Effects of composition interactions on the response of a turnbull blueradiochromic gel dosimeter

Jiunn-I Shieh a, Kai-Yuan Cheng b, Huey-Lih Shyu c, Yi-Chen Yu b, Ling-Ling Hsieh b,n

a Department of Applied Informatics and Multimedia, Asia University, No. 500 Lioufeng Road, Wufeng, Taichung 413, Taiwanb Department of Medical Imaging and Radiological Sciences, Central Taiwan University of Science and Technology, Taichung, Taiwanc Department of Medical Laboratory Science and Biotechnology, Central Taiwan University of Science and Technology, Taichung, Taiwan

H I G H L I G H T S

� Analysis of the composition that influence TBG dosimeters via the design of experiments.� Cross interactions between factors in the TBG dosimeters through multi-factor ANOVA.� Two two-way interactions and one three-way interaction in the TBG dosimeters are significant.

a r t i c l e i n f o

Article history:Received 4 June 2013Accepted 1 March 2014

Keywords:Taguchi methodTurnbull blueRadiochromic gel

a b s t r a c t

In this study, the Taguchi statistical method was used to design experiments for investigating the effectsof interactions among compositions on the performance of a Turnbull blue gel (TBG) radiochromicdosimeter. Four parameters were considered as the design factors: (A) concentration of ferric chloride,(B) concentration of potassium ferricyanide, (C) concentration of sulfuric acid, and (D) amount of gellingagent added. Two levels were selected for each factor. The change in optical absorbance at 695 nm underUVA exposures was monitored to determine the response of the dosimeters. The results showed that thecontributions of factors A–D on the absorbance were 20.01%, 23.16%, 27.03%, and 0.49%, respectively. Thecontributions of significant interaction effects were AC (8.60%), BC (5.61%), and ABC (10.56%). This findingindicated that sulfuric acid (C) was the most influential factor, whereas gelling agent (D) was the leastinfluential factor. Sulfuric acid had an important function in two two-way interactions and one three-way interaction in the response of TBG to UV exposure.

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1. Introduction

Ultraviolet radiation (UVR) is the section of the electromagneticspectrum that lies between X-rays and visible light. Human exposureto UVR is mainly due to the sun, which is the most important lightsource on earth. Solar UVR mainly comprises of UVC (100–280 nm),UVB (280–315 nm), and UVA (315–400 nm). However, almost allUVC and a large part of the UVB spectrum are absorbed by the ozoneand other atmospheric gases. On the other hand, almost all solar UVApass through the atmosphere and reach the surface of the earth.The damaging effects and the premature photoaging of humanskin because of cumulative exposure to long UVA wavelengths(320–400 nm) have been reported (Bissett et al., 1992; Lavker et al.,1995). A predominance of UVAmutations in the basal cell layer of the

human skin has also been reported (Agar et al., 2004). Thus, UVA hasbeen classified as a potential carcinogen to the human skin, since itcan penetrates the human skin at considerable depths.

Gel dosimeters was developed and used for measuring three-dimensional dose distribution for radiation (Bero et al., 2000). Thegel itself absorbs UV radiation to a much greater extent whencompared with water (Su and Yeh, 1996; Diffey, 1999). A newradiochromic gel based on the radiation-induced creation of theTurnbull blue dye (Turnbull blue gel [TBG] dosimeter) was devel-oped and used to measure the spatial dose distribution in radio-therapy (Šolc et al., 2010). The gel itself has good sensitivity toUVR, and the effects of UVA radiation exposure can be quantita-tively measured using a standard spectrophotometer. This studyexamined the quantitative contribution of each composition andits effects on the characteristics of TBG dosimeter by using theTaguchi method. The effects of the chemical interactions of thecomposition on the response of the dosimeter during photoreac-tion were also discussed.

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Radiation Physics and Chemistry

http://dx.doi.org/10.1016/j.radphyschem.2014.03.0030969-806X & 2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: þ886 422391647x7116; fax: þ886 422396762.E-mail address: llhsieh2013@gmail.com (L.-L. Hsieh).

