Optimizing cardiac CT angiography minimum detectable difference via Taguchi’s dynamic algorithm, a V-shaped line gauge, and three PMMA phantoms

2.1Orthogonal array

The unique feature of Taguchi’s algorithm is that it not only optimizes assigned factors from a particular dataset but also identifies and ranks factors influencing the main variable. The six factors for cardiac CTA scan protocol were kVp, mAs, pitch (the distance of table travel per a 360∘ gantry rotation ratio to the whole thickness of all acquired slices simultaneously), FOV (field of view, mm), iDose (a reconstruction algorithm to improve the image quality through artifact prevention and increased spatial resolution at low dose) and reconstruction filter type [14]. In total, 486 (2 × 3 × 3 × 3 × 3 × 3) combinations were analyzed since each of the six factors was defined into three or two levels. Adopting the Taguchi’s algorithm, the samples could be organized into only eighteen groups, which were concluded results with same confident level as those obtained via the conventional and more thorough optimization processes [15]. Table 1 presents a standard L18 (21× 35) orthogonal array suggested by Taguchi; the numbers in each column indicate the practical arrangements or factor’s levels for the individual factors (A-F). The assigned six factors, namely (A) kVp, (B) mAs, (C) pitch, (D) FOV, (E) iDose, and (F) reconstruction filter, are listed in Table 2.

2.2Taguchi’s dynamic algorithm

Unlike the static preset in Taguchi’s optimization, the dynamic one is reputed for its strong flexibility in satisfying various conditions in a clinical environment. The unique definition of sensitivity (β) allows one to correlate the expectation value, i.e., signal-to-noise ratio versus the main variable. The latter may involve various PMMA phantom weights defined in this study or exposed radioactive doses [8, 13]. Nevertheless, the β parameter is preset via “higherthe-better” criterion to intensify good quality characteristics in the conventional robust designation. However, β was redefined as “lowerthebetter” to reduce the sensitivity of phantom’s weight in this study and reduced to

where β is the sensitivity, and Y is the ranking of the V-shaped line gauge in 18 groups for the specific phantom weight (i.e., 50, 70, or 90 kg). Here, stdev is the standard deviation of the repeated ranking in obtaining the gauge ranks, averaged over n (reviewers × repeated times) rankings for all m weights. In this study, n=9⁢(3×3) and m=3. Taguchi proposed the signal-to-noise ratio (S/N, dB) to integrate the functional performance and quantify the effect of beta or stdev. A high S/N indicates a low stdev or beta in the practical survey, which is preferable to satisfy the aim of this study.

Figure 1.

(A) implies a special-made V-shaped line gauge with 20 mm-high, 60 mm-long, and 30 mm-wide cuboid. In contrast, the two V-shaped lines had 0.5 or 0.7 widths, and the slit depth changed from 0.2 mm in the top to 0.8 mm in the bottom. The quantified survey focused on the left V-shaped line with a 0.5 mm width to justify the MDD in this measurement, (B) the commercial 320 ECG simulator was adopted to synchronize the CTA scanning frequency and simulated 60 BPM (beats per min.), (C) the tightly-composed cardiac ball with two vertical and horizontal V-shaped line gauges, and (D) three cardiac balls were placed into the 50, 70, and 90 kg PMMA phantoms, respectively.

