Food Microbiology, 1988, 5, 163-176

Use of response surface methodology in shelf life extension studies of a bakery product J. P. Smith .1, S. Khanizadeh 2, F. R. van de Voortl, R. Hardin 3, B. Ooraikul 3 and E. D. Jackson 4

12 Departments o f Food Science & Agr icul tura l Chemis try and P lan t Science, McGiU University, Quebec, Canada, 3 Departments o f A n i m a l and Food Science, University o f Alberta, Canada, and 4 Agr icul tura l Canada Research Station, Kentville, Nova Scotia, Canada

Received 28 Apr i l 1988

Effects of water activity, pH, storage temperature, concentration of potassium sorbate, C02 concentration in the package headspace and inoculum level on growth of Aspergillus niger, the major spoilage isolate of English style crumpets, was studied on an agar model system using an experimental design termed Response Surface Methodology. The initial screening design indicated that aw, pH, levels of potassium sorbate, C02 and storage temperature were significant variables. When a central composite rotatable design was subsequently applied to four variables with pH held constant at pH 6.5 only aw, storage temperature and C02 level were found to have a significant effect on mold growth. Using multiple regression analysis, a second order polynomial model was derived and used to predict the number of days to visible mold growth under various combinations of the remaining three variables. Generation of contour plots enabled selection of levels for each variable to give a product with a desired mold free shelf life. Typically, crumpets with an aw of 0.96, packaged in 62% C02 had a mold free shelf life of 20 d when stored at 20°C. The observed shelf life results agreed well with predicted values on Potato Dextrose Agar and demonstrated RSM as a powerful and elegant research tool when several variables are to be evaluated simultaneously.

Introduction English style crumpets, a wheat flour based bakery product with a~ of 0.98 and pH of 6.5 have traditionally been mar- keted as a breakfast or snack food in a frozen form. In an effort to reduce pro- duction and storage costs and to increase product turnover, crumpets have recently been packaged in air and stored at ambient temperature in the retail environment. However, under such packaging and storage conditions the shelf life of product was limited to 3-4 d

*To whom correspondence should be addressed. 0740~3020/88/030163 + 14 $03.00/0

by mold spoilage (Ooraikul et al. 1984). In an attempt to extend shelf life of product beyond 3-4 d without refrigera- tion, factors affecting mold growth were thoroughly investigated. Factors con- sidered included water activity (aw), pH, level of headspace CO2, storage tem- perature, concentration of inhibitor (potassium sorbate), and inoculum levels. The influence ofaw, pH, inhibitors and CO2 enriched atmospheres on the rate of mold growth have been exten- sively investigated but mainly by evalu- ating the variables individually (Seiler 1978, Bogadtke 1979, Pomeranz 1979). However, the examination of several

© 1988 Academic Press Limited

164 J.P. Smith et al.

var iab les one a t a t i m e is labor ious and t ime consuming, it r esu l t s in la rge quan- t i t ies of da t a which a re difficult to in t e rp re t and it fails to m e a s u r e in terac- t ion effects. To overcome the l imi ta t ions of the one va r i ab l e a t a t ime approach and to a d e q u a t e l y descr ibe the effect of severa l e n v i r o n m e n t a l factors, inc luding the i r i m p o r t a n t in te rac t ions , a tech- n ique involv ing factor ia l e x p e r i m e n t a l des igns and mul t ip l e regress ion ana ly- ses t e r m e d Response Surface Methodol- ogy (RSM) was used in th is s tudy. RSM pe rmi t s fact6rs of in te res t to be var ied , not s imply one a t a t ime, bu t s imul- t aneous ly in a s ingle se t of e x p e r i m e n t a l runs. M a t h e m a t i c a l models , gene ra l ly f irst and second order polynomials , a re gene ra t ed to def ine the op t ima l levels of the mos t s igni f icant factors r equ i red to opt imize the desi red response (Box et al. 1978). Developed in i t ia l ly for process opt imiza t ion s tudies in chemica l engine- er ing, RSM has been appl ied to s tudies of bac te r ia l g rowth (Schroder and B u s t a 1973), case in ex t rus ion (van de Voor t and S tan ley 1984), canola sauce produc- t ion (Ma and Oora iku l 1986) and folacin re ten t ion in cookies (Connor and K e a g y 1981). This p a p e r descr ibes the use of RSM in she l f life ex tens ion s tudies of Eng l i sh s tyle c r u m p e t s and the advan- tages of the t echn ique as a r e sea rch tool in food microbiology.