Please cite this article as: Shieh, Jiunn-I, et al., Effects of composition interactions on the response of a turnbull blue radiochromicgel dosimeter. Radiat. Phys. Chem. (2014), http://dx.doi.org/10.1016/j.radphyschem.2014.03.003i

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2. Materials and methods

2.1. Preparation of the TBG dosimeters

The components of TBG include ferric chloride (98%, AlfaAesar), potassium ferricyanide (99%, Sigma-Aldrich), diluted sul-furic acid (98%, Sigma-Aldrich), and gelling agent. Agarose (Agar-ose ME, Alfa Aesar), which was used as the gelling agent, wasdissolved in deionized water (0.08% or 0.25% w/mL agarose) andplaced into an 80 1C water bath. The solution became clear andtransparent. Ferric chloride (1 mM or 20 mM) was dissolved in thediluted sulfuric acid. Before gel mixing, this solution was cooled to35 1C. Ferric chloride was added into the solution by continuousstirring. Subsequently, potassium ferricyanide solution (1 mM or40 mM) was added to the mixture. Gel samples were placed incuvettes after TBG was mixed. Finally, the gel samples werewrapped in aluminum foil and stored in a refrigerator at 4 1C toprevent light-induced pre-photoreaction.

2.2. UV irradiation and optical spectroscopic measurements of theTBG dosimeters

The UV irradiation of the TBG samples were measured using a UVA(λmax emission¼365 nm) lamp, which comprises three fluorescencetubes (Philips Actinic BL 8W). The UV intensities (unit: mW cm�2)were measured using a UVX-36 radiometer (UVP, CA, USA). The UV/visabsorption spectra were obtained using a ChromTech CT-8600 UV/Visspectrophotometer (Chrom Tech, Inc., Singapore).

2.3. Orthogonal array and experimental factors based on theTaguchi method

In this study, four parameters were considered as designfactors, namely, (A) ferric chloride concentration, (B) potassium

ferricyanide concentration, (C) sulfuric acid concentration, and(D) amount of agarose. Two levels were selected for each factor, asshown in Table 1. We conducted an experiment with an L16 (215)orthogonal array (16 tests, four variables, and two levels). Theexperiment design is shown in Table 2, and the variation in theabsorbance at λmax was assessed.

In the Taguchi method, the terms ‘signal’ (S) and ‘noise’(N) represent the desirable and undesirable values for the outputcharacteristics, respectively. The Taguchi method involves the useof the S/N ratio to measure the quality of the characteristic thatdeviates from the desired value. The S/N ratios differ according tothe type of characteristic. Characteristic, and in case where highvalues are desired, the S/N ratio (η) is defined as (Roy, 1995)

η¼ �10 log1n

∑n

i ¼ 1

1xi

� �2 !

; ð1Þ

where xi is the measured data for the performance objectives andn is the number of measurements. In this study, n¼3 was used forall experiments.

3. Results and discussion

3.1. Optical characteristics of TBG dosimeters

When the TBG dosimeters were exposed to UVA irradiation, theunirradiated gel transforms gradually from transparent yellow togreen and blue, due to the radiation-induced creation of theinsoluble Turnbull blue dye. The spectrophotometric measure-ments of the TBG dosimeters were also recorded as a function of

Table 1Design factors and their levels

Factor Levels

1 2

[FeCl3] (mM) 0.06 1.23K[Fe(III)(CN)6](mM) 0.03 1.21[H2SO4] (mM) 1 100Agrose (%) 0.08 0.25

Fig. 1. UV/visible absorption spectra of unirradiated and irradiated TBG dosimeters.

Table 2Layout of the L16 (215) orthogonal array.

