Introduction

According to the European Working Group on Sarcopenia in Older People (EWGSOP), sarcopenia is defined as the loss of both muscle mass and function1,2. Computed tomography (CT) imaging is the most widely used cross-sectional imaging modality worldwide and can accurately quantify fat and muscle tissue, though its use is limited by radiation exposure and cost3. CT is considered a reference standard imaging modality in assessments of body composition; however, its use is mostly limited to research, and validated sarcopenia thresholds remain an area of active discussion4. Assessments of muscle mass can be performed using CT measurements of skeletal muscle cross-sectional area (SMA) at the third lumbar vertebra (L3), with cutpoints for low muscle mass consistent with sarcopenia set at two standard deviations below the mean (-2SD) of a young, healthy adult population5,6,7,8,9,10,11,12,13,14,15,16,17,18. Muscle quality is assessed using skeletal muscle radiation attenuation (SMRA), intramuscular adipose tissue area (IMAT), and the skeletal muscle gauge (SMG)—the product of SMRA and skeletal muscle index (SMI)14,19,20,21,22,23,24. Reference ‘young, adult’ populations generally use an 18–40 or 20–40 age range15,24,25,26,27,28,29,30,31,32,33,34,35. The upper bound of 40 is supported by the observation that muscle mass loss accelerates after age 40, while differences in the lower bound (18 vs. 20) have not been explored.

Other vertebrae besides L3 have also been used in certain situations24,31,36,37,38,39. Furthermore, the particular slice used as ‘the L3 slice’ has varied between groups. While we (and others) have used an inferior slice (e.g., ‘at the level of the inferior endplate’)16,24,34, others have used a mid-vertebral slice (e.g., ‘where both transverse processes were visible’)32,40,41,42. While multiple slices have been previously examined39, it remains unclear how much difference (of one-half a vertebral body) the location of measurement affects the resulting skeletal muscle measures, or whether single-slice sarcopenic cutpoints developed at an inferior aspect slice would apply to mid-vertebral slice measures.

Revised EWGSOP guidelines note that ‘fundamentally, muscle mass is correlated with body size; i.e., individuals with a larger body size normally have larger muscle mass’2. In prior work we confirmed this relationship between body size and muscle mass, and derived the optimal L3 SMA adjustment for height (SMA/height) using allometric analysis43, a finding which has since been confirmed elsewhere44,45. We also found that direct adjustment for weight (SMA/weight) or BMI (SMA/BMI) resulted in sub-optimal, highly biased indices which should be avoided, and that the traditional skeletal muscle index using height-squared (\(SMA/height^2\))5,7,12,16,24,46,47 retained a significant negative correlation with height and positive correlation with BMI.

We proposed that the optimal body size adjusted skeletal muscle index meet two simple criteria: it should be uncorrelated with (1) height and (2) BMI in a young, healthy reference population. In doing so, it would exclude the variation in muscle quantity explained by height and BMI, resulting in a metric that distinguishes between ‘more muscular’ and ‘less muscular’ body compositions at any height or BMI. Therefore, we developed a relative muscle index (RMI) equation which converted L3 SMA into an index that is uncorrelated with height and BMI43. L3 \(RMI_{HT}\) quantified sarcopenic low L3 muscle mass across the full range of human body sizes and was unbiased in tall, short, thin, or obese individuals. However, it was limited to measurements of SMA at the inferior L3 level.

In this manuscript, we expand our analysis of young, healthy adult skeletal muscle measurements to include both a mid-vertebral and inferior aspect slice for each vertebra from T10 to L5, enabling sarcopenia assessment in CT scan protocols that do not include L3. We assess the difference between SMA measured at a mid-vertebral versus inferior aspect slice, and the effect of age group 18–40 versus 20–40 on reference values. We perform allometric analysis of proper height adjustment and report RMI equations for SMA at each slice location. Finally, we report reference means, standard deviations, and cutpoints [mean-2SD (-2SD) and 5th percentile (P5)] for younger and older age groups (18–40, Over 40) to enable comparison with other published healthy adult reference values.

Results

Population summary

Compared to the ‘Over-40’ cohort, ‘Under-40’ men and women were not significantly heavier by weight or BMI (\(p>0.18\)), nor were they significantly taller (\(p>0.02\)) (Table 1). Women were 1.64 meters tall with a BMI of 27 on average, while men were 1.79 meters with a BMI of 28 in both cohorts. In both men and women, race was significantly different between the older and younger cohorts. The younger cohort included lower proportions of Caucasian subjects than the older cohort.

