DYNAMICAL CONTROL OF THE DIALYSIS PROCESS .1. STRUCTURAL CONSIDERATIONS AND FIRST MATHEMATICAL APPROACH

Individual optimization of the dialysis process requires the (open-loo p or closed-loop) control of many different variables, e.g. plasma ion concentrations, acid base state, volemic state and hemodynamic quanti ties. For this purpose a general concept for multiple-input-multiple-o utput (MIMO) control of the dialysis process is presented. Tile contro lled variables have been differentiated into variables which can be mo deled mechanistically (primary controlled variables, PCVs) and (hemody namic) variables for which no mechanistic model has been developed up to now (secondary controlled variables, SCVs). Accordingly the control ler is decomposed into two stages. Stage 1 contains an expert system w hich links the PCVs to the SCVs and provides the generation of optimal profiles for the PCVs with respect to maximum hemodynamic stability o f the patient. Stage 2 is a tracking controller for the PCVs. An algor ithm for the multidimensional tracking problem at stage 2 has been dev eloped. It can be used for open-loop and future closed-loop control. T he algorithm has been tested for 4 controlled (plasma Na+, plasma K+, plasma volume and ratio between intra- and extracellular volume) and 3 control variables (dialysate Na+, dialysate K+, ultrafiltration rate) up to now. It renders possible the exact tracking of the prescribed t rajectories as long as all points are reachable under consideration of all physical and physiological boundary conditions. If they are not, appropriate weighting of the conflicting optimization goals must be ap plied. An extension towards more than 4 controlled variables is possib le on principle. Main advantages of the method are its mathematical si mplicity and the applicability of standard optimization subroutines.