Experiment number Design factor

A B AB C AC BC ABC D AD BD ABD CD ACD BCD ABCD

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 2 2 2 2 2 2 2 23 1 1 1 2 2 2 2 1 1 1 1 2 2 2 24 1 1 1 2 2 2 2 2 2 2 2 1 1 1 15 1 2 2 1 1 2 2 1 1 2 2 1 1 2 26 1 2 2 1 1 2 2 2 2 1 1 2 2 1 17 1 2 2 2 2 1 1 1 1 2 2 2 2 1 18 1 2 2 2 2 1 1 2 2 1 1 1 1 2 29 2 1 2 1 2 1 2 1 2 1 2 1 2 1 210 2 1 2 1 2 1 2 2 1 2 1 2 1 2 111 2 1 2 2 1 2 1 1 2 1 2 2 1 2 112 2 1 2 2 1 2 1 2 1 2 1 1 2 1 213 2 2 1 1 2 2 1 1 2 2 1 1 2 2 114 2 2 1 1 2 2 1 2 1 1 2 2 1 1 215 2 2 1 2 1 1 2 1 2 2 1 2 1 1 216 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1

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irradiation time, as shown in Fig. 1. As seen, the maximumabsorption peak of the TBG dosimeters approximately correspondsto 695 nm. Thus, all absorbance values were measured at thiswavelength. Quantitative measurements of optical absorbance canbe used to establish a proportional relationship between theabsorbed UVA dose and the change in TBG absorbance.

3.2. Analysis of the composition that influence TBG gels via theTaguchi method

The TBG dosimeter is composed of a gel matrix, potassiumferricyanide, and ferric chloride dissolved in an acidic solution. Inthis study, four design factors were used, considering two levels foreach factor for analysis by the Taguchi method. Only two levels foreach factor were used because for experiments in which the effectsof many factors are screened, only two levels of each factor areusually considered (SAS Publishing, 2010). This method allows theexamination of many factors with a minimum number of runs (SASPublishing, 2010). Table 3 shows the measurement results of TBGexposed to UVA irradiation (1.86 mW cm�2) for 8 min. The prioritiesof the four factors that influence the response were determined byusing delta statistics. Delta statistics demonstrate the differencesbetween the highest and lowest mean ratios of each factor and alarge delta means that the respective factor has more influence onthe model. In our case, factors A, B, and C have delta values of10.4659, 11.2617, and 12.1652, respectively, thereby indicating thatthey are the most influential factors. The percentage contribution foreach factor was determined using the results of analysis of variance(ANOVA). The results of ANOVA for the effects of the four compo-nents on the TBG dosimeters are shown in Table 4. From the resultsof ANOVA, we can get the sum of squares for each of the factors,composition interactions, and error. In our study, the total sum ofsquares for the composition interactions and their main effects onTBG response with 4 factors at 2 different levels are

SST ¼ ∑13

p ¼ 1SSpþSSe

where SST denotes the total sum of squares; SSp denotes the sum ofsquares of the factors and composition interactions where p¼1, 2, 3,

4, 5, 6, 7, 8, 9, 10, 11, 12, and 13 corresponding to the factors andcomposition interactions A, B, C, D, AB, AC, BC, CD, ABC, ABD, ACD,BCD, and ABCD, respectively; and SSe denotes the error sum ofsquares. The percentages of the contribution for each factor andcomposition interactions are as follows:

The total sum of squares, SST , from the S/N ratio can becalculated as

SST ¼ ∑m

iη2i �

1m

∑m

i ¼ 1ηi

" #

where m is the total number of experiments, and ηi is the S/N ratioat the ith test. The sum of squares from the parameter p, SSP , can becalculated as

SSP ¼ ∑a

j ¼ 1

ðSηpjÞt

� 1m

∑m

i ¼ 1ηi

!2

;

where p represents one of the factors and composition inter-actions; a is the number of levels; j is the level number of thespecific parameter p; t is the repetition of each level of theparameter p; Sηpj is the sum of the S/N ratio involving thisparameter p and level j.

The sum of squares from error parameters SSe is calculated as

SSe ¼ SSr�∑pSSp

The percentage of the contribution to the total variation (P). Let Ppbe the percentage of the total variation from each parameter p andPe be the percentage of the total variation from error parameters.They are calculated as the following:

Ppð%Þ ¼ SSpSSr

100; Ppð%Þ ¼ SSeSSr

100:

The results show that the contributions of factors A–D are20.01%, 23.16%, 27.03%, and 0.49%, correspondingly. A factor with ahigh percentage contribution significantly influences the perfor-mance objectives of the TBG dosimeters. These results are in closeagreement with those a previous study involving the light-induced formation of Turnbull blue, K[Fe(II)Fe(III)(CN)6], whichrevealed a two-step process as follows: after a pseudo-first-orderreaction, an autocatalytic formation of Turnbull blue occurs (Balog

Table 3Measurement results of TBG exposed to UVA irradiation and S/N ratios.

