Probabilistic Description of Model Set Response in Neuromuscular Blockade

Abstract. This work addresses the problem of computing the time evo-lution of the probability density function (pdf) of the state in a nonlin-ear 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 stochas-tic differential equation, the pdf of the state verifies a special case of the Fokker-Planck equation in which the second derivative terms van-ish. 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 com-parison of the predicted state pdf with clinical data for real patients is provided