1. School of Biomedical Engineering, Science & Health Systems
Modeling of the Vascular Endothelial Growth Factor Gradient for Study of Collective Migration
Soumya S. Iyer1; Adam C. Canver1; Alisa Morss Clyne, Ph.D.²
1School of Biomedical Engineering, Science, and Health Systems,
²Mechanical Engineering and Mechanics Department, Drexel University, Philadelphia, PA
INTRODUCTION
OBJECTIVE
Develop a gradient model to show VEGF diffusion in
the microfluidic device over a period of 24 hours.
METHODS
Collective migration is vital to endothelial cells undergoing
angiogenesis, endothelialization after stenting, and vascularization of
large tissue engineered constructs. Endothelial cells’ motility is
affected by vascular endothelial growth factor (VEGF). The endothelial
cells’ ability to react to VEGF sensed by the cellular integrin receptors
is dependent upon substrate stiffness.
The purpose of this study was to model a microfluidic device to
generate a gradient that was formed by sustained release of VEGF.
Using COMSOL modeling software, a time-dependent mass
transfer model was developed to predict the gradient strength over
time. This gradient would then be used during the collective
migration studies on four mechanically-tunable, collagen-coated
polyacrylamide (PA) hydrogels:
1. soft gel without VEGF or a gradient (control)
2. soft gel with VEGF and a gradient
3. stiff gel without VEGF or a gradient
4. stiff gel with VEGF and a gradient
VEGF would be integrated into sodium alginate and heparin-
alginate (H/A) hydrogels to observe sustained release over 24 hours
on these hydrogels with varying stiffness. The results of this study will
validate the overall hypothesis that stiffer substrates enhance the
endothelial response to VEGF during collective migration.
MODELING
• A 2D stationary diffusion model was produced to determine the initial
release rate for the VEGF gradient.
• A 1D time-dependent mass transfer model was designed to graphically
represent the diffusion of VEGF down one channel of the micro device
on COMSOL Multiphysics® 4.0a.
• A 2D transient mass diffusion model was created to express the change
in VEGF concentration in the device over 24 hours.
TESTING
• 4% (w/v) sodium alginate gels were made in a 500 mM calcium chloride
solution. Aliquots of that solution were taken at specific times. Bovine
serum albumin (BSA) was loaded into the gels and then measured with
the nanodrop device to define BSA protein concentration change over
time.¹
• Heparin-alginate gels were made in the chemical hood with 1% (w/v)
heparin solution, 1% (w/v) alginate solution, 0.031 M ethylenediamine,
and 0.33 M 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide
hydrochloride (EDAC). They were stabilized over a 3-day time period.
• The H/A gels were washed with a 2.5 mM calcium chloride and 143 mM
sodium chloride solution, and with distilled water before being freeze-
dried with the lyophilizer.² BSA was loaded into the gels after they were
lyophilized to conduct BSA protein concentration studies.
RESULTS CONCLUSIONS
FUTURE WORK
ACKNOWLEDGEMENTS
REFERENCES
PARAMETERS 2D STATIONARY DIFFUSION MODEL OF THE VEGF GRADIENT
1D TIME-DEPENDENT MASS TRANSFER MODEL OF THE VEGF GRADIENT
2D TRANSIENT MASS DIFFUSION MODEL OF THE VEGF GRADIENT
FORMATION OF SODIUM ALGINATE HYDROGELS FORMATION OF HEPARIN-ALGINATE HYDROGELS
Parameters
2D Stationary
Diffusion Model
1D Time-
Dependent Mass
Transfer Model
2D Transient
Mass Diffusion
Model
Diffusion Coefficient 9.4 x 10-7 cm²/s 9.4 x 10-7 cm²/s 9.4 x 10-7 cm²/s
Length -- 7 mm. --
Maximum Time -- 24 hours 24 hours
VEGF Concentration at
the Source 100 mol/m³ 100 mol/m³ 100 mol/m³
VEGF Concentration at
the Sink 0 mol/m³ 0 mol/m³ 0 mol/m³
Source (radius) 0.5 mm. 0.5 mm. 0.5 mm.
