Association between six anthropometric indexes and kidney stones: a population-based cross-sectional study

Introduction

Kidney stones (KS) are a common disease of the urinary system, and their incidence varies globally, with male prevalence significantly higher than that of females (1). KS have emerged as a worldwide public health issue, which has an consequence on patients’ quality of life and health status (2). According to statistics, the incidence of KS has shown a rising trend in recent years, especially in developed countries, and its prevalence has reached a worldwide concern (3). The prevalent KS population includes individuals with genetic predisposition, high blood pressure, high salt dietary habits, and metabolic disorders (4). The main causes of KS formation include abnormalities in urine composition, such as oxalate and calcium overload, and changes in urine pH, which lead to the deposition of crystals in the kidneys and the formation of stones (5). Poor dietary habits and lifestyles also increase the risk of stone formation (6). Therefore, in-depth studies on the factors involved in the formation of KS are of great clinical significance.

Anthropometric indexes have become one of the most essential tools for assessing an individual’s health status and risk of disease (7,8). Measures such as a body shape index (ABSI), lipid accumulation products (LAPs), triglyceride-to-high-density lipoprotein cholesterol (TG/HDL-C), triglyceride and glucose index (TyG), visceral adiposity index (VAI), and waist triglyceride index (WTI) have demonstrated their value in assessing metabolic health and chronic disease (9). The ABSI, an index based on waist circumference (WC) and height, is considered a powerful tool for assessing abdominal obesity and associated conditions (10). LAP reflects the accumulation of lipids in the body through the combined measurement of WC and TG levels and is often used to assess the risk of metabolic disease (11). TG/HDL-C is considered a valid predictor of the risk of cardiovascular disease (CVD) and metabolic disorders (12). TyG combines TG and glucose measurements to assess the extent of insulin resistance and abnormal glucose metabolism (13). VAI and WTI reflect the accumulation of visceral fat and waist fat, respectively, and are relevant for assessing the risk of obesity-related diseases (14). Among these measures, those related to visceral fat accumulation and metabolic abnormalities have attracted particular attention. Excessive accumulation of visceral fat is strongly linked to a variety of diseases such as inflammation, insulin resistance, and metabolic syndrome, and is also considered to be an essential risk factor for the formation of KS (15). Therefore, it is crucial to explore the link between these anthropometric indexes and KS to gain a deeper understanding of the mechanisms and factors influencing the formation of KS. Although some studies have examined the link between obesity, metabolic abnormalities and KS, there is a lack of in-depth research on the correlation between these specific anthropometric indexes and KS (16). Therefore, our study aimed to investigate the role of ABSI, LAP, TG/HDL-C, TyG, VAI, and WTI in KS formation by analyzing the associations between these anthropometric indexes and KS in adults. We present this article in accordance with the STROBE reporting checklist (available at https://tau.amegroups.com/article/view/10.21037/tau-2025-738/rc).

Methods

Study population

This study utilized a cross-sectional design, analyzing data from National Health and Nutrition Examination Survey (NHANES) to examine the prevalence and relationships between key variables at specific time points. As a repeated cross-sectional survey, NHANES collects snapshot observations from different population samples each cycle, enabling the assessment of population-level characteristics and associations without establishing temporal sequences between exposures and outcomes. All analytical methods were appropriately adapted for the complex survey design, incorporating sampling weights, stratification, and clustering to ensure nationally representative estimates.

The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. In this study, a total of 59,842 people participated in the 2007–2018 NHANES survey. We excluded participants with age <20 years (n=25,072), missing information on assessment data of KS (n=91), who were pregnant (n=372), and participants with miss data in components of anthropometric indexes (n=20,175). A total of 14,132 participants were included for the study (Figure S1).

Assessment of KS

The determination of KS was based on self-reported questionnaire data. Participants were asked, “Have you ever had kidney stones?” This question was administered consistently across all NHANES survey cycles from 2007 to 2018. Individuals who responded affirmatively were classified as having a history of physician-diagnosed KS (1).

