The Theory of HPLC
Quantitative and Qualitative HPLC
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Aims and Objectives
Aims and Objectives
Aims
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To define Quantitative HPLC and explain the information that can be derived from
this type of HPLC analysis
To examine the use of Peak Height or Area in quantitative calculations and to
investigate Integration of chromatographic peaks
To explain the use of Calibration and Calibration curves in Quantitative HPLC
To outline the principles of Single and Multi-level calibration in Quantitative
analysis
To investigate practical uses of External Standard, Internal Standard and
Normalisation methods of Quantitative analysis
To outline example calculations for the various Quantitative methods
Objectives
At the end of this Section you should be able to:
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To define Qualitative HPLC and explain the information that can be derived from
this type of HPLC analysis
To define and explain the principles of peak identification and analyte
characterisation from a practical perspective
Content
Qualitative Analysis Overview
Peak Identification and Assignment
Sample Spiking
Spectral Peak Identification
Peak Purity
Spectral Characterisation
Quantitative Analysis Overview
Chromatographic Requirements
Peak Integration
Integration Events
Peak Height or Peak Area
Principles of Quantitative Analysis
Area %/ Height % (Normalisation)
External Standard Quantitation
Calibration Curve
Statistical Information
External Standard Multi-level Calibration
Calibration Curve Information
Internal Standard Analysis
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Qualitative Analysis Overview
The aim of qualitative analysis is to answer the question ‘What’ is in the sample?
Options for Qualitative HPLC Analysis
Two discrete situations exist for qualitative analysis:
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the sample components are known and peaks within the chromatogram need to be
assigned to the known components
the sample is a complete unknown which you are attempting to characterise
In the former case, it might be possible to inject standards of the pure compound, and
assign the peaks in the chromatogram based on the retention time of the standard.
Having a selective detector, such as diode-array UV or Fluorescence detector, that assists
in identification by producing spectra or a specific response can assist in peak
assignment.
In the second case, it may be necessary to employ detectors that can be used to aid in
identification, such as mass spectrometers. It may also be necessary to collect the eluent
fraction containing the peak of interest for off-line characterisation using Infra-red or
Nuclear Magnetic Resonance Spectroscopy (NMR).
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Peak Identification and Assignment
Perhaps the most straightforward way to assign peaks within the chromatogram of a
sample solution is to inject standard solutions under identical analytical conditions. By
comparing the retention factor (k) and response of the peak in the chromatogram of the
standard solution, with the sample chromatogram, peaks may be tentatively assigned.
It is important that the concentration of the standard solution is matched to the sample
solution as closely as possible. This avoids peak mis-assignment due to peak shape
effects.
Using reference standards for Peak Identification
For more rigorous peak assignment it is important that the analysis is also carried out
under orthogonal (different) conditions. The analysis is carried out in the reversed phase
using a different column and mobile phase, and the retention factor and response
compared again. If a match is found, then the confidence in the peak identification is
increased.
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Sample Spiking
The technique of ‘spiking’ a sample involves the addition of a known reference material to
a sample matrix, in order to confirm the identity of one of the sample component peaks.
Use of sample spiking to increase confidence in Peak Identification
In this case, one of the peaks in the sample is suspected to be insulin. The sample is
spiked with insulin at approximately the same concentration as the sample components. If
any of the peaks within the chromatogram gets larger, then that peak may be insulin. If a
new chromatographic peak is seen, or if any of the peaks develops a ‘shoulder’, then it is
unlikely that any of the peaks in the chromatogram is due to insulin within the sample.
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Spectral Peak Identification
The identification and assignment of peaks within sample chromatograms using retention
time alone can be unreliable.
The use of selective detectors and spectrometers can greatly increase the confidence in
the peak assignment. Detector systems such as Diode Array UV Spectrometers or Mass
Spectrometers are able to record unique spectra for each peak within the sample
chromatogram. The spectra may be recorded in ‘real time’ as the eluent can be directly
introduced into the detector system.
The use of Spectral Detectors to assist with Peak Identification
It is usual that the spectrum obtained from the unknown peak is compared with a
spectrum from either a standard solution of pure reference standard run alongside the
sample, or with spectra from a library held within the chromatographic data system.
