Theory of Sampling (TOS) for Development of Spectroscopic Calibration Models

• University of Puerto Rico
• Alborg University

Introduction

This feature presents a brief of the principles of the Theory of Sampling (TOS) and these help to develop more effective spectroscopic calibration models.¹ TOS shows that sampling is both a science and a practice building on a set of principles developed over the last 60 years, starting in the mining industry but since then accepted in many other process industries, indeed broadly within science, technology and industry. As such TOS is also an asset for spectroscopic measurements and in Process Analytical Technology (PAT).³ Many opportunities exist for improving Quality Control by including these principles in pharmaceutical manufacturing.⁴ There is now a concerted effort for widespread application of the TOS and the 8th World Congress on Sampling and Blending is being organized for this purpose.⁵

Theory of Sampling

TOS outlines how sampling errors always occur due to the heterogeneity of materials (homogeneous materials would not lead to a sampling error). TOS defines homogeneity as a state which is never reached by naturally occurring, processed or manufactured materials (homogeneity – a state where all particles or fragments of the lot are strictly identical).⁶ This very strict definition of homogeneity is not followed in the pharmaceutical industry, where blend homogeneity is defined as an acceptable distribution of drug particles within a powder mixture. TOS states that sampling errors unavoidably occur due to the interaction of the sampling process with material heterogeneity.

In the pharmaceutical industry a production lot could consist of a blend of excipients and active pharmaceutical ingredient of 300 kg or more, and thus any “sample” is a mass-reduction performed to determine the composition of this lot. TOS stipulates that for correct sampling to occur all sampling parts of a lot (‘increments’ in TOS parlance) must have the same possibility of being selected. Deviations from the Fundamental Sampling Principle (FSP) are often ignored in pharmaceutical sampling when material is obtained from preselected locations using a sample thief.⁷ The sample should also be selected in a manner that does not disturb or affect the composition of the lot, ibid. This principle is also violated when a scoop or sample thief is used.

TOS has thoroughly characterized all types of sampling errors.⁷ Two of these are basic: the Fundamental Sampling Error (FSE) and the Grouping and Segregation Errors are unavoidable (but they can be reduced in impact by diligent TOS-compliant work). There are three other sampling errors that arise due to incorrect sampling procedures and these may be eliminated (again, dependent upon strict TOScompliant measures).^3,6,7 TOS has thoroughly developed a complete set of practices to avoid or minimize the effect of all sampling errors. Sampling is not limited to extraction of a material from a blender or other processing equipment. NIR or Raman spectra in Process Analytical Technology (PAT) are also examples of sampling efforts, albeit optical.^3,7 Spectra result from the interaction of light with a localized mass of the entire batch or lot. Thus, the principles of TOS are equal determinants also in the development of NIR or Raman calibration models.³

In TOS, composite sampling reigns supreme to obtain a reliable (representative) average concentration for the entire lot. One increment, or fundamental sampling unit, cannot be representative of the entire lot, due to its inherent localization w.r.t. the whole lot, which makes any single-sample clashing fatally with FSP. This case is termed grab sampling by TOS and is to be avoided at all costs. But the use of spectroscopic methods makes it easy to obtain a composite sample, for example when a number of spectra (scans) are averaged for a flowing powder as shown in Figure 1. In many cases the averaging of scans also increases the signal to noise ratio of the spectra obtained. These principles are especially important when NIR or Raman calibration models are developed. Calibration models cannot be developed with a single spectrum of each calibration sample, since this would in effect be optical grab sampling, plain and simple, and thus still clash with FSP. A single spectrum would not consider the inherent heterogeneity of blends.

 Figure 1. Representation of composite sampling with a spectroscopic system as powder moves over a conveyor belt. Each spectrum that is averaged corresponds to a slightly different set of particles, thus obtaining a composite sample.

