A Two-Compartment Model of VEGF Distribution in the
Phillip Yen., Stacey D. Finley*., Marianne O. Engel-Stefanini, Aleksander S. Popel
Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland, United States of America
Vascular endothelial growth factor (VEGF) is a key regulator of angiogenesis – the growth of new microvessels from existing
microvasculature. Angiogenesis is a complex process involving numerous molecular species, and to better understand it, a
systems biology approach is necessary. In vivo preclinical experiments in the area of angiogenesis are typically performed in
mouse models; this includes drug development targeting VEGF. Thus, to quantitatively interpret such experimental results, a
computational model of VEGF distribution in the mouse can be beneficial. In this paper, we present an in silico model of VEGF
distribution in mice, determine model parameters from existing experimental data, conduct sensitivity analysis, and test the
validity of the model. The multiscale model is comprised of two compartments: blood and tissue. The model accounts for
interactions between twomajor VEGF isoforms(VEGF120and VEGF164)and their endothelial cell receptors VEGFR-1, VEGFR-2,and
co-receptor neuropilin-1. Neuropilin-1 is also expressed on the surface of parenchymal cells. The model includes transcapillary
macromolecular permeability, lymphatic transport, and macromolecular plasma clearance. Simulations predict that the
concentration of unbound VEGF in the tissue is approximately 50-fold greater than in the blood.These concentrations are highly
dependent on the VEGF secretion rate. Parameter estimation was performed to fit the simulation results to available
experimental data, and permitted the estimation of VEGF secretion rate in healthy tissue, which is difficult to measure
experimental studies in the development of pro- and anti-angiogenic agents. The model approximates the normal tissue as
skeletal muscle and includes endothelial cells to represent the vasculature. As the VEGF system becomes better characterized in
other tissues and cell types, the model can be expanded to include additional compartments and vascular elements.
Citation: Yen P, Finley SD, Engel-Stefanini MO, Popel AS (2011) A Two-Compartment Model of VEGF Distribution in the Mouse. PLoS ONE 6(11): e27514.
Editor: Christos Chatziantoniou, Institut National de la Sante ´ et de la Recherche Me ´dicale, France
Received June 7, 2011; Accepted October 18, 2011; Published November 8, 2011
Copyright: ? 2011 Yen et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was supported by the National Institutes of Health (NIH) grants R01 HL101200 and R01 CA138264. The funders had no role in study design,
data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: email@example.com
. These authors contributed equally to this work.
Vascular endothelial growth factor (VEGF) belongs to a family of
cytokines that play an important role in angiogenesis – the formation
of new capillaries from pre-existing vessels. The VEGF family in
mammals is composed of VEGF-A, VEGF-B, VEGF-C, VEGF-D
and placental growth factor (PlGF). The most well-studied member is
VEGF-A (generally referred to as VEGF) that consists of several
splice isoforms including VEGF121, VEGF145, VEGF165, VEGF189
and VEGF206in humans, where the subscripted number indicates
the number of amino acids [1,2]. The amino acid number for all
splice isoformsisone lessthaninhumansforrodent VEGF orthologs.
The roles of VEGF189and VEGF206in vivo are currently still unclear
. Therefore, in our model, we consider the two most abundant
isoforms of VEGF-A in the mouse: VEGF120and VEGF164.
The tyrosine-kinase receptors of VEGF include VEGFR-1 (Flt-1),
VEGFR-2 (Flk-1 or KDR in humans), and VEGFR-3 (Flt-4).
VEGFR-1 and VEGFR-2 are the primary receptors for VEGF-A
and play a major role in angiogenesis, while VEGFR-3 binds VEGF-
C and VEGF-D and plays a major role in lymphangiogenesis.
VEGFR-1 and VEGFR-2 are predominantly expressed on endothe-
lial cells; however,thesereceptorshave alsobeen shown to be present
and cancer cells. The binding of VEGF-A to VEGFR-2 is believed to
be the main signaling pathway for angiogenesis . In addition to the
tyrosine-kinase receptors, VEGF-A binds to co-receptor neuropilin-1
endothelial cell surfaces , and has been shown to enhance the
binding of VEGF165to VEGFR-2. VEGF can also bind to heparan
sulfate proteoglycans in the extracellular matrix (ECM), endothelial
cell basement membrane (EBM) and parenchymal cell basement
Computational models of VEGF-mediated angiogenesis have
been developed to study various aspects of the angiogenic process
. A single-compartment model of the human tissue was initially
developed to study the kinetic ligand-receptor interactions of
multiple VEGF isoforms with endothelial cell surface receptors
(VEGFR-1, VEGFR-2, NRP-1) and extracellular matrix binding
sites . This model was later expanded to include three
compartments, including a tumor compartment, to study tumor
angiogenesis  and peripheral arterial disease . These
compartment models describe spatially averaged VEGF distribu-
tions and receptor bindings in the tissue, blood and tumor.
However, these models were based on human data and are not
immediately applicable to animal data. Mouse animal models
have been extensively used to study cardiovascular diseases such
PLoS ONE | www.plosone.org1November 2011 | Volume 6 | Issue 11 | e27514
Figure 1. Two compartment model. The model is divided into the tissue and blood compartments. VEGF120and VEGF164- are secreted by the
parenchymal cells (myocytes) into the available interstitial space at rate qv. VEGFR-1, VEGFR-2 and NRP-1 are localized on the luminal and abluminal
surfaces of the endothelial cells. NRP-1 is also found on the myocyte cell surface. Inter-compartmental transport includes lymphatic drainage (kL) and
microvascular permeability (k-p). Receptors and VEGF/receptor complexes on endothelial cells and myocytes can be internalized (kint). VEGF is
removed from the blood compartment via plasma clearance (cv).
Figure 2. Molecular interactions. The binding interactions of VEGF120and VEGF164are different. VEGF-120binds to VEGFR-1 and VEGFR-2 but not
to NRP-1. VEGF164binds to VEGFR-1, VEGFR-2, NRP-1, and glycosaminoglycan (GAG) chains in the extracellular matrix. In simulations where the anti-
VEGF agent (VEGF Trap) is added, both isoforms bind to the anti-VEGF agent to form a complex. Binding and unbinding of VEGF to receptors are
denoted as konand koff, respectively. kcdenotes the coupling of NRP-1 and VEGFR-1 and of NRP-1 to VEGFR-2. While only the internalization of NRP-1
is shown, all VEGF receptors and complexes can be internalized at a rate kint. Similarly, while only the insertion of NRP-1 is shown, VEGFR-1 and
VEGFR-2 also appear via insertion at a rate s. The blue bar is used to distinguish NRP-1 expressed on the myocytes from NRP-1 on the endothelial cells
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org2 November 2011 | Volume 6 | Issue 11 | e27514
as peripheral arterial disease and coronary artery disease .
Mouse tumor xenograft models are also commonly used to study
different cancers and to develop anti-tumor therapies. Mice are
convenient animal models to study human diseases because the
overall biology of the mouse is in many respects similar to that of
humans, and the two species share many similar characteristics of
pathological conditions . Anatomically based three-dimen-
sional models of VEGF-mediated angiogenesis have also been
developed to study processes such as endothelial cell migration
and proliferation, and capillary sprout formation [12,13];
however, 3D models are typically limited to smaller scales:
microscopic and mesoscopic.
Under physiological conditions, VEGF level in the mouse blood is
low (,1.5 pM) , possibly as a result of VEGFhaving a shorthalf-
life in this species (3 minutes) [14,15]. One example of an important
mouse study is the work performed by Rudge et al., who describe a
high-affinity VEGF antagonist called Aflibercept, engineered to
sequester VEGF by forming a complex . The protein is a fully
human soluble decoy receptor made by fusing the second Ig domain
of human VEGFR-1 to the third Ig domain of human VEGFR-2
commercially as ‘‘VEGF Trap,’’ forms an inert complex with VEGF,
and the complex has a much longer half-life than unbound VEGF.
This anti-VEGF agent is in Phase II studies as an anti-tumor
angiogenesis therapy . VEGF Trap was tested on mice bearing
mouse tumors as well as mice bearing human tumors. It was found
that the mice bearing mouse tumors did not have a significantly
higher level of complex in the blood than non-tumor bearing mice,
implying that tumor-derived VEGF constituted only a small fraction
of total body VEGF or circulating bioavailable VEGF in those mice.
be readily assayed in the blood, Rudge and coworkers used the
concentration of the complex to calculate the production rates of
VEGF by the host and by the tumor. For mice not bearing tumors,
the authors noted that the estimated production rate of VEGF was
high compared to previous estimates .
Due to the large number of experimental studies performed in
mice, including the work of Rudge et al., and given the vast amount
of experimental data available from these studies, we have
developed a whole-body computational model of VEGF distribu-
tion in the mouse, expanding our previous models of VEGF
distribution in human [8,18–20]. In this model we take into account
VEGF receptor expression on both luminal and abluminal surfaces
of endothelial cells, and expression of neuropilin-1 on endothelial
cells and myocytes. Parameter estimation was performed to fit the
model to available experimental data. Sensitivity analysis was
performed to investigate the role of parameters including VEGF
secretion rate, VEGF plasma clearance rate, and microvascular
permeability to VEGF. Computational modeling of the VEGF
system in the mouse provides parameter estimates that are difficult
or impossible to extract purely experimentally. In particular, by
fitting our model simulation results to the experimental data from
Rudge et al., we estimated the value of the endogenous VEGF
secretion rate by the myocytes. The mouse model of VEGF
distribution can be used in tandem with the previously developed
human models to compare the two systems and to scale-up pro- and
anti-angiogenic therapeutics for translation from mouse studies
(preclinical studies) to human studies (clinical trials).