Assessment of six anthropometric indexes

After 8.5 hours of fasting, individual blood samples were tested for lipids, including total cholesterol (TC), TG, low-density lipoprotein cholesterol (LDL-C), and high-density lipoprotein cholesterol (HDL-C). The measurement of fasting blood glucose (FBG) was measured through enzymatic assays on Roche Cobas 6000 chemistry analyzers. The hexokinase-mediated reaction was utilized on Roche/Hitachi Cobas C 501 chemistry analyzers for measuring FBG. Individuals’ height (m), weight (kg), and WC (cm) were measured by standardized protocols. Body mass index (BMI) was calculated by dividing weight (kg) by the square of height (m). ABSI, LAP, TG/HDL-C, TyG, VAI, and WTI were calculated by using the following formulas (10-13): ABSI = WC (cm)/[BMI (kg/m²)^2/3 − height (m)^1/2]; LAP = [WC (cm) − 65] × TG (mmol/L) for male and [WC (cm) − 58] × TG (mmol/L) for female; VAI = [WC (cm)/39.68 + (1.88 × BMI (kg/m²))] × (TG (mmol/L)/1.03) × (1.31/HDL-C (mmol/L)) for male and [WC (cm)/36.58 + (1.89 × BMI (kg/m²))] × (TG (mmol/L)/0.81) × (1.52/HDL-C (mmol/L)) for female; TG/HDL-C = TG (mg/dL)/HDL-C (mmol/L); TyG = Ln [TG (mg/dL) × FBG (mg/dL)/2]; WTI = Ln [TG (mg/dL) × WC (cm)/2].

Assessment of covariates

We collected information about age (years), sex (male or female), race/ethnicity (Mexican American, other Hispanic, non-Hispanic White, non-Hispanic Black, or other race), education level (below high school, high school, or above high school), marital status (married/living with partner, or single/divorced/widowed), total energy intakes (kcal/day), serum calcium (mmol/L), serum phosphorus (mmol/L), estimated glomerular filtration rate (eGFR; mL/min/1.73 m²), and urinary creatinine (mg/dL) from NHANES. Based on their marital status, participants were categorized as married/living with a partner and single/divorced/widowed (1,3). Poverty-to-income ratios (PIRs) were calculated by dividing household income by specific factors of household size and composition, and categorized into three groups (≤1.0, 1.1–3.0, or >3.0) (17). Smoking status was categorized as never smoker (reported smoking <100 cigarettes in lifetime), former smoker (≥100 cigarettes and quit smoking), or current smoker (≥100 cigarettes and still smoking), based on standardized NHANES questionnaire items (18). Drinking status was classified as nondrinker, low-to-moderate drinker, or heavy drinker (male: ≥2 drinks/day; female: ≥1 drinks/day) (18). Physical activity was divided into three groups: inactive, insufficiently active [moderate activity 1–5 times per week with metabolic equivalents (MET) 3–6 or vigorous activity 1–3 times per week with MET >6], and active (19,20). CVD diagnosis was established by self-reported physician diagnoses gathered through standardized medical questionnaires during individual interviews. Participants were asked about prior diagnoses of congestive heart failure, coronary heart disease, angina pectoris, myocardial infarction, or stroke. Any affirmative response to these inquiries indicated the presence of CVD (21). Dietary total energy intake was determined from detailed dietary recall data obtained during interviews, encompassing all consumed foods and beverages. Serum calcium, serum phosphorus, eGFR, and urinary creatinine, categorized into quartiles, were also recorded for analysis. For further details regarding NHANES data collection and testing procedures, please refer to the official website: https://wwwn.cdc.gov/nchs/nhanes/default.aspx.

Statistical analysis

Following NCHS analytical guidelines, we adhered meticulously to integrating primary sampling units, sample weights, and strata across all stages of data analysis to produce reliable national estimates. Weighted analyses were conducted using the “survey” package in R to ensure accuracy and representativeness. Normally distributed continuous variables were presented as means with standard errors (SEs), whereas non-normally distributed continuous variables were presented as medians with interquartile ranges (IQRs). Categorical variables were presented as numbers with percentages. Continuous variables were compared using Student’s t-test (for normal distribution) or Mann-Whitney U test (for non-normal distribution), while categorical variables were compared using the Chi-squared test.