Materials and Methods (a) Experimental design To determine the effects of individual factors on mold growth, a preliminary fractional factorial screening design was performed. The fractional factorial design chosen was the 2 e-3, as described by Box et al. (1978) and the factors evaluated initially included aw (0-96- 0.98), pH (5-7), storage temperature (20- 30°C), concentration of inhibitor (potassium serbate) (650-1300 ppm), C02:ai r ratio (0 : 100, 50: 50%) and inoculum level (102--103 spores/plate). The levels of each factor, shown in brackets, were selected from prevous product analyses and practical possibilities

for re-formulation. Temperature levels were restricted to those most likely to be encountered during distribution and storage in the retail environment. Levels of inhibitor were restricted to the maximum amounts legally permitted in bakery products. Inocu- lum levels were selected on the basis of the range of levels which might occur in the product under poor manufacturing condi- tions. The fractional factorial design and coded levels of each factor are shown in Table 1 and the experimental runs were carried out in a randomized order. Variables were coded as + 1 (upper level) and - 1 (lower level) to facilitate statistical analyses. Values of coded levels used in the fractional factorial design and method of coding, as described by Box et al. (1978), are shown in Table 2.

A more elaborate 4 factor, 5 level Central Composite Rotatable Design (CCRD) of Box et al. (1978) was used for fitting second order response surfaces. Factors and levels of each factor in the CCRD (Table 4) were selected on the basis of significant regression coefficients generated from the initial screening design as those likely to optimize the response. In the CCRD, pH was kept constant at pH 6.5, the pH of the final product and variable levels were ceded -2 , -1 , 0, +1, +2 to facilitate statistical analysis (Table 5). Upper levels of - 2 and +2, used in a four factor CCRD, were obtained from Box et al. (1978).

(b) Adjustment and inoculation of media Potato Dextrose Agar (Difco) was used as the basal medium throughout this study. Water activity (aw) was adjusted using glucose, the required concentrations being obtained from the data of Christian (1980). Measurements of aw of the adjusted media were made using the manometric technique of Taylor (1961) as modified by Lewicki et al. (1978) and pot- assium sorbate (13% w/v) was added in appropriate amounts as a preservative. Media were autoclaved at 121°C for 15 min, the pH adjusted on cooling using 1N HC1 or 1N NaOH and media were dispensed into 150 mm Petri dishes. Aspergillus niger, a com- mon con~minant of crumpets, was chosen as the test mold with mold spores produced on PDA slopes incubated at 25°C. Serial dilu- tious of conidia were made using the talc method of Seller (Personal Communication) and in the initial screening design, 0-1 g of the appropriate dilution was sprinkled onto

Response surface methodology 165

Table 1. A 2 e-3 f r a c t i o n a l f a c t o r i a l d e s i g n ( c ode d ) to determine factors inf luencing g r o w t h o f Aspergillus niger.