Materials and Methods
The basis of this mouse model is the human model developed by
Stefanini and co-workers that was used to explore the VEGF
distributions in humans in health and disease [8,18,19,21]; the model
is significantly expanded as explained below. The mouse is divided
approximation, the tissue compartment is represented by skeletal
muscle that comprises the majority of its mass (43% of total body
mass ). To build the tissue compartment, the skeletal muscle is
represented as cylindrical fibers (myocytes) aligned in parallel with
cylindrical microvessels dispersed between the muscle fibers. The
space between the muscle fibers and microvessels is designated as the
interstitial space, which is itself composed of the basement
membranes of the parenchymal cells/myocytes (PBM) and endothe-
lial cells (EBM), in addition to the extracellular matrix (ECM). VEGF
to VEGF receptors VEGFR-1, VEGFR-2, and NRP-1 on the
abluminal surface of the endothelial cells, as well as to glycosamino-
glycan chains (GAG) in the basement membranes and extracellular
matrix. The binding of VEGF to NRP-1 on the surface of the
myocytes is also included. VEGF can be transported to the blood via
the lymphatics at a rate kLand can be exchanged between the blood
and interstitium via microvascular permeability at a rate kp. VEGF in
the blood can bind to receptors on the luminal surface of the
endothelial cells and can be removed via plasma clearance at a rate
rate kint. Figure 2 summarizes the molecular interactions of VEGF120
and VEGF164with their receptors and with GAGchains in the PBM,
EBM, and ECM.
In our model, we include an anti-VEGF agent that can bind to
and form a complex with VEGF in both the blood and tissue. The
unbound anti-VEGF agent and the complex are also subject to
intercompartmental transport via permeability and lymphatic
drainage, and can also be cleared from the blood. The molecular
interactions between the two VEGF isoforms and the anti-VEGF
agent are illustrated in Figure 2.
We incorporate pore theory in modeling the interstitial space to
reflect the available volume for VEGF to diffuse. The VEGF
molecules are free to diffuse in the available interstitial fluid
volume, denoted KAV, which is defined as the available fluid
volume (UAV) divided by the total tissue volume (U). Based on the
geometry of the pores in the basement membranes and
extracellular matrix, the partition coefficient and available fluid
volume can be calculated as follows:
total tissue volume
f~fluid fraction~interstitial fluid volume
W~partition coefficient~available fluid volume
interstitial fluid volume
eIF~porosity~interstitial fluid volume
total tissue volume
KAV~available volume fraction
~available fluid volume
total tissue volume
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org3November 2011 | Volume 6 | Issue 11 | e27514
The model is fully described with forty coupled ordinary
differential equations (ODEs) including 24 molecular species in the
tissue and 16 molecular species in the blood, representing a total of
94 chemical reactions. The complete set of equations and chemical
reactions are presented in Text S1. Equations 1–3 show the ODEs
for VEGF164, VEGF120, and the anti-VEGF agent (A) in the tissue
(denoted by superscript or subscript N for normal tissue), and
equations 4-6 show the ODEs for these same molecular species in
the blood (denoted by superscript or subscript B).
½ ½ ?NzkN
In these equations, qVrepresents the secretion of VEGF in the
tissue, and qArepresents the injection rate of the anti-VEGF agent
in the blood. Transport parameters include plasma clearance (cV),
lymphatic drainage (kL), and microvascular permeability (kp). kon
and koffrepresent the kinetic binding and unbinding rates of VEGF
with the receptors and with the anti-VEGF agent. Geometric
parameters include the total surface area of microvessels at the
blood/tissue interface (SNB), the total tissue volume (UN), the total
blood volume (UB), and the total plasma volume (Up). KAV,N
represents the available volume fraction for VEGF in the tissue.
The forty differential equations were implemented in MA-
TLABH (v184.108.40.2069 R2010a, MathworksH) using the SimBiolo-
gyH toolbox and the simulations were run on a laptop PC. All
simulations were performed using the sundials solver routine with
an absolute tolerance of 10220and a relative tolerance of 1025.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org4November 2011 | Volume 6 | Issue 11 | e27514
The overall model is parameterized for a 25-gram mouse and is
not currently strain specific. Model parameters are summarized in
Tables 1, 2, 3, 4, and 5.
The formulation of the two-compartment mouse model follows
the scheme we previously applied to the human model . That is,
we first begin by determining parameters of the whole mouse, such
as the mass and blood volume. The whole-mouse is then divided
into the blood and tissue compartments. Then the blood and tissue
compartments are further characterized by parameters detailing
the plasma volume and tissue geometry, respectively.
The parameters describing the whole mouse are presented in
Table 1. The volume of blood for a mouse is 6–8 mL per 100 g
body weight , yielding 1.75 mL of blood for a 25-gram mouse.
Plasma volume used in our model is 0.85 mL, based on 3.42 mL
of plasma per 100 g body weight . Hence, the plasma volume
accounts for 49% of the blood volume. We consider the volume of
the tissue to be the difference between the total volume of the
mouse and the volume of the blood. The density of whole blood is
1.002 g/cm3; thus the mass of blood is calculated to be
1.75 g. This yields 23.25 g as the mass of the tissue, and using
1.06 g/cm3as the density of skeletal muscle , we calculate the
volume of the tissue to be 21.93 cm3.
To model the tissue compartment, we used many properties of
the mouse gastrocnemius muscle since this muscle is extensively
studied and characterized (Table 2). However, not all necessary
parameter values for the mouse gastrocnemius are available and
we had to use available parameters from other muscles. The
interstitial space in the mouse pectoral muscle is 14.4 mL/100 mg
wet weight  and thus the fraction of tissue that is interstitial
space is calculated to be 0.15, using 1.06 g/mL as the density of
skeletal muscle . The capillary density of the mouse
gastrocnemius has been measured to range from 300 to 1,700
capillaries/mm2[28–33]. This wide range is due to different
factors such as mouse strain, age and exercise level.
Because we first constrained the fractional volume of interstitial
space, other tissue parameters needed to be adjusted accordingly
to yield reasonable values for fractional volumes of muscle fibers
and blood. Particularly, the capillary density, capillary/fiber ratio,
and fiber cross-sectional area determine the remaining parameters
required to characterize the mouse model. We used a capillary
density of 650 capillaries/mm2, a capillary/fiber ratio of 1.95, and
a fiber cross-sectional area of 2,500 mm2, which are consistent with
experimental measurements [28–33]. This then yields a fiber
density of 333 fibers/mm2and a fiber fractional volume of 0.83.
This leaves a blood fractional volume of 0.014, which requires the
luminal capillary diameter to be 5.25 mm. Capillary diameters in
the mouse have been measured to range from 3.6 mm in the calf
muscle to 5.9 mm in the skin [34–37]. Assuming the capillary wall
thickness to be 0.5 mm, the external capillary diameter is then
6.25 mm and the capillary volume is calculated to be 2% of the
total tissue volume. The capillary cross-sectional area is 30.67 mm2
and using a capillary perimeter to cross-sectional area correction
factor of 1.23 [38,39], the capillary perimeter is calculated as
21.77 mm. A capillary surface area correction factor of 1.1 
yields the capillary surface area of 155.68 cm2/cm3tissue. The
abluminal and luminal surface areas of one endothelial cell are
each taken to be 1,000 mm2.
The fiber volume fraction is corrected to account for the
capillary wall thickness and is calculated to be 82.74%. Using a
fiber perimeter correction factor of 1.21 , the fiber perimeter is
calculated to be 214.10 mm and the surface area is then
713.68 cm2/cm3tissue. The gastrocnemius is a mixed muscle;
however, it has been reported that the outer zone comprises most
of the mouse gastrocnemius, and that it is comprised of 94% type
IIA fibers . Hence in the model, we base the fiber geometry on
type IIA fibers. In particular, the myonuclear domain size for
mouse type IIA fibers is 21,400 mm3/myonucleus . Using this
estimate and a fiber cross-sectional area of 2,500 mm2, the
calculated length of one muscle fiber myonuclear domain is
8.56 mm. The surface area of a myonuclear domain is then
calculated to be 1.8361025cm2. Although the calculated muscle
fiber length is shorter than that calculated for other animals and
muscle types, similar measurements have been observed experi-
mentally. For example, in the rat gastrocnemius, type IIA muscle
fibers were found to have approximately 50 nuclei/mm (myo-
nuclear fiber length of 20 mm) and cross-sectional areas of
2500 mm2. In the mouse, the extensor digitorum longus
(EDL) and soleus have approximately 40 and 60 nuclei/mm
(myonuclear fiber lengths of 17 and 25 mm), respectively .
However, the EDL and soleus muscles are primarily composed of
type I and type IIB fibers, respectively , and have cross-
sectional areas of less than 2,000 mm2.
