- Research
- Open Access
Evaluation of the Taguchi methods for the simultaneous assessment of the effects of multiple variables in the tumour microenvironment
- Hisham Morsi^{1},
- Kwee L Yong^{2} and
- Andrew P Jewell^{1}Email author
https://doi.org/10.1186/1477-7800-1-7
© Morsi et al; licensee BioMed Central Ltd. 2004
- Received: 11 August 2004
- Accepted: 20 September 2004
- Published: 20 September 2004
Abstract
Background
The control of proliferation, differentiation and survival of normal and malignant cells in the tumour microenvironment is under the control of a wide range of different factors, including cell:cell interactions, cytokines, growth factors and hormonal influences. However, the ways in which these factors interact are poorly understood. In order to compare the effects of multiple variables, experimental design becomes complex and difficult to manage. We have therefore evaluated the use of a novel approach to multifactorial experimental design, the Taguchi methods, to approach this problem.
Method
The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In order to evaluate these methods, we have used a simple and robust system to compare a traditional experimental design with the Taguchi Methods. The effect of G-CSF, GM-CSF, IL3 and M-CSF on daunorubicin mediated cytotoxicity in K562 cells was measured using the MTT assay.
Results
Both methods demonstrated that the same combination of growth factors at the same concentrations minimised daunorubicin cytotoxicity in this assay.
Conclusions
These findings demonstrate that Taguchi methods may be a valuable tool for the investigation of the interactions of multiple variables in the tumour microenvironment.
Keywords
- Malignant Cell
- K562 Cell
- Orthogonal Array
- Daunorubicin
- Taguchi Method
Introduction
The control of proliferation, differentiation and survival of normal and malignant cells is under the control of a wide range of different factors. These include cell:cell interactions, immune regulatory factors, hormonal influences, and local environmental influences. However, the way in which these factors interact to regulate the dynamics of the malignant cell population are poorly understood. It is important to identify important factors and the way that they interact in order to rationalise treatment and develop new therapeutic options. However, one of the main problems is the difficulty in designing experiments to compare the effects and interactions of multiple variables. For example, a traditional experimental design to compare seven independent variables at three different concentrations each requires a large number of individual experiments (2187 experiments). The logistical and resource implications of this experimental design make these experiments very difficult to carry out. We have investigated the use of an alternative approach to experimental design, the Taguchi Methods [1]. Taguchi methods use orthogonal array distribution to design an experiment producing smaller, less costly experiments that have a high rate of reproducibility. A study involving 7 factors at 3 different concentrations can be conducted with only 18 individual experiments. Besides being efficient, the procedures for using Taguchi designs and methods are straightforward and easy to use. These methods have previously been used in PCR optimisation [2, 3], baculovirus expression [4], ball and socket prosthesis design for total hip replacement surgical procedure [5], ELISA optimisation [6], and also in the evaluation of medical diagnostic tests [7, 8].
We have therefore used a simple and reproducible assay, the MTT assay, to evaluate whether the Taguchi methods can be used to investigate the effect of G-CSF, GM-CSF, IL3 and M-CSF on daunorubicin mediated cytotoxicity in K562 cells.
Taguchi Methods
Orthogonality. The relationship between one column and another is arranged so that for each level within one column, each level within any other column occurs an equal number of times as well. Factor A, at level 1 occurs 4 times and at level 2 occurs 4 times as well. This equal occurrence is true for all factors involved in any orthogonal array.
A | B | C | D | E | F | G | Results | |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | Y1 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | Y2 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | Y3 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | Y4 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | Y5 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | Y6 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | Y7 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | Y8 |
Each array can be identified by the form L_{ A }(B^{ C }), the subscript L, which is designated by A, represents the number of experiments that would be conducted using this design, B denotes the number of levels or concentrations within each column which denotes how many levels or concentrations could be investigated, while the letter C identifies the number of columns available within the orthogonal array which indicates how many factors or variables could be included in the experiment [1]. For example the orthogonal array L_{8}(2^{7}) means that 8 experimental runs are needed to investigate 7 different factors, each of which is set at 2 predetermined levels or concentrations (Table 1). The statistical independence of these arrays enables the effect of each factor to be separated from the others, the effects to be accurate and reproducible because the estimated effect does not include the effects of other factors and the interactions between these factors to be determined.
