Celal Gungor1 Forest Industrial Engineering, Izmir Katip Celebi University, Cigli, Izmir 35620, Turkey e-mail: [email protected]

Ruoliang Tang Occupational Science and Technology, University of Wisconsin-Milwaukee, Milwaukee, WI 53211 e-mail: [email protected]

Richard F. Sesek Associate Professor Industrial and Systems Engineering, Auburn University, Auburn, AL 36849 e-mail: [email protected]

Kenneth Bo Foreman Associate Professor Physical Therapy, University of Utah, Salt Lake City, UT 84108 e-mail: [email protected]

Sean Gallagher Associate Professor Industrial and Systems Engineering, Auburn University, Auburn, AL 36849 e-mail: [email protected]

Prediction Models for the Erector Spinae Muscle Cross-Sectional Area Accurate and reliable “individualized” low back erector spinae muscle (ESM) data are of importance to estimate its force producing capacity. Knowing the force producing capacity, along with spinal loading, enhances the understanding of low back injury mechanisms. The objective of this study was to build regression models to estimate the ESM cross-sectional area (CSA). Measurements were taken from axial-oblique magnetic resonance imaging (MRI) scans of a large historical population [54 females and 53 males at L3/L4, 50 females and 44 males at L4/L5, and 41 females and 35 males at L5/S1 levels]. Results suggest that an individual’s ESM CSA can be accurately estimated based on his/ her gender, height, and weight. Results further show that there is no significant difference between the measured and estimated ESM CSAs, and expected absolute error is less than 15%. [DOI: 10.1115/1.4029984]

Gerard A. Davis Associate Professor Industrial and Systems Engineering, Auburn University, Auburn, AL 36849 e-mail: [email protected]

1

Introduction

Knowing the CSA of an individual’s ESM is important for estimating the force producing capacity of an individual’s low back ESM. In addition to estimating force producing capacity, knowing an individual’s ESM CSA also allows better calculation of spinal loading and assessment of low back pain (LBP) risk for this individual. The relationship between the ESM CSA and variables, such as gender, age, height, and weight, has been studied for several decades to understand the variation among the measurements and to develop subject specific estimation models [1–11]. However, some of these studies were limited to small sample sizes (20 subjects) [1], (13 subjects) [2], (26 subjects) [6], (24 subjects) [8], resulting in limited statistical power to determine the variation in measurements. Other studies could not address potential gender effects on ESM CSA since they were limited to a single gender (male subjects [1–3,6] or female subjects [4,10]). Subject age was not considered by others [2,5]. On the other hand, some studies included relatively old subjects [4] (mean age 49.6 years for females) and [11] (mean age 58.1 years for females and 59.4 years for males). Since age related muscle atrophy has been reported by 1 Corresponding author. Manuscript received August 26, 2014; final manuscript received January 26, 2015; published online June 3, 2015. Assoc. Editor: Brian D. Stemper.

Journal of Biomechanical Engineering

several studies [12–14], elderly subjects may not provide sufficient reference values. Therefore, there is a need for a study that includes a larger sample size, investigates gender effect, and is free from age bias. The present study includes a large sample of live subjects from both genders, incorporates a computerized, reliable, and repeatable technique to measure ESM CSAs from high resolution MRI scans, and analyzes data for three intervertebral disk (IVD) levels. The objective of the present study was to perform low back morphometric analyses to construct regression models that can accurately estimate the CSA of the ESM based on subject characteristics (gender and age) and easily measure anthropometric variables (height and weight).

2

Methodology

2.1 Subjects. This study included medical patients who had undertaken an MRI scan at the University of Utah Hospital. MRI scans were reviewed by an anatomist with experience analyzing spinal abnormalities. Subjects who had (1) degenerative changes in the lumbar spine (e.g., crushed vertebral body, trauma, etc.) and/or ESMs (e.g., atrophy), (2) obvious spinal deformities, or (3) any known pathology relevant to and likely to alter low back geometry (e.g., scoliosis and tumor) were not included. This research was approved by the Institutional Review Boards at the University of Utah and Auburn University. A total of 112 subjects (58 females and 54 males) were included in the study; however,

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Table 1 Subject demographics IVD level L3/L4 (54 females 53 males)

