
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39294201
71613
10.1038/s41598-024-71613-x
Article
Relative muscle indices and healthy reference values for sarcopenia assessment using T10 through L5 computed tomography skeletal muscle area
Derstine Brian A. bderstin@med.umich.edu

1
Holcombe Sven A. 1
Wang Nicholas C. 1
Ross Brian E. 1
Sullivan June A. 1
Wang Stewart C. 1
Su Grace L. 12
1 https://ror.org/01zcpa714 grid.412590.b 0000 0000 9081 2336 Michigan Medicine, Ann Arbor, MI USA
2 https://ror.org/018txrr13 grid.413800.e 0000 0004 0419 7525 VA Ann Arbor Healthcare System, Ann Arbor, MI USA
18 9 2024
18 9 2024
2024
14 217996 5 2024
29 8 2024
© The Author(s) 2024
2024
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Sarcopenia is the age-related loss of skeletal muscle mass and function. Computed tomography (CT) assessments of sarcopenia utilize measurements of skeletal muscle cross-sectional area (SMA), radiation attenuation (SMRA), and intramuscular adipose tissue (IMAT). Unadjusted SMA is strongly correlated with both height and body mass index (BMI); therefore, SMA must be adjusted for body size to assess sarcopenic low muscle mass fairly in individuals of different heights and BMI. SMA/height (rather than SMA/height2) provides optimal height adjustment, and vertebra-specific relative muscle index (RMI) equations optimally adjust for both height and BMI. Since L3 measurement is not available in all CT scans, sarcopenic low muscle mass may be assessed using other levels. Both a mid-vertebral slice and an inferior slice have been used to define ‘L3 SMA’, but the effect of vertebral slice location on SMA measurements is unexplored. Healthy reference values for skeletal muscle measures at mid- and inferior vertebra slices between T10 and L5, have not yet been reported. We extracted T10 through L5 SMA, SMRA, and IMAT at a mid-vertebral and inferior slice using non-contrast-enhanced CT scans from healthy, adult kidney donor candidates between age 18 and 73. We compared paired differences in SMA between the mid-vertebral slice versus the inferior slice. We calculated the skeletal muscle gauge as SMGHT=SMRA∗SMIHT. We used allometric analysis to find the optimal height scaling power for SMA. To enable comparisons with other published reference cohorts, we computed two height-adjusted measures; SMIHT=SMA/height (optimal) and SMIHT2=SMA/height2 (traditional). Using the young, healthy reference cohort, we utilized multiple linear regression to calculate relative muscle index z-scores (RMIHT, RMIHT2), which adjust for both height and BMI, at each vertebra level. We assessed Pearson correlations of each muscle area measure versus age, height, weight, and BMI separately by sex and vertebra number. We assessed the differences in means between age 18–40 versus 20–40 as the healthy, young adult reference group. We reported means, standard deviations, and sarcopenia cutpoints (mean-2SD and 5th percentile) by sex and age group for all measures. Sex-specific allometric analysis showed that height to the power of one was the optimal adjustment for SMA in both men and women at all vertebra levels. Differences between mid-vertebra and inferior slice SMA were statistically significant at each vertebra level, except for T10 in men. SMIHT was uncorrelated with height, whereas SMIHT2 was negatively correlated with height at all vertebra levels. Both SMIHT and SMIHT2 were positively correlated with BMI at all vertebra levels. RMIHT was uncorrelated with BMI, weight, and height (minimal positive correlation in women at L3inf, L4mid, and L5inf) whereas RMIHT2 was uncorrelated with BMI, but negatively correlated with height and weight at all levels. There were no significant differences in SMA between 18–40 versus 20–40 age groups. Healthy reference values and sarcopenic cutpoints are reported stratified by sex, vertebra level, and age group for each measure. Height to the power of one (SMA/height) is the optimal height adjustment factor for SMA at all levels between T10mid through L5inf. The use of SMA/height2 should be discontinued as it retains a significant negative correlation with height and is therefore biased towards identifying sarcopenia in taller individuals. Measurement of SMA at a mid-vertebral slice is significantly different from measurement of SMA at an inferior aspect slice. Reference values should be used for the appropriate slice. We report sarcopenic healthy reference values for skeletal muscle measures at the mid-vertebral and inferior aspect slice for T10 through L5 vertebra levels. Relative muscle index (RMI) equations developed here minimize correlation with both height and BMI, producing unbiased assessments of relative muscle mass across the full range of body sizes. We recommend the use of these RMI equations in other cohorts.

