n:"“'7. :v‘8' V“ ‘ . it"; \ {f 24! '3:ng ”(5%) J?!“ ”“1““ 3’1: ‘ ‘1:qu- ‘ ’- I, . ', . I ,. . -r .|._ ¢:~'. ./ ' ‘_ ' . V: : V- - A.’ we}, . x J (4'. u». oox v ~~oJ - .133 :-u“..n a" \‘tq'l .‘I ‘75! “C . in}: o u. ""I'l-h‘ w 31%;" “8‘1!!!ng \ R- "J ' ’78.; “(Id-3"“! 2 - “:"'?“~'8‘17“'.... L..I .Iy .1112)? , J . I ‘ I" "Rig“ ‘ d.. '. fl . v . g! A F 1 3H0!“ . _ H . 3,. ,4 7 . . 10'? '.‘;‘ -) I ‘ r. f! r l :1 . ' ,r\ .. ). .. ‘l ‘ mama Y Michigan State University l -\ fit” This is to certify that the thesis entitled PREDICTING THE NDISTURE UPTAKE OF TABLETS PACKAGED IN SEMIPERMEABLE BLISTER PACKAGES AND STORED UNDER STATIC CONDITIONS OF TEMPERATURE AND HUMIDITY presented by JOHN STEVENSON FULCOLY has been accepted towards fulfillment of the requirements for PAC KAG I NG 01k. a» M DR. ACK GIACIN & DR,3Rucg flARTE M ' S ' degree in Major professor Date NOVEMBER 9, 1981+ 0-7639 MSU is an Affirmative Action/Equal Opportunity Institution IVIESI.) RETURNING MATERIALS: Place in book drop to LIBRARJES remove this checkout from _ your record. FINES will be charged if book is returned after the date stamped below. JUL212009 5-6410 PREDICTING THE MOISTURE UPTAKE OF TABLETS PACKAGED IN SEMIPERMEABLE BLISTER PACKAGES AND STORED UNDER STATIC CONDITIONS OF TEMPERATURE AND HUMIDITY By John Stevenson Fulcoly A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1984 @1985 JOHN STEVENSON FULCOLY All Rights Reserved ABSTRACT PREDICTING THE MOISTURE UPTAKE OF TABLETS PACKAGED IN SEMIPERMEABLE BLISTER PACKAGES AND STORED UNDER STATIC CONDITIONS OF TEMPERATURE AND HUMIDITY By John Stevenson Fulcoly A simulation modeling technique is presented that predicts the moisture gain of a packaged product. The moisture isotherm of the product and the water vapor permeability of the package are measured and incorporated into the model with values representing the environmental severity. The study provides improvements over previous reports in that l) it presents a detailed description of methods to accurately measure the package NVTR, tablet moisture isotherm, and moisture uptake of packaged product; 2) further, a new technique of using a mathematical fit to describe the moisture isotherm is presented; 3) and a computer program was used requiring a minimum of data entry that enables the differences between isotherm expressions to be evaluated. The simulated results agree well with experimentally measured moisture gain of tablets packaged in three different materials. A discussion is included that presents several applications of the simulation technique that lead to a timely cost effective package develOpment program. DEDICATION This thesis is dedicated to my family, especially to my parents, Mr. and Mrs. Joseph E. Fulcoly, Jr.. Their love and support gave me the strength and spirit to complete this project. Their values have served as an example for me to follow, and have contributed to the success of this achievement as well as to other areas of my personal growth. ii ACKNOWLEDGEMENTS The author wishes to thank Dr. Jack Giacin for his significant contributions toward the completion of this thesis. Also, thanks to Dr. Bruce Harte for his continued guidance and help while serving as major advisor. The- author also thanks Dr. Eric Grulke for his service as a committee member and Dr. Hugh Lockhart for his efforts as a reviewer. And thanks to Dr. Donald C. Liebe for his valuable input and sincere support. The author also acknowledges Dr. Julian Lee and Mr. Mark Wang for their contribution of the computer model used in this manuscript. Further, the author wishes to thank G.D. Searle Inc. for the use of their facilities throughout this project. A special note of thanks is extended to Mr. William Coppola, Mr. Douglas Miller, Mr. Tony O'Callaghan, and Mr. Charles Thompson for their extensive support and encouragement. TABLE OF CONTENTS LIST OF TABLES. LIST OF FIGURES . INTRODUCTION. BACKGROUND. MATERIALS . EQUIPMENT . EXPERIMENTAL. MATHEMATICAL MODEL. RESULTS AND DISCUSSION. APPLICATIONS. CONCLUSION. APPENDICES. REFERENCES.~. iv Page vi 12 I7 18 21 24 56 62 64 66 Table 10 11 12 13 14 15 LIST Flexible materials. Relative humidities Percent moisture of 11% RH. Percent 33% RH. Percent 48% RH. Percent 7l% RH. Percent 80% RH. Percent 89% RH. moisture moisture moisture moisture moisture of of of of of OF TABLES of salt tablets tablets tablets tablets tablets tablets solutions stored at stored at stored at stored at stored at stored at at 40°C 40°C, 40°C, 40°C, 40°C, 40°C. 40°C, Equilibrium moisture contents of tablets at 40°C. Moisture permeability of blister packages Moisture content of packaged tablets stored at 40°C, 80% RH. Equilibrium moisture content of tablets at different relative humidities at 40°C Experimental and calculated moisture content of tablets packaged in PVC blisters. Experimental and tablets Experimental and calculated moisture content of tablets packaged packaged calculated moisture content of in saran-coated PVC blisters in vinyl-aclar blisters. Page l3 l5 25 26 27 . 28 29 30 36 38 41 , 46 48 50 Figure 10 11 LIST OF FIGURES Blister package dimensions. Moisture contents of tablets at 40°C and varying relative humidities . . . Moisture loss of tablets at ambient condi- tions (taken from storage conditions 40°C 80% RH) . . . . Moisture sorption isotherm of tablets at 40°C. Weight gain of blisters at 40°C 80% RH due to moisture transmission . . Moisture content of packaged tablets stored at 40° C, 80% RH . . . . . . . . . . Moisture sorption isotherm described by three mathematical equations. . . . . . Experimental vs predicted moisture content of tablets in PVC blisters at 40°C 80% RH. Experimental vs predicted moisture content of tablets in PVC/PVDC blisters at 40°C, 80% RH. Experimental vs predicted moisture content of tablets in PVC/Aclar blisters at 40°C, 80% RH. . . . . . . . . Predicted effect of humidity on moisture uptake of tablets packaged in Vinyl -Aclar blisters at 40° C. . vi Page 14 31 33 35 39 42 45 51 52 53 60 INTRODUCTION A package designed to contain a pharmaceutical product ‘ must insure the product's safety and efficacy from time of manufacture until time of use by the consumer. The responsibility for developing an appropriate package rests with the packaging development team, who in an appropriate time, must evaluate the protective properties of the package while considering economic, manufacturing, and marketing concerns. This thesis will/present 3 cost and time efficient method for evaluating the protective capability of a Unit-dose blister paCkage,”i A blister package may be required to provide protection from light, oxygen, moisture, and in some cases physical abuse. The most common feature desired in a unit-dose blister, intended to contain a tablet or capsule, is moisture protection. Protection from moisture is important since it is often the determinant of product stability and performance (Hollenbeck, 1982). Water may act as a reactant in drug degradation, or serve as a solvent providing a medium for degradation reactions to proceed in (Carstensen, 1980). The adsorption of moisture by a tablet may also influence such physical properties as hardness and friability, cause swelling, affect dissolution 1 ‘ "1 rate, and promote color change. Techniques used for evaluating the stability of a product stored in a unit-dose package include long-term ambient storage tests, accelerated "stress" tests, and more recently, shelf—life simulation modeling. Present FDA regulations require three year ambient data to support a three year expiration date. To wait three years is not only a financial burden, but may lead to poor product success due to a late launch allowing a competing product to capture some of the market. To facilitate earlier product submissions, the FDA _.will