Peritoneal dialysis (PD) is a kidney replacement therapy for patients with end-stage renal disease. It is becoming more popular as a result of a rising interest in home dialysis. Its effectiveness depends on several physiological and technical factors, which have led to the development of various computational models to better understand and predict PD outcomes. In this review, we traced the evolution of computational PD models, discussed the principles underlying these models, including the transport kinetics of solutes, the fluid dynamics within the peritoneal cavity, and the peritoneal membrane properties, and reviewed the various PD models that can be used to optimize and personalize PD treatment. By providing a comprehensive overview, we aim to guide both current clinical practice and future research into novel PD techniques such as the application of continuous flow and sorbent-based dialysate regeneration where mathematical modeling may offer an inexpensive and effective tool to optimize design of these novel techniques at a patient specific level.

Keywords: mathematical modeling; parameter determination; peritoneal dialysis; solute flux; volume flux.