Design Space in pharmaceutical industry

Design Space in pharmaceutical industry Anton Sellberg Department of Chemical Engineering, Lund University, Sweden October 2, 2013 Abstract The pharmaceutical industry have long been crippled by the restrictions on the production routes. This have made production expensive without assuring a good end result. To make pharmaceutical production more flexible new guidelines have been developed. With the new guidelines pharmaceuticals can be produced as long as the critical process parameters are within the Design space. The Design space consists of the combinations of critical process parameters and process inputs which results in critical quality attributes reaching their minimum values. To find the design space several different methods have been developed and evaluated. The methods work very well but visualizing the design space becomes harder and harder as the dimension increases. The optimal design space was created to make the design space easier to grasp and to take the process economy into account. When finding the optimal design space the problem was reduced to an optimization problem were the economical parameters (yield and productivity) were maximized. The critical process parameters could then be expressed as a function of yield and load resulting in an optimal design space which only contains the optimal way of running the process and is easy to visualize. Variations are always present in all processes and this should also be considered when creating the design space and thus a robust optimal design space would be ideal but by adding process variation the optimization problem gets harder and local minima can occur. Keywords: Chromatography, Design Space, Optimization, Biopharma Introduction The pharmaceutical industry is quite different from other chemical and biochemical industries in the sense that the regulations are very strict. The restrictions put on the industry have crippled the development of new production and downstream processing techniques. With the new guidelines suggested by International Conference on Harmonization (ICH, 2009), more flexibility is introduced to the pharmaceutical industry but more emphasis is put on the downstream processing. Essentially the new guidelines means that more variations in production can be allowed as long as the final results are satisfying. In the case of insulin production, chromatographic separation of impurities is a big part of the downstream processing. Thus evaluating how variations in the production and the early downstream processing affects the outcome of the chromatographic separations and how to control the process to ensure a satisfying outcome becomes increasingly important. By taking advantage of this new flexibility in chromatography, the number of failed batches can be kept to a minimum and more consistent result can be achieved by changing the operating conditions to cancel out inconsistencies in the feed. Critical quality attributes Critical quality attributes (CQAs) are properties possessed by the pharmaceutical which assures the quality of the drug. The critical quality attributes should be measurable and controlled in such a way that end product meets the minimum requirement for all the CQAs. Critical quality attributes can regard potency or concentration but it can also concern the side effects of the drug or the concentration of impurities. In pharmaceutical production important critical quality attributes are purity and concentration. Apply- 1

ing this to chromatography means that after the chromatography step a certain purity in the pool have to be achieved, but it also means that the pool cannot be to diluted because then the concentration will become too low. The combination and interaction between the process inputs (e.g concentration of product and impurities) and the critical process parameters (e.g. load volume and gradient volume) determines if the critical quality attributes meets the minimum requirements. Critical process parameters Critical process parameter, or CPP is defined by ICH (2009) as A parameter whose variability has an impact on a critical quality attribute and therefore should be monitored or controlled to ensure the process produces the desired quality. The second approach means that the CPP should be monitored and as long as the variation does not compromise the quality of the end product nothing needs to be done. This approach is very similar to the traditional way of producing pharmaceuticals since this does not add any flexibility in the process. The other approach is to find a control strategy for the CPP. By doing this a lot of flexibility is added to the process. Since the CPP has an impact on the CQAs this impact should be used to cancel out inconsistencies in the process inputs if possible. Some CPPs cannot easily be changed (e.g. column packing in the case of chromatography) while others (e.g. buffer mixing) can. The control strategy should take the process inputs into account and from that set the CPP to a value which gives the best end product. Design space Design space is defined by ICH (2009) as The multidimensional combination and interaction if input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality. This means that some of link between the CPPs, process inputs and the CQAs should be established and all the combinations of CPPs which gives satisfying results are considered the design space. The process should be controlled in such a way that the CQAs reach their expected values. Depending on the CQA this can be done in numerous ways but it is always the process inputs (e.g. material attributes) and the process parameters that will dictate the final values of the CQAs. From the definition of design space it is also clear that the actual values for the CPPs and process inputs are unimportant, only the combination between process inputs and CPPs make up the design space, unlike the traditional way of producing pharmaceuticals where the actual values of the parameters played a much bigger part. Any combination of input variables and process parameters that produces a product with sufficient quality then becomes a legit way of producing it. By having a greater understanding for the different production steps will yield a bigger design space thus more flexibility in the production. By providing the regulatory agencies with a design space a number of different operating conditions can be approved at the same time. The design space shows which combinations of process inputs and CPPs that yields an end product that fulfills all the constraints in CQAs. Thus a change within the design space required no post-approval submissions to the regulatory agencies. A change outside the design space still requires post-approval submission and therefore submitting a large design space could be of great benefit but comes with potential downsides (e.g., more validation work might be needed). Another downside of a large design space is the fact that if only purity and concentration is taken into account when creating the design space, a lot of the combinations found will not be feasible from an economical point of view. Theory Chromatographic model For this thesis the kinetic dispersive model (equation 3) with langmuir adsorption (equation 4 was chosen to model the chromatographic process. The kinetic dispersive model, models the adsorption to the stationary phase, diffusion and the convection in the column but disregards the diffusion into the stationary phase. The kinetic dispersive model In Equation 1 the diffusion velocity is calculated from the Peclet number (Pe), the particle diameter 2

