Experiences and Challenges with Isoconversional Kinetics Stability Modeling of Packaged Amorphous Solid Dispersions Russell Hertzler, Ph.D. Principal Research Scientist, Analytical R&D AbbVie John C. Strong, Ph.D. Associate Research Fellow, Formulation Sciences AbbVie
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Russell Hertzler , Ph.D. Principal Research Scientist, Analytical R&D AbbVie
Experiences and Challenges with Isoconversional Kinetics Stability Modeling of Packaged Amorphous Solid Dispersions. Russell Hertzler , Ph.D. Principal Research Scientist, Analytical R&D AbbVie John C. Strong, Ph.D. Associate Research Fellow, Formulation Sciences AbbVie. Contents. - PowerPoint PPT Presentation
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Experiences and Challenges with Isoconversional Kinetics Stability Modeling of Packaged Amorphous Solid DispersionsRussell Hertzler, Ph.D.Principal Research Scientist, Analytical R&DAbbVie
John C. Strong, Ph.D.Associate Research Fellow, Formulation SciencesAbbVie
Stability studies at accelerated condition are desired to determine the shelf-life of pharmaceutical products without having to wait for the entire real-time degradation to occur.
However, chemical kinetic models used to describe solid state systems (heterogeneous samples) are complex.
Typical Examples are o diffusion modelso phase boundary modelso nucleation and growth models
Determination of the exact model can be difficult in heterogeneous systems due to the irreproducibility of rate data.
The object is to design an experiment such that at each temperature & humidity condition, we know how long it takes to achieve some fractional degradation (i.e. 0.2%), typically the specification limit.
Then we can ignore “how” the impurity got to the level of failure for determination of kinetic parameters to be used in further modeling.
If no physical changes in the dosage form occur, then the Arrhenius model for chemical reaction rates should apply. In this case, we can establish a range of temperature (T) and
humidity (h) values within which the extended Arrhenius model correctly predicts shelf-life:
If physical changes occur, even if they are reversible, reaction rates will not follow Arrhenius model.
*Genton & Kesselring, Effect of temperature and relative humidity on nitrazepam stability in solid state. J Pharm Sci 66: 676–680 (1977)
*Waterman KC, Carella AJ, Gumkowski MJ, Lukulay P, MacDonald BC, Roy MC, Shamblin SL. Improved protocol and data analysis for accelerated shelf-life estimation. Pharm Res 24(4):780–790 (2007).
where h is the equilibrium relative humidity and B is a constant
Characteristics of Amorphous Solid Dispersion (ASD) Formulations
• Dispersion of an API in an inert carrier in the solid state prepared by solvent evaporation, melting or solvent-melting methods.
• Used to increase the bioavailability of poorly soluble drugs by improving their rate and extent of dissolution.
• Displays a glass transition temperature (Tg), below which the ASD has the appearance of a solid and are considered as a one phase system in which all molecules of the API are intimately mixed with the carrier molecules.
• The “Tg minus 50” rule-of-thumb states that the molecular mobility of an ASD becomes negligible 50°C below Tg.
• As we approach the Tg, chemical instability can become significant. Physical stability may also become a problem.
• The Tg is also a function of the water content of the system.
Stability Points in Relation to Glass Transition Temperature (Tg)
Temperature % Relative Humidity
Days(1st sample)
Days(2nd sample)
40 60 14 28
40 43 21 42
50 38 14 21
50 60 14 28
60 20 28 56
60 46 7 14
70 10 14 28
Example Stability Protocol, based on Tg–RH relationship
Graphical Representation of Stability Study Design
% RH
0 20 40 60 80
Tem
p (C
)
0
20
40
60
80
Slow Degradation Rates
Fast, non predictive Degradation Rates
Stability Study Designs for ASD formulations:o Stability study protocol needs to be constructed based on Tg–RH relationshipo ASDs typically will require more time to reach isoconversion levels of degradant than
1) isoconversion experiments2) regression of degradation rate constants k from experimental data3) regression of kinetic parameters from rate constants k
B. Measurement of moisture isotherms, packaging permeability, initial moisture content and mass of the drug product & desiccant
• Packaging ModelA. Numerical integration of an ODE for Fickian moisture transfer through
package wallB. Solve for moisture content and internal RH at any time during the shelf
lifeC. Degradation growth can be determined by solving another ODE at the
same time with known environmental conditions inside the package.
