Systematic Statistical-Based Approach for Product Design: Application

Nov 10, 2009 - implemented in other applications. ... In our application of disinfectant ... database using appropriate experimental design techniques...
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Ind. Eng. Chem. Res. 2010, 49, 204–209

Systematic Statistical-Based Approach for Product Design: Application to Disinfectant Formulations Navid Omidbakhsh, Thomas A. Duever,* Ali Elkamel, and Park M. Reilly Department of Chemical Engineering, UniVersity of Waterloo, Waterloo, Canada N2L 3G1

Product formulation development is a difficult and challenging task. The challenges include modeling complex systems and chemicals. Various tests are performed, often on a trial and error basis, to evaluate the performance of the prototypes in the product development process. These tests can be very expensive and time-consuming. A methodology is presented to shorten the product development time and reduce the costs given a database of historical data. It is based on augmenting the existing data set through designed experiments. An empirical model is first developed by analyzing the augmented data set using least-squares regression analysis. The model is then inverted by using an optimization technique, and the product formulation can be predicted on the basis of the desired product specifications. An iterative, sequential approach is employed in which the knowledge gained at each stage is applied in a systematic manner to design further experiments so that the future efforts will need fewer trials. This methodology is illustrated by a case study of disinfectant formulations and is proven to be superior to conventional formulation design methods. These disinfectant formulations consist of primarily water and small amounts of surfactants, oxidizing agents, chelating agents, pH buffers, and pH adjusters and consequently the resulting products are clear liquids. Although the methodology is illustrated on disinfectant product development, it is introduced in this paper in a general way and can be implemented in other applications. Introduction Market competition and the need for product differentiation require the chemical industry to consistently explore new products with improved properties. Despite greater expectation for researchers to develop new products in shorter periods of time, research budgets have not usually increased to meet the demand. On the other hand, traditional trial and error design procedures are labor intensive and expensive in that they require a large number of trials and tests, resulting in a large delay time to market, and do not in general guarantee the optimal formulations. To address this problem, chemical product designs have been given great attention in recent years. The increasing usage of computers in chemical research enables scientists to take advantage of computer-based techniques to design products possessing desired properties. In our application of disinfectant formulations, many of the product types have existed for a very long time; however, only limited knowledge and know-how exists about a systematic approach to design such chemical formulations. In this paper, a systematic methodology for product formulation is presented. First an empirical model is developed relating the formulation ingredients to the product specifications. To start, a historical database is available consisting of previously developed and tested formulations. This database may have to be augmented by a small number of designed experiments to improve the information content of the data. An empirical model is then developed on the basis of the augmented information, where the objective is to obtain a model having good predictive capabilities. By inverting the model, a product specification can then be input into the model and an initial formulation calculated. This formulation is then fine-tuned by conducting a small number of experiments. The methodology that will be discussed is based on recently developed chemical product design concepts in conjunction with * To whom correspondence should be addressed. E-mail: [email protected].

statistical test methods. The objective is to develop a robust approach that can be employed to obtain new formulations based on market demands in the shortest possible time and the least resources. The remainder of this paper is organized as follows. First, a description of the concept of the product formulation design is given, and the new methodology is explained. Subsequently, the methodology is tested in a case study that deals with disinfectant formulations. Product Formulation Design Chemical product design is the procedure consisting of defining product specifications based on market needs, generating ideas to meet these specifications, screening, and, finally, deciding what the product should look like and how it should be manufactured.1 In defining needs, the expectations of the customers should be emphasized. A system of ranking is often employed such as essential, desirable, and useful. The essential needs are those without which the product cannot succeed, and these cannot be neglected. Desirable and useful needs differentiate the product from the competitor products and can have more of a marketing value. Next, the qualitative list of needs must be converted into specifications, including as much quantitative and chemical detail as possible. The final step in the needs stage is to specify a benchmark. This can be an already existing or idealized product against which to measure the new design. If the benchmark cannot be beaten, the product is not worth developing. Once the specifications for the target product formulation are chosen, good product ideas must be generated. In the case of a formulation design, these ideas are usually based on using an appropriate mix of raw materials which leads to the desired specifications. Some candidate raw materials from a previous product design project might be already available. This is the case with most formulation development projects, unless a revolutionary product is

