An Empirical Model for Predicting Harwell Dose Variation During Gamma Process Interruption Using Experimental Design

 MAPAN-Journal of Metrology Society of India (June 2015) 30(2):85–90 DOI 10.1007/s12647-014-0129-6

REVIEW PAPER

An Empirical Model for Predicting Harwell Dose Variation During Gamma Process Interruption Using Experimental Design A. Mejri1,3*, K. Farah3, F. Hosni1,3, A. H. Hamzaoui4 and H. Eleuch2 1

Laboratoire de Dosime´trie des Rayonnements Ionisants, Centre National des Sciences et Technologies Nucle´aires, 2020 Sidi-Thabet, Tunis, Tunisia

2

Institute for Quantum Science and Engineering, Texas A & M University, College Station, TX 77843, USA 3

Unite´ de recherche: Maıˆtrise et De´veloppement des Techniques Nucle´aires a` Caracte`re Pacifique, Centre National des Sciences et Technologie Nucle´aires, 2020 Sidi-Thabet, Tunisia

4

Laboratoire des Mate´riaux, Institut National de Recherche Scientifique et Technique, B.P. 95, 2050 HammamLif, Tunisia Received: 05 May 2014 / Accepted: 18 December 2014 / Published online: 25 January 2015 Ó Metrology Society of India 2015

Abstract: During routine dosimetry for radiation processing applications, process interruption is widely encountered; in this case dosimeters may receive their target dose in two or more absorbed-dose increments. Some interruptions may be planned, for example double side irradiations may be used to improve dose distribution. Other interruptions may be the result of unplanned irradiator shutdowns. In this case, dosimeters may be exposed to outside factors, such as temperature, without exposure to ionizing radiation. The responses of these dosimeters are usually influenced because the conditions in irradiation facilities may differ considerably from the conditions in which the dosimeters were calibrated. These differences may lead to expected systematic errors in dose estimation. An original approach is proposed in this work in order to simulate a process interruption within limits and quantify the effects of a combination of factors on dosimeter response using complete factorial design 2n. We present an in-depth experimental study on the response of dosimeters that have been irradiated, stored for a fixed period of time at several temperatures, and then re-irradiated. This study was performed using Harwell Red Perspex dosimeter type 4035. Keywords:

Dosimeter; Fractional dose; Experimental design; Harwell Red Perspex; Modeling

1. Introduction Several kinds of dosimeters are widely used for the process control of the radiation processing applications such as sterilization of medical devices, food preservation and other applications. Dosimeters based on the radiationinduced colouration properties are also extensively used for the routine measurements of the absorbed dose such as Harwell Red Perspex dosimeter. Dosimeter usage is of vital importance in industrial radiation processing and as a result understanding how a dosimeter is affected by outside variables, is also of great concern. The responses of the dosimeter used in routine dosimetry are usually influenced by environmental conditions

*Corresponding author, E-mail: [email protected]

such as the temperature during irradiation, dose rate and post-irradiation storage [1]. Many problems may be encountered in the routine dosimetry for radiation processing applications, because the conditions in irradiation facilities may differ considerably from the conditions in which the dosimeter was calibrated. These differences may lead to expected systematic errors in dose estimation. In recent years, many people have been extending the range over which the dosimeters are used consequently stretching the capabilities of these dosimeters. Several studies have been conducted to investigate the effects of temperature [2, 3] and temperature during interruption irradiation [4, 5]. In order to overcome this problem, experiments on optimization studies have been carried out using statistical design technique. This technique can be used for process characterization, optimization and modelling. It has been

123

86

A. Mejri et al.

widely accepted in the manufacturing industry for improving product performance and reliability, process capability and yield. In the statistical design experiments, the factors involved in an experiment at their respective levels, were simultaneously varied. Thus, a lot of information can be obtained with a minimum number of experiment trials [6]. The experiments in which the effects of more than one response factor are investigated are known as full factorial experiments. The most important advantages are that not only the effects of individual parameters, but also their relative importance in the given process are obtained, and the interactional effects of two or more variables can also be known. This is not possible in a classical experiment [7]. The aim of the present paper is to find out the effects of the number of interruptions, the duration of interruption and the temperature during interruption into absorbed doses measured by Harwell Red Perspex dosimeter. Two level Factorial designs were used to determine the effects of the factors and their interactions. The observed effects of fractionation dose and storage time on the response of dosimeters are the continuity of our previous published work [8].