accept accelerated test data in support of shorter expiration dates. This allows a company to get a product on the market with a short expiry, and as more data become available, the expiration date may be increased. The test conditions of three months storage at 40°C, and 80% RH are accepted to support two year dating. Therefore many companies design packages that will survive these acceler- ated conditions. A problem with this approach is that by designing a package that provides adequate protection at the accelerated conditions, the resulting package may offer more than adequate protection at ambient conditions. Gyeszly (1977) has discussed the problems associated with comparing accelerated data to ambient performance. The "overpackaging" that can result from this technique leads to unnecessary material costs. Additionally, to change the package, one must repeat the entire process to satisfy regulatory requirements. Accordingly, a procedure that can identify the performance of a package prior to initia- ting stability studies will result in considerable time and cost savings. Predicting shelf-life involves combining expressions for product sensitivity, package effectiveness, and environmental severity into a mathematical model. When dealing with a moisture sensitive tablet, the key parameters include tablet hygroscopicity, package water vapor trans- mission rate (WVTR), temperature, and relative humidity. The model is capable of predicting the moisture content of the product at any time. Therefore, by knowing the maximum allowable moisture content, the shelf-life can be deter- mined. Once an apprOpriate model has been developed it can be used as a tool for preliminary screening of packages. For example, by measuring the (WVTR) of several packages and applying the results to the predictive model, one can ascertain which package will perform most satisfactorily in the long run. Alternately, knowing the critical moisture content and the desired shelf-life, the model can be used to determine the required package permeability. A valuable application of the model is the ability to predict the performance of the same package-product system at more than one condition, enabling one to make direct correlations between accelerated data and ambient performance. This kind of insight can lead to financial savings by selecting the most efficient packages for stability testing and avoiding the need to test additional package systems that later will be proved unsatisfactory. The predictive capability of the modeling technique makes it suitable for early appraisals of the cost- effectiveness of potential packages. For example, is the additional shelf-life provided by a vinyl-aclar blister over a saran-coated vinyl blister worth the approximately forty percent added material cost? Also it could be that a less expensive, lower barrier material package is suitable for the dry arid conditions of the Middle East, whereas a more protective barrier is required for a hot humid region such as South America. It is the desire to answer questions such as these in a timely and cost efficient manner that provides the impetus for the investigation into shelf-life prediction models. A technique is described in this thesis for predicting the moisture gain of tablets packaged in semipermeable blisters and stored under static conditions of temperature and humidity. As will be described in the Background section of this thesis, most of the literature to date on predicting moisture gain of packaged products has been directed primarily to foods with a limited number of investigations involving drug formulations. The methods developed in this thesis have been used to predict the moisture gained by tablets stored in three different packages under static conditions. The results show 'excellent agreement between the predicted and experimentally measured moisture contents. The method is time and cost efficient, since easily measured package and product properties are used in the predictive model. The technique enables one to Optimize package requirements, and thereby prevent overpackaging at an early point in the package development program. BACKGROUND Investigations into predicting shelf-life began in the mid-forties when Oswin (1946) developed a model to predict the adsorption of moisture by a food to a defined critical limit. Similarly, Felt et al. (1946) predicted the storage-life of cereals based on moisture gained to a critical value related to texture. The Felt model included expressions for package permeation, product formulation and the prevailing storage relative humidity. Paine (1963) extended this work to predict the shelf-life of cigarettes. A model formulated by Salwin and Slawson (1959) predicted equilibrium moisture contents of components of dried food mixes stored in impermeable containers. This work was expanded by Iglesias et al. (1979) to enable a similar prediction for dried food mixes packaged in permeable containers. Throughout the late sixties and early seventies, extensive research was carried out at the Massachusetts Institute of Technology (MIT) on the subject of using models to predict shelf-life. While previous studies had emphasized predicting moisture gained to a critical content related to physical properties such as crispness and 6 flowability, the MIT studies began to examine the prediction of chemical deterioration caused by moisture and gas permeation. Simon (1969) developed a computer program to predict storage stability of fruit based on the amount of gas in the headspace. Mizrahi (1970) predicted the extent of browning in dehydrated cabbage as a function of moisture uptake. Quast and Karel (1972) predicted the extent of oxidation in packaged potato chips due to oxygen and moisture permeation. Karel and Labuza (1969) developed" shelf-life prediction models for dehydrated foods in conjunction with the development of packages for the NASA Space Program. 'Labuza (1972) reviewed mathematical models available for package optimization of foods for storage. The status of models for_predicting quality loss of packaged foods was updated by Saguy and Karel (1980). Only in the last few years has the prediction approach been applied to pharma- ceutical products. Nakabayashi et al. (l980a,b,c,d,e) predicted both physical and chemical changes of tablets packaged in semipermeable blister packages. Included in this work were predictions of tablet hardness, chemical assay, color, disintegration, and dissolution rate as they relate to moisture change. Kentala et al. (1982) used a computer simulation to predict the moisture gained by tablets repackaged at the hospital pharmacy level. Jagnanden (1980) predicted the extent of drug degradation of packaged aspirin using an inverse phase gas chromato- graphic technique. 