Variable

Gender

Mean

SD

Min

Max

Age

Female Male Female Male Female Male Female Male

29.2 30.1 165.3 178.6 76.7 84.5 28.1 26.4

5.4 5.7 9.0 8.9 21.6 19.5 8.2 5.2

21 21 142.2 157.5 45.5 36.3 19.1 13.7

39 39 195.6 200.7 136.1 178.7 53.2 52.0

Female Male Female Male Female Male Female Male

29.2 29.7 164.9 178.4 77.2 85.1 28.5 26.7

5.4 5.5 8.9 9.1 22.0 19.2 8.4 5.2

21 21 142.2 157.5 45.4 59.0 19.1 19.2

39 39 195.6 200.7 136.1 178.7 53.2 52.0

Female Male Female Male Female Male Female Male

30.1 30.0 166.1 178.1 74.4 84.7 27.2 26.7

5.3 5.7 9.3 9.4 19.3 19.6 7.7 5.6

22 21 142.2 157.5 45.4 58.1 19.1 17.9

39 39 195.6 200.7 136.1 178.7 53.2 52.0

Female Male Female Male Female Male Female Male

29.3 30.1 165.4 178.6 76.6 84.0 28.1 26.3

5.2 5.7 8.9 8.8 21.1 19.6 8.0 5.3

21 21 142.2 157.5 45.4 36.3 19.1 13.7

39 39 195.6 200.7 136.1 178.7 53.2 52.0

Height Weight BMI L4/L5 (50 females 44 males)

Age Height Weight BMI

L5/S1 (41 females 35 males)

Age Height Weight BMI

Total (58 females 54 males)

Age Height Weight BMI

there were some missing scans at some levels, yielding fewer subjects at each specific level: 54 female and 53 male subjects at the L3/L4 level, 50 female and 44 male subjects at the L4/L5 level, and 41 female and 35 male subjects at the L5/S1 level. Axialoblique scans were not captured for all subjects, which explain why there were fewer subjects at some levels. A cohort of 20 male subjects was recruited from the student body at the Auburn University for regression model validation. Subject demographics are given in Table 1. The average age was 29.3 (5.2) years for females and 30.1 (5.7) years for males. Male subjects were significantly taller (p < 0.000) and heavier (but not significantly, p ¼ 0.055) than female subjects at each IVD level. The average height and weight were 165.4 (8.9) cm and

76.6 (21.1) kg for females and 178.6 (8.8) cm and 84.0 (19.6) kg for males. The average body mass index (BMI) was 28.1 (8.0) kg/ m2 for females and 26.3 (5.3) kg/m2 for males; the average BMI for both genders fell into the overweight category based on the World Health Organization classification [15]. 2.2 Data Collection. The ESM can be described as the whole muscle structure posterior to the spinal column, filling the space between the spinous and transverse processes, and laying longitudinally throughout the torso. The ESM in this study consists of the ESM group (the spinalis thoracis, longissimus thoracis, and iliocostalis lumborum), the transversospinalis group (the multifidus and

Fig. 1 Low back muscles and spinal structures at the L3/L4 IVD level

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Fig. 2 Sagittal and axial-oblique MRI scans at the last three lumbar IVD levels

rotatores), and the segmental muscles (the interspinales and intertransversarii) (Fig. 1). The term ESM is used to describe the whole deep group of low back muscles. The prevalence and percentages of these muscles are dependent upon the vertebral level. The longissimus thoracis, iliocostalis lumborum, and multifidus are the major muscles in the low back region, and they constitute the main focus of the present study since they are the major muscles responsible for concentric extension and eccentric flexion of the trunk. An open-bore 1.5 T MRI scanner (MAGNETOM Avanto, Siemens AG, Munich, Germany) was used to capture scans from the lumbar region. Subjects were placed in a head-first-supine posture while their arms placed on their sides and their knees were slightly flexed with a cushion under the legs. T2-weighted standard soft-tissue MRI scans were used to measure muscle CSAs. One axial-oblique (parallel to the IVD) scan was taken for each IVD level (Fig. 2). Note that MRI images are viewed inferiorly (from the feet); therefore, the right/left sides appear reversed. All MRI data were collected with parameters that supported morphometric analysis. Magnetic resonance (MR) repetition time ranged from 3000 to 4770 ms, echo time between 80 and 110 ms, and slice thickness between 3 and 4.5 mm.