Variable**

Run No.* Block X1 2:2 X3 X4 X5 )/6

Days to visible growth

1 - 1 - 1 - 1 1 1 - 1 9"0 2 1 - 1 - 1 - 1 - 1 1 3.0 3 - 1 1 - 1 - 1 1 1 6-0 4 1 1 1 - 1 1 - 1 - 1 4.0 5 - 1 - 1 1 1 - 1 1 3"5 6 1 - 1 1 - 1 1 - 1 7.0 7 - 1 1 1 - 1 - 1 - 1 5-0 8 1 1 1 1 1 1 6.0 9 - 1 - 1 - 1 1 1 - 1 10"0

10 1 - 1 - 1 - 1 - 1 1 4"0 11 - 1 1 - 1 - 1 1 1 7.0 12 2 1 1 - 1 1 - 1 - 1 5"0 13 - 1 - 1 1 1 - 1 1 6.0 14 1 - 1 1 - 1 1 - 1 8.0 15 - 1 1 1 - 1 - 1 - 1 6"0 16 1 1 1 1 1 1 7"0

* Each run replicated twice for a total of 32 runs. ** X1 = aw; X2 = pH; )(3 = Inoculum level; X 4 = Conc. of inhibitor; )(5 = CO2: air ratio; )/8 = Temp. °C.

Table 2. Value of coded levels used in 2 e-3 f r a c t i o n a l f a c t o r i a l screening des ign for A. niger.

Coded levels*

Var iab le - 1 0 + 1

aw X1) 0-96 0.97 0.98 pH (X2) 5.0 6-0 7-0 Inoculum,

spores/plate 0(3) 102 5.5 × 102 103 Conc. of inhibi tor ,

ppm (X4) 650 975 1300 CO2 : a i r rat io, % (Xs) 0 :100 25 :75 50 :50 Tempera tu re , °C (X6) 20 25 30

* Coded variable (-1, 1) - Actual value - 0.5 (high value + low value)

0.5 (high value - low value)

PDA pla tes us ing a 100 ~t mesh sieve. In the CCRD, all p la tes were inocula ted wi th 10 S spores/plate us ing the same inoculat ion tech- nique. Spore numbers were checked by sp r ink l ing s t anda rd amounts of talc suspen- sion onto unadjus ted PDA pla tes incubated a t 25°C under aerobic conditions. Al l inocula ted tes t p la tes (2/pouch) were packaged in 30 × 30 cm pouches of po lye thylene coated nylon film hav ing average pe rmeab i l i t i e s of: 02, 40 cc; N2, 14 cc; CO2, 155 cc; wa te r vapor,

11 g per m2 24 h - i , a t 25°C. Gas packag ing was achieved us ing a Mul t ivac Type AG500 vacuum/gas packag ing un i t (W. R. Grace and Co., Ajax, Ont. Canada) and the proport ions of gases from separa te cy l inders were regu- la ted by a Smi th ' s Propor t ional Mixer (Tes- corn, Minneapol is , Minnesota) . Random sam- ples were selected from each exper imen ta l run for headspace gas ana lys i s immed ia t e ly af ter packing to ensure the des i red concentra- t ion of gases had been a t t a ined and also

166 J.P. Smith et al.

Table 3. Ana lys i s of v a r i a n c e of p r e l i m i n a r y f ac to r i a l s c r een ing des ign for A. niger.

Sum of Mean Source d.f.* Squares Square F

Due to regression 6 173.2 28.86 33-87*** aw (X1) 1 40-64 47-71"** pH (X2) 1 10.12 11.89"* Inoculum (X3) 1 0.78 0.92-8 Conc. of inhibitor (X4) 1 9.03 10.60"* CO2 : air ratio (Xs) 1 84.50 99-19"** Temperature (X6) 1 28.12 33.02*** Residual (error) 25 21.29 0.85 Total 31 194.50 R2t 0.87

|

* Degrees of freedom; Level of significance ***P<0.001; Level of significance ** P<0.01; ns = non significant; t Coefficient of determination.

Table 4. Coded level c o m b i n a t i o n s for a four v a r i a b l e Cen t ra l Compos i t e R o t a t a b l e Design to opt imize she l f life of c r u m p e t s in r e l a t i o n to spo i lage b y A. niger.

