3.1. Linearity

Linearity is the method’s ability to obtain test results, which are directly proportional to the concentration of the analyte in the sample. (1)

The term linearity of signal, in the context of LC–MS, has two closely linked meanings: (a) linear relationship between analyte signals and analyte concentrations in calibration samples and (b) linear relationship between analyte signals and analyte concentrations in samples containing matrix components. The latter meaning is becoming increasingly more used and is also used in this course. The reason being that, if the analyte signal in samples is linear, then it is almost certain that it is also linear in calibration solutions, while the opposite might not be true. The most common cause for this is the phenomenon called matrix effect, which is addressed in the chapter 5 of this course. Linearity of the calibration graph is closely related to choosing the calibration model and working range.

Factors affecting linearity:

• Firstly, the ion source behaves linearly only if the ionization efficiency of the analyte is independent of its concentration in the effluent. As the ionization efficiency of the analyte and its behaviour at different concentrations depends on the used ion source, the linear ranges differ between different ion sources. In the ESI source, the linear dependence usually holds at lower concentrations, but at higher concentrations, the excess charge on the surface of the droplets becomes limiting and linearity is lost. Also the co-eluting compounds can influence the ionization process (the so-called matrix effect) and lead to the decrease or loss of linearity. Therefore, it is very important to investigate linearity in the presence of matrix compounds.
• Secondly, during the ion transport from the ion source to the mass analyzer, the number of successfully transported ions must be proportional to the number of ions formed in the source. (2)
• Thirdly, the linearity of the ion signal depends on the mass analyzer design and on the linearity of the detector’s signal. The contemporary ion detectors are highly linear, so that the mass analyzer design is the deciding factor here. Mass analyzers are characterized by the transmission efficiency (3), which is the ratio of number of ions that are finally detected and number of ions that entered the mass analyzer. In order to demonstrate the linear behaviour, the transmission must be independent from the concentration.

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(1) The term “linear” can in mathematics refer to the fact that the statistical models considered are linear in terms of all parameters (coefficients), also including polynomial relationships. However, in analytical method validation, the term “linear” is used to describe the case where a straight line can be used to describe the relationship between the LC–MS signal and concentration of the analyte.

(2) This ion transport is, in essence, the transport of ions from the atmospheric pressure region in the ion source to the low pressure region of mass spectrometer with minimum loss. Collisions or formation of the clusters can cause losses of ions.

(3) Transmission (in mass spectrometry) – the ratio of the number of ions leaving a region of a mass spectrometer to the number entering that region. [http://goldbook.iupac.org/T06478.html]
Transmission efficiency – how many of the ions produced in the source region actually reach the detector. This is an important measure of sensitivity for mass spectrometers.[http://science.widener.edu/svb/massspec/massspec.pdf]