Taguchi’s experimental designmethod on improvement of

medical image qualityMehmet Tolga Taner and Bulent Sezen

Department of Management, Gebze Institute of Technology,Kocaeli, Turkey

Abstract

Purpose – The aim of this article is to show how Taguchi methods can be applied to health care toimprove the quality of medical images. Quality is often integrated with the performance andparameters of the design of medical applications. Many imaging methods can be designed by settingthe correct combination of parameters and estimating the contribution of individual qualityinfluencing factors by means of incorporating parameter design and orthogonal arrays. Theperformance of any imaging equipment can be measured by signal-to-noise ratio. This inherent indexcan give a sense of how close the performance is to the ideal.

Design/methodology/approach – Data were collected from a database of 82 diagnostic thoraciccomputed tomography (CT) scans. Signal-to-noise ratios (S/N) were calculated.

Findings – Given the S/N’s, the best CT level was found to be level 4.

Originality/value – To reduce bias resulting from the observer’s readings, robust equipmentsshould be designed incorporating Taguchi’s experimental design. Further work is needed to establishimaging protocols and new hardware design.

Keywords Taguchi methods, Quality, Image processing equipment

Paper type Technical paper

IntroductionMedical imaging is often thought of as a way of viewing anatomical structures of thebody. Indeed, x-ray computed tomography and magnetic resonance imaging yieldexquisitely detailed images of such structures. It is often useful, however, to acquireimages of physiologic function rather than of anatomy. Such images can be acquiredby imaging the decay of radioisotopes bound to molecules with known biologicalproperties. This class of imaging techniques is known as nuclear medicine imaging(Webb, 1988).

The imaging methods used in biomedical applications include (Krestel, 1990):. X-ray projection imaging;. X-ray computed tomography (CT);. magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS);. single photon emission computed tomography (SPECT);. positron emission tomography (PET);. Ultrasonics;. electrical source imaging (ESI);

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Leadership in Health ServicesVol. 20 No. 1, 2007pp. 42-51q Emerald Group Publishing Limited1751-1879DOI 10.1108/17511870710721480

. electrical impedance tomography (EIT);

. magnetic source imaging (MSI); and

. medical optical imaging.

In the emerging world of biomedical science, imaging plays an expanded role indiagnosis and therapy, and sophisticated image processing gives medical personnelaccess to much greater insight into their patients’ conditions.

On the other hand, in the world of technology and design, creation of a producthaving low cost and ideal functions is of utmost importance. This perspective isrelative to the concept of quality. As the general aspect of quality engineering, aproduct must satisfy the following points at the development stage:

. it should be of the lowest cost possible at all stages from raw material to theconsumer (low cost);

. it should satisfy its target values (stable quality); and

. its development time should be quicker than that of its competitors (shortdevelopment time).

These points constitute the ideal conditions for new product development,manufacturing equipment and optimum process operation. Therefore, newphilosophies and concrete methods are needed to accomplish these goals. Thisapproach can be applied to develop new tools for measuring medical imaging quality.

Fundamental to the evaluation of a medical imaging technique is a reliable andvalid measure of diagnostic accuracy. Ideally, an assessment of accuracy will beexpressed in such terms that it can also serve as the basis for a valid description of thattechnique’s utility, in terms of cost and benefit. The evaluation of diagnostic deviceswith an emphasis on imaging modalities involves the efficacy of diagnostic imagingtechniques.

Many new diagnostic tests and many new expensive imaging modalities areintroduced into the healthcare system each year. Experimental design techniques canbe successfully employed to efficiently improve a variety of medical imagingtechniques. Evaluating them can be easy by means of Taguchi methods, particularly ifalternative means exist to approximately the same diagnostic end. Taguchi Methodsmay be used to reduce experimental endeavor and at the same time produce sufficientinformation to reduce variation in the parameters of the imaging design. Yet, last newtechniques be introduced haphazardly, critical protocols and methods must beavailable so that they can promptly be addressed. Thus, Taguchi methods can also beapplied in imaging protocol design and improvement (Taner and Antony, 2000). Alldiagnostic tests, methods and protocols are for the assessment of diagnostictechnologies. As a result, higher performance of diagnostic modalities indicates thebetter image quality.

Nuclear medicineNuclear medicine imaging is an imaging modality that has the ability to demonstratephysiology and function as opposed to the anatomy as in radiology. The detectabilityof small lesions with small object contrast offers a challenge in nuclear medicine. In

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order to overcome this problem, high-count rates, high-resolution collimators andfavorable film processing are employed.