1 A model intended to predict moisture change of a packaged tablet must describe two phenomena, transport of water through the packaging material, and adsorption of water by the drug product. The permeation of water vapor through a polymeric film can be described by Fick's First Law of Diffusion and Henry's Law of Solubility, and depends on the permeant concentration gradient that exists across the film. Most of the early prediction models used relatively simple expressions for describing the transport of moisture through the package and onto the food. Felt et al. (1945) described moisture permeation through a film by equation (1). W = R x A x T x (pi - po) (1) where: W = the weight of water transferred (grams) R = the permeance of the barrier material (grams/cmZ-day-mmHG) A = permeable area of the package (cm2) T = time (days) pi = vapor pressure of higher humidity atmosphere (mm Hg) po = vapor pressure of lower humidity atmosphere (mm Hg) More recently Peppas (l980a) applied a more detailed mathematical analysis to the transport properties of polymer films. He described the transport of moisture through a hydrophobic film by equation (2) Nw Pw (Cwi - Cwe) (2) 2 where: Nw = total mole flux of water (moles/cm -s) Pw = film permeability to water (grams-mil/100 inZ-day-cm Hg) Cwi = concentration of water inside the package (moles/cm3) Cwe = concentration of water outside the package (moles/cm3) For this investigation equation (3) was used to describe the transfer of water through semipermeable blister packages. dQ/dt = Pp x Ps/100 x (He - Hi) (3) II where: Q the quantity of water transferred (grams) t = time (days) PP = the package permeability constant (grams/pkg-day-Atm) P5 = the saturated vapor pressure at the test conditions (Atm) He = the external relative humidity (%) Hi = the internal relative humidity (%) The vapor pressure inside the package will be determined by the equilibrium moisture sorption isotherm of the 10 packaged product. The moisture isotherm is a plot of the moisture content of the product versus relative humidity. In early models, and some of the more recent studies described by Geyesly (1977) and Kentala (1982), the iso- therm was described by an equation for a straight line function as illustrated by equation (4). beH+c (4) a 11 moisture content (grams water/100 grams solids) where: m b = the slope of the line (m/%RH) RH = relative humidity c = the y intercept Both Labuza et al. (1972) and Peppas (1980a) have reported that the straight line interpretation is limited in scope, and is best suited for low values of RH. Peppas and Khanna (l980b) compared five isotherms for effective range of application. They reported that of the five isotherms studied, (BET, Langmuir, Halsey, Oswin, and Freundlich), the Halsey isotherm described the water sorption by foods over the widest humidity range (11% to 90%). The Halsey isotherm is shown in equation (5). ln aw = -ax(m)'r (5) where: aw water activity 3 ll grams water constants GI u '5 II 11 This investigation uses three mathematical fits to the data to represent the moisture isotherm. The first equation used was the straight line equation described earlier. The region of the isotherm between 35 and 80% RH was used to calculate the line equation and subsequently, accurately describes the isotherm only in that range of humidities. At high humidities the straight line equation yields lower than actual moisture content, and at low humidities higher than actual moisture contents are calculated. The subsequent expressions used to describe the moisture sorption of the tablet were found by fitting the experi- mental data to second and third order polynomial. This approach was found to describe the adsorption of moisture by the tablets over the humidity range of 11 to 90% RH. The second order polynomial is shown as Equation (6), and the third order polynomial is described by Equation (7). m = A + Baw + Caw2 (6) m = A + Baw + Caw2 + Daw3 (7) where: m = moisture content (grams per 100 grams solids) ’ aw = water activity A,B,C,D = constants found by data fitting The incorporation of the permeation and sorption equations into a predictive model is described in the Experimental section, and the solution of the sorption equations is discussed in the Results section. MATERIALS Tablets Tablets used in this study were supplied by 6.0. Searle Inc., Chicago, IL. The composition of the tablets is propietary. The tablets were round with a diameter of 9.0 mm, and an average weight of 200 mg. Packages Foil-backed blister packages constructed of three different materials were investigated. The materials of construction are listed in Table l. The dimensions of the capsule shaped blisters are shown in Figure l. Blister strips, and foil lidding, were supplied by Paco Packaging, Lakewood, NJ. Salts Saturated salt solutions were prepared to maintain constant relative humidities inside dessicators. Binary salt solutions were selected that would provide a range of relative humidities (RH) from 11 to 90 percent as reported by Greenspan (1976). The salts, and the humidities they maintain at 40°C are listed in Table 2. 12 13 Table 1. Flexible materials. Material Manufacturer Polyvinylchloride, 7.5 mil, MCFD 1025 Polyvinylchloride/Polyvinlidene (saran) coating, 8.0 mil Polyvinylchloride/Polyethylene/ Aclar, 10 mil SBS Paper/Foil/Vinyl coating, 1 mil Tenneco, Inc. Allusuisse Gravure Flex American Can 14 _ F— a O 8 o’ .2 1 0.125" L (1575” _ F 0.92 5” _ __ _ 0.200” 0.400" Figure 1. Blister package dimension. 15 Table 2. Relative humidity of salt solutions at 40°C. RH‘ , Salt 11.21 Lithium Chloride Granules 33.60 Magnesium Chloride, 4 Hydrate Crystals 48.42 Magnesium Nitrate, 6 Hydrate Crystals 71.00 Sodium Chloride Crystals 89.03 Potassium Nitrate Crystals 1Based on values reported by Greenspan (1979). 16 Water Water used in preparing the salt solutions was distilled and deionized. Dessicant Grade 944 indicating pellets, part number 944-08-Xl746, supplied by Hunt Sales Company, Phoenix, M0, were used in the package water vapor transmission determination. Glass Beads Solid glass beads (6 mm), supplied by Scientific Products, McGraw Park, IL were used as control fill in the package water vapor transmission determination. Glassware KIMEX crystallizing dishes, 6.5 cm x 12.5 cm, manu- factured by Kimble, Chicago, IL, were used to contain the salt solutions. Tablets used for determining the moisture isotherm were contained in 7 ml capacity weighing bottles with ground glass stoppers, also manufactured by Kimble. EQUIPMENT Balance A Mettler (Hightstown, NJ) model H51 analytical balance, sensitive to the nearest 0.01 milligram, was used for all weighings in the study. Desiccators Space-Saver desiccators manufactured by Bel-Art Products (Pequannock, NJ) were used in the study. These were plastic desiccators measuring 10.75 inches in diameter, and 12.25 inches high, with neoprene 0—ring seals. Environmental Cabinet A Lunaire (Williamsport, PA) model CL0632-4 environ- mental cabinet set at 40°C, and 80% RH was used in the study. Heat Sealer A Paco (Lakewood, NJ) model 153 heat sealer set at 275°F, and 2 sec dwell was used to seal the paper-foil lid stock to the blisters. Leak Tester An ARO (Buffalo, NY) model F099-1llO-l leak tester was used to test for seal integrity. Samples were exposed to a 15 inch vacuum for 30 seconds. 17 EXPERIMENTAL Initial Moisture Content The initial moisture content of the tablets was deter- mined by Karl Fisher Titration. Tablets (15) were crushed, transferred into 3 weighing spoons, and placed into titra- tion beakers. Each sample was titrated to the end point with Karl Fisher reagent. The average percent moisture was reported on a (w/w) basis. Salt Solutions Salt solutions were prepared by heating approximately 100 ml of water to 50°C in a crystallizing dish. Salt was slowly added while stirring with a glass rod until no more would dissolve. The solutions were set in desiccators which were placed in the environmental cabinet. The solutions were monitored for one week to assure saturation. Where necessary salt or water was added so that a layer of salt (.25 inch) was always visible under a layer of water (.50 inch). Moisture Sorption Isotherm The moisture sorption isotherm was determined by plotting equilibrium moisture content (EMC) versus relative humidity. Tablet EMC's were determined by storing the 18 19 tablets inside the desiccators, and observing weight change due to moisture gain or loss. Tablets were weighed to the nearest 0.01 mg in tared weighing bottles. Five bottles were placed in each desiccator and five set in the cabinet outside of the desiccators, all with the lids off. At selected times the desiccators were opened, and the lids quickly replaced on each bottle. The bottles were