OR WAIT 15 SECS
Volume 31, Issue 2
For solid oral-dosage forms, water testing usually is performed to control the chemical, physical, or microbiological properties of the drug product. Measurements of total water as made with Karl Fischer (KF) techniques is not needed and water-activity often will provide a better correlation with changes in chemical, physical, or microbiological properties than KF techniques. In these cases, water activity testing can easily replace KF testing. Water-activity measurements are nondestructive, require little labor, and the equipment required is generally inexpensive. Only a few simple checks are needed to ensure the validity of measurements. Strategies for implementing water activity testing are described.
Most pharmacopeial monographs that have procedures for the measurement of water are based on the measurement of total water either by the Karl Fischer titration or by loss on drying. Karl Fischer titrations have dominated the measurement of water in pharmaceutical products for many years. Although the technique is reliable under carefully controlled conditions, it is subject to a variety of problems such as sample handling and side-reactions that cause erroneous results. Results commonly vary with changes in room relative humidity (RH). In addition, general models for describing the effect of water on physical, chemical, and microbiological characteristics recognize that different types of water may be present (1–3) and that the measurement of total water may not be the best approach for understanding the effects of water.
According to most common definitions, water can be present in at least three forms: free water, adsorbed water, and bound water. Free water is present in the void volume or in the pores. Free water can serve as a dispersing agent, as a solvent for crystalline compounds, or for microbiological growth. Adsorbed water is located on the surface of the material. Bound water is defined as the water of hydration bound to the product by strong H-bonds. Bound water relates to the monolayer of water molecules, whereas adsorbed water is present in the form of multilayers in the matrices. Water also may be present as a crystal hydrate that effectively is the same as bound water. An example of another type of water is structural water associated with hydrogen bonding between helices of polymer in a gel network (4). This explanation follows the theory of the BET isotherm describing vapor desorption or adsorption isotherms (3).
When water interacts with solutes and surfaces, it is unavailable for other hydration interactions. The term water activity (aw) describes the (equilibrium) amount of water available for the hydration of materials. Water activity is unitless and a value of unity indicates pure water, whereas zero indicates the total absence of water molecules. Water activity is the effective mole fraction of water, defined as: aw = λw xw = p /p0 in which λw is the activity coefficient of water, xw is the mole fraction of water in the aqueous fraction, p is the partial pressure of water above the material, and p0 is the partial pressure of pure water at the same temperature (i.e., the water activity is equal to the equilibrium relative humidity [ERH]), expressed as a fraction. The relationship between water activity and weight percent water is shown in a sorption isotherm (see Figure 1). Figure 1 also shows the hysteresis observed when the sorption isotherm depends on whether the water is added to the dry material or removed from the wet material. This hysteresis is caused by nonreversible structural changes and/or kinetic effects.
Figure 1: Water sorption isotherm.
The sorption isotherm for a formulated drug product is the result of the combination of the individual-component sorption isotherms. Sorption isotherms for excipients and the drug substance may be used to model the sorption isotherm of the finished dosage form (5). Figure 2 shows an example of an adsorption isotherm for a typical oral formulation. Two recently published studies present adsorption and desorption isotherms for several common excipients (5–6).
Figure 2: Typical adsorption isotherm for tablet formulation.
Materials of differing water activity exhibit time- and temperature-dependent water migration from areas with high to low aw . For example, a gelatin capsule filled with a powder that has a different water activity will undergo water migration and, at equilibrium, the capsule shell and powder contents have the same aw . For packaged products, the moisture-vapor barrier properties of the packaging become crucial in the rate of moisture loss or gain. In addition, desiccants inside a package change the initial water activity as well as the subsequent rate of water activity change. Because the humidity of the air is defined as 60% (aw = 0.6) by the International Conference on Harmonization under Climatic Zones II, materials with lower aw tend to gain water and those with higher aw tend to lose water. Most solid oral-dosage forms are produced with water activities of 0.3 to 0.5 and thus gain water in stability studies.
