Dynamical control of the dialysis process. Part I: Structural considerations and first mathematical approach

Area of Science:

• Biomedical Engineering
• Control Systems
• Nephrology

Background:

• Dialysis requires precise control of multiple physiological variables for individual optimization.
• Current methods often lack a unified approach for managing these complex parameters.
• Hemodynamic stability is a critical factor during dialysis, yet difficult to model mechanistically.

Purpose of the Study:

• To introduce a general concept for multiple-input-multiple-output (MIMO) control of the dialysis process.
• To develop a two-stage controller addressing both mechanistically modeled and hemodynamically relevant variables.
• To enable optimized dialysis treatment with enhanced patient stability.

Main Methods:

• A two-stage controller was designed, integrating an expert system (Stage 1) and a tracking controller (Stage 2).
• Stage 1 links primary controlled variables (PCVs) to secondary controlled variables (SCVs) for hemodynamic stability.
• Stage 2 employs a novel multidimensional tracking algorithm for precise trajectory control of PCVs.

Main Results:

• The developed algorithm successfully tracks prescribed trajectories for key variables like plasma ion concentrations and volume status.
• The system demonstrated accurate control of plasma Na+, plasma K+, plasma volume, and intra/extracellular volume ratio.
• Control variables including dialysate Na+, dialysate K+, and ultrafiltration rate were effectively managed.

Conclusions:

• The proposed MIMO control concept offers a mathematically simple and effective approach to dialysis optimization.
• The controller ensures exact tracking of desired variable profiles within physical and physiological constraints.
• This method is extendable to more controlled variables and applicable to both open-loop and future closed-loop systems.