Numerical analysis of the electrical effects accompanying nanocolumn patterning at the cathode-organic interface in an injection-limited, single-layer organic light-emitting diode (SLOLED) is conducted. We introduce a carrier-decoupled framework based on the Scott-Malliaras current injection mechanism in the double-sided, injection-limited current regime to simplify the multi-dimensional semiconductor equations in order to analyze the device function in the presence of a periodic nanocolumn array. A semi-analytical treatment is developed to solve the drift-diffusion equations. A common problem in SLOLEDs is unbalanced carrier currents arising from asymmetric injection and transport characteristics. The numerical results for the cathode nanopatterned device predict increased current injection with strongly asymmetrical current enhancement, which is shown to promote carrier injection parity in electron-deficient, single-layer devices by preferentially augmenting cathode-side injection current. Finally, the recombination current enhancement is attained and is shown to be increased by a factor of 8.52 and 3.00 when comparing the nanopatterned SLOLED device with planar devices of thicknesses equal to the unpatterned thickness and nanoimprint-thickness-reduced devices, respectively.