allowed to cool to room temperature, and weighed. This procedure was repeated until no significant weight change was observed. EMC's were calculated at each time point using Equation (8). Percent Moisture (g H20/lOOg Solids) = (M1 + M2)/Dw x 100 (8) where M1 = Initial moisture content (grams) M2 = Moisture content gained or lost (grams) OH = Dry weight Package Water Vapor Transmission Rate Package water vapor transmission rates (WVTR) were determined by a method similar to that specified in the US Pharmacopeia XX, 1980. Ten blisters were filled with desiccant tablets, and five with glass beads. Five empty blisters were tested for seal integrity. The filled packages were weighed to the nearest 0.01 mg and stored in the Lunaire cabinet set at 40°C, 80% RH. At certain 20 time intervals, the blisters were removed from the cabinet, cooled to room temperature, and weighed. Net weight gains were determined for the desiccant filled blisters by subtracting the average control package weight change from the observed gain of each blister. The average net gain of the ten samples was plotted versus time, and the lepe of the steady state portion of the resulting plot was used as the package WVTR. Moisture Content of Packaged Tablets The moisture increase of packaged tablets was deter- mined similarly to the package WVTR. Ten blisters were filled with tablets that had been weighed to the nearest 0.01 mg, and five blisters were filled with glass beads. The strips were sealed, and the five empty blisters were tested for seal integrity. The packages were weighed to the nearest 0.01 mg and stored in the environmental cabinet. At selected times, packages were removed, allowed to cool for 15 minutes and weighed to the nearest 0.01 mg. The net weight gain by the tablets was determined by subtracting the average control package gain from the observed test package gain. The percent moisture was determined at each point by using Equation (8). MATHEMATICAL MODEL The moisture content of packaged tablets, stored under constant external conditions, will depend upon the perme— ability of the package and the sorption characteristics of the tablet. Therefore to calculate the moisture content of the tablets, a model must be developed to describe the transport of moisture into the package, and the adsorption of moisture by the tablet. The model must also be able to account for changes in both moisture transport and adsorption over time. The total moisture in a package at any time (Mt) will equal the moisture in the headspace (Mh) and the moisture in the product (Mp). Mt = Mh + Mp (9) In the case of a blister package with a volume of one cubic centimeter, the amount of water in the headspace is insignificant in relation to the quantity in the tablet. Accordingly, Equation (9) can be changed. Mt = Mp (10) The change in moisture inside the package can be described by Equation (11). 21 22 th/dt = M (11) where (M) is the amount of water entering the package in (t) time. The amount of water entering the package will be dependent on the permeability of the package, which is described by: dM/dt = Pp x Ps x (aw ext - aw int) (12) where: Pp package permeability constant (grams water/pkg-day-Atm) P3 = saturated vapor pressure at the test conditions (Atm) aw ext the external water activity aw int the internal water activity The relationship between the equilibrium moisture content of the tablet and water activity is described by the following: aw = f(EMC) (13) Note that f(EMC) will be the equation chosen to describe the moisture sorption isotherm. Equation (12) can now be written as follows: dM/dt = Pp x Ps x (aw ext - f(EMC)) (14) or dM = Pp x Ps x (aw ext - f(EMC)) dt (15) 23 This can also be written as: dM/ aw ext - f(EMC) = (Pp x Ps) dt (16) Since it is assumed that Mp >> Mh, and Mt = Mp, then the total moisture in the package will equal the EMC times the weight of the dry product (W). M = EMC X N (17) Therefore d(EMC x W)/ (aw ext - f(EMC)) = (Pp x Ps) dt (18) Rearranging Equation (18) and integrating will give: . M1 12 w I d(EMC) / (aw ext - f(EMC)) = (prP5) fdt (19) Mo 0 where Mo = moisture content at time = 0 \D Virnxnrb Mi = moisture content at time = t ~ ‘ ~ G) vacuum-5‘49 ' ' ' n.1- . -1,” ‘ solving for time, 02.1»481'4’ f‘\ ®,.d\\.,.cb-1 A" Q) ‘2‘- °‘*b‘~ ng +5 . MI \\J ,, "fl ‘1‘ t =.\w_/)Op x PS I d(EMC1/(aw ext - (f (EMC)) (20) ‘ Mo Substituting the appropriate equation for the sorption isotherm into Equation (20) and integrating gives the moisture content of the product as a function of storage time for a situation of constant storage conditions of , 3X ‘M temperature and humidity where there is an interaction ~$S'-*‘”'TT' qi+bituxh§ between the product and the internal package environment. >-——-—-"‘ of". +51; “Ce RESULTS AND DISCUSSION The moisture sorption properties of the tablets were characterized by storing tablets for three months in desiccators containing saturated salt solutions. At selected times during the storage period, the tablets were weighed to determine any change in weight due to moisture transfer. The moisture content at each time interval was then calculated as described in the Experimental section (see Equation 8). The calculated moisture contents are presented in Tables 3 to 8. Specifically, each table reports the moisture content for individual tablets over the entire storage time at one humidity condition. Also reported are the average tablet moisture content and the standard deviation at each sampling point. The results demonstrate that the tablets reach equilibrium in two weeks. This is shown graphically in Figure 2, where the average moisture content is plotted as a function of storage time for the respective humidity conditions employed. Comparing the results of tablets stored at the same conditions allows the variability of the test method to be examined. At all conditions the results were found to be very consistent. Statistical analysis by the student's t-test showed that with a 95% confidence interval, the 24 25 .muwpom msmcm cop emu Loam: mango mm cmucoamm — Nmo.o m~F.o mcF.o omo.o Nmo.o mmo.o mmo.o .>mo .tum mm.m Noo.m mm~.N mem.~ mmP.N emm.~ mm~.~ mamgm>< omm.~ omm.~ cmm.~ epm.m —mp.m mom.~ mmN.N m mpm.m mmm.~ mPP.N FNN.N mmP.N NPN.N mm—.N v mom.~ Npm.m ¢mm.m moe.m NNN.N mm¢.N mum.m m opm.m moo.m «mm.m No¢.~ omp.m —mm.m Nem.m N nmm.m moo.m omN.N «mm.m «PN.N mmm.~ pom.m P mPP mm mm om om MN mp wFQEmm mAmo .Im N_P .oooa an catapm mum_nau co mesamwos actuate .m mynmp P 26 .muP—om mamgm oop emu Loam: mango mm umueoamm_ Nmm.o PNP.o Pom.o ooo.o upp.o moo.o No_.o .>mo .uam K¢~.¢ cmm.m mwm.m mvm.m Rpm.m on~.m mmK.m mmmem>< opm.¢ omp.¢ F_m.m Fmo.m ¢mw.m NNm.m mom.m m mmn.m _om.m mmo.m mmm.m opo.m .ms.m opu.m v mmm.¢ emo.¢ N¢¢.e mmm.m _om.m mpm.m mpm.m m Now.m mom.m oum.m mpu.m moo.m New.m omm.m N opN.e mum.m m¢¢.m «mm.m m_m.m Nom.m wmm.m P opp m“ mo om om mN mp mPaEmm mama .zm Nmm .uooe um umcoum mampnmu we assum_os acmocma .e mpnmh _ 27 .mnwpom manna cop Ema Laue: mEoem mm uwucoqwm P a~o.o mo_.o mm_.o oNP.o mmp.o Npp.o Fm_.o .>mo .cum mvm.m mNm.m moo.m mm~.m omp.m mmN.m _m—.m mmmem>< omN.m o¢_.m Kom.¢ mom.e moo.m Pop.m mmo.m m cum.m PoN.m omm.¢ omp.m omo.m mmN.m mm~.m e mmm.m ovm.m Kmp.m mON.m «KN.m mNN.m mep.m m omN.m mm¢.m m¢P.m PPm.m ooe.m me¢.m mm¢.m N mee.m omN.m moK.¢ Poo.m mmo.m _m_.m omo.m P o- mu mm om om mN mp «Fasmm mama .zm xme .uooe um cmeoum mampnmp to Pmesum_os “amuse; .m mpnmh .mcwpom msmgm oo_ emu Lopez msmcm mo umucoamm F mmo.o omo.o emp.o Nmo.o epo.o m~o.o omo.o .>wo .uum mpm.m mo¢.m mmN.m mNm.m eem.m mwe.m om¢.m mmmgm>< mam.m omm.m pmN.m mmN.m mmm.w omm.m N¢¢.m m mom.m Pm¢.w moe.w moN.m ocm.m mmm.m ome.m e mNm.m mm¢.m «NN.m Rpm.m .. cmm.m mmm.m m —Pm.m Nmm.m oeN.m om¢.m 1- Kem.m 5mm.m N mem.w mum.m mmo.m com.m cmm.m c_¢.m Pme.w F opp an we cm om mN m— m_asmm mzmo .zm x—N .uoov um umcoum mumpnmp we mczpmwoe acmucmq .m wpnmp P 29 .muwpom msmgm cop can Loam: mamcm mm nmucoawm F mpp.o mmo.o meo.o c~o.o c~o.o «Nm.o mno.o .