Probabilistic Description of Model Set Response in Neuromuscular Blockade
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.
KeywordsStochastic systems state estimation fokker-Planck equation
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- 2.Silva, M.M., Wigren, T., Mendonça, T.: Nonlinear identification of a minimal neuromuscular blockade model in anesthesia. IEEE Transactions on Control Systems Technology 20(1), 181–188 (2012)Google Scholar
- 6.Mukherjee, A., Strikwerda, J.C.: Analysis of dynamic congestion control protocols – a fokker-planck approximation. In: Proc. ACM Sigcomm, Zurich, Switzerland, pp. 159–169 (1991)Google Scholar
- 7.Lemos, J.M., Moura, J.M.F.: Time sampling of diffusion systems using semigroup decomposition methods. In: MTNS 2004, 16th Int. Symp. on Mathematical Theory of Networks and Systems, Leuven, Belgium (2004)Google Scholar
- 8.Brockett, R.: Notes on the Control of the Liouville Equation. In: Cannarsa, P., Coron, J.-M. (eds.) Control of Partial Differential Equations, ch. 2. Springer (2010)Google Scholar
- 11.McBride, A.C.: Semigroups of linear operators: An introdution. Longman Scientific & Technical, London (1987)Google Scholar