What role does the peritoneal membrane play in peritoneal dialysis?

The peritoneal membrane acts as the dialyzing surface during peritoneal dialysis. This membrane, which lines the abdominal cavity, facilitates the diffusion and osmosis of solutes and fluids between the blood and the dialysis solution that is instilled into the peritoneal cavity. This process effectively removes waste products and excess fluid from the blood, thereby serving the key function of filtration similar to that of a kidney.

The other options mentioned do not accurately define the role of the peritoneal membrane. The connection to a dialysis machine, the provision of oxygen, and the collection of waste are functions associated with different components of the dialysis process or organs and systems within the body, rather than the specific role of the peritoneal membrane in peritoneal dialysis.