Experiment Design factor ΔAbs695

number A B C D 1 2 3 S/N

1 1 1 1 1 0.3129 0.2432 0.2674 �11.36712 1 1 1 2 0.2651 0.2721 0.2844 �11.25993 1 1 2 1 0.0051 0.0022 0.0060 �49.60994 1 1 2 2 �0.0114 �0.0270 �0.0117 �37.36405 1 2 1 1 0.3124 0.3270 0.3337 �9.78846 1 2 1 2 0.2647 0.2808 0.2764 �11.25387 1 2 2 1 0.1538 0.1712 0.1720 �15.65168 1 2 2 2 0.1491 0.1398 0.1298 �17.14549 2 1 1 1 0.2441 0.2392 0.2442 �12.307310 2 1 1 2 0.2716 0.1970 0.2237 �12.960511 2 1 2 1 0.1554 0.1456 0.2088 �15.701112 2 1 2 2 0.1552 0.1447 0.1778 �16.053313 2 2 1 1 0.6494 0.6064 0.6506 �3.952714 2 2 1 2 1.0224 1.0035 0.9675 �0.025815 2 2 2 1 0.3020 0.3118 0.3798 �9.728916 2 2 2 2 0.3460 0.3759 0.3470 �8.9831Level 1 �163.4400 �166.6230 �72.9155 �128.1069Level 2 �79.7128 � 76.5298 �170.2373 �115.0459

Delta 10.4659 11.2617 12.1652 1.6326Rank 3 2 1 4

ΔAbs695, The variation in TBG absorbance at 695 nm.

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et al., 1999). The rate-limiting step is dependent on ferricyanide,Fe (III), and acid concentrations.

3.3. Cross interactions between factors in the TBG dosimeters

In multi-factor ANOVA, we studied the composition interac-tions and their main effects on TBG response. Interactions aredefined as the extent to which the effects of one factor differaccording to the levels of another factor. If an interaction existsbetween factors A and B, then A, which is best for a particular levelof factor B, is different from the one that is best for another level offactor B. If no interaction exists between the factors, then the effectof one factor is the same for all levels of the other factor. Supposethat four factors, namely, A, B, C, and D, exist in the experiments.The interaction is defined as the influence of the levels of factor Aon the effect of another factor B.

If A is solely influenced by B, then only AB is considered.However, if A is somewhat influenced by B, then A can also beinfluenced by C. Thus, a three-factor interaction (ABC) can beconsidered. These three-factor interactions may be influencedby D. Thus, a four-factor interaction (ABCD) can be considered(Gomez and Gomez, 1984; Palanikumar et al., 2004).

The model in this study can be written as (Montgomery, 2001)

yijklm ¼ μþαiþβjþγkþδlþαβijþαγikþαδilþβγjkþβδjl

þγδklþαβγijkþαβδijlþαγδiklþβγδjklþαβγδijklþεijklm

where, i¼1, 2,…, a; j¼1, 2,…, b; k¼1, 2,…, c; l¼1, 2,…, d; m¼1,2,…, r.Model parameters

yijklm¼Response in the mth replication with factors A, B, C, andD at levels i, j, k, and l, respectively.μ¼Mean response.αi¼Effect of factor A at level iβj¼Effect of factor B at level j.γk¼Effect of factor C at level k.δl¼Effect of factor D at level l.PQij¼ Interaction between P and Q at levels i and j, where P¼α,β, γ, δ; Q¼α, β, γ, δ.PQRijk¼ Interaction between P, Q and R at levels i, j, and k,where P¼P¼α, β, γ, and δ; Q¼P¼α, β, γ, δ; R¼P¼α, β, γ, δ.PQRSijkl¼ Interaction between P, Q, R and S at levels i, j, k, and l,where P¼P¼α, β, γ, δ; Q¼P¼α, β, γ, δ; R¼P¼α, β, γ, δ; S¼P¼α, β,γ, δ.