(d p ) and the internal velocity (v int ). D ax = v int d p Pe (1) The apparent velocity (v app ) was calculated according to Equation 2 where F v is the volumetric flow, A t is the cross-section area of the column, ε C is the void of the column, ε p,i is the particle void for component i and ε t,i is the total void for component i. v app,i = F v A t (ε C + (1 ε C ) ε p,i ) = F v (2) A t ε t,i Equation 3 shows how the concentration of component i in the mobile phase changes over time and position in the column (Schmidt-Traub (2012);Guiochon et al. (2006)). c i 2 c i = D ax r 2 v c i app,i Langmuir adsorption r (1 ε c) ε c q i (3) For the adsorption part of the process, langmuir mobile phase modulator (Karlsson et al., 2004) was used. In equation 4 the expression for how the concentration of component i changes in the stationary phase depending on time and Henrys constant (Melander et al., 1989). q i ( ( = k kin,i H i c i 1 q ) ) i q i q max (4) Equation 5 comes from the work of Johansson (2013) and is the Henrys constant used in Equation 4.This expression takes both the effect of ionexchange and hydrophobic interaction characteristics into account. Boundary values H i = H 0,i e C salt(p 1,i +p 2,i C ethanol) (5) At the inlet of the column a Dirichlet condition was used and at the outlet a von Neuman condition was used. At time zero, the salt and ethanol concentration in the column is set to be the same as in buffer A. The amount of proteins in the mobile phase and adsorbed to the stationary phase is set to zero. Equation 6 shows the Dirichlet condition at the inlet and c in is the concentration at the inlet. c r=0 = c in (6) Equation 7 shows the von Neuman condition used at the outlet. Discretization c r = 0 (7) r=l To be able to solve the partial differential equations stated above a semidiscretization (Davis, 1984) was used to approximate them to ordinary differential equations. This technique is called the method of lines. After the space dimension (along the column axis) was discretized, the system of ordinary differential equation was solved using ode15s (Shampine and Reichelt, 1997) in MATLAB. Methods There are several different ways to find the design space for a process. What they all have in common is that a lot of experiments or simulations have to be done in order to find the design space. To minimize the time and effort needed to find the design space four different algorithms have been created and evaluated. To find the optimal design space some process outputs have to be considered critical performance attributes (compare to critical quality attributes). These outputs should affect the economy of the process in a direct way. As discussed previous in the thesis, yield and productivity can be directly related to the cost of running the process and the ratio between the two can set using normalized earnings. By maximizing the productivity and yield given a feed composition, an optimal design space can be found. Since there are always a tradeoff between yield and productivity the design space will be a pareto front. If the load can be varied an overall pareto front can be found. This pareto is the best 3

