Optimisation and robustness analysis of a hydrophobic interaction chromatography step

Process development, optimisation and robustness analysis for chromatography separations are often entirely based on experimental work and generic knowledge. The present study proposes a method of gaining process knowledge and assisting in the robustness analysis and optimisation of a hydrophobic interaction chromatography step using a model-based approach. Factorial experimental design is common practice in industry today for robustness analysis. The method presented in this study can be used to find the critical parameter variations and serve as a basis for reducing the experimental work. In addition, the calibrated model obtained with this approach is used to find the optimal operating conditions for the chromatography column. The methodology consists of three consecutive steps. Firstly, screening experiments are performed using a factorial design. Secondly, a kinetic-dispersive model is calibrated using gradient elution and column load experiments. Finally, the model is used to find optimal operating conditions and a robustness analysis is conducted at the optimal point. The process studied in this work is the separation of polyclonal IgG from BSA using hydrophobic interaction chromatography.     

Using computer simulation to assist in the robustness analysis of an ion-exchange chromatography step

This paper presents a methodology to gain process knowledge and assist in the robustness analysis of an ion-exchange step in a protein purification process using a model-based approach. Factorial experimental design is common practice in industry today to obtain robustness characterization of unit operations with respect to variations in process parameters. This work aims at providing a better insight into what process variations affect quality and to further reduce the experimental work to the regions of process variation that are of most interest. This methodology also greatly increases the ability to predict process performance and promotes process understanding. The model calibration part of the methodology involves three consecutive steps to calibrate a steric mass action (SMA) ion-exchange chromatography model. Firstly, a number of gradient elution experiments are performed. Secondly, experimental breakthrough curves have to be generated for the proteins if the adsorption capacity of the medium for each component is not known. Thirdly, a multi-component loading experiment is performed to calibrate the multi-component effects that cannot be determined from the single-component experiments. The separation process studied in this work is the separation of polyclonal IgG from a mixture containing IgG, myoglobin and BSA. The calibrated model is used to simulate six process variations in a full factorial experiment. The results of the simulations provide information about the importance of the different process variations and the simulations are also used to determine the crucial points for the process parameter variations. The methodology can be used to assist in the robustness analysis normally performed in the pharmaceutical industry today as it is able to predict the impact on process performance resulting from variations in salt concentration, column load, protein concentration and flow rate.     

Quality‐by‐design‐based ultra high performance liquid chromatography related substances method development by establishing the proficient design space for sumatriptan and naproxen combination

Quality‐by‐design‐based methods hold greater level of confidence for variations and greater success in method transfer. A quality‐by‐design‐based ultra high performance liquid chromatography method was developed for the simultaneous assay of sumatriptan and naproxen along with their related substances. The first screening was performed by fractional factorial design comprising 44 experiments for reversed‐phase stationary phases, pH, and organic modifiers. The results of screening design experiments suggested phenyl hexyl column and acetonitrile were the best combination. The method was further optimized for flow rate, temperature, and gradient time by experimental design of 20 experiments and the knowledge space was generated for effect of variable on response (number of peaks ≥ 1.50 – resolution). Proficient design space was generated from knowledge space by applying Monte Carlo simulation to successfully integrate quantitative robustness metrics during optimization stage itself. The final method provided the robust performance which was verified and validated. Final conditions comprised Waters® Acquity phenyl hexyl column with gradient elution using ammonium acetate (pH 4.12, 0.02 M) buffer and acetonitrile at 0.355 mL/min flow rate and 30°C. The developed method separates all 13 analytes within a 15 min run time with fewer experiments compared to the traditional quality‐by‐testing approach.     

