One of them, artificial neural network (ANN), is a powerful empirical pattern-recognition and mapping tool for approximation of complex nonlinear relationships. Instead of imposing an a priori model on the data, ANN learns input and output relationships directly from the data. The flexibility of the ANN models has led to successful application in population pharmacokinetic and pharmacodynamic data analysis. Using the blood concentrations of remifentanil and EEG data obtained from our previous clinical investigation, the primary objective of this study was to evaluate if the pharmacodynamic model of ANN, in which complete ApEn data ( n = 24 509) were used, can predict the overshoot of ApEn during recovery from profound remifentanil effect. The secondary objective was to evaluate the predictive performance of the pharmacokinetic model, and the pharmacodynamic models of ANN with respect to datasets used in the pharmacodynamic analysis, i.e. measured concentrations of remifentanil and corresponding ApEn data ( n = 1077) vs. predicted concentrations of remifentanil calculated from the pharmacokinetic model of ANN and complete ApEn data ( n = 24 509). SAS ENTERPRISE MINER Release 4.1 was used for ANN analysis (SAS Institute Inc., Cary, NC, USA). Of many different architectures of ANN, the multilayer perceptron (MLP) network has been most commonly used to analyse pharmacokinetic data.
An ANN of MLP architecture is capable of approximating any existent nonlinear solution and has demonstrated advantages in at least one population pharmacodynamic analysis.
A three-layered MLP, with input, hidden and output layers, was used for pharmacokinetic and pharmacodynamic modelling. A hyperbolic tangent function was used as the activation function. By standard deviation method, the continuous input variables (time, amount, rate, age, height and weight in pharmacokinetic modelling time, age, height, weight, concentrations of remifentanil in pharmacodynamic modelling) were normalized to a mean of 0 and a SD of 1. ĭue to its robustness and fast convergence, the Levenberg–Marquardt method was used for training of pharmacokinetic and pharmacodynamic models.
This method adjusts the network weights using the following formula. Where w is the network weight, J is the Jacobian matrix that contains first derivatives of the network output with respect to the weights, e is the vector of network errors and I is the identity matrix. The coefficient μ controls the step size of the weight update and is varied based on the error convergence.
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