The digital measurement of biometric parameters as well as the preoperative planning of orthopedic interventions was shown to have good to excellent reliability, e.g., for Cobb angle in scoliosis [26, 27], planning of hip prostheses [28, 29] or leg axis determinations in long-leg X-rays [30,31,32,33]. The correct and reliable analysis of static parameters of the lower extremity is essential for an adequate treatment of pediatric orthopedic diseases. In addition to the clinical appearance, these measurements play a significant role in determining the indication for guided growth intervention of the lower limb using THE. In the present study the intra- and interobserver reliability for almost all lower limb alignment measurements in full-length standing anteroposterior radiographs of the frontal plane were found to be good to excellent.

Our study is the first that investigates all relevant malalignment parameters in the frontal plane in children and adolescents regarding intra- and interobserver reliability, SEM95% and proportional errors in order to make the best possible and the least error-prone decision on the indication and timing of THE, on postoperative follow-up and on the right time for removal of the tension band plates after completion of growth guidance.

According to the study of Specogna et al. [34], reliability of repeated lower limb frontal plane alignment measures is high for planning a high tibial osteotomy with OA affecting the medial compartment of the knee due to varus malalignment (MFA Intra-ICC2,1 = 0.98; 95% CI = 0.97 − 0.99, Inter-ICC2,1 = 0.98; 95% CI = 0.91–0.99; MAD Intra-ICC2,1 = 0.98; 95% CI = 0.97 − 0.99, Inter-ICC2,1 = 0.97; 95% CI = 0.90–0.99). Specogna et al. [34] elucidated that the estimates of error for the measurements of MFA need to be considered with ± 1.50° and for the MAD ± 4.3 mm. These findings are largely consistent with the results of our investigation. In contrast to our findings, the mentioned study investigated MFA and MAD on radiographs collected from adult patients (mean age 44 (21–65) years). When analyzing leg axis on skeletally immature patients, Gordon et al. [31] were able to show that intra- and interobserver reliabilities for each of the measurements (mLDFA, mMPTA and MAD) were ≥ 0.90 (0.90–0.99) in children (mean age 11.2 (7.1–14.7) years) with neutral alignment and both varus or valgus malalignment regardless of the level of observer experience. Gordon et al. [31] pointed out that the overall mean interobserver differences were ± 1.4° for the mLDTA, ± 1.6° for the mMPTA and ± 3.1 mm for the MAD measurement. In a similar study, Schmale et al. [32] have shown that the intraobserver ICC values ranged from 0.27 to 0.94 for the mLDFA and from 0.88 to 0.97 for the mMPTA in patients with open distal femur and proximal tibia physes at the time of a transphyseal anterior cruciate ligament reconstruction. Furthermore, the reliability (interobserver ICC: MAD 0.92, mLDFA 0.86 and mMPTA 0.98) of leg axis measurements were rated as good to excellent. Nowicki et al. [33] evaluated the MAD, mLDFA, mMPTA and JLCA of pediatric lower extremities (mean age 13.5 years) with neutral, varus or valgus (mal)alignment but not the MFA and they did not calculate the SEM95% for all relevant parameters. They could also show comparable values for the intraobserver ICC of the four measurement parameters: 0.756–0.990 for mLDFA, 0.489–0.958 for mMPTA, 0.831–0.927 for JLCA and 0.974–0.993 for MAD. Interobserver ICC values of 0.732–0.977 could be presented for the respective parameters. Feldman et al. [35] came to a similar conclusion that planning guiding treatment on those digital radiograph measurements is reliable and reproducible with intraobserver ICC of 0.77 (0.65–0.86) for mMPTA and mLDTA 0.80 (0.77–0.84). In this study, however, only the relevant joint surface angles of the tibia were comparable to our finding, because they chose to measure and analyze the anatomical angles instead of the mechanical angles. Furthermore, MAD and MFA were not investigated as well. Table 5 shows a summary of all the studies just mentioned. This is to illustrate the investigated parameters and the respective differences in our manuscript.

When looking at the results of the present study, it becomes obvious that nearly all ICCs represent good to excellent correlations. Only the intra- and interobserver ICCs for JLCA are out of line and provide solely poor correlations. At a closer look at the standard values of the JLCA (1 ± 1°), it becomes apparent that a planning discrepancy of 1.38° in two successive examinations of two different observers of the same X-ray results in a relatively large discrepancy (proportional error = 138%; Table 4). This might explain why even small measurement inaccuracies become noticeable in a relatively smaller ICC. In accordance with objective 1, it can be concluded that the reliability of the individual parameters is good, except of the JLCA.

Furthermore, it was investigated which parameter is most susceptible to observer-dependent errors in determining lower limb alignment in the frontal plane. To date, there are no clear criteria for the indication of THE. The growth of the child and the development of the leg axis in children and adolescents show a high physiological range in younger patients and a typical course. While children under 2 years of age show a physiological varus alignment, a valgus leg axis develops until about 7 years of age. With advancing skeletal maturation (about 8 to 10 years of age), the range decreases significantly, which is also reflected in a decrease in the spontaneous correction of the existing leg axis deformities [36]. The results of this study refer to children aged 10 years and older, in whom the spontaneous correction potential is already reduced. Radtke et al. [8] indicate a THE of the knee at a MAD of > 10 mm, regardless of whether the deviation is medial or lateral. They were not using the MFA for indication. The same applies to other studies. Gupta et al. [37] considered a MAD of 3 mm both medial and lateral as a normal value and described a deviation of the MFA lateral to the lateral intercondyloid tubercle as valgus malalignment and a deviation medial to the medial intercondyloid tubercle as varus malalignment. In contrast, Stevens et al. [38] divide the knee joint in an anteroposterior radiograph into three zones lateral and three zones medial, mirrored at the knee joint center. Here, neither the MFA nor the MAD is directly considered. They see an indication for a THE in the case of a deviation of the mechanical bearing line in zones 2 and 3 [38].