Variable**

Run No.* X1 X2 X3 X4

Days to visible growth

1 - 1 - 1 - 1 - 1 14 2 1 - 1 - 1 - 1 7 3 - 1 1 - 1 - 1 16 4 1 1 - 1 - 1 8 5 - 1 - 1 1 - 1 5 6 1 - 1 1 - 1 3 7 - 1 1 1 - 1 6 8 1 1 1 - 1 3 9 - 1 - 1 - 1 1 32

10 1 - 1 - 1 1 12 i i - I 1 - I 1 36 12 1 1 - I 1 13 13 -1 -1 1 1 8 14 I -1 1 1 5 15 -1 1 1 1 11 16 1 1 1 1 6 17 -2 0 0 0 16 18 2 0 0 0 6 19 0 -2 0 0 7 20 0 2 0 0 8 21 0 0 -2 0 12 22 0 0 2 0 5 23 0 0 0 -2 6 24 0 0 0 2 11 25 0 0 0 0 7

* Each run replicated twice for a total of 50 runs. ** XI = aw; X2 = Conc. of inhibitor; Xs = Temp. °C; )/'4 = CO2 : air ratio.

Response surface methodology 167

Table 5. Va lues o f c o d e d l eve l s used in Central Compos i t e Rotatable Des ign for A. niger.

Levels

Variables - 2 - 1 0 1 2

aw (X1) 0-94 0.95 0.96 0-97 0-98 Conc. of inhibitor ppm, (X2) 600 750 900 1050 1200 Temperature, °C (X3) 20 21 22 23 24 CO2: air ratio % (X4) 50 : 50 55:45 60:40 65 : 35 70 : 30

throughout the storage trial to ensure pack- aging integrity had been maintained. Head- space gas was analysed according to the technique described by Smith et al. (1983). Plates were incubated at 25 and 30°C in a Fisher isotemp (+0-25°C) incubator (Fisher Scientific Co., Pittsburgh, Pennsylvania) while for plates stored at 20-24°C, a Psycrotherm incubator (_+0-1°C) was used (New Brunswick Scientific Co. Inc., New Brunswick, New Jersey). All plates were examined daily for visible signs of mold growth.

(c) Test bakes To test the accuracy of the response surface model to predict mold free shelf life of product, crumpets were reformulated to desired aw values as described by Smith et al. (1984) and had an accuracy of +0-2% when checked using the method described previ- ously. Individual crumpets (50 g) were inocu- lated with 103 spores of A. niger using a talc inoculation method, packaged (2/pouch) in 20 × 20 cm pouches of polyethylene-nylon film under the appropriate gas atmosphere, stored at 20-24°C and checked daily for visible signs of mold growth.

(d) Statistical analyses Statistical analyses (regression coefficients, analysis of variance and correlation coeffi- cients) were computed using the Statistical Analysis System (SAS, 1982)..All 3 dimen- sional graphs and 2 dimensional contour plots were done using the SAS/Graph pro- gram on a McGill University mainframe and a Zeta Plotter.

Results and Discussion Response Surface Methodology is a pro- cess optimization technique which deter-

mines optimum conditions by combining special experimental designs with modelling by first and second order polynomial equations in a sequential testing procedure. Init ial ly in this study, a 26-~ fractional factorial screening design was carried out (Table 1) and the actual levels of variables used in each experimental run are shown in Table 2. The main advantage of this class of design is tha t it enables one to study five or more variables simultaneously in a single experimental design of practic- able size by confounding the main factors in their higher order interactions and determine which variables have an important effect on the chosen response (Mullen and Ennis 1985).