The missing data for the covariates were interpolated using the “mice” package, employing the random forest algorithm. For most covariates, the proportion of missing data was less than 5.0%. However, 9.2% of the study participants had missing data for the PIR, 7.1% for drinking status, and 5.1% for total energy intakes. As a sensitivity analysis, we repeated the multivariable logistic regression using a complete-case dataset by excluding participants with any missing covariate data.

The anthropometric indexes were divided into quartiles, with the lowest quartile serving as the reference category. Multiple logistic regression models were employed to determine the adjusted odds ratios (ORs) and 95% confidence intervals (CIs) for the association between six anthropometric indexes and the prevalence of KS. Restricted cubic spline (RCS) regression models were used to assess potential non-linear associations between anthropometric indexes and KS prevalence. To determine the optimal knot placement, we compared models using three knots (placed at the 10th, 50th, and 90th percentiles of each index distribution) and four knots (placed at the 5th, 35th, 65th, and 95th percentiles). The model with three knots was selected for the final analysis based on a lower Akaike information criterion (AIC) value, indicating a better balance between model fit and complexity, and in accordance with the principle of parsimony for RCS regression in large epidemiological samples. Threshold effect analysis of LAP and VAI on the prevalence of KS using piecewise binary logistic regression models.

Plotting receiver operating characteristic (ROC) curves and assessing the ability of six anthropometric indexes to identify individuals with KS used area under the curve (AUC). Spearman’s correlation analysis was used to calculate the correlation coefficients among six anthropometric indexes. The XGBoost model was used to explore the relative importance of anthropometric indexes in predicting the presence of KS. To enhance the robustness of the findings, we applied 10-fold cross-validation during model training to reduce overfitting and improve generalizability. The XGBoost model comes with the feature importance attribute, which is a measure of the contribution of the features in the model, and helps us find the features that are the most important for the prediction of KS.

In addition, stratified analyses were also conducted to assess whether subgroup variables (age, sex, race, marital status, education level, family PIR, smoking status, drinking status, physical activity, and self-reported CVD) had an impact on the association between six anthropometric indexes and the prevalence of KS. All statistical analyses were conducted using R software (version 4.2.0). A two-sided P value <0.05 was considered statistically significant.

Results

The characteristics of all participants at baseline

Table 1 describes in detail the demographic and clinical characteristics of the study participants. The final analysis included 14,132 individuals, of whom 1,353 (53.1%) were diagnosed with KS. The mean age of the participants was 47.36 years old, and 49.0% were male. The median of ABSI, LAP, TG/HDL-C, TyG, VAI, and WTI was 0.081 (IQR, 0.078–0.085), 40.95 (IQR, 22.61–72.34), 0.23 (IQR, 0.16–0.33), 8.54 (IQR, 8.12–8.97), 1.37 (IQR, 0.83–2.35), and 111.14 (IQR, 71.44–173.84), respectively. Persons with KS may be older men, non-Hispanic White, single/divorced/widowed, nondrinkers, former smokers, and less physically active compared to persons without KS (P<0.05). Serum phosphorus and eGFR were significantly lower and urinary creatinine was significantly higher in individuals with KS compared to those without KS (P<0.05). In addition, six anthropometric indexes were significantly higher in participants with KS (P<0.05).

Association between six anthropometric indexes and the prevalence of KS

Table 2 shows the association of six anthropometric indexes with the prevalence of KS among the general adults. In the unadjusted model, the fourth quartile of ABSI, LAP, TG/HDL-C, TyG, VAI, and WTI were positively linked with the prevalence of KS. After adjusting for age, sex, race, and marital status, the relationship remained statistically significant (P<0.05). Further adjustment in Model 2 for education level, family PIR, drinking status, smoking status, physical activity, total energy intakes, serum calcium, serum phosphorus, eGFR, urinary creatinine, and self-reported CVD revealed that compared to the first quartile, the fourth quartile of ABSI [OR =1.460; 95% confidence interval (CI): 1.106–1.925], LAP (OR =1.880; 95% CI: 1.487–2.377), TG/HDL-C (OR =1.334; 95% CI: 1.058–1.682), TyG (OR =1.303; 95% CI: 1.018–1.688), VAI (OR =1.516; 95% CI: 1.206–1.906), and WTI (OR =1.559; 95% CI: 1.236–1.967) were positively linked with the prevalence of KS after multivariable adjustment.