TOS and Spectroscopic Calibration Models

Composite sampling should be included in all plans for development of calibration models. A recent study compared two different approaches for obtaining spectra for calibration models to determine drug concentration in powder blends. In the first approach the calibration spectra were obtained from 60 different sections of a tray where a powder blend was deposited.8 These 60 calibration spectra were obtained without movement of the powder. However, in the second approach, the calibration spectra were obtained as the powder flowed by the diffuse reflectance probe. Each spectrum was the average of 12 spectra collected with an integration time of 6.6 ms, thus producing a true composite sample. The accuracy of the calibration model improved by a factor of approximately three for the flowing powder system.

Composite sampling was also part of the strategy for a partial least squares (PLS) regression model developed for real time determination of acetaminophen in a continuous manufacturing process.⁷ Each spectrum was the average of 16 scans again obtained as the powder flowed but this time down a cylindrical chute for an estimated composite sample of 90 mg. The calibration model was developed with 100 spectra of each the calibration powder mixtures prepared at 10%, 12%, 14%, 16%, 18% and 20% (w/w) APAP. Thus, the calibration included 100 composite samples at each concentration.

PLS calibration models are based on developing a mathematical relationship between an X matrix that holds the NIR or Raman spectra, and Y matrix with the reference values. A good calibration model cannot be developed when sampling errors result in X matrix spectra that do not correspond to Y values.^9,10 Chemometric algorithms cannot overcome sampling errors. Thus, sampling errors are likely the most dominant source of errors in real time spectroscopic measurements and need to be addressed.^3,7

Acknowledgements

This work has been supported in part by the National Science Foundation Engineering Research Center on Structured Organic Particulate Systems through Grant NSFECC 0540855, and the Puerto Rico Science Technology and Research Trust. Kim Esbensen thanks GEUS management for the foresight to consider the importance of application of correct TOS sampling principles also in systems without the geo pre-fix since sampling errors are universal. Such insight is rare in strictly utilitarian sector institutions.

References

1. Esbensen KH. Reprint: 50 years of Pierre Gy’s “Theory of Sampling”—WCSB1: a tribute. TOS Forum. 2016;6(6):4-7.
2. Esbensen KH, Paoletti C, Theix N. Special Guest Editor Section (SGE): Sampling for Food and Feed Materials. Journal AOAC International. 2015;98(2):249-320.
3. Esbensen KH, Paasch-Mortensen P. Process Sampling: Theory of Sampling – the Missing Link in Process Analytical Technologies (PAT). Process Analytical Technology: John Wiley & Sons, Ltd; 2010:37-80.
4. Romañach RJ, Esbensen KH. Sampling in pharmaceutical manufacturing - Many opportunities to improve today’s practice through the Theory of Sampling (TOS). TOS Forum. 2015;4:5-9.
5. WCSB8. 8th World Conference on Sampling and Blending. 2016; http://www.wcsb8.com/.
6. Gy P. Sampling of discrete materials - a new introduction to the theory of sampling - I. Qualitative approach. Chemometrics Intellig Lab Syst. 2004;74(1):7-24.
7. Esbensen KH, Román-Ospino AD, Sanchez A, Romañach RJ. Adequacy and verifiability of pharmaceutical mixtures and dose units by variographic analysis (Theory of Sampling) – A call for a regulatory paradigm shift. Int J Pharm. 2016;499(1–2):156-174.
8. Mateo-Ortiz D, Colon Y, Romanach RJ, Mendez R. Analysis of powder phenomena inside a Fette 3090 feed frame using in-line NIR spectroscopy. J Pharm Biomed Anal. 2014;100:40-49.
9. Mark H. Principles and Practice of Spectroscopic Calibration. Wiley; 1991.
10. Green RL, Thurau G, Pixley NC, Mateos A, Reed RA, Higgins JP. In-Line Monitoring of Moisture Content in Fluid Bed Dryers Using Near-IR Spectroscopy with Consideration of Sampling Effects on Method Accuracy. Anal Chem. 2005;77(14):4515-4522.