Introduction

Osteoclastogenesis is tightly regulated by osteoblasts via the secretion of a receptor activator of nuclear factor kappa B ligand (RANKL) and osteoprotegerin (OPG), to ensure adequate bone modeling in childhood and adolescence and thus achieve proper peak bone mass in young adulthood [1,2,3,4]. The binding of RANKL to its receptor RANK, expressed by osteoclast progenitor cells and dendritic cells, triggers the activation and differentiation of osteoclasts along with the prevention of their apoptosis, which causes resorption of newly formed bone allowing osteoblasts to lay down new bone, resulting in bone metabolic turnover [1, 2, 4]. RANKL exists in three forms: as a transmembrane protein expressed by osteoblasts and other cells of the mesenchymal lineage, as a soluble molecule released by enzymatic cleavage, and as a primary secreted form produced by activated T-lymphocytes [2]. OPG acts as a decoy receptor by blocking the binding between RANKL and RANK and is therefore the major inhibitor of osteoclast development and bone resorption [5, 6]. OPG exists as monomer, dimer and RANKL/OPG complexes [1].

An increased ratio of soluble RANKL (sRANKL) to OPG is associated with increased bone turnover and bone loss in adults [4]. Preliminary studies suggest that elevated sRANKL and/or reduced OPG concentrations result in increased bone resorption and reduced bone mass in children suffering from rheumatoid arthritis, systemic lupus erythematodes, and obesity [6,7,8,9,10,11]. However, the interpretation of these studies is hampered by the lack of adequately sized control cohorts, especially since they included boys and girls of different ages and stages of maturation. The development of Lambda-Mu-Sigma (LMS)-based continuous reference percentiles for laboratory parameters allows calculation of patient z-scores and improved data interpretation in clinical practice and studies [12,13,14,15].

To fill the gaps, we established the LMS-based continuous pediatric reference percentiles for sRANKL, OPG and sRANKL/OPG ratio in the HAnnover Reference values for Pediatrics (HARP) study.

Methods

Study design and subjects

HARP, a monocentric cross-sectional study aiming to establish reference values for important laboratory parameters in children, began in 2021. Children aged 0.1–18.0 years were enrolled either from outpatient clinics at University Children’s Hospital, Hannover Medical School, Hannover, Germany, referred for diagnostic work-up, or participated in a study on the effects of a school-based exercise program (only samples at study begin were included) (Fig. 1). Exclusion criteria for this study were: growth retardation, malnutrition, diabetes mellitus, history of fractures, reduced mobility, bone disease, infections (C-reactive protein (CRP) > 5 mg/l), inflammatory or liver disease, anemia (hemoglobin levels below the age-related lower limit), estimated glomerular filtration rate (eGFR) below the age-related normal range, proteinuria (protein to creatinine ratio > 0.2 g/g), tubular dysfunction or medication potentially interfering with bone or mineral metabolism. In this analysis a total of 300 children (166 boys) with a median age of 11.5 years (interquartile range (IQR) 7.6–14.8 years) were included (Table 1). The study protocol was approved by the Ethics Committee of Hannover Medical School and the study was performed in accordance with the Declaration of Helsinki. Informed consent was obtained from all parents/guardians with age-appropriate consent from the children and adolescents.

Fig. 1
figure 1

Flow chart for the selection of participants in the HAnnover Reference for Pediatrics (HARP) study for the measurement of OPG and sRANKL. CRP, C-reactive protein; eGFR, estimated glomerular filtration rate

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Table 1 Demographic, anthropometric and biochemical parameters in boys and girls
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Sample collection, anthropometric, and laboratory analyses

All children underwent standardized anthropometric evaluation including height/length and weight. Blood samples were obtained between 8:00 and 12:00 am, usually at least 2 h after the last intake of a meal, in parallel with the second morning urine. Samples were stored at -80 °C until assayed. Calcium (Ca), phosphate (Pi), CRP, creatinine (Crea) and 25-hydroxy-vitamin D (25(OH)D) in serum, as well as Ca, Pi and Crea in urine were determined via established automated procedures (Cobas 8000, module c701, Roche Diagnostics, Mannheim, Germany). 25(OH)D levels were subdivided into insufficient and deficient concentrations as previously described [16]. eGFR was calculated by the Schwartz formula [17, 18]. Serum sRANKL (Human Free soluble RANKL, BI-20462, Biomedica Immunoassays) and plasma OPG (Human Osteoprotegerin ELISA, #RD194003200, BioVendor) levels were determined in duplicate by sandwich enzyme-linked immunosorbent assays (ELISA) according to the manufacturer´s protocol using Tecan 96-well plate reader (Tecan infinite M200 PRO). sRANKL and OPG concentrations were quantified with Magellan software (Magellan 7.2 SP1). and the sRANKL/OPG ratio was calculated for every subject. The limit of detection for these assays were 0.01 pmol/L (sRANKL) and 0.03 pmol/L (OPG) with an intra- and inter-assay precision of ≤ 4% and ≤ 3% for sRANKL and ≤ 4.9% and ≤ 9.0% for OPG, respectively.