10.1021/ie900196u CCC: $40.75  2010 American Chemical Society Published on Web 11/10/2009

Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010

targeted. The previous projects are usually reviewed to see what useful information can be derived and used in the new project. For example, to design a new disinfectant, this might be achieved using a combination of two or three active ingredients that have been used in an earlier product, or a surfactant blend to increase the cleaning activity of the formulation. Generally speaking, previous information cannot fulfill the requirements of a new product completely, and therefore new concepts need to be investigated. Patents, books, and papers are useful resources to find new concepts for formulation development. They can give very good ideas about some candidate ingredients that were not previously employed and which might be worth trying. The candidate ingredients can be numerous, and it is not realistic or even possible to test them all. Therefore, a few of them must be selected for further investigation. The selection can be done on the basis of some criteria such as candidate ingredients toxicity profile, regulatory limitations, compatibility with other ingredients in the formulation, patent rights, and manufacturing. After the selection of some candidate ingredients, testing must be carried out. By fully taking advantage of a historical database; the final formulation can be obtained by augmenting this database using appropriate experimental design techniques in order to maximize information about the new ingredients at the least possible cost. As an illustration of the above discussion, consider the case of disinfectant formulation. The needs here can be defined as cleaning performance, level of disinfection kill, product toxicity, materials compatibility, and finally product stability. First, brainstorming and research are required to identify possible candidate ingredients. In the case of a revolutionary product, a comprehensive literature search is needed to trigger some valid ideas about new ingredients. Usually, the list of ingredients that contribute to achieve the product specifications is limited, and for each product design, a selection of ingredients from a known list of chemicals that involves antimicrobial agents, builders, surfactants, solvents, and pH buffers is made. Antimicrobial agents can be selected from alcohols, phenols, oxidizing agents (chlorine dioxide, sodium hypochlorite, hydrogen peroxide, and peracetic acid), and aldehydes (glutaraldehyde, orthophtaldehyde, and formaldehyde), etc. Surfactants can be used in the formulation to improve the cleaning and disinfection properties. Builders are used to improve other properties including the shelf life by stabilizing the antimicrobial active agent. A pH buffer is usually chosen from weak acids (e.g., phosphoric acid, citric acid, lactic acid, and boric acid) and is used to stabilize the pH of the solution since pH is an important factor in antimicrobial activity.2 Such ingredients can be found by conducting a literature search in disinfection and detergent textbooks, patents, and papers.3-5 In selecting combinations of such ingredients in a formulation, different factors should be considered such as the following: (1) the toxicity of each ingredient (ingredients in the same class, with lower toxicity, should be considered); (2) regulatory considerations (each government has a list of banned ingredients which should be avoided); (3) cost of raw material (the product should not be too expensive to be economically viable); (4) patent rights (especially in selecting combination of ingredients, the formulator must take into account the competitor patents, to avoid any infringements and subsequent legal prosecutions).

