Pharmaceutical
`Stress Testing
`Predicting Drug Degradation
`
`edited by
`Steven W. Baertschi
`Eli Lilly and Company
`Indianapolis, Indiana, U.S.A.
`
`Boca Raton London New York Singapore
`
`© 2005 by Taylor & Francis Group, LLC
`
`Opiant Exhibit 2305
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 1
`
`

`

`Published in 2005 by
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`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 2
`
`

`

`Contents
`
`iii
`Preface . . . .
`Contributors . . . . xi
`
`1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
`Steven W. Baertschi and Dan W. Reynolds
`I. General Information/Background . . . . 1
`II. Definitions/Terms . . . . 2
`III. Historical Context . . . . 4
`IV. Regulatory Context . . . . 8
`References . . . . 9
`
`13
`
`. . . . . . . . . . . . . . . . . .
`2. Stress Testing: A Predictive Tool
`Steven W. Baertschi and Patrick J. Jansen
`I. Introduction . . . . 13
`II. Predictive Versus Definitive . . . . 15
`III. Intrinsic Stability: Conditions Leading to
`Degradation . . . . 18
`IV. Intrinsic Stability: Rates of Degradation . . . . 28
`V. Intrinsic Stability: Structures of the Major Degradation
`Products . . . . 29
`VI. Intrinsic Stability: Pathways of Degradation . . . . 36
`VII. Interpretation of the Results of Stress Testing . . . . 39
`VIII. Summary . . . . 43
`References . . . . 44
`
`v
`
`© 2005 by Taylor & Francis Group, LLC
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`Page 3
`
`