Keywords

Sarcopenia
Skeletal muscle
Morphomics
Subject terms

Skeletal muscle
Diagnostic markers
Obesity
issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

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 population5–18. 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)14,19–24. Reference ‘young, adult’ populations generally use an 18–40 or 20–40 age range15,24–35. 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 situations24,31,36–39. 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’)32,40–42. 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/height2)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 RMIHT 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.

Sex	Variable	Under-40	Over-40	p	
N	Mean	s.d.	N	Mean	s.d.	
F	Age (year)	638	31.08	5.88	816	50.56	6.73	< 0.001	
Height (m)	638	1.65	0.07	816	1.64	0.06	0.021	
Weight (kg)	638	73.49	15.74	816	72.88	13.38	0.439	
BMI (kg/m2)	638	27.10	5.40	816	27.16	4.64	0.830	
 Underweight	10	1.6%		3	0.4%			
 Normal	255	40.0%		289	35.4%			
 Overweight	175	27.4%		307	37.6%			
 Obese class I	141	22.1%		162	19.9%			
 Obese class II	46	7.2%		51	6.2%			
 Obese class III	11	1.7%		4	0.5%			
Race	638			816			< 0.001	
 African American	92	14.4%		65	8.0%			
 Asian	12	1.9%		9	1.1%			
 Caucasian	465	72.9%		675	82.7%			
 Other	23	3.6%		13	1.6%			
 Unknown	46	7.2%		54	6.6%			
M	Age (year)	465	30.22	5.77	448	50.54	7.05	<.001	
Height (m)	465	1.79	0.07	448	1.79	0.07	0.169	
Weight (kg)	465	89.01	16.83	448	89.56	13.40	0.584	
BMI (kg/m2)	465	27.69	4.69	448	28.05	3.56	0.183	
 Underweight	2	0.4%		0	0%			
 Normal	131	28.2%		90	20.1%			
 Overweight	207	44.5%		238	53.1%			
 Obese class I	83	17.8%		99	22.1%			
 Obese class II	39	8.4%		21	4.7%			
 Obese class III	3	0.6%		0	0%			
Race	465			448			0.002	
 African American	58	12.5%		24	5.4%			
 Asian	6	1.3%		1	0.2%			
 Caucasian	350	75.3%		368	82.1%			
 Other	13	2.8%		13	2.9%			
 Unknown	38	8.2%		42	9.4%			
P-values less than 0.01 shown in bold. s.d., standard deviation.

Table 2 Sex-specific paired t-test results comparing within-subject mid-vertebra and inferior aspect slice SMA (cm2).