There are many ways to compare spectra, and many algorithms exist for producing a
‘Match’ between the recorded spectra and the sample spectrum. These statistical
methods of comparison give a ‘quantitative’ measure of confidence in the peak
assignment.
Mass spectra and higher order (derivative) UV spectra can also be used to check for
‘peak purity' – whether the peak is due to a single component or is an amalgamation of
two or more peaks.
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Peak Purity
Peak purity can be established by taking the ratio of two signals (wavelengths) across the
peak(s) of interest. If the peak is pure, then the ratio of the two signals should be constant
across the peak.
If the peak is impure, then the ratio between the two signals (wavelengths) will change
across the peak as the spectral differences caused by the interfering peak change the
signal ratio.
Spectral Characterisation
Mass Spectrometric detectors can be configured to produce fragmentation patterns that
can be assigned to analyte moieties, so building up a ‘picture’ of the analyte molecule.
The spectral peaks and patterns combined with the molecular (pseudomolecular) weight
acquired can be used to characterise the analyte molecule.
Determination of Peak Purity using Spectral Detectors
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Quantitative Analysis Overview
After the peaks have been integrated and identified, the next step in the analysis is
quantification. Quantification uses peak areas or heights to determine the concentration of
a compound in the sample.
Quantitative Analysis in HPLC
A quantitative analysis involves many steps that are briefly summarised as follows:
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Know the compound you are analysing
Establish a method for analysing samples containing this compound
Analyse a sample or samples (the Standard) containing a known concentration or
concentrations of the compound to obtain the response due to that concentration
(called ‘Calibration’)
You may analyse a number of these samples with different concentrations of the
compounds of interest if your detector has a non-linear response (referred to as
‘multi-level calibration’), or if a wide concentration range is to be measured in the
samples
Analyse the sample containing an unknown concentration of the compound to
obtain the response due to the unknown concentration
Compare the response of the unknown concentration to the response of the known
(standard) concentration to determine how much of the compound is present
To obtain a valid comparison for the unknown sample response to that of the known
standard, the data must be acquired and processed under identical conditions.
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Chromatographic Requirements
A requirement for quantitative analysis is that the peaks to be quantified are ‘known’ (i.e.
characterised), so that standard solutions may be prepared for instrument response
calibration. There are notable exceptions to these requirements, for example, impurity
and degradation product analysis in Pharmaceutical Stability Studies. In this case,
‘surrogate’ standards must be used which are representative of the general compound
class – more on this later.
The accuracy of the quantitation is strongly influenced by the resolution of the peaks and
the state of the baseline surrounding the peaks of interest. Well separated peaks can be
easily and reproducibly integrated because other peaks do not influence the height and
area. Peaks eluting on sloping or noisy baselines can be difficult to integrate reproducibly.
Peak symmetry is also a performance characteristic for a good quantitative result. Peaks
with symmetry values exceeding three cannot be properly or reproducibly integrated.
Peak shoulders or tailing / fronting may be a result of two improperly separated
compounds, and shouldered peaks are difficult to integrate reproducibly. Improve
chromatography prior to quantitative analysis if possible.
Chromatographic Requirements for Robust Quantitative Analysis in HPLC
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Peak Integration
Chromatographic peak integration defines an operation in which the area under the
chromatographic peak is measured. The measurement is based on the integral technique
of splitting the peak into a large number of rectangles, which are then ‘summed’ to provide
an estimate of the total area under the peak – a measure of the cumulative ‘absorbance
versus time’ signal.
Two events need to be defined in order for the data system to carry out the calculation,
these are the peak start and the peak end – these will be determined using threshold and
peak width settings in the data system. The method of determination has to be
reproducible for rugged integration.
The baseline is then drawn between the peak start and end points created by the data
system.
Methods of Integration and Key Integration events
Several other ‘integration events’ exist to give ruggedness and flexibility to peak
integration, however these are manufacturer dependant and outside the scope of this
discussion.
It is important to note that peak height measures the distance between the peak apex to
the intersection with the integrated peak baseline.