2. Material 2.1. Dosimeters Polymethylmethacrylate (PMMA) dosimeter is used especially for radiation processing applications [1, 9]. The active substance of the PMMA film dosimeters is a dye dispersed in the PMMA. Ionizing radiation leads to the ionisation of the PMMA and the added dye. The radicals of ionised polymer react with the dyed molecules to produce an optical absorption in the visible spectrum. In this work, Red Perspex type 4034, (batch KS, dose range: 5–50 kGy) are used. Perspex dosimeters, sealed in polyethylene-aluminium sachets (produced by Harwell Dosimeters, UK), were evaluated at 640 nm, using Aerial Optical Dosimetry Equipment [10]. 2.2. Irradiation The irradiations have been performed in air at the Tunisian semi-industrial 60Co gamma-irradiation facility at dose

rates: 100 Gy/min [11]. The dose rate was established with the alanine/EPR dosimetry system in term of absorbed dose traceable to the National Physical Laboratory, UK. Before the experiment the dose rate was verified by Fricke standard dosimeter. 2.3. Temperature Control To control and maintain the dosimeters at the desired temperature during irradiation interruption, Julabo frigerated circulator type F25-EC, with ultra-purified water for the temperature range 5–90 °C or a mixture of water and glycol for the range -25 to 50 °C as coolant liquid, was used. Samples were placed on an aluminium cylinder which circulates the liquid that was maintained at the desired temperature. Before using the circulator, the set-up was kept for 20 min to allow for the temperature equilibrium. Temperature fluctuation of the aluminium cylinder is within ±2 °C. 2.4. Experimental Design Experimental design technique has been widely applied for processes optimisation in different field such as food [12], chemical, biochemistry process [13], geotechnical engineering [14] animal science and nutrition studies [15, 16]. In the statistical design experiments, the factors involved in an experiment at their respective levels, were simultaneously varied. Thus, a lot of information can be obtained with a minimum number of experiment trials [6] such as effects of individual parameters, their relative importance and the interactional effects in the given process. This is not possible in a classical experiment [7]. 2.5. Experimental Design for Red Perspex Dosimeter Investigation A Full Factorial Experimental Design was used to study the influence of four factors (dose interruption, temperature, duration of interruption and target dose) and the possible interactional effect. Each factor is ‘coded’ as (-) low or (?) high level (Table 1). The selected factors and their corresponding ranges (high and low level of variation) were determined after preliminary study [8]. As usual, the experiments were carried out in random order to minimize

Table 1 Actual and corresponding coded values of parameters in 24 full factorial design Level of variables

Temperature (°C)

Target dose (kGy)

Interruption number

Duration interruption (min)

Actual (x1)

Actual (x2)

Actual (x3)

Coded (X3)

Actual (x4)

Coded (X4)

Coded (X1)

Coded (X2)

Upper level

40

?

40

?

5

?

1440

?

Lower level

10

–

10

–

1

–

60

–

123

An Empirical Model for Predicting Harwell Dose Variation

87

Table 2 Experimental design matrix for Y as absorbed dose (kGy)

—The dispersion matrix (Xt. X) -1. The regression equation developed from different sets of experiments show the dependence of yield on individual parameters as well as interactions for simultaneous variations of parameters (Eq. 2) [18]:

Exp. number

X1

X2

X3

X4

Y (kGy)

1

-1

-1

-1

-1

10.917

2

1

-1

-1

-1

10.873

3

-1

1

-1

-1

41.334

4

1

1

-1

-1

42.535

5

-1

-1

1

-1

10.655

6

1

-1

1

-1

11.463

þ 1:032X 2 X4 þ 0:681X3 X4 þ 0:091X1 X2 X3

7

-1

1

1

-1

41.757

8

1

1

1

-1

40.327

þ 0:760X1 X2 X4 þ 0:678X2 X3 X4 þ 0:907X1 X3 X4 þ 0:525X1 X 2 X3 X4

9

-1

-1

-1

1

11.247

10

1

-1

-1

1

12.202

11 12

-1 1

1 1

-1 -1

1 1

41.225 45.306

13

-1

-1

1

1

10.195

14

1

-1

1

1

13.220

15

-1

1

1

1

43.903

16

1

1

1

1

54.983*

* Value out of the range of use of Harwell Red Perspex dosimeter (5–50 kGy)

the effect of systematic errors. 24 or 16 experiments were carried out according to Full Factorial Design methodology [7] (Table 2).

