent sprouting morphogenesis, i.e., collective cellmovement to migrate away from the bead surface andinto the collagen gel matrix as a cohesive, columnarstructure (Fig. 1c). More details about the microfluidicsystem are presented in the supplementary section (S1).Collagen matrices of varying densities ranging fromcompliant gels to stiffer matrices were used to studythe effect of matrix density on the sprout morphology,dynamics and branching. To obtain different matrixdensities, the collagen concentration was altered whilethe final fibronectin, microcarrier bead, endothelialcell, and media concentrations were kept uniform. Theformation of endothelial sprouts was detected andrecorded using time-lapse imaging.

Characterization of Endothelial Cell Sprouts andStatistical Analysis

Individual beads were imaged every 24 h for 3 daysusing phase contrast and fluorescence microscopy.ImageJ software (NIH freeware) was used to measurethe number of cells per sprout, the sprout averagethickness, the sprout length and the sprout elongationrate. The average thickness of each sprout was deter-mined by dividing the projected sprout surface area bythe length of the sprout centerline. For each condition,between three and six independent experiments wereperformed, such that the number of beads imaged foreach condition totaled 60–120. The one-tailed, non-paired, Student’s t test was used to determine the sta-tistical significance of differences between pairs ofconditions.

Cell Fluorescent Staining

Sprouts within collagen gels were fixed by injecting4% paraformaldehyde into the source and sink chan-nels and incubating at 4 �C for approximately 1 h. Thesamples were washed at least four times by injectingPBS into the source and sink channels. The cells were

blocked with 10% normal goat serum in PBST (0.3%Triton X-100 in PBS solution) for 3 h. The cellularactin cytoskeleton was stained overnight at 4 �C usingAlexa Fluor 555-conjugated phalloidin (Invitrogen)while the cell nuclei were stained using DAPI. Sampleswere washed with PBS at least four times and thenincubated with PBS at 4 �C for 12 h prior to imaging.An inverted fluorescence microscope was used to ac-quire images.

Computational Model of Angiogenesis

We also developed and validated a 2D (x, y, t) cell-based, multi-scale model of angiogenesis that inte-grates tissue, cellular, and molecular scale dynamics toanalyze cell–cell and cell–matrix interactions. Usingthis model, a gradient of VEGF concentration wasgenerated in the simulation domain that is shown inFig. 1e. This spatio-temporal mathematical modelcombines a lattice-based cellular Potts model describ-ing individual cellular interactions, a partial differen-tial equation to describe the spatio-temporal dynamicsof VEGF, and the Boolean model of intracellular sig-naling pathways critical to angiogenesis7 (Fig. 1f). Asummary of the computational model is presented inthe supplementary section (S2).

Since the VEGF field (V(x, y, t)) exerts an influenceon cell chemotaxis, the discrete and continuous partsof the model feedback on each other at the cell mem-brane through the chemotaxis term in the total energyequation. Considering the effect of cell phenotype onthe chemotaxis potential is one of the notable featuresof this multi-scale mathematical model. This modeldistinguishes between the cells that are proliferatingand the ones that are migrating. Cells migrate towardincreasing concentrations of VEGF from the parentvessel to facilitate sprout extension. The fibrousstructure of the ECM is another feature of this model.ECM collagen fibers are randomly distributed at ran-dom discrete orientations between 290� and 90�. Themesh-like anisotropic structure of the extracellularmatrix is modeled by the heterogeneous and randomdistribution of these fibers. The cell membrane inter-acts with these ECM fibers through the adhesion termin the total energy equation.

The VEGF and cellular distributions and thegeometry of the computational model have been ini-tialized to approximate the in vitro microcarrier beadsprouting morphogenesis experiment. Our computa-tional model captures realistic vascular structuresincluding branching as well as contact guidance andinhibition. Computational simulations and experi-mental observations of soluble factor gradients are inexcellent agreement and allow exact specification of the

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soluble factor concentration at every location withinthe device (comparison of Figs. 1d, 1e).