Sagittal and axial-oblique plane images of the spine were carefully evaluated using OSIRIXV. Figure 2 shows sagittal (on the left) and axial-oblique (on the right) MR images in OSIRIXV software. One oblique image was selected for each IVD level. Selected images were transferred to architectural design software, RHINOCEROS (v4.0). Contours of the right and left ESMs were manually traced on a high resolution computer screen (1280  1024 pixels, 60 Hz, Dell 1905FP). An example of contour tracing is presented in Fig. 3. A model was created using GRASSHOPPER software (plug-in software for RHINOCEROS) to compute ESM CSAs. A second, independent, researcher outlined and measured the same muscles for reproducibility tests. R

R

2.3 Statistical Tests. Independent sample T tests were used to compare descriptive statistics such as male and female heights. The Kolmogorov–Smirnov test was used to evaluate the normality of dependent variables. Skewness and kurtosis were also evaluated to better understand the data distribution. Paired-samples T tests were used to compare the right and left CSAs of the ESM to determine if any asymmetry exists between them. Split plot factorial (SPF) design analysis of variance (ANOVA) tests were used

Fig. 3 Tracing of contours in RHINOCEROS

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Table 2 Lin’s repeatability ESM side Right ESM Left ESM

CCCs

for

agreement

on

measurement

A1–A2

B1–B2

A1–B1

A1–B2

A2–B1

A2–B2

0.981 0.968

0.987 0.990

0.867 0.817

0.872 0.807

0.889 0.867

0.882 0.834

A: first researcher, B: second researcher, 1: first measurement, 2: second measurement.

to determine the effect of gender, IVD level, and interaction of these two factors on the CSA of the total ESM. Intraclass correlation coefficients and Lin’s concordance correlation coefficients (CCCs) were calculated for reproducibility tests. Backward stepwise regression analyses were performed to determine prediction models for the CSA of the total ESM. To validate regression models suggested in the present study, paired-samples T tests were conducted. Lin’s CCC values were also calculated to validate regression models. Statistical tests were performed using IBM SPSS STATISTICS (version 19.0), R statistical software (version 3.1.2), and MINITAB (version 15.1). 2.4 Reproducibility Tests (Intra- and Inter-Rater Reliability Tests). Forty scans (20 males and 20 females) were randomly selected to conduct reproducibility tests. A researcher measured the CSA of the right and left ESMs at the L5/S1 IVD level. A second, independent, researcher also used the same scans and measured the same ESM CSAs. The L5/S1 level was selected because it is the most problematic level among IVD levels regarding measurement repeatability. Each researcher independently repeated all measurements after 4 weeks. Statistical tests for intra- and interclass correlation coefficients (ICCs) were performed to test how much agreement there was between and within researchers for first and second measurements.

3

Results

3.1 Preliminary Model Investigations for Regression Analyses. Some preliminary model investigations were performed to understand the dataset and check multiple linear regression assumptions regarding normality. The results of Kolmogorov–Smirnov tests indicated that the CSA data were normally distributed (p > 0.005). The skewnesses (SE) were 0.059 (0.234), 0.083 (0.249), and 0.434 (0.276) at the L3/L4, L4/L5, and L5/S1 levels, respectively. Since all skewness values were between 0.5 and þ0.5, it was concluded that the distributions were approximately symmetric. The kurtosis was not significant, and the distribution was approximately normal (mesokurtic). Therefore, it can be concluded that the normality assumptions necessary for regression analyses have been satisfied. 3.2 Reproducibility Tests. Results of these intra- and interrater reliability tests indicate highly significant correlations between first and second measurements (excellent ICC, ranging from 0.968 to 0.990) and between researchers (good ICC, ranging

Table 4 ANOVA summary table for main and interaction effects of gender and IVD level on the total ESM size Source Between subjects Gender Subject (gender) Within subjects IVD level Gender  IVD level IVD level  subject (gender) Total

SS

df

MS

F stat

Sig.