`

`vi
`
`Contents
`
`. . . . .
`
`3. Stress Testing: The Chemistry of Drug Degradation
`Steven W. Baertschi and Karen M. Alsante
`I. Introduction . . . . 51
`II. Degradation of Common Functional Groups . . . . 52
`III. Computational Tool for Evaluating Potential
`Degradation Chemistry-CAMEO . . . . 126
`IV. Conclusion . . . . 128
`References . . . . 128
`
`51
`
`141
`. . . . . . . . . . . .
`4. Stress Testing: Analytical Considerations
`Patrick J. Jansen, W. Kimmer Smith, and Steven W. Baertschi
`I. Stress-Testing Conditions and Sample
`Preparation . . . . 141
`II. Methods of Analysis . . . . 160
`III. Conclusions . . . . 170
`References . . . . 171
`
`173
`. . .
`5. Stress Testing: Relation to the Development Timeline
`Steven W. Baertschi, Bernard A. Olsen, and Karen M. Alsante
`I. Drug Discovery Stage (Structure–Activity Relationship
`and Compound Selection Stage) . . . . 174
`II. Pre-Clinical/Early Phase
`(Pre-Clinical to Phases I/II) . . . . 175
`‘‘Commercialization’’ Stage or Late-Phase Development
`(Phase II/III to Regulatory Submission) . . . . 177
`IV. Line-Extensions (New Formulations, New Dosage Forms,
`New Dosage Strengths, etc.), Older Products Already
`on the Market (Updating Methods, Assessing Process
`Changes) . . . . 178
`References . . . . 179
`
`III.
`
`6. Role of ‘‘Mass Balance’’ in Pharmaceutical
`181
`Stress Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`Mark A. Nussbaum, Patrick J. Jansen, and Steven W. Baertschi
`I. Introduction . . . . 181
`II. Why Is Mass Balance Important? . . . . 182
`III. How Is Mass Balance Measured and
`Expressed? . . . . 183
`IV. Stress Testing and Mass Balance . . . . 186
`
`© 2005 by Taylor & Francis Group, LLC
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`Contents
`
`vii
`
`V. Causes of and Approaches to Solving Mass Balance
`Problems . . . . 186
`VI. Practical Approaches to Solving Response Factor
`Problems . . . . 195
`VII. Response Factor Example: Nifedipine . . . . 199
`VIII. Conclusions . . . . 202
`References . . . . 203
`
`. . . . . . . . . . . . . . . . . .
`
`7. Oxidative Susceptibility Testing
`Giovanni Boccardi
`I. Mechanistic Background . . . . 205
`II. Practical Tests . . . . 213
`III. Oxidation of the Most Common Organic Functional
`Groups . . . . 225
`IV. Strategy of Oxidative Susceptibility Testing . . . . 229
`References . . . . 230
`
`205
`
`8. Comparative Stress Stability Studies for Rapid Evaluation
`of Manufacturing Changes or Materials
`from Multiple Sources
`. . . . . . . . . . . . . . . . . . . . . . . . .
`Bernard A. Olsen and Larry A. Larew
`I. Introduction . . . . 235
`II. Considerations for Comparative Stress
`Stability Studies . . . . 237
`III. Literature Examples . . . . 241
`IV. Statistical Design Studies . . . . 248
`V. Summary and Conclusions . . . . 256
`References . . . . 256
`
`9. Physical and Chemical Stability Considerations in the
`Development and Stress Testing of Freeze-Dried
`Pharmaceuticals
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`Steven L. Nail
`I. Introduction . . . . 261
`II. A Brief Description of the Freeze Drying
`Process . . . . 262
`III. An Overview of the Physical Chemistry
`of Freezing and Freeze Drying . . . . 264
`IV. Conclusion . . . . 288
`References . . . . 288
`
`235
`
`261
`
`© 2005 by Taylor & Francis Group, LLC
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`
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`viii
`
`Contents
`
`293
`
`327
`
`10. Photostability Stress Testing . . . . . . . . . . . . . . . . . . . . .
`Elisa Fasani and Angelo Albini
`I. Introduction . . . . 293
`II. Photochemistry of Drugs—Background
`Information . . . . 294
`III. Photostability Studies . . . . 310
`References . . . . 319
`
`11. The Use of Microcalorimetry in Stress Testing . . . . . . . .
`Graham Buckton and Simon Gaisford
`I. Introduction . . . . 327
`II. Microcalorimetry . . . . 328
`III. Analysis of Microcalorimetric Data . . . . 333
`IV. Drug Stability . . . . 342
`V. Drug–Excipient Stability . . . . 344
`VI. Water–Drug, Water–Excipient Stability . . . . 344
`VII. Accelerated Rate Studies . . . . 348
`VIII. Further Information . . . . 351
`References . . . . 352
`
`12. The Power of Computational Chemistry to Leverage Stress
`Testing of Pharmaceuticals . . . . . . . . . . . . . . . . . . . . . .
`Donald B. Boyd
`I. Introduction . . . . 355
`II. Timely Tools of Computational Chemistry . . . . 361
`III. Selecting Software . . . . 378
`IV. A Modeling Scenario . . . . 380
`V. Specialized Applications . . . . 395
`VI. Conclusions . . . . 408
`References . . . . 409
`
`355
`
`419
`
`13. Solid-State Excipient Compatibility Testing . . . . . . . . . .
`Amy S. Antipas and Margaret S. Landis
`I. Designs of Traditional Excipient Compatibility
`Experiments . . . . 420
`II. Appropriate Stress Conditions . . . . 426
`III. Analysis . . . . 436
`IV. Kinetics and Predictions Based on Excipient
`Compatibility Data . . . . 446
`References . . . . 452
`
`© 2005 by Taylor & Francis Group, LLC
`
`Opiant Exhibit 2305
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
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`
`

`

`Contents
`
`14. Stress Testing: Frequently Asked Questions
`Steven W. Baertschi and Karen M. Alsante
`References . . . .
`468
`
`ix
`
`. . . . . . . . . .
`
`459
`
`© 2005 by Taylor & Francis Group, LLC
`
`Opiant Exhibit 2305
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
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`
`

