Journal Article

Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics

Umberto Picchini, Susanne Ditlevsen and Andrea De Gaetano

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 2, pages 141-155
Published in print June 2008 | ISSN: 1477-8599
Published online May 2008 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqn011
Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics

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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. 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. 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 modelling. Furthermore, it can introduce the demonstrably essential concept of system noise in this branch of physiological modelling.

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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Subjects: Applied Mathematics ; Biomathematics and Statistics

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