Model-based optimization of a preparative ion-exchange step for antibody purification

A method using a model-based approach to design and optimize an ion-exchange step in a protein purification process is proposed for the separation of IgG from a mixture containing IgG, BSA and myoglobin. The method consists of three steps. In the first step, the model is calibrated against carefully designed experiments. The chromatographic model describes the convective and dispersive flow in the column, the diffusion in the adsorbent particles, and the protein adsorption using Langmuir kinetics with mobile phase modulators (MPM). In the second step, the model is validated against a validation experiment and analyzed. In the third and final step, the operating conditions are optimized. In the optimization step, the loading volume and the elution gradient are optimized with regard to the most important costs: the fixed costs and the feed cost. The optimization is achieved by maximizing the objective functions productivity (i.e. the production rate for a given amount of stationary phase) and product yield (i.e. the fraction of IgG recovered in the product stream). All optimization is conducted under the constraint of 99% purity of the IgG. The model calibration and the analysis show that this purification step is determined mainly by the kinetics, although as large a protein as IgG is used in the study. The two different optima resulting from this study are a productivity of 2.7 g IgG/(s m3) stationary phase and a yield of 90%. This model-based approach also gives information of the robustness of the chosen operating conditions. It is shown that the bead diameter could only be increased from 15 microm to 35 microm with maximum productivity and a 99% purity constraint due to increased diffusion hindrance in larger beads.     

Numerical optimization of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry: application to synthetic polymer molecular mass distribution measurement

A novel approach is described for the selection of optimal instrument parameters that yield a mass spectrum which best replicates the molecular mass distribution of a synthetic polymer. The application of implicit filtering algorithms is shown to be a viable method to find the best instrument settings while simultaneously minimizing the total number of experiments that need to be performed. This includes considerations of when to halt the iterative optimization process at a point when statistically-significant gains can no longer be expected. An algorithm to determine the confidence intervals for each parameter is also given. Details on sample preparation and data analysis that ensure stability of the measurement over the time scale of the optimization experiments are provided. This work represents part of an effort to develop an absolute molecular mass distribution polymer Standard Reference Material.     

Simple and Efficient Solution for Robustness Testing in Gradient Elution Liquid Chromatographic Methods

In this paper, an efficient way for robustness testing of gradient elution liquid chromatographic methods is proposed and tested on model mixtures comprising cilazapril, hydrochlorothiazide, and their degradation products, solutes that differ not only in polarities, but also in solubility and absorption characteristics. In general, the robustness could be tested with respect to various responses: resolution, retention factor, selectivity factor, change of detector response, etc. In chromatographic methods, the separation of the adjacent peaks is mandatory, and, consequently, the resolution is usually used as response. In isocratic elution methods, the resolution threshold depends on many factors, such as sizes of adjacent peaks, peak shapes, and asymmetry factor. At the same time, the situation is even more complex in gradient elution methods, because separation depends on a larger number of parameters, such as gradient profile, column geometry, mobile phase flow rate, column equilibration between gradient runs, etc. To ensure baseline separation, the authors propose application of separation criterion (s) as response and indirect modeling in the robustness evaluation. Examined response in this approach is represented by the difference between the retention time of the beginning of the peak and the retention time of the end of the previously eluting peak of the critical pair. Moreover, the proposed methodology included reusing experiments from the optimization phase to define a robust chromatographic region without increasing the number of experiments. It was shown that method robustness can be easily and efficiently evaluated by this methodology.     

Quality by Design: Design of Experiments Approach Prior to the Validation of a Stability-Indicating HPLC Method for Montelukast