`

`2
`
`Stress Testing: A Predictive Tool
`
`Steven W. Baertschi and Patrick J. Jansen
`Eli Lilly and Company, Lilly Research Laboratories, Lilly Corporate Center,
`Indianapolis, Indiana, U.S.A.
`
`I.
`
`INTRODUCTION
`
`As described in Chapter 1, stress testing is the main tool that is used to
`predict stability-related problems, develop analytical methods, and identify
`degradation products and pathways. Stability-related issues can affect many
`areas, including the following:
` Analytical methods development
` Formulation and package development
` Appropriate storage conditions and shelf-life determination
` Safety/toxicological concerns
` Manufacturing/processing parameters
` Absorption, distribution, metabolism, and excretion (ADME)
`studies
` Environmental assessment
`It is worth discussing briefly each of these stability-related areas.
`
`A. Analytical Methods Development
`
`In order to assess the stability of a compound, one needs an appropriate
`method. The development of stability-indicating analytical method, particu-
`larly an impurity method, is a ‘‘chicken and egg’’ type of problem. That is,
`how does one develop an impurity method to detect degradation products
`
`13
`
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`14
`
`Baertschi and Jansen
`
`when one does not know what the degradation products are? Stress-testing
`studies can help to address this dilemma. Stressing the parent compound
`under particular stress conditions can generate samples containing degrada-
`tion products. These samples can then be used to develop suitable analytical
`procedures. It is important to note that the degradation products generated
`in the stressed samples can be classified as ‘‘potential’’ degradation products
`that may or may not be formed under relevant storage conditions. It is also
`important to note that not all relevant degradation products may form
`under the stress conditions. Both accelerated and long-term testing studies
`are used to determine which of the potential degradation products actually
`form under normal storage conditions and are, therefore, relevant degrada-
`tion products. The strategy for developing a stability-indicating method is
`described in detail in Chapter 4.
`
`B. Formulation and Packaging Development
`
`The knowledge gained from stress testing is useful for formulation and
`packaging development. Well-designed stress-testing studies can determine
`the susceptibility of a compound to hydrolysis, oxidation, photochemical
`degradation, and thermal degradation. This information is then taken into
`consideration when developing the formulation and determining the appro-
`priate packaging. For example, if stress-testing studies indicate that a com-
`pound is rapidly degraded in acid, then consideration might be given to
`developing an enteric-coated formulation that protects the compound from
`rapid degradation in the stomach. Similarly, if a compound is sensitive to
`hydrolysis, packaging that protects from water vapor transmission from
`the outside of the package to the inside of the package may be helpful to
`ensure long-term storage stability. Other degradation mechanisms (e.g.,
`oxidative degradation or photodegradation) can also be prevented or
`minimized by the use of appropriate packaging and/or formulation.
`Knowledge of potential drug–excipient interactions is also critical to devel-
`oping the best formulation.
`
`C. Appropriate Storage Conditions and Shelf-Life Determination
`
`Determining appropriate storage conditions for a drug substance or product
`requires knowledge of the conditions that induce degradation and the
`degradation mechanisms. Most of this information can be obtained from
`stress-testing studies combined with accelerated stability testing. Accurate
`shelf-life predictions, however, are best made with data from formal
`long-term stability studies.
`
`D. Safety/Toxicological Concerns
`
`If stress-testing studies indicate the formation of (a) known toxic com-
`pound(s), steps can be taken early on to inhibit the formation of the toxic
`
`© 2005 by Taylor & Francis Group, LLC
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`

