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.
|Publication date||Dec 2009|
The PhD project was an industrial PhD programme with a collaboration between Department for informatics and mathematical modelling (IMM), Technical University of Denmark and Biomodelling, Novo Nordisk A/S (NN)