The interstitial space is assumed to be composed of the
extracellular matrix (ECM), parenchymal basement membrane
(PBM) and endothelial basement membrane (EBM). Although
VEGF is able to diffuse in the interstitial space, part of this volume
is inaccessible to VEGF. The thicknesses of the basement
membranes are 154 nm , yielding volume fractions of
0.0020 and 0.0091 cm3/cm3tissue for the EBM and PBM,
respectively. The remaining interstitial space volume of 0.14 cm3/
cm3tissue is taken to be the extracellular matrix. These three
elements of the interstitial space are assumed to have a solid
fraction composed primarily of collagen, which is unavailable to
VEGF, and a fluid fraction that is accessible to VEGF. The
fraction of body weight that is composed of collagen in the mouse
is estimated to be 2.5% . Using a density of 1.41 g/cm3for
collagen , the total volume of collagen in the interstitial space
in a 25-gram mouse is 0.443 cm3. The ratio of basement
membrane collagen to total body collagen is 0.0083 . Using
this ratio, the total collagen in the ECM, EBM, and PBM is then
calculated to be 0.4396 cm3, 0.0007 cm3, and 0.0030 cm3,
respectively. Hence, the non-collagen fractions of the ECM,
EBM, and PBM volumes are 86%, 98%, and 98%, respectively.
We further consider pores in the ECM, EBM, and PBM, which
may be inaccessible to freely diffusible molecules in the interstitial
space. The EBM pore size for rat brain capillaries has been
measured to be 7 nm  and the ECM pore size is 66 nm in
humans . With these pore sizes, the partition coefficients of the
EBM and PBM are 0.35, and the partition coefficient for the ECM
is 0.90 . The available space for the ECM and basement
membranes for VEGF to diffuse is then calculated as the product
Table 1. Whole-body mouse parameters mouse.
Mass of mouse25g 
Blood volume1.75 mL 
Plasma volume 0.85mL 
Plasma fraction0.49- Calculated (see manuscript)
Mass of blood 1.75g Calculated (see manuscript)
Mass of tissue 23.25g Calculated (see manuscript)
Tissue volume 21.93cm3
Calculated (see manuscript)
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org5 November 2011 | Volume 6 | Issue 11 | e27514
of the volume, fluid fraction, and partition coefficient. The total
available space in the interstitial space (KAV) is then calculated to
be 0.113 cm3/cm3tissue.
Receptor densities and ECM binding site densities are listed in
Table 3. VEGF receptors VEGFR-1, VEGFR-2, and co-receptor
NRP-1 are assumed to be evenly distributed along both the luminal
and abluminal surfaces of the microvessels [19,52]. Furthermore,
NRP-1 is distributed on the surface of myocytes. Based on quantitative
flow cytometry measurements in the mouse gastrocnemius in vivo, the
concentrations of VEGFR-1, VEGFR-2 are 1,050 and 700 dimerized
receptors per endothelial cell, respectively (Imoukhuede and Popel,
unpublished observations). The number of NRP-1 dimers per
endothelial cell is approximately 35,000 based on in vitro studies .
Additionally, in vitro characterization of human quadriceps muscles
estimated 35,000 neuropilin-1 dimers per myonuclear domain
(Imoukhuede and Popel, unpublished observations). To our knowl-
edge, there are currently no quantitative measurements in vivo of NRP-
1 on endothelial and myocyte cell surfaces.
It is known that VEGF164 binds to the glycosaminoglycan
(GAG) chains of the heparan sulfate proteoglycans in the
extracellular matrix ; however to our knowledge, there are
currently no direct experimental measurements of binding
affinities of VEGF to the ECM. Based on the binding affinities
of basic fibroblast growth factor to GAG chains in the ECM,
which are assumed to be similar to VEGF binding affinities, the
ECM, PBM, and EBM binding site densities are taken to be 0.75,
13, and 13 mM respectively .
Transport parameters for VEGF, anti-VEGF, and the VEGF/
anti-VEGF complex are listed in Table 4. In mice, the half-life of
VEGF in the circulation has been reported to be approximately
3 min [15,16]. The VEGF clearance rate in plasma is then
0.23 min-1, which is equal to ln(2)/half-life. VEGF is assumed to
be a 45-kDa globular molecule and its microvascular permeability
is taken to be 4.061028cm/s in accordance with previous models
based on the molecular weight [8,18,19,21,56,57]. In previous
models, the microvascular permeabilities for molecules were
determined based on their molecular weights and Stokes-Einstein
radii [18,56,57]. In particular the permeability for bevacizumab, a
VEGF antibody, was 361028cm/s based on a molecular weight
of 150 kDa . VEGF Trap, which has a molecular weight of
115 kDa , is taken to have a comparable size compared to
bevacizumab. Thus the permeability of VEGF Trap is also chosen
to be 361028cm/s. The VEGF secretion rate, lymphatic
drainage rate, and clearance rates of anti-VEGF and the
VEGF/anti-VEGF complex were determined using experimental
data and are discussed in the ‘‘Free parameters’’ subsection of the
The kinetic parameters for the binding and unbinding of VEGF
to VEGFR-1, VEGFR-2, NRP-1, and GAG chains are listed in
Table 5 and are identical to those used in previous models
[7,10,21]. Kinetic parameters for the binding and unbinding of
VEGF to the anti-VEGF agent were fitted parameters and are
discussed in the ‘‘Free parameters’’ subsection of the Results.
Because VEGF Trap is the anti-VEGF agent used in the model
Table 2. Geometric parameters of mouse gastrocnemius muscle.
Capillary/fiber ratio1.95- [28–33]
Fiber cross-sectional area (FCSA) 2,500
Luminal capillary diameter5.25
Capillary wall thickness 0.5
External capillary diameter6.25
mmCalculated (see manuscript)
Capillary volume1.99%cm3/cm3tissue Calculated (see manuscript)
mmCalculated (see manuscript)
Capillary surface area155.68 cm2/cm3tissueCalculated (see manuscript)
Fiber volume82.74%cm3/cm3tissue Calculated (see manuscript)
Fiber perimeter 214.10
mm Calculated (see manuscript)
mmCalculated (see manuscript)
Single myonuclear domain (SMND) surface area1.8361025
Calculated (see manuscript)
EBM thickness154 nm
PBM thickness 154nm 
BM pore size7 nm
ECM pore size66 nm
EBM volume 0.002014 cm3/cm3tissueCalculated (see manuscript)
of which available to VEGF0.001983 cm3/cm3tissue Calculated (see manuscript)
PBM volume0.009123cm3/cm3tissueCalculated (see manuscript)
of which available to VEGF0.008986 cm3/cm3tissueCalculated (see manuscript)
ECM volume0.141463cm3/cm3tissueCalculated (see manuscript)
of which available to VEGF0.121419 cm3/cm3tissueCalculated (see manuscript)
0.113117cm3/cm3tissue Calculated (see manuscript)
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org6November 2011 | Volume 6 | Issue 11 | e27514
presented here, VEGF Trap and anti-VEGF are used inter-
changeably throughout this text.
The experiments of Rudge et al. detail the effects of injecting
VEGF Trap subcutaneously into mice . The bioavailability of
VEGF Trap and the VEGF/VEGF Trap complex is the same
whether the drug is injected subcutaneously or intravenously .
Since our model explicitly includes the blood compartment, it is
straightforward to model drug delivery directly into the blood.
Thus, we have simulated an intravenous injection of the anti-
VEGF agent. The experimental plasma concentration profiles of
the VEGF/VEGF Trap complex and unbound VEGF Trap in the
mice at different doses of VEGF Trap are shown in Figure 3. We
have used these data to develop an experiment-based model.
In order to fit the simulation results to the experimental
concentration profiles, the values of a subset of model parameters
were chosen to be optimized, specifically the following five
parameters: VEGF secretion rate, lymphatic drainage rate, clearance
rate of VEGF Trap, clearance rate of the VEGF/VEGF Trap
complex, and the dissociation constant of VEGF and VEGF Trap.
These five parameters are denoted as the free parameters. We chose
to optimize these free parameters based on the uncertainty of the
parameter values in the literature and our sensitivity analysis. The
sensitivity analysis systematically investigated the impact of individual
parameters on the model output (namely, the concentration profiles
of VEGF, VEGF Trap, and the complex; data not shown).
The multiple VEGF isoforms have different expression levels
depending on the species and tissue type . In mouse skeletal
muscle, the mRNA expression ratio of VEGF164:VEGF120was
measured to be 92%:8% . In our model, we assume that the
secretion rates of VEGF120and VEGF164by the myocytes follow
this ratio as well. In the parameter estimation, the lower and upper
bounds that the secretion rate of VEGF164(qV164) was allowed to
take were 0.01 and 0.20 molecules/cell/s, respectively. The ratio
between the secretion rate of VEGF120 (qV120) and that of
VEGF164(qV164) is taken to be 8:92. The total VEGF secretion
rate is the sum of qV64and qV120.
The lymphatic drainage rate has been measured to be 0.2–
0.3 mL/hr in suckling rats weighing 35–45 g , corresponding
to approximately 761025cm3/s. This is consistent with observa-
Table 3. Receptor densities.
Model parametersTissue parameters
ValueUnitValue (Tissue)Value (Blood)Unit
VEGFR-1 1,050 dimers/ECpmol/cm3tissue
Luminal EC525 dimers/EC- 1.7061021
Abluminal EC525 dimers/EC1.3661022
Luminal EC 350 dimers/EC- 1.1361021
Abluminal EC 350 dimers/EC9.0761023
Neuropilin-135,000 dimers/EC pmol/cm3tissue
Luminal EC 17,500dimers/EC- 5.67pmol/cm3tissue
Abluminal EC 17,500 dimers/EC4.5361021
Myocytes 35,000 dimers/myocyte2.26-pmol/cm3tissue
ECM binding density 0.75
mM 82.50- pmol/cm3tissue
EBM binding density13
mM 9.02- pmol/cm3tissue
PBM binding density13
mM 40.95- pmol/cm3tissue
EC = endothelial cell.
