Mixture Component Prediction Using Iterative Optimization Technology (Calibration-Free/Minimum Approach)

Abstract

Process analytical technology (PAT) plays an important role in the pharmaceutical industry. PAT is used extensively in process development, process understanding, and process control. Often, quantitative measurements are desired/required and a calibrated model will have to be developed and implemented. The development, implementation, and maintenance of these quantitative models are both resource and time intensive. This paper describes a calibration-free/minimum approach, iterative optimization technology (IOT), which is used to predict (without calibration standards) the composition of a mixture while maintaining a similar predictability to calibration standard models. It typically involves using only pure standard spectra (collected prior to the analysis) and sample spectra collected during the analysis. This technology is applicable for predicting compositions during development of pharmaceutical products (where the synthetic route, formulation, or process is not set) and is not intended for use in good manufacturing practice (GMP) manufacture where quantitative measurements are made using validated models. For ideal mixture cases, the mixture composition is iteratively computed at every sample time point to minimize an excess absorption subject to constraints (e.g., mixture constraints, upper/lower limits). Linear IOT is used to describe these ideal mixture cases. For nonideal mixture cases, the excess absorption, including the nonlinear characteristic, is first represented by a Box-Cox transformation. A limited number of training/calibration samples is required for these nonlinear examples. The mixture composition is then iteratively obtained in a similar optimization framework as linear IOT. Nonlinear IOT is used to describe these nonideal mixture cases. Linear and nonlinear IOT have provided comparable prediction accuracy on binary and ternary mixtures as compared to a calibrated partial least squares (PLS) model. IOT enhanced the understanding of dosage form blending processes by determining the composition/ratio of all (spectrally discriminated) components in the blend in real time. As composition is predicted each revolution, determination of the blending end point (does each component trend meet the known target mixture ratio) can be easily determined. Linear and nonlinear IOT can also be used to aid process understanding via detecting/representing molecular interaction effects utilizing the excess absorption calculation. The effectiveness of the linear and nonlinear IOT is demonstrated through four online and offline pharmaceutical process examples (bin-blending process, rotary tablet press feed frame process, and two different solvent mixtures).

Iterative optimization technology combined with wavelength selection based on excess absorption for a process analytical technology calibration–minimum approach

“…IOT is a calibration-free concentration prediction method; it is explained in detail in Appendix A and the literature [13]. IOT minimizes the excess absorption x excess given by the following equation:…”

“…However, calibration-free methods cannot accurately predict component concentrations, although component concentrations in mixtures provide a deep understanding of processes. To tackle this problem, a calibration-free method called iterative optimization technology (IOT) has been recently reported [13]. IOT is a type of least squares method that is based on the BeerLambert law considering some physical constraints.…”

“…However, formulation with few calibration samples is difficult. Nonlinear IOT has been proposed for prediction of nonideal mixtures [13]. However, the predictive accuracy of nonlinear IOT largely depends on training samples and the wavelength regions used.…”

A Procedure for Developing Quantitative Near Infrared (NIR) Methods for Pharmaceutical Products

“…(b) PCA scores plot for laboratory powder samples and production tablets of 600 and 400 mg. Spectral treatment: first derivative + SNV over the wavelength range 1100-2500 nm subtraction because linear features are eliminated and new features emerge. The excess absorbance concept was later associated to the composition of pharmaceutical blends [70]. The minimum in the excess of absorbance was proposed as an estimate of the composition of powder mixtures (see Eq.…”

“…The nonlinear approach proposed [70] consists in a previous transformation by using Box-Cox and perform prediction as described by the linear approach.…”