1 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Chemical and Biochemical Engineering, Technical University of Denmark4 Department of Applied Mathematics and Computer Science, Technical University of Denmark
The thesis deals with the development of "Predictive tools for designing new insulins and treatments regimens" and consists of two parts: A model based approach for bridging properties of new insulin analogues from glucose clamp experiments to meal tolerance tests (MTT) and a second part that describes an implemented software program able to handle stochastic differential equations (SDEs) with mixed effects. The thesis is supplemented with scientific papers published during the PhD. Developing an insulin analogue from candidate molecule to a clinical drug consists of a development programme including different phases targeting safety and efficacy. The focus of this thesis is the shift from Phase I, targeting safety, to Phase II, targeting efficacy. An insulin analogue is typically tested for safety in glucose clamp experiments in Phase I clinical trials and progresses into Phase II where dose and efficacy are investigated. Numerous methods are used to quantify dose and efficacy in Phase II - especially of interest is the 24-hour meal tolerance test as it tries to portray near normal living conditions. Part I describes an integrated model for insulin and glucose which is aimed at simulating 24-hour glucose profiles from a MTT with treatments based on the new insulin analogue that previously only has been tested in clamps. The bridge between insulin analogue properties determined in clamp experiments to meal tolerance test outcomes in Phase II trials is not simple and is complicated by shifts in experimental setup, time horizon and treatment regimen. A bridging strategy was introduced where an integrated model simulating MTTs was extended with models developed on clamp data that described PK and PD for the new insulin analogue. The bridging strategy was tested by building an integrated model based on human insulin trials which was then evaluated using insulin Aspart (IAsp). The integrated model was estimated in two separate sub models due to computational complexity. Insulin model challenges were faced at the estimation step regarding separability of insulin input pathways (exogenous/secretion) which resulted in several fixed parameters but also an insulin delivery model as opposed to a prehepatic insulin secretion model coupled with hepatic extraction. The glucose model was an extended version of the oral glucose minimal model [Man et al., 2002] which had a meal function incorporated. The two sub models were combined into an integrated model which was evaluated in different scenarios: An iso-glucaemic glucose clamp, an insulin tolerance test and comparing derived measures of glucose eeffectiveness. The model evaluation pinpointed insulin sensitivity issues which were accommodated with a change in model building towards a more insulin sensitive model type. Conclusively, the integrated model fitted estimation data well both for insulin and glucose. Furthermore, the evaluation scenarios showed overall correspondence with literature with only minor discrepancies. The evaluation on insulin Aspart required a PK model for IAsp and a model describing IAsp action in MTTs. The IAsp PK model was available from a different Novo Nordisk project and the action transfer function was estimated on cross-over clamp data with human insulin and insulin Aspart. The two components were then embedded into the integrated model. The extended integrated model was used to simulate 24-hour profiles of insulin and glucose from meal tolerance tests including treatments with biphasic insulin Aspart. The evaluation showed that the extended integrated model was able to predict insulin levels reasonably both mean profile and variation whereas glucose proles were not predicted accurately. Post modelling analysis targeting both insulin and glucose components showed that preconditions for the bridging strategy which implied the use of a mean IAsp PK model, could be the cause for the mis-predictions. Future research should look into ways for individualising the insulin treatment when no information on individual level is present. The model building process could have benefitted from the use of SDEs. Unfortunately, availability of a software program able to handle mixed effects and SDEs resulted in a modelling approach based on ordinary differential equations. The absence of such a program motivated the development of new a tool with PK/PD features, SDEs and mixed effects. Part II presents a software package which was developed in order to be able to handle SDEs with mixed effects. The package was implemented in R which allowed for a single environment for data preparation, model building and results handling but also provided accessibility for users and ease of installation. The R-package implements the (Extended) Kalman Filter for handling SDEs and uses the FOCE approximation to calculate the marginal likelihood for parameters used in maximum likelihood estimation. A number of applications of PSM are presented in which deconvolution is the topic for most. Deconvolution based on SDEs was used to determine pre-hepatic insulin secretion rates; hepatic insulin extraction rates using both insulin and C-peptide measurements, and glucose appearance rates constrained to be in the positive range in a simulated minimal model setting. More applications included an insulin secretion model based on an intervention model type and an analysis of in fluence from input error propagation as estimated with ODEs and SDEs.
Main Research Area:
Madsen, Henrik, Kristensen, Niels Rode
Technical University of Denmark, DTU Informatics, Building 321, 2009