Abluminal EC receptors: 2.5961025(pmol/cm3tissue)/(dimers/EC).
Luminal EC receptors: 3.2461024(pmol/cm3tissue)/(dimers/EC).
Myocyte receptors: 6.4661025(pmol/cm3tissue)/(dimers/myocyte).
Table 4. Transport parameters.
VEGF secretion rate
0.0680molecules/cell/s see manuscript
VEGF164secretion rate0.0626molecules/cell/s see manuscript
VEGF120secretion rate 0.0054molecules/cell/s see manuscript
Lymphatic drainage* 7.0061026
anti-VEGF & VEGF/anti-VEGF
VEGF 0.23 min21
*Optimized parameter values.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org7November 2011 | Volume 6 | Issue 11 | e27514
tions in male mice, where the lymph flow rate was measured to be
4 mL/min, corresponding to 0.24 mL/hr . In the parameter
estimation, the lower and upper bounds that the lymphatic
drainage rate (kL) was allowed to take were 7.061026and
The half-life of VEGF Trap in mouse serum was reported as
72 h , which corresponds to a clearance rate (cA) of 1.60610-4
min21. This clearance rate is a first estimate as we assume that the
elimination of VEGF Trap in vivo is a first order process. In
addition, the half-life in the serum is not necessarily the same as
the half-life in the plasma because molecules contained in platelets
may not be degraded at the same rate as molecules in direct
contact with the plasma. Since the VEGF/VEGF-Trap complex
can also be sequestered and transported by platelets, the same
argument holds for its clearance rate (cVA). Hence, both clearances
were chosen to be free parameters, and their allowable lower and
upper bounds in the parameter estimation were both 1.6061025
and 1.6061023min21, respectively. This corresponds to a half-life
of 4.336104and 4.336102min, respectively.
Kinetic parameters for the binding and unbinding of VEGF to
the anti-VEGF agent are based on the pharmacokinetic parameters
for VEGF Trap: The unbinding rate (koff) is 4.2361025s21[64,65].
The equilibrium dissociation constant (Kd) has been reported to
range from ,1 pM  to 5 pM . In the parameter estimation,
the lower and upper bounds that the dissociation constant was
allowed to take were 0.25 and 5 pM, respectively.
The estimation of the free parameters was treated as a non-
linear optimization problem. We used an automated optimiza-
Table 5. Kinetic parameters of VEGF and anti-VEGF.
Measured parametersTissue parameters
VEGF binding to VEGFR-1Value Unit Value (Tissue)Value (Blood)Unit
VEGF binding to VEGFR-2
VEGF164binding to NRP-1
VEGF164binding to GAGs
Coupling of NRP-1 and
Coupling of NRP-1 and
VEGF binding to anti-VEGF*
0.37 pM 4.1861025
*Optimized parameter values.
Tissue: 1.136108(pmol/cm3tissue)/M and 1.5661014(pmol/cm3tissue)/(mol/cm2EC).
Blood: 4.886108(pmol/cm3tissue)/M and 1.9561015(pmol/cm3tissue)/(mol/cm2EC).
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org8November 2011 | Volume 6 | Issue 11 | e27514
tion approach that explored the free parameter space and
returned the combination of free parameter values that allowed
the simulation results to best fit the experimental data from
Rudge et. al  (Figure 3, open circles). The parameter
optimization was performed using MATLABH, which solves the
non-linear least squares problem and uses the trust-region-
reflective optimization algorithm [66,67]. The objective func-
tion that was minimized was the weighted sum of squared
residuals (WSSR) and obeyed:
minWSSR(h) ~ min
where Cexperimental,i is the ithexperimentally measured plasma
concentration data point of VEGF Trap or VEGF/VEGF Trap
complex (Figure 3, open circles), and Csimulation,i(h) is the ith
simulated plasma concentration at the corresponding time point
(Figure 3, solid lines). The number of experimental measurements
n includes both VEGF Trap and VEGF/VEGF Trap complex
concentrations for all four doses of VEGF Trap, totaling 58 data
points. The weights Wiwere taken to be 1/Cexperimental,i. hlb
and hubare the lower and upper bounds, respectively, that the free
parameters were allowed to take.
Because the optimization function only minimizes the objective
function locally, twenty optimization trials were performed such
that for each trial, the initial value of each of the free parameters
was randomly generated within hlband hub. The final set of
optimized free parameters was taken to be the trial that yielded the
smallest WSSR. The final optimized free parameters were: qV164
= 0.0626 molecules/cell/s, kL= 7.0061026cm3/s, cA= 8.866
1024min21, cVA= 2.7961024min21, and Kd= 0.37 pM. These
optimized values yielded a WSSR value of 8.137. For comparison,
the largest WSSR of the twenty trials was 8.382. The results of the
optimization are summarized in Table 6. The optimized values
from each of the twenty optimization trials are presented in Table
S1. With the free parameters optimized, we completed the
formulation of the model. This resulting model is denoted as the
optimized model, and all subsequent results are based on this model.
Using the optimized model, we were able to fit the concentration
profiles for VEGF Trap and the VEGF/VEGF Trap complex
(Figure 3, solid lines).
Figure 3. Parameter optimization. Model parameters were optimized computationally to fit simulation results (solid lines) to experimental data
(open circles)  for the concentration profiles of the unbound VEGF Trap and the VEGF/VEGF Trap complex. VEGF Trap was injected intravenously
(into the blood compartment) at (A) 1 mg/kg, (B) 2.5 mg/kg, (C) 10 mg/kg, and (D) 25 mg/kg.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org9 November 2011 | Volume 6 | Issue 11 | e27514
Concentrations of molecular species
The optimized model was first simulated to achieve steady-
state concentrations. The steady-state concentrations of VEGF
were 0.098 pM and 5.27 pM in the blood and tissue, respective-
ly. This plasma concentration is consistent with experimental
measurements in mice. Multiple studies have shown that the
VEGF plasma concentration is low in mice. It ranges from
13.7 pg/mL  to 65 pg/mL , which corresponds to 0.30
to 1.4 pM, respectively, converted using a VEGF molecular
weight of 45 kDa. To our knowledge, the concentration of VEGF
in the tissue interstitial space has not been measured experimen-
After the steady-state was achieved, we simulated an injection
of 25 mg/kg VEGF Trap into the blood compartment, which
lasted for one minute. The concentration of unbound VEGF in
the blood and tissue compartments decreases after the injection as
VEGF Trap and VEGF bind to form a complex (Figure 4A). At
2.7 weeks post-injection, the concentration of unbound VEGF in
the blood reaches a maximum of 1.6 pM, which is greater than
the initial pre-injection concentration. This increase in the
plasma concentration of unbound VEGF was also observed in
the human model  and has been hypothesized to be due to a
‘‘shuttling’’ effect where, on average, the VEGF Trap forms a
complex with VEGF in the tissue compartment, after which the
complex is transported into the blood where it dissociates and
releases the free VEGF.
It is interesting to note that while the increase in blood VEGF
levels occurs over the course of a few weeks in this mouse model,
the human model predicts this similar increase over the course of
only a few days. The difference in the time scale of the VEGF
increase can be attributed to the fact that in the human model, the
kinetic parameters of the anti-VEGF agent were based on those of
bevacizumab (Avastin), which are different from those of VEGF
Trap . The dissociation constant of bevacizumab and VEGF is
greater than that of VEGF Trap and VEGF, which means that
bevacizumab does not bind as strongly to VEGF as VEGF Trap
does. The larger dissociation constant of bevacizumab allowed the
concentrations of VEGF to return to pre-injection levels in the
human model more rapidly whereas in this mouse model, the
concentrations of unbound VEGF returned to the pre-injection
levels only after 10 weeks post-injection.
Figure 4B shows that after a rapid increase in concentration
following the injection, the concentration of unbound VEGF Trap
decreases and is no longer in the body by 2 weeks after injection.
In Figure 4C, the concentration of the VEGF/VEGF Trap
complex reaches maximum levels of 16.8 and 16.4 nM in the
Table 6. Summary of parameter optimization (n=20).
Lower boundUpper boundMin MaxOptimal* Unit
VEGF164secretion rate 0.010.200.0544 0.06470.0626molecules/cell/s
Clearance of VEGF Trap1.6061025
Clearance of VEGF/VEGF Trap
Kdof VEGF and VEGF Trap 0.255.000.32 0.48 0.37pM
*Of the 20 trials, the optimal trial was the one that yielded the smallest weighted sum of squared residuals.
Figure 4. Concentration profiles following the injection of the anti-VEGF agent (VEGF Trap). A 25 mg/kg injection of anti-VEGF in the
blood at time 0 was simulated using the optimized parameters. The profiles of (A) unbound VEGF, (B) unbound anti-VEGF, and (C) VEGF/anti-VEGF
complex are shown in the blood (red) and tissue (blue) compartments. In (A), VEGF level in the tissue drops significantly after injection. Blood VEGF
concentration increases to levels greater than steady-state reaching a maximum at 2.7 weeks post-injection, and returns to original steady-state levels
by approximately 10 weeks after injection. Note that the axes of the panels are on different scales.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org10 November 2011 | Volume 6 | Issue 11 | e27514
blood and tissue, respectively, at 1.9 weeks post-injection. The
complex is cleared from the body by 7 weeks post-injection.
