Quantitative Impurity Rejection Analysis for Crystallization - Organic

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Quantitative Impurity Rejection Analysis for Crystallization Daniel David Caspi, and Fredrik L Nordstrom Org. Process Res. Dev., Just Accepted Manuscript • DOI: 10.1021/acs.oprd.8b00143 • Publication Date (Web): 28 May 2018 Downloaded from http://pubs.acs.org on May 28, 2018

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Organic Process Research & Development

Quantitative Impurity Rejection Analysis for Crystallization Daniel D. Caspi* and Fredrik L. Nordstromi Research & Development, AbbVie Inc., 1 N Waukegan Rd, North Chicago, Illinois, 60064, USA * Corresponding author email: [email protected] i Material and Analytical Sciences, Boehringer-Ingelheim, 900 Ridgebury Rd, Ridgefield, CT, 06877, USA

TOC GRAPHIC:

ABSTRACT: The analysis of impurity profiles is one of the most frequently performed activities in drug development. While mass-based quantification using a reference standard often provides the highest degree of accuracy, carrying this out on every impurity across the synthetic scheme can quickly become untenable when considering the often-large number of impurities and requirement for a synthesized and characterized reference standard. These labor-intensive activities are generally only reserved for select impurities using a science- and risk-based approach, and approximations such as ‘purge factor’ or ‘before and after peak area%’ are often used in the remaining cases when a wider margin of error is acceptable. Presented herein is a simple mathematical framework to perform mass-based quantification for impurity rejection in silico using the principles of mass balance, without the burdensome requirements of obtaining individual response

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factors or reference standards. This analysis is expected to provide useful guidance for process and analytical chemists.

KEYWORDS: Impurity rejection, impurity, crystallization, HPLC, purge factor

Crystallizations are routinely carried out in the pharmaceutical industry across the synthetic scheme: from early starting materials to Active Pharmaceutical Ingredient (API). Other than providing a convenient means to isolate the product as a solid, the most important objective in crystallization is purification. Common impurities such as reactants, reaction by-products, degradants, chiral impurities, genotoxic or mutagenic impurities (MI) and even inorganic impurities can often be removed through crystallization. In extreme cases, impurities can persist over several synthetic steps, requiring numerous crystallizations to reduce impurities below acceptable levels. These purifications are critical in producing a drug substance suitable for use in preclinical and clinical trials, as well as for marketed drugs. Stringent regulatory requirements are also in place to ensure that the API meets all purity and quality attributes, which are enforced through comprehensive quality control systems.1 Despite the ubiquity of impurity control through crystallizations, very few reported studies have aimed at understanding the mechanism of impurity rejection (e.g., incorporated into the crystal lattice, surface adsorption, solubility-limited, etc.) or even determine the impurity rejection across the crystallization on a mass-basis.2–4 Chromatography (e.g., HPLC, UPLC, SFC, GC) is the predominant technique of choice across the pharmaceutical industry to identify impurities and quantify their concentrations in isolated products and process solutions. Once a suitable method has been developed that provides adequate resolution of product and impurities, the level of an impurity is estimated from the peak area percentage (area%) in the chromatogram (Figure 1). Effective comparison of crystallization conditions (i.e., over a series of solvents and conditions) for purification relies on the method development, analysis, and interpretation of this chromatographic data. ACS Paragon Plus Environment

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Figure 1. Example HPLC chromatogram with product eluting at 4.3 min and impurity eluting at 6.4 min.

Although relative area percentage is frequently used as a basis for comparison, it is only an estimate of relative concentration. Since the response factor for the product and impurities can often differ, the area% does not necessarily correspond to the concentration of the impurity (or product). In order to determine the actual mass-based concentration of all impurities, the response factor for each component needs to be determined (Figure 2).5

Figure 2. Relationship between concentration and area; for example, Product and Impurity with differing response factors

Performing this type of analysis requires that each component is isolated in sufficient purity and with known potency. Development work like this can easily become insurmountable as each individual impurity needs to be synthesized, isolated, and characterized, particularly when many impurities are present or are synthetically challenging to prepare.6 Therefore, a common approach is to approximate the relative impurity concentration before and after a unit operation by using impurity area%.7 As a result, when varied process



