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Intravitreal injection of anti-VEGF (vascular endothelial growth factor) antibodies or antibody fragments has been shown to be a highly effective treatment for neovascular age-related macular degeneration (wet AMD). The ocular half-life (t1/2) of these large molecules, determined in ocular fluids or derived from serum levels, varies with molecular size and is larger in humans than in preclinical animal species. The high affinity binding of VEGF to these molecules lowers the free concentration of VEGF and reduces its occupancy on VEGF receptors in ocular tissues. To understand the biophysical determinants of t1/2 for anti-VEGF antibodies and the time-course of VEGF in ocular fluids, we developed a mechanistic model of intravitreal pharmacokinetics (IVT PK) for anti-VEGF antibodies and combined it with a mechanistic model of the pharmacodynamics (RVR PD) of VEGF suppression by ranibizumab, an anti-VEGF recombinant, humanized monoclonal antibody fragment (Fab). Our IVT PK model predicts that the ocular t1/2 of a large molecule will be approximately four-times the calculated value of its vitreous diffusion time (Tdiff), defined as rvit(2)/6D, where rvit is the radius of the vitreous chamber in that species (modeled as a sphere), and D is the diffusion coefficient of the molecule in physiological saline at 37 °C obtained from the Stokes-Einstein relation. This prediction is verified from a compilation of data and calculations on various large molecules in the human, monkey, rabbit, and rat and is consistent with the reported t1/2 values of ranibizumab in humans (mean value 7.9 days) and the calculated Tdiff of 1.59 days. Our RVR PD model is based on the publication of Saunders et al. (Br. J. Ophthalmol. 2015, 99, 1554-1559) who reported data on the time-course of VEGF levels in aqueous humor samples obtained from 31 patients receiving ranibizumab treatment for wet AMD and developed a compartmental mathematical model to describe the VEGF suppression profiles. We modified Saunders' model with the known 2:1 stoichiometry of ranibizumab-VEGF binding and included the association and dissociation kinetics of the binding reactions. Using the RVR PD model, we reanalyzed Saunders' data to estimate the in vivo dissociation constant (KD) between ranibizumab and VEGF. Our analysis demonstrates the delicate interrelationship between the in vivo KD value and the intravitreal half-life and yields an in vivo KD estimate that is appreciably larger than the in vitro KD estimates reported in the literature. Potential explanations for the difference between the in vivo and in vitro KD values, which appear to reflect the different methodologies and experimental conditions, are discussed. We conclude that the combined mechanistic model of IVT PK and RVR PD provides a useful framework for simulating the effects of dose, KD, and the molecular weight of VEGF-binding molecules on the duration of VEGF suppression.

Original publication




Journal article


Molecular pharmaceutics

Publication Date





2941 - 2950


Wolfson Centre For Mathematical Biology, Mathematical Institute, Andrew Wiles Building, University of Oxford, Radcliffe Observatory Quarter , Woodstock Road, Oxford OX2 6GG, U.K.


Animals, Rabbits, Haplorhini, Humans, Rats, Angiogenesis Inhibitors, Vascular Endothelial Growth Factor A, Kinetics, Models, Theoretical, Wet Macular Degeneration, Intravitreal Injections, Ranibizumab