Quantification of Collagen Fibril Density

Scanning electron microscopy (SEM) was used todetermine collagen fibril distribution within collagenmatrices of varying densities. To quantify the collagenfibril density, an image analysis algorithm was used topredict the vacant spaces in collagen matrix and thespaces filled with collagen fibrils using an in-houseMATLAB image analysis code. Using this code, wecategorized the image pixel counts based on theirnormalized intensity. By estimating the minimumnormalized intensity of the pixels that represent col-lagen fibers on the SEM images, we determined a cri-terion showing fibrillar and non-fibrillar spaces in thecollagen matrix. We define a ratio of fibrillar spaces tothe total matrix space as the number of pixels havingintensity greater than the threshold divided by the total

number of pixels. This ratio was used as an input forfibril density, or fractional filled area, in the simulationstudies. More details about this innovative method arepresented in the supplementary section (S3).

RESULTS

Quantification of Collagen Fibril Density for VaryingCollagen Gel Concentration

As previously described, scanning electron micro-scopy (SEM) was used to determine collagen fibrildistribution within collagen matrices of varying den-sities: 0.7, 1.2, 1.9 and 2.7 mg/ml (Figs. 2a–2d). Amodel was also made to simulate the distribution ofcollagen fibers in the in silico study. The architecture ofthe ECM is anisotropic, with regions of varying den-sities. A single collagen fibril is ~300 nm long and1.5 nm wide and is substantially smaller than an EC,which is ~10 lm in diameter.1 Many individual

FIGURE 2. Scanning electron microscopy (SEM) shows the distribution of collagen fibers within collagen matrices of varyingdensities (0.7, 1.2, 1.9 and 2.7 mg/ml) (a–d); The anisotropic structure of ECM of various densities is effectively generated in themathematical model by randomly distributing 1.1 lm thick bundles of individual collagen fibrils at random orientations (e–h);Histogram of normalized pixel intensity analysis of SEM is presented for the collagen densities of 0.7, 1.2, 1.9 and 2.7 mg/ml (i); Plot(j) shows the relation between the SEM analyzed fractional filled area (i.e., portion of the matrix that is filled with collagen fibrils)and the collagen density used to prepare the matrices. A significant increase in the fractional filled density is observed as a resultof an increase in the experimental collagen matrix density. Statistical analysis showed that the fibril densities are significantlydifferent within varying collagen matrices.

A Comparative Study of Collagen Matrix Density Effect

FIGURE 3. Experimentally and computationally observed sprouting morphogenesis at varying matrix densities over a time periodof 72 h. Within matrices of 0.7 mg/ml density unstable or broken sprouts are observed due to minimal cell–cell interactions. Arrowsshow minimal cell contact zones. (a). At intermediate collagen densities (1.2 and 1.9 mg/ml) stable sprouts are formed (c and e);however, thicker sprout morphologies formed in 1.9 mg/ml density matrices (e) compared to those formed in 1.2 mg/ml densitymatrices (c). High matrix density (2.7 mg/ml) inhibited sprout elongation and yielded thicker sprouts (g). Predictions from therespective comparable computational simulations are remarkably close to in vitro observations (b, d, f, and h). The ratio ofproliferating to migrating cells of sprouts formed within matrices of varying density (i), *p< 0.05, **p< 0.01.

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collagen fibrils and other matrix proteins are boundtogether constituting larger cords or bundles of matrixfibers estimated to be between 100 and 1000 nmthick.22 Our mathematical model accurately capturesthe heterogeneity and random distribution of a typicalECM fiber matrix, such as a Type I collagen matrix.We model this mesh-like anisotropic structure of theECM by randomly distributing 1.1 lm thick bundlesof collagen fibrils at random orientations rangingbetween 290� to 90� until the desired percentage oftotal ECM space occupied by collagen fibers isachieved (Figs. 2e–2h).

Using an innovative approach, we calculated thefibril density of ECM by means of an image analysisalgorithm that is described in supplementary section S3(Fig. 2i). According to image analysis data which wasshown in Fig. 2j, the collagen fibril density is very lowin the lowest collagen gel density (0.7 mg/ml yields afibril density of ~0.13). Analyzing the fibril density athigher collagen gel densities reveals that fibril densityincreases significantly from ~0.13 to ~0.38 when thecollagen gel density is increased from 0.7 to 1.2 mg/ml(Fig. 2j). Fibril density increases from ~0.38 to ~0.68when we increased collagen gel density from 1.2 to1.9 mg/ml (Fig. 2j). The collagen matrix with 2.7 mg/ml density yielded a fibril density of ~0.89. These col-lagen matrix densities approximately correspond to thefibril densities used in the matrices in the computa-tional model. The sprout characteristics from the

experimental and simulation platforms were comparedand results are discussed below.

