Vascular Regeneration by Local Growth Factor Release Is
Self-Limited by Microvascular Clearance
Kha N. Le, PhD; Chao-Wei Hwang, MD, PhD; A. Rami Tzafriri, PhD; Mark A. Lovich, MD, PhD;
Alison Hayward, DVM; Elazer R. Edelman, MD, PhD
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Background—The challenge of angiogenesis science is that stable sustained vascular regeneration in humans has not been
realized despite promising preclinical findings. We hypothesized that angiogenic therapies powerfully self-regulate by
dynamically altering tissue characteristics. Induced neocapillaries increase drug clearance and limit tissue retention and
subsequent angiogenesis even in the face of sustained delivery.
Methods and Results—We quantified how capillary flow clears fibroblast growth factor after local epicardial delivery.
Fibroblast growth factor spatial loading was significantly reduced with intact coronary perfusion. Penetration and
retention decreased with transendothelial permeability, a trend diametrically opposite to intravascular delivery, in which
factor delivery depends on vascular leak, but consistent with a continuum model of drug transport in perfused tissues.
Model predictions of fibroblast growth factor sensitivity to manipulations of its diffusivity and transendothelial
permeability were validated by conjugation to sucrose octasulfate. Induction of neocapillaries adds pharmacokinetic
complexity. Sustained local fibroblast growth factor delivery in vivo produced a burst of neovascularization in ischemic
myocardium but was followed by drug washout and a 5-fold decrease in fibroblast growth factor penetration depth.
Conclusions—The very efficacy of proangiogenic compounds enhances their clearance and abrogates their pharmacological
benefit. This self-limiting property of angiogenesis may explain the failures of promising proangiogenic therapies. (Circulation.
2009;119:2928-2935.)
Key Words: angiogenesis 䡲 collateral circulation 䡲 growth substances 䡲 ischemia 䡲 microcirculation
䡲 pharmacokinetics
S
timulation of neovascularization with angiogenic growth
factors might reduce myocardial infarct size and improve
cardiac function1 and peripheral tissue2 perfusion. Yet, impressive results in tissue culture and animal studies3–7 have
not been sustained in clinical trials.8 –11 Intravascular delivery
of angiogenic factors is convenient but challenged by the
requirements for high doses and long residence times.8,10 Cell
and gene injections might provide a continuous source of
growth factor, and intramyocardial or pericardial delivery has
elevated local tissue drug concentrations with lower systemic
exposure in animal models.12 However, the promise of
symptomatic improvement and increased capillary density
seen in early clinical trials with intramyocardial injections of
fibroblast growth factor (FGF) after coronary artery bypass
grafting13 has not endured in larger clinical trials, and clinical
outcomes in general with local growth factor delivery have
been mixed.9,14 –18
Clinical Perspective on p 2935
Some have postulated that myocardial growth factor concentrations, drug residence time, or both were inadequate for
sustained angiogenesis despite controlled release delivery.19
However, the local pharmacokinetic processes governing the
uptake and distribution of growth factors in highly vascularized tissues such as myocardium remain ill defined. It is
therefore possible that the reverse is true and that growth
factor concentrations were actually more than sufficient
initially. We hypothesized that local delivery can induce
neocapillary growth but, in doing so, changes the balance
between drug delivery and microvascular drug clearance to
favor the latter, so that the very pharmacological efficacy of
these compounds limits their biological effect.
We used a series of ex vivo analytical and in vivo
experimental animal models to quantify how growth factors
Received September 23, 2008; accepted February 23, 2009.
From the Harvard–MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge (K.N.L., A.R.T., E.R.E.);
Division of Cardiology, Department of Medicine, Johns Hopkins Hospital, Johns Hopkins School of Medicine, Baltimore, Md (C.-W.H.); Department
of Anesthesiology and Pain Medicine, Caritas St Elizabeth’s Medical Center, Boston Mass (M.A.L.); Division of Comparative Medicine, Massachusetts
Institute of Technology, Cambridge (A.H.); and Cardiovascular Division, Department of Medicine, Brigham and Women’s Hospital, Harvard Medical
School, Boston, Mass (E.R.E.).
The online-only Data Supplement is available with this article at http://circ.ahajournals.org/cgi/content/full/CIRCULATIONAHA.108.823609/DC1.
Guest Editor for this article was Michael Simons, MD.
Correspondence to Kha N. Le, Division of Health Sciences and Technology, Massachusetts Institute of Technology, Room E25– 442, 77 Massachusetts
Ave, Cambridge, MA 02139. E-mail [email protected]
© 2009 American Heart Association, Inc.
Circulation is available at http://circ.ahajournals.org
DOI: 10.1161/CIRCULATIONAHA.108.823609
2928
Le et al
distribute within vascularized tissue and how neovascularization after delivery of angiogenic growth factors affects their
pharmacokinetics and efficacy. These studies strongly suggest that angiogenesis is powerfully self-regulating in that the
capillaries induced by angiogenic drug therapy may increase
clearance rates, limiting tissue levels of growth factor and
subsequent angiogenesis even with sustained delivery.
Methods
Ex Vivo Myocardial Drug Delivery With and
Without Perfusion
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Sprague Dawley rats (0.5 to 0.6 kg) were anesthetized with 35 mg/kg
ketamine and 5 mg/kg xylazine and anticoagulated with 1000 U
heparin SC before to CO2 euthanasia. The aorta was cannulated and
the heart was retrograde perfused with cardioplegia (osmolality,
289⫾5% mOsm/kg H2O) composed of Krebs-Henseleit buffer
(Sigma-Aldrich, St Louis, Mo) with high potassium (30 mmol/L
KCl) and 4% BSA (Sigma-Aldrich) to establish diastolic arrest. The
heart was excised and perfused at 95 mm Hg. Coronary flow was
monitored periodically and ranged from 8 to 10 mL/min throughout
the experiment. The perfusate was oxygenated by a foam bubble
oxygenator with 95% O2/5% CO2 at 37°C. Samples also were
examined in the absence of coronary perfusion to eliminate other
effects. Here, the aorta was cannulated and flushed with perfusate.
As blood cleared from the circulation, coronary outflow from the
coronary sinus was stopped by clamping the right atrium and
pulmonary artery, ensuring the patency of myocardial capillaries and
ensuring that the only difference between the control and perfused
cases was coronary perfusion. The entire configuration resided within an
enclosed box with 100% humidity. We ascertained myocardial viability
at 6 hours by quantitatively documenting no additional tissue edema on
hematoxylin and eosin–stained sections. Experimental protocols were in
accordance with National Institutes of Health guidelines for the humane
care and use of laboratory animals and the MIT Committee on Animal
Care.