Sink (radius) 2 mm. 2 mm. 2 mm.
Channel Length 2 mm. 2 mm. 2 mm.
Channel Width 0.3 mm. 0.3 mm. 0.3 mm.
Stationary Diffusion Model: VEGF Gradient
Length(mm.)
Width (mm.)
Figure 1. The table above consists of all the parameters used for each model
since the certain parameters varied based on the model.
Figure 2. A simplified 2-dimensional source/sink
model was produced, which is independent of time
and assumes infinite an infinite source. The
dimensions of the model are identical to the actual
device, which are listed in Figure 1.
Figure 3. VEGF release down the channel of the microfluidic
device was graphed to express how the gradient only reaches
the beginning of the channel. A distance of 0 mm. indicates the
start of the source and 7 mm. indicates the end of the sink.
0
5
10
15
20
25
0 6 12 18 24
GradientStrength(mM/mm)
Diffusion Time (hours)
VEGF Gradient Strength over 24 Hours
Figure 4. The 1D time-dependent mass transfer model displays the change
in concentration against the distance over one-hour intervals for 24 hours
only down the channel. It can be determined that the concentration of
VEGF is sustained for a greater distance at 24 hours than at 0 hours.
Figure 5. The graph of the gradient strength of VEGF over 24 hours shows
that the strength is greatest at the 5-hour time point (red point). It
gradually decreases from 24 mM/mm to 17 mM/mm. This indicates that
the gradient should at least be sustained for 5 hours.
Width (mm.) Width (mm.) Width (mm.)Width (mm.)
Figure 6. The transient mass diffusion model presents
the initial VEGF gradient (t=0 s). VEGF would be loaded
into the source and would be ready to release down the
channel.
Figure 7. The transient mass diffusion model displays
the VEGF gradient at t=18000 s (5 hours). This time
point is when the gradient strength peaks, as shown in
Figure 5.
Figure 8. The transient mass diffusion model displays
the VEGF gradient at t=28800 s (8 hours). It illustrates
that most of the VEGF has left the source and the
channel, and is starting to release into the sink.
Figure 9. The transient mass diffusion model illustrates
the VEGF gradient at t=86400 s (24 hours). This is the last
time point in this model, and it is seen that VEGF has
diffused into the infinite sink.
Figure 10. The sodium alginate gel (bottom of
the tube) is washed with distilled water.
Figure 11. The H/A gel (midway in the tube) is
washed with a calcium chloride and sodium
chloride solution.
• The 2D transient mass diffusion model predicts
that the peak gradient strength will be at 5 hours.
• According to the transient mass diffusion model,
most of the VEGF is released from the hydrogels
within the first 8 hours so decreasing the release
rate during that time period would allow for better
sustained release.
• Conduct release-rate experiments with VEGF-
loaded H/A gels.
• Use VEGF-loaded H/A gels in 2D migration assays
to study collective migration of endothelial cells.
• Incorporate VEGF-loaded H/A gels in the 2D
migration assay on soft substrates to investigate if
the VEGF gradient enhances collective migration.
• Determine whether the VEGF gradient improves
collective migration when the 2D migration assay
is performed on stiff substrates with VEGF-loaded
H/A gels.
We would like to thank the S.T.A.R. Scholars Program for
funding and providing this opportunity for research.
We would also like to thank Gary Tang for providing training
in cell culture techniques.
¹ Tanaka, H., Matsumura, M. and Veliky, I. A. (1984), Diffusion
characteristics of substrates in Ca-alginate gel beads. Biotechnol.
Bioeng., 26: 53–58. doi: 10.1002/bit.260260111
² Tanihara, M., Suzuki, Y., Yamamoto, E., Noguchi, A. and Mizushima, Y.
(2001), Sustained release of basic fibroblast growth factor and
angiogenesis in a novel covalently crosslinked gel of heparin and
alginate. J. Biomed. Mater. Res., 56: 216–221. doi: 10.1002/1097-
4636(200108)56:2<216::AID-JBM1086>3.0.CO;2-N