by Shulamit Levin, Medtechnica Feb 2010

**2. HPLC Theory: System
Suitability Parameters**

High performance liquid chromatography is
defined as a
separation of mixtures of compounds due to differences in their
distribution
equilibrium between two phases, the stationary phase packed inside
columns and
the mobile phase, delivered through the columns by high pressure pumps. Components whose distribution into the
stationary phase is higher, are retained longer, and get separated from
those
with lower distribution into the stationary phase.
The theoretical and practical foundations of
this method were laid down at the end of 1960s and at the beginning of
1970s. The theory of chromatography has
been used as
the basis for *System- Suitability* tests, which are set of
quantitative
criteria that test the suitability of the chromatographic system to
identify
and quantify drug related samples by HPLC at any step of the
pharmaceutical
analysis.

*Retention Time (t _{R}), Capacity
Factor k' and
Relative Retention Time (RRT)*

_{ }

The time elapsed between the injection of the
sample
components into the column and their detection is known as the
Retention Time
(t_{R}). The retention time
is
longer when the solute has higher affinity to the stationary phase due
to its
chemical nature. For example, in reverse
phase chromatography, the more lypophilic compounds are retained longer. Therefore, the retention time is a property
of the analyte that can be used for its identification.

A non retained
substance passes through the column at a time t_{0}, called the
Void
Time. The *Retention Factor* or *Capacity
Factor k'* of an analyte is measured experimentally as shown in
Figure 3 and
Eqn 1:

Eqn 1a
_{ }

The *Capacity Factor* describes the
thermodynamic
basis of the separation and its definition is the ratio of the amounts
of the
solute at the stationary and mobile phases within the analyte band
inside the
chromatographic column:

Eqn 1b
_{ }

Where C_{s} is the concentration of
the solute
at the stationary phase and C_{m} is its concentration at the
mobile
phase and ? is the ratio of the stationary and mobile phase volumes all
within the chromatographic band.

The *Retention Factor* (Eqn 1a) is used
to
compare the retention of a solute between two chromatographic systems,
normalizing it to the column's geometry and system flow rate. The need
to
determine the void time can be tricky sometimes, due to the instability
of the
elution time of the void time marker, t_{0}, therefore, when
the
chromatogram is complex in nature, and one known component is always
present at
a certain retention time, it can be used as a retention marker for
other
peaks. In such cases the ratio between
the retention time of any peak in the chromatogram and the retention
time of
the marker is used (t_{R (Peak) }/ t_{R (Marker)}) and
referred
to as the *Relative Retention Time* (RRT).
RRT is also used instead of the capacity ratio for the
identification of
the analyte as well as to compare its extent of retention in two
different
chromatographic systems.

Figure 3:
Example of Capacity
factor calculation in LC. In this case: t_{R} = 0.739, t_{0} = 0.17, therefore k'
= (0.739-0.176)/0.176 = 3.20

*Efficiency: Plate
Count N and Peak Capacity P _{c}*

Figure 4 describes a chromatogram with 4
peaks and a
detected void peak. The parameters of
the System Suitability are displayed in the inserted table. The sharpness of a peak relative to its
retention time is a measure of the system's efficiency, calculated as
N, plate
count. Band-broadening phenomena in the
column such as eddy diffusion, molecular diffusion, mass-transfer
kinetics and
extra-column effects reduce the efficiency of the separation (33). The sharpness
of a peak is relevant to the limit of detection and limit of
quantification of
the chromatographic system. The sharper
the peak for a specific area, the better is its signal-to-noise; hence
the
system is capable of detecting lower concentrations.
Therefore, the efficiency of the
chromatographic system must be established by the system suitability
test
before the analysis of low concentrations that requires high
sensitivity of the
system, such as the analysis of drug impurities and degradation
products.

The efficiency of the separation is
determined by the
Plate Count N when working at isocratic conditions, whereas it is
usually
measured by Peak Capacity P_{c} when working at gradient
conditions (34). The following
equation for the plate count is used by the United States Pharmacopoeia
(USP)
to calculate N (See Figure 5):

Eqn. 2
_{ }

Where *w* is measured from the baseline
peak
width calculated using lines tangent to the peak width at 50 % height
(See
Figure 5). European and Japanese
Pharmacopoeias use the peak width at 50% of the peak height (See Figure
5),
hence the equation becomes:

Eqn 3
_{ }

*Peak Capacity* *P*_{c}
is defined as number of peaks that can be separated within a retention
window
for a specific pre-determined resolution. In other words, it is the
runtime
measured in peak width units (34). It is assumed that peaks occur
over the gradient
chromatogram. Therefore, *Peak Capacity* can be calculated from
the peak
widths *w* in the
chromatogram as follows:

Eqn. 4:
_{ }

Where *n* is the number
of peaks at
the segment of the gradient selected for the calculation, *t*_{g}.
Thus peak capacity can be simply the gradient run time divided by the
average
peak width. The sharper the peaks
the
higher is the peak capacity, hence the system should be able to resolve
more
peaks at the selected run time as well as detect lower concentrations.

