This study describes the theoretical background necessary for a systematic design process of an implantable artificial kidney and provides a basic tool for further design stages. In designing an implantable artificial kidney, the natural stages of blood filtration in the kidney, including glomerular filtration (blood cell separation) and tubular separation (ion separation), are followed. The focus of this study is on pore design and the hydrodynamics of plasma, which is considered a Newtonian fluid after the pore inlet, during hemo-filtration with a varying pore longitudinal cross-section in a solid membrane. To prevent membrane clogging, two pore geometry solutions are proposed and justified in detail. One optimizes pore entrance shape and the other uses a diffuser-nozzle channel to provide backwash which removes undesired deposits on membrane pores. In the micro-filtration of fluids, pore geometry, pore size ratio, and pore edge shape affect fluid hydrodynamics in terms of pressure drop, velocity, shear stress, and flow rate. The calculation results indicate that a diffuser channel provides a smaller pressure drop than that produced by a straight channel for a variety of cross sections (rectangular, elliptical, and circular).