The regression equation obtained from the initial screening design is shown in Equation 1:

Y = 87.41 - 76.69X1 - 0.56X2 - 0-001X3 + 16-34X4 + 0-065X5 - 0.2Xe [1]

The analysis of variance (A_NOVA) for the prel iminary screening design is shown in Table 3. The ANOVA for Y, days to visible growth, indicated tha t the model was significant (P < 0.01) and had an R 2 value of 0.89 i.e. accounting for 89% of experimental variation a/ter being corrected for the mean. Examina- tion of the fitted coefficients using the F-test (1 d.f.) showed tha t aw (X1), pH (X2), level of inhibitor (X4), CO2 (Xs), and storage temperature (Xs) were signifi-

168 J.P. Smith et al.

cant variables and could be used to control mold spoilage of crumpets. While aw, potassium sorbate, CO2 and storage temperature have been used effectively to control mold growth, the significance of pH in the screening design was con- trary to the observations of Seiler (1965). He reported that molds could grow over a pH range of 5-7-5 in cakes and concluded that pH had little effect on mold free shelf life extension of bakery products (Seiler 1965). The lack of significance of mold inocuhtm (X3) was also somewhat surprising since it was assumed that a greater number of mold spores contami- nating the surface of a product prior to packaging would enhance mold spoilage. Seiler (1965) however, also reported that mold inoculum had little or no effect on shelf life extension of high ratio Madeira cake.

Surface Response Methodology was then applied to predict the optimal levels of aw, inhibitor, CO2 and storage tem- perature in combination with one another which could be used to extend the mold free shelf life of product. While pH was significant in the screening design it was kept constant in the response surface design at pH 6-5 since it is generally the final pH of English style crumpets. The Central Composite Rotat- able Design (5 levels for 4 variables) used for fitting the second order response surface and uncoded levels used in each experimental run are shown in Tables 4 and 5 respectively. CCRDs have 2 k + 2k + 1 t reatment combinations where k equals the number of variables under study and the experimental design is said to be rotatable since the variance of the predicted response, Y, at designated points, (X's), is a function only of the distances of the points from the centre, rather than a function of their direction. This implies that the variance contours of Y are concentric circles and a design with this property will leave the

variance of Y unchanged when the design is rotated about the centre (0, 0, 0, 0), leading to the term rotatable (Mont- gomery 1984).

Table 4 shows the number of days to visible mold growth with the correspond- ing coded values of aw (X1), level of inhibitor (X2), storage temperature (X3) and CO2 : air ratio (X4). The second order polynomial model using multiple regres- sion analysis of the coded data is presen- ted as Equation 2:

Y = 7.51 - 3.83X1 + 0-62X2 - 4.38X3 + 2 . 5 8 X 4 + 1.85X21 + 0.48X22 + 0.73X23 + 0-73X24 - 0.44X~X2 + 2.81X1X3 -- 2 " 0 0 X 1 X 4 - 0.25)/2)/3 + 0 .31X2X4- 2 .20X~4 [2]

Examination of the fitted model (Table 6) with t-test (35 d.f.) indicated that three linear terms aw, temperature and CO2 (X],)/3, and X 4 ) , o n e quadratic term aw 2

(X12) and three interaction terms a~.T (X1X3), aw.CO2 (X1X4) and T.CO2 (X~X4) were significant. The lack of significance

Table 6. Analys i s o f least squares esti- mates of s e c o n d order p o l y n o m i a l m o d e l p a r a m e t e r s

Model term Estimate T ratio

Intercept 7.51 (2.38) a 3.15"* X1 -3-83 (0.48) -7.89*** X2 0.62 (0.48) 1-29-s X3 -4.38 (0.48) -9.00*** X4 2.58 (0-48) 5.31"** X12 1.85 (0-71) 2.61"* )/22 0.48 (0.71) 0.68 ~ X32 0.73 (0.71) 1.03 "8 )/42 0.73 (0.71) 1.03"" XI*X2 -0.44 (0.59) -0.73 n8 XI*X3 2.81 (0.59) 4.72*** XI*X4 -2.00 (0.59) -3.36** X2*X3 -0.25 (0.59) -0.42 n8 X2*X4 0.31 (0.59) 0.52"~ X3*X4 -2.20 (0-59) -3.67** R 2 t 0"89

a The number in parentheses is the s tandard error; Level of significance **P<0.01, ***P<0.001; ns = non significant; t Coefficient of determination.