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Integration Events
Peak Height or Peak Area
For most HPLC analyses, peak areas are used for quantitative calculations, although, in
most cases, equivalent results may be achieved with peak height.
Peak area is especially useful because HPLC peaks may be tailed. In this case, because
peak heights may vary (although area will remain constant), area vales are more
repeatable.
There are however, instances when peak height calculations may be better. For trace
analysis, when the peak of interest is very small, use peak height for calculations, this
reduces the error sustained in small changes in peak start and end time variation.
The figure shown below illustrates the fact that areas of a chromatographic peak will
change if the flow rate changes. Be aware that poorly maintained pump systems will have
an unstable flow rate resulting in a loss of peak area precision (reproducibility). For this
reason, always perform routine maintenance on the pump seals, check valves and filters.
Make certain that the pump has been primed and dissolved gasses removed.
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Quantitative analysis can be carried out using either peak height or peak area
measurements
Both peak height and area measurements will be irreproducible if injection volume varies
– therefore it is important to also ensure the injection or autosampler system is also well
maintained, paying particular attention to the needle and injection valve.
Principles of Quantitative Analysis
Although there are many different types of detector used for quantitative HPLC analysis,
the quantitative premise remains constant. Each detector will produce a response that
depends upon the AMOUNT of analyte to which it is responding. The magnitude of the
response may be dependent on the analyte itself as well as the matrix from which it
comes – and therefore standards are usually employed to ‘calibrate’ the instrument
response.
There are some general requirements that must be met before a quantitative analysis can
be undertaken, and these include:
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The identity of the component to be analysed should be known
The best possible separation of the component should be achieved
Standards of known purity should be available (otherwise accuracy may be
compromised)
Sample preparation and the quality of the separation (governed by the stationary
phase) should be reproducible
If internal standards are not used, then mobile phase flow rate and injection
volume should be reproducible
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Primary Methodologies for Quantitative Analysis
Of course, quantitative analysis may be possible without meeting all of the above
conditions, however, in such cases lower accuracy or precision must be expected.
The analytical approach (method), and mathematical model used to calculate the quantity
of an analyte can vary and is of great importance.
Area %/ Height % (Normalisation)
The Area% calculation procedure reports the area of each peak in the chromatogram as a
percentage of the total area of all peaks. Area% does not require prior calibration and
does not depend upon the amount of sample injected within the limits of the detector. No
response factors are used. If all components respond equally in the detector and are
eluted, then Area% provides a suitable approximation of the relative amounts of
components.
Area or Height % Quantitation
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It is very important to note restrictions associated with this quantitative methodology –
which may reduce the accuracy or precision:
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The method assumes equal detector response for all analytes
The method assumes that all components in the sample are seen in the
chromatogram (i.e. they all elute from the column and produce a response in the
detector)
Peaks in the chromatogram due to analytical artefacts (solvents, carry-over etc.),
may interfere with quantitation
Area% is used routinely where qualitative results are of interest and to produce
information used to create the calibration table required for other calibration procedures.
The Height% calculation procedure reports the height of each peak in the run as a
percentage of the total height of all peaks in the run.
External Standard Quantitation
The external standard (ESTD) quantitation procedure is the basic quantification procedure
in which both calibration and unknown samples are analysed under the same conditions.
The results (usually peak height or peak area measured using a data system) from the
unknown sample are then related to those of a calibration sample, using a calibration
curve, to calculate the amount in the unknown.
The ESTD procedure uses absolute response factors. The response factor is normally
calculated as amount / area of the analyte in the calibration sample. The response factors
are obtained from a calibration and then stored. Response factors are normally viewed as
a single point calibration curve, using the origin to determine the second point for the
regression line – this approach is often called ‘Single Point Calibration’. In subsequent
sample analyses, component amounts are calculated by applying the response factor to
the measured sample area, or by interpolating the result from the calibration curve as
shown.
Principle of External Standard Calibration
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One precaution that must be observed in this type of calculation is that the sample
injection size must be reproducible from run to run, since there is no (internal) standard in
the sample to correct for variations in injection size or sample preparation. The method
type also assumes a linear detector response and that samples do not contain a wide
range of analyte concentrations.