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conditions or solvents are screened to identify optimum purification, relative area percentages are generally relied upon for comparison. As a typical example, compare the following crystallizations of two different batches of a crude product to reject an impurity. In the first batch, the impurity was reduced from 1.0 area% to 0.40 area% after crystallization with a yield of 85%. In the second batch, the impurity level in the crude was reduced from 1.5 area% to 0.54 area% after crystallization with a yield of 94%. In comparing the impurity rejection efficacy, if only the before and after area% of the impurity is considered, then crystallization of the first batch is able to reduce the impurity area% by 60% (1.0 to 0.40 area%) versus 64% (1.5 to 0.56 area%) for the second. Using purge factors, this corresponds to 2.5 for the first batch and 2.8 for the second. Thus, it may appear that the crystallization of second batch was more effective at rejecting the impurity. However, as will be presented, the actual mass-based impurity rejections in both crystallizations are identical (i.e., 66%). The potential impact of comparing meaningful and accurate data cannot be overstated particularly at early stages of process development. For instance, the choice of crystallization solvents can often be directly tied back to simple impurity rejection studies. Solvent selection and crystallization optimizations can have profound implications on downstream development in terms of timelines, efficiency and impurity controls. Furthermore, only by analyzing physically relevant data can proper conclusions be made in regards to the prevailing impurity rejection mechanism in the crystallization.

Figure 3. Example of purification in two crystallizations

The intent of this report is to establish a mathematical framework for calculating and comparing impurity rejections over crystallizations through the use of simple mass balances. A complete data set for the calculations can generally be gathered from an additional 0–1 analytical samples apart from those gathered ACS Paragon Plus Environment

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during routine testing, necessitating minimal additional effort from a scientist in the laboratory. Straightforward equations are presented that can easily be used in determining impurity rejections and in assessing all the data in the mass balance. Finally, the utility of the derived equations will also be demonstrated in simulating impurity purges across various process scenarios. RESULTS AND DISCUSSION The Mass Balance. In crystallization, a crude solution is partitioned into solid and liquid phases. The crude (denoted with superscript C) is a liquid and comprises all dissolved components. The solid (denoted with superscript S) is primarily made up of the product and is preferably exhibiting higher purity than the crude. The corresponding liquid (denoted with superscript L), or supernatant, is made up of low concentrations of product and impurities and is preferentially enriched in impurities. This separation through crystallization is illustrated in Figure 4.

Figure 4. Separation of product and impurities through crystallization

The following mass balances can be established for the product and impurity (for simplicity only one impurity is addressed). Product (P): m PC = m PS + m PL

(1)

miC = miS + miL

(2)

Impurity (i):



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Impurity rejection (Ri) is defined herein as mass of a given impurity in the liquid phase divided by mass of the impurity in the crude. Thus, Ri ranges from 0% (all impurity in solid) to 100% (all impurity in liquor).

Ri =

miL miC

(3)

The product yield (YP) can similarly be written:

mPS mPC

YP =

(4)

The concentration, C, of product or impurity in a solid or liquid is determined from the HPLC chromatogram. When linearity applies (as in Figure 2), the following relationship can be established for the product:

and impurity:

Γ௣ = ݂௣ ‫ܥ‬௣

(5)

Γ௜ = ݂௜ ‫ܥ‬௜

(6)

where Γ is the peak area (e.g., mAUs, milli-absorbance units) at a specific wavelength and f is the response factor. Dividing the corresponding terms in Equation 6 and 5 yields: ஼೔

஼೛

=

୻೔ ௙೛

୻೛ ௙ ೔

=ி

ଵ ୻೔

୻೛

(7)

where F is the relative response factor. ‫=ܨ‬

௙೔

௙೛

(8)

Since the volume or mass of solvent is the same for the product and impurity (regardless of dilution), Equation 7 can be written for the crude, solid and liquid, respectively: ݉௜஼ = ݉௜ௌ =

಴ ಴ ௠೛ ୻೔

ி ୻಴ ೛

ೄ ೄ ௠೛ ୻೔

ி ୻ೄ ೛

(9)

(10)


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݉௜௅ =

ಽ ಽ ௠೛ ୻೔

ி ୻ಽ೛

(11)

