Maximum likelihood estimation of
a time-inhomogeneous stochastic differential model of glucose dynamics
U. Picchini, S. Ditlevsen and A. De Gaetano
Published on
Mathematical Medicine and Biology (2008) 25(2):141-155.
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preprint (492 Kb, pdf)
Stochastic differential equations (SDEs) are assuming an important role in the definition
of dynamical models allowing for explanation of internal variability (stochastic noise).
SDE models are well-established in many fields, such as investment finance, population
dynamics, polymer dynamics, hydrology and neuronal models. The metabolism of glucose
and insulin has not yet received much attention from SDE modellers, except from
a few recent contributions, because of methodological and implementation difficulties in
estimating SDE parameters. Objectives: here we propose a new SDE model for the dynamics
of glycemia during a euglycemic hyperinsulinemic clamp experiment, introducing
system noise in tissue glucose uptake, and apply for its estimation a closed-form Hermite
expansion of the transition densities of the solution process. Results: the present
work estimates the new model parameters using a computationally efficient approximate
maximum likelihood approach. By comparison with other currently used methods, the
estimation process is very fast, obviating the need to use clusters or expensive mainframes
to obtain the quick answers needed for everyday iterative modeling. Furthermore, it can
introduce the demonstrably essential concept of system noise in this branch of physiological
modeling. Conclusions: SDE modeling for metabolic processes is physiologically
pertinent and computationally feasible using commonly available resources.
Keywords: stochastic differential equations, dynamical models, non-autonomous differential
equations, system noise, parameter estimation, closed-form transition density expansion,
Hermite expansion, insulin, euglycemic hyperinsulinemic clamp.
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