Comparison of Sprout Morphology and Cell Count inVarying Collagen Densities Using Experimental and

Computational Platforms

Endothelial cells cultured on surfaces of microcar-rier beads within collagen matrices of varying densitiesdemonstrated a distinctive dependency between sproutmorphology and matrix density. Tracks of endothelialcells were observed over a 72-h time period withincollagen gel matrices of 0.7, 1.2, 1.9 and 2.7 mg/mldensity and simulated computationally on matriceswith corresponding fibril densities of <0.1, 0.4, 0.7,and >0.9. On the corresponding 0.7 mg/ml collagenmatrix density, endothelial cell tracks show minimalcell contact resulting in unstable or broken sprouts(Fig. 3a). This was predicted by the numerical simu-lations of sprouting angiogenesis on a matrix with alow fibril density (Fig. 3b). In contrast, Fig. 3c showsnarrow but stable sprout formation using the experi-mental platform within a collagen matrix of density of1.2 mg/ml. The cells forming these sprouts are wellconnected with each other. Narrow, stable sproutformation was independently predicted using themathematical model on a matrix with a fibril densityof 0.4 (Fig. 3d). Sprouts forming on 1.9 mg/ml den-sity matrices show thicker morphologies in the

FIGURE 4. Fluorescent inverted (a, b, and c) and confocal (d) images of sprouts formed within matrices of various collagendensities. Red and white colors represent a phalloidin stain of the F-actin cytoskeleton and a DAPI stain of nuclei, respectively.

A Comparative Study of Collagen Matrix Density Effect

experimental platform (Fig. 3e). Greater levels of cellcontact for these sprouts make them more capable offorming stable multi-cellular structures. Thicker sproutmorphologies on matrices with higher fibril densitywas also borne out in simulations using fibril density of0.7 (Fig. 3f). Interestingly, cell migration was inhibitedin the stiffest collagen gel matrices (2.7 mg/ml)(Fig. 3g). Suppression of sprout formation was alsoobserved in simulation studies on matrices of associ-ated collagen fibril density (>0.9) (Fig. 3h). Theinability of the tip cells to penetrate, elongate, andmigrate into matrices of very high density indicates thecritical role of biomechanical effectors during newblood vessel formation. As can be seen in Fig. 3i, abalance between proliferation and migration wasobserved on matrices with 1.2 and 1.9 mg/ml collagendensity. A higher ratio of proliferation to migrationwithin collagen density of 1.9 mg/ml led to thicker andmore stable sprouts compared to the ones within1.2 mg/ml collagen density, whereas broken andunstable sprouts formed on 0.7 mg/ml density due tothe low ratio of proliferating to migrating cells. Fur-thermore, no significant migration of the cells wasobserved within matrices of 2.7 mg/ml collagen den-

sity, so the ratio of proliferation to migration was notreported in this case. These results suggest that thedensity of ECM affects sprout morphogenesis by reg-ulating the proliferation and migration of endothelialcells. (As can be seen in Fig. 3i, the ratio of prolifer-ating cells to migrating cells are 0.4 and 0.55 forintermediate collagen densities within which stablesprouts are formed).

Sprout morphology was further characterized bycalculating the average sprout thickness measuredalong the length of each sprout formed within theexperimental and simulation platforms. The number ofcells per sprout and per sprout length was obtained inthe experimental platform by staining the cell nucleiand actin cytoskeleton followed by manual counting(Figs. 4a–4d). Figure 5 compares sprout thickness,sprout length, and number of cells per sprout and persprout length showing quantitative agreement betweenthe experimental and computational results. Quantifi-cation of observed and simulated results confirms thatsprout thickness increases by increasing matrix density(Fig. 5a). It was also observed that the length ofsprouts within collagen matrix of 2.7 mg/ml density issignificantly lower compared to the sprouts within

FIGURE 5. Comparison of experimental and simulated sprout thickness (a), and sprout length (b), number of endothelial cells persprout length (c) and number of cells per sprout (d) formed within different collagen densities, *p< 0.05, **p< 0.01. Since brokenand unstable sprouts formed within collagen matrix density of 0.7 mg/ml, we were not able to report observed data of sproutthickness for this density. Therefore, only the simulated data is presented for this matrix density (a).