Texas Red–FGF2 (TR-FGF2; 17 kDa; 5.88⫻10⫺2 ␮mol/L) or
Texas Red–labeled FGF2 conjugated to sucrose octasulfate (SOS)
complex [TR-(FGF2)2-SOS complex; ⬇35 kDa; 2.86⫻10⫺2 ␮mol/L]
was delivered to the rat myocardium from a drug-releasing chamber
affixed to the anterior epicardial surface by a cyanoacrylate-based
surgical adhesive (Glustitch, Point Roberts, Wash). Hearts were
placed on a shaker at 100 rpm to ensure a well-mixed epicardial drug
source. A core of myocardial tissue in contact with and immediately
adjacent to the drug source was harvested 6 hours later with an
8-mm-diameter biopsy punch (Miltex, York, Pa). Tissue cores were
cryosectioned (Leica CM1850, Leica, Germany) perpendicular to the
epicardium for quantitative epifluorescence imaging (Leica DMRA2
microscope; Hamamatsu C4742–95 camera, Bridgewater, N.J.;
MetaMorph software, Sunnyvale, Calif; Texas Red filter set). Because the fluorescent intensity of TR-FGF2 is linearly proportional to
fluorophore,20 total drug deposition in the absence (Mdiff) or presence
(Mdiff-clear) of coronary perfusion was calculated by summing fluorescence intensities in the spatial distributions. Percent clearance of
drug from coronary perfusion is given by Equation M1:
%clearance⫽100⫻(1⫺Mdiff-clear /Mdiff).
In Vivo Myocardial Drug Delivery
Rabbits (New Zealand White, 3 to 3.5 kg) received an intramuscular
injection of 35 mg/kg ketamine and 5 mg/kg xylazine, inhaled
isoflurane anesthesia (1% to 3%), and positive pressure ventilation
via a 3.0-mm endotracheal tube. The chest was shaved and sterilely
prepared with Betadine and alcohol. A left thoracotomy was performed after local lidocaine injection. A clamp kept the chest open,
and a small opening in the pericardium was created with care to
minimize pericardial damage. The left anterior descending coronary
artery was ligated. Ischemia was confirmed by ST-segment elevation
on simultaneous continuous ECG. Sodium alginate polymeric de-
Local Angiogenic Therapy Is Self-Limited
2929
Table. Continuum Pharmacokinetic Model Equations for
Epicardial Drug Delivery
Equation 1
Equation 2
Equation 3
Equation 4
Equation 5
⭸2C
⭸C
⫺D 2⫽⫺kC
⭸t
⭸␹
冉 冊
k⫽
2 Pmv ␾mv
Rmv 1⫺␾mv
冉冑 冊
冑
冋 冑冑 册
C/C0⬇erfc
␹
2 Dt
D
k
C⫽C0e⫺␹/ᐉ , ᐉ⫽
%clearance ⫽ 100⫻ 1⫺
ᐉerf( kt )
4Dt/␲
Detailed derivations are included in the Methods section of the online-only
Data Supplement. Equation 1 describes the transport of drug in the presence
of capillary clearance. C represents the drug concentration in the tissue as a
function of time t, distance from the epicardium x, diffusivity D, and apparent
clearance constant k. Equation 2 relates the apparent clearance constant k to
capillary permeability Pmv, capillary volume fraction, and capillary diameter Rmv.
Equation 3 describes steady-state tissue concentration normalized to source
concentration, Co, in the absence of capillary perfusion. Equation 4 shows the
steady-state tissue concentration in the presence of capillary perfusion, where
ᐉ is drug penetration depth. Equation 5 shows the percentage of drug
clearance by capillary perfusion as a function of k and D.
vices sustain-releasing 35S-FGF1 from encapsulated heparin Sepharose beads (see the Materials section in the online-only Data
Supplement) were placed in the pericardial space, and the pericardiotomy suture was repaired to prevent leakage. The thoracotomy
and skin incision were closed. Positive end-expiratory pressure
ventilation and a negative pressure chest tube prevented pneumothorax. Analgesia was with 0.03 mg/kg buprenorphine SC injections
every 8 hours for the first 72 hours. Control animals received
alginate-encapsulated heparin Sepharose beads without FGF. Hearts
were harvested 2, 8, 16, and 31 days after surgery, and the aortas
were cannulated, flushed retrogradely with PBS, and snap-frozen in
liquid nitrogen.
Quantification of In Vivo FGF1 and Blood
Vessel Distribution
Two frozen myocardial cores were excised adjacent to the polymeric
devices with an 8-mm-diameter biopsy punch (Miltex). One core
was mounted and cryosectioned (Leica CM1850) into 100-␮m
sections parallel to the epicardium. Sections were digested in 1 mL
solvable tissue solubilizer (Perkin Elmer, Waltham, Mass) at 60°C
overnight before radioactivity quantification (2500TR Liquid Scintillation Analyzer, Packard). The discrete spatial FGF1 concentration
data were fit to the exponential profile implied by Equation 4 given
in the Table with GraphPad software (Prism 5, La Jolla, Calif). The
fit was used to estimate the penetration depth (x90), defined as the
distance from the source to 90% drop-off threshold, as x90⫽ᐉ⫻ln(10).
The other tissue core was cryosectioned into 10-␮m-thick sections in the
transmural direction. Sections were fixed for 5 minutes with 4%
paraformaldehyde (Electron Microscopy Sciences, Hatfield, Pa),
washed for 30 seconds with cold acetone (Sigma-Aldrich, St. Louis,
Mo), incubated in blocking serum (200 ␮L 1% chicken serum for 1 hour
at 37°C) and then in goat anti–PECAM-1 IgG (Santa Cruz Biotechnology, Santa Cruz, Calif; 200 ␮L of 1:50 dilution for 2 hours at 37°C),
washed 3 times in 0.1% Tween 20 in PBS, incubated again with Alexa
Fluor 488 chicken anti-goat IgG (Invitrogen, Carlsbad, Calif; 200 ␮L of
1:200 dilution for 2 hours at 37°C), washed 3 times in Tween 20/PBS,
coverslip mounted, and imaged immediately with a fluorescence microscope (Leica DMRA2, FITC filter set). The images were thresholded to
maximize the signal-to-noise ratio with Matlab (MathWorks, Natick,
Mass), yielding binary images of vessel distribution. Neovascular
formation of tissue regions within 500 ␮m from the epicardial source
was quantified by computing the tissue area fraction stained by
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June 9, 2009
Figure 1. Myocardial capillary perfusion impedes drug penetration. Distribution and representative fluorescence microscopy
images of TR-FGF2 in rat myocardium with (magenta) and without (blue) coronary perfusion. Data represent mean⫾SEM (n⫽3).