These equations provide the basis for expressing the impurity rejection (Equation 3) and product yield (Equation 4) in terms of peak area (e.g., from HPLC). Substituting Equation 9 and 11 into Equation 3, and including Equation 4 and 1, yields after simplification:  ΓiL   L  Γ Ri = (1 − YP )  PC   Γi   C   ΓP 

(12)

It should be noted that the relative response factor F is cancelled out in this operation. This expression provides a simple algebraic solution to determine the impurity rejection based on HPLC chromatograms of the crude and liquid, where product yield normally is determined from the concentration in the liquid, that is, from the same chromatogram. Similarly, Equation 9 and 10 can also be used with Equation 1, 3 and 4, giving:  ΓiS   S  Γ Ri = 1 − Yp ⋅  PC   Γi   C   ΓP 

(13)

Equation 13 can thus be used to determine impurity rejection based on the HPLC chromatograms of the isolated solid, crude and product yield. The third variation is obtained when Equation 10 and 11 are used with Equation 1, 3 and 4:  ΓiL   L Γ   p Ri =  Yp   ΓiS   ΓiL   ⋅  +   1 − Y   ΓS   ΓL  p   p    p

(14)

That is, impurity rejection determined from the HPLC chromatograms of the isolated solid, liquid and product yield. The final permutation can be derived by combining Equation 12 and 13 and only express impurity rejection from the HPLC chromatograms of the crude, solid and liquid:



 ΓpC ΓpS   C − S Γ Γi  i  Ri =  ΓpL ΓpS   L− S Γ   i Γi 

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(15)

Analogously, the same operation can be done to express product yield:  ΓiC ΓiL   C − L Γ Γp  p Yp =   ΓiS ΓiL   S − L Γ   p Γp 

(16)

Thus, the theoretical product yield over the crystallization can be determined without even knowing the response factor of any component with concentration (Figure 2), and solely by using the HPLC chromatograms of the crude, solid and liquid as long as at least one impurity is present. Impurity rejection calculations. As mentioned above, the ‘before and after area%’ approach to calculate impurity purge of impurity i is determined from the change in area% before and after the crystallization. Mathematically, this is expressed as:  ΓiC ΓiS  −  ΓC + ΓC Γ S + Γ S i p i p * Ri =  C  Γi    C C Γ +Γ  p   i

   

(17)

when only one impurity is accounted for. Using Equation 5 and 6, Equation 17 can be rearranged into the following format: ܴ௜∗ = 1 − ೔಴ ೔ೄ ೛ೄ ஼ (஼ ା஼ /ி)

஼ ೄ (஼ ಴ ା஼ ಴ /ி) ೔

೛

೔

(18)

Replacing mass for concentration affords: ܴ௜∗ = 1 − ೎೔ ൫࢓࢏࢙ ࢙ ௠ ା࢓ /ࡲ൯ ࢉ ௠ೞ ൫࢓ ା࢓ࢉ࢖ /ࡲ൯ ೔

࢏

࢖

(19)

since the volume or mass of solvent is the same for the product and impurity. From the mass-based impurity rejection expression (Equation 3) in combination with Equation 2, we can write: ACS Paragon Plus Environment

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Ri = 1 −

miS miC

(20)

Comparing the impurity rejection in the ‘before and after area%’ approach (Equation 19) with the impurity rejection obtained using actual mass balances (Equation 20) reveals an error factor that is highlighted in blue in Equation 19. This represents the error in calculating the impurity rejection by solely resorting to area% before and after the crystallization. The magnitude of the error depends on product yield, response factor differences, purity of crude and purity of final solids. An example of the manifested error is visualized in Figure 5 where a crude comprising 5% of an impurity was crystallized with a product yield of 85%. The error increases as relative response factor (F) increases, and to a smaller extent, as a function of the remaining impurity in the solids after crystallization. While product yield accounts for the majority of the error in Figure 5, very large values of the relative response factor (F) can also lead to significant discrepancies. Even if 100% product yield is obtained, there are only three cases where no errors can be obtained, namely when F is unity, 0% impurity rejection, and 100% impurity rejection. Obviously, these conditions seldom, if ever, occur in the laboratory.

