Stuck in Modelling – Attempts to describe disease progress and the action of oral hypoglycaemic agents in type 2 diabetes
Nick Holford (1), Jenny Chien (2), Vikram Sinha (2), David Manner (2), Michael Heathman (2), Jeanne Geiser (2)
(1) Dept of Pharmacology & Clinical Pharmacology, University of Auckland, Auckland, New Zealand; (2) Lilly Research Laboratories, Indianapolis, USA
Background: The modeling of time course of glucose and insulin changes during prolonged treatment with oral hypoglycaemic drugs has to consider disease progression mechanisms as well as drug action. De Winter et al. (1) proposed a mechanism-based model for changes in beta cell function and insulin potency during treatment with gliclazide (GLZ), metformin (MET) and pioglitazone (PIO).
Methods: Steady state solutions to modified HOMA for glucose-insulin regulation models (2-4) were used to describe glucose and insulin responses to changes in beta cell function (BF) and insulin potency (IP). Models for disease progress and effect compartment concentrations of drug treatments were implemented using differential equations. Predictions of glucose and insulin can be obtained by solving a system of algebraic equations. This solution is not required to solve the differential equations but NONMEM attempts to solve both algebraic and differential equations simultaneously. Parameter estimation used ADVAN9 in NONMEM VI level 1.3.
Results: Run times for this problem were extremely long even with the simplest glucose-insulin regulation model. The algebraic equation solver failed at initialization when random effects were added to the baseline BF and IP parameters for more complex regulation models. Therefore it was not possible to use these more realistic regulation systems.
Conclusions: Possible solutions to the problem include 1) calling a root finder subroutine to obtain the algebraic equation solutions independently of the solution to the differential equations 2) using a closed form solution to the algebraic equations (only possible for very simple regulation models) 3) using a more robust estimation method (e.g. MCPEM or SAEM) 4) using a parallel processing implementation (e.g. S-ADAPT).
References:
[1] de Winter W, DeJongh J, Post T, Ploeger B, Urquhart R, Moules I, et al. A mechanism-based disease progression model for comparison of long-term effects of pioglitazone, metformin and gliclazide on disease processes underlying Type 2 Diabetes Mellitus. J Pharmacokinet Pharmacodyn. 2006;33(3):313-43.
[2] Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC. Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man. Diabetologia. 1985;28(7):412-9.
[3] Sturis J, Polonsky KS, Mosekilde E, Van Cauter E. Computer model for mechanisms underlying ultradian oscillations of insulin and glucose. Am J Physiol. 1991;260(5 Pt 1):E801-9.
[4] Silber HE, Jauslin PM, Frey N, Gieschke R, Simonsson US, Karlsson MO. An integrated model for glucose and insulin regulation in healthy volunteers and type 2 diabetic patients following intravenous glucose provocations. J Clin Pharmacol. 2007;47(9):1159-71.