The object of the radioisotope imaging procedure is to produce a faithfulinterpretable display of the distribution of the radionuclides that have been introducedinto human body or some organ. The actual radionuclide distribution is called theobject and it is expressed in terms of radioactivity units, i.e. in millicuries. The displayproduced by the imaging device is called the image and has units of counts perunit-time. These two are never exactly equal and the aim of nuclear medicine imagingis to obtain an image that is as nearly equal as possible to the object. The image isdistorted representation of the object (Mettler and Guiberteau, 1991).

Image quality is a function of the following:. Resolution. System spatial is defined as the parameter of a gamma camera and

collimator that characterize its ability to accurately determine the originallocation of a gamma ray on an X-Y plane. This ability is a function of both thecollimator and crystal and its associated electronics.

. Contrast. Image contrast refers to differences in density or intensity in parts of theimage corresponding to different concentrations of radioactivity in the patient.

. Noise. Image noise may be either random (statistical) noise or structured noise.Random noise refers to random statistical fluctuations in radioactive decay, i.e.count rate. Random noise is related directly to the number of counts recorded orthe information density of the image. Information density is the number of countsrecorded per unit area of the image. On the other hand, structured noise is thenon-random variations in counting rate occurring due to instrument artifacts (e.g.non-uniformity in Anger Camera images), radionuclide distribution (e.g. boweluptake in studies with 67Ga) and object motion (e.g. in rectilinear scanning).

Evaluating diagnostic proceduresOne procedure is to measure fidelity, i.e. how well the system reveals the presence anddetail of a standard test object called phantom. The drawback of this approach is thatwhat is measured is only the potential for mediating accurate detection and diagnosisof real lesions.

The other approach, although based on using real cases and examining actualdiagnostic performance, has been inadequate because of the simplistic accuracyindices that are usually obtained. Indices such as the proportion of true-positive rate(TPR), false-positive rate (FPR), false-negative rate (FNR), true-negative rate (TNR),single pairs of sensitivity and specificity values, and agreement scores do not controlfor the influence of the observer’s confidence cut-off or decision criterion, i.e. tendencyto overcall or undercall disease, nor for the prevalence of disease in the studypopulation at hand.

If a variable is subject to measurement errors and these errors are the accumulationof many small deviations then the behavior of the variable is often well described bythe normal or Gaussian distribution (Figure 1).

Receiver operating characteristic (ROC) curve is constructed by plotting TPRagainst FPR as the cut-off for diagnosis (XC) is altered on the decision axis. ROCcurve analysis is useful in any area with inter-observer variation, non-quantifiable

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judgment, opinion or sensory differences, or with the selection of a criterion priorto making a decision (Metz, 1978). ROC curves have become increasingly popularover the last two decades as the medical community has become concerned withthe measurement of the information content of a variety of imaging systems(Katsuragawa, 2004).

The ROC is a curve showing the various trade-offs existing between proportions ofTPR and FPR as the decision criterion is systematically varied, for a given capacity todiscriminate between positive and negative cases.

A practical technique for generating response data that can be used to plot an ROCcurve in such a subjective judgment situation is called the “rating method”, i.e. discreteordinal data with only a few categories (King et al., 1993). Essentially, the methodrepresents a compromise between accepting a yes-no response and requiring that theobserver selects a value from a continuous scale to represent his confidence that thecase in question is positive. Instead, the observer is required to select one of severalratings or categories of confidence to represent his judgment, based on the informationprovided by the diagnostic test (Figure 2). These categories can be given qualitativelabels as follows:

. definitely or almost definitely negative;

. probably negative;

. possibly positive;

. probably positive; and

. definitely or almost definitely positive.

The use of five categories seems to represent a reasonable compromise between theneeds of ROC analysis and the precision with which an observer can be expected toreproduce his ratings. It is shown that use of N categories will yield (N-1) cut-off points.

The rating data obtained in this way are used to compute points on the ROC curveas follows: first only those responses in the category corresponding to highest certaintythat a case is positive are scored as positive decisions, and the rest are scored negativedecisions. Thus, for the category labels listed above, only responses in category 5would be scored as positive “decisions” at this stage of data analysis. These decisionsare then compared with the actual presence or absence of disease for each case, andTPR and FPR are calculated. This combination of TPR and FPR is plotted as a point in

Figure 1.Two Gaussian probability

density functionsdescribing the distributionof a test result for normal

individuals (left-curve)and for individuals withthe disease (right-curve)

with respect to apre-determined cut-off

point, XC

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the ROC space and can be interpreted as the ROC curve operating point correspondingto use of a strict cut-off, with which a case is called positive if and only if the observer iscertain, or almost certain, that the case in question is actually positive.

