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Probabilistic Description of Model Set Response in Neuromuscular Blockade

  • Conceição Rocha
  • João M. Lemos
  • Teresa F. Mendonça
  • Maria E. Silva
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 240)

Abstract

This work addresses the problem of computing the time evolution of the probability density function (pdf) of the state in a nonlinear neuromuscular blockade (NMB) model, assuming that the source of uncertainty is the knowledge about one parameter. The NMB state is enlarged with the parameter, that verifies an equation given by its derivative being zero and has an initial condition described by a known pdf. By treating the resulting enlarged state-space model as a stochastic differential equation, the pdf of the state verifies a special case of the Fokker-Planck equation in which the second derivative terms vanish. This partial differential equation is solved with a numerical method based on Trotter’s formula for semigroup decomposition. The method is illustrated with results for a reduced complexity NMB model. A comparison of the predicted state pdf with clinical data for real patients is provided.

Keywords

Stochastic systems state estimation fokker-Planck equation 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Conceição Rocha
    • 1
    • 2
  • João M. Lemos
    • 3
  • Teresa F. Mendonça
    • 1
    • 2
  • Maria E. Silva
    • 4
    • 2
  1. 1.Departamento de MatemáticaFaculdade de Ciências da Universidade do PortoPortoPortugal
  2. 2.Center for Research & Development in Mathematics and Applications (CIDMA)Universidade de AveiroAveiroPortugal
  3. 3.INESC-ID/ISTTechnical University of LisbonLisboaPortugal
  4. 4.Faculdade de Economia da Universidade do PortoPortoPortugal

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