>mo .uum Neo.m 5mm.m mom.w mom.m m~o.m ohm.m omm.w mmmgm>< vm~.m Pmp.m ocn.m Non.m mm~.m Fem.m Nom.m m mqo.m emo.m Pom.m mec.m moo.m Nmn.m mom.m c ow¢.m mpm.w mmo.m m_0.m mmm.m mmo.m mpm.m m cmo.a mNm.m mon.m PNN.m eon.w wmm.m oom.m N mon.m m~m.m mcm.m mmm.m mmo.m NNm.m mmm.m _ opp mm om um mN m_ op mpasmm mxmo .2m New .uooe an umcopm mumpnmu to mczumwoe acmogmm .N mpamh p 30 .muwpom mango oop Lea Logo: mango mm umueoqmm _ PNo.o mNo.o muq.o mmo.o mmo.o mum.o awo.o .>mo .num ¢P_.N_ mmm._~ mem.pp wNN.N_ NNm.NP NmN.N_ PNo.NP mmmem>< omo.NP mem.PP NPm.PP mpN.N~ FmN.N~ oeN.N_ meo.NP e mo_.N_ nem._P omm.—P mmP.NP mmN.NP ONm.N_ mpo.Np m oNP.N_ Pmo.N~ ONm.PF mKN.N_ ooe.Np mam.N_ FNP.NP N mmp.NF omm.F~ oou.PP mPN.NP mpm.N_ mmp.N_ oo_.NP P o—P mK mo om om mN mp mFQsmm mama .zm nwm .uooq um esteem mumpaau to Possumvos actuate .m mpnac 31 rm Ran In Ron 5. R—h In Nov :8 Rnn :8 R: QXUENX cacao; r1 r0 IN— 05 0.0— o.o . ow a.“ a ( lxlillllellwi X X1 > El Lrwl\\1m.r U m 1m . mmEQIDI u>_._.<._um Qz;m<> oz< 0.91.2 8.54.... no mrzwhzoo map—£02 .N Mano—L (891108 6w oat/mom 61») mamoo summon man 32 slope of the respective sorption profile curves are approximately zero, indicating that the tablets had reached equilibrium and the moisture content values, represented actual equilibrium conditions. As shown, tablets in general were observed to vary in weight by only fractions of a milligram. The highest variation observed between individual values of the average (2.5 mg) occurred at 80% RH and is likely due to cabinet variability. Chart recordings verified that the humidity inside the cabinet, normally 80%,f1uctuated in the range of t i 5%. It should be noted that at this high humidity range, fluctuations will have a greater effect on moisture content than fluctuations at lower humidity conditions. Further,small differences in moisture content may be due to the assumption that the initial moisture content of all tablets was identical. The use of glass weighing bottles provided greater accuracy than many previous simulation studies which measured moisture change by storing tablets on open weighing trays. Originally a similar approach was used for this study but was found to give inaccurate results. When tablets were placed on open dishes, within 20 minutes enough moisture was lost to lower the moisture content by as much as 1.0% of the original weight value. The rate of moisture loss that occurred under these circumstances is shown in Figure 3, where the weight change of the OJ «.3 Anzac—Ev u}: or. 02 on 3 on ON on Pa O Q 2 ad! (6w) aouvuo .LHSBM AI”. x8 ob... 82:28 882... E9... :93 mzoEozoo 5%? E 8.55 .._.o 83 $55.02 .m umDOE 34 tablets is plotted as a function of time stored after initial weighing. The equilibrium moisture content was plotted versus relative humidity to show the moisture sorption isotherm of the tablets at 40°C (Figure 4). The average moisture content, standard deviation and 95% confidence interval for each condition are reported in Table 9. It should be noted that at each humidity condition, all calculated moisture contents were treated as one population to obtain the average EMC's reported. Examining the moisture isotherm by itself allows one to draw some conclusions on the type of packaging that will be needed to protect a product. Knowing the initial g'moisture content of a product, one can observe that storage conditions at which the product will begin to gain or lose moisture. The tablets tested in this study had an initial moisture content of 3.1% and from Figure 4 it can be seen that the relative humidity associated with this moisture content was approximately 25%, at the temperature of test. Thus at a humidity of 60%, which is likely to be encoun- tered in actual storage, the tablets will equilibrate to a moisture content of 6.0% (Figure 4). Further, it can be expected that the tablets will equilibrate to a higher moisture content at a lower temperature. Therefore if a 6.0% moisture content is unacceptable, a high barrier package must be used, whereas if a moisture content of 35 R E923: u>_._.<._um 8. 8 on 2 ow S 3 on n h - ON rN 1* r. no r I 5 9 5 (891108 Bus 001/4010» 6w) 111311103 aamslon 1.31m 90¢ ._.< 9.59% no 251.5% ZOFEmOm map—.902 .V HEDGE 0— 36 Table 9. Equilibrium moisture contents of tablets at 40°C. Relative EMC‘ Std. Dev. 95% C.L. n2 humidity 11.21 2.383 0.164 1 0.056 35 33.60 3.831 0.253 0.046 35 48.42 5.208 0.166 0.263 35 71.00 8.413 0.130 0.046 35 80.00 8.995 0.458 0.159 35 89.03 12.101 0.200 0.078 28 1Reported as grams water per 100 grams solids. 2Number of observations. 37 12.0% is the critical value, a lower barrier would be required since the tablet would not be expected to reach that value unless exposed to 90% RH. Package water vapor transmission rates (WVTR) are listed in Table 10. Blisters were filled with desiccant and glass beads as described in the Experimental section and the gain in weight was measured at selected time intervals. The average gain in moisture of each package as a function of time is shown in Figure 5. A least- squares analysis was used to determine the best fitting line to the data. The slope of each line is equal to the package WVTR and represents the amount of water entering the package in one day under the test conditions. Dividing the WVTR by the water vapor partial pressure gives the permeability constant of each package. These values are reported in Table 10 and are used in the predictive model. The WVTR results clearly show the superior moisture protection of the vinyl-aclar blisters. The WVTR of the vinyl-aclar blisters (0.21 mg/day), was 50% of the trans- mission rate of the saran-coated blisters (0.48 mg/day), and less than one-tenth that of the PVC blisters 3.5 mg/day. Tablets were packaged in the three blisters and stored at 40°C, 80% RH to generate storage stability data with which to compare predicted values. Moisture contents of tablets packaged in each blister structure and stored at 38 Table 10. Moisture permeability of blister packages. Material WVTR1 Permeability Constant2 Polyvinylchloride (PVC) 3.50 7.9 x 10 (-5) Saran Coated PVC 0.48 1.1 x 10 (-5) Vinyl-Aclar Laminate 0.21 4.8 x 10 (-6) 1Expressed as milligrams water per day-package. 2Expressed as grams water per package-day-Atm. 39 cjo< >._ I ongo>m 0 oz. 0 cacao; O N O '- 0 '- *3 fi O - PC 5'. h”. co_wm_Emco._._. 0.5.662 0+ 2.5 ImNom 069‘ +0 9.0.55 *0 £00 2935 .m wane: (51») vao .LHSBM 4O 40°C, 80% RH are reported in Table 11 and presented graphically in Figure 6. The moisture contents were calculated as described in the Experimental section. The package WVTR and moisture sorption data provide some insight as to the expected moisture uptake of the packaged tablets. The package WVTR's indicate that the tablets in the PVC blisters should gain moisture more rapidly than the higher barrier packages. Further, as the vapor pressure differential between the inside of the package and outside decreases, the rate of moisture gain will slow. These points are reinforced by the experimental results. The moisture gain vs storage time plots presented in Figure 6 show that the tablets in PVC blisters gained moisture most rapidly and equilibrated to a moisture content of 8.0%. This value is slightly lower than expected from the sorption isotherm. Unfortunately the cabinet mal- functioned and it could not be determined if the tablets in the other packages would equilibrate to the same moisture content. As discussed earlier, the experimental isotherm was fitted by three techniques and the resulting equations were incorporated into the predictive model. A minitab statistical program was used to obtain the equations that described the data by a linear fit, a second order and a third order polynomial expression. The following equations were calculated to describe the sorption isotherm: Moisture content1 41 Table 11. of packaged tablets stored at 40°C and 80% RH. Storage time PVC Package System PVC/Aclar days PVC/PVDC 0.0 3.10 3.10 3.10 0.8 4.04 -- -- 2.0 5.12 -- -_ 4.2 6.33 -- -- 5.8 6.86 -- -- 9.0 7.57 4.76 3.95 18.0 -- 5.39 4.46 21.0 8.03 -- -- 30.3 8.23 6.04 4.92 44.0 8.11 6.58 5.40 1 Reported as grams water per 100 grams solids. 