The combination αβij can be read as a single symbol. Thiscombination is called the two-factor interaction between A and B.

In computer models and output, this interaction is denoted by ABor AnB. This denotation is not the product of αi and βj, whichwould be written as αiβj. The use of αβij rather than a new symbolsuch as ωij allows the notation to represent many factors in aconvenient manner. In a study involving four factors, four maineffects, six two-factor interactions, four three-factor interactions,and one four-factor interaction exist. Sixteen unique symbolswould be required to represent all of the effects, and the under-lying model would be difficult to read. However, αβδijl is easilyunderstood to be the three-factor interaction between factors A, B,and D. Furthermore, αβγδijkl is understood to be the four-factorinteraction between factors A, B, C, and D.

Our data analysis was performed in two stages. The first stagewas to find possible significant factors of design factors A, B, C, andD and all interactions including AB, AC, AD, BC, BD, CD, ABC, ABD,ACD, BCD, and ABCD based on the percentage contributions of thedesign factors and all interactions by using the orthogonal arrayL16 (215). The results are 20.01%, 23.16%, 27.03%, 0.49%, 1.31%,8.60%, 0.09%, 5.61%, 0.08%, 0.24%, 10.56%, 1.26%, 0.64%, 0.70%, and0.22%, respectively. The second stage was to assign the factors thathave small contributions to error estimation (or noises). When thethreshold value was set to 0.1%, the percentage contributions of ADand BD are small enough to be pooled as estimation error (ornoises) in the Taguchi method. We then performed one final F-test(Table 4) to determine if the null hypothesis of the interactionshould be rejected or not. The F-value is significant (Po0.05) fortwo two-way interactions (AC and BC) and one three-way inter-action (ABC). Sulfuric acid (factor C) has an important function inthe interaction of components in the response of TBG dosimetersto UV exposure. This result can be explained by the presence ofFe3þ ions, which undergoes a photochemical reaction in an acidsolution (Balog et al., 1999), and the addition of acid to the gel inorder to dissolve the ferric chloride precipitate (Šolc et al., 2010).The incorporation of sulfuric acid into the agarose gels results in adecrease in the elasticity and consistency of the gels. Subsequentmanipulation becomes increasingly difficult with increasing acidconcentration (Schulzf, 1990). However, gel fogging occurs whenpotassium ferricyanide is present in an insufficiently acidic gel.Thus, a similar conclusion about the effect of acid on the UVresponse of TBG can be observed in the Fricke gels.

4. Conclusion

An experimental design based on the orthogonal array of theTaguchi method was conducted to investigate the influence offactors and their interactions. The relative significance of each

Table 4ANOVA results on the effect of components on TBG dosimeters.

Factor Degree of freedom (DF) Sum of squares (SS) Mean square F-value P-value Contribution (%)

A 1 438.1409 438.1409 226.6454 0.0044 20.01B 1 507.3000 507.3000 262.4206 0.0038 23.16C 1 591.9717 591.9717 306.2203 0.0032 27.03D 1 10.6620 10.6620 5.5153 0.1433 0.49AB 1 28.7035 28.7035 14.8480 0.0612 1.31AC 1 188.2479 188.2479 97.3785 0.0101 8.60BC 1 122.9070 122.9070 63.5784 0.0154 5.61CD 1 5.3249 5.3249 2.7545 0.2389 0.24ABC 1 231.3365 231.3365 119.6678 0.0083 10.56ABD 1 27.5375 27.5375 14.2448 0.0636 1.26ACD 1 14.0449 14.0449 7.2652 0.1145 0.64BCD 1 15.3063 15.3063 7.9178 0.1065 0.70ABCD 1 4.7143 4.7143 2.4386 0.2588 0.22Error 2 3.8663 1.9332 0.18

Po0.05, significant.

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factor on the response of TBG dosimeters can be arranged indecreasing order as follows: C4B4A4ABC4AC4BC. Sulfuricacid (factor C) had an important function in two two-way inter-actions and one three-way interaction in the TBG response to UVexposure.

Acknowledgments

This research was funded by the Central Taiwan University ofScience and Technology (CTU101-PC-006).

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