Worked Example of an External Standard Calculation
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Calibration Curve
A calibration curve is a graphical representation of the amount and response data for a
single analyte (compound) obtained from one or more calibration samples.
The curve is usually constructed by injecting an aliquot of the calibration (standard)
solution of known concentration and measuring the peak area obtained. Peak height is
sometimes used but only in exceptional circumstances.
Construction of a calibration curve for quantitative analysis in HPLC
A line of best fit (regression line) is used to join the points of the curve obtained. When
only one calibration sample is used (i.e. at a single concentration), the origin (X0:Y0) is
used as a second point to enable a regression line to be drawn (you can’t draw a line
through a single point – what would the slope be??). With multi-level calibration (using
several calibration samples at different analyte concentrations), the origin may be
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included, excluded or forced depending upon the calibration model and application
specifics.
The line of best fit is usually given a ‘correlation coefficient’ which is the square root of the
regression coefficient and gives a measure of how well the data points fit a straight line.
Of course, the instrument response may be exponential or second (or higher) order
polynomial – however these relationships are often more difficult to model and wherever
possible a linear calibration relationship is preferred.
Statistical Information
Statistical Information of the nature of a regression line
The intercept of the regression equation indicates systematic error – a large positive or
negative value may indicate an inherent error within the sample preparation or analysis
The slope of the line indicates the analytical ‘sensitivity’
The regression co-effcient is a statistical measure for ‘goodness of fit’ to a straight line,
calculated using the residuals (error) of each data point, an r value of +1 indicates a
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straight line with positive slope. Some typical ‘r’ values are shown – it is important to
always plot data to check the fit. As can be seen from the examples – r values can be
misleading! Workers sometimes use an r2 value which is statistically more rigorous.
External Standard Multi-level Calibration
Multilevel calibration can be used when it is not sufficiently accurate to assume that a
component shows a linear response or to confirm linearity of the calibration range.
Each calibration level corresponds to a calibration sample with a particular concentration
of components. Calibration samples should be prepared so that the concentration of each
component varies across the range of concentrations expected in the unknown samples.
In this way, it is possible to allow for a change in detector response with concentration and
calculate response factors accordingly.
Principle of External Standard Analysis with Multi-Level Calibration and an Example
Calculation
This multilevel calibration curve has three levels and shows a linear fit through the origin.
This method of linear fit through the origin is similar to the single level calibration method.
The detector response to concentration is assumed to be linear. The difference between
the two calibration types is that, with multi-level calibration, the slope of the detector
response can be determined by a best fit through a number of points, one for each level,
and the regression coefficients used to substantiate the assumption of linearity.
Unknowns are determined in the same way as the single level calibration model – the
difference is now that the method may be used to determine analyte concentrations over a
wider range as the detector response has been calibrated with greater rigor.
Most data systems will allow the input of calculation variables to allow a ‘final result’ to be
automatically calculated and printed.
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Calibration Curve Information
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Important Parameters in Multi-Level Calibration
LOD (Limit of detection) – The minimum amount of analyte that can be reliably detected.
The limit of detection, expressed as the concentration, cL, or the quantity, qL, is derived
from the smallest measure, xL, that can be detected with reasonable certainty for a given
analytical procedure. The value of xL is given by the equation:
xL = xbi - + ksbi
where: xbi - is the mean of the blank measures, sbi is the standard deviation of the blank
measures, and k is a numerical factor chosen according to the confidence level desired.
A sample that contains a complex matrix (e.g. environmental, biological sample) may
show response from the matrix. To determine the response a matrix sample without the
compounds of interest should be analysed under same condition . The so-called ‘blank’
chromatogram is treated as a starting point for the determination of LoD.
The LoD is often defined as a ratio of S/N or peak area measurement precision. Examples
of defining criteria are S/N ratio > 3 - peak height is compared to the noise height of the
blank chromatogram to define the signal to noise ratio. Many modern data systems are
capable of automatically providing a very accurate signal to noise ratio.