42 on 0.... 0% $63 ”1:: 85.85 6.... cm 1'9 o \ 5\\.. .. \. 11m111 1.. \ 1111 111m11 1 11 \I O. 0111 \.l\ \ \I1\1 1 1. 1-1- \ \\\\1\. 6. ..... . o -11 -61 1 I”. Now .0 60% ._.< amohm mgmfl. omo<¥o25% RH). It should be noted that the moisture isotherm was also fitted by the following exponential function (see Appendix A). Log y = mx + b . . 27) This expression was found to accurately describe the isotherm and should be considered when selecting an expression of the isotherm to incorporate into the simula- tion model. It was however, not used in the actual simulation modeling, only the linear and polynomial expressions were considered. The calculated moisture contents obtained using equations 21 to 23 are reported in Table 12. These results indicate that the linear model best describes the isotherm in the humidity range of 45 to 70%. The second and third order polynomials accurately describe the isotherm over the entire humidity range of interest. The isotherms calculated by each equation are shown in Figure 7 where they are compared to the experimentally determined iso- therm. It should be noted that higher moisture contents at 80% RH were calculated using the equations than 1 amgifi -l .3232; 32: 352.530 0 Uc0034 £9231 u>F5m¢ cm: 00 an on OD on or! on ON 9 a b h — \ \ \R \X p p — b B mZOFm ommfiomuo Emu—1.5% ZOFnEOm HEP—MEI .N. Mano: (spuos 6w oat/101011 641) 111311103 38n1s10w 1318171 46 Table 12. Equilibrium moisture content1 of tablets at different relative humidities at 40°C. RH (%) Experimental Isotherm M0d91 ,#_ Linear Binomial Trinomial 11.21 2.38 2.28 2.48 2.44 33.60 3.80 3.80 3.60 3.87 48.42 5.20 5.61 5.10 5.29 71.00 8.40 8.14 8.36 8.41 80.00 8.99 9.13 9.74 10.00 89.03 12.10 10.12 11.65 12.25 1 . Reported as grams water per 100 grams sol1ds. 47 determined experimentally. Accordingly, moisture contents predicted using these isotherm equations will be higher than the experimentally measured value. Equation (20) was used to predict the moisture gain of packaged tablets using the three isotherm models previously described. A computer program (Appendix B) written by Dr. Julian Lee and Mr. Mark Wang of Michigan State Univer- sity School of Packaging was utilized for solving equation 20. The data that must be entered are the test temperature and humidity, the saturated vapor pressure at the test temperature, the package permeability constant, the initial moisture content of the tablet, and the equation for the moisture isotherm. The moisture uptake of tablets stored in each package was calculated using the program shown in Appendix B. Each isotherm equation was used in the model to determine if there was a significant difference in results. There- fore there are three sets of results for each package. The predicted moisture contents are reported in Tables 13-15 for the PVC, saran-coated PVC, and vinyl-aclar blisters respectively. Each table includes the experimentally measured moisture contents and the predicted values using the three expressions for the isotherm. The results are shown graphically in Figure 8-10. As shown, good agreement between the predicted values and the experimental data was obtained, with the predicted values being within 10% of 48 Table 13. Experimental and calculated moisture content"2 of tablets packaged in PVC blisters. Days Experimental Linear Binomial Trinomial 0.0 3.1 3.1 3.1 3.1 0.8 4.04 4.00 4.00 4.00 1.8 -- 5.00 5.00 5.00 2.0 5.12 -- -- -- 4.1 -- 6.50 -- -- 4.2 6.33 -- -- -- 4.3 -- -- 6.50 6.50 5.1 -- 7.00 -- —- 5.5 -- -- 7.00 7.00 5.8 6.86 -- -- -- 8.3 -- 8.00 -- -- 9.0 7.57 -- -- -- 9.3 -- -- 8.00 8.00 17.0 -- 9.00 -- -- 17.8 -- -- 9.00 9.00 21.0 8.03 -- -- -- 30.0 8.23 -- -- -- 32.0 -- -- -- 9.50 34.0 -- -- 9.50 ~- 44.0 8.11 -- -- -- 1 2 Reported as grams water per 100 grams solids. Storage conditions of 40°C, 80% RH. 49 Table 14. Experimental and calculated moisture content"2 of tablets packaged in saran-coated PVC blisters. Days Experimental Linear Binomial Trinomial O. 8. 9. 17. 18. 23. 23. 30. 44. 46. 50. 51. 79. 88. 95. 122. 3.10 3.10 3.10 3.10 -- -- 4.50 4.50 4.76 4.50 -- -- -- 5.50 -- -- N U1 O wm—rmmmpuhowm—Iouowo I I \1 U1 O I I I I 282. 1Reported as grams water per 100 grams solids. 2Storage conditions of 40°C, 80% RH. SO Table 15. Experimental and calculated moisture content"2 of tablets packaged in vinyl-aclar blisters. Days Experimental Linear Binomial Trinomial 0.0 3.10 3.10 3.10 3.10 9.0 3.95 -- -- -- 11.5 -- -- 4.00 4 00 12.0 -- 4.00 -- -- 18.0 4.46 -- -- -- 20.0 -- -- 4 50 4 50 20.5 -- 4.50 -- -- 29.7 -- -- 5 00 5 00 30.0 -- 5.00 -- -- 30.3 4.92 -- -- -- 40.7 -- 5.50 -- -- 41.1 -- -- 5 50 5 50 44.0 5.40 -- -- -- 84.6 -- 7.00 -- -- 90.5 -- -- 7.00 -- 91.7 -- -- -- 7.00 181.6 -- 8.50 -- -- 202.2 -- -- 8.50 -- 204.7 -- -- -- 8.50 1Reported as grams water per 100 grams solids. 2Storage conditions of 40°C, 80% RH. 51 263 us: 3365 Wm 01 ohm cu oh 9 P on 1'8 .588... .565. 1232—63 . r N ucomfi (£01106 6w 001/101M 5114) 111311103 38ms1011 IIIBVI 0— 1”. Now .0691 ._.< mam—53m o>m z. Bur—mgr LO ._.zm=zoo HEP—MOE OEQEME .m> 1_<._.7m2_mu$0 .m ”#50: ..... fixmmmm msioza .32: 1:3: £1.53. 6 bacon; 363 w}: 8365 6m. 6.. s. e. 8. 5.6 5.. 5.. ‘C.’ 66666 OOOOOOOOOOOOOOOOOOOOO OOOOOOOOOO rN op Ix .Row .0691 be. mam—.mjm oo>m\o>n_ z. Ems. no E00 ”DD—EOE QEQEuE .m> 43.52% .m ”$50.... (8131108 5111 001/101” 6111) 111311103 311ms10M 1315111 53 ..... gamma “ziozu 32: 45.51.58 C 2.503 363 w}: 8365 can can new 09 09 om - P b b r0 op 1m New .0 .OV ._.< mfimflm mjo<\o>n_ Z_ whims. “.0 (spuos 6w oat/mom 6w) mamas aamsmw man Hzmhzoo map—m5} omhoaumm .m> ._<._.2u2.mu%0 .9 H50: 54 the experimental data. As discussed previously, a small difference in RH will have a large impact on moisture content at the test conditions of 80% RH. For the three package systems, the differences between the calculated moisture content values based on the respective isotherm expressions are insignificant. This can be explained by the fact that the isotherms calculated by the linear and by the curve fitting method are very close and in fact overlap in the region from 50 to 75% relative humidity (Figure 7). Accordingly, for this product all three isotherm expressions accurately predict changes of moisture in this region. It would be expected from Figure 7 that if the area of interest was 90% RH a greater difference in predicted values would result and the values predicted by thesecond and third order poly- nomials would be more accurate. Further, if the product was different and did not have a linear isotherm, again the second and third order expressions would provide a more accurate prediction. Using the three isotherm equations, higher values of moisture content at 80% RH were calculated than found experimentally (Figure 7). These values are reported in Table l2 and range from 9.2% for the linear model to l0.00% for the third order expression, as compared to the experimental value of 8.99%. This explains the difference between the linear based predictions and the polynomial 55 based predictions. The isotherm results (Figure 7) indi- cate that at 80% RH the tablets should equilibrate to a moisture of 8.99%. However, the tablets packaged in the PVC blisters equilibrated to only 8.l% moisture and therefore the predictions appear