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Annals of Biomedical Engineering ( 2015)
DOI: 10.1007/s10439-015-1416-2
A Comparative Study of Collagen Matrix Density Effect on Endothelial
Sprout Formation Using Experimental and Computational Approaches
Center 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 factors
in angiogenesis is a necessary step to control the development
of new blood vessels. Extracellular matrix density is known
to have a significant influence on cellular behaviors and
consequently can regulate vessel formation. The utilization of
experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of
new capillary sprout formation. In this study, using an
integrative method, the interplay between the matrix density
and angiogenesis was investigated. Owing the fact that the
extracellular matrix density is a global parameter that can
affect other parameters such as pore size, stiffness, cell–
matrix adhesion and cross-linking, deeper understanding of
the most important biomechanical or biochemical properties
of the ECM causing changes in sprout morphogenesis is
crucial. Here, we implemented both computational and
experimental methods to analyze the mechanisms responsible
for the influence of ECM density on the sprout formation
that is difficult to be investigated comprehensively using each
of these single methods. For this purpose, we first utilized an
innovative approach to quantify the correspondence of the
simulated collagen fibril density to the collagen density in the
experimental part. Comparing the results of the experimental
study and computational model led to some considerable
achievements. First, we verified the results of the computational model using the experimental results. Then, we
reported parameters such as the ratio of proliferating cells
to migrating cells that was difficult to obtain from experimental study. Finally, this integrative system led to gain an
understanding of the possible mechanisms responsible for the
effect of ECM density on angiogenesis. The results showed
that stable and long sprouts were observed at an intermediate
collagen matrix density of 1.2 and 1.9 mg/ml due to a balance
between the number of migrating and proliferating cells. As a
result of weaker connections between the cells and matrix, a
lower collagen matrix density (0.7 mg/ml) led to unstable and
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: [email protected]
broken sprouts. However, higher matrix density (2.7 mg/ml)
suppressed sprout formation due to the high level of matrix
entanglement, which inhibited cell migration. This study also
showed that extracellular matrix density can influence sprout
branching. Our experimental results support this finding.
Keywords—Endothelial sprout, Matrix density, Microfluidic
device, Cellular Potts Model, Multi-scale model.
The formation of new blood vessels via angiogenesis
is a rate-limiting step for normal development and
physiology, as well as numerous pathologic processes,
including cancer and ophthalmologic disorders such as
macular degeneration.20 In cancer, the concept of an
‘‘angiogenic switch’’, whereby neovascularization both
precedes and is necessary for tumor progression and
metastasis, was proposed by Folkman and Hanahan.27
The development of tumor angiogenesis is mechanistically quite complex, involving vessel growth into an
initially avascular tumor mass,21 the early recruitment
of vasculature from neighboring tissue,30 and the
contribution of circulating endothelial stem cells.3 Given the anti-cancer therapeutic potential of an angiogenesis blockade, significant efforts have been devoted
toward understanding the molecular mechanisms
underlying blood vessel formation.19,29,60,63 Potential
therapies for numerous other diseases (e.g., peripheral
arterial disease, diabetic wound healing, macular
degeneration, stroke, myocardial infarction) include
either the prevention or promotion of angiogenesis.
Many biochemical factors have been identified that
either deter or encourage blood vessel formation.41
However, very little is known quantitatively about the
interrelationship between the cell and the biochemical
2015 Biomedical Engineering Society
SHAMLOO et al.
and biomechanical environment. Although significant
strides have been made, a comprehensive and multiscale understanding of the relationships involved in
angiogenesis and tumor growth, and thus an effective
cure or treatment, is still a work in progress.
What is known is that blood vessel formation and
cohesive vascular network structures require the
coordinated motion of a multitude of cells, favorable
environmental factors, and successful signal transduction. These complex vascular networks exhibit
dynamic behavior including endothelial cell migration,
proliferation, elongation, and branching.14 As
endothelial cells migrate into the extracellular matrix
(ECM), they undergo cell-type specific specialization,
with tip cells forming filopodia to sense and migrate
toward chemoattractants such as vascular endothelial
growth factor (VEGF), while stalk cells proliferate and
form vascular tubes.15,23,49 Tip cells express receptors
including VEGFR2 and VEGFR3 that are not expressed by stalk cells and that are functionally required
for angiogenesis.46,59 These molecular level differences
between tip cells and stalk cells result in different
migration and proliferation rates.23 While observations
at and below the single cell length scale have led to
advancements in our understanding of tissue formation, this process cannot be truly described and studied
without observing the systems of collective cell phenomena that occur across much larger time and length
scales. It is this system of cellular communication and
interaction that ultimately results in coordinated cell
motion and cohesive tissue formation.