Table 1 Study cohort demographics; p-values compare ‘Over-40’ to ‘Under-40’ group stratified by sex.
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Table 2 Sex-specific paired t-test results comparing within-subject mid-vertebra and inferior aspect slice SMA (\(cm^2\)).
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Vertebra slice comparison

SMA was significantly different between the mid-vertebra slice and the inferior aspect slice for all pairs except T10 in men (both cohorts) and L5 in ‘Under-40’ women (Table 2). Mid-vertebra SMA was smaller than inferior SMA for all vertebra except L4, for which mid-vertebra SMA was greater than inferior SMA. Absolute differences were greatest for L2 in women (‘Under-40’: − 8.1 \(cm^2\), ‘Over-40’: − 7.1 \(cm^2\)) and both L2 (‘Under-40’: − 13.2 \(cm^2\)) and L4 (‘Over-40’: 12.4 \(cm^2\)) in men. Percentage differences were greatest for L2 (‘Under-40’: − 7%) and T12 (‘Over-40’: − 6.9%) in women, and L4 (‘Under-40’: 7.4%, ‘Over-40’: 7.5%) in men. The mean absolute difference across all vertebra was 4.2%; 3.92% (women) and 4.2% (men) in the ‘Under-40’ cohort, and 4.39% (women) and 4.22% (men) in the ‘Over-40’ cohort. Peak SMA was observed at the L3 inferior slice in all cohorts (Fig. 1).

Figure 1
figure 1

Mid-vertebra (e.g., \(\hbox {T10}_{mid}\)) and inferior aspect (e.g., \(\hbox {T10}_{inf}\)) slice distribution of SMA (top), and allometric height-scaling coefficients (bottom) split by cohort and sex.

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Body size adjustment

Allometric analysis of weight versus height resulted in optimal coefficients of 2.1 (men) and 1.8 (women), or 2 when rounded to the nearest integer. SMA versus height analysis across vertebra levels resulted in optimal coefficients between 0.806 and 1.32 (men) and 0.845 to 1.33 (women), or 1 when rounded to the nearest integer (Fig. 1 and Table 3). Unadjusted SMA and height-adjusted SMA measures were differently correlated with age, BMI, height, and weight in both cohorts (Tables S1–S4). In the ‘Under-40’ cohort, SMA and \(SMI_{HT}\) were uncorrelated with age in women (Pearson r: − 0.076 to 0.04), but positively correlated with age in men at \(\hbox {T11}_{inf}\) through \(\hbox {L2}_{inf}\) and at \(\hbox {L5}_{inf}\)/\(\hbox {L5}_{mid}\) (r: 0.125 to 0.242) and uncorrelated at other vertebrae (r: − 0.183 to 0.131). \(RMI_{HT}\) was uncorrelated with age in both men and women (r: − 0.192 to 0.127). SMA was positively correlated with BMI (r: 0.316 to 0.775), height (r: 0.187 to 0.368), and weight (r: 0.429 to 0.803) in both men and women. \(SMI_{HT}\) was not significantly correlated with height (r: − 0.047 to 0.093), whereas \(SMI_{HT2}\) was significantly negatively correlated with height at all vertebra levels except \(\hbox {T10}_{mid}\) which did not reach statistical significance (r: − 0.326 to − 0.201). Both were positively correlated with BMI (r: 0.360 to 0.801) and weight (r: 0.208 to 0.737). Both \(RMI_{HT}\) and \(RMI_{HT2}\) were uncorrelated with BMI by design (r: 0.0), however, \(RMI_{HT}\) was uncorrelated with weight (r: − 0.016 to 0.044) and uncorrelated with height at all levels (r: − 0.034 to 0.099) except for \(\hbox {L3}_{inf}\), \(\hbox {L4}_{mid}\), and \(\hbox {L5}_{inf}\) in women (r: 0.105 to 0.121), whereas \(RMI_{HT2}\) was significantly negatively correlated with both height (r: − 0.388 to − 0.214) and weight (r: − 0.175 to − 0.090) at all vertebra levels except \(\hbox {T10}_{mid}\) (height), and \(\hbox {T10}_{inf}\)/\(\hbox {T10}_{mid}\) and \(\hbox {L5}_{inf}\)/\(\hbox {L5}_{mid}\) (weight) in both women and men, and \(\hbox {T11}_{mid}\) in men.