Level average analysis, as described by Taguchi [1] is one of the techniques used to explore the results of the Taguchi methods. The name derives from determining the average effect of each factor on the outcome of the experiment. The goal is to identify those factors that have the strongest effects and whether they exert their effect independently or through interacting with other factors.
The equation below illustrates the method of calculating the average effect of the experiment where Y1 is the result of the first experiment, Y2 is the result of the second experiment...etc, T is the overall average of the experiment, and n is the number of the experimental runs.
For example, in order to calculate the effect of the two concentrations of factor A, which are denoted A1 and A2, where A1 is the average effect of factor A at concentration 1, A2 is the average effect of the same factor at concentration 2.
The relative impact of each factor (ΔX) is simply the range, which could be calculated as the difference between the highest and lowest average response of each level. For example the impact of factor A on the experiment outcome is the difference between A1 & A2. (Known statistically as the range (Δ)). The effects of all factors are calculated in the same way, then arranged in a response table, and examined for those factors with the strongest effect (i.e. highest difference Δ), in order to separate them from the weak effects. The breaking point between the strong and weak effects is identified as a change in the pattern of the difference between the ranges around the median.
Besides determining the effects of the individual factors, the same technique is used to determine the strength of the impact of interactions on the product of the experiment. The calculations are performed as the previous section. In order to determine the interactions between A and B, the average result of each 2 factors combined must be determined. This is achieved through calculating the values of 4 points: A1B1, A1B2, A2B1, and A2B2, where A1B1 is the average result generated due to the interaction between concentration 1 of both factors, A1B2 is the result of the interaction between concentration 1 of factor A and concentration 2 of factor B, A2B1 represents the interaction between factor A at concentration 2 and factor B at concentration 1, while the fourth point A2B2 is the interaction between both factors at concentration 2. These 4 points are then presented graphically to show the strength or weakness of the interaction. Whether the interaction is weak, mild, or strong depends on whether the two response lines are parallel, converging or intersecting, with intersecting lines indicate a strong interaction, and parallel lines indicate no interactions. Once the strong factors and interactions have been identified, an estimate of their combined effect is calculated and the new experiment is designed according to these assumptions. An experiment is then carried out – referred here to as "confirmation run"- to validate the assumptions upon which the new experiment was based. Conducting a confirmation run and the comparison between the actual and the predicted results is necessary. If however, the confirmation results are disappointing, the planning phase must be re-evaluated and the elements that went into the experiment must be reviewed. A possible cause could be the omission of a key factor from the experiment, for example a powerful interaction was not considered. Another common cause is the setting of factor levels too close together for the experiment. In these situations, the factor is found insignificant during the analysis and is not accounted for in the validation. The confirmation run should include the best or preferred settings for mild and weak influences as well as the strong ones. However, the less influential factors are not incorporated into the prediction equation. The reasoning is that the differences in the average results may be due to experimental variation, and to incorporate their effects could result in an overestimate of the predicted results. This could lead to a disappointing confirmation run when actually the results would have validated the experiment analysis if the predicted results had not been artificially high or low.
Methods
Cell Culture
K562 cells were cultured in RPMI-1640 medium supplemented by 10% (v/v) foetal bovine serum, 50 μg/ml penicillin and 25 μg/ml streptomycin at 37°C in a humidified atmosphere of 5% CO_{2}-95% air. Cells were plated in 96 well microtiter plates (200 μl) at a density of 3 × 10^{4} cells/ml. Cells were co-cultured in the presence of 0.1 μg/ml daunorubicin.
Cytokines
Concentrations of cytokines used.