At any time t in the solution, we know the amount of water inside the packaging (based on initial water contents and calculated mass transfer rates)
Equilibrium internal RH (symbol h) is determined such that the adsorbed moisture amounts in of each material inside the package add up to the total known moisture inside the packaging at that time point. It will in general require a numerical root-finding algorithm (e.g., Newton’s method, secant method, etc.
The determination of the equilibrium RH allows the solution to progress to the next time step via solution of the ODE.
If the degradant growth can be modeled using an ODE that can likewise be integrated WRT time alongside the Fickian diffusion equation, then it is straightforward to solve for degradant growth in the packaging model.
• Due to limited resources, open dish data typically consists of 2 points for each condition:— Concentration at time t = 0— Concentration at some time t predicted to be close to the true ttf
• Zero-order rate constants k(T,h) are slopes calculated from the measured concentration and time of measurement— Since zero order is assumed (straight line), this rate constant is equivalent to one
derived from the ttf at Ciso
Data AnalysisOpen-dish degradant concentration data
1. Calculate rate constants k(T,h) for each set of T,h conditions
2. Assume a model of the form
3. Regress rate constants to obtain model parameters• Weighted Levenberg-Marquardt method for nonlinear regression
– Sensitive to starting estimates, can use linearized model to generate– Frequency factor A moved inside exp() term to improve numerical stability
• In general, 5-10 observations (T,h conditions) used to predict 3 parameters– Enough to get a good estimate of standard error of regression?– Some overfitting may be occurring
Data AnalysisRegression approach
𝑘𝑇 ,𝐻=𝐴𝑒𝑥𝑝(−𝐸𝑅𝑇 + h𝐵 )Three parameters• E – apparent activation energy• A – frequency factor• B – humidity factor
Two independent variables• T – temperature• h – relative humidity
• Open dish conditions need to be within narrow range of Tg (e.g., ± 5°C) in order to achieve sufficiently fast rates yet not be at risk of physical instability
• This places extra emphasis on precise control of temperature and RH in open dish isoconversion studies
• Although T and RH are treated as known quantities in the regression, practically speaking they do have an uncertainty associated with themo RH sensors typically ±2% uncertaintyo Temperature sensors can be as low as ±0.2°C
uncertainty, but temperature uniformity in a chamber may be ± 2°C or greater.
• What is the impact of temperature and humidity uncertainty?
Suppose we use the parameter estimates for the example data, and R is the gas constant 0.008314 kJ/mol K. At 25°C and 60% RH,
Sensitivity of rate constant to uncertainty in T and h
𝜎 𝑘2=( 𝜕𝑘𝜕𝑇 )
2
𝜎𝑇2 +(𝜕𝑘𝜕h )
2
𝜎 h2=𝑘2[( 𝐸
𝑅𝑇2 )2
𝜎 𝑇2 + ( h𝐵 )2𝜎 h
2]
𝜎 𝑘2=𝑘2 [3.3E−2𝜎𝑇+9.0 E−4 𝜎 h
2 ]𝜎𝑘
𝑘 ≅ 0.2𝜎𝑇
For example, if sT is ~ 1°C (perhaps due to chamber temperature non-uniformity), the magnitude of error in rate estimate will be large relative to the rate itself. It could be even larger if physical stability is compromised.
• A “screening design” can be proposed where Tg is not a factor, but this is more difficult to implement with an ASD due to Tg restrictions, and may not be practical for ASD formulations in general.
• It does not seem straightforward how to obtain a good estimate of uncertainty in rate constant estimates from small data sets, and the uncertainty from imprecise temperature control may be just as large (depending on quality of stability chamber)
• What can we do to improve parameter estimation with small data sets?
• What can we do to minimize impact of temperature uncertainty in open dish studies?
• Is there a better quantitative way of detecting outliers or minimizing their impact?