Table 3 Sex-specific allometric coefficients for SMA by cohort and vertebra.
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Relative muscle index equations for each slice are reported in Tables 4 and S9. Across regression equations, sex and BMI explained between 63 and 79.9% of the variation in \(SMI_{HT}\) and between 46.3 and 72.4% of the variation in \(SMI_{HT2}\) (Adjusted \(R^2\)), depending on the vertebra slice used.

Table 4 \(RMI_{HT}\) equation coefficients (a–d) and adjusted r-squared (Adj. \(R^2\)).
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Reference values

Reference cutpoints for low muscle quantity using -2SD and P5 values are shown for SMA, \(SMI_{HT}\), and \(RMI_{HT}\) by vertebra slice, split by sex and age group (Tables 5 and 6). ‘Under-40’ SMA, \(SMI_{HT}\), and \(RMI_{HT}\) were significantly higher than ‘Over-40’ at all vertebra levels for women, and at \(\hbox {L2}_{mid}\) through \(\hbox {L4}_{inf}\) (all), \(\hbox {T10}_{inf}\) (SMA, \(SMI_{HT}\)), and \(\hbox {T11}_{inf}\) (\(RMI_{HT}\)) in men. Reference values for height-squared based measures are reported in Tables S5 and S6 and for muscle quality measures SMRA, IMAT, and \(SMG_{HT}\) in Tables S7 and S8.

When comparing 18–40 vs. 20–40 age group means of SMA, there were no significant differences at any vertebra level for men or women (Table S10). Differences in -2SD cutpoints ranged from − 0.7 to 1.5 with a mean difference of 0.36 across vertebra levels.

Table 5 (Women) Skeletal muscle area reference values by age group and vertebra slice.
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Table 6 (Men) Skeletal muscle area reference values by age group and vertebra slice.
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Discussion

It is widely recognized that muscle quantity measures must be properly adjusted for body mass in order to accurately identify sarcopenic low muscle mass, however, there is no agreement on what that adjustment should be2,48,49. We propose two body mass adjusted muscle indices—a height index (\(SMI_{HT}\)), and a height-and-BMI index (\(RMI_{HT}\)). We base these indices upon the same mathematical framework as BMI. That is, since human body mass (weight) is correlated with height, a relative weight index was developed using allometric analysis of weight vs. height, which demonstrated that weight scales approximately with \(height^2\) and resulted in the body mass index (\(BMI = weight/height^2\))43,44,50,51,52. The same allometric analysis of SMA vs. height has demonstrated that SMA scales with height, not \(height^2\), and this finding has been confirmed in multiple datasets for L3 SMA. In this manuscript, we extended this finding from L3 to apply to SMA measured at all vertebrae between T10 through L5, at both mid- and inferior-aspect slices. Therefore, we propose that SMA/height be used as the consensus height-adjusted index and that \(SMA/height^2\) be discontinued.

We found that even with proper height adjustment, the resulting height-adjusted index retains a significant, positive correlation with BMI (Pearson’s r: between .36 and .80), meaning that any sarcopenic cutpoints derived from this index would be strongly biased towards identifying sarcopenia only in individuals with low BMI, which in many cases is likely to be correct. However, it limits this index’s ability to identify sarcopenia in individuals of average to high BMI (i.e., sarcopenic obesity). Therefore, we derived relative muscle index (RMI) equations for each vertebra-based SMI measure which convert height-adjusted SMI into a measure that is uncorrelated with height and BMI. Unlike SMA and SMI, RMI is decoupled from both height and BMI, therefore RMI is unbiased and able to identify sarcopenic low relative muscle mass across the full range of height and BMI in both men and women (e.g., Fig. 2). Because RMI is unitless with mean 0 and standard deviation 1 it is simple to interpret; values greater than 0 indicate higher-than-average muscle mass and values less than 0 indicate lower-than-average muscle mass for any given values of sex, height, and BMI.