Recently, several groups have developed in vitro
models of angiogenesis that have produced new insights into the mechanisms of coordinated endothelial
cell movement.10,12,24,34,38,40,47,51–53,56,57,61,62 Although
various in vitro and in vivo assays have been developed
to provide precise insight into the field of angiogenesis,31,44 microfluidic devices show a considerable
potential for angiogenesis studies because they allow
precise and quantitative control over the extracellular
microenvironment, thereby enabling direct testing of
hypotheses that cannot be achieved using in vivo
models alone.64 For example, a variety of microfabricated culture devices apply quantified concentration
gradients of soluble factors to two-dimensional (2D)
monolayer cultures and/or three-dimensional (3D)
sprouting morphogenesis cultures of endothelial
cells.10,18,51,52 These quantitative in vitro results were
validated through design of an optimized VEGF-delivery system for in vivo murine hind leg ischemia,10 but
there remains a need for a high-throughput approach
with the ability to test the simultaneous effects of
biochemical and biomechanical factors and to explain
the mechanisms behind these effects. Furthermore,
Mathematical investigations of angiogenesis have
employed continuous, discrete, and mechanical models
to describe a variety of dynamics believed to influence
angiogenesis.2,9,13,16,17,36,42,50,58 However, despite clear
evidence that the ECM is crucial to cellular behavior
and vascular patterning, most models of angiogenesis
neglect the dynamic interaction between endothelial
cells and the ECM. Until recently, no single mathematical model existed that (a) couples multiple time
and length scales, (b) generates realistic capillary
structures, including branching and anastomoses,
without a priori prescribing rules and probabilities to
these events, and (c) considers the complex biochemical and mechanical interactions that occur between
endothelial cells and the ECM.4,5
Computational techniques can be applied to simulate a wide range of biological phenomena including
intracellular processes, formation of multi-cellular
structures and distribution of biochemical factors
within cellular microenvironments.4–6,26,28,32,33,35,45
These computational methods, when combined with
experimental verifications, have the potential to help
explain the mechanisms behind biological processes
that cannot be understood from in vivo or in vitro
techniques alone.8,48 It was shown that maximal cell
migration happens at an intermediate binding level of
the cells to the matrix, but more compliant matrices are
more favorable for 3D cell movement when keeping
the cell–matrix binding level constant.65 Another
group applying both experimental and computational
techniques to study leukocyte rolling found that in
addition to the ligand surface density the convective
flux of the bonds and the dissociation rate at the back
of a cell’s contact zones determines the rolling velocity
of the cells.39 In addition, a recent analysis on neuronal
axon path-finding integrating experiment and simulation has found that different mechanisms may be
responsible for neuronal axon path-finding.43 It was
shown that at steeper gradients axon turning is the
more possible response of neuronal cells to neurotrophic factors whereas at shallower gradients biased
axonal growth rate towards biochemical gradients is a
more probable cause for directional path-finding of
In this study, we have developed experimental and
computational platforms capable of testing multiple
variables and explaining the interplay between biochemical and biomechanical factors in a study of the
effects of matrix density on endothelial sprout morphogenesis. Our simulation results were verified on our
experimental platform. Both computational and
experimental observations illuminated collagen fibril
density as a critical factor in the morphology and
characteristics of sprouts within matrices of varying
stiffness. Our studies elucidate the role of collagen fibril
density as a determinant factor affecting the formation
A Comparative Study of Collagen Matrix Density Effect
of multi-cellular structures from single endothelial cells
during angiogenesis. Comparing the results from
experimental and computational methods introduced
the binding affinity between the cells and the collagen
fibers as the main factor affecting endothelial sprout
formation within collagen matrices of varying densities.