Use of water activity. The food industry has long used water activity to control microbial growth and chemical stability. Consistent with the US Food and Drug Administration's use of water activity in controlling the microbial attributes of food (7), water activity also is being used to control the microbiological properties of pharmaceutical products (8, 9). The growth of most bacteria is inhibited below approximately aw = 0.91. Similarly, most yeasts cease growing below aw = 0.87, and most molds stop growing below aw = 0.80. The absolute limit of microbial growth is approximately aw = 0.6.
The importance of water activity in controlling the microbial properties of pharmaceutical products was added to US Pharmacopeia (USP ) Chapter ‹2023›, "Microbiological Attributes of Nonsterile Nutritional and Dietary Supplements," and a new USP chapter was written: ‹1113›"Application of Water Activity Determination to Nonsterile Pharmaceutical Products." USP Chapter ‹1113› primarily describes the application of water-activity measurement for the control of a nonsterile formulation's microbial attributes, but also mentions the control of chemical degradation. The correlation of water activity and chemical changes in food also has been investigated extensively (10). A correspondingly common practice in pharmaceutical development is to equilibrate products at different humidities (water activities) and study their degradation rates. Water activity also correlates with changes in chemical and physical stability (11, 12). The degradation rate of several pharmaceutical products is well modeled by water activity using the BET function (rate is proportional to 1/[1 – aw ]) (11) as well as other approaches (12–15).
Measurement of water activity. Water activity is determined by the measurement of water in the gas phase immediately surrounding the sample. The measurement of water activity in foods is described by AOAC's Official Methods of Analysis, No.978.18, "Water Activity of Canned Vegetables" (16). The principal techniques are changes in electrical capacitance or resistance of polymer thin films and dew point by chilled mirror. Newer techniques include the measurement of water in the headspace either spectroscopically (17) or chromatographically (18).
Method Number 978.18 also compares various types of instruments. For sensor-type instruments, a typical instrument chamber would have a depth of approximately 1.3 cm and a diameter of 4.2 cm. Sufficient sample is needed to fill the chamber to the appropriate level (one-half to two-thirds full). Probes also are available for insertion into bulk materials or possibly through product packaging. Measurement time is controlled by sensor measurement time (usually a few minutes) and time for the headspace to equilibrate (the time for water activity in the headspace to come into equilibrium with the material being tested). Typical equilibration times vary from 5 to 30 minutes.
The rate of equilibration of the dosage form with the chamber's headspace depends on several factors, including:
The gas-phase diffusion rate of water is not a significant factor based on the configuration of typical sensor cells. The gas-phase diffusion rate is approximately 0.1 cm2 /s and the largest distance in the chamber is approximately 4 cm. Because the sample occupies most of the chamber, the largest distance is actually closer to 0.5 cm (from the top of the sample to the top of the chamber). The transfer rate of water between the sample and the gas phase is related to the specific sample for evaluation. Depending on the sample, the transfer rates within the sample and between the sample and the gas phase can vary significantly. Heterogeneous samples such as intact capsules or coated tablets may have longer equilibration times than uniform powder samples.
Although sample transfer can be performed rapidly to minimize changes to the sample moisture content, moisture still must be absorbed or desorbed from the sample to equilibrate the measuring chamber's headspace. For a typical sample, the change in the sample's moisture content during this equilibration process will not have a significant effect on the accuracy of the sample's final aw reading. Air at a temperature of 25 °C contains approximately 0.023 mg/mL of water at 100% RH. For a sample at 75% RH, with the external environment at 0% RH and a sample chamber headspace of 6 mL, the sample must replace only approximately 6 mL × 0.023 mg/mL × (0.75 – 0.10) or 0.01 mg of water. With a sample weight of 2 g in the chamber and a water content of 2%, the total amount of water in the sample is 40 mg. In this case, only a very small fraction of the total water is removed from the dosage form to equilibrate the humidity in the headspace (the water content of the sample would drop by less than 0.01%).