We further explored whether there was a nonlinear link between the six anthropometric indexes and the prevalence of KS (Figure 1). Study showed that LAP and VAI were positively and non-linearly related to the prevalence of KS, with inflection points of 50.45 and 1.62, respectively. The correlations between the remaining four indexes and the prevalence of KS were linearly positive. Segmented binary logistic regression modeling showed that the positive association of LAP and VAI with the prevalence of KS existed only in those with LAP ≤50.45 and VAI ≤1.6 (Table 3). When LAP ≤50.45, the prevalence of KS increased by 200% for each 1-standard deviation (SD) increase in LAP (OR =2.003; 95% CI: 1.162–3.450). When VAI ≤1.6, the prevalence of KS increased by 276% for each 1-SD increase in VAI (OR =2.764; 95% CI: 1.337–5.715).

Figure 1 The exposure-response associations of six anthropometric indexes with the prevalence of kidney stones by restricted cubic spline. Analyses were adjusted for covariates age (continuous), sex (male or female), race/ethnicity (non-Hispanic White, non-Hispanic Black, or other race), marital status (married/living with partner, or single/divorced/widowed), education level (below high school, high school, or above high school), family PIR (≤1.0, 1.1–3.0, or >3.0), drinking status (nondrinker, low-to-moderate drinker, or heavy drinker), smoking status (never smoker, former smoker, or current smoker), physical activity (inactive, insufficiently active, or active), total energy intakes (in quartiles), serum calcium (continuous), serum phosphorus (continuous), eGFR (continuous), urinary creatinine (in quartiles) and self-reported CVD (yes or no). ABSI, a body shape index; CVD, cardiovascular disease; eGFR, estimated glomerular filtration rate; LAP, lipid accumulation product; PIR, poverty-to-income ratio; TG/HDL-C, triglyceride-to-high-density lipoprotein cholesterol; TyG, triglyceride-glucose index; VAI, visceral adiposity index; WTI, waist triglyceride index.

Anthropometric indexes for predicting KS

Based on the ROC curve analysis, we found that LAP (AUC =0.592) was the strongest predictor of KS among six anthropometric indexes (Figure 2A). The correlations among six anthropometric indexes were showed in Figure 2B. We found a strong positive correlation between LAP and WTI (r=0.95). The XGBoost model showed that LAP had the highest importance among the six anthropometric indexes associated with KS (Figure 2C).

Figure 2 Ability of six anthropometric indexes to identify individuals with kidney stones. (A) The ability of six anthropometric indexes to identify individuals with kidney stones was assessed by ROC curves. (B) Spearman’s correlation analysis was used to calculate the correlation coefficients among six anthropometric indexes. (C) Use the XGBoost model to find the anthropometric indexes with the most significant features. ABSI, a body shape index; AUC, area under the curve; FPR, false positive rate; PIR, poverty-to-income ratio; LAP, lipid accumulation product; ROC, receiver operating characteristic; TG/HDL-C, triglyceride-to-high-density lipoprotein cholesterol; TPR, true positive rate; TyG, triglyceride-glucose index; VAI, visceral adiposity index; WTI, waist triglyceride index.

Stratified analysis and sensitivity analysis

Table 4 presents the results of stratified analyses examining the associations between quartiles of LAP and the prevalence of KS among adult. The analyses were stratified by various demographic and lifestyle factors, including age, sex, race, marital status, family PIR, education level, smoking status, drinking status, physical activity, and self-reported CVD. Overall, significant associations between higher LAP quartiles and increased prevalence of KS were observed across most subgroups. However, the relationship between LAP and KS prevalence was not affected by these stratification characteristics. Additionally, we conducted stratified analyses examining the relationship between the remaining five anthropometric measures and the prevalence of KS (Tables S1-S5). Similar results were observed, reaffirming the consistent positive association between these anthropometric measures and the prevalence of KS across various subgroups.

As a sensitivity analysis, we re-ran the multivariable logistic regression models using only participants with complete data on all covariates (n=11,499, Table S6). The associations between the six anthropometric indexes and the prevalence of KS remained materially unchanged in both direction and magnitude compared to the primary analysis using imputed data, indicating that our findings were robust to the handling of missing covariate data.