In Vitro Endothelial Sprouting Assays
Microfluidic devices were fabricated in PDMS
(Sylgard 184, Midland, MI) using soft lithography as
previously described51,52 (Fig. S1). Transparency
masks were generated from CAD files of fluidic
channels using negative photoresist (SU-8). Sharpened
needles (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 and
the glass substrate, both surfaces were exposed to
oxygen plasma treatment for 2–3 min and brought
immediately into contact. This microfluidic device enables quantifiable measurements of endothelial cell
chemotaxis in response to known gradients of soluble
factors that remain stable from 1 h to weeks (Fig. 1a).
The microfluidic device also enables real-time imaging
of cellular dynamics in both 2D and 3D culture models. A stable concentration gradient across the cell
culture chamber was generated as shown in Fig. S2.
Rheological tests on the collagen/fibronectin matrix
samples were performed using an oscillatory rheometer
(Anton-Paar) in parallel-plate geometry.
Adult human dermal microvascular endothelial cells
(HMVEC, Lonza, Walkersville, MD) were first grown
as monolayer cultures on the surfaces of collagen-
FIGURE 1. The diffusion-based microfluidic gradient generator device (a); Three dimensional monolayer cultures of adult human
dermal microvascular endothelial cells (HMVEC) on the surfaces of collagen-coated dextran beads were embedded within collagen
I/fibronectin matrices. (b); Collective cell migration and endothelial sprout formation in response to VEGF gradient (c); the equilibrium profile of VEGF concentration within the cell culture chamber; see also Fig. S1 (d); the initial VEGF field in the computation
domain (e); the systems integrated mathematical multi-scale model (f).
SHAMLOO et al.
coated dextran beads (Cytodex, GE, d ~ 170 lm) to
form endothelial sprouts (Figs. 1b, 1c). These beads
were then suspended within a 3D matrix containing rat
tail collagen Type I (BD Biosciences) and fibronectin
(final concentration of 5 lg/ml, 10% total volumetric
mixture) and consequently cultured inside the
microfluidic device (~20 beads/device) that generated
precise and stable VEGF gradients (Fig. 1d).
Endothelial Growth Medium-2MV (EGM-2MV) supplemented with various concentrations of VEGF
(VEGF-A isoform VEGF (165), R&D Systems, Minneapolis, MN) was continuously supplied to the source
reagent channel, while EGM-2MV with no VEGF was
supplied to the sink reagent channel. The injection flow
rate was 40 nl/min. Upon VEGF stimulation, ECs
underwent sprouting morphogenesis, i.e., collective cell
movement to migrate away from the bead surface and
into the collagen gel matrix as a cohesive, columnar
structure (Fig. 1c). More details about the microfluidic
system are presented in the supplementary section (S1).
Collagen matrices of varying densities ranging from
compliant gels to stiffer matrices were used to study
the effect of matrix density on the sprout morphology,
dynamics and branching. To obtain different matrix
densities, the collagen concentration was altered while
the final fibronectin, microcarrier bead, endothelial
cell, and media concentrations were kept uniform. The
formation of endothelial sprouts was detected and
recorded using time-lapse imaging.
Characterization of Endothelial Cell Sprouts and
Statistical Analysis
Individual beads were imaged every 24 h for 3 days
using phase contrast and fluorescence microscopy.
ImageJ software (NIH freeware) was used to measure
the number of cells per sprout, the sprout average
thickness, the sprout length and the sprout elongation
rate. The average thickness of each sprout was determined by dividing the projected sprout surface area by
the length of the sprout centerline. For each condition,
between three and six independent experiments were
performed, such that the number of beads imaged for
each condition totaled 60–120. The one-tailed, nonpaired, Student’s t test was used to determine the statistical significance of differences between pairs of
Cell Fluorescent Staining
Sprouts within collagen gels were fixed by injecting
4% paraformaldehyde into the source and sink channels and incubating at 4 C for approximately 1 h. The
samples were washed at least four times by injecting
PBS 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 cellular
actin cytoskeleton was stained overnight at 4 C using
Alexa Fluor 555-conjugated phalloidin (Invitrogen)
while the cell nuclei were stained using DAPI. Samples
were washed with PBS at least four times and then
incubated with PBS at 4 C for 12 h prior to imaging.
An inverted fluorescence microscope was used to acquire images.
