Step 1: Understand the Process of Blood Purification.
An artificial kidney is used to perform dialysis, a process that removes waste products and excess fluids from the blood when the kidneys are unable to function properly. The specific type of dialysis performed using an artificial kidney is called haemodialysis.
Step 2: Analyze Each Option.
Option (1): Dialysis — Incorrect, as "dialysis" is a general term for the process of removing waste products from the blood. While haemodialysis is a type of dialysis, this option is too broad.
Option (2): Haemodialysis — Correct, as this is the specific process performed using an artificial kidney.
Option (3): Filtration — Incorrect, as filtration is a broader term that describes the separation of substances based on size, not the specific medical procedure performed by an artificial kidney.
Option (4): None of these — Incorrect, as haemodialysis is a valid and well-known medical procedure.
Step 3: Final Answer.
$$
(2) \mathbf{\text{Haemodialysis}}
$$