possible for the process. But the load variable is often determined in the production step or steps previous to the chromatographic step. If the load cannot be varied or only varied in a small range, the pareto front will change. Each load will form a suboptimal pareto front with some of its points in the overall pareto front but most of them beneath the pareto front (suboptimal points). Since the load has such a great effect on the final results it was chosen as the parameter which all others parameters should be related to, to find the optimal design space. To be able to find multidimensional interaction which gives the desired results either the yield or productivity must be set to a value within the design space. Combining this with knowledge of the load, all the other parameters can be chosen thus a multidimensional design space have been constructed. Instead of describing the design space with an actual space, the interaction between the different parameters can be described by a mathematical expression for each decision variable (Equation 8). X i = f (Load,) (8) By making smart decisions the mathematical expression itself can be very valuable when running the process. By knowing the load and a desired yield, the design space acts as a simple process control for the other process parameters. Productivity Ethanol concentration in buffer A 0.22 0.2 0.18 0.16 0.14 0.12 0.1 Variable load 0.08 0.06 0.75 0.8 0.85 0.9 0.95 1 0.065 0.06 0.055 0.05 0.045 0.04 0.035 Figure 1: The results of the optimization. 0.03 0.025 0.02 Figure 2: The ethanol concentration in the buffer plotted against yield for different loads. Results When yield and productivity are maximized a pareto front is obtained (Figure 1). It is clear that each load fits to the overall pareto at different points, thus having a fixed load will result in a less flexible design space. On the other hand the load depends on the cultivation and previous purification steps and it is important to realize what yield and productivity you can expect from a given load. The pareto front contains all the optimal operating points but no suboptimal points therefore the optimal design space will only contain optimal operating points. The data from the pareto front is then used to create the optimal design space by fitting a equation to the process parameters (Figure 2, 3, 4 and 5). Salt concentration in buffer A 2000 1900 1800 1700 1600 1500 1400 1300 Figure 3: The salt concentration in the buffer plotted against yield for different loads. 4

3 2.5 From the pareto front obtained from the optimization the design space could be created by plotting the decision variables against yield and fitting curves to the data. The design space then became the mathematical correlation between the decision variables (CCPs) and the yield and load. By defining the design space like this it assures that the process is always run in a way which produce results which are at the pareto front. UV cut point 1 2 1.5 1 0.5 0 Figure 4: The first UV cut point plotted against yield for different loads. UV cut point 2 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 Figure 5: The second UV cut point plotted against yield for different loads. Discussion The thought behind optimal design space was to reduce the design space problem to an optimization problem which could be solved to find the design space. The economy i.e. yield and productivity should be maximized (the objective function) by regulating the process using the critical process parameters (the decision variables) but still keeping the critical quality attributes at satisfying levels (the constraints). Conclusions To improve the design space concept the optimal design space needed to take the economic aspects into account. The optimal design space also needed to be easier to visualize than the design space. To achieve this the problem was reduced to an optimization problem were only the optimal points (in regards to yield and productivity) were used to create the design space. References M. E Davis. Numerical methods and modeling for chemical engineers. John Wiley & Sons, 1984. G. Guiochon, D. G. Shirazi, A. Felinger, and A. M. Katti. Fundamentals of preparative and nonlinear chromatography. Elsevier Academic Press, 2006. ICH. Ich harmonised tripartite guideline: Pharmaceutical development q8(r2). International conference on harmonisation, 2009. K. Johansson. Model for ethanol and salt concentration in preparative chromatography. a, 2013. D. Karlsson, N. Jakobsson, K-J. Brink, A. Axelsson, and B. Nilsson. Methodologies for model calibration to assist the design of a preparative ionexchange step for antibody purification. Journal of chromatography a, pages 71 82, 2004. W. R Melander, Z El Rassi, and C Horvath. Interplay of hydrophobic and electrostatic interactions in biopolymer chromatography: Effect of salts on the retention of proteins. J. of Chromatogr. A, 1989. H. Schmidt-Traub. Preparative chromatography. Wiley VCH, 2012. L. F. Shampine and M. W. Reichelt. The matlab ode suite. SIAM journal on scientific computing, 1997. 5