The invention provides a method and an apparatus or system for dialysis. The method and apparatus or system are useful for removing an undesirable protein-binding substance such as a toxin from a biological fluid such as blood or blood plasma. As such, the method and apparatus or system are useful for treating a subject in need of dialysis such as a subject suffering from hepatic disease. The methods feature a) dialyzing a biological fluid against a dialysis fluid containing an adsorber for a protein-binding substance to be removed through a semipermeable membrane, b) adjusting the dialysis fluid so that the binding affinity of the adsorber for the protein-bound substance to be removed is lowered and the substance to be removed passes into solution, and c) balancing the volume or flow of one or more fluids in the apparatus or system suitable for dialyzing a biological fluid containing a protein-binding substance to be removed. The apparatus or system features a) a biological fluid circuit (3)； b) a dialysis fluid circuit (2)； c) a means (4； 6； 7； 8； 9) for solubilizing the protein-binding substance to be removed； d) a dialysis, filtration or diafiltration device (5)； e) a balancing system or apparatus suitable for balancing the volume or flow of one or more fluids in the apparatus or system suitable for dialyzing a biological fluid containing a protein-binding substance to be removed； and f) a dialysate regeneration unit.