Response surface methodology 169

of inhibitor (X2) can be attr ibuted to the pH of test medium since sorbic acid has been shown to be more effective in an undissociated form at more acid pH values than at neutral pH values where it is more dissociated (Monsanto Tech- nical Bulletin 1984). The F-value and overall correlation coefficient (r) of the model were also significant at P < 0.05, the equation having an R 2 = 0.87 accounting for 87% of the variation in terms of days to visible growth.

Only the significant terms in the second order polynomial were used to generate 3 dimensional response surface graphs and 2 dimensional contour plots of days to visible growth. Examples of response surface graphs for aw vs CO2:air ratio with temperature held constant at 20°C, aw versus temperature with C02 held constant at 70% and for temperature versus CO2:air ratio with aw held constant at aw 0-94 are shown in Figs 1-3 respectively. These graphs are

40

x:

cD~

>

o

28

4 O" 97

0"940

Fig. 1. Three dimensional response surface graph showing the effect of aw and CO2 concentration with temperature held constant at 20°C on growth of A. niger on Potato Dextrose Agar.

170 J.P. Smith et al.

28

x=

0

.Q

>

0

{:3

16

4 0 .97 [

25.7

40,

0.940

Fig. 2. Three dimensional response surface graph showing the effect of aw and storage temperature with CO2 concentration held constant at 70% on growth of A. niger on Potato Dextrose Agar.

examples of response surfaces known as a saddle point (Box et al. 1976) where the optimum response is either along the sides or in one or more of the four corners. As Figs 1 and 3 illustrate, a decrease in aw and storage temperature and increase in CO2 concentration re- sulted in an increase in days to visible growth while a similar trend was obser- ved for a decrease in aw and storage

temperature with CO2 held constant at 70% (Fig. 2). While these graphs can assist the researcher determine the direction to take to increase a desired response, it is difficult to specify levels of variables to give a specific shelf life from graphs such as these. This can more readily be achieved from contour plots of the same variables, examples of which are shown in Figs 4-6 respectively. By

Response surface methodology 171

o or,

0 E

x n

>

o

r.-,,

6 8

- ' ~ t - C ) 2 0 " 0

Fig. 3. Three dimensional response surface graph showing the effect storage temperature and CO2 concentration with aw held constant at 0.94 on growth of A. niger on Potato Dextrose Agar.

referring to these plots, levels of factors can be selected to inhibit mold growth and assist the manufacturer in produc- ing a product with the desired mold free shelf life. For example, a shelf life of 10-15 d could be expected if crumpets were reformulated to aw 0-97, packaged in 57-65% CO2 and stored at 20°C (Fig. 4). However, if the tempera ture in the retail environment was 23-24°C, the

same product would need to be packaged in 70% CO2 to achieve a shelf life of 10-15 d (Fig. 5). For an extended shelf life of 30 d the product would need to be reformulated to an aw of 0.94, packaged in 65% CO2 and stored at 21°C (Fig. 6) while an even longer shelf life of 40 days could be achieved by reformulating crumpets to aw 0-94, packaging in 67% CO2 and storage at 20°C (Fig. 6). To test

172 J.P. Smith et al.

0-976

0 .967

0-J58

0"949

Temp. = 2

0 .940 z 40 47 54 61 66

co~(% vh)

Fig. 4. Two dimensional contour plot showing the levels of aw and CO 2 with temperature held constant at 20°C needed to inhibit growth of A. niger for 5--40 d on Potato Dextrose Agar.

the accuracy of the fitted model to predict shelf life of product from 10 to 30 d, crumpets were formulated to the desired aw, packaged in 57-70% CO2 and stored at the temperatures shown in Table 7. Correlation analysis between the predic- ted shelf life and the actual shelf life showed a highly significant relationship (r = 0.98, d.f. = 20) indicating the accuracy of the fitted model to predict shelf life of crumpets. However, in crum- pets reformulated to 0.97 aw or higher, CO2 production occurred after packaging and all packages were visibly swollen after 3-4 weeks, especially when stored at higher temperatures. Extensive mic- robiological analyses have shown that CO2 production was mainly due to the growth and heterofermentative activity

of Leuconostoc mesenteroides (Ooraikul et al. 1984) and the swelling problem and its control are currently being investi- gated.