Since TPR and FPR as well as accuracy change with the criterion level employed,comparison of imaging tests in these terms may yield ambiguous or misleading results.ROC curves provide and unambiguous representation of the relative inherentdetectability of disease by the diagnostic imaging tests being compared.

Consensus has been developing over the past few decades on a number ofmeasurements required for the laboratory assessment of medical imaging modalities.Nevertheless, understanding of the connection between the above mentionedmeasurements and the performance of human observer remains far from complete.Focusing primarily on projection radiography to provide concrete samples, thisoverview indicates areas in which consensus on methodology for physical imagequality measurement has been established. Concepts such as “noise equivalent quanta”(NEQ) and “detective quantum efficiency” (DOE) have been found useful formeasurements to the decision performance of a hypothetical ideal observer thateffectively performs decision tasks from the image data (Faulkner and Moores, 1984;

Figure 2.Decision criterion levelsfor rating method

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Krestel, 1990). The connection between ideal observer and human performance, asdetermined by ROC analysis, remains to be understood for many clinically relevanttasks.

To date, ROC has widely been used in providing a measure of accuracy that islargely independent of decision biases when compared with other techniques. In thisstudy, a new approach for assessment of medical images technologies is introduced. Asa result, based on Taguchi Method, an alternative method for nuclear imagingmodalities is proposed.

Experimental designExperimental design consists of two techniques, namely orthogonal arrays andANOVA. Layout of factors is achieved by assigning many factors to an orthogonalarray. An orthogonal array experiment must satisfy the following conditions:

. the experiment must be conducted under different combinations of factor levels;

. the number of experiments required must remain within practical limits; and

. comparison of factor levels must be balanced.

After the orthogonal array experiment design method is chosen to determine theexperimental plan according to the most suitable conditions being investigated, eachimaging trial can be repeated under the same conditions at different times in order tosee the effects of the noise sources such as the lesion size and the patient. Then, theperformance statistics, i.e. S/N, is chosen as the optimization criterion (Antony, 2003).

What one should do in this step is to judge the effect of each factor on the objectivecharacteristic value and, the strength and weakness of factors against noise. Thisshould be based on experimental results using the orthogonal arrays. One shouldcontrol only these factors that have a strong relationship. There is no need to controlfactors with weak effects, and then one can set those factors at any level he chooses.Since there is a need to achieve the objective value and reduce through selection of thebest combination of these factors, one may need many controllable factors.

It is most important to know where to apply these techniques in the varioustechnological fields. While using experimental design in designing new products of thedevelopment of manufacturing process, the application of ANOVA to obtain areasonable estimate of functional quality is of foremost importance. There includes thefollowing three items:

(1) Selection of characteristics for measurement.

(2) Selection of test conditions, i.e. Levels.

(3) Selection of the appropriate S/N as an estimator characteristic to determineoptimum conditions.

Since design information is efficiently obtained two key points are important:

(1) The factors that can be controlled in the actual equipment.

(2) The levels of factors that will make the objective value and the output coincidewhile remaining robust against changes in the environment, raw materials andother noise components.

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When engineers determine optimum levels, it is usually better to use transformed datarather than raw data. Although measured (observed or unprocessed) raw data containthe original information form experiments, there are many cases that engineers fail toderive appropriate optimum levels from the raw data if one does not process sit. Theobjective performance should not vary much in the face of large changes in theenvironment or in raw materials in the actual equipment. In order to select such levelsmore efficiently, one can transform the data into what is called the S/N. Continuousdata can be grouped into smaller-the-better (STB) data, nominal-the-best (NTB) data,and larger-the-better (LTB) data (Antony et al., 2001).

Engineering experimental objectives can be summarized as follows:. adjust the output average to the target value (NTB);. reduce variability;. reduce the output level as much as possible (STB);. increase the output level as much as possible (LTB);. reduce the number of defects; and. expand the stable region.

Design problems can be broadly classified into static and dynamic problemsdepending on the absence or presence of signal factors. Signal factor is set by theuser/operator to attain the target performance or to express the intended output. Staticand dynamic problems can be further classified depending on the nature of signalfactor and the response variable (Figure 3).