Figure 5. Example of the absolute error in calculating impurity rejection over crystallization using area% before and after crystallization

Similarly, the purge factor (Pi) approach to assess purification over crystallization can be expressed mathematically as:



ܲ௜ =

൮ ൮

಴

Γ೔

಴

಴൲

Γ೔ శΓ೛ ೄ

Γ೔

ೄ

ೄ൲

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(21)

Γ೔శΓ೛

This means that if the impurity level is 1 area% in the crude and 0.1 area% in the crystallized solids then the purge factor is 10. Through Equation 5–7 we may rearrange Equation 21 as a function of mass instead of area%: ܲ௜ =

ೄ /ி൯ ௠೔಴ ൫௠೔ೄ ା௠ು

಴ /ி൯ ௠೔ೄ ൫௠೔಴ ା௠ು

(22)

It should be noted that mass-based impurity rejection, Ri, and purge factor are inversely related and can, through Equation 3, be written as: ܲ௜ = ቀ ቁ ೔ ು ଵିோ ൫௠಴ ା௠಴ /ி൯ ଵ

೔

൫௠ೄ ା௠ೄ /ி൯ ು

೔

(23)

In this case the same error function that is present in Equation 19 is also obtained in Equation 23. In order to relate impurity purge to the actual mass or mole of impurity rejected product normalization is needed. This can be expressed as: ߚ௜ = (ଵିோ ) ௒೛

೔

(24)

Where βi is then the mass-based impurity purge of impurity i relative to loss of product and Ri can be calculated by any of Equation 12–15. This simple relationship thus provides a straightforward mean to compare impurity purges over crystallizations that are based on changes in masses rather than changes in area%. Applications of the mass balance. As explained above, the calculation of impurity rejection via mass balances can be done in four different ways depending on what information is available of the crude, solid, liquid and product yield. Hence, not all parameters are needed to determine the impurity rejection. If the HPLC chromatogram of the crude has not been determined, the impurity rejection can still be determined


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using Equation 14. If the HPLC chromatogram of the solid is not available, it is still possible to determine the impurity rejection using Equation 12, and so on. Limitations of the mass balance. These relationships and calculations presume a mass balance and hence are only applicable when the components of the separated solid and liquid phases are equal to their sum in the crude. Hence, the mass balance is not satisfied in cases where the product or impurities react or new impurities form or degrade during the course of the crystallization or subsequent analysis. Another potential restriction is that all of the assays need to have the same the relative response factor for each impurity; i.e., using different methods, detection lamps, sample preparations, or instruments may result in different relative response factors, and correspondingly, a mass balance that is not fulfilled. 1. Determination of the fourth, missing parameter. An important implication of these relationships is that combining these equations allow for calculation of the fourth missing parameter, whichever that may be. For example, Equation 12 and 13 afford (after rearranging):

 ΓiS  1  ΓiC  (1 − YP )  ΓiL   S  =  C  −   YP  ΓPL   ΓP  YP  ΓP 

(25)

Hence, this equation can be used to determine the theoretical area% of an impurity or impurities in the solid. This may be especially useful as a complementary technique when impurities need to be calculated that are near or below the detection limit by HPLC. An example of this is determining low levels of genotoxic impurities in the isolated solids when these are enriched in the liquor. Similarly, the theoretical purity profile of the crude and liquor, as well as, product yield can be calculated based on the Equation 12– 16, without de facto analyzing them. The value of this approach can be illustrated by the following example. Consider that a purification screening is carried out by suspending a crude material in various solvents overnight. In addition to obtaining chromatographic data of the crude mixture, the chromatograms of the solids and liquors are obtained and analyzed after equilibration. For each experiment, the impurity rejection and product yield is then calculated for each impurity using Equation 15 and 16. This step can easily be automated by using a spreadsheet utility ACS Paragon Plus Environment