In conclusion, RSM is an elegant stat- istical technique that uses quanti tat ive data to determine and simultaneously solve mult ivariate equations which spe- cify the optimum shelf life for a specified set of factors through mathematical models. This s tudy has shown that by using RSM the scientist and/or manu- facturer can consider a much wider range of combinations and factors to control mold spoilage than would nor- mally be possible using the one variable at a time approach. According to Henika (1982) the advantages of RSM in food microbiology and food research in

Response surface methodology 173

Table 7. Predicted levels of aw, CO2 and storage temperature generated from two dimensional contour plots to inhibit g rowth of A. niger in c rumpe t s for 10-30 d.

Days to visible growth

aw C02 (% v/v)t Temp. °C Predicted Actual*

0.97 57 20 10 9.5 0.97 64 20 15 13.5 0.96 62 20 20 18-5 0.94 60 20 30 31"0 0.96 70 24 10 9-0 0"95 70 23 15 15.5 0"95 70 21-5 22 21.0 0.94 65 24 10 9.0 0.94 60 22 20 18.0 0"94 65 21 30 31-0

t Balance air; * Average of three replicates with standard deviation 0.5-1-5.

0"976

0-967

0 . 9 5 8

0 . 9 4 9

0"94C 20 21 "4 72"~ 24-2 ~-5 "(=

Tempereture (°C)

Fig. 5. Two dimensional contour plot showing the levels of aw and temperature with CO2 concentration held constant at 70% needed to inhibit the growth of A. niger for 5-40 d on Potato Dextrose Agar.

174 J.P. Smith et al.

G o

68 443 ' '

61

15

47 - ~ ~ a. = 0 " 9 4

40 I I i 20 "1_1 -,~ '~2-£ 24 -~ -

Terr perot,Jre (°C)

25 "g

Fig. 6. Two dimensional contour plot showing the levels of temperature and C02 with aw held constantat 0.94 needed to inhibit the growth of A. niger for 5-40 d on Potato Dextrose Agar.

general can be summarized as follows:

(a) it provides more information in less time at less cost than the one variable at a time approach; (b) it suggests combinations of the most important variables, processing and storage conditions to give a desired response and; (c) it allows the presentations of results in a readily understood graphical form.

While RSM has many advantages, it does have certain limitations, the major one being the selection of factor levels under investigation. In the initial screening design used in this study, levels ofaw ranged from 0.85 to 0.95 with other factor levels remaining at levels shown in Table 2. Examination of the fitted model revealed that the low aw

level (0-85) masked the effect of all other factors under study and, consequently, aw was the only factor of significance. These results were unexpected consider- ing the xerophilic nature of A. niger which has been reported to grow as low as aw 0.8 when all other conditions were near optimal (Christian 1980). Conse- quently, a fractional factorial design with a more restricted range ofaw values (0.96-0.98), was carried out to determine the influence of other environmental on mold growth and compute the first order polynomial model (Table 2). This emphasizes the importance of the correct choice of factor levels in experimental designs which are generally based on l i terature values, previous screening designs, practical experience, on regula- tory constraints or on commercial specif-

Response surface methodology 175

ications. Second, the results obtained by regression analyses are only estimates of shelf life for a particular set of data and may vary for another set of experimental data. Third, while the regression data can be used to predict extended shelf life, it is inadvisable to extrapolate too far outside the range of levels of factors actually used in experimental runs.

Despite these minor limitations, RSM is a powerful and elegant research tool and has yet to be used to any great extent in food microbiology research. According to Mead and Pike (1975) the limited use of RSM in research and development is due to the fact tha t most researchers are

References Bogadtke, B. (1979) Use of CO2 in packaging

generally unaware of the technique. It is hoped tha t this application assists in making food researchers more aware of the RSM technique and the many advan- tages it offers in comparison to the traditional approach to experimenta- tion.

