Understanding the interaction of electric fields with the complex anatomy of biological excitable media is key to optimizing control strategies for spatiotemporal dynamics in those systems. On the basis of a bidomain description, we provide a unified theory for the electric-field-induced depolarization of the substrate near curved boundaries of generalized shapes, resulting in the localized recruitment of control sites. Our findings are confirmed in experiments on cardiomyocyte cell cultures and supported by two-dimensional numerical simulations on a cross section of a rabbit ventricle.