3. Results and Discussion 3.1. Molding of the Fractionation Dose Effect 2 factorial design was selected in this study. The number of experiments required for understanding all the effects is given by ak = 24 = 16 where (a) is the number of levels and (k) is the number of factors. As can be seen from Table 1, x1, x2, x3 and x4 show the temperature, target dose, number of irradiation interruptions and the duration of each one, respectively. X1, X2, X3 and X4 represent the coded forms of temperature, target dose, number of irradiation interruptions and the duration of etch interruption as previous one. Table 2 summarizes the experimental design matrix for dose response. While Y is the dose response (kGy). The regression coefficients are computed as below (Eq. 1), [17]: t

1

t

b ¼ ðX : XÞ :X : Y

ð2Þ This equation reveals the effect of individual variables and interactional effects for dose estimation. As can be seen from Eq. (2), the temperature, target dose, number of irradiation interruptions and the duration of interruptions have a positive effect on the dose estimation, in the range of variation of each variable selected for our work. The greatest effect on dose estimation was supplied by irradiation dose. The lowest contrast of variable was noted for the interaction effect X1X2X3. All of the variables have a positive influence on estimated dose indicating that the amount of estimating dose increased while the factor varied from low level to its high level. To assess the significance of a coefficient, t Student is applied [19–21]. If we set the acceptance probability coefficients of 0.2 (p value), the final model is then (Eq. 3): Y ¼ 26:635 þ 1:229X1 þ 16:287X2 þ 1:4X4 þ 1:163X1 X4

4

^

Y ¼ 26:635 þ 1:229X1 þ 16:287X2 þ 0:679X3 þ 1:4X4 þ 0:637X1 X2 þ 0:455X1 X3 þ 1:163X1 X4 þ 0:642X2 X3

ð1Þ

where Xt is the transpose matrix of X. Two matrices constantly intervene in the theory of design of experiments: —The information matrix (Xt. X).

þ 1:032X 2 X4 þ 0:681X3 X4 þ 0:76X1 X2 X4 þ 0:678X2 X3 X4 ð3Þ where: ðT  25Þ ðd  3Þ ðn  3Þ ; X2 ¼ ; X3 ¼ ; X4 15 2 2 ðt  750Þ ¼ 690

X1 ¼

We check that this model has a good coefficient of correlation (R2 = 0.99) and p values of the coefficients are always less than 0.2. 3.2. Metrological Analyze of the Proposed Model Figure 1, reveal the distribution of the calculated versus experimental values for Y response, it shows that the points are almost randomly distributed about the line representing exact agreement providing little evidence of lack-of-fit for the linear model. The deviation in the graph correspond to root mean square error RMSE of 2.23 (Eq. 4) for the

123

88

A. Mejri et al.

response Y [20, 22]. The maximum value that the standardized residual SR take is 1.65 (Eq. 5), which does not exceed ±2 at 95 % confidence level.

RMSE ¼

n 1X ^i  wi Þ2 ðw n i¼1

^i  wi Þ=std ðRÞ SRi ¼ ðw

ð5Þ

where n is the number of experimental point, std (R) is the standard deviation of the residuals. According to Variance Analysis (Table 3), the Ratio between the regression mean square and the residual mean square for the Y response is about 148.81; it is superior to the tabled Fisher’s value F 0:05 ¼ 3:81 [22–24]. Secondly, it is worth noting that the value of multiple correlation coefficients is 0.99. Thus, it is possible to confirm the validity of the elaborated linear model.