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other matrix densities confirming that this matrixdensity is preventive for sprout elongation (Fig. 5b).Analyzing the experimental and simulation results alsoshowed that the number of cells per sprout and persprout length increases by increasing collagen matrixdensity. This is an evidence corroborating higher ratiosof cell proliferation to migration within collagenmatrices of higher densities (Figs. 5c, 5d).

Dynamics of Sprout Elongation Within Matrices ofVarying Densities

Time lapse imaging of sprouts within varying collagendensities was performed to determine the rate of sproutelongation.Observationsobtained fromthe experimentalplatform showed that by increasing collagen density, therate of sprout elongation decreases (Figs. 6a–6f). Sproutlengths were quantified at three consistent time points forthe two intermediate collagen densities. Comparing thesprout morphogenesis at consistent time points acrossdifferent matrix densities shows that sprouts within1.2 mg/ml matrix density elongate more quickly com-pared to the ones within 1.9 mg/ml matrix density over atime period of 48 h (Table 1). However, thicker sproutsformwithin 1.9 mg/mlmatrix densities. As can be seen inTable 1, sprout elongation occurs prominently between24 and 48 h within 1.2 mg/ml collagen matrices andbetween 48 and 72 h within 1.9 mg/ml collagenmatrices.Table 1 results demonstrate that the elongation rate washigher on lowermatrix densities. Additionally,more time

is needed for sprouts to start elongation within stiffermatrices.

Tip Cell Filopodia Extension and Sprout Branching

Figure 7a shows sprout formation on a 1.2 mg/mlcollagen matrix. The tip cell of this sprout has long,thin protrusions, called filopodia. Filopodia have beenfound to play a critical role in the path finding anddirectional navigation of endothelial sprouts.23 Inter-estingly, sprout branching can be observed frequentlyat this collagen density (1.2 mg/ml) (Fig. 7b). Anincreased incidence of branching within a specificrange of fibril densities was predicted by our compu-tational model (fibril density of 0.4) (Fig. 7c). Byquantifying the percentage of branches per sproutformed within varying collagen matrix densities, it wasobserved that branching occurs significantly within aspecific range of matrix density (0.7–1.2 mg/ml). Theincidence of branching was less likely on other densi-ties considered (Fig. 8). In the present study, ourexperimental model verified the hypothesis of ournumerical model that a specific range of matrix density(fibril densities of 0.1 and 0.4) can cause higherincidence of sprout branching compared to the highermatrix densities (Fig. 8).

DISCUSSION AND CONCLUSIONS

The development of complex vascular networks is acritical process during embryonic development, adulttissue remodeling, cancer progression, and for regen-erative medicine therapies. The goal of this researchwas to synergistically and synchronously develop the-oretical, computational models and experimental,laboratory models to predict the fundamental bio-physics and biochemistry regulating vascular net-works.

FIGURE 6. Time-lapse imaging of sprout morphology within 1.2 mg/ml (a, b, and c) and 1.9 mg/ml collagen densities (d, e, and f).

TABLE 1. Elongation rate of sprouts within various collagendensities.

Collagen density (mg/ml)

Elongation rate (lm/h)

24–48 h 48–72 h

1.2 8.1 ± 2.4 0.5 ± 0.2

1.9 2.2 ± 0.7 4.5 ± 1.5

A Comparative Study of Collagen Matrix Density Effect

Previous studies have demonstrated the dependencyof cell morphology and function to matrix densitywithin various tissues of the body.11,25,37,51,54,55 How-ever, the mechanism responsible for the effect of matrixstiffness on cellular responses has not yet been entirelyelucidated. Complex interplay between biochemical andbiomechanical factors has made these studies morechallenging. Unfortunately, the implementation oftechniques that can facilitate the control of key variablesare complicated by the difficulty of testing various andsimultaneous hypotheses. However, experiments andcomputation can be integrated to achieve precise con-trol of measured variables and to test multiplehypotheses at low cost to potentially explain some of themechanisms controlling biological phenomena. Forexample, although previous separate studies had iden-tified collagen density as playing a role in endothelialsprout formation,5,51 there was still a demand for a joint