Effect of VEGF secretion, clearance, and permeability on
steady-state VEGF levels
While the parameter optimization resulted in the optimized
model, single parameter values can be varied individually to
explore the robustness of the model output with respect to these
individual parameters. To investigate the sensitivity of VEGF
levels to systemic model parameters, VEGF secretion rate,
VEGF clearance rate, and microvascular permeability to VEGF
were varied individually. VEGF164 secretion rate was varied
from 0.01 to 0.20 molecules/cell/s (Figure 5A). A 92%:8%
simulations. While the steady-state concentration of unbound
VEGF in the blood remained relatively low (, 0.4 pM) and
relatively constant, the concentration of unbound VEGF in the
tissue increased significantly with the secretion rate, reaching
nearly 21 pM when the secretion rate of VEGF164was 0.20
molecules/cell/s. Increasing the plasma clearance rate caused
the depletion of VEGF from the blood (Figure 5B). As
microvascular permeability was increased, the concentrations
of unbound VEGF in the blood and tissue compartments
equilibrated to 2.25 pM (Figure 5C).
was used in all
Effect of geometric tissue parameters on steady-state
In addition to systemic model parameters, geometric parame-
ters were varied to examine their effect on steady-state VEGF
levels. In particular, the length of the myonuclear domain was
changed from 8.56 mm to 20 mm, as the latter value is closer to the
upper limit reported in the literature [43,44]. In this context, a
myocyte is equivalent to a single myonuclear domain; hence,
increasing the myonuclear domain length from 8.56 mm to 20 mm
increased the surface area
4.2861025cm2. However, since the fraction of tissue that is
occupied by myocytes is fixed, an increase in the myonuclear
domain length resulted in a decrease in the total number of
myocytes per unit volume of tissue. Since the number of NRP-
1dimers per myocyte has a fixed value of 35,000 dimers/myocyte,
the total number of NRP-1 per unit volume of tissue decreased.
Additionally, because the secretion rate of VEGF is expressed in
units of molecules/myonuclear domain/s, increasing the myo-
nuclear domain length to 20 mm required that the optimized
secretion rate be scaled up to 0.15 molecules/myonuclear
domain/s to preserve the total number of VEGF molecules
secreted per unit volume of tissue. By doing this, the only effective
change that occurred as a result of increasing the myonuclear
domain length was a decrease in the total NRP-1 concentration on
the myocytes per unit volume of tissue. In this case, the
concentration of unbound VEGF in the blood and tissue
compartments increased to 0.11 and 6.70 pM, respectively
(compared to the original concentrations of 0.098 and 5.27 pM,
respectively). Thus, selecting a myonuclear domain length at the
upper limit of the reported values increased the concentration of
VEGF in the blood and tissue compartments 1.1- and 1.3-fold,
Flow of molecular species between compartments at
The model predicted the flows of VEGF in the mouse at
steady state (no injection of VEGF Trap) normalized to that of
the secretion. The majority (99.2%) of VEGF produced by
secretion was removed from the tissue compartment via
internalization of the VEGF/receptor complexes (Figure 6).
Specifically, 62.4% was removed via the internalization of
VEGF/NRP-1 complexes on the myocytes, and 36.8% was
removed via the internalization of VEGF/receptor complexes
on the endothelial cells. Although the flows of VEGF from
intravasation and extravasation were low compared to the
secretion flow rate, there was a net flow of VEGF out of the
tissue compartment into the blood compartment via microvas-
cular permeability at steady state. Lymphatic drainage trans-
ported 0.04% of the secreted VEGF from the tissue to the
blood. A small portion of the secreted VEGF was removed from
the blood compartment via plasma clearance (0.33%).
Figure 5. Steady-state concentration of free VEGF. (A) The steady-state concentration of VEGF in the tissue compartment but not in the blood
is highly dependent on the VEGF secretion rate. (B) The VEGF concentration in the blood is more sensitive to the VEGF plasma clearance rate than the
VEGF concentration in the tissue. (C) As microvascular permeability of VEGF increases, VEGF concentrations in the tissue and blood compartments
equilibrate to 2.25 pM. For all simulations, unless the parameter is varied: VEGF164secretion rate qV164= 0.063 molecules/cell/s (optimized value),
plasma clearance rate cV= 0.23 min21, and permeability kp = 4.061028cm/s.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org 11 November 2011 | Volume 6 | Issue 11 | e27514
VEGF distribution in the body at steady state
The model provided an estimate of the steady-state fraction of
total VEGF bound to receptors and to GAG chains located in the
extracellular matrix and basement membranes. In the blood,
39.5% and 36.4% of total VEGF was in the form of the VEGFR-
2/VEGF164/NRP-1 and VEGF120/VEGFR-1/NRP-1 ternary
complexes, respectively (Figure 7A). Free circulating VEGF
accounted for only 5.23% of the total VEGF in the blood. The
ratio of unbound VEGF164to unbound VEGF120in the blood was
11.5%:88.5%. In the tissue, because of the large total surface area
of myocytes compared to endothelial cells and thus the
significantly larger number of total NRP-1 molecules on myocytes
compared to endothelial cells, the majority of VEGF (37.6%) was
bound to NRP-1 on the myocyte cell surfaces (Figure 7B). A
significant portion of total VEGF (23.6%) was bound to the
extracellular matrix. Unbound VEGF in the interstitial space
comprised just 2.3% of the total VEGF in the tissue. The ratio of
unbound VEGF164 to unbound VEGF 120 in the tissue was
33.7%:66.3%. The effect of ratio between the secretion rate of
VEGF120and that of VEGF164is clearly seen in the distribution of
total VEGF, which closely resembles the distribution of VEGF164
(Figure 7B). This indicates that the majority of the total VEGF in
the tissue is in the form of VEGF164, a direct result of the VEGF
isoform secretion ratio VEGF164: VEGF120being set to 92%:8%.
VEGF receptor occupancy at steady state
Fractional occupancies of VEGF receptors at steady state were
calculated. In the blood, unbound NRP-1 constituted 95.1% of the
receptors on the luminal surface of endothelial cells (Figure 7C).
Looking at VEGFR-1, VEGFR-2, and NRP-1 individually, we
found that the majority of NRP-1 and VEGFR-2 remained
unligated, and the majority of VEGFR-1 was coupled to NRP-1.
This is because the concentration of unbound VEGF in the blood
is small compared to the concentrations of these receptors. In the
tissue, unligated NRP-1 on the myocytes and abluminal surfaces of
the endothelial cells made up 82.8% and 16.0% of the total
receptors, respectively, since there is more NRP-1 expressed per
endothelial cell and per myocyte compared to VEGFR-1 and
VEGFR-2 (Figure 7D). 89.0% of total VEGFR-1was found as
VEGFR-1/ NRP-1. The majority of total VEGFR-2 in the tissue
was found as either unbound VEGFR-2 (60.9%) or as VEGFR-2/
Intercompartmental flows upon injection of VEGF Trap
Using the optimized model, we explored the effects of injecting
VEGF Trap into the blood as a function of time, after an initial
steady state had been achieved. To visualize the relative amounts
of VEGF, VEGF Trap and VEGF/VEGF Trap complex moving
between two compartments, the net flows of these molecular
species after a 25 mg/kg injection of VEGF Trap into the blood
were calculated. The net flow for each molecular species is the
summation of the flows from intravasation, extravasation, and
lymphatic drainage. The sign of the net flow indicates the net
direction of flow of the molecule. Flow of a molecule from the
tissue to the blood via intravasation and lymphatic drainage has a
positive sign, while flow from the blood to the tissue via
extravasation is considered to be negative. The flow of unbound
VEGF remained positive during the course of the simulation and
is smaller relative to the flow of the VEGF/VEGF Trap complex
(Figure 8A). The model predicted that upon the intravenous
injection of VEGF Trap, there is an initial flow of VEGF Trap
from the blood to the tissue (Figure 8B). Then the direction of the
flow is inverted (from tissue to blood) and deceases in intensity.
The flow of the complex was positive during the entire time that
it is in the body (Figure 8C). This suggests that quickly after the
injection, VEGF Trap extravasates from the blood and binds to
VEGF in the tissue. The complex then moves back into the blood
via intravasation and lymphatics, after which it unbinds and
releases VEGF in the blood, which is the proposed mechanism
for the increase in blood VEGF levels after the injection and
agrees with the shuttling effect predicted by Stefanini et. al .
Note that the flows for VEGF, VEGF Trap and the VEGF/
VEGF Trap complex have different orders of magnitudes, as
shown in Figure 8.
Figure 6. Normalized flows at steady-state. Flows of VEGF are normalized to that of the secretion flow. Most of the VEGF/receptor complexes
are removed from the tissue through internalization. As with Figure 1, internalization in the tissue compartment includes both that of VEGF/receptor
complexes on the abluminal surfaces of endothelial cells as well as VEGF bound to NRP-1 on myocyte cell surfaces. There is a net flow of VEGF from
the tissue into the blood compartment via microvascular permeability.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org12 November 2011 | Volume 6 | Issue 11 | e27514
Figure 7. VEGF distributions and VEGFR occupancies at steady-state. The distributions of total VEGF and of the two individual isoforms are
shown for the (A) blood and (B) tissue compartments. In the blood compartment, the majority of VEGF is found in the form of the VEGFR-2/VEGF164/
NRP-1 and VEGF120/VEGFR-1/NRP-1 ternary complexes. In the tissue compartment, most of the VEGF is in the form of the VEGF164isoform bound to
NRP-1 on the myocytes. The occupancies of total VEGF receptors and of the individual receptors are shown for the (C) blood and (D) tissue
compartments. Unbound NRP-1 on the luminal endothelial cell surface makes up the majority of total receptors and complexes in the blood
compartment. Similarly, unbound NRP-1 on the abluminal endothelial cell and myocyte cell surfaces makes up the majority of total receptors and
complexes in the tissue compartment.