LOQ (Limit of quantitation) - Lowest concentration of an analyte in a defined matrix
where positive identification and quantitative measurement can be achieved using a
specified method. The term limit of quantitation is preferred to limit of determination to
differentiate it from LOD. LOQ has been defined as 3 times the LOD (Keith, 1991) or as
50% above the lowest calibration level used to validate the method (US-EPA, 1986).
The LoQ is often defined as a ratio of S/N or peak area measurement precision and has
much less stringent requirements than for limit of detection. Examples of defining criteria
are S/N ratio > 20, or peak area precision better than 10%. The peak height is compared
to the noise height of the blank chromatogram to define the signal to noise ratio. Many
modern data systems are capable of automatically providing a very accurate signal to
noise ratio.
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Linear range - Concentration range over which the intensity of the signal obtained is
directly proportional to the concentration of the species producing the signal.
The linear range of a chromatographic detector represents the range of concentrations or
mass flows of a substance in the mobile phase at the detector over which the sensitivity of
the detector is constant within a specified variation, usually ±5 percent.
The linear range of a detector may be presented as the plot of peak area (height) against
concentration or mass flow-rate of the test substance in the column effluent at the
detector. This plot may be either linear or log/log. The upper limit of linearity is that
concentration (mass flow-rate) at which the deviation from an ideal linearity plot is greater
than the specified percentage deviation (± x % window).
Numerically, the linear range can be expressed as the ratio of the upper limit of linearity
obtained from the linearity plot and the minimum detectability, both measured for the
same substance.
When presenting the linear range of a detector, either as a plot or as a numerical value,
the test substance, the minimum detectability, and the specified deviation must be stated.
Linearity is often expressed using the regression coefficient.
Linear and Dynamic Range of Calibration Curves
Slope – the slope of the calibration line is often used to determine the sensitivity of the
analytical method.
Intercept – the intercept indicates the degree of systematic error within the method and is
the direct result of ‘background’ response. Many workers often include the results of a
‘blank analysis (i.e. where no analyte is added and x=0) as a point in the calibration curve
from which the regression line and regression co-efficient are calculated.
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Internal Standard Analysis
The ISTD procedure eliminates the disadvantages of the ESTD method by adding a
known amount of a component that serves as a normalizing factor. This component, the
internal standard, is added to both calibration and unknown samples and ‘compensates’
for losses during sample preparation or variability during the analytical determination.
General Quantitative Principle of Internal Standard Analysis
The compound used as an internal standard should be similar to the calibrated compound
(analyte), chemically and in retention time, but it must be chromatographically
distinguishable.
If the ISTD procedure is used for calibrations with a non-linear characteristic, care must be
taken that errors resulting from the calculation principle do not cause systematic error. In
multi-level calibrations, the amount of the ISTD compound should be kept constant, i.e.
the same for all levels. The internal standard is usually added at a concentration of
approximately one third to one half of the expected MAXIMUM analyte concentration. This
is especially important when using MS detectors to ensure the internal standard does not
interfere with the ionisation of the analyte molecule.
For internal standard analysis, the amount of the component of interest is related to the
amount of the internal standard component by the ratio of the responses of the two peaks.
This is normally achieved by plotting the response ratio against the concentration ratio as
shown next.
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Principle and Calculation for Single Level Internal Standard Calibration
Internal standards are usually well characterised compounds which are not present in the
sample and is added in a known (constant) concentration to standard and sample
solutions (or matrices) – usually at the beginning of the analytical process to compensate
for losses and variability throughout the sample preparation and analytical processes.
Good internal standards:
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elute near to, but are well resolved from, the analyte of interest
are chemically and physically similar to the analyte
are not present in the original sample mixture
are unreactive towards any of the sample components
are available in highly pure form
are added in the concentration range 0.3 – 0.5 of the expected MAXIMUM analyte
concentration
It is often fairly difficult to fulfil all of these requirements for HPLC analysis. Often for MS
detection, the internal standard will be an isotopically labelled version of the analyte,
which can be spectrally rather than chromatographically resolved (i.e. the labelled version
has a different mass than that analyte). Care must be taken when using this approach to
avoid ion-suppression effects, which can serious affect the reproducibility of the analysis.
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