Penetration depth (x90) is estimated as the location of the 90%
drop-off from the threshold (vertical dashed lines).
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PECAM-1 (total number of pixels with PECAM-1 stain divided by the
total number of pixels of tissue area).
Statistical Analysis
All data are presented as mean⫾SEM, except values for the
clearance rate constants (k), which are reported as mean⫾propagated
SE. Propagated errors, sk, were calculated with this formula:
冉冊 冉 冊 冉 冊
Sk
K
2
⫽
SD
D
2
⫹2
Sx
90
x 90
2
,
where sD and sx90 are SEs for effective diffusivity, D, and penetration
depth, x90, respectively. Statistical analyses were performed with the
Student t test when appropriate. Values of P⬍0.05 (2 tailed) were
considered statistically significant. Nonlinear regression was performed with GraphPad software (Prism 5) to fit steady-state spatial
drug distributions to Equations VI and XI in the online-only Data
Supplement in obtaining values for the clearance rate constant and
effective diffusivity, respectively.
Results
FGF Distribution Is Limited by Myocardial Perfusion
Drug transport through and deposition within tissues are
governed by molecular weight– dependent processes such as
diffusion and convection and physicochemical attributes such
as binding, partitioning, and metabolism.21–23 We examined
the effects of capillary perfusion on myocardial growth factor
transport in rat hearts incubated at constant epicardial source
concentrations (Figure I in the online-only Data Supplement)
with and without controlled coronary flow. When delivered to
the ex vivo myocardium in the absence of flow, TR-FGF2
distributed via diffusion to a penetration depth of 66 ␮m in 6
hours (Figure 1). Restoration of coronary perfusion reduced
TR-FGF2 penetration depth ⬎2-fold to 28 ␮m, localizing
growth factor closer to the epicardial drug source (Figure 2).
Drug Diffusivity, Transendothelial Permeability,
and Vessel Density Influence Local Drug
Distribution and Deposition
We examined the impact of coronary flow on drug penetration within the context of a continuum pharmacokinetics
model of drug diffusion in the face of microvascular
clearance (Equation 1 in the Table). In the absence of
Figure 2. Continuum pharmacokinetic model. Penetration depth
(x90), defined as the distance from the source to the 90% dropoff threshold, x90⫽ᐉ⫻ln(10), where ᐉ is calculated based on
Equation 4 (the Table), is expressed as a function of drug diffusivity (A), transendothelial permeability (B), and capillary volume
fraction (C). Parameter values cover a range of 2 orders of magnitude below to above those of FGF2 in the heart. FGF2 diffusivity⫽0.02 ␮m2/s and clearance constants k were empirically
verified, and transendothelial permeability was derived from
Equation 2 in the Table. Capillary volume fraction (␸mv) was varied over 3 log orders between the extremes of ischemic and
normal tissue vascularity.25 These relationships are linear in loglog scale axes, demonstrating adherence to power law
functions.
perfusion, the growth factor distribution curve mimics the
analytical solution of the diffusion equation (Equation 3 in
the Table) with an apparent diffusivity of 0.021⫾0.001 ␮m2/s
for TR-FGF2. This value is 4 orders of magnitude smaller
than the reported diffusivity of FGF in free aqueous solution,24 reflecting the impact of steric hindrance and binding
within tissues. TR is small (600 Da) and hydrophilic. Its
diffusion is significantly higher than FGF in heparin sulfate
proteoglycan-rich myocardium, and detected fluorescence is
likely specific for TR-FGF-2. In the presence of coronary
perfusion, the capacity of capillaries to clear drugs is restored,
and the distribution of TR-FGF2 at 6 hours approaches an
exponential steady-state profile consistent with an apparent clearance rate constant: k⫽1.15⫾0.06⫻10⫺4 s⫺1 (Equation 4 in the
Table). Given a normal myocardial capillary density of
⬇12.9%25 and FGF2 aqueous diffusivity of 2.2⫻102 ␮m2/s,24
our estimate of the clearance rate constant of FGF2 implies
Le et al
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that the transendothelial permeability and ratio of permeability
to diffusivity are ⬇1.9⫻10⫺3 ␮m/s and 8.8⫻10⫺6 ␮m⫺1. This
estimate is in line with the transendothelial permeability of a
molecule with a molecular size of FGF2.26
Analytic models of drug transport and loss to capillary
flow were evaluated across a range of diffusivities, transendothelial permeabilities, and microvascular volume fractions.
Steady-state results (Equations VII and IX in the online-only
Data Supplement Methods section) were used because equilibrium is rapidly achieved. Penetration depth at steady state
increases as the square root of the diffusion coefficient
(Figure 2A) and decreases as the square root of the transendothelial permeability constant (Figure 2B). It is worth
contrasting our results with those from systemic drug delivery
through an intravascular route, in which tissue absorption is
proportional to transendothelial permeability. Increasing
transvascular penetration in systemic delivery requires drugs
that permeate across the endothelium and interventions that
increase, rather than decrease, vascular permeability.27–29
Tissues with higher degrees of vascularization, as embodied
by the vascular volume fraction, clear drugs faster and have
lower steady-state drug penetration (Figure 2C). Thus,
steady-state drug penetration and distribution are highly
dependent on drug diffusivity through tissue and net microvascular clearance, the compounded effect of transendothelial
permeability and microvascular volume fraction (Equation 2
in the Table).
The theoretical reduction in total deposition caused by
capillary clearance was calculated (Equation 5 in the Table)
and expressed as a function of the clearance rate constant, k
(Equations VIII and XII in the online-only Data Supplement).
Percentage clearance of drug with coronary perfusion is most
sensitive for clearance rate constants ranging between 1⫻10⫺5
and 1⫻10⫺2 s⫺1 (Figure 3A). Notably, our measurement of the
clearance rate constant of TR-FGF2 falls within this range,
suggesting that FGF clearance is highly sensitive to transendothelial permeability and microvascular volume fraction.
To examine whether the clearance rate constant of FGF
might be modulated by altering its physicochemical properties, we used quantitative fluorescence imaging to contrast the
distribution of TR-FGF2 alone or in association with SOS.