1158.31 13,936.32

1 67

1158.31 208.00

5.57 9.52

0.021

718.47 1084.42 2927.88

2 2 134

371.56 542.21 21.85

17.01 24.82

0.000 0.000

19,825.4

206

from 0.811 to 0.891). ICC interpretations are based on the criteria of Portney and Watkins [16]. In addition to those Pearson’s ICC values, Lin’s CCCs [17] were also calculated (Table 2). Lin’s CCCs agree with the ICCs and indicate high repeatability/reproducibility of measurements. Readers should be aware that the reliability analyses were conducted by remeasuring the same scans. However, correlation coefficients would likely be smaller if scan–rescan reliability analyses had been performed. Acquisition variability, field variability, subject variability are all possible factors that should be taken into consideration in reliability of measurements. A future study that considers both scan–rescan and segment based reliability would better address reliability concerns. 3.3 Descriptive Statistics. The mean CSA of the right, left, and total ESMs as well as standard deviation of these measurements is presented in Table 3. The total ESM CSA was 47.12, 49.01, and 48.93 cm2 for females and 59.15, 55.52, and 47.79 cm2 for males at the L3/L4, L4/L5, and L5/S1 levels, respectively. To test the effect of gender and IVD level on the CSA of the total ESM at the same time, a SPF ANOVA test was performed. There were 69 subjects (34 females and 35 males) who had measurements at all three IVD levels. SPF analyses were performed with these 69 subjects. Results of the SPF ANOVA analysis for the total ESM CSA are given in Table 4. The ANOVA found a main effect of gender (p ¼ 0.021) and a main effect of the IVD level (p ¼ 0.000). The effect of interaction between gender and IVD level on the total ESM CSA was also significant (p ¼ 0.000). CSAs were significantly different between males and females at the L3/L4 and L4/L5 levels only. Figure 4 demonstrates how gender and IVD level affect the ESM CSA. To determine whether there were any significant differences between the right and left ESM CSAs, paired-sample T tests were performed (Table 3). Results suggested that there were no significant differences between muscle sizes for both genders at all IVD levels (all p values  0.05). Correlation analyses (Table 3) also support that the CSAs of the right and left ESMs were highly correlated (correlation coefficients ranged between 0.845 and 0.938). 3.4 Regression Analyses. Backward regression analyses were performed to determine ESM CSA estimation models based on the

Table 3 CSAs of the ESMs and comparison of the right and left ESMs Total (cm2)

Right (cm2)

Left (cm2)

Correlations

Paired-samples tests

N

Mean

SD

Mean

SD

Mean

SD

Coeff.

Sig.

t

df

Sig.

L3/L4

Female Male

54 53

47.12 59.15

8.17 10.28

23.62 29.53

4.35 5.22

23.50 29.62

3.98 5.23

0.926 0.937

0.000 0.000

0.523 0.330

53 52

0.603 0.743

L4/L5

Female Male

50 44

49.01 55.52

8.29 8.54

24.39 27.58

4.19 4.15

24.62 27.95

4.23 4.62

0.938 0.897

0.000 0.000

1.110 1.206

49 43

0.272 0.234

L5/S1

Female Male

41 35

48.93 47.79

10.02 10.43

24.08 23.50

4.75 4.82

24.86 24.29

5.68 5.97

0.845 0.866

0.000 0.000

1.647 1.550

40 34

0.107 0.130

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Table 6 Comparison of subject anthropometrics of the historical dataset and the validation dataset IVD L3/L4

Variable

Data

N

Mean

SD

Height

His. Val. His. Val. His. Val. His. Val. His. Val. His. Val. His. Val. His. Val. His. Val.

53 20 53 20 53 20 44 20 44 20 44 20 35 20 35 20 35 20

178.57 177.04 84.53 83.96 26.41 26.74 178.43 177.04 85.11 83.96 26.68 26.74 178.09 177.04 84.74 83.96 26.72 26.74

8.86 8.06 19.45 10.43 5.23 2.34 9.12 8.06 19.19 10.43 5.22 2.34 9.36 8.06 19.64 10.43 5.61 2.34

Weight BMI L4/L5

Height Weight BMI

L5/S1

Height Weight BMI

t

df

Sig.

0.672

71

0.504

0.124

71

0.902

0.274

71

0.785

0.587

62

0.559

0.251

62

0.803

0.049

62

0.961

0.418

53

0.677

0.165

53

0.870

0.018

53

0.985

Dataset ¼ His: historical, Val: validation; height: cm; weight: kg, BMI: kg/cm2.

independent variables gender (XG), age (XA), height (XH), and weight (XW). BMI was not considered as a predictor since it was highly correlated with height (p ¼ 0.005) and weight (p ¼ 0.000) and higher correlations among dependent and independent variables, inherently, result in multicollinearity problems. Regression analyses were performed for the total ESM CSAs at each IVD level. Right and left ESM CSAs were not studied separately because there were no statistically significant differences between them. The summation of both CSAs gives the total ESM CSA.