60

Calculated Values (kGy)

ð4Þ

50

40

30

20

3.3. Experimental Validation of the Proposed Model 10 10

20

30

40

50

60

Experimental Values (kGy)

Fig. 1 Calculated versus experimental values for dose estimation (kGy) with 5 % error bar

Table 3 Analysis of variance F-ratios and decisions Source of variation

SS

DF

MS

F ratio

Significance

Regression

4,404.150

13

338.781

148.807

**

Residual

4.553

Total

4,408.700

2 15

Fig. 2 Tunisian Cobalt-60 Gamma irradiation source and single use medical device product position

123

2.277

In order to validate the proposed model, Performance Qualification of single use medical device product with a density of 0.15 g/cm2 is carried out to confirm the locations of critical areas (the maximum and minimum dose zone). Figure 2 shows the irradiation of an eight boxes Product with dosimeters position on the product. The centre of the batch is raised to about 160 cm from the ground (source centre). Dosimeters used for confirmation of the location of minimum dose zones are positioned along the board of the vertical median plane (Plan M) of the product. For the localisation of the zone of maximum dose, dosimeters are implemented in the middle of the Plan A, B and M, according to Fig. 2.

An Empirical Model for Predicting Harwell Dose Variation

89

Fig. 3 Graphic representation in tree dimensions of the dose distribution on the medium plane (M) of the product. a Experimental dose cartography. b Computed dose cartography

Irradiation is performed at 25 kGy, 1 interruption of 1 h and at 27 °C in double side irradiation (up/down and front/rear). At all 17 sets of dosimeters are located in the product, 9 sets to control Maximum dose (middle of the Plan A, B and M), and 8 sets for the control of minimum dose (in the tow Board of Plan M). Measurement of Harwell Red Perspex dosimeters was performed 24 h after irradiation using Ae´rODE dosimetry equipment [10]. Figure 3a, shows a representation in two dimensions of the dose distribution on the median plane (M). The positions of the maximum doses are located on the center of Plan M. The positions of minimum doses are identified in the board of medium plan (Plan M). The value of the absorbed dose is decreasing from the center to the board of the product. In Plan A and B we find an equivalent behaviour concerning the maximum zone. In Fig. 3b, a computed dose cartography using the linear model is carried out according to the protocol of irradiation detailed previously. The positions of maximum and minimum dose zone are confirmed (Fig. 3b). The computation cartography was done using the 17 dose measured previously, by adjusting the target dose in the model. These results despite the fact that experimental and computed dose cartography are comparable within the permitted limit ([2r at 95 % confidence interval) [3]. The behaviour of the Harwell Red Perspex dosimeters can be explained by the conditions in irradiation facilities may differ considerably from the conditions in which the dosimeters were calibrated. These differences may lead to expected systematic errors in dose estimation. For this reason the established model is very useful in radiation processing dosimetry and it is an effective method to predict the dosimeter behaviour following

process interruption. And a dose correction coefficient can be evaluated using this model.

4. Conclusion Four Full factors Factorial Design was employed in order to model and optimize the chosen response (Dose). According to the four factors fields, a valid model was established. These results despite the fact that they are in same case above the permitted limit ([2r at 95 % confidence interval). This can be explained by the conditions in irradiation facilities may differ considerably from the conditions in which the dosimeters were calibrated. These differences may lead to expected systematic errors in dose estimation. However, we believe that the established model is very useful in radiation processing dosimetry and it can be improved by studying the effect of new factors as relative humidity and dose rate. Finally this work permits to make available, an original and effective method to predict over dose gated by dosimeter and a correction coefficient can be calculated.

References [1] W.L. McLaughlin and M.F. Desrosiers, Dosimetry systems for radiation processing, Radiat. Phys. Chem., 46 (1995) 1163–1174. [2] S. Biramonttri, N. Haneda, H. Tachibana and T. Kojima, Effect of low irradiation temperature on the gamma ray response of dyed and undyed PMMA dosimeters. Radiat. Phys. Chem., 48 (1996), 105–109. [3] A. Mejri, K. Farah, H. Eleuch and H. Ben Ouada, Application of commercial glass in gamma radiation processing. Radiat. Meas., 43 (2008) 1372–1376.