Samples that contain very little water or have a very shallow slope for the sorption isotherm in the region of interest will be problematic with regards to bias during equilibration in the chamber. The use of laser-absorption spectroscopy (which can determine the water activity in the headspace of a sample vial without breaching the seal) would be beneficial for these types of samples. An example of a product that could be difficult is a lyophilized cake with very low water content. Nonetheless, the typical capsule or tablet product generally contains a large amount of water and is an excellent candidate for water-activity testing.
Table I: Examples of required changes in water activity to double degradation rate.
For most solid oral-dosage forms, the range of interest for water activity is 0.30–0.75. Water-activity measurements are generally precise and accurate to 0.01–0.02 units. Thus, water activity should be capable of providing 23 levels ([0.75 – 0.30]/0.02) of distinction over this measurement range. Several examples of degradation as a function of water activity are shown in Table I, and water activity changes of about 0.1–0.2 are needed to double the degradation rate. In a case for which a 0.1 change in water activity is critical, tighter controls of calibration may be needed. In general, the water activity would be controlled at a level well below when significant degradation occurs. Thus, the examples in Table I represent mostly the worst cases in terms of required accuracy. Compared with Karl Fischer water testing, water activity has particular advantages when:
Calibration. Calibration is accomplished with the use of either saturated salt solutions or solutions with well-characterized water activities. Saturated salt solutions that have reference values traceable to National Institute of Standards and Technology standards (24) are available. Figure 3 shows the effect of temperature on some typical water-activity standards.
Figure 3: Relative humidity as a function of temperature for saturated salt solutions used for calibration (only the magnesium nitrate standard is sensitive to temperature).
Over-the-counter tablets of ibuprofen, naproxen, and enteric-coated aspirin were obtained from a local retail establishment for evaluation. Two developmental capsule formulations also were evaluated. Capsule A was a starch-based formulation and Capsule B contained enteric-coated beads. The water-activity instruments used were from the same manufacturer (Novasina, Pfäffikon, Switzerland) but obtained from Omnimark Instrument Corp. (Tempe, AZ). The names of the two models are the Ms1 and the AW Lab.
Both instruments use the same measuring cell and sensor. The AW Lab model has an additional capability of determining whether the measurement has reached equilibrium by establishing a limit of the change in water activity with time. All measurements were made using the mechanical prefilter, except for those made for Capsule B. For the Capsule B measurements, all of the protective filters listed in Table II were evaluated.
Water-activity standards (saturated salt solutions) were obtained from the instrument supplier. Both Novasina instruments take into account temperature during calibration as long as the temperature is between 15 °C and 30 °C.
The Novasina instruments do not allow for temperature control. To obtain temperature-effect data, the measuring chamber was placed in a plastic bag and immersed in a water bath. Measurements were only recorded after the sensor temperature reading agreed with the external water-bath temperature.
Table II: Protective filters used with water-activity instruments from Novasina for Capsule B measurements.
Because it is not easy to predict the effect of test samples on the instrument sensor, bracketing readings of water activity standards were performed regularly (one low and one high standard reading during each period of use, typically 24 hours).
The equilibration of dosage forms to different water activities were performed to ensure the validity of the water-activity measurement. In general, the same type of salt solutions used in sealed desiccators also were used for calibration. Intact tablets or capsules were equilibrated for 7–14 days. Crushed or composited dosages were equilibrated for 24 hours.
Studies requiring RH control were performed with a humidity-controlled glove box (Coy Laboratory Products, Grass Lake, MI).
Results and discussion
Key operating conditions that were investigated include the effects of sample temperature, equilibration time, and sample handling (in particular, the humidity of the environment in which samples are transferred). In addition, the factors affecting the specificity of the sensor must be considered to support the validation of the technique. Based on an earlier discussion, changes in aw of >0.01 to 0.02 were not considered significant.