SOS induces FGF dimerization and increases the effective
molecular weight of TR-FGF2.30 The increase in size was
confirmed by size-exclusion chromatography and should
reduce transendothelial permeability, capillary washout, and
effective diffusivity. Indeed, in the absence of coronary
perfusion, TR-(FGF2)2-SOS penetrated 40% less than TRFGF2 into the myocardium (40 ␮m, with an effective
diffusivity of 0.013⫾0.001 ␮m2/s), reflecting its increased
size (Deff TR-FGF⫽0.021⫾0.001 ␮m2/s; Figure 1 versus 3B).
But, the larger compound also was less affected by coronary
perfusion, with penetration depth falling only 26% to 30 ␮m
and total deposition falling by only 12% (Figure 3B). The
muted sensitivity of TR-(FGF2)2-SOS to flow is consistent with the
estimated clearance rate constant (k⫽4.37⫾0.33⫻10⫺5 s⫺1), model
predictions (Figure 3A), and our hypothesis that larger
molecules enter capillaries less readily.
Local Angiogenic Therapy Is Self-Limited
2931
Figure 3. FGF distribution is sensitive to alteration in drug clearance. A, Percentage of drug cleared by capillaries calculated
using the analytical model (Equation 5 in the Table) as a function of clearance rate constant, k (black line). Experimental data
points for TR-FGF2 and TR-(FGF2)2-SOS analyzed by Equation
M1 are superimposed (magenta squares) on model predictions
providing perspective on the sensitivity of FGF2 to manipulation
of its clearance constant. B, Distribution and representative fluorescence microscopy images of TR-(FGF2)2-SOS in rat myocardium with coronary (magenta) and without (blue) coronary perfusion. Data represent mean⫾SEM (n⫽3).
In Vivo Angiogenic Response Limits
Drug Distribution
Conventional pharmacokinetic models for drug distribution
do not take into account the potential that drugs can alter
capillary density, transendothelial permeability, or drug clearance. Yet, angiogenic growth factors such as FGF1 and FGF2
are specifically administered to induce capillary growth, and
it would be unreasonable to assume that transendothelial
permeability and drug clearance are not similarly modified.
Induced neovascularization implies an increase in the density
of blood capillaries that could provide negative feedback,
limiting growth factor tissue penetration (Figure 2C). Our
analysis of myocardial drug transport suggests that FGF
would be particularly sensitive to induced capillary washout
(Figures 1 and 3A). We tested this hypothesis in vivo using
radiolabeled FGF1 (35S-FGF1). TR-FGF2 could not be used
in vivo because its labeling intensity is much lower than that
of 35S-FGF1, rendering it virtually transparent at the doses
delivered. Notably, ex vivo experiments with 35S-FGF1 were
well explained by the diffusion-clearance model and suggest
that the transport parameters estimated for TR-FGF2 are
similar to those of 35S-FGF1 (online-only Data Supplement).
Heparin-bound biologically active 35S-FGF1 fractions were
isolated, incorporated into heparin Sepharose-alginate wafers
that sustain-release FGF1 for over 30 days in vitro and in vivo
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June 9, 2009
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Figure 4. Polymeric devices sustain release FGF1 over 30 days.
A, Cross-sectional area of hematoxylin and eosin–stained rabbit
myocardial tissue shows location of drug release source (adjacent to left ventricular free wall) and interface between drug
source and myocardium. B, Percentage of cumulative 35S-FGF1
released into PBS buffer in vitro (䉫; data represent mean⫾SEM
[n⫽10]; 100% corresponds to ⬇90 ␮g 35S-FGF1 per circular
disk of 8-mm diameter and 1-mm thickness). Throughout the in
vivo experiment (䢇; data represent mean⫾SEM; n⫽3), 100%
corresponds to ⬇450 ␮g 35S-FGF1 per device (20⫻20⫻1 mm),
calculated as follows: percent drug released⫽(total drug within
source⫺total drug remaining)/total drug within source⫻100%.
(Figure 4B), and implanted in the pericardial space of
ischemic rabbit hearts (Figure 4A). FGF1 successfully penetrated 442⫾91 ␮m into the myocardium over the first 2 days
after release initiation. Yet, despite sustained delivery, penetration regressed over time, falling 5-fold by day 8 (81⫾30
␮m), and remained low through day 31 (Figure 5A). Enhanced growth factor clearance was associated with the
induction of neovasculature. Two days after device implantation, the fraction of PECAM-1–stained tissue was 56%
greater in animals receiving FGF1 (4.4%) compared with
baseline density (2.8%) in control animals with identical
devices devoid of growth factor (P⬍0.05; Figure 5C). Neovascularization peaked at day 8 (8.7%), double that from day
2 (P⬍0.01; Figure 5C), coinciding with the drop in drug
distribution. Similarly, the fraction of PECAM-1–stained
tissue decreased significantly from day 8 to 31 (⫺62%;
P⬍0.01; Figure 5C), most likely from regression of neocapillaries as the concentration of FGF1 becomes subtherapeutic.
Examination of drug delivery devices for remaining drug
content confirmed that the decreasing myocardial concentrations arose from increasing capillary clearance rather than
decreasing drug delivery. None of the delivery devices were
depleted of drug, and all continued to release drug with
constant flux (Figure 4B) after the expected burst release of
⬇37.5% during the first 6 hours.
Discussion
The potential of angiogenic promoters of endothelial cell
growth and neovascularization is well established in cell and
tissue culture.31,32 However, angiogenic growth factors have
yet to produce stable sustained angiogenesis in clinical
trials.8,10 Although there are undoubtedly biological factors
involved,33 our study suggests that fundamental transport
barriers, particularly the self-limiting pharmacokinetics of
angiogenic therapy, also may impair the realization of sustained neovascularization.