1 | 2 | ||
---|---|---|---|
A | MCSF | 100 U/ml | 300 U/ml |
B | IL3 | 10 ng/ml | 50 ng/ml |
C | GMCSF | 10 ng/ml | 50 ng/ml |
D | GCSF | 10/ ng/ml | 50 ng/ml |
MTT Assay
50 μl of MTT (3–4,5-dimethylthiazol 2,5-diphenyl tetrazolium bromide) (5 mg/ml) was then added to each well and incubated at 37°C for 4 hours. The resulting deep blue crystals were dissolved in 0.04 N HCl Isopropyl alcohol, and the absorbance measured using a scanning multiwell spectrophotometer at dual wavelength 570–630 nm. All measurements were performed in triplicates.
The % survival was calculated as
Classical Experimental Design
The whole set of the 49 experiments carried out. Runs 1–16 included all possible combinations of all cytokines together (see text above). In runs 17–24 individual cytokine were added to the medium, two concentrations of each cytokine was tested. For example in run 17 MCSF was added to the medium at concentration 1 (100 U/ml), while in run 18 the same cytokine was added at concentration 2 (300 U/ml). Runs 25 – 48 included the different possible interactions between each 2 cytokines, for example in run 25 both MCSF (100 U/ml) and IL-3 (10 ng/ml) were added, in run 26 MCSF (100 U/ml) and IL-3 (50 ng/ml) were added, in run 27 MCSF (300 U/ml) and IL-3 (10 ng/ml) were added, and in run 28 MCSF (300 U/ml) and IL-3 (50 ng/ml) were added. Experimental run 49 was carried out without adding any cytokines to the medium. All experimental runs were done in triplicate and repeated three times.
A MCSF | B IL-3 | C GMCSF | D GCSF | |
---|---|---|---|---|
1 | 1 | 1 | 1 | 1 |
2 | 1 | 1 | 2 | 2 |
3 | 1 | 2 | 1 | 2 |
4 | 1 | 2 | 2 | 1 |
5 | 2 | 1 | 1 | 2 |
6 | 2 | 1 | 2 | 1 |
7 | 2 | 2 | 1 | 1 |
8 | 2 | 2 | 2 | 2 |
9 | 1 | 1 | 1 | 2 |
10 | 1 | 2 | 1 | 1 |
11 | 1 | 1 | 2 | 1 |
12 | 1 | 2 | 2 | 2 |
13 | 2 | 1 | 1 | 1 |
14 | 2 | 2 | 2 | 1 |
15 | 2 | 1 | 2 | 2 |
16 | 2 | 2 | 1 | 2 |
17 | 1 | 0 | 0 | 0 |
18 | 2 | 0 | 0 | 0 |
19 | 0 | 1 | 0 | 0 |
20 | 0 | 2 | 0 | 0 |
21 | 0 | 0 | 1 | 0 |
22 | 0 | 0 | 2 | 0 |
23 | 0 | 0 | 0 | 1 |
24 | 0 | 0 | 0 | 2 |
25 | 1 | 1 | 0 | 0 |
26 | 1 | 2 | 0 | 0 |
27 | 2 | 1 | 0 | 0 |
28 | 2 | 2 | 0 | 0 |
29 | 1 | 0 | 1 | 0 |
30 | 1 | 0 | 2 | 0 |
31 | 2 | 0 | 1 | 0 |
32 | 2 | 0 | 2 | 0 |
33 | 1 | 0 | 0 | 1 |
34 | 1 | 0 | 0 | 2 |
35 | 2 | 0 | 0 | 1 |
36 | 2 | 0 | 0 | 2 |
37 | 0 | 1 | 1 | 0 |
38 | 0 | 1 | 2 | 0 |
39 | 0 | 2 | 1 | 0 |
40 | 0 | 2 | 2 | 0 |
41 | 0 | 1 | 0 | 1 |
42 | 0 | 1 | 0 | 2 |
43 | 0 | 2 | 0 | 1 |
44 | 0 | 2 | 0 | 2 |
45 | 0 | 0 | 1 | 1 |
46 | 0 | 0 | 1 | 2 |
47 | 0 | 0 | 2 | 1 |
48 | 0 | 0 | 2 | 2 |
49 | 0 | 0 | 0 | 0 |
Taguchi Design L_{8}(2^{7})
Taguchi method L_{8}(2^{7}). This array accommodated 4 different factors (MCSF, IL-3, GMCSF, and GCSF) each at 2 different concentrations (see above). 8 experimental runs were carried out according to the combination of factors in the array, for example, in experimental run 1 the MTT assay was carried out after mixing the cells with 100 U/ml MCSF, 10 ng/ml IL-3, 10 ng/ml GMCSF, and 10 ng/ml GCSF. The interaction between MCSF and the other three factors (IL-3, GMCSF and GCSF) was studied in this array.