`Stress Testing: A Predictive Tool
`
`15
`
`compound(s) and to develop sensitive analytical methods to accurately
`detect and quantify. Stress-testing studies can also facilitate preparation/
`isolation of a degradation product for toxicological evaluation when syn-
`thetic preparation is not feasible.
`
`E. Manufacturing/Processing Parameters
`
`Degradation can also occur during manufacturing or processing steps.
`Knowledge of what conditions lead to degradation of the parent compound
`can help to design appropriate controls/conditions during manufacturing/
`processing. For example, if a compound is susceptible to degradation at
`low pH, then either the manufacturing steps under low pH conditions can
`be avoided or the time and/or temperature can be more carefully controlled
`to minimize the degradation. It is not uncommon to observe degradation
`during formulation processing, for example, wet granulation, milling, etc.
`An understanding of the degradation that may occur during the formulation
`processing steps can help in choosing conditions to ensure maximum stabi-
`lity of the drug substance (e.g., oxidative susceptibility may lead to the use
`of processing in an inert-gas atmosphere).
`
`F. ADME Studies
`
`ADME characteristics of a drug are extensively studied prior to marketing.
`These studies typically involve identification of the major metabolites, a pro-
`cess that can be difficult owing to the complex matrix (living organism) and
`often very low levels. Occasionally, degradation products detected in stress-
`testing studies are also metabolites. In these cases, it is usually easier to gen-
`erate larger quantities of the metabolite for characterization using the stress
`condition rather than isolate it from the living organism. It is also possible
`that nonenzymatic degradation can occur in vivo, and therefore an under-
`standing of what degradation pathways might be relevant under physiologi-
`cal conditions can be important to understanding the ADME of a new drug.
`
`G. Environmental Assessment
`
`The environmental assessment deals with the fate of the drug in the environ-
`ment. The information gained from stress testing can be useful for designing
`and interpreting environmental studies, as the degradation of the drug in
`the environment will often be similar to degradation observed during
`stress-testing studies.
`
`II. PREDICTIVE VERSUS DEFINITIVE
`
`It is important to remember that stress testing is predictive in nature (as
`opposed to definitive). That is, the degradation products formed under stress
`
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`16
`
`Baertschi and Jansen
`
`conditions may or may not be relevant to the actual storage conditions of
`the drug substance and/or to the degradation chemistry of the drug pro-
`duct. This reality is reflected in the ICH definition of stress testing, where
`it is stated:
`
`Examining degradation products under stress conditions is useful in
`establishing degradation pathways and developing and validating
`suitable analytical methods. However, such examination may not
`be necessary for certain degradation products if it has been demon-
`strated that they are not formed under accelerated or long term
`storage conditions (from Ref. 1.)
`
`Therefore, the degradation products formed during stress testing can
`be thought of as ‘‘potential’’ degradation products. Ideally, stress conditions
`should result in the formation of all potential degradation products. The
`‘‘significant’’ or ‘‘relevant’’ degradation products that occur during long-
`term storage or shipping (as revealed by accelerated testing and long-term
`stability studies) should thus be a subset of the ‘‘potential’’ degradation pro-
`ducts. This concept is illustrated in Figure 1. The overall strategy of stress
`testing is, therefore, to predict potential issues related to stability of the
`molecule—either as the drug substance alone or as a formulated product.
`This strategy is outlined in Figure 2.
`As shown in Figure 2, the overall strategy is similar for both drug sub-
`stance and product. The strategy begins with stress testing of the drug sub-
`stance using discriminating or ‘‘screening’’ methods (2). Such methods
`should be capable of separating and detecting a broad range of degradation
`products and can be used for degradation and impurity investigations. In
`practice, RP-HPLC with UV detection is by far the most common analytical
`technique currently used for the detection of impurities. A discriminating
`RP-HPLC method utilizing a broad gradient elution is recommended for
`covering a wide polarity range. Other separation techniques or detection
`modes may be employed, but the key concept is to develop and use metho-
`dology that will maximize separation and provide the most universal detec-
`tion. The screening method can be developed/optimized by analysis of
`partially degraded samples and the use of standard method development
`procedures and tools (3). The analysis of stressed samples should reveal
`the ‘‘potential’’ degradation products formed under the various stress con-
`ditions. Accelerated testing and analytical evaluation using the same broad
`screening method can determine the ‘‘significant’’ degradation products.
`Methods designed to separate and detect only the significant degradation
`products (i.e., those that form at significant levels under accelerated and
`long-term storage conditions) can then be developed and optimized. Such
`methods, which have been referred to elsewhere as ‘‘focused’’ methods (2),
`are designed for regulatory registration in the marketing application and
`use in quality control laboratories for product release and stability.
`
`© 2005 by Taylor & Francis Group, LLC
`
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`