Statistical analysis

Data is presented as mean ± SD or median (IQR) according to Shapiro–Wilk normality tests. Differences between groups were assessed by unpaired t-test or Mann–Whitney U test, respectively, with two-sided p values and p < 0.05 considered to be statistically significant. Correlation analyses were performed using the Pearson or Spearman correlation coefficients, respectively. All statistical analyses were performed with IBM SPSS Statistics version 27 and GraphPrad Prism version 9. Age and sex-related z-scores for height/length, weight and body mass index (BMI) were calculated using national reference values according to the following formula: z = ((x/M)L-1)/(S \(\times\) L) for L \(\ne\) 0 [19]. Z-scores for serum Ca and Pi, and urinary Ca/Crea and Pi/Crea ratios were calculated using reference values from healthy children [20, 21] according to the following equation [22], POI = parameter of interest, upper = upper limit of range, lower = lower limit of range, SD = standard deviation, and ln = natural log (i.e. Log base e):

  • Step 1: \(PO{I}_{logmean}=\frac{ln\left(upper\right)+ln(lower)}{2}\)

  • Step 2: \(PO{I}_{logSD}=\frac{ln\left(upper\right)-ln(lower)}{4}\)

  • Step 3: \(PO{I}_{z-score}=\frac{ln\left(POI\right)-PO{I}_{logmean}}{PO{I}_{logSD}}\)

LMS-based continuous reference percentiles for sRANKL, OPG, and sRANKL/OPG ratio were created using the open-source software RefCurv 0.4.2 for Windows with generalized additive models for location, scale and shape (GAMLSS) package developed by Winkler et al. [23]. The mathematical method is based on the Box-Cox-Cole-Green distribution (BCCG) and penalized splines in the distribution parameters Lambda (skewness), Mu (median) and Sigma (coefficient of variation) [24,25,26]. The degree of freedom of each penalized spline of L, M and S determines the outcome of the model. A higher degree of freedom results in greater flexibility of the curves. The Bayesian Information Criterion (BIC) was used as a decision support for model selection. The combination of L, M and S with the lowest BIC is assumed the most suitable in the tradeoff between the best fit and complexity regarding the chosen data. The following combinations were used to calculate the percentile curves and LMS values: sRANKL boys: L = 1, M = 2, S = 0 with BIC = -88.7889; sRANKL girls: L = 0, M = 1, S = 0 with BIC = -125.8139; OPG: L = 0, M = 0, S = 0 with BIC = 1032.98; sRANKL/OPG boys: L = 0, M = 2, S = 0 with BIC = -507.0101; sRANKL/OPG girls: L = 0, M = 1, S = 0 with BIC = -439.1746. Normal distribution of residuals including QQ-plots and worm plots were verified as quality control steps for each LMS model computed with RefCurv (Supplemental Figs. 1–5).

Results

Demographic, anthropometric and biochemical characteristics of the HARP cohort

The demographic, anthropometric and biochemical parameters of 300 children (55% boys) enrolled in HARP are summarized in Table 1. The median standardized values for height/length, weight and BMI, serum/urine parameters for mineral metabolism, and eGFR did not differ from healthy children. As expected in this North European population studied at different times of the year many children showed reduced serum 25(OH)D levels (56%).

LMS-based percentiles and LMS values for sRANKL, OPG, and sRANKL/OPG ratio

Both serum concentrations for sRANKL and OPG were negatively associated with age, while sRANKL also associated with sex (Fig. 2a–c, Table 2). In boys, sRANKL percentiles were highest during infancy (0—2 years), followed by a continuous decline until the age of 7 years, and a second peak at 12–13 years of age, the time of expected onset of pubertal growth spurt, to then drop to adult values by the age of 18 years (Fig. 2a, Table 2a). In girls, a continuous slow decline of sRANKL percentiles was noticed from infancy (0—2 years) onwards until the age of 13 years, followed by a rapid decline until adulthood (Fig. 2b, Table 2b). OPG percentiles continuously declined from infancy to adulthood, irrespectively of sex (Fig. 2c, Table 3). The percentiles for sRANKL/OPG ratio paralleled those of sRANKL in both boys and girls (Fig. 2d and e, Table 4).

