1. A method of modeling a concentration of citrate and calcium in dialyzing blood of a patient, the method comprising the computer implemented steps of: a) determining a blood flow rate from and back to the patient through an extracorporeal dialysis circuit including a dialyzer having semi-permeable dialysis membranes and a dialysate chamber surrounding the membranes; b) determining a flow rate through the dialysate chamber of the dialyzer of a dialysate that includes a predetermined amount of calcium and a predetermined amount of citrate, the amount of calcium eliminating the need for calcium addition into the blood downstream of the dialyzer; and c) computing an amount of citrate to be introduced into the blood, upstream of the dialyzer, such that ionized calcium is reduced upstream of the dialyzer to a concentration that is sufficiently small to reduce clotting of the flowing blood without the necessity for periodic measurement of a systemic ionized calcium in the blood of the patient, and such that the systemic ionized calcium in the blood of the patient is predicted using a mathematical model to avoid systemic hypo- or hypercalcemia in the patient.