Discussion

In this study, we included 14,132 adults to investigate the association between six anthropometric indexes and the prevalence of KS. The study showed a linear positive correlation between ABSI, TG/HDL-C, TyG, and WTI and the prevalence of KS. However, we found that LAP and VAI were positively and non-linearly related to the prevalence of KS. Further studies found that the positive trend of correlation between LAP and VAI with the prevalence of KS existed only in those with LAP ≤50.45 and VAI ≤1.6. The ROC curves indicated that LAP was the strongest predictor of KS in adults. The XGBoost model also confirmed that LAP was the most important anthropometric indexes in individuals with KS. Stratified analyses revealed no discernible interactions between LAP and the prevalence of KS.

It is important to note that while LAP emerged as the strongest predictor among the indexes studied, the AUC value of 0.592, though statistically significant, is modest. This indicates that the anthropometric indexes examined here are not, in isolation, sufficient for precise individual-level diagnosis of KS disease. Their primary value lies instead in population-level risk stratification and in highlighting the shared metabolic underpinnings of adiposity, dyslipidemia, and nephrolithiasis. They may serve as simple, non-invasive indicators that prompt further clinical assessment or lifestyle intervention, particularly in primary care or public health settings where more complex metabolic workups are not readily available.

Epidemiologic studies have shown that the prevalence of KS has been on the rise over the past few decades and is strongly linked to factors such as dyslipidemia, obesity, and metabolic syndrome (16). Torricelli et al. found that lipid levels may be related to urine composition and stone formation (22). Taylor et al. concluded that BMI is linked to the risk of KS formation (23). Liu et al. found that weight-adjusted waist index levels were linked to an increased prevalence of KS in adults (24). Zheng et al. showed that body fat percentage (BFP) can be used to predict KS formation in bus drivers (25). Abufaraj et al. found that total fat and trunk body fat were linked to a higher prevalence of KS in adults (26). Fat distribution has a greater metabolic impact on the body than total fat (27). Visceral obesity characterized by accumulation of visceral fat is considered a strong predictor of the incidence of some diseases, but its link to KS has not yet been elucidated (28). Li et al. showed a strong link between body fat distribution (especially liver, pancreas and kidneys) and KS (29). Kim et al. found that obesity as defined by visceral adipose tissue was linked to urinary stone formation (30). Bartani et al. found a higher visceral to subcutaneous fat ratio in individuals with KS compared to controls (31). Elevated mean visceral fat area as an independent risk factor for uric acid urolithiasis according to Zhou et al. (32). Liu et al. hypothesize that visceral fat accumulation may be linked to increased risk of KS (24).

Anthropometric indices serve as cost-effective, non-invasive tools for assessing health status, predicting disease risks, and guiding clinical and public health interventions (33,34). Previous studies have shown that ABSI, LAP, TG/HDL-C, TyG, VAI and WTI can better reflect the body fat distribution and obesity level. Lin et al. indicated that ABSI and body roundness index were positively correlated with the prevalence of KS (35). Wang et al. found that a higher TyG index was linked to an increased likelihood of KS (13). Wang et al. revealed a link between VAI and the prevalence of KS in U.S. adults, and they found that those with higher VAI had a higher prevalence of KS (36). A cross-sectional study by Lee et al. reached the same conclusion (37). Our study also confirmed a significant positive correlation between six anthropometric indexes and the incidence of KS, and that LAP was the strongest predictor of KS in adults. LAP is a valuable way to identify patients with diabetes and acute pancreatitis (9). To our knowledge, this is the first study on the link between LAP and the prevalence of KS. The increase in LAP reflects the inflammatory state of adipose tissue in the body, and the inflammatory response may lead to an increase in inflammatory mediators in the urine, which in turn affects the chemical composition of the urine (38).