2.3A V-shaped line gauge and PMMA phantoms

Figure 1A depicts a specially made V-shaped line gauge with 20 mm-high, 60 mm-long, and 30 mm-wide cuboid. As shown, the two V-shaped lines had 0.5 or 0.7 widths, and the slit depth gradually changed from 0.2 mm in the top to 0.8 mm in the bottom. Specifically, the top two lines were preset to barely contacted each other with a shallow slit of 0.2 mm depth only. In contrast, the gap between the two lines became 8.45 mm (for the 0.5 mmwide slit) or 7.94 mm (for the 0.7 mm-wide slit) in 0.8 mm-deep at the bottom. The quantified survey focused on the left V-shaped line with a 0.5 mm width to solidify the MDD in this measurement, (B) A commercial 320 ECG simulator was adopted to synchronize CTA scanning frequency and the simulated 60 BPM (beats per min.), (C) the tightly-composed cardiac ball with two vertical and horizontal V-shaped line gauges and (D) three cardiac balls were placed into the 50, 70, and 90 kg PMMA phantoms, respectively. The PMMA phantoms were revised according to the original ICRU-48 report [16]. In addition, a commercial phantom (model 4550-122-01471) for Philip Brilliance CT (model 128-sliced Philips Ingenuity) was also put aside for size comparing.

2.4The MDD definition and application

The minimum detectable distance (MDD) between two peak centers was determined via the revised Student’s t-test equation with a constant multiplication factor of 1.96, demonstrating two peak centers X1 and X2 deviated divergent enough to create a 95% confident level of success [17]:

where X1 and X2 is the center of peaks 1 or 2, whereas FWHM is defined as full width at half the maximum of the specific peak. The MDD among line pairs was proposed to quantify the two overlapped-peak profiles that were collected from a tangent slice of a 0.5 mm-deep V-shaped slit with two neighboring peaks, followed the various confident levels of success as implied in Eq. (4).

Figure 2.

(A) two peaks were recognized as fully separated; (B) two peaks scarcely passed the Student’s t-test identification, while in (C), the differentiation failed because the two peaks were too close to each other.

The MDD evaluation from two adjacent peaks via the specific V-shaped slit was performed by a gradual changing of the valley edge of two peaks and a quantitative assessment of the originally designed edge width. Unlike V-shaped water phantoms used in nuclear medicine examinations [18], the 0.5 mm-deep V-shaped slit (cf. Fig. 1A) provided the finest edge between line pairs to ∼ 0.5 mm in a 0.2 mm-deep slit, exceeding the distinguishable ability of average CT scan facilities. Therefore, various confidence levels of success can be assigned for the MDD assessment. Small MDD values of CT scan images imply a high distinguishable capability in cardiac artery or vein image analyses. As shown in Fig. 2A, two peaks were recognized as fully separated; (B) two peaks scarcely passed the Student’s t-test identification, while in (C), the differentiation failed because the two peaks were too close to each other. This approach advantage over the qualitative judgment of radiologists is that the latter can be biased by the human factor, while the standard of failing or passing the revised Student’s t-test are purely quantitative, fully based on the calculation results, and thus provide a more accurate and robust MDD assessment via quantified calculations [3, 4, 5].

2.5Cardiac CTA scan and ranking

The imaging quality of the cardiac CT scan protocol was simulated by the V-shaped line gauge, as shown in Fig. 1A. To survey the gauge images’ quality, each slit was infused contrast media solution (∼ 3 c.c. Optiray® 320, a 68% Ioversol injection) and dyed with dark blue ink to pretend the real CT scan for the patient cardiac syndrome. Other factors for CT spiral rotation scanning were preset as follows: a spiral rotation time of 0.4 s/roll, a 400 mm collimator, and a slice thickness of 0.9 mm [4]. According to a 128-slice CT lung scan survey earlier conducted at Taichung Armed Forces General Hospital, Taiwan, the CT scan protocol underwent a minor revision for the 128-sliced Philips Ingenuity located at the above hospital. Three viewers ranked the scanned V-shaped gauge images from 18 groups with three repeated judgments under the double-blinded principle. Thus, every viewer had to check a total number of 162 images (3 × 3 × 18 = 162) before the data analysis and further optimization.

