MOESM1 of Determination of physiological parameters for endogenous glucose production in individuals using diurnal data

Preprocessing of data set 1 (experimental data set). Ref. [28] gives mean data input curves of 20 subjects. To test the new procedure developed in this paper, a set of data curves for plasma glucose ( Gp), plasma insulin ( Ip) and insulin secretion rate (ISR) for a single subject needed to be generated that would produce the mean EGP data curves of the 20 subjects. To this end, the parameters (p), kp2, kp3 and kp4 plus additional parameters representing the mean input data (i.e. Gp, Ip and ISR) at time points 20, 30, 60, and 90 minutes for 3 meals (see below), were optimized using the gradient-based least squares solver lsqnonlin in MATLAB (see Additional file 1: Figure S1). This was performed by minimizing the preprocessing experimental data objective function (Eq. 24): Obj(p)=(EGPi,jcalc(p,t)−EGPi,jexp(t))2,(24) $ Obj (p) = \sqrt {(EGP_{i,j}^{calc}(p,t) - EGP_{i,j}^{exp}(t))^{2}}, \qquad \text {(24)} $ wherein the function Obj is defined as the squared difference between the Dalla Man [20] model output (EGPi,jcalc$EGP^{calc}_{i,j}$) and experimental EGP (EGPi,jexp$EGP^{exp}_{i,j}$) for every time step, i, and for breakfast, lunch and dinner, j. For experimental data (EGPi,jexp$EGP^{exp}_{i,j}$) in Eq. 24 is taken from Saad et al. [28].The additional parameters for single-subject Gp, Ip, and ISR at t=20, 30, 60, and 90 minutes were defined as the shifts from the mean data values and were constrained within ±10 mg/dl, ±25 pmol/l, and ±1 pmol/kg/min, respectively. Additional file 1: Table S1 displays the values for these shifts that resulted from the optimization procedure. The resulting single-subject data were used as data set 1 (Fig. 2).