This paper describes a systematic design of experiments (DoE) approach by applying the principle of quality by design (QbD) to determine the design space for a stability-indicating HPLC method prior to validation. By employing DoE, a simultaneous multivariate approach was carried out for mobile phase pH, flow rate, percentage of organic content and column temperature. A two-level fractional factorial design (2^4?1 + 2 center points = 10 experiments) was employed and statistical analysis of the experimental data uncovered the significant influential chromatographic factors. The experimental data for USP tailing and resolution were analyzed statistically to screen the chromatographic factors. This approach determined the most influential chromatographic factors. During this process, inferences were evaluated from various data tables, for example, analysis of variance, summary of fit, lack of fit, and parameter estimates. The study also explained various plots such as actual vs. predicted plot, Pareto plot, and prediction profiler. The acceptable range of the chromatographic factors was displayed as a Contour plot defining the ‘design space’ of the method. The range of operating conditions that guarantee a satisfactory QbD was deduced to finalize the method prior to validation. The method is simple, rapid, and robust for the determination of montelukast in montelukast sodium oral granules dosage form. The method was validated according to ICH guidelines for accuracy, precision, linearity, range, specificity, ruggedness and robustness (one factor varied at a time). The method has been successfully transferred to the quality control department for quality analysis of manufactured batches and stability samples.     

Factorial Design in Optimization of Chromatographic Separation of Ramipril and Its Impurities

In this paper optimization of chromatographic retention of ramipril and its five impurities employing factorial design is presented. On the basis of preliminary experiments three factors were chosen as inputs (acetonitrile content, pH of the mobile phase and buffer concentration) and retention factor as output. As optimal full factorial design 2³ was chosen, factors were examined at two different levels “low” and “high”. Three replications at zero level were added in order to check linearity and complete statistical tests. Relationship between inputs and output is presented in form of second order interaction model. Adequacy of model was explained using analysis of variance. After analysis of results optimal chromatographic conditions were set. Separations were conducted on a C₁₈ column with a mixture of acetonitrile and water phase (TEA in potassium dihydrogen phosphate) in ratio 23:77 v/v. Finally, the LC method was validated and applied for quality control analysis of commercially available tablets. The proposed method is simpler and faster as compared to existing official methods and therefore more adequate for routine control of ramipril during shelf life. Also a general approach which includes factorial design in method optimization offers a possibility for predicting and following the chromatographic behavior of such complex mixtures.     

Robustness testing of a reversed-phase high-performance liquid chromatographic assay: comparison of fractional and asymmetrical factorial designs

Robustness tests were performed on a reversed-phase HPLC assay for triadimenol. Different experimental designs were compared. Two-level fractional factorial designs with different resolutions were used to study the influence of procedure-related factors. The factors chromatographic column manufacturer at four levels and instrument at three levels were stepwise included in the study using asymmetrical factorial designs. The significance of the factor effects was determined statistically, using two types of error estimates in the calculation of critical effects, and graphically, by means of half-normal plots. The asymmetrical designs turned out to be an efficient and economic method to examine the influence of factors at different numbers of levels in the robustness testing of analytical methods.     

Quality by Design: Design of Experiments Approach Prior to the Validation of a Stability-Indicating HPLC Method for Montelukast

This paper describes a systematic design of experiments (DoE) approach by applying the principle of quality by design (QbD) to determine the design space for a stability-indicating HPLC method prior to validation. By employing DoE, a simultaneous multivariate approach was carried out for mobile phase pH, flow rate, percentage of organic content and column temperature. A two-level fractional factorial design (2⁴⁻¹ + 2 center points = 10 experiments) was employed and statistical analysis of the experimental data uncovered the significant influential chromatographic factors. The experimental data for USP tailing and resolution were analyzed statistically to screen the chromatographic factors. This approach determined the most influential chromatographic factors. During this process, inferences were evaluated from various data tables, for example, analysis of variance, summary of fit, lack of fit, and parameter estimates. The study also explained various plots such as actual vs. predicted plot, Pareto plot, and prediction profiler. The acceptable range of the chromatographic factors was displayed as a Contour plot defining the ‘design space’ of the method. The range of operating conditions that guarantee a satisfactory QbD was deduced to finalize the method prior to validation. The method is simple, rapid, and robust for the determination of montelukast in montelukast sodium oral granules dosage form. The method was validated according to ICH guidelines for accuracy, precision, linearity, range, specificity, ruggedness and robustness (one factor varied at a time). The method has been successfully transferred to the quality control department for quality analysis of manufactured batches and stability samples.