Fig. 4 Gender comparisons on the CSAs of ESMs: (a) right ESM, (b) left ESM, and (c) total ESM

3.4.1 Regression Models. Results of regression analyses to determine coefficients are given in Table 5. The “use of probability of F” was selected as 0.05 for entry and 0.0501 for removal; therefore, only independent variables whose p value is less than 0.05 can enter the final model. Regression equations produced from these coefficients are also presented in Table 5. ANOVA tests revealed that all three regression models were significant (all p values  0.05). At the L3/L4 level, the coefficient for gender is positive and significant (average male subject CSA was larger than average female subject CSA). At the L4/L5 level, the gender coefficient was not significant. At the L5/S1 level, the gender coefficient was negative (average female subject CSA was larger than average male subject CSA). Note that the gender multiplier is “0” for

Table 5 Coefficients of independent variables and ESM CSA prediction models Unst. Cf. bi

Model L3/L4

L4/L5

L5/S1

B

St. Cf. SE

Beta

t

b0 9.262 13.882 — 0.667 bG 7.146 1.841 0.325 3.882 bH 0.244 0.088 0.246 2.785 0.209 0.038 0.394 5.474 bW CSA of ESM 5 29.262 1 (7.146 3 XG) 1 (0.244 3 XH) 1 (0.209 3 XW) Constant b0 20.378 11.160 — 1.826 0.358 0.069 0.449 5.224 Height bH 0.138 0.037 0.322 3.753 Weight bW CSA of ESM 5 220.378 1 (0.358 3 XH) 1 (0.138 3 XW) Constant b0 20.300 19.146 — 1.060 Gender bG 6.811 2.548 0.336 2.674 0.356 0.117 0.388 3.034 Height bH 0.135 0.056 0.265 2.392 Weight bW CSA of ESM 5 220.300 2 (6.811 3 XG) 1 (0.356 3 XH) 1 (0.135 3 XW) Constant Gender Height Weight

Sig.

R2

Adj. R2

SE

p value

0.537

0.524

7.61

0.000

0.398

0.385

7.04

0.000

0.209

0.176

9.22

0.001

0.506 0.000 0.006 0.000 0.071 0.000 0.000 0.293 0.009 0.003 0.019

CSA of ESM (cm2); XG: gender (0 for female and 1 for male); XH: height (cm); XW: weight (kg).

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females and “1” for males. Height and weight had positive coefficients since they had positive linear relationships with the CSA of the total ESM. This means that the CSA of the total ESM increases with height and weight. For example, the CSA of the total ESM at the L5/S1 level increases by 0.356 cm2 per cm increase in subject height; and increases by 0.135 cm2 per kg increase in subject weight. Other fitted regression models (i.e., quadratic and exponential) were also evaluated. More independent variables (two-way interactions between all four independent variables and square-terms of all four independent variables) were included in regression analyses. Results showed that adding square-terms and interaction terms did not significantly alter R2 values. The added complexity of quadratic and exponential regressions was not deemed worth the trade-off for potentially slightly improved R2 values. Slight improvements in R2 associated with these models were more likely due to an increase in the number of explanatory variables rather than the explanatory power of these variables. These terms made the models more complex to interpret. Therefore, first-order regression models with only simple independent variables (gender, height, and weight) are presented in this paper. 3.4.2 Validation of Regression Models. To assess how well these models estimate the total ESM CSA, 20 asymptomatic, male subjects were recruited for validation of regression results. The same methodologies for measuring the total ESM CSA were applied. Comparisons of the historical (patient) dataset and the validation dataset regarding subject anthropometrics are given in Table 6. Statistical tests revealed that subjects in both datasets had the same anthropometrics. Therefore, it is expected that regression models derived from the historical dataset should closely estimate the total ESM CSAs of the new subjects (validation dataset). Paired-samples T tests were performed to test whether there were any significant differences between the “measured” values measured from MRI scans and the “estimated” values estimated from the regression models. Results suggested that for these 20 subjects there were no significant differences between the measured and estimated values (p ¼ 0.659 at the L3/L4 level, p ¼ 0.311 at the L4/L5 level, and p ¼ 0.097 at the L5/S1 level). This suggests that the regression models are valid and estimate the total ESM CSA very closely. Lin’s CCCs were calculated as 0.289, 0.255, and 0.197 at the L3/L4, L4/L5, and L5/S1 levels, respectively. Similar to the regression R2 values, these CCC values were relatively low and demonstrated the same decreasing pattern with lower levels. Relatively low CCC values indicate that the estimated values deviate from the line of perfect concordance suggesting an over- or underestimation. Paired T tests showed no significant differences between two measurements (measured and estimated). However, they do not report the “absolute” difference between two measurements. The mean absolute differences between the measured and estimated total ESM CSAs were also calculated and given in Table 7. Absolute values may be preferred over the mean difference to demonstrate expected differences.

