Optimal Equidose Inputs and Role of Measurement Error for Estimating the Parameters of a Compartmental Model of Glucose Kinetics from Continuous- and Discrete-Time Optimal Samples CLAUDIO COBELLI zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCB AND KARL THOh4ASETH Instiiute for System Dynamics and Bioengineering (LA DSEB-CNR), Padua, Ita[y, and Department of Electronics and Informatics, University of Padua, Italy Received 22 July I987; revised 10 December 1987 ABSTRACT The optimal input design for estimating all the parameters of a two-compartment model of glucose kinetics is studied. The problem is solved by simulation for the class of equidose rectangular-shaped inputs with both continuous- and discrete-time optimal sam- ples. The important role of the measurement error in determining the optimal input is analyzed by examining four error structures. With continuous-time measurements the optimal input depends on the measurement error, but rather efficient suboptimal inputs can be obtained with small infusion periods. The impulse input is optimal among the considered error structures with discrete-time optimal samples. 1. INTRODUCTION In a previous paper [l] we have studied the optimal-input-design problem for individually estimating any of the parameters of a two-compartment model of glucose tracer kinetics, assuming continuous-time measurements for both equienergy and equidose classes of admissible inputs. Dealing with one parameter at a time allowed us to solve the optimal-input problem within the classical framework of the Pontryagin maximum principle. The scalar case is however of limited interest in practice, because of the correla- tion of the parameter estimates. In this paper we study the design of the optimal input for estimating simultaneously the parameters of the same two-compartment model of glucose tracer kinetics. Optimal inputs are determined not only for continuous-time measurements but also for the discrete-time optimal sampling scheme. The equidose class of admissible inputs is considered, and within it only rectangular test inputs are admitted in view of their practical relevance. Finally, particular attention is devoted to examining the role of the measurement error in determining the optimal MATHEMATICAL BIOSCIENCES 89:135-147 (1988) OElsevier Science Publishing Co., Inc., 1988 52 Vanderbilt Ave., New York, NY 10017 135 0025-5564/88/$03.50