Our results reveal that drug transendothelial permeability
plays a vital role in governing drug distribution. Lower
transendothelial permeability ensures greater myocardial
drug penetration after local application (Figure 2B). FGF is
an arterial vasodilator, but this cannot explain our results
because expected changes in arteriolar volume34 could not
reach the scale of our results or explain the difference in
growth factor distribution between perfused and static flow
conditions, both of which saw growth factor. The dependence
of drug distribution on transendothelial permeability and
capillary density takes on further complexity for angiogenic
compounds that can remodel their tissue environment. Over
the course of treatment, vessel density in ischemic tissues
increases in FGF1-laden tissue regions (within 500- to
600-␮m depth from epicardium; Figure 5B). Indeed, abundant neovascularization occurs from day 2 to 8, but drug
washout rises as well, precipitously dropping the local tissue
concentration of FGF1 (Figure 5A) and penetration depth of
FGF1 despite no quantifiable change in growth factor delivery. The instability of FGF1 in the absence of heparin35
cannot account for the observed effects because the factor
was released directly from the heparin Sepharose devices to
the epicardial tissue. Released FGF1 likely binds reversibly to
myocardial heparin sulfate proteoglycans, prolonging its
tissue half-life. Indeed, angiogenic activity was observed 8
days after delivery (Figure 5). Moreover, changes in angiogenic action correlated with regression of FGF1 distribution,
not a decrease in activity or stability. Continuum pharmacokinetics (Equation XV of the online-only Data Supplemental
Methods) suggest a 5-fold increase in capillary washout between
day 2 and 8. Such an increase in the FGF1 clearance could arise
from an increase in microvascular density and/or transendothelial permeability (Equation 2 in the Table). The observed 65%
rise in capillary density between days 2 and 8 indicates that the
latter plays a dominant role and suggests that the induced
vasculature is immature and highly permeable to FGF1.
Our findings, therefore, offer possibilities for engineering
drugs to penetrate tissue better by reducing their transendothelial permeability. FGF2 lies within the region where drug
penetration depth is highly sensitive to the clearance rate
constant, k (Figure 4A), which is directly proportional to
transendothelial permeability (Equation 2 in the Table),
whereas (FGF2)2-SOS, with its 2.6-times-lower clearance, is
less affected by flow. More than 50% of FGF2 but only 12%
of (FGF2)2-SOS is cleared by coronary perfusion (Figure 1
versus 3B). Therefore, one way to decrease permeability is to
consider drugs of higher molecular weight. Although higher
molecular weight implies lower myocardial drug diffusivity,
the ratio of permeability to diffusivity can drop 2 orders of
magnitude as molecular radius increases from 2.4 to 36 Å.26
A different method for modulating transendothelial permeability is by modification of drug charge. Indeed, it has been
shown that negatively charged dextrans exhibit 10-times-
Le et al
Local Angiogenic Therapy Is Self-Limited
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Figure 5. In vivo ischemic heart model. A, Spatial distributions of tissue S35-FGF1 concentration at days 2, 8, and 31 after coronary
ligation and implantation of sustained release source. FGF1 was quantified with liquid scintillation counting after serial sectioning. Data
represent mean⫾SEM (n⫽3). B, Representative fluorescent images of PECAM-1–labeled blood vessels in tissue regions adjacent to
drug source for experimental animals receiving heparin-Sepharose beads/alginate source with S35-FGF1 and control animals receiving
devices without FGF1. Dashed red line on the right edge denotes the interface between the source and epicardium. Magenta, blue, and
green dashed lines represent the penetration depth at the 90% drop-off threshold from the tissue/source interface calculated from spatial S35-FGF1 distributions. C, Fraction of vascular to tissue surface fraction (calculated by normalizing total number of pixels stained by
PECAM-1 to total tissue area within 500-␮m depth from the source) is expressed as a function of time. Scale bars⫽100 ␮m. Data
points represent PECAM-1–stained surface fraction of individual hearts (n⫽3), and connecting lines denote trend of mean value.
*P⬍0.05; **P⬍0.01 (P⫽0.007 between days 2 and 8; P⫽0.003 between days 8 and 31).
lower transendothelial permeability than neutral analogs.36
This approach may present a method for lowering transendothelial permeability of a drug to increase penetration depth
and deposition.
Our study also highlights the impact of capillary clearance
on myocardial drug distribution and elimination and sets a
ceiling for the depth of drug penetration at steady state. Such
clearance is dependent on the transendothelial permeability of
the delivered drug and tissue vascularity. At normal arterial
PO2, a significant portion of capillaries are relatively constricted. Normal myocardium can respond swiftly to arterial
hypoxia through active hyperemia by dilating capillaries and
effectively decreasing the intercapillary distance and thus the
oxygen diffusion barrier.37 Through reactive hyperemia, the
glycocalyx lining of endothelial cells can be modified by
reactive oxygen species to increase transendothelial permeability and capillary and postcapillary venule diameter.38
However, myocardial capillary density declines markedly
with ischemia and infarction, limiting capillary reserve.39 – 41
Because capillaries act as spatially distributed sinks to drug,
myocardium with denser functional vascularity will clear
drug more efficiently and rapidly, creating zones of low drug
concentration. Gradation in vascularity in diseased tissue thus
has important consequences for local drug delivery. Because
capillary flow in ischemic and infarcted regions is substantially lower than in normal tissue, our data predict that drug
penetration would be greater. Placing delivery devices directly in the ischemic region should confer the pharmacoki-
netic advantages of decreased capillary washout; in wellperfused regions, drug molecules may never reach ischemic
areas at sufficient levels. Pericardial delivery of growth
factors to target endocardial ischemic regions may thus prove
futile because drugs will not easily cross well-perfused
epicardial regions. Indeed, drug penetration in the presence of
capillary perfusion was limited ex vivo (Figure 1) and in vivo
(Figure 5) despite ample time for distant diffusion.
The integrated studies presented suggest that angiogenesis
is powerfully self-regulating in that the very capillaries
induced by angiogenic drug therapy may increase clearance.
The pharmacodynamic changes during the early angiogenic
therapy can tip the pharmacokinetics to conditions that are
unfavorable for growth factor penetration, which in turn
affects long-term therapeutic goals. This mechanism implies
a natural upper limit effect for pharmacological revascularization, which restricts angiogenic drug penetration and
spatially confines the sprouting of new vessels near the drug
source. At day 31, the FGF1 level in the 100- to 500-␮m
tissue region falls to undetectable levels, and significant
regression of neovascularization consequently occurs in the
absence of local growth factor (Figure 5C). One might well
imagine that such forces are essential to endogenous regulation of tissue morphogenesis and repair and that loss of such
regulation may help explain the growth of vascular tumors
and other arteriovenous malformations and anomalies.
The interdependence of the pharmacokinetics and pharmacodynamics elucidated in this study may explain the diffi-
2934
Circulation
June 9, 2009
culty of realizing the clinical potential of angiogenic compounds and suggests that efficacy becomes critically dependent
on device placement and the transendothelial permeability of the
drug. The quantitative framework presented here may help guide
rational selection of angiogenic compounds based on a favorable
physicochemical profile and drug delivery strategies that take
advantage of the regulation between growth factor pharmacokinetics and angiogenic pharmacodynamics.