3.1Taguchi’s optimization

Figure 3 shows typical V-shaped line gauge images from cardiac CTA scans of 18 groups in the 70 kg PMMA phantom Since those obtained via 50 or 90 kg ones were quite similar, they were omitted for brevity. Some of them had low contrast ratios, being too bright or too dark to identify the V-shape. Table 3 lists the raw data obtained from the practical survey of CTA images. Each viewer ranked the 18 images three times for three different phantom sizes; thus, a total of 486 (3 × 3 × 3 × 18 = 486) ranking results were collected and statistically processed Beta, stdev, and S/N values derived via Eqs (1)–(3) are also included in the last three columns of Table 3. Furthermore, the fish-bone plots of various factors were constructed via Taguchi’s dynamic algorithm [4, 5]. As seen in Fig. 4, beta, stdev, and S/N exhibited strong fluctuations. Theoretically, low beta and stdev values and high S/N provide the best expectation. Therefore, despite strong cross-interactions among factors, the preliminary suggestion (cf. Fig. 4) comprised A2 (120 kVp), B1 (600 mAs), C1 (pitch 0.126 mm), D3 (FOV 280 mm), E3 (iDose 5), and F3 (filter XCA). Upon minimizing the cross-interactions among factors, the final optimal combination of factors became A1 (100 kVp), B1 (600 mAs), C3 (pitch 0.200 mm), D3 (FOV 280 mm), E3 (iDose 5), and F3 (filter XCA).

Figure 3.

Typical V-shaped line gauge images from cardiac CTA scans of 18 groups in the 70 kg PMMA phantom. Since those obtained via 50 or 90 kg ones were quite similar, they were omitted for brevity.

Figure 4.

The beta, stdev, and S/N exhibited strong fluctuations. Theoretically, low beta and stdev values and high S/N provide the best expectation.

3.2MDD of PMMA phantoms with various weights

Table 4 shows the revised Student’s t-test results for MDD derived via 50, 70, 90 kg PMMA phantoms. The optimal cardiac CTA scan factor combination was obtained, revealing the following trend: the right side’s peaks failed the revised Student’s t-test, while the left side’s adjacent two peaks successfully passed it. The derived MDD values were 2.15, 2.32, and 1.87 mm for 50, 70, and 90 kg phantoms, respectively. The last one had the most precise spatial resolution, while that of 70 kg was the worst. The geometrical size/weight of the phantom significantly affected the image quality. Thus, a more precise factor combination of cardiac CTA had to be found according to the various phantom weights to ensure the best image quality. Specifically, Fig. 5 depicts the line-cut SPECT profile from the V-shaped line gauge for various phantom weights that just passed the Student’s t-test. The SPECT data were converted via the MATLAB default software in this study. A too-large FWHM of the two peaks from the 70 kg phantom’s SPECT profile deteriorated the MDD and reduced the spatial image resolution.

Figure 5.

The line-cut SPECT profile from the V-shaped line gauge for various phantom weights that just passed the Student’s t-test.

4.1The ANOVA analytical result

Static Taguchi’s optimization requires the ANOVA analysis to discriminate dominant and minor factors via the variance analysis. In contrast, for dynamic Taguchi’s one, the ANOVA is optional because the integrated performance is dominated by the unique quality characteristic of dynamic analysis, namely sensitivity [15]. However, by checking the sum of squared variances for various phantom weights, one can get a deeper insight into the fluctuation patterns. Consider the following parameters:

where S⁢S𝑇𝑜𝑡𝑎𝑙 is the sum of squares for all variances; yi⁢j, is the ranked grade of an image for the ith group in the jth trial of one specific phantom weight; r is the total number of trial repeats in each group (in this study, r=3×3=9, since the same gauge image was ranked for three rounds by three reviewers). Besides, y¯¯ is the average of all ranked values from the prompt phantom image (i.e., the theoretical value is 9.5). Parameter S⁢S𝐹𝑎𝑐𝑡𝑜𝑟 is the sum of squares according to the specific factor, and yk¯ is the mean ranked value assigned to specific factor. Constants L or n is the numbers of levels assigned to the factor or to all groups. In this study, n= 18 and L and n= 2 or 3. Finally, S⁢S𝑒𝑟𝑟𝑜𝑟 is the sum of squared random errors.

