Frontiers in hemodialysis: Solutions and implications of mathematical models for bicarbonate restoring

Acid–base correction is one main goal of hemodialysis therapy, some aspects of which are not yet well understood. This work considers a novel mathematical model of the patients’ response to the rapid addition of base, providing closed-form analytical expressions for the bicarbonate concentration in the patient blood versus the time on dialysis, in function of the main physiological/clinical parameters. A signal processing model of the dialysis is proposed, in which the metabolic processes are represented by a combination of first-order linear systems with input step-signals that correspond to the external stimuli. The model sheds a light on important features of the therapy, highlighting the main medical implications, and revealing new challenges. With current dialysis protocols, it is shown that the base added actually decreases during the last two-thirds of the therapy, and the net amount of bicarbonate in the patient blood does not reach a steady-state value. Elaborating on the mathematical model, more sophisticated clinical protocols are suggested to counteract the potentially maladaptive patient response to treatment.