Figure 8. Intercompartmental flows following the intravenous injection of the anti-VEGF agent (VEGF Trap). Instantaneous net flow
rates of (A) unbound VEGF, (B) anti-VEGF, and (C) VEGF/anti-VEGF complex are calculated upon a 25 mg/kg injection of anti-VEGF into the blood. A
positive net flow indicates movement from the tissue into the blood via intravasation and lymphatics, and a negative net flow indicates movement
from the blood into the tissue via extravasation. Note that the y-axes of the panels are on different scales.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org13 November 2011 | Volume 6 | Issue 11 | e27514
VEGF distribution in the body upon injection of VEGF
The percentages of total VEGF in the two compartments were
calculated after a 25 mg/kg intravenous injection of VEGF Trap.
In the blood, most of VEGF became sequestered by VEGF Trap
shortly after the injection (Figure 9A). A similar effect was seen in
the tissue (Figure 9B). By 14 weeks, VEGF distributions in both
compartments returned to the initial steady-state levels as in
Figure 7A and 7B.
VEGF receptor occupancy upon injection of VEGF Trap
The receptor occupancies of the VEGF receptors were
calculated following the injection of 25 mg/kg VEGF Trap into
the blood compartment. The percent of ligated VEGFR-1
decreased in both tissues (Figure 10A). In the blood, the percent
of ligated VEGFR-1 increased to levels above pre-injection before
returning to pre-injection steady-state levels. The increase in
ligated VEGFR-1 occurred because more VEGF is available in
blood plasma, due to the shuttling effect described above. In the
tissue, the percent of ligated VEGFR-1 simply returned to pre-
injection levels. Similar behaviors were also seen for VEGFR-2
(Figure 10B), as well as for NRP-1 (Figure 10C) in both
Predicted secretion rate of VEGF
The VEGF secretion rate from the muscle fibers was calculated
by parameter optimization. From the twenty optimization trials
that were performed, the minimum and maximum optimized
VEGF164secretion rates were 0.0544 and 0.0647 molecules/cell/
s, respectively. In the trial that yielded the smallest WSSR, the
VEGF164secretion rate was 0.0626 molecules/cell/s, which was
the value used in the optimized model. Since the expression ratio
of VEGF164:VEGF120is taken to be 92%:8% in accordance to Ee
et al , the combined secretion rate of the two isoforms was then
predicted to be 0.0680 molecules/cell/s, which is equivalent to
6.1561029pmol/cm2/s, or 4.3961026pmol/cm3tissue/s, based
on a myocyte cell surface area of 1.8461025cm2/cell and a
muscle fiber surface area of 713.68 cm2/cm3tissue.
Effect of VEGF degradation on parameter estimation
Up to this point, we have not included any specific degradation
mechanisms of VEGF in the model. However, in vivo, circulating
and tissular enzymes such as plasmin and matrix metalloprotei-
nases actively degrade the VEGF ligand. Therefore, we have
added a degradation term for VEGF in the normal tissue. Based
on the half-life of human VEGF determined in various in vitro
experiments [70–72], we have set the VEGF degradation rate
constant to be 1.9361024s21(1.1661022min21), which corre-
sponds to a half-life of 60 minutes. We have assumed that in the
blood, the clearance rate of VEGF includes degradation since the
clearance rate constant is 20 times larger than that for
degradation. With the addition of VEGF degradation in the
normal tissue, an additional twenty optimization trials were
performed to determine the optimal free parameter values as
shown in Table S2. As before, the final set of optimized free
parameters was taken to be the trial that yielded the smallest
WSSR. The final optimized free parameters were: qV164= 0.0627
molecules/cell/s,kL= 7.0061026cm3/s, cA= 8.8561024min21,
cVA = 2.7961024min21, and Kd = 0.37 pM. These optimized
values yielded a WSSR value of 8.161. The percent changes of the
each of the free parameter values with and without degradation
were all less than 1%, which suggests that the inclusion of VEGF
Figure 9. VEGF distributions upon injection of anti-VEGF (VEGF Trap). The distributions of VEGF in the (A) blood and (B) tissue
compartments are shown subject to a 25 mg/kg injection of the anti-VEGF agent into the blood compartment at 0 weeks. Before the injection, 95%
of VEGF in the blood compartment is receptor bound. In the tissue compartment, 38% of VEGF is sequestered in the extracellular matrix and
endothelial and parenchymal basement membranes. 60% of VEGF is receptor-bound. Shortly following the injection of the anti-VEGF agent,
essentially all of the VEGF in both compartments becomes sequestered by the anti-VEGF agent. By 14 weeks, VEGF distributions return to original
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org14 November 2011 | Volume 6 | Issue 11 | e27514
degradation does not greatly affect the results obtained from the
model when degradation was absent.
Effect of VEGF degradation on steady-state VEGF levels
Steady-state concentrations of unbound VEGF were simulated
using the optimal free parameter values obtained with the
inclusion of VEGF degradation. The steady-state concentrations
of VEGF in the normal tissue and blood compartments were
4.61 pM and 0.082 pM, respectively. These constitute a 12% and
16% decrease in the steady-state concentrations of VEGF in the
normal tissue and blood compartments, respectively, from the
optimized model obtained before the addition of VEGF
degradation. Additionally, the steady-state VEGF concentrations
were determined as the VEGF degradation rate was varied
(Figure 11). Unbound VEGF levels in the normal tissue and blood
decrease as the VEGF degradation rate increases.
We have extended the previously developed compartmental
model of VEGF distribution in humans to investigate the VEGF
distribution in the mouse. As with the previous version of the
human model , VEGF receptors are expressed on both
abluminal and luminal surfaces of endothelial cells. NRP-1 is
known to be expressed on muscle fibers; hence, one major change
that was introduced in this model was the addition of NRP-1 on
the myocyte cell surfaces to better reflect physiological conditions.
The effects of VEGF Trap on the distribution of VEGF in mice
have been measured experimentally by Rudge et al. VEGF Trap
was tested under physiological conditions (i.e. no tumor), which
allowed us to fit our physiologically-based model of the mouse to
the experimental data and to validate the model. In the previous
model iterations, validating the model against experimental data
involved adjusting the VEGF secretion rate until the concentration
of VEGF in the blood was within the range reported in the
literature. With the mouse model, five free parameters were
estimated simultaneously, thus estimating ranges for several
Figure 10. VEGF Receptor fractional occupancies upon injection of anti-VEGF (VEGF Trap). The fractional occupancies of (A) VEGFR-1, (B)
VEGFR-2, and (C) NRP-1 are shown for the blood (red) and tissue (blue) compartments following a 25 mg/kg injection of the anti-VEGF agent into the
blood compartment at 0 weeks. For all three receptors in the blood compartment, the percent of receptors ligated with VEGF decreases to essentially
zero quickly after the injection of the anti-VEGF; however, the percent of ligated receptors then increases to values above pre-injection levels before
returning to pre-injection levels. In the tissue compartment, this effect is not seen as the percent of ligated receptors decreases quickly after injection
and then returns to pre-injection levels. Note that the y-axes of the panels are on different scales.
Figure 11. Effect of VEGF degradation on unbound VEGF
levels. A VEGF degradation rate constant of 1.1661022min21
(corresponding to half-life of 60 minutes) in the normal tissue was
added before re-performing the estimation of the free parameters.
Using the new set of optimized parameter values, the steady-state
concentrations of unbound VEGF were calculated as the degradation
rate was varied. The concentration of unbound VEGF in the normal
tissue decreases as the degradation rate increases.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org15 November 2011 | Volume 6 | Issue 11 | e27514
parameters that have high degrees of uncertainty. The parameter
estimation was performed on a subset of the model parameters,
selected based on how they influenced the model output.
Of these free parameters, the endogenous VEGF secretion rate
by the myocytes and its predicted value was of particular interest,
as direct experimental measurement of this parameter is non-
trivial, and it is predicted to have a drastic effect on the
concentration of unbound VEGF in the tissue. VEGF levels are
typically measured from blood samples experimentally; however,
different transport routes aside from VEGF secretion such as
lymphatic drainage, microvascular permeability, internalization,
and plasma clearance all contribute to the VEGF concentration
measured in the blood. By allowing the VEGF secretion rate to be
one of the free parameters, we were able to find the best fitted
value for the secretion rate of VEGF by the myocytes, which is not
significantly changed by the inclusion of VEGF degradation in the
Several assumptions used in the model contribute to model
limitations. The different mouse tissues were represented by a
spatially averaged compartment denoted as the tissue compart-
ment. Skeletal muscle is the primary tissue for which the VEGF
system is well characterized. Additionally, skeletal muscle
constitutes a large percentage of the mouse body weight.