Sex	VB	Under-40	Over-40	
n	Mid	Inf	d¯	%	p	n	Mid	Inf	d¯	%	p	
F	T10	86	89.4	91.3	– 1.9	– 2.1%	< 0.001	110	81.5	83.4	– 1.9	– 2.3%	< 0.001	
T11	293	87.2	90.6	– 3.4	– 3.7%	< 0.001	384	81.9	85.3	– 3.4	– 4.0%	< 0.001	
T12	556	89.0	95.6	– 6.6	– 6.9%	< 0.001	692	86.4	92.8	– 6.4	– 6.9%	< 0.001	
L1	627	98.8	104.2	– 5.3	– 5.1%	< 0.001	805	95.9	100.3	– 4.4	– 4.4%	<.001	
L2	635	108.6	116.8	– 8.1	– 7.0%	< 0.001	813	104.0	111.1	– 7.1	– 6.4%	< 0.001	
L3	634	121.8	126.4	– 4.7	– 3.7%	< 0.001	812	115.2	118.6	– 3.3	– 2.8%	< 0.001	
L4	623	126.3	123.3	3.0	2.4%	< 0.001	798	117.5	112.4	5.1	4.5%	< 0.001	
L5	521	113.8	114.4	– 0.6	– 0.5%	0.145	645	105.7	109.9	– 4.3	– 3.9%	< 0.001	
M	T10	49	138.8	139.2	– 0.4	– 0.3%	0.604	49	134.7	135.9	– 1.2	– 0.9%	0.206	
T11	195	134.6	137.3	– 2.7	– 1.9%	< 0.001	196	129.4	133.2	– 3.8	– 2.8%	< 0.001	
T12	381	137.6	146.2	– 8.6	– 5.9%	< 0.001	372	136.5	145.0	– 8.5	– 5.9%	< 0.001	
L1	451	151.2	160.3	– 9.1	– 5.7%	< 0.001	419	150.7	157.6	– 6.9	– 4.4%	< 0.001	
L2	461	169.3	182.5	– 13.2	– 7.2%	< 0.001	432	164.4	175.4	– 11.1	– 6.3%	< 0.001	
L3	464	189.3	191.6	– 2.3	– 1.2%	< 0.001	431	182.4	184.3	– 1.9	– 1.0%	< 0.001	
L4	450	185.1	172.4	12.7	7.4%	< 0.001	434	178.2	165.8	12.4	7.5%	< 0.001	
L5	353	164.3	171.2	– 6.9	– 4.0%	< 0.001	318	163.6	172.0	– 8.5	– 4.9%	< 0.001	
P-value less than 0.01 shown in bold. d¯ is the mean of the paired differences (Mid−Inf). % is the mean of the paired differences expressed as a percentage of the inferior VB value, i.e., ((Mid-Inf)/Inf∗100).

VB, vertebral body; s.d.; standard deviation; Mid, mid-vertebra slice; Inf, inferior slice.

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 cm2, ‘Over-40’: − 7.1 cm2) and both L2 (‘Under-40’: − 13.2 cm2) and L4 (‘Over-40’: 12.4 cm2) 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 Mid-vertebra (e.g., T10mid) and inferior aspect (e.g., T10inf) slice distribution of SMA (top), and allometric height-scaling coefficients (bottom) split by cohort and sex.

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 SMIHT were uncorrelated with age in women (Pearson r: − 0.076 to 0.04), but positively correlated with age in men at T11inf through L2inf and at L5inf/L5mid (r: 0.125 to 0.242) and uncorrelated at other vertebrae (r: − 0.183 to 0.131). RMIHT 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. SMIHT was not significantly correlated with height (r: − 0.047 to 0.093), whereas SMIHT2 was significantly negatively correlated with height at all vertebra levels except T10mid 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 RMIHT and RMIHT2 were uncorrelated with BMI by design (r: 0.0), however, RMIHT 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 L3inf, L4mid, and L5inf in women (r: 0.105 to 0.121), whereas RMIHT2 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 T10mid (height), and T10inf/T10mid and L5inf/L5mid (weight) in both women and men, and T11mid in men.Table 3 Sex-specific allometric coefficients for SMA by cohort and vertebra.

