### Introduction

^{1)}and is now known as the most common cause of acquired heart disease in children in developed countries

^{2)}. The appropriate initiation of treatment with intravenous immunoglobulin reduces the incidence of coronary artery aneurysms from 25% to 4%

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^{6)}.

^{7)}. Until recently, these criteria were widely used as they were easy to memorize and use. However, an underestimation of the incidence of coronary arterial lesions and an inability to reflect children's body growth in the application of these criteria have been pointed out

^{8)}. A standardized score (

*z*score) for assessing cardiovascular structures has been developed for use in pediatric clinical environments as children undergo rapid changes in their physical development with resultant variations in their body size

^{9)}. Several coronary artery

*z*score models have been subsequently proposed

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^{15)}; a relatively large number of subjects was included, and nonlinear regression methods were adopted in four of models

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^{15)}. In a recently published practice guideline by the American Heart Association, the classification of coronary arterial lesions is based on the

*z*score of coronary artery diameter

^{2)}. The previously reported

*z*score model for Korean children has two major limitations: firstly, the number of subjects included in the study for the model was too small and secondly, a linear regression was adopted for model fitting of the body surface area

^{16)}. The

*z*score model by Kobayashi et al.

^{15)}, which was derived from the lambda-mu-sigma method in 3,851 Japanese children, holds promise for use in Korean children due to its large sample size and the racial similarity between the Japanese and Korean populations.

*z*score models, including the Japanese model, was performed in relation to 181 healthy Korean children. We expected the results of this investigation to present useful information on the selection of

*z*score models in clinical practice in Korea.

### Materials and methods

### 1. Subjects

^{17)}.

### 2. Echocardiography and coronary measurements

^{18)}. The intraluminal diameter of the coronary artery segments was measured from the inner to inner edges. The left main coronary artery (LMCA) was measured midway between the ostium and the bifurcation of the circumflex artery and the left anterior descending coronary artery (LAD) in the parasternal short-axis view. The LAD was measured distally to the bifurcation and before the start of the first marginal branch. A measurement for the right coronary artery (RCA) was obtained in the relatively straight section, just after the initial rightward turn from the anterior-facing sinus of the Valsalva. In a case with a visible origination of the conal branch, the RCA segment distal to the conal branch was measured (Fig. 2). The offline measurement of coronary artery diameters was performed by one author (JJY). The reproducibility of coronary artery diameter measurements has already been reported in another study which was performed by same echocardiographers

^{19)}(an intraobserver variability in the measurement of the LMCA, LAD, and RCA as 5.4%, 8.7%, and 5.1%, respectively, and the interobserver variability as 5.8 %, 10.4%, and 7.0%, respectively).

### 3. Statistical analysis

*z*score using the previously reported regression equations or spreadsheet file for calculation

^{12,}

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^{15)}. The results of the

*z*score of coronary artery diameter were analyzed using the Kolmogorov-Smirnov test on a normal distribution and using the 1-sample

*t*test on a convergence of the average value to zero. Statistical analysis was performed using IBM SPSS Statistics ver. 21.0 (IBM Co., Armonk, NY, USA). Statistical significance was defined as

*P*<0.05.

### Results

^{2}(range, 0.201–1.909 cm

^{2}). The median diameter of LMCA, LAD, and RCA was 2.13 mm (range, 1.35–4.01 mm), 1.65 mm (range, 1.10–3.26 mm), and 1.60 mm (range, 0.82–3.65 mm), respectively (Table 1).

### 1. The descriptive statistical properties of *z* score value

*z*score values must be normally distributed and the mean value should converge to zero, the standard deviation to 1, the skewness to zero, and the kurtosis to zero. The descriptive statistical characteristics of the

*z*score value is presented in Table 2 and plotted as a histogram in Fig. 3, 4, 5. The mean value of the

*z*score of the RCA was less than zero in all 4 models. The values of skewness and kurtosis of the LMCA were above zero in all models. The

*P*value on the Kolmogorov-Smirnov test for the

*z*score value was ≥0.050 in three coronary arteries in all four models, which suggests the statistical feasibility of normal distribution. One sample

*t*test showed that the mean

*z*score value was significantly different from zero (Table 3); the only exception was a

*z*score of the LAD in the Japanese model (

*P*=0.582).

### 2. The proportion of *z* scores with extreme value

*z*score of the LMCA ≥2.0 in the Dallaire and Japanese models appears higher (4.9% and 7.1%, respectively) than 2.3% which is the proportion of the

*z*score ≥2.0 in standard normal distribution (Table 4). Moreover, the percentage of the

*z*score of the LMCA ≥2.5 also appears higher (3.3% and 3.8%, respectively) than 0.6% which is the proportion of the

*z*score ≥2.5 in standard normal distribution in those 2 models. The extremely high

*z*score of the LMCA seems to be more frequent in the Dallaire and Japanese models than in the other 2 models.

### Discussion

*z*scores in 181 normal children were performed using four frequently used

*z*score models (Table 5)

^{12,}

^{13,}

^{14,}

^{15)}. As all models are designed to represent a normal population, we expected that the calculated

*z*scores for healthy children would also follow a normal distribution. The Kolmogorov-Smirnov test showed

*P*≥0.050 in three coronary arteries in all 4 models, implying the statistical feasibility of normal distribution. Therefore, it was consequently estimated that the four

*z*score models would be distributed normally, which justifies the application of these models to Korean pediatric populations.

*z*score should converge to zero since the subjects were normal healthy children. However, the mean

*z*score value of the 3 coronary arteries was significantly different from zero in each of the four models, except for one of the LADs in the Japanese model. The limited number of subjects in this study could be one of causes. Another explanation for this difference could be the subtle differences in the measuring points. In this study, the mean

*z*score of the RCA was consistently less than zero in all models, which implies that the measured RCA diameters were smaller than the reference values of the

*z*score models. It is reported in the

*z*score model reference papers that the RCA measurements were obtained 2–5 mm distal to its origin in the parasternal short-axis view

^{13,}

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^{15)}. In this study, the RCA segment distal to the conal branch was measured in a case with a visible origination of the conal branch to avoid an exaggerated measurement on the branching point. In addition, the measurement point was more distal to 5 mm from the origin of the RCA in some of such cases. As a result, the RCA diameters in this study would have been smaller accordingly. We think that more precise instructions are needed for an accurate and reproducible measurement of the RCA proximal diameter on the issue of the conal branch.

*z*score models, the Dallaire and Japanese models were more favorably recommended for use in recent American Heart Association guidelines because they included a relatively larger number of subjects and provide normative data on the left circumflex branch

^{2)}. Incidentally, the percentage of subjects with an extreme

*z*score of the LMCA appears to be higher in the Dallaire and Japanese models in this study than the expected level under normal distribution. This higher percentage could be due to anatomic variation in several cases, which can be seen in the histograms for the LMCA (Fig. 3). The positive skewness and kurtosis in the distribution of the LMCA

*z*score would not impact on the higher percentage of subjects with extreme

*z*scores of the LMCA. It is well known that anatomic variations are frequent in the LMCA

^{2)}. Additionally, caution in the interpretation of the LMCA

*z*score was also recommended in recent guideline

^{2)}. For the other branches of coronary arteries, all four

*z*score models could reasonably be used for the evaluation of vascular dilatation.

*z*scores of the LMCA is compatible with a commonsense understanding of anatomic variations of the LMCA.