`Stress Testing: A Predictive Tool
`
`17
`
`Figure 1 Cartoon illustration of hypothetical chromatograms from stress testing
`(upper) and accelerated or long-term stability studies. Peaks A–I represent all the
`degradation products from stress-testing studies under various stress conditions
`and are therefore classified as ‘‘potential’’ degradation products. Peaks B–E and G
`represent the products that form at significant levels during formal stability studies
`and are therefore classified as the ‘‘actual’’ or ‘‘relevant’’ degradation products.
`
`The information gathered during stress testing of the drug substance is
`used to guide the formulation of the drug product. As described in detail in
`Chapter 13, drug-excipient compatibility studies (4–7) can be performed to
`determine whether or not individual excipients, excipient blends, or trial
`formulations have any significant adverse interactions with the parent drug.
`A broad screening method such as that developed for drug substance stress
`testing should be used for the analytical evaluation of such studies. As dis-
`cussed in Chapter 11, microcalorimetric techniques may also be useful for
`the analysis of drug–excipient interactions (8–11). Once a suitable formula-
`tion has been developed, stress-testing studies can be performed on the for-
`mulation and any resulting degradation products can be compared to the
`degradation products formed during stress-testing studies of the drug
`substance alone. In an analogous manner to the strategy for the drug sub-
`stance, the ‘‘significant’’ degradation products can be determined via accel-
`erated and long-term stability studies, and focused methods can be
`developed for regulatory registration and use in quality control laboratories
`for product release and stability.
`
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`18
`
`Baertschi and Jansen
`
`Figure 2 Overall strategy for the prediction,
`stability-related issues.
`
`identification, and control of
`
`The key to the strategy outlined earlier is to have well-designed stress-
`testing studies that form all potential degradation products. As discussed in
`Section II, ICH defines stress testing as an investigation of the ‘‘intrinsic stabi-
`lity’’ characteristics of the molecule. As the term ‘‘intrinsic stability’’ appears to
`be foundational to the understanding, yet has no clear definition, it is worth dis-
`cussing. The concept of ‘‘intrinsic stability’’ has four main aspects:
`
`1. Conditions leading to degradation
`2. Rates of degradation (Relative or Otherwise)
`3. Structures of the major degradation products
`4. Pathways of degradation
`
`Once these four areas have been investigated and understood, stability-
`related issues can be identified or predicted. It is worth considering in more
`detail the four main aspects of intrinsic stability mentioned earlier.
`
`III.
`
`INTRINSIC STABILITY: CONDITIONS LEADING TO
`DEGRADATION
`
`As described in the PhRMA ‘‘Available Guidance and Best Practices’’ arti-
`cle on forced degradation studies (12), stress testing should include condi-
`
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`Stress Testing: A Predictive Tool
`
`19
`
`tions that examine specifically for four main pharmaceutically relevant
`degradation mechanisms (2): (a) thermolytic, (b) hydrolytic, (c) oxidative,
`and (d) photolytic. The potential for these degradation pathways should
`be assessed in both drug substance and formulated product (and/or drug–
`excipient mixtures). These mechanisms can be assessed in a systematic
`way by exposure to stress conditions of heat, humidity, photostress (UV
`and VIS), oxidative conditions, and aqueous conditions across a broad
`pH range.
`
`A. Thermolytic Degradation
`
`Thermolytic degradation is usually thought of as degradation caused by
`exposure to temperatures high enough to induce bond breakage, that is,
`pyrolysis. For the purposes of simplification (although, admittedly, perhaps
`oversimplification) in the context of drug degradation, we will use the term
`thermolytic to describe reactions that are driven by heat or temperature.
`Thus, any degradation mechanism that is enhanced at elevated temperatures
`can be considered a ‘‘thermolytic pathway.’’ The following list of degrada-
`tion pathways, while not an exhaustive list, can be thought of as thermolytic
`pathways: hydrolysis/dehydration, isomerization/epimerization, decarbox-
`ylation, rearrangements and some kinds of polymerization reactions. Note
`that hydrolytic reactions are actually a subset of thermolytic pathways using
`this construct. In addition, note that oxidative and photolytic reactions are
`not included in this list (as they are not primarily driven by temperature) but
`are discussed separately in more detail (see below). The ICH Stability guide-