Sex	Vertebra	Under-40	Over-40	
Intercept	log (height)	log (age)	Intercept	log (height)	log (age)	
F	T10mid	4.209	0.904	-0.053	4.904	1.142	-0.274	
T10inf	3.984	0.973	-0.001	4.833	0.996	-0.24	
T11mid	3.909	0.962	0.02	4.755	0.992	-0.217	
T11inf	4.048	0.852	-0.012	4.757	0.941	-0.213	
T12mid	3.999	0.851	0.015	4.713	0.962	-0.189	
T12inf	3.988	0.909	0.025	4.791	0.88	-0.187	
L1mid	4.076	0.971	0.006	4.702	1.053	-0.171	
L1inf	4.129	1.043	-0.004	4.883	1.015	-0.201	
L2mid	4.166	1.044	-0.003	4.967	1.037	-0.216	
L2inf	4.242	1.053	-0.005	5.163	0.968	-0.24	
L3mid	4.215	1.168	-0.002	5.239	0.994	-0.253	
L3inf	4.247	1.202	-0.004	5.371	0.967	-0.276	
L4mid	4.233	1.235	-0.005	5.51	0.922	-0.308	
L4inf	4.255	1.219	-0.016	5.6	0.845	-0.333	
L5mid	4.159	1.235	-0.014	4.812	0.935	-0.159	
L5inf	4.11	1.326	-0.012	4.212	1.093	-0.016	
M	T10mid	4.827	0.95	-0.134	6.145	0.806	-0.44	
T10inf	4.048	0.907	0.096	5.293	1.245	-0.294	
T11mid	4.04	0.827	0.108	5.174	1.271	-0.269	
T11inf	3.756	0.824	0.187	4.84	1.119	-0.163	
T12mid	3.604	0.891	0.232	4.762	1.117	-0.129	
T12inf	3.691	0.947	0.209	4.685	1.177	-0.106	
L1mid	3.842	1.013	0.169	4.908	1.106	-0.139	
L1inf	4.103	0.972	0.116	5.056	1.096	-0.164	
L2mid	4.148	0.95	0.124	5.131	1.118	-0.175	
L2inf	4.259	0.98	0.108	5.26	1.187	-0.202	
L3mid	4.361	0.979	0.089	5.359	1.147	-0.211	
L3inf	4.451	0.976	0.067	5.446	1.049	-0.216	
L4mid	4.457	0.998	0.052	5.328	0.997	-0.187	
L4inf	4.428	1.024	0.035	5.102	0.967	-0.143	
L5mid	4.014	1.215	0.109	4.648	1.205	-0.066	
L5inf	4.087	1.178	0.106	4.473	1.322	-0.026	
Coefficients with p-value less than 0.01 shown in bold.

mid, mid-vertebra slice; inf, inferior slice.

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 SMIHT and between 46.3 and 72.4% of the variation in SMIHT2 (Adjusted R2), depending on the vertebra slice used.Table 4 RMIHT equation coefficients (a–d) and adjusted r-squared (Adj. R2).

Variable	VB	a	b	c	d	e	f	Adj. R2	
RMIHT	T10mid	16.07	1.243	28.98	- 0.214	7.224	4.334	0.660	
T10inf	19.413	1.152	7.674	0.488	6.395	2.779	0.738	
T11mid	15.727	1.27	7.003	0.493	5.866	2.670	0.767	
T11inf	13.595	1.388	4.041	0.599	5.897	2.606	0.784	
T12mid	13.054	1.492	2.322	0.677	6.040	2.459	0.799	
T12inf	16.295	1.504	0.166	0.777	6.558	2.098	0.792	
L1mid	23.913	1.335	3.79	0.705	6.619	2.412	0.780	
L1inf	29.604	1.245	5.199	0.719	6.933	2.802	0.768	
L2mid	31.219	1.284	5.99	0.784	7.508	3.301	0.764	
L2inf	35.97	1.291	8.685	0.777	7.979	3.714	0.761	
L3mid	41.326	1.206	12.093	0.681	8.362	3.114	0.759	
L3inf	46.215	1.129	15.503	0.504	8.222	2.688	0.750	
L4mid	48.428	1.044	17.869	0.291	8.077	2.417	0.711	
L4inf	49.838	0.926	10.828	0.357	7.980	2.425	0.630	
L5mid	45.872	0.863	4.048	0.648	7.431	2.060	0.688	
L5inf	44.767	0.917	5.165	0.732	8.286	2.432	0.695	
Coefficients with p-values less than 0.01 shown in bold. Residual standard error (RSE) values (e-f). RMIHT=[(SMA/Height)-(a+b∗BMI+c∗male+d∗BMI∗male)]/(e+f∗male), where male = 1 if male or 0 if female, height in meters, and SMA in cm2.

VB, vertebral body; mid, mid-vertebra slice; inf, inferior slice.

