Theory of hplc_quantitative_and_qualitative_hplc

Quantitative & Qualitative HPLC
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Contents Page
1 Aims and Objectives 2
2 Qualitative Analysis Overview 3
3 Peak Identification and Assignment 4
4 Sample Spiking 5
5 Spectral Peak Identification 6-8
5.1. Peak Purity 7
5.2. Spectral Characterization 8
6 Quantitative Analysis Overview 9
7 Chromatographic Requirements 10
8 Peak Integration Events 11-12
8.1. Integration Events 12
9 Peak Height or Peak Area 13
10 Principles of Quantitative Analysis 14
11 Area%/Height% (Normalization) 15
12 External Standard Quantitation 16-17
13 Calibration Curve 18-20
13.1. Statistical Information 19-20
14 External Standard Multi-Level Calibration 21-24
14.1. Calibration Curve Information 23-24
15 External Standard Multi-Level Calibration Curve - Typical Calculation 25-26
16 Internal Standard Analysis 27-29
17 Multi-Level Calibration Curve 30-31

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1. Aims and Objectives
Aims
 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 Normalization
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:
 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 characterization from
a practical perspective

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2. Qualitative Analysis Overview
The aim of qualitative analysis is to answer the question ‘What’ is in the sample?
Figure 1: Options for qualitative HPLC analysis.
Two discrete situations exist for qualitative analysis:
 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 characterize
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, which 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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3. 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.
Figure 2: 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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4. 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.
Figure 3: 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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5. 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.
Figure 4: 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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5.1. 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.
Figure 5: Peak purity determined from the ratio between two signals.

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5.2. Spectral Characterization
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.
Figure 6: Determination of peak purity using spectral detectors.

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6. 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.
Figure 7: Quantitative analysis in HPLC.
A quantitative analysis involves many steps that are briefly summarised as follows:
 Know the compound you are analyzing
 Establish a method for analyzing samples containing this compound
 Analyze 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 analyze 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
 analyze 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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7. 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.
Figure 8: Chromatographic requirements for robust quantitative analysis in HPLC.

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8. 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.
Figure 9: 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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8.1 Integration Events
Figure 10: Peak integration.

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9. 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.
Figure 11: 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.

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10. 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:
 The identity of the component to be analyzed 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
Figure 12: 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.

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11. Area %/ Height % (Normalization)
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.
Figure 13: Area or height % quantitation.
It is very important to note restrictions associated with this quantitative methodology – which may
reduce the accuracy or precision:
 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.

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12. 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.
Figure 14: Principle of external standard calibration.
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
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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.
Example calculation:
An injection containing benzene at a concentration of 2,000 µg/mL is made and results in a peak
area of 100,000.
The response factor for benzene:
An injection of the sample with the unknown concentration of benzene has a peak area of 57,000.
The amount of benzene present in the sample:

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13. 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.
Figure 15: Construction of a calibration curve for quantitative analysis in HPLC.

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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 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.
13.1. Statistical Information
Figure 16: Statistical information of the nature of a regression line.

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Figure 17: Lines of best fit.
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 coefficient 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 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.

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14. 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.
Figure 18: Principle of external standard analysis with multi-level calibration.

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Example calculation:
An injection containing benzene at a concentration of 2,000 µg/mL is made and results in a peak
area of 100,000.
The response factor for benzene:
An injection of the sample with the unknown concentration of benzene has a peak area of 57,000.
The amount of benzene present in the sample:
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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14.1. Calibration Curve Information
Figure 19: 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:
Where:
xbi - is the mean of the blank measures
sbi is the standard deviation of the blank measures
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).
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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.
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.
Figure 20: 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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15. External Standard Multi-Level Calibration Curve - Typical Calculation
Figure 21: Multi-level calibration curve.
Typical Calculation
From the calibration curve, a regression analysis will yield an equation which describes the line of
best fit through the data points, with the form:
Where:
y = the peak area
m = the slope of the regression line
c = the intercept of the regression line with the y-axis
Dilution factors (D) and multipliers (M) may be used to calculate the final analyte concentration, if
required, and are typically used to correct for known purity of the standard used, analyte dilutions
etc.

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Therefore, for a regression equation obtained from a multi-level calibration, such as that shown, the
equation of the best fit line is:
If a sample peak area of 327 units is obtained, the absolute amount of sample is calculated as
follows (solve for x = interpolated amount):
If the sample had been diluted from 10 mL to 25 mL during sample preparation then a dilution factor
(D) should be used. This is calculated as follows:
If a standard purity of 98.6% had previously been determined, then a multiplier (M) would be
required.
Therefore, the final amount of sample would be:

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16. 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.
Figure 22: 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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Single level calibration:
Where:
is = internal standard
sc = specific compound of interest
Where:
is = internal standard
sc = specific compound of interest
IRF = internal response factor
Prepare a sample containing 2,000 µg/mL of toluene (the internal standard) and 1,000 µg/mL
benzene (the analyte). Then inject the sample. The resulting peak areas are 120,000 for toluene and
67,000 for benzene. The internal response factor for benzene is calculated as follows:
Inject the sample containing 2,000 µg/mL of toluene and an unknown amount of benzene using the
same chromatographic conditions. The resulting areas are 122,000 for toluene and 43,000 for
benzene. The amount of benzene present in the sample can be calculated as follows:
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.

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Good internal standards:
 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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17. Multi-Level Calibration Curve
Figure 23: Multi-level calibration curve.
Remember that we are now dealing with a calibration curve built with RESPONSE RATIO and
AMOUNT RATIO as shown.
From the calibration curve, a regression analysis will yield an equation which describes the best fit of
the line through the data points, with the form:
Where:
y = RESPONSE RATIO for the sample
m = the slope of the regression line
c = intercept of the regression line with the y-axis
The final calculation of the amount of an unknown is carried out as follows:
Therefore, for a regression equation obtained from a multi-level calibration, such as that shown, the
equation of the best fit line is:
If a sample peak area of 3,000 units and an internal standard peak of 2,800 units is obtained, the
absolute amount of sample is calculated as follows:
Solve for x (interpolated amount).

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REMEMBER
Therefore, the equation of the regression line becomes
Therefore the final amount, based on an internal standard mount of 0.110 units being added to the
sample solution would be:
Multipliers (M) and dilution factors (D) may also be included in the final calculation of the amount of
the sample, however, theses have been omitted here for clarity, but were included in the external
multi-level calibration curve (page 15).

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