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After the candidate list of ingredients is screened according to these criteria, the product is developed on the basis of the procedure shown in this paper, a schematic of which is shown in Figure 1. Case Study Infection control is now one of the biggest challenges in the health care industry. Infectious diseases are the third leading cause of death in the United States, behind heart disease and cancer.6 With the emergence of new pathogens as well as antibiotic resistant microorganisms, more effective disinfectants are required. Designing a disinfecting formulation is a difficult task, as the formulator has to make a balance between product safety and antimicrobial activity.7 A disinfecting formulation must be tested for its antimicrobial efficacy to make sure that it is effective. The quantitative antimicrobial test results can be presented in kill percentage, such as 99 or 99.9%, or in log reduction, which is the log of the kill percentage. Therefore, when designing a new product, the antimicrobial activity is expressed in terms of one of these measures and has to be greater than a specified value. It is desired to develop a new antimicrobial formulation to reduce the count of bacteria by 99.9999% or a 6 log reduction. To evaluate the bactericidal activity of antimicrobial formulations, a quantitative carrier test method8 was used. In this method, the inside bottom surface of glass vials is used as the carrier for all tests except those against viruses. For inoculation of the carriers, all test organisms are first suspended in bovine serum at a final concentration of 5%. Letheen broth (with 0.1% sodium thiosulfate pentahydrate) is used as the neutralizer and as a rinse for the membrane filters and the filter holder unit. Normal saline is used to make dilutions of the bacterial suspensions and as the final rinse of the carrier vials and the filter holder unit to aid in rinsing off the froth created by the Letheen broth. The test involves drying a microbial suspension on a hard surface carrier and covering the dried inoculum with the disinfectant for the specified contact time at room temperature. At the end of the contact time, an eluent/rinse is used to recover the reaction mixture from the carrier and the eluate is passed through a membrane filter (0.22 µm pore diameter) to capture the test organism. The filters are then placed on plates of suitable recovery agar medium and incubated to allow viable organisms to form visible colonies. The numbers of colony forming units (CFU) are recorded, and the level of inactivation of the test organism is calculated. Different types of microorganisms can be used with this test method. However, to reduce the number of experiments in the screening process, a surrogate from each category of microorganisms is used. The surrogate is a microorganism which is known to have the least biocide susceptibility in its class. A standard strain of Staphylococcus aureus (S. aureus; ATCC 6538) was used in this study. Table 1 shows the historical data from previous experiments performed in Virox Technologies, Ontario, Canada. For confidentiality purposes, the ingredients in the formulations are illustrated by variables x1, x2, x3, ..., x8, where x1 is an oxidizing agent, x2, x6, and x7 are surfactants, x3 is a chelating agent, x4 is the pH of the solution, x5 is a stabilizer, x8 is a buffering agent, and LR is the microbial log reduction in 3 min contact time using the QCT test method as specified above. In the following, where the factors have been shown in capital letters (X1-X8), they represent the coded factors, and the small letters (x1-x8) represent the weight percentages or for pH; x4 presents the actual value of the pH.

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Figure 1. Systematic disinfecting formulation product design. Table 1. Historical Data for Antimicrobial Tests against Staph in Coded Format X1

X2

X3

X4

X5

X6

y

0.88 1.2 0.88 0.88 1.2 1.2 2.2 1.4 0.6 2.2

0.733333 1 0.733333 0.733333 1 1 0.666667 0.666667 0.666667 0.666667

0.868 0.92 0.868 0.868 -1 0.92 -1 -1 -1 0.92

-1 1.625 -1 -1 -0.9375 1 -1 -1 -1 -1

0.733333 1 1 1 1 1 -1 -1 -1 -1

0.666667 1 0.666667 -1 -1 1 -1 -1 -1 -1

6.13 4.3 6.24 6.24 6.85 3.5 6.76 6 5 7

pH has been used here as an independent factor since it is known to affect the antimicrobial activity of solutions. Therefore, it is controlled in each trial by using either potassium hydroxide

or sulfuric acid to either increase or decrease it. These pH adjusters, at the levels used in these experiments, do not have any antimicrobial activity and therefore do not interfere with other factors used here. It can be easily seen from Table 1 that the changes in X1 and X2 are not large enough, thus leading to a poor estimate of the effects of these factors. Since it is already known from the literature that these two factors are effective antimicrobials, analyzing the above historical data cannot be conclusive. These have been generated during previous formulation development projects in the past and are not based on statistically designed experiments. The historical data were augmented with additional experiments so that the new data set will yield a more conclusive model. In this case study, two new ingredients were also tested

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Table 2. Fractional Factorial Design To Augment the Historical Data X1