Fig. 2
figure 2

LMS percentiles for serum sRANKL (a, boys; b, girls), OPG (c), and the sRANKL/OPG ratio (d, boys; e, girls) according to age. The 2.5th, 10th, 25th, 50th (bold line), 75th, 90th, and 97.5th percentiles are given

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Table 2 Age-specific percentile limits and LMS values for soluble receptor activator of nuclear factor kappa B ligand (sRANKL) in boys and girls
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Table 3 Age-specific percentile limits and LMS values for osteoprotegerin (OPG) independent of sex
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Table 4 Age-specific percentile limits and LMS values for sRANKL/OPG ratio in boys and girls
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Correlations of sRANKL and OPG with anthropometric and mineral metabolism parameters

In both boys and girls, serum concentrations of sRANKL correlated with OPG (boys: r = -0.171, p = 0.034; girls: r = -0.365, p < 0.0001) (Fig. 3a and b) and serum phosphate z-scores (boys: r = 0.2216, p = 0.0093; girls: r = 0.2743, p = 0.0044; Fig. 3c and d). OPG concentrations were inversely associated with standardized body weight (r = -0.266, p < 0.0001), BMI (r = -0.239; p < 0.0001) and urinary phosphate to creatinine ratio (r = -0.172; p = 0.0165) (Fig. 3e–g). In contrast, neither absolute nor categorized values for 25(OH)D serum concentrations nor serum/urinary calcium values were significantly associated with serum sRANKL or OPG levels (data not shown).

Fig. 3
figure 3

Associations between sRANKL and OPG with anthropometric and mineral metabolism parameters in the HARP cohort. a-d: associations between sRANKL and OPG and serum phosphate z-scores in boys (a: r = -0.171, p = 0.0342; c: r = 0.222, p = 0.0093) and girls (b: r = -0.365, p < 0.0001; d: r = 0.274, p = 0.0044), respectively. e–g: associations between OPG plasma concentrations and standardized weight (e: r = -0.266, p < 0.0001), BMI (f: r = -0.239; p < 0.0001) and urinary phosphate to creatinine ratio (g: r = -0.172; p = 0.0165). Pi, phosphate; crea, creatinine

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Discussion

This is the first study establishing LMS-based continuous pediatric reference percentiles for sRANKL, OPG and sRANKL/OPG ratio, which were derived from the HARP cohort. This allows the calculation of standardized patient z-scores to improve assessment and monitoring of bone modeling in children in clinical practice and studies.

In the present study, LMS percentiles for serum sRANKL, OPG and sRANKL/OPG ratio were negatively associated with age, while sRANKL and sRANKL/OPG ratio also associated with sex. Boys, but not girls, showed a second although lower peak for sRANKL and sRANKL/OPG ratio during ages 12–13 years. The strong age-dependence of all parameters assessed, with highest values during infancy, is striking. This most likely represents the physiologically highest growth rates and thus higher bone modeling in infancy compared to childhood and adolescence [3]. A second peak for sRANKL and the sRANKL/OPG ratio was observed in boys at the ages of 12–13, the point of physiological onset of pubertal growth spurt, indicating a high bone modulation with relatively increased bone resorption at this age. This further supports the concept, that increased bone modeling in early puberty, together with the strongly increased gains of height and weight but lag of bone mineral accrual, contributes to a more filigree long bone and explains the observed increased fracture rate in early puberty [27]. In addition, it has been demonstrated that sex hormones regulate RANK and sRANKL expression, possibly leading to an increase in their concentrations during puberty [28]. The absence of a second peak for sRANKL and the sRANKL/OPG ratio during puberty in girls may, at least partly, be due to the fact that girls show less bone mass accrual during puberty and consequently have less bone remodeling than boys during this period [29].

The previously largest pediatric cross-sectional study reporting on sRANKL, OPG and sRANKL/OPG ratio included 259 healthy children aged 1 to 20 years [5]. The authors noted significant associations between sRANKL and categorized values for age, Tanner stage, and BMI z-score. In addition, OPG values were inversely associated with standardized BMI. The comparison of this report with the present study is hampered, since only median and IQR, but no upper and lower limits (97.5th and 2.5th percentiles), are given in this study. In general, however, median and IQR for sRANKL/OPG appeared to be somewhat higher in the present study when compared to the 4 available age cohorts reported by Akhtar Ali et al. whereas median and IQR values for the sRANKL/OPG ratio were comparable. These discrepancies may be due, at least in part, to differences in cohort compositions and/or methodology. For example, Akhtar Ali et al. did not include infants and used very wide age ranges instead of continuous LMS percentiles, as well as a different assay, to assess OPG compared to the present study. Overall, the LMS percentiles for sRANKL, OPG and sRANKL/OPG ratio show a smoother variation with age and splitting between boys and girls, likely reflecting the physiological differences in bone modeling during puberty in boys compared to girls, when compared to the study of Akhtar Ali et al.