`line suggests studying ‘‘ . . . the effect of temperatures in 10C increments
`above the accelerated temperature test condition (e.g., 50C, 60C,
`etc.) . . ..’’ It is not clear why the guideline suggests 10 C increments, but
`it may be related to the importance of understanding whether or not any
`degradation (in the solid state) mechanisms change as a result of increasing
`temperature. Studies with such temperature increases would be useful for
`constructing Arrhenius plots to allow prediction of degradation in the solid
`state rates at different temperatures; however, for many pharmaceutical
`small molecule drug substances, it would take several months of storage
`at the elevated temperatures to induce enough degradation to provide mean-
`ingful kinetic data from which to construct such plots.
`As discussed in Chapter 1 (Sections III and IV), the kinetics of drug
`degradation has been the topic of numerous books and articles. The Arrhe-
`nius relationship is probably the most commonly used expression for evalu-
`ating the relationship between rates of reaction and temperature for a given
`order of reaction (For a more thorough treatment of the Arrhenius equation
`and prediction of chemical stability, see Ref. 13). If the decomposition of a
`drug obeys the Arrhenius relationship [i.e., k ¼ A exp(Ea/RT), where k
`rate constant, A is
`is
`the degree of
`the ‘‘pre-exponential
`factor’’
`
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`20
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`Baertschi and Jansen
`
`or ‘‘frequency factor’’ (i.e., the frequency of collisions among reactants irre-
`spective of energy), R is the universal gas constant, and T is the temperature
`in degrees in Kelvin], it is possible to estimate the effect of temperature on the
`degradation rate of a compound, providing the ‘‘energy of activation’’ (Ea) is
`known (14).
`Connors et al. (15) assert that most drug substances have energies of
`activation (Eas) of 12–24 kcal/mol, although Eas > 24 kcal/mol are not
`uncommon (16). In 1964, Kennon (17) compiled the activation energies
`for decomposition of a number of drug compounds and found the average
`to be 19.8 kcal/mol. Davis (18), a retired FDA reviewer, has asserted that
`20 kcal/mol is a ‘‘quite conservative’’ estimate for the average Ea of decom-
`position of drug compounds. The ‘‘Joel Davis Rule’’, an historical rule-of-
`thumb that has been commonly used in the pharmaceutical industry, states
`that acceptable results from 3-month stability testing of a drug product at
`37–40C can be used to project a tentative expiry date of 2 years from the
`date of manufacture. Yang and Roy (19) have shown that this rule-of-
`thumb is valid only if the Ea is >25.8 kcal/mol (19). The PhRMA ‘‘Available
`Guidance and Best Practices’’ on forced degradation provides estimates of
`the effects of elevated temperature based on a very conservative assumption
`of 12 kcal/mol (12). Waterman (20) has asserted that the relative humidity
`under which a solid drug product is stored is a critical variable when
`attempting to use the Arrhenius relationship. Waterman showed evidence
`that degradation rates of formulated products (with pathways involving
`hydrolytic or oxidative degradation) often hold to the Arrhenius relation-
`ship if the relative humidity is held constant at the different elevated tem-
`peratures. Further
`research in this area may provide
`significant
`improvements in the predictability of solid state drug degradation rates
`from stress testing and accelerated stability studies.
`C assuming energies
`Table 1 shows rates of degradation relative to 25
`of activation of 12, 15, and 20 kcal/mol assuming that the degradation
`kinetics follows Arrhenius kinetics. Table 2 shows the increase in rate for
`each 10C increase in temperature for the same 12, 15, and 20 kcal/mol
`energies of activation. Tables 1 and 2 can be used to estimate the effect of
`stress temperatures on the rate of a degradation reaction for a particular
`Ea. It is apparent from Tables 1 and 2 that the increase in reaction rate is
`dependent on the Ea, and that a low energy of activation (e.g., 12 kcal/
`mol) results in a less-dramatic increase in reaction rate as temperature is
`increased.
`The PhRMA guidance and Alsante et al. (21) have recommended a
`conservative approach of assuming that for every 10C increase in tempera-
`ture the reaction rate approximately doubles. This is approximately equiva-
`lent to assuming an Ea of 12 kcal/mol.
`Using the information provided in Tables 1 and 2, it is straightforward
`to calculate the effect of temperature on the degradation rate to enable
`
`© 2005 by Taylor & Francis Group, LLC
`
`Opiant Exhibit 2305
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 15
`
`

