Mathematical models for the effect of anti-vascular endothelial growth factor on visual acuity

Abstract

The standard of care treatment for neovascular age-related macular degeneration, delivered as ocular injection, is based on anti-vascular endothelial growth factor (anti-VEGF). The course of treatment may need to be modified quickly for certain patients based on their response. Models that track both the concentration and the response to an anti-VEGF treatment are presented. The specific focus is to assess the existence of analytical solutions for the different types of models. Both an ODE-based model and a map-based model illustrate the dependence of the solution on various biological parameters and allow the measurement of patient-specific parameters from experimental data. A PDE-based model incorporates diffusive effects. The results are consistent with observed values, and could provide a framework for practitioners to understand the effect of the therapy on the progression of the disease in both responsive and non-responsive patients.

Appendix

Table 2 Parameter values

Parameter values from the literature are listed in Table 2, along with dimensionless parameters computed from our definitions. Here the subscripts “A” and “B” refer to two different medications with different dosage recommendations.

The value of $k_C$ was calculated using the quoted value of a half-life of 9 days in Mulyukov et al. (2018). The values of $\kappa$ were calculated using a time of 28 days between visits. The value of $R_{\mathrm{l}}$ was calculated as a rough average of the measured values in Bergmanson and Martinez (2017). The values of $R_{\mathrm{i}}$ and $R_{\mathrm{i}}$ were chosen to maximize $R_{\mathrm{d}}$. The value of $D_{\mathrm{d}}$ was calculating using the treatment B dosage. The value of V is that for the vitreous fluid, not the entire eyeball.