X2

X3

X4

X5

X7

X8

X6

y

-1 1 -1 0 1 -1 0 -1 1 0 1 -1 -1 1 1 0 -1 1 1 -1

1 -1 1 0 -1 -1 0 -1 1 0 1 1 1 -1 -1 0 -1 1 1 -1

1 -1 1 0 -1 1 0 1 -1 0 -1 -1 -1 1 1 0 -1 1 1 -1

1 -1 -1 0 1 -1 0 1 -1 0 1 1 -1 -1 1 0 -1 1 -1 1

-1 1 -1 0 1 1 0 1 -1 0 -1 1 1 -1 -1 0 -1 1 1 -1

-1 1 1 0 -1 -1 0 1 -1 0 1 -1 1 1 -1 0 -1 1 -1 1

-1 1 1 0 -1 1 0 -1 1 0 -1 1 -1 -1 1 0 -1 1 -1 1

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

1.5 7 3.24 4 3.11 3.9 3.89 1 6.28 3 2.34 1.33 6.46 4.5 1.12 4 2.04 4.1 6.68 1.8

in addition to the existing ones. These were selected on the basis of their known low toxicity and potential antimicrobial activity. Furthermore, it was decided to eliminate x6 from the experiments since it is known from the literature that this ingredient has no antimicrobial activity. A disinfection formulation is a mixture of different ingredients such as oxidizing agents, surfactants, and stabilizers, etc. Ordinarily, the general approach to designing experiments for determining an optimal disinfectant recipe is to use mixture designs.9 Recipe formulation experiments differ from other experiments involving process variables such as pressure and temperature in that we are interested in the effects of the proportions rather than the absolute level of a factor. Of course the proportion over all the ingredients must equal 100%. However in the case where the majority of the ingredients are present in small quantities and can be considered to be additives to the major component such as water in the disinfectant formulation, the strategy which can be used is to study the effects of the different amounts of the additives using a factorial design. The amount of water used is therefore equal to 100% minus the sum of the additives. This approach is used here. Two-level or fractional two-level factorial designs are particular efficient designs to use for this purpose.10 They are designed to yield uncorrelated estimates of the effects of the input factors and their interactions and hence maximize the information obtained. It is anticipated that the addition of information obtained from such an experiment to the historical data set will significantly improve the predictive capabilities of the resulting models. If a full factorial design is implemented, 28 or 128 trials will be required to be performed. Therefore, a fractional factorial design is used here to only test a portion of the 128 trials. In this case study, a resolution IV fractional factorial design is performed as shown in Table 2. A resolution R design confounds main effects with interactions of no more than (R 1) factors. So if a design is of resolution IV, main effects are confounded with at most three-factor interaction. The fractional factorial design experiments data are added to the historical data, and the full data set is then analyzed using a multiple regression analysis. This analysis is performed to develop a model for the microbial log reduction versus ingredient concentrations and pH. The theoretical background for the least-squares multiple regression analysis has been published extensively by many authors.11

Figure 2. Box-Cox transformation for a linear model for the microbial data.

A simple form of the linear model can be written as follows: y ) β0 + β1x1 + β2x2 + ...+βkxk + 

(1)

where y denotes the response, x1-xk are the predictor variables, and β0, β1, ..., βk are the unknown parameters. This model would be applicable if only main effects were important. However, in this case study, the model is not this simple. Although the model being developed is empirical in nature, some prior knowledge about the nature of the relationship between variables was injected. For example, it is known from experience that log reduction (LR) varies with the reciprocal of pH (X4). Therefore, new predictive variables were generated by dividing each variable by X4. The new variables will be z1, z2, z3, z4, z5, z6, z7, and z8, where zi ) xi/x4. In many cases the original metric of the response variable (y) may not necessarily be the correct one to use. To ensure that the standard assumptions of linear regression are met, we allow for a possible transformation of y. Here we employ the Box-Cox transformation methodology11 to search for an optimal metric. The model therefore has the following general form: LRλ ) β0 + β1z1 + β2z2 + β3z3 + ...+

(2)

Figure 2 shows the results of the Box-Cox analysis. This plot shows the log-likelihood function for the parameter λ. The optimum value is 1.7; however, the confidence interval for λ includes 2, which is the value used here. The fitted model then is LR2 ) -3.24 + 87.6x1 + 145x2 - 15.8x3 + 647.7x5 + 89.53x6 x4

(3)

R2 ) 93.7% adjusted R2 ) 92.4% predicted R2 ) 88.92% In eq 3, the variables x1-x6 are in uncoded format. Both the R2 and adjusted R2 values are reasonably large, given the relative large error which is present in the log reduction measurements. Furthermore the predicted R2 which is defined as 1 - (PRESS/SST), where PRESS represents the prediction error

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Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010 Table 3. Analysis of Variance source

DF

SS

MS

F

P

regression residual lack of fit pure error total

5 24 20 4 29

7712.8 520.1 485 34.3 8232.9

1512.8 21.7 24.3 8.6

71.18

0.000

2.83

0.161

model gives a reasonably good fit to the data and provides good predictive power. Optimization

Figure 3. Normal probability plot of the residuals.