Sample temperature. If the sample and the equilibration chamber are at the same temperature, then temperature has a small effect on water activity within the temperature range of most laboratories. The authors previously discussed the effects of temperature on the water activity of the saturated salt standard solutions used for calibration. Those effects are generally small and taken into account by the instrument. The effect of temperature on solid oral-dosage forms was studied for two samples: Capsule A and naproxen. The observed effects of temperature changes on water activity were 0.003 and 0.004 aw /°C and were similar to those reported by a manufacturer (25). The small effect of temperature is explained by the fact that the change in the partial pressure of water vapor (p ) with temperature for the sample is similar (but not equal) to the magnitude of the change of the saturation pressure (p0) above pure water. Any change in the temperature of a hygroscopic product automatically causes the product to exchange moisture with the air (or gas) that surrounds it. Moisture is exchanged until the partial water-vapor pressure at the product's surface and in the air is equal. For this reason, a constant temperature is important when measuring aw .
Figure 4: Rate of equilibration of Capsule A.
Equilibration time. To understand the time required for the headspace to come into equilibrium with the sample, water activity was measured as a function of time for the products shown in Figures 4 and 5. The results for Capsule A indicated that equilibration occurred within 10 minutes and no significant changes occurred over the subsequent 12 hours (see Figure 4). Figure 5, which includes two typical tablet formulations and an enteric-coated aspirin tablet, shows that a 30-minute equilibration time was appropriate for the tablet formulations. A longer equilibration time would be needed with the enteric-coated formulation for the same degree of accuracy. In general, the authors have used an accuracy of ±0.02 aw as being acceptable. Another alternative would be to crush the enteric-coated tablet, but this procedure needs special precautions.
Figure 5: Rate of equilibration of several solid oral-dosage forms.
For some instruments, the equilibration time is not a concern. These instruments measure the rate of change of aw with time and will indicate a stable reading only when the rate of change is below a selected threshold. Other instruments use a mathematical function to estimate the final equilibrium value. The advantage of measuring water activity on intact tablets is shown in Table III, in which the water activity of intact tablets is compared with that of crushed tablets under 10% and 80% RH. The total exposure time to the ambient RH was approximately 2 min (including the time to crush the tablets with a mortar and pestle). This time was used to simulate rapidly crushing, weighing, and transferring tablets in alternative methods such as Karl Fischer. Whereas the low humidity only created a small bias, the high humidity created a large error. There was a larger difference between the sample water activity and the ambient conditions for the high humidity (45% RH higher) versus the low humidity (22% RH lower). The rate of water uptake versus loss is not expected to be the same. A technique for reducing water changes during crushing is to use a device sold to home customers that sandwiches the sample between two holders, thus reducing contact with the ambient atmosphere.
Table III: Effect of sample grinding on measured water activity.
Sample handling. The effect of ambient humidity on sample handling was assessed by transferring Capsule A in environments of 10% and 80% RH. As shown in Figure 6, the effect of high or low humidity is to increase the equilibration time with little effect on the final measured value. An equilibration time of 30 minutes was considered adequate.
Figure 6: Effect of ambient relative humidity during transfer on rate of equilibration.
A second issue with sample handling is the equilibration of water within the dosage unit. For tablets, a blended powder is compressed and there should be little inhomogeneity of water content. For capsules, the powder fill will be at a different water activity than the gelatin. A study was undertaken to measure the time required for equilibration to occur between the fill and the capsule. For dry contents (aw = 0.38) within a wetter gelatin capsule shell (aw = 0.54), approximately one hour was required to be within 0.01 of the final water-activity value. The same contents within a very dry shell required approximately three hours to be within 0.01 of the final water-activity value. Thus, equilibration within the dosage unit would only be a concern for in-process testing. For in-process testing, the capsule could be opened, and the capsule shell and powder could be placed within the testing chamber.