A complex mechanism of association exists between several anthropometric indexes and increased prevalence of KS. High ABSI is often linked to obesity, which leads to metabolic disorders and alterations in urine composition, increasing the likelihood of precipitation of crystalline material in the urine and thus promoting KS formation (39). High TG/HDL-C and TyG are indicative of disturbed lipid metabolism and abnormal blood glucose levels, respectively, which may affect the excretion of calcium and uric acid in the kidneys and increase the risk of crystalline material deposition in the kidneys (40). VAI and WTI reflect visceral and waist fat accumulation, respectively. High visceral fat accumulation releases inflammatory mediators and hormones that affect the metabolic function of the kidneys and increase the risk of KS (41). Taken together, these increases in anthropometric indexes may lead to an increased prevalence of KS through a variety of pathways that affect metabolism, inflammatory responses, and urine composition in the body.

There are several notable strengths in this study. Firstly, the utilization of data from the nationally representative NHANES database ensures a robust and comprehensive assessment of the associations examined. Secondly, the incorporation of ABSI, LAP, TG/HDL-C, TyG, VAI, and WTI as anthropometric measures provides a holistic evaluation of body fat distribution and metabolic health, surpassing the limitations of traditional measures. Thirdly, this study utilized the XGBoost machine learning method to evaluate the association between six anthropometric indexes and KS. XGBoost is adept at capturing nonlinear relationships, thereby enhancing performance through optimization techniques like gradient boosting. Its feature importance ranking capability aids in identifying the most influential anthropometric indexes. Additionally, XGBoost’s robustness to overfitting ensures dependable predictions, while its scalability renders it efficient for analyzing large datasets.

A key methodological limitation is the reliance on self-reported KS history, which is subject to recall bias and was not verified by radiologic imaging or medical record review in NHANES. This methodology also does not allow for verification of stone type, burden, or recurrence. Our analysis therefore treats KS as a single outcome, without differentiation between stone types (e.g., calcium-based, uric acid) or between individuals with a single episode versus recurrent stone disease. This limits our ability to identify subtype-specific risk relationships or to assess the strength of association with more severe, recurrent disease. The cross-sectional study cannot establish causal relationships between anthropometric measures and KS risk due to inherent temporal limitations, including potential misclassification from grouping distinct stone-forming populations and discordance between current metabolic profiles and those during active stone formation. Furthermore, a major limitation of this study is the exclusion of over 50% of the initial NHANES cohort due to missing anthropometric data required to compute the six indexes. While this was methodologically necessary to maintain a consistent and well-defined exposure across all participants, it may have introduced selection bias and limited the representativeness of the final sample. The excluded individuals may differ systematically from those included in terms of health status, healthcare access, or socioeconomic factors, potentially affecting the generalizability of our findings. Although we applied multiple imputation for covariates with low missingness, the core anthropometric exclusions were unavoidable and underscore the need for cautious interpretation of the observed associations. Third, although we adjusted for a wide range of demographic, lifestyle, and clinical covariates, the possibility of residual confounding persists. Notably, detailed dietary factors (e.g., intake of oxalate, calcium, sodium, or animal protein), genetic predisposition to nephrolithiasis, and family history of KS were not comprehensively measured in the NHANES data and thus could not be fully accounted for in our models. These unmeasured factors may influence both anthropometric profiles and KS risk, potentially confounding the observed associations. Lastly, the focus on the U.S. population may constrain the generalizability of findings to other populations or geographic regions, necessitating future research involving diverse cohorts to ensure a comprehensive understanding of the associations between anthropometric indexes and KS.

Conclusions

Our findings revealed a positive association between six anthropometric indexes (ABSI, LAP, TG/HDL-C, TyG, VAI, and WTI) and the prevalence of KS, with LAP emerging as the most significant anthropometric index in individuals with KS. Future research may explore interventions targeting LAP to mitigate the risk of KS development and further elucidate the underlying mechanisms linking anthropometric indexes to KS formation.

Acknowledgments

We would like to thank the people who contributed to the NHANES data we studied.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://tau.amegroups.com/article/view/10.21037/tau-2025-738/rc

Peer Review File: Available at https://tau.amegroups.com/article/view/10.21037/tau-2025-738/prf

Funding: This work was supported by the project “Establish an Early Warning Model for Renal Calculi in Civil Aviation Pilots” (No. 254).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tau.amegroups.com/article/view/10.21037/tau-2025-738/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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