Reference values

Reference cutpoints for low muscle quantity using -2SD and P5 values are shown for SMA, SMIHT, and RMIHT by vertebra slice, split by sex and age group (Tables 5 and 6). ‘Under-40’ SMA, SMIHT, and RMIHT were significantly higher than ‘Over-40’ at all vertebra levels for women, and at L2mid through L4inf (all), T10inf (SMA, SMIHT), and T11inf (RMIHT) in men. Reference values for height-squared based measures are reported in Tables S5 and S6 and for muscle quality measures SMRA, IMAT, and SMGHT 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.

Variable	VB	Under-40	Over-40	p	
N	Mean	s.d.	2SD	P5	N	Mean	s.d.	2SD	P5	
SMA	T10mid	86	89.42	16.62	56.17	66.67	110	81.54	14.15	53.24	62.10	< 0.001	
T10inf	285	87.70	14.84	58.01	64.97	373	81.19	13.00	55.19	63.33	< 0.001	
T11mid	293	87.21	14.90	57.41	64.66	384	81.92	13.24	55.43	62.77	< 0.001	
T11inf	538	85.38	16.02	53.33	63.26	683	81.39	14.06	53.28	60.56	< 0.001	
T12mid	557	89.09	16.96	55.18	64.66	692	86.38	14.60	57.17	64.46	0.003	
T12inf	625	93.83	17.58	58.66	67.68	805	90.78	15.10	60.57	68.16	< 0.001	
L1mid	627	98.84	16.63	65.58	74.12	806	95.90	14.27	67.35	74.71	< 0.001	
L1inf	634	104.20	16.52	71.16	79.26	811	100.20	14.16	71.87	79.88	< 0.001	
L2mid	635	108.63	17.45	73.73	83.81	814	103.98	15.30	73.39	81.66	< 0.001	
L2inf	636	116.74	18.15	80.45	90.28	813	111.10	16.14	78.82	87.49	< 0.001	
L3mid	635	121.77	18.34	85.08	94.49	813	115.26	16.18	82.91	90.94	< 0.001	
L3inf	634	126.43	17.87	90.68	100.00	813	118.57	15.93	86.71	94.43	< 0.001	
L4mid	625	126.25	17.31	91.63	101.78	801	117.54	15.62	86.31	92.95	< 0.001	
L4inf	627	123.33	16.54	90.25	97.62	798	112.39	15.12	82.15	88.45	< 0.001	
L5mid	523	113.85	15.41	83.02	90.17	650	105.66	13.85	77.97	84.63	< 0.001	
L5inf	522	114.42	16.91	80.61	91.28	646	109.99	16.12	77.75	86.81	< 0.001	
SMIHT	T10mid	86	54.31	9.79	34.73	40.71	110	50.16	8.30	33.56	37.91	0.002	
T10inf	285	53.49	8.78	35.93	40.49	373	49.65	7.67	34.30	38.75	< 0.001	
T11mid	293	53.24	8.84	35.56	40.18	384	50.08	7.85	34.38	38.60	< 0.001	
T11inf	538	51.92	9.55	32.82	38.22	683	49.74	8.37	33.01	37.35	< 0.001	