Therefore, the majority of the properties of the tissue were based
on available literature characterization of the mouse gastrocne-
mius muscle. To more accurately describe the mouse, specialized
compartments may be added to better detail the distribution and
flows of VEGF throughout the animal body. For example, it may
be beneficial to distinguish a compartment representing the liver
or the kidneys, as these organs play a role in the clearance of
VEGF and may affect the estimated model parameters. Although
vascular elements, such as pericytes, are also important in
angiogenesis, for simplicity we have represented the vasculature
using only endothelial cells. Including additional compartments
and vascular structures would require experimental data for
VEGF secretion and the density of VEGF receptors and co-
receptors. We can easily expand the model as these data become
available. Similarly, we could extend the model to include
additional receptors and co-receptors, such as soluble VEGFR-1
or neuropilin-2, which also influence angiogenesis [73,74]. These
additional model elements can be added in a step-by-step manner
in order to understand the effect that each has on the distribution
VEGF120and VEGF164are the two VEGF-A isoforms that are
predominantly expressed and hence are the two isoforms included
in our model. A human VEGF isoform, VEGF189has been shown
to correlate with xenotransplantability of colon cancer tumor in
mice, where increased expression of this isoform was correlated
with successful transplantations . A similar correlation was
observed in esophageal cancer transplantability . Another
experiment has shown that VEGF189is expressed more predom-
inantly in solid tumor xenografts than in primary tumors .
Adding the VEGF189/VEGF188isoform in the mouse model may
be important if the model is extended to include a tumor xenograft
compartment to study cancer.
Degranulation of platelets have been shown to be a source of
growth factors, such as VEGF, in the blood . As more data
become available, circulating platelets may be added to the model.
The in silico mouse model described here can be used to provide
ranges for important biological parameters that are not easily
measureable experimentally. Additionally, the model can serve as
a foundation for exploring diseases dependent on angiogenesis and
as a tool for predicting the effects of pro- and anti-angiogenic
therapies. As mice are often used in preclinical settings to study
diseases such as peripheral arterial disease, coronary artery
disease, and cancer, the model also provides a computational
framework to investigate these diseases in parallel with experi-
ential equations describing the model, and glossary.
Chemical reactions, system of ordinary differ-
Optimized parameter values from twenty
optimization trials when VEGF degradation is included.
Optimized parameter values from twenty
The authors thank Dr. Gang Liu and the other members of the Popel Lab
for their helpful discussions. The authors thank Dr. Princess Imoukhuede
for providing experimental values of receptor densities.
Conceived and designed the experiments: PY SDF MOS ASP. Performed
the experiments: PY. Analyzed the data: PY SDF MOS ASP. Wrote the
paper: PY SDF MOS ASP.
1. Leung DW, Cachianes G, Kuang WJ, Goeddel DV, Ferrara N (1989) Vascular
endothelial growth factor is a secreted angiogenic mitogen. Science 246:
2. Nakamura M, Abe Y, Tokunaga T (2002) Pathological significance of vascular
endothelial growth factor A isoform expression in human cancer. Pathol Int 52:
3. Roskoski R, Jr. (2007) Vascular endothelial growth factor (VEGF) signaling in
tumor progression. Crit Rev Oncol Hematol 62: 179–213.
4. Ferrara N, Davis-Smyth T (1997) The biology of vascular endothelial growth
factor. Endocr Rev 18: 4–25.
5. Ferrara N, Gerber HP, LeCouter J (2003) The biology of VEGF and its
receptors. Nat Med 9: 669–676.
6. Stefanini MO, Qutub AA, Gabhann FM, Popel AS (2011) Computational
models of VEGF-associated angiogenic processes in cancer. Math Med Biol.
7. Mac Gabhann F, Popel AS (2007) Interactions of VEGF isoforms with VEGFR-
1, VEGFR-2, and neuropilin in vivo: a computational model of human skeletal
muscle. Am J Physiol Heart Circ Physiol 292: H459–474.
8. Stefanini MO, Wu FT, Mac Gabhann F, Popel AS (2010) Increase of plasma
VEGF after intravenous administration of bevacizumab is predicted by a
pharmacokinetic model. Cancer Res 70: 9886–9894.
9. Wu FT, Stefanini MO, Mac Gabhann F, Kontos CD, Annex BH, et al. (2010)
VEGF and soluble VEGF receptor-1 (sFlt-1) distributions in peripheral arterial
disease: an in silico model. Am J Physiol Heart Circ Physiol 298: H2174–2191.
10. Testa U, Pannitteri G, Condorelli GL (2008) Vascular endothelial growth factors
in cardiovascular medicine. J Cardiovasc Med (Hagerstown) 9: 1190–1221.
11. Fox J (2007) The Mouse in Biomedical Research. New York: Academic Press.
12. Liu G, Qutub AA, Vempati P, Mac Gabhann F, Popel AS (2011) Module-based
multiscale simulation of angiogenesis in skeletal muscle. Theor Biol Med Model
13. Qutub AA, Liu G, Vempati P, Popel AS (2009) Integration of angiogenesis
modules at multiple scales: from molecular to tissue. Pac Symp Biocomput. pp
14. Sugimoto H, Hamano Y, Charytan D, Cosgrove D, Kieran M, et al. (2003)
Neutralization of circulating vascular endothelial growth factor (VEGF) by anti-
VEGF antibodies and soluble VEGF receptor 1 (sFlt-1) induces proteinuria.
J Biol Chem 278: 12605–12608.
15. Folkman J (1995) Angiogenesis in cancer, vascular, rheumatoid and other
disease. Nat Med 1: 27–31.
16. Rudge JS, Holash J, Hylton D, Russell M, Jiang S, et al. (2007) Inaugural
Article: VEGF Trap complex formation measures production rates of VEGF,
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org 16November 2011 | Volume 6 | Issue 11 | e27514
providing a biomarker for predicting efficacious angiogenic blockade. Proc Natl Download full-text
Acad Sci U S A 104: 18363–18370.
17. Leighl NB, Raez LE,Besse B, Rosen PJ, Barlesi F,etal. (2010) A multicenter, phase
2 study of vascular endothelial growth factor trap (Aflibercept) in platinum- and
erlotinib-resistant adenocarcinoma of the lung. J Thorac Oncol 5: 1054–1059.
18. Stefanini MO, Wu FT, Mac Gabhann F, Popel AS (2008) A compartment
model of VEGF distribution in blood, healthy and diseased tissues. BMC Syst
Biol 2: 77.
19. Stefanini MO, Wu FT, Mac Gabhann F, Popel AS (2009) The presence of
VEGF receptors on the luminal surface of endothelial cells affects VEGF
distribution and VEGF signaling. PLoS Comput Biol 5: e1000622.
20. Wu FT, Stefanini MO, Mac Gabhann F, Popel AS (2009) Modeling of growth
factor-receptor systems from molecular-level protein interaction networks to
whole-body compartment models. Methods Enzymol 467: 461–497.
21. Wu FT, Stefanini MO, Mac Gabhann F, Popel AS (2009) A compartment
model of VEGF distribution in humans in the presence of soluble VEGF
receptor-1 acting as a ligand trap. PLoS One 4: e5108.
22. Yang J, Ratovitski T, Brady JP, Solomon MB, Wells KD, et al. (2001)
Expression of myostatin pro domain results in muscular transgenic mice. Mol
Reprod Dev 60: 351–361.
23. Hoff J (2000) Methods of Blood Collection in the Mouse. Lab Animal 29: 7.
24. Sassen A, Reuter AM, Kennes F (1968) Determination of plasma volume in the
mouse with screened iodine-labelled proteins. Experientia 24: 1203–1204.
25. Hinghofer-Szalkay H, Greenleaf JE (1987) Continuous monitoring of blood
volume changes in humans. J Appl Physiol 63: 1003–1007.
26. Mendez J, Kollias J (1977) Diet and starvation on the composition and
calculated density of fat-free body mass. J Appl Physiol 42: 731–734.
27. Sheff MF, Zacks SI (1982) Interstitial space of mouse skeletal muscle. J Physiol
28. Hagstrom L, Agbulut O, El-Hasnaoui-Saadani R, Marchant D, Favret F, et al.
(2010) Epo is relevant neither for microvascular formation nor for the new
formation and maintenance of mice skeletal muscle fibres in both normoxia and
hypoxia. J Biomed Biotechnol 2010: 137817.
29. Medeiros A, Vanzelli AS, Rosa KT, Irigoyen MC, Brum PC (2008) Effect of exercise
training and carvedilol treatment on cardiac function and structure in mice with
sympathetic hyperactivity-induced heart failure. Braz J Med Biol Res 41: 812–817.
30. Olfert IM, Howlett RA, Tang K, Dalton ND, Gu Y, et al. (2009) Muscle-specific
VEGF deficiency greatly reduces exercise endurance in mice. J Physiol 587:
31. Tang K, Breen EC, Gerber HP, Ferrara NM, Wagner PD (2004) Capillary
regression in vascular endothelial growth factor-deficient skeletal muscle. Physiol
Genomics 18: 63–69.
32. Wagatsuma A, Tamaki H, Ogita F (2005) Capillary supply and gene expression
of angiogenesis-related factors in murine skeletal muscle following denervation.
Exp Physiol 90: 403–409.
33. Wong LE, Garland T, Jr., Rowan SL, Hepple RT (2009) Anatomic
capillarization is elevated in the medial gastrocnemius muscle of mighty mini
mice. J Appl Physiol 106: 1660–1667.
