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

Picchini, Umberto LU ; Ditlevsen, Susanne and De Gaetano, Andrea (2008) In Mathematical Medicine and Biology 25(2). p.141-155
Abstract
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... (More)
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. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematical Medicine and Biology
volume
25
issue
2
pages
141 - 155
publisher
Oxford University Press
external identifiers
  • scopus:45749143180
ISSN
1477-8602
DOI
10.1093/imammb/dqn011
language
English
LU publication?
no
id
f024a533-41f1-4866-b4c0-03a0a6ec6926 (old id 4215989)
date added to LUP
2014-01-13 14:39:05
date last changed
2017-04-09 03:27:07
@article{f024a533-41f1-4866-b4c0-03a0a6ec6926,
  abstract     = {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.},
  author       = {Picchini, Umberto and Ditlevsen, Susanne and De Gaetano, Andrea},
  issn         = {1477-8602},
  language     = {eng},
  number       = {2},
  pages        = {141--155},
  publisher    = {Oxford University Press},
  series       = {Mathematical Medicine and Biology},
  title        = {Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics},
  url          = {http://dx.doi.org/10.1093/imammb/dqn011},
  volume       = {25},
  year         = {2008},
}