Validation. Specificity. For the Novasina instruments, the sensor responds to any polar volatile component that affects the resistance or the capacitance of the polymer used in the sensor. Most pharmaceutical tablets or capsules either will have no solvents or the solvents are removed during the processing and drying of the dosage form. Bracketing check standards (one low and one high standard check) were used during each period of use (typically 24 hours) to ensure that any changes in sensor response were readily detected. Potential interferences also were removed through the use of prefilters.
Interferences from the enteric-coated beads in Capsule B caused some difficulty. The problem appeared as a failure of the check standard and subsequent poor sensor performance with respect to drift. The sensor was replaced with a new sensor, and the authors evaluated each of the chemical filters described in the experiment section for their ability to prevent sensor failure. All filters were capable of removing the interfering components, but the general chemical filter (activated carbon) greatly reduced response time and required as much as an hour for equilibration to occur. The interference arises from the degradation of the hydroxypropyl methylcellulose acetate succinate (HPMCAS) polymer to yield acetic and succinic acids. The acetic acid is a known potential interferant for this type of measurement cell (26).
Linearity. The general calibration approach ensures a linear response to within 0.01 aw over the operating range of the instrument.
Accuracy. Accuracy at equilibrium is assessed by comparing the water activity of equilibrated samples with the theoretical water activity (the RH to which the sample was equilibrated using a controlled humidity chamber). Samples were equilibrated over the same type of saturated salt solutions used to calibrate the instrument. This approach was evaluated with an enteric-coated aspirin tablet and two other tablet formulations as shown in Table IV with a general accuracy of 0.01–0.02 aw . The same approach was taken by Mahajan et al., with a similar degree of accuracy (17). As previously mentioned, a 30-minute equilibration time generally has been adequate for capsules and tablets.
Table IV: Water activity after equilibration and absolute error (measured aw and theoretical aw).
Precision. Replicate measurements were made for two tablet formulations and one capsule formulation (see Table V). The relative standard deviations for replicate measurements were 1–3%.
Instrument qualification of maintenance (Novasina Instrument). Using the guidelines published in a recent white paper (27), water-activity instruments would be Class B, principally requiring calibration to ensure performance. At the initial installation and every 6 months thereafter, four standards are checked (0.11, 0.33, 0.75, and 0.90). If the measured results are more than 0.02 aw outside of the theoretical value, then the instrument calibration for that standard is changed. Note that the 0.53 standard may be used for laboratories with adequate temperature control or the reading must be corrected for temperature (see Figure 3). The use of daily bracketing standards is recommended to ensure that the instrument continues to work properly and that the sample does not affect instrument performance.
Table V: Replicate measurements of water activity.
The instrument is operated with the alcohol prefilter, and records are maintained for the installation of the prefilter. The replacement of the prefilter depends on the type and number of samples measured, but it should be replaced at least every six months. The standards themselves are available from the vendor with a certificate, and the vendor recommends a use period of several years. Some water activity standards will dry out over time, and some water must be added to maintain a saturated suspension. Aqueous, single-use solution standards also are available from some vendors. The stainless steel chambers also should be cleaned and sanded periodically to remove any rust. The o-ring seal on the chamber should be inspected regularly and replaced if any cracking or other defects are noted. A significant failure of the chamber seal integrity should be evidenced by a failure of standards that are dissimilar from the RH of the room.
Water activity as part of a control strategy
Water measurements as part of a control strategy generally must be quantitative (correcting for water content in a drug substance) or must be related to a change in a chemical or physical property. For solid oral-dosage forms, water is usually measured because of an adverse effect of water on either chemical stability or a physical attribute of the formulation such as drug release. Much of current measurement of water by Karl Fischer testing could be replaced with water-activity testing because water activity is easier to measure, less subject to handling problems, and as good or better at correlating to physical and chemical changes than total water.
Additional advantages of water activity testing are:
Where water measurements are part of a regulatory commitment, water-activity results would need to be related to Karl Fischer measurements by the sorption isotherm. The specification for water activity then could be set to correspond to the Karl Fischer specification.
The establishment of water activity as an analytical procedure would generally involve:
Table VI describes some differences in the types of instruments. Only representative manufacturers are included.