With parameter design, one can determine the optimum level combination of controlfactors. If parameter design alone does not sufficiently reduce the impact of inner andouter noise, the variability caused by inner and outer noise factors must still be

Figure 3.Fishbone diagram of brainimaging in single photonemission computedtomography (SPECT)showing the parametersaffecting the image quality

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controlled, even if additional cost is incurred. The acceptance limits for a condition arecalled tolerances. Tolerance design uses ANOVA to determine which factorscontribute to the total variability and the loss function to obtain a trade-off betweenquality and cost (Antony, 2003).

DiscussionData were collected from a database of 82 diagnostic thoracic CT scans. The imageswere presented to four radiologists first without and then with the computer output, toindicate their confidence level regarding the malignancy of a nodule, and theperformance was evaluated by ROC analysis. ROC analysis was used to evaluate theability of the observer to differentiate nodule candidates that corresponded to actualnodules from false-positive candidates (Figure 4 and Table I).

The S/N is a metric that provides one number that appropriately encompasses bothdesirable and undesirable aspects of performance is needed. Classically, it is anexpression relating the useful part of the response to the non-useful variation in theresponse and gives a sense of how close the design is to the optimum performance of aprocess.

Figure 4.The resulting receiver

operating characteristic(ROC) curve from Table I

XC1 XC2 XC3 XC4

TPR 0.65 0.70 0.75 0.93FPR 0.05 0.08 0.19 0.65p0 5.94 5.18 3.58 2.68S/N 3.13 2.26 20.325 2.80

Table I.Comparison of TPR, FPR,p0, S/N values at different

cut-off points

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Regardless of the type of characteristic, the transformations are such that the S/N ratiois always interpreted the same way: the S/N ratio should be lower than 3.00. The closerthe S/N ratio to the value of 3.00, the greater the performance, the less variabilityaround the target and the less the loss-to-society (Taner and Antony, 2004).

Taguchi suggests the use of the following general formula for approximatelydetermining the leveling cut-off, p0 that is derived from TPR, TNR, FNR and FPR(Taner and Antony, 2000):

p0 ¼1

1 þ ð12TNRÞÞð12TPRÞFPR:FNR

� �1=2

Smaller p0 values yield less values of loss-to-society. In addition, S/N is calculated fromp0 by the following formula:

S=N ¼ 10 log 10ð1 2 2p0Þ2

2p0ð1 2 p0Þ

The fourth cut-off point is found to be the best CT level. At this level, S/N and p0 werefound to be 2.80 and 2.68, respectively. According to Taguchi, this is the level wherethere is the lowest loss-to-society.

ConclusionBiomedical imaging has seen truly exciting advances in recent years. Many of theenvisioned innovations in medical imaging are fundamentally dependent on themathematical sciences. While designing new systems with ideal combination ofparameters by orthogonal arrays and ANOVA, simulation of imaging methods playsan essential role in separating errors of noise from errors in the design of themathematical methods, and simulation allows the mathematician and physicist tocritically evaluate new ideas in the emerging field of dynamic biomedical imaging.Taguchi methodology shows greatest potential in medical applications which havetechnology-oriented systems that depend on multiple parameters such as medicalimaging systems. By means of Taguchi, robust and reliable medical systems can bemanufactured to avoid observer’s bias. It is also envisaged that Taguchi methods willhave relevant applications to redesign for cost and medical management.

References

Antony, J. (2003), Design of Experiments for Engineers and Scientists, Butterworth-HeinemannPublishers, New York, NY.

Antony, J., Knowles, G. and Taner, T. (2001), “10 steps to optimal production”, Quality, Vol. 40No. 9, pp. 45-9.

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Katsuragawa, S. (2004), “Subjective evaluation of medical images by using ROC analysis”,Nippon Hoshasen Gijutsu Gakkai Zasshi, Vol. 60 No. 3, pp. 309-16.

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King, J.L., Britton, G.D., Rockette, H.E. and Davis, P.L. (1993), “On the validity of the continuousand discrete confidence rating scales in ROC”, Investigative Radiology, Vol. 28, pp. 962-3.

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Taner, T. and Antony, J. (2000), “The assessment of quality in medical diagnostic tests:a comparison of ROC/Youden and Taguchi methods”, International Journal of Health CareQuality Assurance, Vol. 13 No. 7, pp. 300-7.

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Corresponding authorMehmet Tolga Taner can be contacted at: mtaner@gyte.edu.tr

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