Acknowledgment
Dr Le initiated research, designed, performed experiments and
analyzed data. Dr Hwang performed experiments and analyzed data.
Dr Tzafriri derived analytical model and analyzed data, Dr Lovich
supervised experiments and analyzed data, Dr Edelman initiated the
research and experimental design, and analyzed data. Dr Hayward
helped in design of the rabbit ischemic heart model and performed
surgeries. Drs Le, Hwang, Tzafriri, Lovich, and Edelman contributed
to the writing of the manuscript. We thank Abraham Wei for his help
in FGF production and labeling.
Downloaded from http://circ.ahajournals.org/ by guest on June 18, 2017
Source of Funding
This work was supported in part by grants from the National
Institutes of Health to Dr Edelman (R01 GM 49039).
Disclosures
None.
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CLINICAL PERSPECTIVE
Proangiogenic growth factors have long been considered for regenerating ischemic tissues. Yet, sustained clinical benefit
has not followed promising preclinical findings even with advances in local delivery technology. Quantitative and animal
models suggest that the limited late efficacy of local delivery of angiogenic factors stems partly from the very early success
at inducing vessel growth. Fibroblast growth factor released from a polymeric implant penetrates ischemic rabbit
myocardium in vivo for the first 2 days of local delivery and indeed induces neovascularization. But, as new vessels are
formed, drug is cleared rapidly, and the induced vessel mass regresses. As each wave of new vessels appears in response
to the angiogenic factor pools, the factors are cleared, and the angiogenic signal abates as a receding wave that implodes
back toward the growth factor source. Despite a constantly eluting source of fibroblast growth factor, the front of new
vessels continues to fall back. Eight days after release initiation, neovascularization remains but only as a regressed zone
immediately around the delivery device. By day 30, there is only a superficial layer of vessels around the release device.
This interdependence of pharmacokinetics and pharmacodynamics may explain the difficulty of realizing sustained clinical
angiogenesis with local release and suggests that efficacy depends on device placement and drug transendothelial
permeability. The quantitative framework presented here may help guide rational selection of specific angiogenic
compounds on the basis of a favorable physicochemical profile and drug delivery strategies that take advantage of the tight
regulation between growth factor pharmacokinetics and angiogenic pharmacodynamics.
Vascular Regeneration by Local Growth Factor Release Is Self-Limited by Microvascular
Clearance
Kha N. Le, Chao-Wei Hwang, A. Rami Tzafriri, Mark A. Lovich, Alison Hayward and Elazer
R. Edelman
Downloaded from http://circ.ahajournals.org/ by guest on June 18, 2017
Circulation. 2009;119:2928-2935; originally published online May 26, 2009;
doi: 10.1161/CIRCULATIONAHA.108.823609
Circulation is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231
Copyright © 2009 American Heart Association, Inc. All rights reserved.
Print ISSN: 0009-7322. Online ISSN: 1524-4539
The online version of this article, along with updated information and services, is located on the
World Wide Web at:
http://circ.ahajournals.org/content/119/22/2928
Data Supplement (unedited) at:
http://circ.ahajournals.org/content/suppl/2009/05/26/CIRCULATIONAHA.108.823609.DC1
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Supplemental Materials
Supplemental Methods
Measurement of FGF in Outflow
We verified that capillary washout of FGF through microvascular clearance was indeed
responsible for the reduction in FGF penetration in the presence of perfusion with 35S-FGF1. Rat
hearts were isolated and perfused using identical procedures and experimental parameters
described in the “Ex-vivo Myocardial Drug Delivery” methods section for perfused hearts. 35SFGF1 (4.2 mg/ml) was applied to the epicardial surface (n=3) for 3 hours. The perfusate in these
experiments was not recirculated, hence presence of 35S-FGF1 in the outflow results from direct
washout of exogenous growth fact in tissue. Outflow perfusate was collected in 6-30m fractions.
At the end of perfusion experiments, 3ml samples of the outflow fractions were decolorized with
0.5ml hydrogen peroxide at 60°C for 1 hour (30%, Sigma-Aldrich), and assayed for
35
radioactivity using liquid scintillation counter (Packard).
Continuum Pharmacokinetic Model of Myocardial Drug Transport
Following Tzafriri et. al. 1 we model interstitial drug transport in a perfused tissue using
the classical diffusion equation with a linear sink term
∂C
∂ 2C
− D 2 = −kC
∂t
∂x
(S1)
where the apparent clearance rate constant k is proportional to trans-endothelial permeability as
k=
Pmv S mv
.
(1 − φ mv )
(S2)
S
Here Smv is the surface fraction of capillaries and φmv is the capillary volume fraction. Since the
surface fraction of a cylinder of radius Rmv is related to the volume fraction as S mv = 2φ mv / Rmv
we can rewrite the proportionality between the apparent clearance rate constant and transendothelial permeability as
⎛ 2 ⎞ Pmvφ mv
⎟⎟
.
k = ⎜⎜
⎝ Rmv ⎠ 1 − φ mv
(S3)
A rich literature exists on the analysis of Eq. S1. For our purposes, it suffices to note that
localization of the experimental growth factor profiles close to the drug source justifies the
analysis of distribution profiles in terms of penetration into a semi-infinite domain 2. Namely, we
assume that the concentration of growth factor at the far end of the tissue is negligible
C = 0, x = L .
(S4)
With this in mind, under the conditions of a constant surface concentration
C = C0 , x = 0
(S5)
the concentration profile takes the form 2
⎞
⎛ x
⎞
⎛ x
C / C 0 = 12 e − x / l erfc⎜⎜
+ kt ⎟⎟ .
− kt ⎟⎟ + 12 e x / l erfc⎜⎜
⎠
⎝ 2 Dt
⎠
⎝ 2 Dt
(S6)
where
l=
D
.
k
(S7)
2
Thus, clearance gives rise to a length scale l that is independent of the dimensions of the
tissue and is inversely related to the clearance rate constant. Correspondingly, using Danckwert’s
method 2 it is possible to show that net tissue deposition M depends on time as
M = C 0 lerf ( kt ) .
(S8)
Thus, k −1 operates as the time scale for the tissue to approach its steady state deposition
M = C0 l
(S9)
and distribution
C = C0e − x / l .