In the previous section, a model was developed to predict the microbial kill. In this section, the question of how to design a product that will possess certain specified properties will be considered. To accomplish this task and predict the formulation based on desired product specifications, an optimization model with the aim of inverting the prepared model is employed. The objective of the case study is to minimize the toxicity of the formulation. The toxicity of a disinfectant can be measured in several ways, but usually human toxicity is estimated on the basis of test results on rats and other animals. One such measure is the acute oral LD50, and it means a dose of a substance that when fed to laboratory animals, causes 50% of them to die12 and is the amount of a substance that is fed to the test animal per unit weight. On the basis of this definition, the higher the LD50 of a substance, the less its toxicity. Therefore, the objective of the optimization model is written as follows: n

f) Σ

xi

i)1 LD50(xi)

Figure 4. Plot of residuals versus observation order.

+

1 x4

(4)

This objective function encourages the optimization program to use the least amount of ingredients at the highest possible pH (X4). In our case study, the solutions are acidic, and therefore the highest possible pH is closest to the neutral value of pH 7. In addition, the following two constraints are applied: (1) microbial log reduction g specified value; (2) ingredients concentration and pH upper and lower bounds (to be in the prespecified range). The microbial log reduction model (eq 3) that was discussed in the last section is nonlinear, and therefore a nonlinear optimization technique should be implemented. In this work, the LevenbergMarquardt (LM) optimization method13,14 will be used. The Matlab software version 7.0 (The MathWorks, Inc., Natick, MA) was used to solve the optimization program. Including values for LD50 for the different ingredients, the objective function is recast as follows: Figure 5. Measured log reduction versus calculated.

sum of squares and SST is the total sum of squares, is also high, indicating that the model has good predictive capability. The normal probability plot as shown in Figure 3 shows that the residuals are reasonably close to normally distributed which satisfies the normality assumption of the least-squares regression analysis. The residual plot in Figure 4 does not show a trend. Also the measured log reductions versus the predicted values in Figure 5 are quite acceptable. Table 3 shows the analysis of variance. The p-value corresponds to the hypothesis test on the regression model. A p-value less than 0.1 indicates that the parameter is significant. The p-value of less than 10-3 shows that the model is significant. The above-mentioned diagnostics indicate that the

{

product toxicity ) min

x2 x3 x1 1 + + + + 4060 1260 2400 x4 x6 x7 x8 x5 + + + 891 2000 5000 1530

}

(5)

The constraint on microbial log reduction becomes, after including the prepared empirical correlation (eq 3), LR )



87.6x1 + 145x2 - 15.8x3 + 647.7x5 + 89.53x6 -3.24 + g6+ x4

t

R ,n-p 2

√σˆ 2(x0′(X′X)-1x0)

(6)

Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010 Table 4. Optimal Formulation Obtained by the Optimization ingredient

lower bound

upper bound

optimization results

X1 X2 X3 X4 X5 X6 X7 X8

-1 -1 -1 -1 -1 -1 -1 -1

1 1 1 1 1 1 1 1

1 1 -1 -0.25 1 1 -1 -1

where x0 is [1, x01, x02, ..., x08] and is defined as a future formulation and [(tR/2n -p)(σˆ 2(x0′(X′ X)-1x0))1/2]1/2 accounts for the prediction error of the model. The formulation of the constraint on LR (eq 6 above) takes into account the model prediction error. In other words, the LR is predicted in this work using a regression model, which leads to a prediction which is subject to uncertainty. Therefore the constraint is specified as the upper limit of the prediction interval. To simplify the optimization program, the average prediction error is calculated and used here. Simulation results for 1000 random x0 show an average of 1.55 for the prediction error. The second constraint details, namely, the upper and lower bounds, as well as the optimization results are shown in Table 4. The lower bounds for all ingredients were set to zero since the ingredient concentrations cannot be less than zero percent. If an ingredient must be present in the formulation for some reason, then the lower bound for this ingredient will be set accordingly. The upper bounds have been defined on the basis of the maximum allowable ingredient concentration. These allowable concentrations can be defined on the basis of regulatory requirements, marketing demands, etc. It should be noted that these ranges should conform to those used in developing the microbial log reduction model due to the fact that the constraint model is empirical and any extrapolation can result in high model prediction error. The predicted formulation was prepared and tested for its microbial activity against S. aureus using the above-mentioned test method and conditions, and it gave about 7.62 LR. The log reduction constraint was 6, and therefore the formulation meets the criterion. In other words, the formulation is optimized in one step, without the need for further fine-tuning experiments. Concluding Remarks Chemical formulation design is a challenging task. It can take a few years of intense research and development from the discovery of an active ingredient until its market introduction. However, a new formulation containing a mixture of already known active ingredients can be on the market much quicker. In addition, it has become more and more difficult to find better active ingredients, which are more user-friendly, safer, and cheaper to manufacture and have increased efficacy. Therefore, the design of the formulation is now business critical. In formulation design, a product formulation has to be developed through a very wide range of chemicals.15 Solvent mixture, polymer, detergent, adhesive formulations, oil blend, and additives in specialty chemical products are examples of