34. Leuenberger PM, Babel J, Full C (1970) Width of retinal capillary basement
membrane of spiny mice (Acomy cahirinus) at various ages. Doc Ophthalmol 28:
35. Mathieu-Costello O (1989) Muscle capillary tortuosity in high altitude mice
depends on sarcomere length. Respir Physiol 76: 289–302.
36. Mayrovitz HN (1992) Skin capillary metrics and hemodynamics in the hairless
mouse. Microvasc Res 43: 46–59.
37. Paques M, Tadayoni R, Sercombe R, Laurent P, Genevois O, et al. (2003)
Structural and hemodynamic analysis of the mouse retinal microcirculation.
Invest Ophthalmol Vis Sci 44: 4960–4967.
38. Olewniczak S, Chosia M, Kolodziej B, Kwas A, Kram A, et al. (2003)
Angiogenesis as determined by computerised image analysis and the risk of early
relapse in women with invasive ductal breast carcinoma. Pol J Pathol 54: 53–59.
39. Olewniczak S, Chosia M, Kwas A, Kram A, Domagala W (2002) Angiogenesis
and some prognostic parameters of invasive ductal breast carcinoma in women.
Pol J Pathol 53: 183–188.
40. Haas TL, Duling BR (1997) Morphology favors an endothelial cell pathway for
longitudinal conduction within arterioles. Microvasc Res 53: 113–120.
41. Sher J, Cardasis C (1976) Skeletal muscle fiber types in the adult mouse. Acta
Neurol Scand 54: 45–56.
42. Liu JX, Hoglund AS, Karlsson P, Lindblad J, Qaisar R, et al. (2009) Myonuclear
domain size and myosin isoform expression in muscle fibres from mammals
representing a 100,000-fold difference in body size. Exp Physiol 94: 117–129.
43. van der Meer SF, Jaspers RT, Jones DA, Degens H (2010) The time course of
myonuclear accretion during hypertrophy in young adult and older rat plantaris
muscle. Ann Anat 193: 56–63.
44. Bruusgaard JC, Liestol K, Gundersen K (2006) Distribution of myonuclei and
microtubules in live muscle fibers of young, middle-aged, and old mice. J Appl
Physiol 100: 2024–2030.
45. Soukup T, Zacharova G, Smerdu V (2002) Fibre type composition of soleus and
extensor digitorum longus muscles in normal female inbred Lewis rats. Acta
Histochem 104: 399–405.
46. Cuthbertson RA, Mandel TE (1986) Anatomy of the mouse retina. Capillary
basement membrane thickness. Invest Ophthalmol Vis Sci 27: 1653–1658.
47. Man M, Adams E (1975) Basement membrane and interstitial collagen content
of whole animals and tissues. Biochem Biophys Res Commun 66: 9–16.
48. Podrazky V, Sedmerova V (1966) Densities of collagen dehydrated by some
organic solvents. Experientia 22: 792.
49. Hicks P, Rolsten C, Brizzee D, Samorajski T (1983) Age-related changes in rat
brain capillaries. Neurobiol Aging 4: 69–75.
50. Gibson JG, Evans WA (1937) Clinical Studies of the Blood Volume. II. The
Relation of Plasma and Total Blood Volume to Venous Pressure, Blood Velocity
Rate, Physical Measurements, Age and Sex in Ninety Normal Humans. J Clin
Invest 16: 317–328.
51. Truskey G, Yuan F, Katz D (2004) Transport phenomena in biological systems.
Upper Saddle RiverNJ: Pearson Prentice Hall.
52. Feng D, Nagy JA, Brekken RA, Pettersson A, Manseau EJ, et al. (2000)
Ultrastructural localization of the vascular permeability factor/vascular
endothelial growth factor (VPF/VEGF) receptor-2 (FLK-1, KDR) in normal
mouse kidney and in the hyperpermeable vessels induced by VPF/VEGF-
expressing tumors and adenoviral vectors. J Histochem Cytochem 48: 545–556.
53. Imoukhuede PI, Popel AS (2011) Quantification and cell-to-cell variation of
vascular endothelial growth factor receptors. Exp Cell Res 317: 955–965.
54. Houck KA, Leung DW, Rowland AM, Winer J, Ferrara N (1992) Dual
regulation of vascular endothelial growth factor bioavailability by genetic and
proteolytic mechanisms. J Biol Chem 267: 26031–26037.
55. Filion RJ, Popel AS (2004) A reaction-diffusion model of basic fibroblast growth
factor interactions with cell surface receptors. Ann Biomed Eng 32: 645–663.
56. Garlick DG, Renkin EM (1970) Transport of large molecules from plasma to
interstitial fluid and lymph in dogs. Am J Physiol 219: 1595–1605.
57. Venturoli D, Rippe B (2005) Ficoll and dextran vs. globular proteins as probes
for testing glomerular permselectivity: effects of molecular size, shape, charge,
and deformability. Am J Physiol Renal Physiol 288: F605–613.
58. Holash J, Davis S, Papadopoulos N, Croll SD, Ho L, et al. (2002) VEGF-Trap: a
VEGF blocker with potent antitumor effects. Proc Natl Acad Sci U S A 99:
59. Vempati P, Popel AS, Mac Gabhann F (2011) Formation of VEGF isoform-
specific spatial distributions governing angiogenesis: computational analysis.
BMC Syst Biol 5: 59.
60. Ng YS, Rohan R, Sunday ME, Demello DE, D’Amore PA (2001) Differential
expression of VEGF isoforms in mouse during development and in the adult.
Dev Dyn 220: 112–121.
61. Ee LC, Zheng S, Yao L, Tso P (2000) Lymphatic absorption of fatty acids and
cholesterol in the neonatal rat. Am J Physiol Gastrointest Liver Physiol 279:
62. Wassmer B, Augenstein U, Ronai A, de Looze S, von Deimling O (1988) Lymph
esterases of the house mouse (Mus musculus)–II. The role of esterase-2 in fat
resorption. Comp Biochem Physiol B 91: 179–185.
63. Wachsberger PR, Burd R, Cardi C, Thakur M, Daskalakis C, et al. (2007)
VEGF Trap in combination with radiotherapy improves tumor control in U87
glioblastoma. Int J Radiat Oncol Biol Phys 67: 1526–1537.
64. Daly T (2009) VEGF-Binding Fusion Proteins. USA: Regeneron Pharmaceu-
65. North Central Cancer Treatment Group (2007) Phase II Trial of VEGF Trap in
Patients with Metastatic Breast Cancer Previously Treated with Anthracycline
and/or Taxane. NCI.
66. Coleman TF, Li Y (1994) On the Convergence of Reflective Newton Methods
for Large-Scale Nonlinear Minimization Subject to Bounds. Mathematical
Programming 67: 189–224.
67. Coleman TF, Li Y (1996) An Interior, Trust Region Approach for Nonlinear
Minimization Subject to Bounds. SIAM Journal on Optimization 6: 418–445.
68. Kenakin TP (2009) 12.4.3. In: Press/Elsevier A, ed. A pharmacology primer:
theory, applications, and methods. Amsterdam: Academic Press/Elsevier.
69. Tissot van Patot MC, Leadbetter G, Keyes LE, Bendrick-Peart J, Beckey VE,
et al. (2005) Greater free plasma VEGF and lower soluble VEGF receptor-1 in
acute mountain sickness. J Appl Physiol 98: 1626–1629.
70. Kleinheinz J, Jung S, Wermker K, Fischer C, Joos U (2010) Release kinetics of
VEGF165 from a collagen matrix and structural matrix changes in a circulation
model. Head Face Med 6.
71. Serini G, Ambrosi D, Giraudo E, Gamba A, Preziosi L, et al. (2003) Modeling
the early stages of vascular network assembly. EMBO J 22: 1771–1779.
72. Chen RR, Silva EA, Yuen WW, Brock AA, Fischbah C, et al. (2007) Integrated
approach to designing growth factor delivery systems. FASEB J 21: 3896–3903.
73. Wu FT, Stefanini MO, Mac Gabhann F, Kontos CD, Annex BH, et al. (2010) A
systems biology perspective on sVEGFR1: its biological function, pathogenic
role and therapeutic use. J Cell Mol Med 14: 528–552.
74. Favier B, Alam A, Barron P, Bonnin J, Laboudie P, et al. (2006) Neuropilin-2
interacts with VEGFR-2 and VEGFR-3 and promotes human endothelial cell
survival and migration. Blood 108: 1243–1250.
75. Rygaard J, Povlsen CO (1969) Heterotransplantation of a human malignant
tumour to "Nude" mice. Acta Pathol Microbiol Scand 77: 758–760.
76. Tokunaga T, Kijima H, Oshika Y, Fukushima Y, Abe Y, et al. (1998) Aberrant
isoform of vascular endothelial growth factor 189 expression is correlated with
xenotransplantability of human esophageal cancer. Oncol Rep 5: 1115–1118.
77. Italiano JE, Jr., Richardson JL, Patel-Hett S, Battinelli E, Zaslavsky A, et al.
(2008) Angiogenesis is regulated by a novel mechanism: pro- and antiangiogenic
proteins are organized into separate platelet alpha granules and differentially
released. Blood 111: 1227–1233.
78. Hernandez N, Torres SH, Finol HJ, Vera O (1999) Capillary changes in skeletal
muscle of patients with essential hypertension. Anat Rec 256: 425–432.
VEGF Distribution in the Mouse
PLoS ONE | www.plosone.org17 November 2011 | Volume 6 | Issue 11 | e27514