high (Figure 8). The cabinet mal- functioned before the tablets in the aclar and saran-coated blisters reached equilibrium and therefore it could not be determined at what equilibrium moisture content the tablets equilibrated in these packages. If it is assumed that the 8.99% moisture would have been reached, then the predictions are accurate to within l2%. The current data indicates that the predictions are within 4% of the experimental values. APPLICATIONS The simulation technique presented has been shown to be effective in predicting the moisture gain of a packaged product. Based on the time and resource efficiencies of the predictive technique and the inability of accelerated stress tests to accurately estimate product quality under ambient conditions it is the recommendation of this author that the simulation modeling technique be used routinely in the early stages of package develOpment for moisture sensitive products. Several key areas where the simulation modeling technique can be applied are discussed below. Shelf-life Estimates By measuring the moisture sorption isotherm of a product at a particular temperature and calculating the moisture permeability constant of a package at that temperature, the shelf-life of the packaged product can be predicted based on moisture uptake. It should be noted that the critical moisture content of the product must be known to fully utilize this concept. The critical moisture content is defined as the highest acceptable moisture content and will depend on the impact of moisture on texture or chemical activity of the product. 56 57 Generating a stability profile using the predictive model as done in Figures 8-lO, in which product moisture content is plotted as a function of storage time, allows one to estimate the time required before the packaged tablet will reach the critical moisture content. For example, as shown in Figure 6, if the critical moisture content of the tablet was 5%, it would take tablets packaged in PVC, PVC/PVDC, and Aclar blisters 2, 14 or 42 days respectively to reach the critical moisture content. Package Comparisons The predictive model can also be used to calculate the impact on shelf-life of alternate packages. The capa- bility to make estimates of this type allows for certain packaging decisions to be made prior to expensive and labor intensive storage studies. The shelf—life estimate can be used to select only the most suitable package or packages for further evaluation, thus saving time and resources upfront. The data that is required to make the estimate are the package WVTR's and the product isotherm. As demon- strated by the results of this study, this testing is not very labor intensive and can be done in a timely manner. It should be noted that once the package WVTR's are measured, they may be applied to more than one product, furthering the utility of this method. 58 Package Requirements The simulation modeling technique can be used to determine the package requirements for a given product. For example, by entering the moisture adsorption data, storage conditions, required shelf-life, and the critical moisture content into the predictive model, an optimum package WVTR can be ascertained. Referring to Figure 6, if the tablet was required to withstand one month at accelerated conditions and the maximum allowable moisture content was 5%, the model would verify that only packages with WVTR's below 0.48 mg/day would be acceptable. Package Cost Effectiveness The simulation modeling technique can be used as an early screen of packages so that the most cost effective package will be placed into stability programs. By using the predictive model to determine the shelf-life provided 'by several packages and comparing the cost of the packages, one can decide the most cost effective material to work with. Using the example described above, it may be decided that the additional shelf-life provided by a vinyl-aclar blister over the saran-coated blister (28 days) may not justify the added package material cost. Environmental Impact The predictive technique can also be used to assess the impact of the storage conditions on shelf-life. This 59 is shown in Figure ll where the computer aided storage stability profile curves for the tablet packaged in PVC/Aclar blisters are presented for storage environments of 40°C and 85, 75, 65, and 55% RH‘s. As shown, the impact of the external humidity on moisture uptake is significant. One very useful way to apply this concept is to relate the performance of a package at accelerated conditions to that at ambient conditions. This capability will explain the difference in performance of a product-package system when stored at high humidity conditions and subsequently should reduce the alarm that often occurs when a package is found to fail at accelerated test conditions. For example, as shown in Figure ll, only 48 days were required for the tablets to reach 6% moisture at conditions of 80% RH whereas it would take 463 days to reach the same moisture content at conditions of 55% RH. It should be noted that both these estimates are based on a temperature of 40°C and that lowering the temperature would be expected to further increase the time required to reach a moisture content of 6%. World-wide Packaging The same principles as described above also provide the capability to make world-wide packaging decisions. If a company is marketing a product in environments that differ significantly, it may be possible to realize cost 60 A963 uzp 85.9.». as am. 2.: om... 2.; 9.x 2.x 8. 8. s o Ix Ran xx Run :3 Run :8 Run ozone; (spuos 6m 0m flaw 6w) moo 3801.90" man o— 0 .9‘ ._.< mfimflm m<._0z_> z. Quo<¥o E1= x1(5.N + 1) D,=x.(~( Nu) PRINT "A: "A1 E ._X ;‘ PRINT "B= "Bl " '(3/N+’ 3 PRINT "C= "C1 PRINT "D= "D1 PRINT "E: "El PRINT PRINT PRINT "HIT ANY KEY TO CONTINUE" GET As: IF AS = "" THEN 368 , L GOSUB 6888 IMXUDl/waxunofiwu HOME a? H PRINT PRINT "ENTER PERMEABILITY CONSTANT IN 1.3; GM*MIVDAY*METER SQURE*MM H " INPUT P /" PLRMCA’MU al‘vaT PRINT“/ A8 = 1132578888 2150 2160 2170 2180 2190 2200 2210 2220 2230 2240 2260 2270 2280 2290 2300 2310 2320 2325 2330 2340 2350 2360 2370 2380 2390 2400 2410 2420 2430 2440 2450 2460 2470 2480‘ 2490 2500 2510 2520 2540 2550 2560? 2570‘ 2580 2590 2600 2610 2620 2630 2640 INPUT PRINT PRINT"ENTER DRY WEIGHT OF PRODUCT IN GRAM" INPUT PRINT PRINT INPUT PRINT PRINT INPUT PRINT PRINT PRINT A1 Bl C1 D1 E1 - PRINT PRINT PRINT INPUTI A2 "l: hi‘ ;/ 1.13.17.) ski, . W lam, : 0.00! LUCP /' "ENTER THICKNESS OF PACKAGE MATERIAL IN MIL" L "ENTER INITIAL MOISTURE CONTENT IN GM/100 GM DRY PRODUCT" MO -Al -Bl -C1 -D1 -El L‘l// / 7‘1? :1“ {3:12 ( Iw% Al,Bl,C1,Dl,El w I” "ENTER THE NUMBER OF STORAGE ENVIRONMENT"(S) N2 0 . . .y. DIM ,1 RH (N2) 4’51 ‘-~' ((0.2 «gnu gt 1 '14 9.411 / FOR K PRINT PRINT INPUT PRINT PRINT PRINT PRINT INPUT PRINT- FOR I PRINT INPUT PRINT {NEXT I in= SUM = FOR J X Y X * X Y1 = IF Y1 T(K.I) GOTO 2670 fl / P/’ a! (Y1 + Q) A4 = SUM = (M1(K,I) ((1 / 2) * Q + M0) = RH(K) + A1 + B1 * X + C1 * x * X + D1 * X * X * X + E1 .. * = 1 T0 N2 "ENTER THE RH% OF THE STORAGE ENVIRONMENT ONE AT A TIME" RH(K)F—' "ENTER THE NUMBER OF FINAL MOISTURE'l "CONTENTS UPON WHICH YOU WOULD LIKE TO" "HAVE SHELF LIFE PREDICTION" ,*_ I _ N N {\ MT LUVCMJIFVTLJ’JMY +211, .19; (‘1 was (w. w) 1481,. ,1" = 1 TO N’”1"'""‘\ "ENTER MOISTURE CONTENT IN GM/100 DRY PRODUCT ONE AT AIIME" ‘ ‘ M1(K.I)4~ PM 8“ 3.1.4 171 ‘ I J l f 6041:») Lumi- ’ I - MO) / 10 0 61 = 0 TO 9 Q * J *\x (1 / Y) > 8 THEN 2638ELSE541 = 8 I’/flMUC'j} 2/ 2 ”(If f / SUM + A4 b l w “in ’(Q) 1: Ax3f3xl+0x + I} 2660 2670 2680 2690 2700 2710 2720 2730 2740 2750 2760 2770 2780 2790 2800 2810 2820 2830 2840\ 2850 2860 2870 2874 2875 2880 5000 S010 5020 5030 5040 5050 5070 5080 5090 5100 5110 5120 5130 5140 5150 5160 5170 5180 5190 5200 5210 5220 f Pl F(K,I) = ((L * M) / (P * A2 * P1)) * SUM NEXT I PRINT PRINT PRINT "M%", "TIME(DAY)" PRINT #/ \ FOR I 1 TO N PRINT M1(K,I),T(K,I) NEXT I PRINT PRINT "DO YOU WANT TO TRY SOME OTHER M%"? ENTER Y FOR YES, N FOR NO." Z$ IINII INPUT IF ZS PRINT GOTO 2430 NEXT K PRINT PRINT "HIT ANY KEY TO PLOT OUT M% VS TIME" \ GET As: IF AS = nu THEN 2840 .’ GOSUB 7000 - PRINT PRINT PRINT PRINT END; REM gbmfifi FOR K = I TO N 0 M1 0 FOR J = K TO N IF ABS (X1(J,K)) GOTO 5090 D = ABS (X1(J'K) IF D > MI THEN 5100ELSE1130 Ml D Pl X1(J,K) M = J NEXT IF ABS (P1) > 0 THEN 5150ELSEI300 IF M < > K THEN 5160ELSE1210 FOR J = K TO N + 1 A = X1(KpJ) X1(KpJ) X1(M,J) X1(M,J) A NEXT FOR J = K X1(K,J) THEN 2810 _ '3 ‘JJJ‘V-‘I ‘IU ISIL‘ 3311.19. Oh” My! k '9 EQJFNPUC “1111121911 1’7) atsupbc DUTY 1‘ "THIS IS THE END OF THE PROGRAM" > 1 THEN 5060ELSE1080 TO bl-+ 1 X1(K,J) / R1 5230 5250 5260 5270 5280 5290 5300 5310 5320 5330 5340 5350 5360 5370 5380 5390 5400 6000 6001 6005 6006 6007 6010 6020 6030 6040 6050 6060 6070 6080 6090 6100 6110 6120 6130 6140 6150 6170 6175 6180 6190 6200 7000 7010 7020 7030 7040 7050 7070 7090 NEXT FOR J = X1(L,J) NEXT NEXT NEXT GOTO 5340 PRINT "DEPENDENT OR INCONSISTANT" PRINT "INPUT DATA ERROR" RETURN FOR J FOR I X1(I,N + l) = x1(I,J) = 0 NEXT NEXT RETURN REM HOME 1 TO K STEP - 1 N + = X1(L,J) - X1(L,K) * X1(K,J) N TO 2 STEP - 1 (J - 1) TO 1 STEP X1(I,N + 1) - 1 - X1(J,N + 1) * Xl(l,J) PRINT "ENTER THE UPPER LIMIT OF M% IN GM/l00GM DRY PRODUCT" INPUT Y2 HGR2 : HCOLOR=3 A = 15:B = 175:C = 275 HPLOT A,5 TO A,B TO C,B Y1 0 RY Y2 - Y1 ST RY / 100 SY (A - B) / RY X1 0:X2 = 100 SX (C - A) / (X2 - X1) DEF FN X(Y) = X1(I,N + 1) + x1(2,N + 1) Y + X1(4,N + 1) * Y * Y * Y FOR 1 = Y1 TO Y2 STEP ST GX = FN X(I) GX = A + SX * GX GY = 175 + SY * I IF GX < 0 OR GX > 279 OR GY < 0 OR GY > 179 THEN 6170 IF GX < 45 THEN 6170ELSE1660 NEXT I GOSUB 7500 FOR I = 1 TO 5000: NEXT TEXT RETURN HOME PRINT "ENTER THE UPPER LIMIT OF TIME" INPUT R PRINT PRINT "ENTER THE UPPER LIMIT OF M%" HGR2 : HCOLOR = 3 A = 15:B = 175:C = 275 X1 = 0:X2 = R * Y + X1(3,N + 1) * Y * 7100 7110 7120 7130 7140 7150 7160 7170 7180 7190 7200 7210 7220 7230 7240 7250 7260 7270 7280 7290 7295 7300 7310 7320 7330 7340 7350 7360 7370 7500 7510 7520 7530 7540 7570 7580 7590 7600 7610 7620 7630 7640 7650 7660 7670 7680 7690 SX = (C - A) / (X2 - X1) Y1 = O:Y2 = MMAX SY = (A - B) / (Y2 - Y1) FOR K = 1 T0 N2 FOR I = 1 TO N GX(K,I) = A + SX * T(K,I) GY(K,I) = 175 + SY * M1(K,I) PRINT GX(K,I),GY(K,I) NEXT I NEXT K M3 = 175 + SY * MO FOR K = 1 T0 N2 FOR I = 1 TO N - 1 IF GX(K,I) < 5 OR GX(K,I + l) < 5 THEN 7270 IF GX(K,I) > 275 OR GX(K,I + l) > 275 THEN 7270 IF GY (K,I) < 15 OR GY(K,I + 1) < 15 THEN 7270 HPLOT GX(K,I),GY(K,I), TO GX(K,I + 1),GY(K,I + 1) NEXT I HPLOT A,M3 TO GX(K,1),GY(K,1) NEXT K GOSUB 8200 FOR I = 1 TO 7000: TEXT HOME PRINT "PLOT AGAIN? ENTER Y OR N" INPUT R$ IF R$ = "N" GOTO 7000 RETURN REM SHAL DEMO PRINT CHR$ (4) ; POKE 232, PEEK (43634): SCALE= 1 ROT= 1 ST$ = "I" VT = 22.4 HT = 48 GOSUB 9000 ST$ = "I" VT 22.4 HT 19.8 GOSUB 9000 ST$ = "O" VT = 23.1 HT = 2 GOSUB 9000 ST$ = "5%" NEXT THEN 7370 "BLOAD SHAPE ALPHABET,A24576" POKE 233, PEEK (43635) 7700 7710 7720 7730 7740 7750 7760 7761 7762 7763 7764 7770 7780 7790 7800 7810 7820 7830 7840 7850 7860 7870 7880 7890 7900 7910 7920 7930 7940 7950 7960 7970 7971 7972 7973 7974 7980 8200 8210 8220 8230 8240 8250 8260 8270 8280 VT = 23.1 HT = 19 GOSUB 9000 ST$ = "100" VT = 23.1 HT = 38 GOSUB 9000 ST$ = "RH%" VT = 23.1 HT = 27 GOSUB 9000 ST$ = u_n VT = 1 HT = 2.8 GOSUB 9000 ST$ = n_n VT = 10.7 HT = 2.8 GOSUB 9000 ST$ = "0" VT = 22.3 HT = 1 GOSUB 9000 ST$ = STR$ (Y2) VT = 1 HT = l GOSUB 9000 Y3 = Y2 / 2 ST$ = STR$ (Y3) VT = 10.7 HT = 1 GOSUB 9000 ST$ = "M%" VT = 5 HT = 1 GOSUB 9000 RETURN REM SHAL DEMO PRINT CHR$ (4);"BLOAD SHAPE ALPHABET,A24576" PEEK (43634): POKE 232, SCALE= 1 ROT= 1 ST$ = "I" VT = 22.4 HT = 48 GOSUB 9888 POKE 233, PEEK (43635) 8300 8310 8320 8340 8350 8360 8370 8380 8390 8400 8410 8420 8430 8440 8450 8451 8452 8453 8454 8460 8470 8480 8490 8500 8510 8520 8530 8540 8550 8560 8570 8580 8590 8600 8610 8620 8630 8640 8650 8660 8661 8662 8663 8664 8670 VT = 22.4 HT = 19.8 GOSUB 9000 VT = 23.1 HT = 2 GOSUB 9000 R1 = R / 2 ST$ = STR$ (R1) VT = 23.1 HT = 19 GOSUB 9000 ST$ = STR$ (R) VT = 23/1 HT = 38 GOSUB 9000 ST$ = "T(DAYS)" VT = 23.1 HT = 27 GOSUB 9000 ST$ = u_n VT = 1 HT = 2.8 GOSUB 9000 ST$ = n_u VT = 10.7 HT = 2.8 GOSUB 9000 ST$ = "0" VT = 22.3 HT = 1 GOSUB 9000 ST$ = STR$ (MMAX) VT = 1 HT = 1 GOSUB 9000 MX = MMAX / 2 ST$ = STR$ (MX) VT = 10.7 HT = 1 GOSUB 9000 ST$ = "M%" VT = 5 HT = 1 GOSUB 9000 RETURN 9000 9010 9020 9030 9040 9050 9060 9070 HT = 7 * (HT - 1):VT = FOR I = 1 TO LEN (ST$) IF CH = 0 THE 9050 XDRAW CH AT HT,VT HT = HT + 7 NEXT I RETURN 8 * VT - l REFERENCES REFERENCES Carstensen, J.T. 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Nakabayashi, K., Shimamoto, T., Mima, H. (l980a) Stability of Packaged Solid Dosage Forms. I. Shelf Life Pre- diction for Packaged Tablets Liable to Moisture Damage, Chem. Pharm. Bull. 28:4, p. 1090-1098. Nakabayashi, K., Shimamoto, T., Mima, H. (l980b) Stability of Packaged Solid Dosage Forms. II. Shelf-Life Prediction for Packaged Sugar-coated Tablets Liable to Moisture ahd Heat Damage, Chem. Pharm. Bull. 28:4, p. 1099-1106. Nakabayashi, K., Shimamoto, T., Mima, H. (l9Bla) Stability of Packaged Solid Dosage Forms. IV. Shelf-Life Prediction of Packaged Aspirin Aluminum Tablets under the Influence of Moisture and Heat, Chem. Pharm. Bull. 29:7, p. 2027-2034. Nakabayashi, K., Shimamoto, T., Mima, H., Okada, J. (1981b) Stability of Packaged Solid Dosage Forms. V. Prediction of the Effect of Aging on the Disintigration of Packaged Tablets Influenced by Moisture and Heat, Chem. Pharm. Bull. 29:7, p. 2051-2056. Nakabayashi, K., Hanatani, S., Shimamoto, T. (1981c) Stability of Packaged Solid Dosage Forms. VI. Shelf-Life Prediction of Packaged Prednisolone Tablets in Relation to Dissolution Properties, Chem. Pharm. Bull. 29:7, p. 2057-2061. Oswin, C.R. (1946) The Kinetics of Package Life III. The Isotherm, J. Chem. Ind. London, 65:419-424. Paine, F.A. (1963) Fundamentals 9: Packaging, p. 275-290. Peppas, NA., Khanna, R., (l980a) Mathematical Analysis of Transport Properties of Polymer Films for Food Packaging II. Generalized Water Vapor Models, Polymer Engineering and Science, 20:17, p. 1147-1156. 68 Peppas, N.A., Sekhon, G.S. (l980b) Mathematical Analysis of Transport Properties of Polymer Films for Food Packaging IV. Prediction of Shelf life of Food Packages Using Halsey Sorption Isotherms, Techn. Paper 37:681. Quast, D. (1969) Computer Simulation of Storage Stability and Package Optimization of Food Products, M.S. Thesis, M.I.T., Cambridge, MA. Quast, D.G., Karel, M. (1972) Computer Simulation of Storage Life and Foods Undergoing Spoilage by Two Interacting Mechanisms, J. Food Sci. 37:679. Sagvy, I., Karel, M. (1980) Modeling of Quality Deterio- ration During Food Processing and Storage, Food Technol. 2:78. Salwin, H., Slawson, V. (1959) Moisture Transfer in Combinations of Dehydrated Foods, Food Technol. 13: 715. Simon, 1.8. (1969) Computer Predictions of Food Storage Stability, M.S. Thesis, M.I.T., Cambridge, MA. U.S. Pharmacopeia, XX. (1980), p. 955. 9.)- ‘ :- f3; qr}? '3 .fivfifi’fl)? 4.1. '3“ TR [A ’ ' w < 7' :15: ' vrr . . . .. L543~1 ‘ . w. 1 _ . ' H on 0‘,‘ v I . .5}- .— 4 .1‘ , .‘ . 'I'; , -': l '-".L?_“_, 1 ' 4n :4. ., . .. “‘1 ' I: 1 1 . 'I . . 31+, ., 'I'1‘- )uf' “III-3‘ :0" T'/ ‘. f . “If“ 1 1411...: I." 5" 11%- T -' , .x f.‘ J? _ ’ ' IM-‘H‘ I'k L. that: r ”I“... ’-- "'21: 1 'v . ' )0.- 1., . In 2;. IL" '9: .1? a”. $1 I y . - ." ,J .32": ' 'f‘; I, 3...,” . 'qu-mcz g, 1.." AL ('1 a“, I I | ”'.' w ' A33" 1 . , ._ § . - I," . . . 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