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formulation design. Here, the goal is to find a combination of different raw materials, which, when mixed together, deliver some desirable properties. In product formulation design, the identity of the final formula is not known, but it is known what the desired behavior is. The problem here is to find the most appropriate formulation that will exhibit the desired behavior. In this work, we have demonstrated a technique for developing a new disinfectant formulation, which combines prior information in the form of an existing database of previous experimental results with new experimental data from designed experiments. Multiple linear regression is then used to fit an empirical model to describe antimicrobial activity (LR) as a function of the formulation ingredients and pH. A new disinfectant formulation is then designed by formulating and solving an optimization problem which inverts the model. Here a case study is presented in which the primary objective is to minimize product toxicity subject to a minimum antimicrobial activity constraint and upper and lower concentration and pH constraints. Subsequent testing showed that the new formulation designed using the proposed procedure met all of the required specifications. Literature Cited (1) Cussler, E. L.; Moggridge, G. D. Chemical Product Design; Cambridge University Press: Cambridge, U.K., 2001. (2) Bean, H. S. Types and Characteristics of Disinfectants. J. Appl. Microbiol. 1967, 30, 6–16. (3) Block S. S. Disinfection, Sterilization, and PreserVation; Lippincott Williams & Wilkins: New York, 2001. (4) Russell, A. D.; Hugo, W. B.; Ayliffe, J. A. Principles and Practice of Disinfection, PreserVation and Sterilization; Blackwell Scientific: Oxford, U.K., 1999. (5) Zoller, U. Handbook of Detergents, Part E: Applications; Surfactants Science Series; CRC Press: New York, 2009. (6) Gurusamy, M. Disinfection and Decontamination; Taylor & Francis: Levittown, PA, 2007. (7) Omidbakhsh, N.; Sattar, S. A. Broad-spectrum microbicidal activity, toxicologic assessment, and materials compatibility of a new generation of accelerated hydrogen peroxide-based environmental surface disinfectant. Am. J. Infect. Control 2006, 34, 251–257. (8) Standard QuantitatiVe Carrier Test Method To EValuate the Bactericidal, Fungicidal, Mycobactericidal and Sporicidal Potencies of Liquid Chemical Germicides, Vol. 11.05; ASTM International: West Conshohocken, PA, 2000; ASTM E2111-05. (9) Cornell, J. A. Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data; John Wiley and Sons: New York, 1990. (10) Montgomery, D. C. Design and Analysis of Experiments; John Wiley and Sons: Hoboken, NJ, 2004. (11) Montgomery, D. C.; Peck, E. A.; Vining, G. G. Introduction to Linear Regression Analysis; John Wiley and Sons: New York, 2006. (12) Miller, T. L., Ed. Oregon Pesticide Applicator Manual: A Guide to the Safe Use and Handling of Pesticides; University Extension Service, Oregon State: Corvallis, OR, 1993. (13) Levenberg, K. A Method for the Solution of Certain Problems in Least Squares. Quart. Appli. Math. 1944, 2, 164–168. (14) Marquardt, D. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. SIAM J. Appl. Math. 1963, 11, 431–441. (15) Gani, R. Chemical Product Design: Challenges and Opportunities. Comput. Chem. Eng. 2004, 28, 2441–2457.

ReceiVed for reView February 4, 2009 ReVised manuscript receiVed October 12, 2009 Accepted October 22, 2009 IE900196U