Computational Model of Angiogenesis
We also developed and validated a 2D (x, y, t) cellbased, multi-scale model of angiogenesis that integrates tissue, cellular, and molecular scale dynamics to
analyze cell–cell and cell–matrix interactions. Using
this model, a gradient of VEGF concentration was
generated in the simulation domain that is shown in
Fig. 1e. This spatio-temporal mathematical model
combines a lattice-based cellular Potts model describing individual cellular interactions, a partial differential equation to describe the spatio-temporal dynamics
of VEGF, and the Boolean model of intracellular signaling pathways critical to angiogenesis7 (Fig. 1f). A
summary of the computational model is presented in
the supplementary section (S2).
Since the VEGF field (V(x, y, t)) exerts an influence
on cell chemotaxis, the discrete and continuous parts
of the model feedback on each other at the cell membrane through the chemotaxis term in the total energy
equation. Considering the effect of cell phenotype on
the chemotaxis potential is one of the notable features
of this multi-scale mathematical model. This model
distinguishes between the cells that are proliferating
and the ones that are migrating. Cells migrate toward
increasing concentrations of VEGF from the parent
vessel to facilitate sprout extension. The fibrous
structure of the ECM is another feature of this model.
ECM collagen fibers are randomly distributed at random discrete orientations between 290 and 90. The
mesh-like anisotropic structure of the extracellular
matrix is modeled by the heterogeneous and random
distribution of these fibers. The cell membrane interacts with these ECM fibers through the adhesion term
in the total energy equation.
The VEGF and cellular distributions and the
geometry of the computational model have been initialized to approximate the in vitro microcarrier bead
sprouting morphogenesis experiment. Our computational model captures realistic vascular structures
including branching as well as contact guidance and
inhibition. Computational simulations and experimental observations of soluble factor gradients are in
excellent agreement and allow exact specification of the
A Comparative Study of Collagen Matrix Density Effect
soluble factor concentration at every location within
the device (comparison of Figs. 1d, 1e).
Quantification of Collagen Fibril Density
Scanning electron microscopy (SEM) was used to
determine collagen fibril distribution within collagen
matrices of varying densities. To quantify the collagen
fibril density, an image analysis algorithm was used to
predict the vacant spaces in collagen matrix and the
spaces filled with collagen fibrils using an in-house
MATLAB image analysis code. Using this code, we
categorized the image pixel counts based on their
normalized intensity. By estimating the minimum
normalized intensity of the pixels that represent collagen fibers on the SEM images, we determined a criterion showing fibrillar and non-fibrillar spaces in the
collagen matrix. We define a ratio of fibrillar spaces to
the total matrix space as the number of pixels having
intensity greater than the threshold divided by the total
number of pixels. This ratio was used as an input for
fibril density, or fractional filled area, in the simulation
studies. More details about this innovative method are
presented in the supplementary section (S3).
Quantification of Collagen Fibril Density for Varying
Collagen Gel Concentration
As previously described, scanning electron microscopy (SEM) was used to determine collagen fibril
distribution within collagen matrices of varying densities: 0.7, 1.2, 1.9 and 2.7 mg/ml (Figs. 2a–2d). A
model was also made to simulate the distribution of
collagen fibers in the in silico study. The architecture of
the ECM is anisotropic, with regions of varying densities. A single collagen fibril is ~300 nm long and
1.5 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 varying
densities (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 the
mathematical 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 result
of an increase in the experimental collagen matrix density. Statistical analysis showed that the fibril densities are significantly
different within varying collagen matrices.
SHAMLOO et al.
FIGURE 3. Experimentally and computationally observed sprouting morphogenesis at varying matrix densities over a time period
of 72 h. Within matrices of 0.7 mg/ml density unstable or broken sprouts are observed due to minimal cell–cell interactions. Arrows
show 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 density
matrices (c). High matrix density (2.7 mg/ml) inhibited sprout elongation and yielded thicker sprouts (g). Predictions from the
respective comparable computational simulations are remarkably close to in vitro observations (b, d, f, and h). The ratio of
proliferating to migrating cells of sprouts formed within matrices of varying density (i), *p < 0.05, **p < 0.01.
A Comparative Study of Collagen Matrix Density Effect
FIGURE 4. Fluorescent inverted (a, b, and c) and confocal (d) images of sprouts formed within matrices of various collagen
densities. Red and white colors represent a phalloidin stain of the F-actin cytoskeleton and a DAPI stain of nuclei, respectively.
collagen fibrils and other matrix proteins are bound
together constituting larger cords or bundles of matrix
fibers estimated to be between 100 and 1000 nm
thick.22 Our mathematical model accurately captures
the heterogeneity and random distribution of a typical
ECM fiber matrix, such as a Type I collagen matrix.
