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Unformatted text preview: ate (28).
koff ¼ 11 × 10−4 s−1 ¼ VEGF-anti-VEGF complex dissociation rate (28).
The constants were obtained from experimental measurements in other
published studies, as referenced beside each constant. In the model, the
VEGF-anti-VEGF-body complex was assumed to have no degradation. VEGF
and anti-VEGF were modeled to only degrade when not bound together. This
should have a negligent impact on the overall dynamics of the system due
to the small magnitude of degradation rates compared to koff . The release
function inside each layer of the scaffolds was determined by the initially
incorporated amount of protein multiplied by the instantaneous release
curve. Effective diffusion coefficients and degradation rates were assumed
to be time-invariant and spatially uniform. Because the effective diffusion
coefficients were experimentally measured, they were assumed to incorporate binding kinetics to the ECM proteins as well as uptake by cells. The
system geometry, equation system, and initial conditions were constructed
in COMSOL Multiphysics using the 3D coefficient form partial differentiation
equation model. The time-dependent system was solved, and the output was
exported and analyzed in Matlab.
2 Mouse Model of Hind-Limb Ischemia and Scaffold Implantation. Scaffolds were
implanted in 6-wk-old SCID mice (Taconic) that had undergone unilateral
ligation of hind-limb blood vessels to create a severe model of hind-limb
ischemia (18). The SCID model was chosen because it offered a stable loss
of perfusion over weeks and the angiogenic effects from inflammation were
reduced. Briefly, animals were anesthetized by i.p. injection of a 7∶1 mixture
of ketamine and xylazine. Ligation sites were made on the external iliac
artery and vein, and on the femoral artery and vein using 5–0 Ethilon
(Ethicon). The vessels were severed between the ligation sites. A scaffold was
implanted such that its rotational axis was perpendicular to the direction of
the severed vessels, with the round edge sitting on top of the muscle. This
orientation effectively made each layer parallel to the original femoral artery
17934 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1001192107 Analysis of Vascularization. Scaffolds and the surrounding muscles from the
ischemic hind limbs were retrieved after 1, 2, and 4 wk. Samples were
embedded in paraffin and sectioned onto slides, as illustrated in Fig. S1.
Detailed protocols are included in SI Text. Muscle and scaffold sections were
stained for CD31. Blood vessel densities, marked by CD31, were manually
determined in the entire scaffold and underlying muscle tissues as previously
described (1, 18). Measurements of the blood perfusion in the ischemic and
normal limb of the anesthetized animals (n ¼ 5) were performed using laser
Doppler perfusion imaging (LDPI; Perimed). To minimize variability due to
ambient light, temperature, and individual heart rate, perfusion in the
ischemic hind limb was normalized by the perfusion in the norma...
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This document was uploaded on 09/21/2013.
- Spring '13