A simple method for bone age assessment: the capitohamate planimetry

Bone age assessment (BAA) is crucial in the evaluation of endocrine disorders and in the prediction of adult height when hormone therapy is the treatment [1].

Radiographic examination is an easy and cost-effective method for the assessment of bone age. BAAs are performed using various body parts such as the hand, elbow, knee, cervical vertebra or pelvis [2]. Hand radiography is certainly the most widely used examination [3].

Several methods have been proposed, including Greulich-Pyle (GP) atlas, Tanner-White (TW) score and Gilsanz-Ratibin (GR) atlas, which are qualitative [4]. The TW method is based on the level of maturity for 20 regions of interest (ROIs), including the epiphysis, metaphysis and diaphysis in the radius, ulna, first, third and fifth fingers and the carpal bones, so it is complex and time-consuming. The GR method is another technique that uses the new digital atlas that includes reference images of the left hand taken at 6-month intervals from birth to age 6 years, and at 1-year intervals from age 7 to 17 years. However, this subjective method relies on matching of the hand radiograph of the subject with the GR atlas. In the GP method, bone age is determined by matching the left-hand radiograph of the subject with reference radiographs from the atlas. This explains why the GP method is generally easier and quicker to use, so it is more often selected over other methods [5‐8]. One disadvantage of the GP method is the characteristics inherent in subjective analysis, and the interobserver reproducibility of BAA with the GP method has been controversial [5, 7].

A quantitative evaluation method with objective parameters is needed. BAA by using the capitate and hamate, which are the first bones to develop embryologically, has been recommended by a previous study but not performed as of yet [9]. In addition, validation of BAA across different ethnicities would be necessary for a more reliable method [10]. Therefore, the aim of this study was to determine if the area of the capitate and hamate bones measured on hand radiography could be a reliable indicator of bone age accuracy, precision, and reproducibility between the planimetry and GP methods.

The age and sex distribution of the Korean subjects are listed in Table 2. There were 242 boys (mean age 75.33 months; age range 1–180 months) and 149 girls (mean age 57.46 months; age range 1–178 months).

For 241 boys (99.59 %) and 149 girls (100 %), irrespective of age, left and right capitate and hamate bones were demonstrated on the radiographs of both hands. The right capitate and bilateral hamates were not demonstrated on the radiograph in only one boy (0.41 %) aged 1 month (Fig. 3).

There were no significant differences in areas between the left and right capitate and hamate of both sexes (Table 3). Additionally, there was also no significant difference in the sum of the area of the capitate and the area of the hamate between right and left hands.

The planimetry curves of the capitate and hamate and the sum of the CH areas demonstrated increased slopes in both sexes (Fig. 4). There was a strong positive correlation between chronological age and the CH planimetry measurement (Table 4). Moreover, strong correlations were found between chronological age and the capitate area of both sexes, as well as between the chronological age and hamate area (Table 4).

In the linear equation y = a + bx, y stands for capitate, hamate and CH area; x stands for age in months; and constants (a and b) were calculated. The equations of planimetry for the left hands of boys and girls are as follows:

By using the CH planimetry and GP methods, the third and fourth reviewers estimated the bone age of 109 patients who were classified into the 50th percentile group. None of the mean areas of the capitate, hamate and sum of the capitate and hamate were significantly different between the two reviewers. The mean value of chronological age of 109 children (mean age 113.07 months; standard deviation 36.07) was not significantly different from that of the estimated bone age measured by both CH planimetry and GP methods (p ≥ 0.1378). There was no statistically significant difference in the mean value of bone age between the two reviewers using CH planimetry. However, the mean values of bone age were significantly different between the two reviewers assessing the bone age according to the GP atlas (Table 5). The mean value of bone age estimated using the GP method was lower than that measured using CH planimetry (p < 0.0001).

When assessing bone age based on the CH planimetry and GP methods, there was no significant difference in the accuracy between the third (CH planimetry, 84.39 % ± 22.33 %; GP method, 85.15 % ± 13.78 %) and fourth (CH planimetry, 84.46 % ± 21.29 %; GP method, 87.66 % ± 12.34 %) reviewers (p ≥ 0.0867) (Fig. 5). Deming regression analysis showed no statistically significant difference in the results between the CH planimetry and GP methods, as the standard errors can be determined from the 95 % confidence intervals (CIs) of intercept (standard error, 4.0028; 95 % CI −4.9522–10.9164) and slope (standard error, 0.03955; 95 % CI, 0.9917–1.1485) including the values 0 and 1, respectively (Fig. 6).

We analysed the interobserver variability of the CH planimetry and GP methods. The values of ρ_c were substantial for both methods for assessing bone age (CH planimetry, 0.9862; GP method, 0.9553) between the two reviewers. However, the precision of CH planimetry (4.42 % ± 3.87 %) was significantly different from that of the GP method (8.45 % ± 8.52 %) (p < 0.001). The Bland-Altman analysis demonstrated that CH planimetry had narrower 95 % limits of agreement (−10.5 to 13.4 months) than the GP method (−29.5 to 21.1 months) (Fig. 6). These results suggest that the interobserver reproducibility of CH planimetry may be greater than that of the GP method.

In our study, there were no significant differences noted in the areas between the right and left capitates and between the right and left hamates. Patterson et al. [15] reported that the volume of carpal bones was not significantly different between the left and right hands, using three-dimensional (3D) computed tomography (CT) volumetry. However, hand PA radiography for bone assessment is usually performed on the left side rather than on the right side, and perhaps because most people are right-handed, the right hand is more prone to get injured and therefore may have deformity. In the early 1900s, a physical anthropologists meeting determined that body measurements should be performed on the left [3].