(S10)
Hence, increasing the clearance rate constant results in less drug penetration and more significant
localization near the drug source. On the contrary, as the clearance rate constant tends to zero,
the limitation on drug penetration is lifted ( l >> L ) such that drug penetration and deposition
reduce to the classical linear diffusion limits
⎛ x
C / C 0 ≈ erfc⎜⎜
⎝ 2 Dt
⎞
⎟⎟
⎠
(S11)
and
M ≈ 2C 0 Dt / π .
(S12)
The preceding analysis wherein the surface concentration was held constant provides
insights on drug transport during the initial burst release phase. Subsequently drug release from
the polymer device occurs at an essentially constant rate. Consider next the extreme limit
wherein the flux F0 rather than the concentration is held constant at the surface
−D
∂C
= F0 , x = 0
∂x
(S13)
3
The steady state distribution of drug implied by Eq. S1 is then
C = (lF0 / D) e − x / l .
(S14)
Thus , in the face of first order clearance, steady state drug distribution is always
exponential with a length scale l ; device release kinetics is seen to only impact the steady state
concentration of drug at the device:tissue interface (x=0). Integrating the steady state distribution
profile Eq. S14 over the entire tissue we find that steady state tissue deposition M scales linearly
with flux and inversely with the apparent clearance rate constant
M=
F0
.
k
(S15)
Using the Danckwert’s method 2, it is possible to derive the time dependent counterpart of Eq
S15, as
M=
F0
(1 − e − kt ) ,
K
(S16)
thus confirming that k −1 also operates as the time scale for the attainment of steady state tissue
deposition when drug is released at a constant flux from the polymeric device.
Analytical Model Calculation of Cummulative FGF Clearance
Cumulative FGF washout through microvascular clearance, between times t1 and t2 can
be calculated from the experimental value of clearance constant k and the total deposition M
(Eqn. S8) by the following relationship:
t2
t2
t1
t1
CL = ∫ kMdt = ∫ kC0 lerf
( kt )dt
(S17)
4
Recombinant FGF2 Production
Recombinant FGF2 was expressed in Escherichia coli strain FICE-127 transformed by
plasmid vector pFC80 that confers resistance to ampicillin and encodes FGF2 under the control
of the tryptophan promoter (the transformed FICE-127 strain was a gift from John Heath,
University of Birmingham, and was originally constructed by Antonella Isacchi, Amersham
Pharmacia Biotech and Upjohn). FICE-127 cells containing pFC80 were inoculated into LB
Medium (MP Biomedicals) containing 0.29 mmol/L (10 mg/dL) of ampicillin (Invitrogen) and
grown overnight at 37°C in a shaker at 250 RPM. The inoculum was diluted 1:100 in M9
Minimal Medium (Fisher Scientific) containing 1 g/L amino acids (Becton Dickinson) without
tryptophan to induce protein production. Cells were grown for 6 h at 37°C in a shaker at 250
RPM. Cells were collected by centrifugation at 8000 RPM for 10 m and kept frozen at -80°C.
Frozen cell pellets were resuspended in 6.94×10-2 mmol/L (100 mg/dL) lysozyme in GET buffer
(100 mmol/L Glucose, 10 mmol/L EDTA, and 50 mmol/L Tris, pH 8.0), vigorously agitated for
5 m and homogenized (Polytron; Kinematica) 5 times for 30 s each with break periods of 60-90 s
at 4°C to prevent overheating and denaturation of proteins.
Bacterial lysate was collected by centrifugation at 9,000 RPM for 10 m at 4°C. FGF2 was
then purified using affinity chromatography with FPLC (Pharmacia Biotech). Lysate was loaded
into 5 mL heparin Sepharose column (HiTrap, GE Healthcare) and allowed to bind for 2 h at
4°C. The FPLC system was programmed to wash the column with phosphate buffered saline
(PBS) containing incrementally concentrated NaCl with a linear gradient (150 mmol/L to 2000
mmol/L). Elutions were collected in sequential 1 mL fractions, with FGF2 eluting at 1400
mmol/L to 1600 mmol/L NaCl. The FGF2 solution was desalted by centrifugation using
5
centrifugal filters with 10 kDa molecular weight cut-off (Centricon, Millipore). After each
purification, the presence of FGF2 was confirmed at a 18kDa band using SDS-PAGE, and
protein concentration was quantified with a BCA assay (Pierce). Bioactivity of FGF2 was
confirmed by in vitro proliferation assays using bovine aortic endothelial cells.
Fluorescence Labeling of FGF2
A heparin Sepharose column (HiTrap, GE Healthcare) was loaded with 1 mL of 0.12
mmol/L (200 mg/dL) FGF2 in PBS and allowed to bind for 1 h at room temperature. The FGF2loaded column was washed with 5 mL of 100 mmol/L NaHCO3 to increase the pH to 8.3 and
loaded with 1 mL of 1.60 mmol/L (100 mg/dL) Texas Red succinimidyl ester (Invitrogen). Texas
Red succinimidyl ester was allowed to react with FGF2 for 10 m at room temperature. The
column was then placed in-line on the FPLC system, and FGF2 was eluted as described above.
Elutions of 1 mL were collected and assayed for protein content (absorbance at 280 nm, FPLC
System) and Texas Red fluorescence intensity (595 nm/615 nm excitation/emission wavelengths,
Fluoroskan II, Lab Systems Oy). Texas Red was appropriately conjugated to FGF2 as indicated
by the concurrence of the elution peaks of fluorescence intensity and protein concentration. Both
were came off the column between 1400 to 1600 mmol/L NaCl, similar to the elution range of
unlabeled FGF2, suggesting that Texas Red conjugation did not change the heparin binding
properties of FGF2. Buffer exchange was performed on the Texas Red labeled-FGF2 (TR-FGF2)
solution by centrifugation as above. SDS-PAGE indicated that the molecular weight of TR-FGF2
is not significantly different from that of FGF2. Fluorescence intensity was calibrated to protein
concentration prior to delivery using microplate fluorometry (Fluoroskan).