Wasilewska et al. investigated sRANKL and OPG values in a cohort of 70 healthy children [1]. They noted significantly higher median sRANKL values in boys compared to girls, irrespective of age, lower values in younger (age < 9 years) compared to older (> 9 years) children, while OPG levels were not associated with age, which is in contrast to the considerably larger-sized studies performed by Akhtar Ali et al. and us. Also in this study, the medians and standard deviations for sRANKL and OPG are somewhat lower compared with the present study, although the same assay for sRANKL was used in both studies. This could be due, at least in part, to the fact that sRANKL levels were undetectable in some patients and/or to the small number of participants included.

Serum sRANKL concentrations were significantly associated with OPG values, irrespective of sex, which supports the concept of strong interrelations within the sRANKL/RANKL/OPG system, which was noted in smaller-sized previous studies [1, 5, 6, 30]. In addition, sRANKL was positively associated with standardized serum phosphate and OPG was inversely associated with standardized urinary phosphate to creatinine ratio in both sexes, suggesting that both high sRANKL and low OPG levels stimulate bone resorption, thereby increasing serum phosphate levels and urinary phosphate excretion, respectively.

We identified an inverse correlation between OPG plasma concentrations and standardized values for body weight and BMI, which is in line with previous studies in healthy as well as obese children and adults [5, 7, 10, 11, 31]. Dimitri et al. investigated OPG plasma levels in healthy lean and obese children and noted that OPG levels were lowest in obese children with a prior fracture, suggesting increased bone resorption in relation to formation in obese children [7]. It has been proposed that obesity may be aggravated by a lack of physical activity, which results in low bone turnover and thus low OPG concentrations. Alternatively, obesity itself may promote osteoclast activity via secretion of adipokines like leptin, resulting in reduced OPG secretion by activation of osteoblast leptin receptors [7].

This study should be considered in the context of its limitations. Firstly, bone marker levels may differ in cohorts of different ethnic background. Due to the composition of the general population in Germany, predominantly Caucasian children were enrolled in HARP. This must be taken into account when using our reference values for children with other ethnic backgrounds. Secondly, RANKL and OPG act at the paracrine level. The determination of serum sRANKL and plasma OPG concentrations was performed using ELISA, which was satisfactory, concerning reproducibility and handling qualities. RANKL concentrations have to be differentiated into total RANKL and freely soluble RANKL. As in most other studies, free soluble RANKL levels were measured [5,6,7, 32]. Another study investigated the total RANKL levels, but specified that it is unknown whether the detected levels and activities of sRANKL are correlated to the membrane-bound protein [30]. Both free soluble and total RANKL levels may be inaccurate because of the lack of information on the tissue source of the measured RANKL concentrations and because of the uncertainty whether circulating RANKL levels represent overall levels or concentrations in specific regions of interest. Moreover, the stability of RANKL and its diurnal fluctuation were not evaluated and it is unclear whether there is an optimal point for sample collection [2]. OPG is present as a free and bound form as RANKL/OPG complexes. The ELISA kit used detects all forms of circulating OPG [30]. Thirdly, bone mass accrual can persist for up to seven years after peak height growth velocity [33]. Thus, the age range used in the present study of 0.1 to 18 years may not be sufficient to represent the entire age-related dynamic of these parameters. Fourthly, we did not evaluate the impact of combined oral contraceptives in female adolescents as they were shown to interact with growth hormone and gonadal steroid hormones [34]. Fifthly, we did not assess Tanner stages in this cross-sectional study and therefore, we could not evaluate the impact of adrenarche and pubarche on the presented reference values in our population.

In conclusion, here we present LMS-based continuous pediatric reference percentiles for sRANKL, OPG and sRANKL/OPG ratio derived from the HARP cohort, that allow calculation of standardized patient z-scores to assess bone modeling in children and adolescents in clinical practice and studies. The observed associations between sRANKL, OPG, and the sRANKL/OPG ratio with age, sex, anthropometric and mineral metabolism parameters underscore the close relationship between bone modeling, growth and maturation in children.