(165b) A Simultaneous Approach for Kinetic Parameter Estimation and Curve Resolution Based on Spectroscopic Measurements
- Conference: AIChE Annual Meeting
- Year: 2016
- Proceeding: 2016 AIChE Annual Meeting
- Group: Pharmaceutical Discovery, Development and Manufacturing Forum
Monday, November 14, 2016 - 12:50pm-1:10pm
This work describes an efficient, unified framework for kinetic parameter estimation and curve resolution that is based on maximum likelihood principles and a simultaneous collocation approach that leads to improved estimates of parameters.
This study considers the dynamic equation model for the reaction kinetics as a stochastic differential-algebraic equation system,Â dc = f(c, y, q) + k dW(t), g(c, y, t) = 0, where c(t) is the concentration vector at time t, y(t) are additional algebraic states, q is the kinetic parameter vector and W(t) is the reaction system noise described by standard Brownian motion or Wiener processes. The spectroscopic measurements d(t, l) are governed by Beer-Lambertâ??s law, d(t, l) = Sk ck (t) sk (l) + z(t, l), with absorbance sk (l) for component k and wavelength l, and measurement noise z(t, l).
Determination of q by parameter estimation requires consideration of a dynamic optimization problem derived from maximum likelihood principles, and this leads to two important challenges. First, an efficient and reliable optimization strategy is required, even for kinetic systems that exhibit open loop instability and dependent kinetic equations. We successfully address this task by applying a direct transcription nonlinear programming (NLP) approach that determines the optimal kinetic parameters and the concentration profiles simultaneously. Second, since only spectroscopic measurements are available, covariances and other distributional information for W(t) and z(t, l) cannot be determined directly. Instead, we apply maximum likelihood principles in order to derive the covariances needed for parameter estimation. Coupled solution of these two tasks leads to an iterative optimization-based approach that provides covariance estimates and initializes the kinetic parameters. These results allow the subsequent solution of the parameter estimation problem with fixed covariance terms. Confidence regions for the kinetic parameter estimates are then obtained through the application of NLP sensitivity, a byproduct of the direct transcription approach.
We demonstrate our proposed approach on six case studies, including a comprehensive treatment of aspirin kinetics. These cases include simulated as well as actual experimental datasets. Detailed numerical results for these cases are presented and compared with the MCR-ALS GUI 2.0 toolbox. These show significant improvements in performance and computational cost over state-of-the-art approaches.