T12mid	557	54.18	10.09	34.00	38.93	692	52.78	8.68	35.42	39.92	0.010	
T12inf	625	57.06	10.46	36.15	40.99	805	55.44	9.01	37.43	41.86	0.002	
L1mid	627	60.09	9.80	40.50	45.52	806	58.56	8.36	41.84	45.73	0.002	
L1inf	634	63.32	9.65	44.02	48.61	811	61.17	8.29	44.60	49.11	< 0.001	
L2mid	635	66.00	10.21	45.57	51.11	814	63.48	8.96	45.57	50.54	< 0.001	
L2inf	636	70.93	10.59	49.76	55.43	813	67.83	9.47	48.89	53.90	< 0.001	
L3mid	635	73.98	10.59	52.80	57.94	813	70.37	9.46	51.45	56.22	< 0.001	
L3inf	634	76.81	10.23	56.35	61.62	813	72.40	9.30	53.80	58.41	< 0.001	
L4mid	625	76.69	9.84	57.00	62.53	801	71.75	9.12	53.52	58.02	< 0.001	
L4inf	627	74.92	9.41	56.10	60.40	798	68.62	8.91	50.80	55.40	< 0.001	
L5mid	523	69.12	8.75	51.63	56.13	650	64.50	8.10	48.31	52.27	< 0.001	
L5inf	522	69.46	9.62	50.21	56.22	646	67.12	9.46	48.20	53.40	< 0.001	
RMIHT	T10mid	86	-0.00	1.00	-2.00	-1.56	110	-0.53	0.95	-2.42	-1.97	< 0.001	
T10inf	285	0.00	1.00	-2.00	-1.53	373	-0.47	1.00	-2.47	-1.97	< 0.001	
T11mid	293	-0.00	1.00	-2.00	-1.50	384	-0.41	1.05	-2.51	-1.98	< 0.001	
T11inf	538	-0.00	1.00	-2.00	-1.57	683	-0.40	1.03	-2.47	-2.04	< 0.001	
T12mid	557	0.00	1.00	-2.00	-1.55	692	-0.28	1.04	-2.37	-1.94	< 0.001	
T12inf	625	-0.00	1.00	-2.00	-1.56	805	-0.27	1.00	-2.27	-1.76	< 0.001	
L1mid	627	-0.00	1.00	-2.00	-1.42	806	-0.25	1.00	-2.25	-1.79	< 0.001	
L1inf	634	0.00	1.00	-2.00	-1.51	811	-0.32	1.01	-2.35	-1.87	< 0.001	
L2mid	635	0.00	1.00	-2.00	-1.60	814	-0.35	1.01	-2.36	-1.87	< 0.001	
L2inf	636	0.00	1.00	-2.00	-1.59	813	-0.40	1.02	-2.44	-1.95	< 0.001	
L3mid	635	0.00	1.00	-2.00	-1.51	813	-0.44	0.99	-2.43	-1.99	< 0.001	
L3inf	634	-0.00	1.00	-2.00	-1.48	813	-0.55	1.00	-2.55	-2.13	< 0.001	
L4mid	625	-0.00	1.00	-2.00	-1.53	801	-0.62	1.01	-2.64	-2.21	< 0.001	
L4inf	627	0.00	1.00	-2.00	-1.59	798	-0.79	1.04	-2.87	-2.44	< 0.001	
L5mid	523	0.00	1.00	-2.00	-1.48	650	-0.64	1.00	-2.64	-2.27	< 0.001	
L5inf	522	-0.00	1.00	-2.00	-1.53	646	-0.30	1.02	-2.34	-1.78	< 0.001	
2SD is the ‘mean - 2 standard deviations’ cutpoint. P5 is the ‘5th percentile’ cutpoint. P-values compare ‘Over-40’ to ‘Under-40’ group stratified by sex and vertebra. P-value less than 0.01 shown in bold.