Table VI: Comparison of instruments for measurement of water activity.
The approach used by all of the instruments is nondestructive. The instruments vary in the cutoff at low RH, the control of temperature, and the detection of the equilibration end-point. Measurement time is faster for the laser absorption and the instruments that extrapolate the detection of the end-point; but, temperature control generally lengthens the measurement time to 10–30-minutes for all the instruments. The Lighthouse instrument would be especially useful for lyophilized formulations because the measurement can be made on the headspace of the product vial. Reference 16 has more details about differences in cost and applicability.
The control strategy also must be consistent with the regulatory strategy. Table VII summarizes options relative to the product registration status.
Table VII: Options for implementing water-activity testing as a function of registration status.
Routine control of instrumentation. For the instruments that have sample contact with the sensor, bracketing readings of the standard solutions should be used to ensure that the sensor is providing accurate results and that the samples did not contaminate the sensor. The use of a protective filter should be tracked such that the filter is replaced at least as frequently as the manufacturer suggests. Standards that are saturated salt suspensions also require some maintenance to replace lost water from evaporation. These standards should be checked each time they are used.
Water activity is a valid alternative to total water measurements (KF) in assessing the potential for water to adversely affect the formulation's microbial or chemical quality. Water activity has been accepted in the food industry and widely discussed in the pharmaceutical industry as an appropriate measurement for water to prevent microbial growth. Likewise, water activity also can be used to evaluate the potential effect of water on chemical and physical changes in the formulation. The Novasina ms1 and AW instruments in particular have proven to be sufficiently precise and accurate to measure the water activity of typical solid oral-dosage forms.
Thanks to Jim Farmer for his assistance.
At the time of the research, Bob Snider, PhD,* was a research advisor with Eli Lilly and Company, firstname.lastname@example.orgPeihong Liang is an analytical chemist at Lilly Research Laboratories, Eli Lilly and Company (Indianapolis, IN), and Neil Pearson is a research scientist at Lilly Research Laboratories, Eli Lilly Canada, Inc. (Toronto, ON, Canada).
*To whom all correspondence should be addressed.
Submitted: July 13, 2006. Accepted: Oct. 11, 2006.
Keywords: Karl Fischer techniques, solid dosage forms, water testing
1. M. Mathlouthi, "Water Content, Water Activity, Water Structure and the Stability of Foodstuffs," Food Control 12 (7), 409–417 (2001).
2. C. Ahlneck and G. Zografi, "The Molecular Basis of Moisture Effects on the Physical and Chemical Stability of Drugs in the Solid State," Int. J. Pharm. 62 (2–3), 87–95 (1990).
3. S. Brunauer, P.H. Emmett, and E. Teller, "Adsorption of Gases in Multimolecular Layers," J. Amer. Chem. Soc. 60, 309–319 (1938).
4. J. Maques et al., "State of Water in Gelatin Solutions and Gels: An 1H n.mr. Investigation," Polymer 27 (7), 1103–1110 (1986).
5. Y. Li, Y.D. Sanzgiri, and Y. Chen, "A Study on Moisture Isotherms of Formulations: the Use of Polynomial Equations to Predict the Moisture Isotherms of Tablet Product," AAPS Pharm. Sci. Technol. 4 (4), article 59 (2003).
6. S. Airaksinen et al., "Role of Water in the Physical Stability of Solid Dosage Formulations," J. Pharm. Sci. 94 (10), 2147–2165 (2005).
7. US Food and Drug Administration, Code of Federation Regulations, Title 21 (FDA, Rockville, MD, 2006), Part 113.3(ii) and 113.81 (f).
8. R.R. Friedel and A.M. Cundell, "The Application of Water Activity Measurement to the Microbiological Attributes Testing of Nonsterile Over-the-Counter Drug Products," Pharm. Forum. 24 (2), 6087–6090 (1998).