Acknowledgements The authors wish to thank Mini IRAP, Forcrest Foods Ltd. and Conseil des recherches en p~che et agro-alimentaire du Quebec (Research Grant No. 2135) for financial assistance to complete this study.

foods. Ernahrungswirtschaft 7/8, 33-34. Box, G. E. P., Hunter, W. G. and Hunter, J. S. (1978) Statistics for Experimenters. An

Introduction to Design Data Analysis & Model Building. New York, John Wiley and Sons. Christian, J. H. B. (1980) Reduced water activity. In Microbial Ecology of Foods, I.C.M.S.F.,

Vol 1. New York, Academic Press. Connor, M. A. and Keagy, P. M. (1981) Folacin retention and cookie diameter in enriched

cookies: regression analysis using factorial design. Cereal Chem. 58, 239-244. Henika, R. G. (1982) Use of Response Surface Methodology in sensory evaluation. Food

Technol. 36, 96-100. Lewicki, P. P., Busk, G. C., Peterson, P. L. and Labuza, T. P. (1978) Determination of factors

controlling accurate measurements of and by the vapor pressure manometric technique. J. Food Sci. 43, 243-246.

Ma, A. Y. M. and Ooraikul, B. (1986) Optimization of enzymatic hydrolysis of canola meal with response surface methodology. J. Food Proc. Preserv. 10, 155-160.

Mead, R. and Pike, D. J. (1970) A review of response surface methodology from a biometric viewpoint. Biometrics 31, 805-809.

Monsanto Technical Bulletin (1984) Monsanto Nutrition Chemicals Division, St. Louis, Missouri.

Montgomery, D. C. (1984) Response Surface Methodology. In Design and Analysis of Experiments, 2nd edn. New York, John Wiley and Sons.

Mullen, K. and Ennis, D. (1985) Fractional factorials in product development. Food Technol. 39, 90-103.

Ooraikul, B., Lim, N. C. S. I. and Koersen, W. J. (1984) Modified atmosphere packaging of selected bakery products as an alternative to low temperature preservation. Progress reports Nos 1-12. Engineering and Statistical Research Institute Report of Contract File No 10 SC. 01916-3-EP. Agriculture Canada, Ottawa, Ontario, 120 pp.

Pomeranz, Y. (1969) A review of some recent studies on prevention of mold spoilage in bakery products. Baker's Digest 43, 61-62, 67.

Schroder, D. J. and Busta, F. F. (1973) Effects of synthetic meat components on growth of Clostridium perfringens. J. Milk Food Technol. 36, 189-193.

Seiler, D. A. L. (1965) Factors influencing the mould free shelf-life of cake with particular reference to the use of antimould agents. Brit. Baking Ind. Res. Assoc. Report No. 81.

Seiler, D. A. L. (1978) The microbiology of cake and its ingredients. Food Trade Rev. 48, 339-344.

Seiler, D. A. L. Personal Communication. Smith, J. P., Jackson, E. D. and Ooraikul, B. (1983) Microbiological studies on gas packaged

crumpets. J. Food Prot. 46, 279-283.

176 J.P. Smith et al.

Smith, J. P., Ooraikul, B. and Jackson, E. D. (1984) Linear Programming: a tool in reformulation studies to extend the shelf life of English style crumpets. Food Technol. A ust. 36, 454--456, 459.

Statistical Analysis System (1982) SAS User's Guide: Basics, Version 5. SAS Institute, Cary, North Carolina.

Taylor, A. A. (1961) Determining moisture equilibria in dehydrated foods. J. Food Technol. 12, 536-540.

van de Voort, F. R. and Stanley, D. W. (1984) Improved utilization of dairy proteins: coextrusion of casein and wheat flour., J. Dairy Sci. 67, 747-758.