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Mathematical modelling of thyrotropic regulatory pathway provides important understanding on the working of hypothalamus-pituitary-thyroid axis. An ordinary differential
equation (ODE) model based on an existing model for euthyroid condition is used and the
model parameters are estimated to fit the available individual subject data using genetic
algorithms. A cosinor model for the circadian variation of thyroid hormones is used to obtain
more reliable results. This parameter determination method is tested on groups of subjects
with similar observations of thyrotropin (TSH), free tri-iodothyroine (FT3) and free thyroxine
(FT4 ), identified through clustering, to determine their parameter values jointly to estimate
parameter sets with lower variation than parameters determined independently.
The regulatory behaviour in case of hypothyroidism is also modelled where the circadian
variations in TSH in central and extreme primary hypothyroidism significantly differ from
that of euthyroidism. An ODE model for thyrotropic regulatory system, inspired by existing
models, encompassing both euthyroid and hypothyroid behaviours of thyroid hormones
is presented. This extended model is validated with clinical data from multiple sources for
general observable behaviours of thyroid hormones and TSH, data related to TSH circadian
variations, levo-thyroxine (LT4 ) and lio-thyronine (LT3) administration effects and TRH tests.
A methodology for detecting personalised model for hypothyroid subject data is developed
to determine optimal drug dosage range using satisfiability modulo theories (SMT) based
approach. A regression based initial drug dosage estimation scheme based on subject specific information is also presented. The results are validated through available data set of
hypothyroid subjects before and after treatment.
The identifiability of the model parameters is also considered. SMT based parameter
space exploration approach to determine parameter identifiable combination is introduced
for structurally unidentifiable models. For higher dimensional systems and for larger parameter space, computationally intractability of this method is mitigated to a large extent by
heuristically limiting the parameter space to be explored using Gaussian process regression
and gradient based approaches. This method is validated on multiple examples.
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Keywords:
Mathematical model, Thyrotropic regulation pathway, Hypothyroidism, Genetic
algorithms, Dosage estimation, Parameter estimation, Parameter identifiability, Satisfiability modulo theories (SMT)
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