`

`Stress Testing: A Predictive Tool
`
`21
`
`Table 1 Rates of Degradation (Relative to 25C) Assuming Arrhenius Kinetics
`and Energies of Activation (Ea) of 12, 15, and 20 kcal/mol
`
`Temperature (C)
`
`Relative rate
`assume
`Ea¼12 kcal/mol
`
`Relative rate
`assume
`Ea¼ l5 kcal/mol
`
`Relative rate
`assume
`Ea¼ 20 kcal/mol
`
`25
`30
`40
`50
`60
`70
`
`1
`1.39
`2.62
`4.78
`8.36
`14.20
`
`1
`1.52
`3.37
`7.10
`14.33
`27.74
`
`1
`1.75
`5.05
`13.65
`34.79
`83.98
`
`prediction/estimation of degradation rates at lower temperatures (e.g., room
`temperature) for different energies of activation. For example, if one assumes
`an activation energy of 12 kcal/mol, stressing at 70C for 1 week would be
`roughly the same as 100 days at 25C (14.2 7 days¼ 99.4 days). Similarly,
`assuming an activation energy of 20 kcal/mol and stressing for one week
`at 70C would be roughly the same as 588 days at 25C (83.98  7 days
`¼ 587.86 days).
`It should be noted here that solid-state reactions often proceed in an
`‘‘autocatalytic’’ pathway (similar to oxidative degradation kinetics) invol-
`ving an induction period (lag), followed by a period of rapidly increasing
`degradation and then a slowing down of the degradation rate as the drug
`is consumed (22,23). Thus, solid-state reaction kinetics will often follow
`an ‘‘S’’-shaped curve when degradation vs. time is plotted. This kind of
`reaction kinetics is often more pronounced in formulated solid oral dosage
`forms (for reasons which will not be discussed here). It is reasonable to ques-
`tion whether or not Arrhenius kinetics will hold if the solid-state degrada-
`tion is autocatalytic. Arrhenius kinetics is typically observed in the
`
`Table 2 Relative Increase in Rates of Degradation as Temperature is Increased,
`Assuming Arrhenius Kinetics and Energies of Activation (Ea) of 12, 15, and
`20 kcal/mol
`
`Temperature (C)
`
`Increase in Rate
`of Reaction
`(Ea¼ 12 kcal/mol)
`
`Increase in Rate
`of Reaction
`(Ea¼15 kcal/mol)
`
`Increase in Rate
`of Reaction
`(Ea¼ 20 kcal/mol)
`
`25–30
`30–40
`40–50
`50–60
`60–70
`
`1.39
`1.88
`1.82
`1.75
`1.70
`
`1.52
`2.22
`2.11
`2.02
`1.94
`
`1.75
`2.89
`2.71
`2.55
`2.41
`
`© 2005 by Taylor & Francis Group, LLC
`
`Opiant Exhibit 2305
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 16
`
`

`

`22
`
`Baertschi and Jansen
`
`degradation of solid pharmaceutical products (within temperature ranges
`discussed in what follows) presumably because most solid-state degradation
`studies involve only modest amounts of degradation (e.g., 5%) and are
`therefore typically operating in the ‘‘induction’’ or ‘‘lag’’ period of the
`solid-state degradation. If solid-state degradation studies are carried out
`to higher levels of degradation (e.g., >10–30% degradation), it is likely that
`degradation rate prediction via Arrhenius kinetics would not be feasible.
`For an in depth discussion of the applicability of Arrhenius kinetics to
`pharmaceutical degradation see Waterman (20).
`Note that the above information assumes that the decomposition fol-
`lows the same pathways at all the temperatures. This assumption will not be
`true for all compounds, but for the majority of small molecule drug com-
`pounds, it is our experience that the degradation pathways will usually be
`the same up to 70C. Precedence can be found in regulatory guidelines
`and in the scientific literature for using temperatures up to 50C (4), 60C
`(1), and even 80C (25) and 85C (17,26) for stress testing and ‘‘accelerated
`stability’’ studies. However, the references to stressing at 80C and 85 C
`suggest that such high temperatures are optional and may lead to different
`decomposition pathways for some compounds. One example of c