A MCSF | B IL3 | AxB | C GMCSF | AxC | AxD | D GCSF | |
---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 |
5 | 2 | 1 | 2 | 1 | 1 | 1 | 2 |
6 | 2 | 1 | 2 | 2 | 2 | 2 | 1 |
7 | 2 | 2 | 1 | 1 | 1 | 2 | 1 |
8 | 2 | 2 | 1 | 2 | 2 | 1 | 2 |
Results and Discussion
Results of the classical design
The survival of K562 cells, using the 4 cytokines simultaneously was maximally enhanced by the addition of 300 U/ml MCSF, 50 ng/ml IL-3, 50 ng/ml GMCSF, and 50 ng/ml GCSF. A significant improvement in cell survival from 69% to 76% (P 0.02) was observed
Taguchi analysis
the results of L_{8}(2^{7}). Each experimental run was done in triplicate and repeated 3 times, the mean values were calculated and the results were expressed as mean ± SE. Y1 (experimental run 1), for example, = the mean survival of the cells at 100 U/ml MCSF, 10 ng/ml IL-3, 10 ng/ml GMCSF, and 10 ng/ml GCSF. The overall average of the experiment (T) was calculated as the mean of all eight experimental runs.
% survival | |
---|---|
Y1 | 60.71 ± 5.9 |
Y2 | 67.83 ± 1.9 |
Y3 | 64.01 ± 1.1 |
Y4 | 63.51 ± 2.0 |
Y5 | 62.97 ± 4.3 |
Y6 | 72.27 ± 4.3 |
Y7 | 62.86 ± 1.1 |
Y8 | 39.84 ± 1.9 |
T | 61.75 |
For example the mean effect of MCSF when added to the medium at a concentration of 100 U/ml was computed as follows:
When MCSF was added to the medium at a concentration of 300 U/ml the mean effect was:
Response table for the orthogonal array L_{8} (2^{7}). The average effect of each factor level is calculated and the range of effect of each factor is calculated as the difference between the two readings. The range of MCSF effect, for example = 64.02-59.48 = 4.53, the higher the range the stronger the effect of the factor. In this experiment the interaction between MCSF and GCSF had the strongest effect on the survival of cells.
A = MCSF | B = IL3 | AxB | C = GMCSF | AxC | AxD | D = GCSF | |
---|---|---|---|---|---|---|---|
1 | 64.02% | 65.95% | 57.81% | 62.64% | 59.21% | 56.76% | 64.84% |
2 | 59.48% | 57.55% | 65.69% | 60.86% | 64.29% | 66.74% | 58.66% |
Δ | 4.53 | 8.39 | 7.88 | 1.77 | 5.08 | 9.98 | 6.17 |
2 | 3 | 1 | 4 |
Descending rearrangement of the response table according to strong and weak effects. The response table was rearranged according to the Δs, and the difference between the Δs was calculated and then scanned to determine the break point, which was identified as a change in the pattern of the difference between the Δs around the median. The strong factors would be on the left hand side of the break point, marked in this table in bold.