We model this mesh-like anisotropic structure of the
ECM by randomly distributing 1.1 lm thick bundles
of collagen fibrils at random orientations ranging
between 290 to 90 until the desired percentage of
total ECM space occupied by collagen fibers is
achieved (Figs. 2e–2h).
Using an innovative approach, we calculated the
fibril density of ECM by means of an image analysis
algorithm that is described in supplementary section S3
(Fig. 2i). According to image analysis data which was
shown in Fig. 2j, the collagen fibril density is very low
in the lowest collagen gel density (0.7 mg/ml yields a
fibril density of ~0.13). Analyzing the fibril density at
higher collagen gel densities reveals that fibril density
increases significantly from ~0.13 to ~0.38 when the
collagen gel density is increased from 0.7 to 1.2 mg/ml
(Fig. 2j). Fibril density increases from ~0.38 to ~0.68
when we increased collagen gel density from 1.2 to
1.9 mg/ml (Fig. 2j). The collagen matrix with 2.7 mg/
ml density yielded a fibril density of ~0.89. These collagen matrix densities approximately correspond to the
fibril densities used in the matrices in the computational model. The sprout characteristics from the
experimental and simulation platforms were compared
and results are discussed below.
Comparison of Sprout Morphology and Cell Count in
Varying Collagen Densities Using Experimental and
Computational Platforms
Endothelial cells cultured on surfaces of microcarrier beads within collagen matrices of varying densities
demonstrated a distinctive dependency between sprout
morphology and matrix density. Tracks of endothelial
cells were observed over a 72-h time period within
collagen gel matrices of 0.7, 1.2, 1.9 and 2.7 mg/ml
density and simulated computationally on matrices
with corresponding fibril densities of <0.1, 0.4, 0.7,
and >0.9. On the corresponding 0.7 mg/ml collagen
matrix density, endothelial cell tracks show minimal
cell contact resulting in unstable or broken sprouts
(Fig. 3a). This was predicted by the numerical simulations of sprouting angiogenesis on a matrix with a
low fibril density (Fig. 3b). In contrast, Fig. 3c shows
narrow but stable sprout formation using the experimental platform within a collagen matrix of density of
1.2 mg/ml. The cells forming these sprouts are well
connected with each other. Narrow, stable sprout
formation was independently predicted using the
mathematical model on a matrix with a fibril density
of 0.4 (Fig. 3d). Sprouts forming on 1.9 mg/ml density matrices show thicker morphologies in the
SHAMLOO et al.
FIGURE 5. Comparison of experimental and simulated sprout thickness (a), and sprout length (b), number of endothelial cells per
sprout length (c) and number of cells per sprout (d) formed within different collagen densities, *p < 0.05, **p < 0.01. Since broken
and unstable sprouts formed within collagen matrix density of 0.7 mg/ml, we were not able to report observed data of sprout
thickness for this density. Therefore, only the simulated data is presented for this matrix density (a).
experimental platform (Fig. 3e). Greater levels of cell
contact for these sprouts make them more capable of
forming stable multi-cellular structures. Thicker sprout
morphologies on matrices with higher fibril density
was also borne out in simulations using fibril density of
0.7 (Fig. 3f). Interestingly, cell migration was inhibited
in the stiffest collagen gel matrices (2.7 mg/ml)
(Fig. 3g). Suppression of sprout formation was also
observed in simulation studies on matrices of associated collagen fibril density (>0.9) (Fig. 3h). The
inability of the tip cells to penetrate, elongate, and
migrate into matrices of very high density indicates the
critical role of biomechanical effectors during new
blood vessel formation. As can be seen in Fig. 3i, a
balance between proliferation and migration was
observed on matrices with 1.2 and 1.9 mg/ml collagen
density. A higher ratio of proliferation to migration
within collagen density of 1.9 mg/ml led to thicker and
more stable sprouts compared to the ones within
1.2 mg/ml collagen density, whereas broken and
unstable sprouts formed on 0.7 mg/ml density due to
the low ratio of proliferating to migrating cells. Furthermore, no significant migration of the cells was
observed within matrices of 2.7 mg/ml collagen den-
sity, so the ratio of proliferation to migration was not
reported in this case. These results suggest that the
density of ECM affects sprout morphogenesis by regulating the proliferation and migration of endothelial
cells. (As can be seen in Fig. 3i, the ratio of proliferating cells to migrating cells are 0.4 and 0.55 for
intermediate collagen densities within which stable
sprouts are formed).