Figure 2
figure 2

A vs. B: L3 axial CT images highlighting skeletal muscle area for two men of similar age, BMI, and height but different muscle area. Individual A has muscle area well within the normal range and would be classified as not sarcopenic by all cutpoints. Individual B has SMA − 1.1 s.d. and \(SMI_{HT}\) − 1.3 s.d. below the reference mean so he would be classified as not sarcopenic using the SMA and SMI -2SD cutpoints. However, his RMI is − 3.5 s.d., suggesting that he is extremely sarcopenic compared to others with similar BMI (sarcopenic obese). C vs. D: L3 axial CT images highlighting skeletal muscle area for two women of similar age, height, and muscle area but different BMI. Both women have low SMA (C = − 2.3 s.d., D = − 2.4 s.d.) and \(SMI_{HT}\) (C = − 2.16 s.d., D = − 2.14 s.d.) and would be classified as sarcopenic using the -2SD cutpoints. However, when accounting for BMI only individual D would be classified as sarcopenic since individual C (RMI = − 1.72 s.d.) is above the − 2.0 cutpoint whereas individual D (RMI = − 2.83 s.d.) is below (sarcopenic overweight). s.d., standard deviations.

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Skeletal muscle healthy reference value manuscripts generally fall into two categories when selecting which slice is used to measure skeletal muscle: an inferior slice versus a mid-vertebral slice. Our prior work had shown significant differences in skeletal muscle measures between adjacent vertebrae when measured at an inferior slice24 but to our knowledge no comparison between inferior and mid-vertebral slice measures has yet been performed. We demonstrate here that there are statistically significant differences in SMA between mid-vertebral and inferior aspect slices, though \(\hbox {L3}_{inf}\)/\(\hbox {L3}_{mid}\) differences were moderate (− 1.2% for men and − 3.7% for women). These differences (all less than 10%) in isolation are unimportant, however, differences in the resulting sarcopenia cutpoints derived from mid-vertebra versus inferior aspect slices should be carefully considered. While some of the cutpoints are different only by a rounding error (i.e., T10 in men: 92.37 vs. 92.95), others are different by far greater amounts (i.e., L1 in men: 102.57 vs. 110.32). The relevant SMA -2SD cutpoints were up to 11.8\(cm^2\) (9.3%) different (\(\hbox {L4}_{inf}\) vs. \(\hbox {L4}_{mid}\) SMA in men). Therefore, cutpoints from mid-vertebra slice measures cannot be directly compared to cutpoints from inferior slice measures for all vertebrae, and in most cases, inferior slice cutpoints should not be used with mid-vertebra slice measures or vice-versa.

Reference mean, SD, and cutpoint values for inferior aspect vertebra levels in this manuscript are similar to, but slightly different from, previously published values24 due to differences resulting from an updated CT segmentation methodology and the inclusion of additional subjects.

While EWGSOP recommends -2SD cutpoints, we opted to include 5th percentile (P5) cutpoints as well for comparison with other reference cohort cutpoints. Since the -2SD cutpoint is approximately equal to the 2.5th percentile (of a Normally distributed random variable), it should therefore be unsurprising that P5 values are greater than -2SD values in all cases. P5 cutpoints for RMI would all be − 1.645 for a Normally distributed random variable with mean 0 and standard deviation 1, however, skeletal muscle is not a perfectly Normally distributed variable so the P5 cutpoints range from − 1.42 to − 1.60 (women) and − 1.35 to − 1.57 (men). Since they represent different percentiles, P5 and -2SD cutpoints should not be used interchangeably.

This study has important limitations. These RMI equations do not apply to SMA measured at other vertebra levels or measured via other imaging modalities, they apply to CT-derived T10 through L5 SMA only. They also have not been tested for validity in children under age 18. While we hope that these equations accurately quantify the relationship between SMA, sex, height, and BMI in healthy, young adult populations around the world, we cannot be sure, and this should be investigated further. These updated cutpoints have not been tested against clinical outcomes. We used non-contrast-enhanced CT scans; previous research has shown that IV contrast has a clinically insignificant effect on SMA but significant effect on muscle density-based measures (e.g., SMRA, SMG)15,53,54.

We propose that \(SMI_{HT} = SMA/height\) and the \(RMI_{HT}\) equations developed here be used for comparing height- and BMI-adjusted SMA values across different cohorts from around the world.

Methods

Study cohort

We retrospectively studied persons who underwent CT scans at the University of Michigan as part of evaluation for kidney donation between 1998 and 2017. We have previously studied subsets of these kidney donor candidates as a healthy reference population and use a similar methodology as is described in those manuscripts15,24,43.