AxD | B = IL3 | AxB | D = GCSF | AxC | A = MCSF | C = GMCSF |
---|---|---|---|---|---|---|
9.985% | 8.391% | 7.884% | 6.173% | 5.088% | 4.533% | 1.774% |
1.594 | 0.507 | 1.711 | 1.085 | 0.555 | 2.759 |
Interaction matrix AxD. The average effect of the four points of this interaction matrix on the survival of K562 cells. The preferred setting of this interaction that would maximise the cytotoxicity of daunorubicin is A2D2 i.e. 300 U/ml of MCSF and 50 ng/ml of GCSF. This combination would result in a survival of 51.67% of the cells.
D1 | D2 | |
---|---|---|
A1 | 62.11% | 65.92% |
A2 | 67.56% | 51.67% |
A1D1 is the average result of the combined effect of MCSF at a concentration 100 U/ml and GCSF at a concentration of 10 ng/ml.
An estimate of the predicted response (μ) based on the selected levels was then computed. The calculations were based on the overall average value (T) and the effect that each of the recommended levels of the strong factors and interactions has on the overall average.
μ = T+(A2D2 - T)+(B2 - T)+(A2C2 - T)+(A2B2 - T)-(A2 - T)-(A2 - T)-(A2 - T)-(B2 -T)-(C2-T).
The reason for subtracting the individual effects of factors A, B, and C from the effects of A2B2 is that A2B2 is comprised of the effects of factor A, factor B and the interaction itself. Unless the effects of the two factors are subtracted these strong effects would be included twice and resulting in an overestimation of the predicted result.
The predicted survival derived from the above prediction equation was 43%. A confirmation run that produces a %survival close to 43%would validate the assumptions of this Taguchi method. The actual confirmation run, in fact, resulted in 39.84% survival rate indicating the success of the Taguchi experiment.
Further comparison of the predicted values from the Taguchi Methods, and the result produced by experimental analysis.
Prediction | Analysis | |
---|---|---|
Experimental run 9 | 66.10% | 70.35% |
Experimental run 10 | 71.93% | 74.38% |
Experimental run 11 | 66.14% | 63.36% |
Experimental run 12 | 67.65% | 65.36% |
Experimental run 13 | 48.90% | 45.69% |
Experimental run 14 | 51.46% | 55.22% |
Experimental run 15 | 63.65% | 74.88% |
Experimental run 16 | 72.19% | 76.74% |
Conclusion
The aim of this study was to evaluate the ability of the Taguchi methods to investigate the effects of several factors simultaneously on the death and/or survival of the malignant cells, and to compare this strategy against a traditional full experimental design.
A major finding of the study was that the Taguchi methods predicted the combination of factors that results in the lowest survival of the malignant cells. This agreed with the conclusions of the full experimental design but required only eight individual experiments to pinpoint this combination. However, it must be stressed that the Taguchi methods are not intended to be a replacement for traditional experimental design, but if used as a complimentary strategy can make analysis of complex interactions feasible and practical. In this study, for example, eight individual experiments produced a testable combination which required 49 individual experiments to produce in the traditional experimental design. In more complex systems, only Taguchi methods become feasible. For example, to study 13 factors at 3 different combinations would require 1,594,323 individual experiments at a cost for re agents alone of over 27 million pounds. If Taguchi methods are used, this can be reduced to just 27 individual experiments at a cost of under 500 pounds.
We have described a novel experimental approach to studying the interactions of several factors on the cytotoxicity of malignant cells. We show that the method is effective in the determination of the optimum conditions, even in the presence of multiple interactions. We anticipate that this experimental strategy will have many applications in the investigation of complex interactions. For example we have used this strategy to model the complex testicular microenvironment and the ability to support the survival of acute lymphoblastic leukaemia cells (manuscript in preparation). These sort of interactions are common in the survival of malignant cells in vivo, and we propose that the Taguchi methods may be a useful strategy to understand these interactions in vitro, and to help devise and implement new therapeutic strategies.
Declarations
Authors’ Affiliations
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