Curved Calibration Functions - how to perform the Regression Calculation?

In analytical laboratories calibrations with linear functions are more or less performed on a routine basis. However sometimes curved calibration functions are more appropriate and in such cases some uncertainty exists about the way of establishing a calibration which is in conformity with DIN/ISO standards.

DIN ISO 8466-2 shows the formulae which have to be applied for the regression calculation if a second degree polynomial (parabola) is used as calibration function. However this standard does not explain how the Limit of Detection and the Limit of Quantification can be determined from such a calibration function. Although this is discussed in DIN 32645 and DIN ISO 11843-2:2000 for calibration lines, the mathematics cannot be transferred from there to polynomials in a straightforward way.

Though DIN ISO 11843-5:2008 ("Capability of detection - Part 5: Methodology in the linear and non-linear calibration case")  explains the fundamental principles of handling curved calibration functions, this standard is not very helpful here because it does not give explicit formulae for polynomials of second degree.

However such formulae have been published recently in an article where the use of curved calibration functions in Ion Mobility Spectrometry (IMS) is described (Zscheppank, C.,U. Telgheder, and K. Molt; "Stir-bar sorptive extraction and TDS-IMS for the detection of pesticides in aqueous samples"; DOI: 10.1007/s12127-012-0097-x 2012; availabe at: http://www.springerlink.com/content/9601737370730200 ).

During the forthcoming QbD/PAT Conference of the University Heidelberg on 26/27 September 2012 one of the authors of this paper (Prof. Karl Molt, University Duisburg-Essen) will give a lecture about calibrations complying with DIN/ISO standards. The title is "Strategies for Linear and Non-linear Calibrations in Instrumental Analysis taking into account applicable Standards" and the speaker will point out sources of Free Software for performing the corresponding calculations.

Author:
Dr. Günter Brendelberger,
CONCEPT HEIDELBERG (a service provider entrusted by the ECA Foundation)