Patient age, sex, height (m), and weight (kg) were obtained from their medical record proximal to the date of evaluation for kidney donation55. Candidates were included if they had a non-contrast-enhanced series CT scan performed as part of evaluation for kidney donation, with a complete fascia boundary visible in the display field of view for at least one vertebra between \(\hbox {T10}_{mid}\) and \(\hbox {L5}_{inf}\), had age, sex, height, and weight recorded in their electronic medical record, and were medically, surgically, and psycho-socially approved for donation.

Body mass index (BMI) was computed and categorized into groups according the World Health Organization International Classification standard56.

CT imaging was extracted for 2367 total donor candidates between the ages of 18 and 73 scanned using the GE ‘Standard’ reconstruction algorithm at 120 kVp and 5 mm slice thickness in a Discovery or LightSpeed scanner. Tube current was automatically modulated in proportion to body mass.

The study was split into two cohorts; \(n=1264\) ‘young adult’ candidates age 18–40 (‘Under-40’) and \(n=1103\) candidates over age 40 (‘Over-40’).

CT image processing

After being transferred into a spatial database, CT images were segmented using an updated version of Analytic Morphomics that uses fully-automated machine learning (ML) models that have been previously described57. ML models written in matlab (The Mathworks Inc, Natick, MA) identified and labelled vertebral bodies, then identified the outer abdominal fascia and inner ventral cavity to create enclosed regions of interest, which were then manually reviewed and edited as needed.

SMA was measured as the area of pixels between − 29 to + 150 Hounsfield Units (HU) in the region of interest on two axial slices per vertebra, one slice nearest the inferior aspect of the vertebral body (e.g., \(\hbox {L3}_{inf}\)) and one slice nearest the midpoint (e.g., \(\hbox {L3}_{mid}\))15,20,53. Skeletal muscle radiation attenuation (SMRA), a measure of tissue density, was measured as the mean attenuation (HU) of all SMA pixels. The skeletal muscle gauge (SMG) was calculated as \(SMG_{HT} = SMI_{HT} * SMRA\). Intramuscular adipose tissue (IMAT) area was calculated as the area of pixels between − 205 and − 51 HU within the SMA region.

Statistical methods

Demographics, CT parameters, and skeletal muscle measurements were summarized separately for men and women in each cohort, reporting mean and standard deviation (s.d.) for continuous variables and proportion for categorical variables. Means were compared using two-tailed t-tests assuming unequal variance, and proportions were compared using the Chi-squared test. Paired t-tests were used to compare the within-subject differences between inferior and mid-vertebral slice values.

Using the ‘Under-40’ cohort, sex-specific allometric regression models were fit to find the optimal integer coefficient for the relationship between weight versus height (BMI), and SMA versus height (SMI). The allometric model \(SMA = \alpha \times height^{\beta } \times age^{\gamma }\) was transformed into the logarithmic form \(log_e(SMA) = \alpha + \beta log_e(height) + \gamma log_e(age) + \epsilon\) and linear regression was used to find the \(\beta\) coefficient (optimal power of height)58. The resulting coefficient rounded to 1 as the nearest integer in both men and women for all vertebrae, ergo two height-adjusted skeletal muscle indices were computed for comparison: the ‘optimal’ SMI using a height power of one (\(SMI_{HT}=SMA/height\)) as suggested by allometric modeling, and the ‘traditional’ SMI using a height power of two (\(SMI_{HT2}=SMA/height^2\)).

To describe the relationship between BMI and height-adjusted SMA in a young, healthy adult cohort, two multiple linear regression models were constructed for each vertebra level using the ‘Under-40’ cohort; one for \(SMI_{HT}\) and one for \(SMI_{HT2}\). In each model, the height-adjusted index (I = \(SMI_{HT}\) or \(SMI_{HT2}\)) was the response, while BMI, male sex, and their interaction were predictors, allowing for different intercept and slope by sex, e.g., \(\widehat{I} = \beta _0 + \beta _1*BMI + \beta _2*sex + \beta _3*sex*BMI\).

Each height-adjusted index was converted into a relative muscle index (z-score with mean zero and standard deviation one) by subtracting the model’s predicted value (\(\widehat{I}\)) and dividing by the sex-specific residual standard error (RSE), e.g., \(RMI = (I - \widehat{I}) / RSE(I)\).

Bivariate scatter plots and Pearson correlation coefficients were used to assess the linear association between each skeletal muscle measure and age, BMI, height, and weight stratified by sex, vertebra level, and cohort.

An alpha level of 0.01 was used to determine statistical significance. All statistical tests were performed in R version 4.3.259, using the package ‘ggplot2’60 for data visualization.