The right capitate and bilateral hamates were not demonstrated on the radiograph in only one boy (0.41 %) aged 1 month. The capitate and hamate are known to emerge most frequently and simultaneously between the first and fourth months from birth; however, occasionally, the capitate emerges first, followed by the hamate. As seen in the GP atlas, the nuclei of the capitate and hamate were more likely to be present earlier in girls than in boys [16].

There was also a strong positive correlation between chronological age and the CH planimetry measurement (Table 3). As shown in Fig. 3, there were increased slopes in the planimetry curves of the capitates and hamates of boys and girls. Canovas et al. [17] reported that there was a strong correlation between chronological age and volumes of the carpal bones of the hands measured using 3D CT volumetry. The strongest correlations were found with the triquetrum, capitate and hamate bones, which were present in all 20 hands.

There was no significant difference between the two methods in accuracy for estimating bone age (CH planimetry, 84.39–84.46 %; GP method, 85.15–87.66 %). The research performed by Roche et al. showed that the median bone ages estimated using the GP method were similar to that of the chronological ages [18]. On the contrary, some researchers reported that the difference between chronological age and bone age estimated using the GP method was −0.6 to 2.15 years [10, 19‐21]. The accuracy of BAA with the GP method has been reported to vary depending on the patient’s age or sex and ethnicity [22]. To date, few studies have evaluated the percentage accuracy of BAA using the GP method. Lee et al. [23] reported that a deep learning system for BAA achieved 57.32 % and 61.40 % accuracies for the female and male cohorts when age was precisely matched. The accuracy of matching bone age within 1 year was 90.39 % and 90.39 %, respectively.

In our study, the mean bone age measured using the GP method (105.49–109.49 months) was significantly lower than the mean bone age measured using CH planimetry (117.43–118.58 months). This result may be attributed to the difference in growth patterns among different ethnicities because the GP method was established in Caucasians [3]. Some researchers reported that bone age measured with the GP method tended to be lower than the chronological age or the bone age measured with the TW3 method or the Korean bone standard method, although there was no significant difference between the estimated bone age and chronological age [21, 24]. These previous studies may have shown no statistically significant difference because of the small number of children or targeting children of a limited age range.

In the second part of our study, the interobserver reproducibility of CH planimetry was greater than that of the GP method. The values of ρ_c were substantial for both methods (CH planimetry, 0.9862; GP method, 0.9553). In Bland-Altman analysis, the 95 % limit of agreement of CH planimetry was −10.5 to 13.4 months and that of the GP method was −21.1 to 29.5 months (Fig. 6). The precision of CH planimetry (4.42 % ± 3.87 %) was significantly different from that of the GP method (8.45 % ± 8.52 %) (p < 0.001). To date, there have been many comparative studies on the interobserver reproducibility of BAA with the GP method by using various statistical tests [5, 7]. Bull et al. [7] reported that the 95 % CI of the GP method (−2.46 to 2.18 years) was greater than that of the TW2 method (−1.48 to 1.43 years). King et al. [5] reported that the average spread of intra-observer variation was 0.96 years for the GP method. These results are similar to those of our study. By contrast, the percentage precision of the GP method was 65.5−88.5 % [8, 25]. Improving the observer variability of manual methods is a motivation for developing automated methods of BAA [26]. To date, computer-assisted or artificial intelligence-based methods have attempted to make accurate measurements, with discrepancies from 0.39 to 2.41 years [27].

This study has several limitations. First, it was performed retrospectively at a single institution. We excluded children with chronic illnesses, nutrition deficiency or growth problems from this study population. However, to our knowledge, this planimetric study is the largest series assessing the areas of the capitate and hamate.

Second, CT scans provide 3D measurements, whereas radiography demonstrates the 2D projected images of 3D objects; therefore, volumetry can be more accurate than planimetry, and may determine bone age more objectively [17]. However, CT volumetry has some disadvantages such as high cost and radiation exposure. In contrast, x-ray planimetry has the advantages of lower costs and lower radiation doses [28]. Moreover, planimetry is an easy-to-use method with an area measurement tool integrated in PACS without any separate software [29, 30].

Third, manually drawing ROIs along the cortical margin of the capitate and hamate may cause interobserver variation, and problems in planimetric analysis. To minimize this variation, another series of consensus measurements was performed in cases in which the differences between the reviewers exceeded 10 % [7, 31].

Fourth, quantitative analyses undertaken using digital radiographs displayed on a PACS monitor could be subject to measurement errors [32]. To avoid this error, to ensure the accuracy of the absolute measurement value, calibration was performed using a coin prior to our study [33]. Different equipment and protocols among different institutions may cause measurement errors. In the future, a multicentre prospective study should be conducted while avoiding this error.

Finally, there is no gold standard for BAA [29]. We set a reference standard with a range < 1 standard deviation of the Korea CDC growth chart. Children were enrolled in the reference standard only if their heights were between the 50th percentile of the pervious age stage and the 50th percentile of the later age stage, so that the height ranges do not overlap [12]. Moreover, as the height of Korean children has changed since the growth chart was published in 2007, it may be necessary to adjust the age range of the reference heights [11].

In conclusion, the CH planimetry method may be useful for BAA. In the future, if automated CH planimetry can be integrated in PACS with validation for ethnicity and sex, it may save time and allow more precise BAA.