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(e.g., Excel8). From this data set, a complete understanding can be gathered on the purge ability and product yield expected across different solvents without having to establish a standard curve or have knowledge of individual response factors (Figure 2). In addition, impurities that cause deviations from the product yield average can be quickly identified as potential sources of HPLC integration errors, system peaks or even reacting impurities. An alternate approach in this scenario would be to only gather the HPLC chromatograms of the liquors, from which also product yield can be determined, and then calculate the purity profile of the solids. This would then reduce the number of collected HPLC chromatograms to almost half. 2. Data integrity. If all four parameters (chromatograms of crude, liquor, and solid, in addition to product yield) have been obtained then the system is over-determined. Hence, another important application of the mass balance is the ability to cross-check the accuracy of the HPLC data over the crystallization. This can be done in several ways. For example, calculated data can be compared with measured data, as illustrated with Equation 25 above. It is also possible to check the accuracy of the data via consistency in the product yield calculations for each individual impurity (Equation 16). If ten impurities are measured, then ten product yield values can be calculated and compared, solely based on the purity profiles. If the mass balance holds and the data are accurate then they should give the same values for product yield over the same crystallization. If the product yield deviates considerably for an individual impurity then that may warrant further investigation of this impurity.9 A complementary approach is to look at the calculated impurity rejection using the four different equations (Equation 12–15). Since impurity rejection can be calculated using four different equations then four different impurity rejection values can be obtained for the same impurity. In a well-behaved data set, the calculated impurity rejection should be the same regardless of equation used. If there again are larger deviations then that may be cause for further investigation. Finally, the residuals in the data set can also be minimized across the four input variables to find the best solution.10 All of these cross-checking calculation options allow for pinpointing whether individual impurities grow or degrade during the crystallization, whether the HPLC peak integration is unsatisfactory, or whether some peaks are actually system peaks.


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Using these relations thus allows for saving time and resources during development and provides confidence in the obtained HPLC data gathered over a crystallization. 3. Calculating number of recrystallizations to meet a target. Even though impurity rejection depends on many complex mechanisms, a simple approximation is to assume that the impurity rejection is fairly constant across several recrystallizations, that is, the crystallized product is recrystallized repeatedly using the same solvents/conditions. Such an analysis may answer how many recrystallizations are needed to reach a target impurity level, or product purity. Algebraically, this can be done by starting with Equation 13. For each crystallization, the area of the solid is used as the crude. For n crystallizations, the following expression can then be derived: ୻ೄ ೔

୻ೄ ೛

=൬

ଵିோ೔ ௒೛

௡

൰ ൬ ಴೔ ൰ ୻಴

୻೛

(26)

Rearranging Equation 26 affords: ݊=

ೄ

ೄ

౳೔ /౳೛ ௟௢௚ቈ ಴ ಴቉ ౳೔ /౳೛ భషೃ೔ ൰ ௟௢௚൬ ೊ೛

(27)

The desired area% of the impurity is then given by the term Γ௜ௌ /Γ௣ௌ . To exemplify, a crude comprises 2.5 area% of an impurity and the acceptable level is 0.10 area%. After crystallization at 90% product yield the impurity is reduced to 0.7 area%. The corresponding impurity rejection can be calculated to 75.3% using Equation 13. Based on Equation 27, a total of 2.5 crystallizations are needed to bring down the impurity to 0.10 area%, that is, three successive crystallizations are needed to meet the target. 4. Effect of process volumes. The final application of the mass balance comes from the influence of process volumes on impurity rejection. Process volumes, Vp, (in L solvent/kg product) is related to product yield and product concentration, Cp, (in kg product/L solvent) in the supernatant through:

ܸ௣ =

ଵି௒೛ ஼೛

(28)



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A change in process volumes will proportionally affect product yield in the crystallization if the same final product concentration is maintained. As such, it is possible to simulate the effect of process volumes on the impurity rejection via changes in product yield. Assuming that only the purity of the solid will change upon changing process volumes, as is the case when the impurity rejection is solubility-limited, Equation 25 and 28 can be combined to yield:

 ΓiS  S  ΓP

  1  ΓiC   VPC p  ΓiL    =  −     C    L  (29)   1 − VPC p  ΓP   1 − VPC p  ΓP 

By letting product concentration and area% of the crude and liquor remain constant and varying process volumes only, different purity profiles of the solids can be simulated. An example is provided in Figure 6.