     

High-throughput logP measurement using parallel liquid chromatography/ultraviolet/mass spectrometry and sample-pooling

A novel approach to high-throughput logP measurement based on liquid chromatography/ultraviolet/mass spectrometry (LC/UV/MS) is proposed. The logP value is determined by correlation with the logk value, where k is the capacity factor k = (t(r)-t(0))/t(0), with the logP value using a defined set of standards. Since the analyte retention time (t(r)) is determined from the appropriate extracted ion chromatogram (EIC), there are no interferences from impurities and this allows the pooling of multiple compounds into one injection. To ensure the accuracy and instrument robustness in a routine high-throughput environment, a simple and MS-friendly mobile phase consisting of 20 mM ammonium carbonate (pH 8.0) for basic compounds or 20 mM ammonium formate (pH 1.0) for acidic compounds, both in combination with methanol at a ratio of 45:55, is used. This approach has been successfully used on single as well as parallel multi-channel LC/UV/MS systems to screen small to large sets of lead compounds and their analogs. A high-throughput capability to analyze over 1000 compounds per day has been achieved.     

Reversed-phase liquid chromatography column testing: robustness study of the test

Choosing the right RPLC column for an actual separation among the more than 600 commercially available ones still represents a real challenge for the analyst particularly when basic solutes are involved. Many tests dedicated to the characterization and the classification of stationary phases have been proposed in the literature and some of them highlighted the need of a better understanding of retention properties to lead to a rational choice of columns. However, unlike classical chromatographic methods, the problem of their robustness evaluation has often been left unaddressed. In the present study, we present a robustness study that was applied to the chromatographic testing procedure we had developed and optimized previously. A design of experiment (DoE) approach was implemented. Four factors, previously identified as potentially influent, were selected and subjected to small controlled variations: solvent fraction, temperature, pH and buffer concentration. As our model comprised quadratic terms instead of a simple linear model, we chose a D-optimal design in order to minimize the experiment number. As a previous batch-to-batch study [K. Le Mapihan, Caractérisation et classification des phases stationnaires utilisées pour l'analyse CPL de produits pharmaceutiques, Ph.D. Thesis, Pierre and Marie Curie University, 2004] had shown a low variability on the selected stationary phase, it was then possible to split the design into two parts, according to the solvent nature, each using one column. Actually, our testing procedure involving assays both with methanol and with acetonitrile as organic modifier, such an approach enabled to avoid a possible bias due to the column ageing considering the number of experiments required (16 + 6 center points). Experimental results were computed thanks to a Partial Least Squares regression procedure, more adapted than the classical regression to handle factors and responses not completely independent. The results showed the behavior of the solutes in relation to their physico-chemical properties and the relevance of the second term degree of our model. Finally, the robust domain of the test has been fairly identified, so that any potential user precisely knows to which extend each experimental parameter must be controlled when our testing procedure is to be implemented.     

Application of nonparametric statistics to the estimation of the accuracy of Monte Carlo confidence intervals in regression analysis

Confidence intervals and their uncertainties for nonlinear regression parameters are obtained using nonparametric statistical methods. The confidence intervals are calculated by means of a Monte Carlo procedure. Their uncertainties depend on the confidence level desired and on the number of Monte Carlo simulations of the data set. They are obtained by calculating the uncertainties in the boundaries of the confidence intervals using a generalization of the nonparametric method used to calculate confidence intervals for medians. The method described here provides reliable confidence intervals at relatively low computational expense. It seems especially suited to the statistical analysis of nonlinear regression problems that are difficult to deal with using conventional methods.     

