What is the medical term for the removal of urine substances from blood through a membrane?

The correct term for the removal of urine substances from blood through a membrane is dialysis. This process is specifically designed to filter and cleanse the blood of waste products when the kidneys are unable to perform this function adequately. During dialysis, a dialysis machine or artificial kidney uses a semipermeable membrane to separate unwanted substances from the blood, allowing for the removal of toxins and excess fluids.

In contrast to the other terms, purge generally refers to the act of clearing or eliminating something—often relating to the digestive system—and is not specific to the filtration of blood. Filtration refers more broadly to a process that separates solids from liquids or gases, which while it does involve a membrane, is not specific to the medical context of blood purification. Hemolysis is the destruction of red blood cells, which is unrelated to the process of clearing waste from the blood. Therefore, the specific mechanism and context of dialysis make it the correct answer.