Figure 6. Simulation of impact of process volumes on purity of the solid phase

It is important to emphasize that this type of simulation does not account for any kinetic effects of crystallization, merely the effect of poorly soluble impurities in the crystallization solvent down to their saturation concentration. CONCLUSIONS The mathematical basis for calculating mass-based impurity rejection for crystallizations was presented algebraically through the use of mass balances. While this technique is not intended to be a substitute for the “gold standard” of mass-based analytical quantification with a characterized reference material, it does provide the scientist with enhanced insight into the impurity rejection when compared to the ‘purge factor’ and ‘before and after area%’ approaches, which do not describe the actual mass or mole of impurity being ACS Paragon Plus Environment

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rejected in the crystallization. Furthermore, these calculations do not require any knowledge of relative response factors. A complete data set for the calculations can generally be gathered from an additional 0–1 analytical samples apart from those gathered during routine testing, necessitating minimal additional effort from a scientist in the laboratory.11 This approach is of particular importance to the pharmaceutical industry as crystallizations are routinely employed during the synthetic sequence to afford high purity API. Furthermore, important applications of the mass balance were highlighted; for example, theoretical determination of the purity of the solid phase, determination of impurity concentration below the experimental detection limit and cross-checking the accuracy in the HPLC data. Finally, simulations of impurity purges across various process scenarios were also demonstrated through the use of the mass balance. ACKNOWLEDGMENT The authors gratefully acknowledge Benoit Cardinal-David (AbbVie) for valuable advice and input. AUTHOR CONTRIBUTIONS The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. FUNDING SOURCES Daniel Caspi is an employee of AbbVie. Fredrik Nordstrom is an employee of Boehringer-Ingelheim. The design, study conduct, and financial support for this research were provided by AbbVie. AbbVie participated in the interpretation of data, review, and approval of the publication.

Supporting Information Available: Contains an Excel file with sample calculations.

REFERENCES (1) An example of a regulatory guidance document is ICH Harmonized Tripartite Guideline: Impurities in New Drug Substances (Q3A), (R2); International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH), 2006. http://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Quality/Q3A_R2/Step4/Q3A_R2__Guideline.pdf.



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(2) Baertschi, S. W.; Pack, B. W.; Hoaglund Hyzer, C. S.; Nussbaum, M. A. Assessing mass balance in pharmaceutical drug products: New insights into an old topic. Trends Analyt. Chem. 2013, 49, 126–136, http://doi.org/10.1016/j.trac.2013.06.006. (3) A literature search on SciFinder (April 6, 2018) returned only 30 results for ‘impurity rejection’ and just 9 results for ‘impurity purge’. (4) Betori, R. C.; Kallemeyn, J. M.; Welch, D. S. A Kinetics-Based Approach for the Assignment of Reactivity Purge Factors. Org. Process Res. Dev. 2015, 19, 1517–1523, http://doi.org/10.1021/acs.oprd.5b00257. (5) Bhattacharyya, L.; Pappa, H.; Russo, K. A.; Sheinin, E.; Williams, R. L. The Use of Relative Response Factors to Determine Impurities. Pharmacopeial Forum 2005, 31, 960–966, http://www.researchgate.net/publication/295423011_The_use_of_Relative_Response_Factors_to_ determine_impurities. (6) In some cases, these impurities may not even be chemically stable to isolation or characterization. (7) Another approach that was fairly recently disseminated is to use purge factors for genotoxic impurities. There are additional conservative safety factors applied in these cases to account for process variation, see: (a) Teasdale, A.; Fenner, S.; Ray, A.; Ford, A.; Phillips, A. A Tool for the Semiquantitative Assessment of Potentially Genotoxic Impurity (PGI) Carryover into API Using Physicochemical Parameters and Process Conditions. Org. Proc. Res. Dev. 2010, 14, 943–945, http://doi.org/10.1021/op100071n. (b) Teasdale, A.; Elder, D.; Chang, S.-J.; Wang, S.; Thompson, R.; Benz, N.; Flores, I. H. S. Risk Assessment of Genotoxic Impurities in New Chemical Entities: Strategies To Demonstrate Control. Org. Proc. Res. Dev. 2013, 17, 221–230, http://doi.org/10.1021/op300268u. (8) See Supporting Information for a sample Excel worksheet. (9) There are many reasons this may be observed, e.g., impurity degradation, impurity growth caused by an internal source (e.g., trace acid) or external source (e.g., oxygen). By tracking the mass balance of these individual impurities, these types of scenarios can be stratified and prioritized on the basis of these results. (10) Procedures to perform these types of minimizations are outside the scope of this report. (11) This mathematical technique can be applied to any impurity rejection scenario wherein a single crude phase is partitioned into two distinct phases.


Quantitative Impurity Rejection Analysis for Crystallization - Organic

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