Sprout morphology was further characterized by
calculating the average sprout thickness measured
along the length of each sprout formed within the
experimental and simulation platforms. The number of
cells per sprout and per sprout length was obtained in
the experimental platform by staining the cell nuclei
and actin cytoskeleton followed by manual counting
(Figs. 4a–4d). Figure 5 compares sprout thickness,
sprout length, and number of cells per sprout and per
sprout length showing quantitative agreement between
the experimental and computational results. Quantification of observed and simulated results confirms that
sprout thickness increases by increasing matrix density
(Fig. 5a). It was also observed that the length of
sprouts within collagen matrix of 2.7 mg/ml density is
significantly lower compared to the sprouts within
A Comparative Study of Collagen Matrix Density Effect
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 collagen
is needed for sprouts to start elongation within stiffer
Elongation rate (lm/h)
Collagen density (mg/ml)
24–48 h
48–72 h
Tip Cell Filopodia Extension and Sprout Branching
8.1 ± 2.4
2.2 ± 0.7
0.5 ± 0.2
4.5 ± 1.5
Figure 7a shows sprout formation on a 1.2 mg/ml
collagen matrix. The tip cell of this sprout has long,
thin protrusions, called filopodia. Filopodia have been
found to play a critical role in the path finding and
directional navigation of endothelial sprouts.23 Interestingly, sprout branching can be observed frequently
at this collagen density (1.2 mg/ml) (Fig. 7b). An
increased incidence of branching within a specific
range of fibril densities was predicted by our computational model (fibril density of 0.4) (Fig. 7c). By
quantifying the percentage of branches per sprout
formed within varying collagen matrix densities, it was
observed that branching occurs significantly within a
specific range of matrix density (0.7–1.2 mg/ml). The
incidence of branching was less likely on other densities considered (Fig. 8). In the present study, our
experimental model verified the hypothesis of our
numerical model that a specific range of matrix density
(fibril densities of 0.1 and 0.4) can cause higher
incidence of sprout branching compared to the higher
matrix densities (Fig. 8).
other matrix densities confirming that this matrix
density is preventive for sprout elongation (Fig. 5b).
Analyzing the experimental and simulation results also
showed that the number of cells per sprout and per
sprout length increases by increasing collagen matrix
density. This is an evidence corroborating higher ratios
of cell proliferation to migration within collagen
matrices of higher densities (Figs. 5c, 5d).
Dynamics of Sprout Elongation Within Matrices of
Varying Densities
Time lapse imaging of sprouts within varying collagen
densities was performed to determine the rate of sprout
elongation. Observations obtained from the experimental
platform showed that by increasing collagen density, the
rate of sprout elongation decreases (Figs. 6a–6f). Sprout
lengths were quantified at three consistent time points for
the two intermediate collagen densities. Comparing the
sprout morphogenesis at consistent time points across
different matrix densities shows that sprouts within
1.2 mg/ml matrix density elongate more quickly compared to the ones within 1.9 mg/ml matrix density over a
time period of 48 h (Table 1). However, thicker sprouts
form within 1.9 mg/ml matrix densities. As can be seen in
Table 1, sprout elongation occurs prominently between
24 and 48 h within 1.2 mg/ml collagen matrices and
between 48 and 72 h within 1.9 mg/ml collagen matrices.
Table 1 results demonstrate that the elongation rate was
higher on lower matrix densities. Additionally, more time
The development of complex vascular networks is a
critical process during embryonic development, adult
tissue remodeling, cancer progression, and for regenerative medicine therapies. The goal of this research
was to synergistically and synchronously develop theoretical, computational models and experimental,
laboratory models to predict the fundamental biophysics and biochemistry regulating vascular networks.
SHAMLOO et al.
FIGURE 7. Sprout initiation and branching is shown within 1.2 mg/ml collagen matrix in vitro (a, b).The computational model
shows sprout branching within matrix with ~0.4 fibrillar density (c).