6
Recombinant S35-FGF1 Production
35
S-FGF1 was chosen as a model for FGF in the in-vivo setting because its high detection
sensitivity allows for the possibility of tracking spatial drug distribution in the setting of
controlled delivery of therapeutic doses. It also presents a safer alternative to using 125I labeled
FGF2 in-vivo. Recombinant human FGF1 was expressed in Escherichia coli strain BL21-pLysS
transformed by plasmid, pET3c that confers resistance to ampicillin and encodes FGF1 (obtained
as a gift from the late Dr. Thomas Maciag, Maine Medical Center, Portland, ME). Transfected
bacteria stocks were added to LB medium (MP Biomedicals) containing 100 µg/mL
Carbenicillin and 35 µg/mL Chloramphenicol (Sigma-Aldrich) and incubated with vigorous
shaking at 250 RPM at 37°C overnight. Bacteria culture was then diluted in antibiotics-free LB
medium (1:40 v/v of bacteria/medium) and incubated with vigorous shaking at 250 RPM and the
optical density of the solution was measured at 600 nm. When cell culture reached an optical
density of 0.6-0.8 bacteria were centrifuged and resuspended in DMEM medium deficient in Lcysteine and L-methionine (Invitrogen) supplemented with 1 % L- glutamine and 7.15 mCi of
35
S (Promix L-[35S]Methionine and Cysteine, GE Healthcare Life Sciences) and buffered with 25
mM HEPES (Invitrogen) and then induced with 0.4 mM IPTG for 3 h with shaking at 250 RPM
at 37°C. Cells were then collected by centrifugation at 8000 RPM for 10 m and kept frozen at 80°C.
Frozen cell pellets were resuspended in 1mg/ml lysozyme in GET buffer (50 mM Tris, 10
mM EDTA, 100 mM glucose, pH 8.0), mixed well for 5 m and then homogenized (Polytron;
Kinematica) 5 times for 30 s each with break periods of 60-90 s at 4°C to prevent overheating
and denaturation of proteins. Cell lysate was collected by centrifugation at 9,000 RPM for 10 m
7
at 4°C. 35S-FGF1 was then purified using affinity chromatography with FPLC. Bacterial lysates
were loaded into 5 ml heparin sepharose column (HiTrap Heparin HP column, GE Healthcare
Life Sciences) and allowed to bind for 1 h at room temperature. The FPLC system was
programmed to wash the column with PBS and gradually increase NaCl concentration with a
linear gradient (0.15-2 M). Elutions of 1 mL were collected and assayed for protein
concentration (absorbance at 280 nm, FPLC System) and radioactivity (2500TR Liquid
Scintillation Analyzer, Packard). Elution peaks of protein concentration and radioactivity
coincided. The 35S protein product came out of the heparin sepharose column at 1.4 M to 1.6 M
NaCl, similar to FGF1, and indicating 35S was incorporated in FGF1. 35S-FGF1 solution was
desalted by centrifugation using centrifugal filter devices with a 10 kDa molecular weight cut-off
(Centricon, Millipore). After each purification, the presence of FGF1 was confirmed at a 18 kDa
band using SDS-PAGE and protein quantification was carried out using BCA assay (Pierce).
Bioactivity of FGF1 was confirmed in proliferation assays of bovine aortic endothelial cells.
FGF1 was further purified from any endotoxin contamination using endotoxin removing
columns (Detoxi-Gel AffinitiPak columns, Pierce), and the FGF1 purity was confirmed with
limulus amebocyte lysate assay (Pyrotell-T, Associates of Cape Cod Inc., MA). Purification was
continued (typically 2-3 times) until endotoxin concentration is below 0.01 EU/µg FGF1.
Fabrication and Kinetics of Controlled Release Device
A slurry mixture of heparin-Sepharose beads/alginate solution was prepared by mixing
sterilized heparin-Sepharose microbeads (GE Healthcare) with filter-sterilized sodium alginate
(Sigma-Aldrich, 5 %), placed in a customized 20mm × 20mm × 1mm glass mold, and incubated
overnight in filter-sterilized 10 % CaCl2. The heparin-Sepharose embedded sodium alginate
8
material is exposed to CaCl2 through two open surfaces of the mold. The gel was further
incubated in the 10 % CaCl2 for 24 h to allow thorough cross-linking of the polymer after being
taken out of the mold under UV light for sterilization. The hardened polymeric gel device was
then incubated in 35S-FGF1 solution for 48 h prior to experiment to allow complete and uniform
loading of drug.
To characterize 35S-FGF1 release kinetics from the device, 8 mm diameter circular shape
devices were made from the 20 × 20 × 1 mm3 polymeric slab using 8 mm biopsy punch (Miltex).
These circular devices were incubated in 1 ml PBS and gently agitated throughout the
experiment with a shaker. At various time points the elution mixture was collected and assayed
for 35S activity using liquid scintillation counter (Packard). Fresh PBS was used to renew the
elution buffer.
9
Supplemental Results
FGF is Washed-out Through Microvascular Clearance Followed Ex-vivo Myocardial
Delivery
35
S-FGF1 was observed in the perfusate at the outflow soon after 35S-FGF1 was delivered
at epicardial surface (Figure S2), suggesting that capillary washout was indeed responsible for
the limited penetration of this growth factor in the presence of perfusion (Figure 1). These results
were further compared to analytical model results of cumulative drug clearance (Eqn S17)
calculated using pharmacokinetic parameters of FGF-2 (k = 1.15 ± 0.06×10-4 s-1and D=0.02
µm2/s) derived from experiment. The experimental results fit the model well within one order of
magnitude, suggesting that the pharmacokinetics of
35
S-FGF1 are well explained by our
diffusion with clearance model and moreover that the clearance constants and diffusivities of
35
S-FGF1 and TR-FGF2 are similar.
10
Figure Legends:
FIGURE S1: Isolated perfused heart apparatus. Rat coronary arteries were perfused
antegrade through an aortic canula at constant physiologic mean pressure while a constant, well
mixed drug source was applied to the epicardial surface. Spatial drug distribution was quantified
in myocardial tissue regions exposed to drug. High magnification schematic illustrates the
examined physiologic forces: drug diffusion within tissue and clearance through convection by
intravascular flow after permeation across capillary wall.
FIGURE S2: FGF is Washed-out Through Microvascular Clearance Followed Ex-vivo
Myocardial Delivery.
35
S-FGF1 in the outflow perfusate was measured as a function of time
after local epicardial 35S-FGF1 delivery (n=3). Experimental washout of
35
S-FGF-1 (in blue) is
well explained by Eq. S17 (magenta line) using the parameter values of TR-FGF2.
11
References
1.
Tzafriri AR, Lerner EI, Flashner-Barak M, et al. Mathematical modeling and
optimization of drug delivery from intratumorally injected microspheres. Clin Cancer
Res. Jan 15 2005;11(2 Pt 1):826-834.
2.
Crank J. The mathematics of diffusion. 2d ed. Oxford, [Eng]: Clarendon Press; 1979.
12
FIG-S1
FIG-S2