Another measure of the column's
chromatographic
efficiency is the *Height Equivalent to Theoretical Plate (HETP)*
which is
calculated from the following equation:

Eqn 5:
HETP
= (L/N)

Where L is column length and N is the plate
count. HETP is measured in
micrometer. For example, in the

Figure 4: Example of a
System Suitability Run’s Result

The behavior of HETP as function of linear
velocity
has been described by various equations (35). It is
frequently called "The Van-Deemter curve", and it is frequently used
to describe and characterize various chromatographic stationary phases'
performance and compare them to each other (36-39). The
lower
are the values of HETP, the more efficient is the chromatographic
system, enabling
the detection of lower concentrations due to the enhanced
signal-to-noise ratio
of all the peaks in the chromatogram.

Figure 5:
System
Suitability measurements on a single peak

Peak *Asymmetry Factor*,
*A _{f} * and

The chromatographic peak is assumed to have a
Gaussian
shape under ideal conditions, describing normal distribution of the
velocity of
the molecules populating the peak zone migrating through the stationary
phase
inside the column. Any deviation from
the normal distribution indicates non-ideality of the distribution and
the migration
process, therefore might jeopardize the integrity of the peak's
integration,
reducing the accuracy of the quantitation.
This is the reason why USP Tailing is a peak's parameter almost
always
measured in the system suitability step of the analysis.

The deviation from symmetry is measured by
the *Asymmetry
Factor*, A_{f}
or *Tailing
Factor* *T*. The
calculation of *Asymmetry Factor*,
A_{f} is described by the following equation:

Eqn 6
_{ }

Where *A* and *B*
are sections
in the horizontal line parallel to the baseline, drawn at 10% of the
peak
height as shown in Figure 5.

The calculation of *Tailing Factor*, *T*, which
is more
widely used in the pharmaceutical industry, as suggested by the
pharmacopeias,
is described by the following equation:

Eqn 7
_{ }

Where A and B are sections in the horizontal
line
parallel to the baseline, drawn at 5% of the peak height, as also shown
in Figure
5. The USP suggests that *Tailing
Factor* should be in the range of 0.5 up to 2 to assure a precise
and
accurate quantitative measurement. The
peaks in Figures 4 and 5 have a tailing factor within the USP
requirements.

*Selectivity
Factor alfa *and
*Resolution Factor Rs*

The separation is a function of the
thermodynamics of
the system. Substances are separated in a chromatographic column when
their
rate of migration differs, due to their different distribution between
the stationary
and mobile phases. The *Selectivity
Factor?, a, *and *Resolution Factor, Rs*, measure the extent
of
separation between two adjacent peaks. The
*Selectivity Factor?* accounts only for the ratio of the *Retention
Factors*, *k'*, of the two peaks (*k' _{2}/k'_{1}*),
whereas the

The equation that describes the experimental
measurement of the *Resolution Factor, Rs*, is as follows:

Eqn 8
_{ }

Where *t _{R}* is
the retention time of peaks 1 and 2 respectively and

The resolution is a critical
value when working with complex samples such as drug impurities and
degradation
products, or when the formulation is complex and excipients might
interfere
with the quantitative measurements.
Therefore, it is an essential part of the system suitability
measurement
stage before the quantitative work of these type of samples.

The sample used for the
measurements of *Rs* during the system suitability runs is
sometimes
called *Resolution Solution*, as can be seen in Figure 4 It usually contains the components that are
the most difficult to resolve.

The theoretical description of
the *Resolution Factor Rs* equation is shown in Equation 9. It includes some of the above parameters, the
plate count *N*, the selectivity *a* and the average of the
two
peaks' capacity factors *k'*:

Eqn 9
_{ }

It can be clearly seen from this equation that the plate count is the most effecting parameter in the increase of the chromatographic resolution. Since the plate count increases with the reduction in particle diameter, it explains the reduction in particle diameter of the stationary phase material during the last 3 decades of HPLC. This is also the rational behind the recent trend in HPLC, the use of sub 2 micron particle columns and the development of a specially design of ultra performance HPLC systems to accommodate such columns (36, 40-42).

References

33. Kirkland, J. J., Yau, W. W., Stoklosa, H. J., and Dilks Jr, C. H. (1977) J Chromatogr Sci 15, 303-16.

34. Neue, U. D. (2005) Journal of Chromatography A 1079, 153-161.

35. Usher, K. M., Simmons, C. R., and Dorsey, J. G. (2008) Journal of Chromatography A.

36. Wren, S. A. C., and Tchelitcheff, P. (2006) Journal of Chromatography A 1119, 140-146.

37. Neue, U. D., and Kele, M. (2007) Journal of Chromatography A 1149, 236-244.

38. Jones, M. D., and Plumb, R. S. (2006) J. Sep. Sci 29, 2409-2420.

39. Gritti, F., and Guiochon, G. (2006) Journal of Chromatography A 1128, 45-60.

40. Swartz, M. (2005) Journal of Liquid Chromatography & Related Technologies 28, 1253-1263.

41. Novakova, L., Matysova, L., and Solich, P. (2006) Talanta 68, 908-918.

42. King, S., Peter, J., Stoffolano, E. R., Eichhold, T. E., Ii, S. H. H., Baker, T. R., Richardson, E. C., and Wehmeyer, K. R. (2005) LC GC North America, 36-39.