9. R.R. Friedel, "The Application of Water Activity (aw) Measurement to the Microbiological Attributes Testing of Raw Materials Used in the Manufacture of Non-Sterile Pharmaceutical Products," Pharm. Forum. 25 (6), 8974–8978 (1999).
10. P.S. Taoukis, T.P. Labuza, and I.S. Saguy, "Kinetics of Food Deterioation and Shelf-Life Prediction" in Food Engineering Practice, K.J. Valentas, E. Rotstein, and R.P. Singh, Eds. (CRC Press, Boca Raton, FL, 1997).
11. J.T. Carstensen and A. Li Wan Po, "The State of Water in Drug Decomposition in the Moist Solid State: Description and Modeling," Int. J. of Pharm. 83 (1–3), 87–94 (1982).
12. E.Y. Shalaev and G. Zografi, "How Does Residual Water Affect the Solid-State Degradation of Drugs in the Amorphous State?" J. Pharm. Sci. 85 (11), 1137–1141 (1996).
13. K.C. Waterman et al. "Hydrolysis in Pharmaceutical Formulations," Pharm. Dev. Technol. 7 (2), 113–147 (2002).
14. K.C. Waterman and R.C. Adam, "Accelerated Aging: Prediction of Chemical Stability of Pharmaceuticals," Int. J. Pharm. 293 (1–2), 101–125 (2005).
15 . L. Bell, "Water Activity and Reaction Rates/Physical Properties/ Shelf-Life," IFT Fundamentals of Water Activity Short Course presented at the 2002 Annual Conference of the Institute Food Technologists, Anaheim, CA, 2002.
16. AOAC, "Water Activity of Canned Vegetables" in Official Methods of Analysis (AOAC, Gaithersburg, MD, 1995), method number 978.18.
17. R. Mahajan et al., "A Novel Nondestructive Approach for Measuring Moisture Activity in Pharmaceutical Samples," Pharm.Technol. 29 (10), 88–104 (2005).
18. B. Duersch et al., "Monitoring the Headspace Inside Pharmaceutical Packaging," presented at IIR conference on "Hydrolysis and Stabilization of Pharmaceuticals," Philadelphia, PA, July 2005.
19. B. Snider, "Mass Balance Issues with Low Dose Compounds," presented at Annual Meeting of the American Association of Pharmaceutical Scientists, Indianapolis, IN, November 2000.
20. Unpublished data.
21. K.C. Waterman et al., "Hydrolysis in Pharmaceutical Formulations," Pharm. Dev. Technol. 7 (2), 113–146 (2002).
22. D. Genton and U.W. Kesselring, "Effect of Temperature and Relative Humidity on Nitrazepam Stability in Solid State," J. Pharm. Sci. 66 (5), 676–680 (1977).
23. L.N. Bell and T.P. Labuza, "Aspartame Degradation as a Function of Water Activity," Adv. Exp. Med. Biol. 302, 337–349 (1991).
24. L. Greenspan, "Humidity Fixed Points of Binary Saturated Aqueous solutions," J. Res. Natl. Bur. Stand. A. Phys. Chem. 81A, 89–96 (1977).
25. Rotronic Instrument Corp.,"Water Activity Varies only by Roughly 0.0005 to 0.005 Aw (0.05 to 0.5 %RH) when Temperature Changes by 1 °C" (Rotronic Instrument Corp., Huntington, NY), http://www.rotronic-usa.com/datasheets/Ref/Aw/aw_define.htm, accessed Jan. 11, 2007.
26. Novasina, "Water Activity Measurement," (Novasina, Pfäffikon, Switzerland), http://www.novasina.ch/wEnglisch/Knowledge_Center/Applikationen/Applikationen-dp-air-aw/Applikationen-Wasseraktivitaet.php, accessed Jan. 8, 2007.
27. S.K. Bansal et al., "Qualification of Analytical Instruments for Use in the Pharmaceutical Industry: A Scientific Approach," AAPS Pharm. Sci. Technol. 5 (1), article 22 (2004).