Regarding the results of the present study, we can postulate that the SEM95% of MFA, MAD, mLPFA, mLDFA, mMPTA and mLDTA are likewise high. Thus, the results suggest that if a MFA measurement of 3° valgus is assumed, an SEM95% of ± 1.39° means that the actual value will range between 1.61° (non-pathologic) and 4.39° (pathologic) valgus. In addition, a MAD measurement of −10 mm lateral to the center of the knee with a SEM95% of ± 3.31 mm means that the actual value ranges between −6.69 mm (non-pathologic) and -13.31 mm (pathologic) valgus. This susceptibility to error must be taken into account not only for leg alignment parameters but also for joint surface angles when interpreting malalignment analysis and must be considered when planning a surgical intervention. An inaccurate and wrong interpreted malalignment analysis may result in an incorrect diagnosis, which in turn leads to an unnecessary indication for surgical therapy. Furthermore, it could lead to termination of the guided growth intervention by a removal of the tension band plates at the wrong point of time. Considering the SEM95% of the MAD and the MFA, a wrong interpretation could also be an explanation for the high rebound rates of up to nearly 50% [39]. Therefore, it must be discussed whether an overcorrection of the leg axis with a minimum of 1.39° MFA and 3.31 mm MAD should be aimed to prevent the common phenomenon of rebound by taking the respective SEM95% into account. This slight overcorrection is already recommended by several authors [40, 41]. Thus, a precise malalignment measurement and the knowledge about the presented SEM95% of the respective parameters is crucial for a correct surgical or nonsurgical treatment. In addition, we were able to show that by measuring the MAD and MFA, the SEM95% are comparable (proportional error = 47.29% vs. 46.33%, respectively). Hereby, we consider the MAD and MFA to be equally (im)precise parameters for the determination of an axial malalignment and initiation of a growth-guiding therapy. In order to decide on which bones to perform growth guidance, mLDFA and mMPTA show distinct observer-dependent differences. The proportional error for mLDFA is lower at 42.2% than for mMPTA at 51.60%.

In addition to the observer-dependent errors, the radiological acquisition technique also influences the result of the respective angles [13, 42, 43]. When taking the full-leg radiograph, the patellae of the extended legs have to be aligned frontally (not the feet) so that the femoral condyles are positioned parallel to the frontal plane. Rotation of the leg at the time the image is taken should be avoided, as should flexion of the knee joint. In the case of increased internal rotation of the knee joints, the leg axis appears more valgus; in the case of external rotation, it appears correspondingly more varus [13]. In our study cohort, an internal quality assessment was performed first by the executing radiology assistants and subsequently by the two analyzing observers. All included patients showed qualitatively unobjectionable radiographs.

Furthermore, SEM95% of tibial and femoral length was determined. Those values are essential for a proper estimation of residual growth and correction potential using the multiplier method according to Paley [15, 16, 44]. The multiplier method need an exact determination of the bone length (either tibia or femur) to give a precise information about the correction potential. We could show that the ICCs of the length determination were good and the SEM95% were relatively high with ± 4.53 mm for the femur and ± 3.12 mm for the tibia. Since the femur length shows no significant difference in the measurement of two different examiners, the measurement method for determining the center of the femoral head with the aid of a circle around the femoral head with the determination of the most distal points of the two femoral condyles does not seem to be examiner-dependent and could be seen as precise when analyzing the residual growth and correction potential with the multiplier method. Due to the slightly lower SEM95% in determining the tibial length, which were 1.64% of the total tibia length and ± 1.96% of the total femur length, the tibial length can be considered as precise as well. Again, it is important to know the error and include it in the analysis in predicting growth potential for each bone.

One limitation of this study is that it did not aim to identify differences in the experience of the two examiners. However, Vaishya et al. [45] showed that more experienced examiners tend to perform more precise measurements. Other studies (e.g., Gordon et al. [31]) did not find any experience-dependent differences in intra- or interobserver reliability with excellent agreement for all observers. In accordance with Vaishya et al. [45], we consider the measured values of this study to be highly reliable and reproducible and may not be improved with further experience of the observers.

In conclusion, a precise malalignment measurement and the knowledge about the presented SEM95% of the respective parameters are crucial for a correct surgical or nonsurgical treatment. The susceptibility to error must be included when interpreting malalignment analysis and must be considered when planning a surgical intervention. The ICC and SEM95% values in this study indicate how reproducible, reliable and precise radiological assessment of variables are obtained from an X-ray. In general, with any individual measurement, it should be understood that a measurement can never be determined exactly but is always subject to a certain measurement error or measurement inaccuracy. The same applies to anatomical standard values, which also have their physiological range. The results of this study elucidate that MAD and MFA show no different susceptibility to observer-dependent errors. In addition, due to no significant difference in determining the femoral length between two different observers and a lower SEM95% for tibial length by two different observers, both femoral and tibial length may be considered precise when analyzing the residual growth and correction potential for the respective bone, for instance, with the multiplier method. This study shows good to excellent intra- and interobserver ICCs for all leg alignment parameters and joint surface angles, except for JLCA. Furthermore, according to the SEM95% and proportional errors the determination of joint surface angels of the femur seems to be more precise than for the tibia. In unclear or borderline cases with marginal MAD and MFA, instrumented gait analysis and the determination of dynamic joint loading [4, 5, 11] should be included to determine whether surgical or nonsurgical treatment should be preferred.