VB, vertebral body; s.d., standard deviation; mid, mid-vertebra slice; inf, inferior slice.

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

Variable	VB	Under-40	Over-40	p	
N	mean	s.d.	2SD	P5	N	mean	s.d.	2SD	P5	
SMA	T10mid	49	138.79	23.21	92.37	109.55	49	134.68	20.18	94.31	104.83	0.352	
T10inf	170	136.38	21.72	92.95	104.76	168	129.91	19.40	91.11	98.31	0.004	
T11mid	195	134.65	21.31	92.03	104.74	196	129.40	19.32	90.76	99.39	0.011	
T11inf	359	132.02	22.88	86.26	98.71	354	129.30	20.87	87.57	96.92	0.098	
T12mid	381	137.64	24.07	89.49	103.43	372	136.47	21.52	93.43	103.71	0.484	
T12inf	437	143.47	25.20	93.08	106.20	420	143.26	21.98	99.29	110.62	0.894	
L1mid	451	151.18	24.31	102.57	115.12	422	150.79	21.16	108.46	118.36	0.800	
L1inf	460	159.77	24.72	110.32	123.70	426	157.39	21.59	114.20	124.99	0.127	
L2mid	461	169.27	26.72	115.83	131.76	434	164.49	23.41	117.67	130.20	0.004	
L2inf	464	182.59	28.08	126.42	141.56	433	175.45	24.49	126.46	139.86	< 0.001	
L3mid	464	189.34	26.92	135.50	148.91	434	182.35	24.51	133.34	146.85	< 0.001	
L3inf	464	191.61	24.91	141.78	152.91	435	184.55	23.63	137.30	148.96	< 0.001	
L4mid	450	185.09	23.04	139.02	148.41	434	178.21	22.58	133.05	144.42	< 0.001	
L4inf	451	172.43	22.64	127.15	137.47	439	165.89	21.83	122.23	133.10	< 0.001	
L5mid	356	164.15	22.68	118.80	132.72	319	163.55	22.27	119.02	131.63	0.730	
L5inf	353	171.19	25.03	121.12	137.91	318	172.04	25.88	120.28	137.88	0.667	
SMIHT	T10mid	49	77.73	12.39	52.95	62.90	49	75.50	11.12	53.25	60.15	0.352	
T10inf	170	76.10	11.67	52.76	57.72	168	72.96	10.36	52.24	56.43	0.009	
T11mid	195	75.09	11.53	52.03	57.56	196	72.53	10.31	51.90	55.99	0.021	
T11inf	359	73.72	12.53	48.66	55.79	354	72.40	11.28	49.84	55.63	0.141	
T12mid	381	76.83	13.14	50.54	56.56	372	76.42	11.64	53.14	57.83	0.649	
T12inf	437	80.04	13.75	52.55	58.45	420	80.20	11.82	56.56	61.78	0.859	
L1mid	451	84.38	13.13	58.11	65.12	422	84.44	11.32	61.79	67.42	0.940	
L1inf	460	89.18	13.38	62.42	69.62	426	88.09	11.50	65.09	71.38	0.193	
L2mid	461	94.49	14.51	65.47	73.17	434	92.08	12.52	67.04	73.43	0.008	
L2inf	464	101.92	15.18	71.56	78.55	433	98.21	12.99	72.22	78.70	< 0.001	
L3mid	464	105.69	14.48	76.72	82.87	434	102.09	12.98	76.13	82.80	< 0.001	
L3inf	464	106.96	13.32	80.31	86.30	435	103.36	12.60	78.16	84.49	< 0.001	
L4mid	450	103.33	12.23	78.87	83.91	434	99.83	12.11	75.61	81.14	< 0.001	
L4inf	451	96.25	12.03	72.20	79.04	439	92.94	11.75	69.44	74.15	< 0.001	
L5mid	356	91.48	11.82	67.84	74.74	319	91.66	11.68	68.30	74.55	0.841	
L5inf	353	95.38	13.17	69.05	76.15	318	96.40	13.53	69.33	78.42	0.325	
RMIHT	T10mid	49	-0.00	1.00	-2.00	-1.35	49	-0.04	0.84	-1.71	-1.35	0.846	
T10inf	170	0.00	1.00	-2.00	-1.47	168	-0.23	0.96	-2.15	-1.78	0.035	
T11mid	195	-0.00	1.00	-2.00	-1.45	196	-0.21	0.96	-2.12	-1.79	0.039	
T11inf	359	-0.00	1.00	-2.00	-1.36	354	-0.19	0.96	-2.11	-1.64	0.010	
T12mid	381	0.00	1.00	-2.00	-1.47	372	-0.07	0.96	-1.98	-1.56	0.336	
T12inf	437	-0.00	1.00	-2.00	-1.52	420	-0.04	0.99	-2.01	-1.60	0.605	
L1mid	451	-0.00	1.00	-2.00	-1.51	422	-0.05	0.99	-2.03	-1.62	0.475	
L1inf	460	0.00	1.00	-2.00	-1.57	426	-0.16	0.98	-2.12	-1.71	0.013	
L2mid	461	0.00	1.00	-2.00	-1.48	434	-0.28	0.93	-2.14	-1.76	< 0.001	
L2inf	464	0.00	1.00	-2.00	-1.42	433	-0.36	0.90	-2.17	-1.82	< 0.001	
L3mid	464	0.00	1.00	-2.00	-1.39	434	-0.36	0.95	-2.26	-1.85	< 0.001	
L3inf	464	-0.00	1.00	-2.00	-1.44	435	-0.37	0.99	-2.36	-1.97	< 0.001	
L4mid	450	-0.00	1.00	-2.00	-1.49	434	-0.37	1.02	-2.41	-1.93	< 0.001	
L4inf	451	0.00	1.00	-2.00	-1.56	439	-0.35	1.00	-2.35	-1.80	< 0.001	
L5mid	356	0.00	1.00	-2.00	-1.47	319	-0.07	1.03	-2.13	-1.58	0.402	
L5inf	353	-0.00	1.00	-2.00	-1.44	318	0.02	1.08	-2.14	-1.54	0.804	
2SD is the ‘mean - 2 standard deviations’ cutpoint. P5 is the ‘5th percentile’ cutpoint. P-values compare ‘Over-40’ to ‘Under-40’ group stratified by sex and vertebra. P-value less than 0.01 shown in bold.