4

Discussion

The measurement technique used in the present study was repeatable and reliable. Reproducibility tests indicated that the agreement between two independent researchers was good (ICC ranging from 0.811 to 0.891). Each independent researcher also repeated measurements with an excellent intrarater agreement (ICC ranging from 0.968 to 0.990). The present study also investigated the effect of muscle side. Results agree with most previous studies [4,18–23] that there were no significant CSA differences between the right and left side. The association between aging and the decrease in the muscle mass has been reported in the literature [12–14]. However, the relationship between aging and low back musculature size is not very obvious. Seo et al. [9] did not find any significant 071012-6 / Vol. 137, JULY 2015

Table 7 “Absolute” differences between the measured ESM CSAs measured for asymptomatic (validation) population (n 5 20) and estimated ESM CSAs estimated with regression equations based on patient (historical) population Absolute differences in CSA

Level

Method

Mean (cm2)

Mean D

SD

Min

Max

Mean (%)

L3/L4

Measured Estimated Measured Estimated Measured Estimated

59.49 58.63 56.78 54.59 50.89 47.25

6.57

5.35

0.09

20.93

11.0

7.00

6.51

1.01

28.61

12.3

7.80

6.04

0.17

21.41

15.3

L4/L5 L5/S1

relationship with subject age and ESM size. Reid et al. [1] also did not observe an age effect on the ESM CSA. However, the age range of their subjects was relatively small. Some previous researchers [2,5] did not study the age–size relationship at all. Anderson et al. [11] were the only researchers, who included age in their estimation models: approximately less than 1 cm2 decrease in muscle size per 25 years. Note that their age coefficient was not statistically significant. The present study did not find any statistically significant relationship between age and muscle size at any IVD level either. However, subject age in the present study was limited (21–39 years), which may explain why age was not predictive for the ESM CSA. Table 8 [1–9,11,24,25] summarizes previous studies that investigated the relationship between the ESM CSA and subject characteristics and anthropometrics. Gender, height, and weight are the most studied subject parameters. Cooper et al. [5], Marras et al. [7], Seo et al. [9], Jorgensen et al. [8], and Anderson et al. [11] indicated an effect of gender on the ESM CSA. The present study also emphasizes that gender is a significant predictor in determining the ESM CSA. However, the gender variable enters regression models at the L3/L5 and L5/S1 levels and not at the L4/L5 level. Jorgensen et al. [8] included gender in their regression models at the L3/L4 and L4/L5 levels, but not for the L5/S1 level. Anderson et al. [11] provided regression models with gender predictor for each vertebral level, but gender was significant at the L3 level and not significant at the L4 and L5 levels. It could be interpreted that gender effect depends on the IVD level. ANOVA results in the present study showed that the effect of gender is not straight forward; the interaction between gender and the IVD level adds more complexity in explaining the gender effect on the ESM size. Unfortunately, Reid et al. [1], McGill et al. [2], Tracy et al. [3], and Wood et al. [6] studied only male subjects and Chaffin et al. [4] studied only female subjects; hence, they could not investigate gender effects on the ESM size. As with gender, height was not consistently evaluated across studies. Some researchers found relationships between height and the ESM CSA [4,7,8,11]. However, some other researchers did not find any relationship between subject height and the ESM CSA [1–3,6]. It should be noted that the ones that did not find relationships had relatively small sample sizes compared to ones that found relationships. Among predictor variables, it seems that subject weight was the most promising variable to estimate the CSA of the ESM. The present study and most previous studies [1,4,5,7–9,11] indicate that there is an association between subject weight and subject ESM CSA. McGill et al. [2], Tracy et al. [3], and Wood et al. [6] did not find any relationship between the ESM CSA and weight. It should be noted that the mean weight was 89.1 kg in the study of McGill et al.’s [2] and 87.3 kg in the study of Wood et al.’s [6], which were the two heaviest sample populations among the studies compared here (Table 8). These subjects were significantly heavier (more obese) than subjects in the other studies and the Transactions of the ASME