123

90 [4] B.L. Gupta, U.R. Kini and R.M. Bhat, Dose-rate and fractionation studies with FBX dosimeter, Int. J. Appl. Radiat. Isot., 32 (1981) 701–704. [5] M.K. Murphy, A. Kovacs, S.D. Miller and W.L. McLaughlin, Dose response and post-irradiation characteristics of the Sunna 535-nm photo-fluorescent film dosimeter, Radiat. Phys. Chem., 68 (2003) 981–994. [6] D.C. Montgomery, Experimental design for product and process design and development, Stat., 48 (1999) 159–177. [7] D.C. Montgomery, Design and analysis of experiments, Wiley, New York (1996) p. 704 . [8] F. Hosni, K. Farah, A. Mejri, A. Khayat, R. Chtourou and A.H. Hamzaoui, A study of the fractionation dose on the radiation response of Harwell Red-Perspex PMMA dosimeter, Nucl. Instrum. Methods Phys. Res. B, 290 (2012) 69–71. [9] ISO/ASTM 51276 Standard, Standard practice for use polymethylmethacrylate dosimetry system. American Society for Testing and Materials, Philadelphia (2002a). [10] F. Kuntz, R. Fung and A. Strasser, A dedicated tool for the quality assurance in the field of radiation processing, Proceeding of the 11th international meeting on radiation processing, Melbourne, Australia (1999). [11] K. Farah, T. Jerbi, F. Kuntz, A. Kovacs, Dose measurements for characterization of a semi-industrial cobalt-60 gamma-irradiation facility, Radiat. Meas., 41 (2006) 201–208. [12] H.N. Sin, S. Yusof, N. Sheikh Abdul Hamid and R. Abd Rahman, Optimization of enzymatic clarification of sapodilla juice using response surface methodology, J. Food Eng., 73 (2006) 313–319. [13] L. Rodrigues, J. Teixeira and R. Oliveira, Response surface optimization of the medium components for the production of biosurfactants by probiotic bacteria, Process Biochem., 41 (2006) 1–10. [14] K. Ravikuma, S. Ramalingam, S. Krishnan and K. Balu, Application of response surface methodology to optimize the process variables for reactive red and acid brown dye removal using a novel adsorbent, Dyes Pigments, 70 (2006) 18–26.

123

A. Mejri et al. [15] N. Zangeneh, A. Azizian, L. Lye and R. Popescu, Application of response surface methodology in numerical geotechnical analysis. 55th Canadian society for geotechnical conference, Hamilton, Ontario (2002). [16] W.B. Roush, R. Petersen and G.H. Arscott, An application of response surface methodology to research in poultry nutrition. Poult. Sci., 58 (1979) 1504–1513. [17] D.C. Montgomery, Introduction to factorial designs, In Design and analysis of experiments. Wiley, New York (1997b), pp. 189–243. [18] S. Akhanazarova and V. Kafarov, Experiment optimization in chemistry and chemical engineering, Mir Publishers. Moscow, p. 13 (1982). [19] B. Hajem, K. Djebali and A. M’nif, Modeling and optimisation of fluoride and cadmium trapping in phosphogypsum using desing methodology, Clean-Soil Air Water, 38 (2010) 859–864. [20] D. Mathieu, R. Phan-Tan-Luu, NemrodW Software. Aix-Marseille III University, Marseillem France (1999). [21] M. Toyomizu, Y. Akiba, M. Horiguchi and T. Matsumuto, Multiple regression and response surface analyses of the effect of dietary protein, fat and carbohydrate on the body protein and fat gains in growing chicks, J. Nutr., 112 (1982) 886–896. [22] C.K. Bayne and I.R. Rubin, Practical experimental designs and optimization methods for chemists. VCH Publishers, USA (1986). [23] T. Lundstedt, E. Seifert, L. Abramo, B. Thelin, A. Nystrom, J. Pettersen and R. Bergman, Estimation of experimental parameters for the determination of ruthenium by flame atomic absorption spectroscopy, Chemom. Intell. Lab. Syst., 42 (1998) 340. [24] M. Nechar, M.F. Molina, J.M. Bosque-Sendra, Application of Doehlert optimization and factorial designs in developing and validating a solid-phase a spectrometric determination of trace levels of cadmium, Anal. Chim. Acta., 382 (1999) 117–130.