5


One and 2-dimensional models


If a chromatographer wants to understand peak movements caused by changes in experimental parameters, they must keep everything constant except one factor, like %B, tG or pH (or one factor at a time, OFAT). This helps to understand how a separation might change. Initially, this may appear to be an inefficient approach to spending time, however the opposite is true, since the chromatographer understands the separation better.


Changes of other parameters can also be modeled in DryLab by calculation: The influence of the flow rate, of the column length and ID, dwell volume, gradient start and end, steps, etc. So even an OFAT-model in DryLab allows the understanding of multifactorial changes. The most successful 2-dimensional model was and is still today the gradient time – temperature- or tG-T- model, especially when combined with a ternary gradient elution technique [17]. The tG-T- model which was used by Snyder in column characterisation [18], has lead to an extension into a 3D-resolution space, the Cube [14].


3-D-Models, the Cube


The first Cube model was demonstrated at the HPLC2009 conference in Dresden [14]. Soon afterwards, a number of papers appeared demonstrating the advantages of this new technology for industrial applications [19-23]. This new technology is especially well suited to improving the speed of older pharmacopoeial methods, as shown by Schmidt, where they reduced a method’s analysis times from 160 to 3 min, using DryLab and UHPLC [24].


The first step in this process is to plan a Design of Experiments (DoE) followed by the so called Peak Tracking process. The most efficient DoE is shown in Figure 1.


Peak Tracking


Figure 1. Design of Experiments (DoE) for the simultaneous optimisation of gradient time (tG), temperature (T) and pH of the eluent A or the ternary composition tC of the eluent B (i.e., B2 in B1 with B1: AN and B2: MeOH). The pH is changed by having two aqueous eluents A1 and A2 with changing ratios. Circles represent the twelve input experiments for the 3-D model. The short gradient time tG1 is at the points 1, 5, 9, 3, 7 and 11, the long gradient time tG2 is at 2, 6, 10, 4, 8, and 12. The low temperature (T1) experiments are: 1, 2, 5, 6, 9 and 10, the high temperature runs (T2) are at 3, 4, 7, 8, 11 and 12. In the present example tG1 was 20 min and tG2 was 60 min (5 to 95%), T1 was 30°C and T2 was 60°C. The composition of the organic eluent (B1:B2) (ternary composition, tC) was varied between 0, 50 and 100% MeOH in AN.


PeakTracking is an important step in method development, as most chromatographers using a method are afraid of unexpected changes. Therefore small variations in working conditions should be carried out to test method robustness. The question is however, “How much should we vary a parameter?”.


Figure 3. Next, the peaks are aligned in runs 1, 2, 3 and 4 (the first tG-T-sheet) with reference to the fixed elution order of run 2, shown in Figure 2. The organic eluent was acetonitrile. Note the differences in selectivities in the runs, indicating changes in relative peak positions, which must be understood before the method is validated. Each peak has to be aligned in a horizontal line. The error between peak areas in such a line should be less than 5-10%. The standard deviation of the sum of peak areas per run is also quite stable, in the above case it is excellent, 0.27%. The prerequisite of the high accuracy is to inject the same sample solution with all compounds included (names are not needed) and the same injection volume in all runs.


Figure 4. Next the peaks of the experiments 5-6-7-8 with the organic eluent (AN:MeOH 50:50 v:v) were aligned. The peak table indicates some double peaks, having the same retention time. These peak pairs are well separated in the other tG-T-sheets however, indicating the advantages of investigating selectivity changes by varying the eluent B between MeOH and AN (or some other eluent combinations.


A peak tracking table of a tG-T-tC (tC = ternary eluent composition) model showing different elution profiles of the same mixture of 18 compounds in fewer than 12 different conditions [14]. The peak areas in those runs have a standard deviation of ca. 2% on average and can therefore efficiently be used to track moving peaks and establish robust conditions for routine applications.


The next step is to align the 12 runs in the 3 tG-T-sheets. This is a process of looking at peak movements, peak overlaps and peak turnovers. Peak identification is based on peak areas, which represent the injected amount of the sample. Keeping this constant we get constant peak areas for a given compound in every run. Peak areas (concentration x volume = mass) are well suited to identify a peak. In peak overlaps the areas are additive. In Figure 3. we show the runs 1-2-3-4, where the organic eluent B1 is AN. Note the selectivity differences between the runs.


Then the peaks of the experiments 5-6-7-8 are aligned (Figure 4). Again there are different selectivities generated and several coeluting peak pairs observed.


At the end the last sheet of runs 9-10-11-12, which is the 100% methanol-sheet, all peaks are fully tracked (Figure 5).


When peak tracking is complete, we then calculate between the 3 core sheets another 97 sheets, filling out the total space so we can simulate any chromatogram at any point in that whole space with more than 106 virtual chromatograms. The results are highly precise, up to 99.8% accuracy in retention times, which is comparable to the operational accuracies of most UHPLC instruments.


Figure 2. The order of elution is established in the reference runs 2, 6 and 10 which are the flat gradients at the low temperature, typically resolving the most peaks. In this particular case eluent B in run 2 was 100% AN, in run 6 it was (AN:MeOH 50:50 v:v) and run 10 it was 100% MeOH. After fixing this table, in all the 3 tG-T- models (and in the whole cube) this elution order will remain constant.


If we change a parameter by very little, then we might not see hidden peaks. Therefore larger changes are required, e.g., two gradient times tG1 and tG2 with a factor 3 difference. In temperature optimisation experiments we should have a difference 30-40°C and with pH, 0.6 pH units over 3 (or more) runs.


With these experiments we can create an experimental design with 4-12 runs, which is sufficient in most cases. We should learn as much as possible with the least possible number of runs.


It is widely accepted, that the so called tG-T-model is the best one to start with. It has only 4 runs and it allows simple peak tracking as shown in the following figures.


Initially the order of elution is established at the experimental points 2, 6 and 10 (see Figure 2).


Method adjustments are much easier to implement when utilising resolution maps, as alterations of the “set point” or “working point” in the Design Space are not considered to be changes with post regulatory approval. This means, that changes in the Design Space (Figure 7) are possible without re-validation, allowing a much greater flexibility in the lab than in previous years.


From Figure 7 we can define several Design Spaces. The extension of the red areas (the possible Design Spaces) will give us a first idea about the robustness. We could also find suitable method parameter in methanol (front sheet of the cube in Figure 7 as well as in acetonitrile (back sheet in Figure 7).


From the design space as defined in Figure 7 we can get robustness information only for the measured parameters: Gradient time, pH and tC [%B2 in %B1] where B1 is acetonitrile and B2 is methanol. However, as DryLab®


4 is able to calculate other changes which might occur at the


same time, we can calculate the influence of additional parameters like flow rate or start- and end-%B of the gradient. No additional experiments are necessary for this kind of robustness calculation. The result is shown in Figure 8.


INTERNATIONAL LABMATE - APRIL 2013


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