VB, vertebral body; s.d., standard deviation; mid, mid-vertebra slice; inf, inferior slice.

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 (SMIHT), and a height-and-BMI index (RMIHT). 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 height2 and resulted in the body mass index (BMI=weight/height2)43,44,50–52. The same allometric analysis of SMA vs. height has demonstrated that SMA scales with height, not height2, 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/height2 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 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 SMIHT − 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 SMIHT (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.

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 L3inf/L3mid 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 11.8cm2 (9.3%) different (L4inf vs. L4mid 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 SMIHT=SMA/height and the RMIHT 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 T10mid and L5inf, 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., L3inf) and one slice nearest the midpoint (e.g., L3mid)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 SMGHT=SMIHT∗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=α×heightβ×ageγ was transformed into the logarithmic form loge(SMA)=α+βloge(height)+γloge(age)+ϵ and linear regression was used to find the β 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 (SMIHT=SMA/height) as suggested by allometric modeling, and the ‘traditional’ SMI using a height power of two (SMIHT2=SMA/height2).

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 SMIHT and one for SMIHT2. In each model, the height-adjusted index (I = SMIHT or SMIHT2) was the response, while BMI, male sex, and their interaction were predictors, allowing for different intercept and slope by sex, e.g., I^=β0+β1∗BMI+β2∗sex+β3∗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 (I^) and dividing by the sex-specific residual standard error (RSE), e.g., RMI=(I-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.

Supplementary Information

Supplementary Tables.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-71613-x.

Author contributions

B.D., S.H., J.S., G.S., and S.W. designed the study. N.W. and S.H. developed the Analytic Morphomics processing code. B.D. and S.H. implemented the machine learning segmentation models. B.D. and B.R. performed CT processing. B.D. collected and interpreted the data, performed the data analyses, prepared the figures, and wrote the manuscript. All authors reviewed the manuscript.

Data availability

The analytic dataset analyzed during the current study has been deposited in the Deep Blue Data repository (University of Michigan Library): 10.7302/ccds-9q38.

Competing Interests

Brian A Derstine, Brian E Ross, Nicholas C Wang, and Grace L Su declare that they have no conflict of interest. June A Sullivan, Sven A Holcombe, and Stewart C Wang are listed as inventors on a US Patent for Analytic Morphomics (#US 20140064583 A1). Stewart C Wang holds equity interest in Applied Morphomics, Inc.

Ethical Approval and Informed Consent

This study was approved by the Institutional Review Board of the University of Michigan. All methods were performed in accordance with the relevant guidelines and regulations of the United States. Because existing CT scans were used retrospectively, the requirement for informed consent was waived by the Institutional Review Board of the University of Michigan.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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