study of this problem since the experimental work wasnot able to isolate the primary cause of this dependencyand the simulation predictions could not be verifiedwithout related experiments. In the present study theeffect of ECM in the computational model was onlyconsidered through the key interactions between cellmembranes and ECM fibers at random orientations.Good agreement between the results of the computa-tional and experimental model leads us to conclude thatthe density of ECM is likely to exert an influence oversprout morphology and stability by regulating the pro-liferation and migration of endothelial cells throughcell–matrix adhesion. It could be stated that the specificranges of extracellular matrix density lead to an opti-mum degree of interactions between cells and extracel-lular matrix and consequently stable sprouts areformed. Synchronizing the experimental and computa-tional studies, we demonstrated that the ECM densitymainly affects sprout morphology by adjusting cell–celland cell–matrix interactions and a balanced ratio ofproliferating cells to migrating cells.

This joint computational and experimental study ofendothelial sprout formation characterized the matrixdensity dependence of cell migration and proliferation inendothelial sprout formation and morphology. Variouscollagenmatrix densities were selected to study a relativelywide range of matrix storage moduli. The plateau storagemoduli of gelswith the selected range of densities (0.7–1.2–1.9–2.7 mg/ml) that represents the stiffness of gels was 30–80–200 and 700 Pa respectively.51 Quantification ofscanning electron microscopy (SEM) of collagen fibersrevealed a correlation between increasing matrix densityand collagen fibril formation and entanglement. Themostcompliant collagen matrix studied had a very sparse dis-tribution of collagen fibrils with a low degree of entan-glement and large mesh sizes. Increasing collagen densityincreased the entanglement of collagen fibrils consider-ably, resulting in smaller mesh sizes of the gel. A very high

FIGURE 7. Sprout initiation and branching is shown within 1.2 mg/ml collagen matrix in vitro (a, b).The computational modelshows sprout branching within matrix with ~0.4 fibrillar density (c).

FIGURE 8. Comparison of experimental percentage of bran-ches per sprout formed within different collagen densitiesin vitro. Branching is more likely on the range of 0.7–1.2 mg/ml collagen matrices (related to fibrillar densities of 0.1–0.4)compared to higher gel densities, **p< 0.01.

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level of entanglementwith tinymesh sizeswasobserved forcollagen matrices with a density of 2.7 mg/ml. Using ourplatforms, sprout formation of dermal microvascularendothelial cells was studied across a range of collagenconcentrations (0.7–2.7 mg/ml) within an equilibriumVEGF concentration gradient. These experiments re-vealed that endothelial sprouting is stabilized at theintermediate collagen matrix densities of 1.2 and 1.9 mg/ml, suggesting that close cooperation betweenbiochemicaland biomechanical factors is necessary for successfulangiogenesis. As suggested by our in silico modeling re-sults, we found that increasing collagen matrix fibril den-sity increased the duration of cell–cell contacts, cellproliferation, and the width of the sprouts. At low matrixdensities (0.7 mg/ml), cells migrate as single entities; atintermediate matrix densities (1.2, 1.9 mg/ml), cellsundergo sprouting morphogenesis to form long, stablesprouts; while at high matrix densities (2.7 mg/ml), cellscluster and are unable to elongate and penetrate into theECM to form viable sprouts. It can be stated that withinintermediate gel densities, a balance between the rate ofproliferation and migration of endothelial cells results inthe formation of stable and long sprouts. This balance candetermine the stability, dynamics, and morphology ofsprout morphogenesis within collagen matrices of varyingdensities. Within stiffer matrices, higher ratio of prolifer-ating cells to migrating cells was observed to cause theformation of thicker sprouts. As predicted computation-ally, our experiments also showed that a specific range ofmatrix density (0.7 and 1.2 mg/ml) was conductive toendothelial sprout branching. The dynamics of sproutelongation and the number of cells per sprout unit lengthwere also studied. The results of this study can be veryhelpful for developing new strategies for enhancing orsuppressing angiogenesis such as developing tunable bio-materials with specified biomechanical and biochemicalproperties.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s10439-015-1416-2) contains supplementary material,which is available to authorized users.

CONFLICT OF INTEREST

None Declared.

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