Table 5 presents a significantly different distribution of S⁢S𝐹𝑎𝑐𝑡𝑜𝑟 at various phantom weights: parameter S⁢S𝑒𝑟𝑟𝑜𝑟 in the 70 kg phantom analysis reached 40%, indicating an enormous discrepancy in viewers’ ranking results, whereas its values in other weights were 7.8% for 50 kg and 20% for 90 kg. This happens because the CTA scan images of 18 groups for the 70 kg phantom have a similar quality to be ranked (cf. Table 3); thus, the results for 70 kg are more controversial than the other two. It becomes difficult to improve the image quality and follow the quality assurance guideline since different radiologists have their interpretations of the imaging quality. However, CTA scan images are ranked easier at lower (50 kg) or larger (90 kg) phantom weights to ensure a similar quality, and S⁢S𝑒𝑟𝑟𝑜𝑟 drops significantly (cf. Table 5). Nevertheless, the dominant factors also fluctuate at different phantom weights. The only unchanged one is factor F (reconstruction filter). Factor A(kVp) is valid for 50 and 70 kg; factor B (mAs) is valid for 70 and 90 kg and factor C (pitch) is valid only for 90 kg. The routine preset of each factor has to be specifically considered in facing different phantom weights, and the cardiac CTA standard protocol also needs to be slightly revised according to various patients’ weights.

4.2Sensitivity in the dynamic algorithm

As the unique quality characteristic of Taguchi’s dynamic algorithm, sensitivity can be customized and revised according to different perspectives. For most dynamic studies, high sensitivity is always preferable [8, 13, 19]. However, the sensitivity has a different interpretation in this study because the sensitivity implies the imaging quality versus various phantoms’ weights. Thus, an insensible quality characteristic is preferable for radiologists in routine cardiac CTA scans. Accordingly, the parameter S/N (η, dB) can be revised as follows:

where avg is the total average of all ranked scores from three viewers and three phantoms’ weights (cf. Table 3, 3 × 3 × 3 = 27 dataset), while β has the same definition as in Eq. (1). The basic idea of Eq. (8) is to intensify the mathematical average without considering different phantom weights, i.e., to ignore the phantoms’ weight change in the real CTA scan and average all terms under the same configuration. Meanwhile, Eq. (9) contains a conventional definition of the routine dynamic algorithm, which is inappropriate in our present scenario. Figure 6 reveals the respective fish-bone plot of S/Ns constructed via Eqs (8) and (9). As clearly illustrated, the variation trend of S/N versus different factors may mislead the interpretation of dynamic algorithm and fail to achieve the required optimization.

Figure 6.

The respective fish-bone plot of S/Ns constructed via Eqs (8) and (9).

4.3Dynamic algorithm superiority over the static one in Taguchi’s suggestion

In the typical static preset case, the original phantom configuration remains unchanged. In the dynamic one, the original phantom can be replaced by others of different sizes to match the real situation in routine work. The dynamic algorithm’s unique sensitivity (β) is a useful index to inspect the quality characteristic in robust designation, whereas the static one provides no such option. The sensitivity of the CTA image can also handle the real situation on a theoretically substantiated basis. In contrast, when the standard static algorithm is used, the ranked scores have to be summed and averaged altogether, although they were ranked under various phantom weights. Therefore, the S/N2 value derived via Eq. (8) (cf. Fig. 6) may be the only option, so a possible misinterpretation of the S/N2 fish-bone plot might yield an irrational solution, which further verification would be useless. For instance, the false optimal suggestion would be A1 (100 kVp), B3 (800 mAs), C3 (pitch 0.200 mm), D1 (FOV 220 mm), E2 (iDose 4), and F1 (filter XCC, whereas the exact optimal combination should be A1 (100 kVp), B1 (600 mAs), C3 (pitch 0.200 mm), D3 (FOV 280 mm), E3 (iDose 5), and F3 (filter XCA). Even the most dominant factor F (reconstruction filter) had an inappropriate setting (XCA instead of XCC).