No abstract

This paper provides a mathematical approach to study metasurfaces in nonflat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase discontinuities. The approach contains both the near and far field cases. A starting point is the formulation of a vector Snell's law in the presence of abrupt discontinuities on the interfaces.

A metasurface is a surface, typically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function must satisfy, i.e., Monge-Ampère partial differential equations, and we prove the existence of solutions.

Guiding the dose selection for monoclonal antibody oncology drugs is often done using methods for predicting the receptor occupancy of the drug in the tumor. In this manuscript, previous work on characterizing target inhibition at steady state using the AFIR metric [1] is extended to include a "target-tissue" compartment and the shedding of membrane-bound targets. A new potency metric AFTIR (Averarge Free Tissue target to Initial target ratio at steady state) is derived, and it depends on only four key quantities: the equilibrium binding constant, the fold-change in target expression at steady state after binding to drug, the biodistribution of target from circulation to target tissue, and the average drug concentration in circulation. The AFTIR metric is useful for guiding dose selection, for efficiently performing sensitivity analyses, and for building intuition for more complex target mediated drug disposition models. In particular, reducing the complex, physiological model to four key parameters needed to predict target inhibition helps to highlight specific parameters that are the most important to estimate in future experiments to guide drug development.Guiding dose selection of monoclonal antibodies 3