FIGURE 8. Comparison of experimental percentage of branches per sprout formed within different collagen densities
in 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.
Previous studies have demonstrated the dependency
of cell morphology and function to matrix density
within various tissues of the body.11,25,37,51,54,55 However, the mechanism responsible for the effect of matrix
stiffness on cellular responses has not yet been entirely
elucidated. Complex interplay between biochemical and
biomechanical factors has made these studies more
challenging. Unfortunately, the implementation of
techniques that can facilitate the control of key variables
are complicated by the difficulty of testing various and
simultaneous hypotheses. However, experiments and
computation can be integrated to achieve precise control of measured variables and to test multiple
hypotheses at low cost to potentially explain some of the
mechanisms controlling biological phenomena. For
example, although previous separate studies had identified collagen density as playing a role in endothelial
sprout formation,5,51 there was still a demand for a joint
study of this problem since the experimental work was
not able to isolate the primary cause of this dependency
and the simulation predictions could not be verified
without related experiments. In the present study the
effect of ECM in the computational model was only
considered through the key interactions between cell
membranes and ECM fibers at random orientations.
Good agreement between the results of the computational and experimental model leads us to conclude that
the density of ECM is likely to exert an influence over
sprout morphology and stability by regulating the proliferation and migration of endothelial cells through
cell–matrix adhesion. It could be stated that the specific
ranges of extracellular matrix density lead to an optimum degree of interactions between cells and extracellular matrix and consequently stable sprouts are
formed. Synchronizing the experimental and computational studies, we demonstrated that the ECM density
mainly affects sprout morphology by adjusting cell–cell
and cell–matrix interactions and a balanced ratio of
proliferating cells to migrating cells.
This joint computational and experimental study of
endothelial sprout formation characterized the matrix
density dependence of cell migration and proliferation in
endothelial sprout formation and morphology. Various
collagen matrix densities were selected to study a relatively
wide range of matrix storage moduli. The plateau storage
moduli of gels with 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 of
scanning electron microscopy (SEM) of collagen fibers
revealed a correlation between increasing matrix density
and collagen fibril formation and entanglement. The most
compliant collagen matrix studied had a very sparse distribution of collagen fibrils with a low degree of entanglement and large mesh sizes. Increasing collagen density
increased the entanglement of collagen fibrils considerably, resulting in smaller mesh sizes of the gel. A very high
A Comparative Study of Collagen Matrix Density Effect
level of entanglement with tiny mesh sizes was observed for
collagen matrices with a density of 2.7 mg/ml. Using our
platforms, sprout formation of dermal microvascular
endothelial cells was studied across a range of collagen
concentrations (0.7–2.7 mg/ml) within an equilibrium
VEGF concentration gradient. These experiments revealed that endothelial sprouting is stabilized at the
intermediate collagen matrix densities of 1.2 and 1.9 mg/
ml, suggesting that close cooperation between biochemical
and biomechanical factors is necessary for successful
angiogenesis. As suggested by our in silico modeling results, we found that increasing collagen matrix fibril density increased the duration of cell–cell contacts, cell
proliferation, and the width of the sprouts. At low matrix
densities (0.7 mg/ml), cells migrate as single entities; at
intermediate matrix densities (1.2, 1.9 mg/ml), cells
undergo sprouting morphogenesis to form long, stable
sprouts; while at high matrix densities (2.7 mg/ml), cells
cluster and are unable to elongate and penetrate into the
ECM to form viable sprouts. It can be stated that within
intermediate gel densities, a balance between the rate of
proliferation and migration of endothelial cells results in
the formation of stable and long sprouts. This balance can
determine the stability, dynamics, and morphology of
sprout morphogenesis within collagen matrices of varying
densities. Within stiffer matrices, higher ratio of proliferating cells to migrating cells was observed to cause the
formation of thicker sprouts. As predicted computationally, our experiments also showed that a specific range of
matrix density (0.7 and 1.2 mg/ml) was conductive to
endothelial sprout branching. The dynamics of sprout
elongation and the number of cells per sprout unit length
were also studied. The results of this study can be very
helpful for developing new strategies for enhancing or
suppressing angiogenesis such as developing tunable biomaterials with specified biomechanical and biochemical
The online version of this article (doi:10.1007/
s10439-015-1416-2) contains supplementary material,
which is available to authorized users.
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