Problem#3Mimicking nature by codelivery of stimulant and inhibitor

Complex formation rate 28 koff 11 104 s1 vegf anti

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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 and vein. 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.

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