Modeling and Uncertainty Quantification of Vapor Sorption and Diffusion in Heterogeneous Polymers

A high‐fidelity model of kinetic and equilibrium sorption and diffusion is developed and exercised. The gas‐diffusion model is coupled with a triple‐sorption mechanism: Henry’s law absorption, Langmuir adsorption, and pooling or clustering of molecules at higher partial pressures. Sorption experiments are conducted and span a range of relative humidities (0–95 %) and temperatures (30–60 °C). Kinetic and equilibrium sorption properties and effective diffusivity are determined by minimizing the absolute difference between measured and modeled uptakes. Uncertainty quantification and sensitivity analysis methods are described and exercised herein to demonstrate the capability of this modeling approach. Water uptake in silica‐filled and unfilled poly(dimethylsiloxane) networks is investigated; however, the model is versatile enough to be used with a wide range of materials and vapors.     

Determining association constants from titration experiments in supramolecular chemistry

The most common approach for quantifying interactions in supramolecular chemistry is a titration of the guest to solution of the host, noting the changes in some physical property through NMR, UV-Vis, fluorescence or other techniques. Despite the apparent simplicity of this approach, there are several issues that need to be carefully addressed to ensure that the final results are reliable. This includes the use of non-linear rather than linear regression methods, careful choice of stoichiometric binding model, the choice of method (e.g., NMR vs. UV-Vis) and concentration of host, the application of advanced data analysis methods such as global analysis and finally the estimation of uncertainties and confidence intervals for the results obtained. This tutorial review will give a systematic overview of all these issues-highlighting some of the key messages herein with simulated data analysis examples.     

Validation of an HPLC Method for the Determination of Valdecoxib and its Degradation Product: a Mixture of α- and β-n-Lactosyl Sulfonamide Anomers

An HPLC method has been developed for the separation of valdecoxib and a degradation product consisting of α and β-N-lactosyl sulfonamide, i.e. α and β anomers (SC-77852). Best results were achieved with a Chromolith Performance RP-18e column (100 mm × 4.6 mm), macropore size 2 μm, mesopore size 13 nm, with an eluent of methanol:water containing a 1% solution of TEA (36:64 v/v), pH 7.4 (adjusted with 85% orthophosphoric acid), at 22 °C. Detection was at 220 nm. The method was validated for its selectivity, linearity, precision (repeatability) and robustness. Quantitation and detection limits were determined for both valdecoxib and SC-77852. Method robustness was further evaluated by performing 2³ full factorial design experiments. The final step, optimisation of the variables, was performed using response surface design. The validated method was used for assay of valdecoxib and SC-77852 in Bextra^® film-coated tablets.     

Simultaneous multiresponse optimization of an HPLC method to separate seven cephalosporins in plasma and amniotic fluid: Application to validation and quantification of cefepime, cefixime and cefoperazone

An HPLC method for the separation of seven cephalosporins [Cefepime (CEP), ceftazidime (CTA), ceftizaxime (CTI), ceftriaxone (CTR), cefotaxime (COT), cefixime (CIX) and cefoperazone (COP)] in human plasma and amniotic fluid has been developed. Optimization of the chromatographic method was performed in three steps: a series of initial experiments followed by two sets of experiments based on different experimental designs. The initial experiments were performed to decide the basic analytical requirements of the method. Then screening experiment fractional factorial design was used in order to decrease the number of parameters by eliminating parameters which having insignificant effect on responses. The parameters having significant effect were further optimized through a full factorial design. Having studied two responses (retention times and resolutions), a desirability function that assess the responses together, was used to find experimental conditions where the system generated desirable results. The desirable results were obtained with XTerra C18 (250 mm × 4.6 mm, 5 μm i.d.) column, 40 mM phosphate buffer, pH 3.2, 18% MeOH, 0.85 mL min⁻¹ flow rate and 32 °C column temperature. Gradient elution with MeOH was applied. A simple and efficient solid-phase extraction was applied for the preparation of plasma and amniotic fluid samples. The validation parameters of the method were evaluated in accordance with ICH guideline. The method validated was applied to the analysis of CEP and COP in maternal venous, fetal venous and fetal arterial plasma, and to the analysis of CIX in maternal venous plasma and amniotic fluid.