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Table 8

Prediction equations for the ESM CSA reported by various authors

Study

Subjects

Age

Height

Weight

Level

Schultz et al. [24] Reid et al. [1] (MRI, healthy)

— 20 male

— 21.2

— 176.9

— 69.7

L3 L5

McGill et al.[2] (CT, supine, LBP) Tracy et al. [3] (MRI, supine, LBP) Chaffin et al. [4] (CT, supine, healthy) Marras and Sommerich [25] Cooper et al. [5] (CT, LBP) Wood et al. [6](MRI) Marras et al. [7] (MRI, supine, and healthy)

13 male

40.5

173.8

89.1

26 male

—

—

96 female

49.6

— 39 male 53 female 26 male 10 male

— 38 39 40.5 26.4

25.0

R2

SE

p value

— 0.77

— —

— —

L4/L5

0.0389 (TD  TW) 54.38 þ 1.00 (W  69.79) þ 1.91 (IC  79.07) þ 2.90 (ARM  30.01)  3.14 (CHW  29.12) þ 5.95 (ABLW  27.33)  2.39 (XIPSPL  37.45) Could not find any regression model for H, W, and H  W

—

—

—

—

L2-S1

Could not find any regression model for H, W, TD, TW, TD  TW, and IF

—

—

—

163.1

67.6

—

— — — 174.5 175.9

— 75 64 87.3 79.8

L5 L4

6.7 þ 0.1166 W þ 0.017 H 14.7 þ (0.0065  TA) 0.0389 (TD  TW) [Approximate equation] ¼ 16 þ 2G þ 0.18 W

0.26 0.12 — —

L3 L4 L5 L3/L4

Could not find any regression model for anthropometric measurements 6.86 þ 0.24 W 53.65  12.34 (H/W) 0.106 þ 57.28 (W/H) 9.27 þ 0.209 W 50.7  11.04 (H/W) 2.83 þ 51.16 (W/H) 7.51 þ 0.408 W 38.21  7.65 (H/W) 8.12 þ 69.25 (W/H) 12.34 þ 0.492 W 43.72  9.54 (H/W) 13.78 þ 85.55 (W/H) 8.63 þ 3.7 G þ 0.001 (H  W)  0.02 (TD  TWI) þ0.74 TWX þ0.07 (L1/L5) 6.48 þ 3.15 G þ 0.29 W  0.03 (TD  TWI) þ 0.52 TWX þ 0.08 (L1/S1) 14.29 þ 0.002 (H  W)  0.58 IC þ 0.69 TWX þ 0.13 (L1/S1) 5.32 þ 0.284 W 11.36 þ 0.001912W2 2.52 þ 3.02 G  0.0439 A þ 0.048 H þ 0.124 W 4.97 þ 1.19 G  0.0234 A þ 0.0198 H þ 0.0808 W [Not sig.] ¼ 8.54  0.37 G þ 0.00953 A  0.0437 H þ 0.366 W 9.262 þ 7.146 G þ 0.244 H þ 0.209 W

— 0.58 0.62 0.59 0.47 0.53 0.50 0.61 0.54 0.61 0.69 0.65 0.72 0.86 0.85 0.73 0.576 0.469 0.55 0.30 0.04 0.537

— 2.87 2.72 2.85 3.12 2.94 3.04 2.15 2.34 2.15 2.19 2.32 2.07 1.9 1.8 2.3 3.70 2.73 3.19 2.82 2.55 7.61

— 0.0103 0.0065 0.0098 0.0283 0.0166 0.0225 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 — — — 0.000

L4/L5

20.378 þ 0.358 H þ 0.138 W

0.398

7.04

0.000

L5/S1

20.300  6.811 G þ 0.356 H þ 0.135 W

0.209

9.22

0.001

L4/L5 Left Right

20 female

Regression equations for the CSA of the ESM

165.5

57.9

Left Right

JULY 2015, Vol. 137 / 071012-7

Jorgensen et al. [8] (MRI, lying on side)

12 male 12 female

23.1 23.8

177.1 162.3

74.5 56.5

Seo et al. [9] (MRI, supine, healthy, Japan) Anderson et al. [11] (CT, supine, jealthy)

152 male 98 female 51 male 49 female

36.2 39.7 59.4 58.1

168.5 155.5 177.6 162.2

65.5 54.4 81.3 68.4

This study (MRI, Supine, Patient)

53 male 54 female 44 male 50 female 35 male 41 female

30.1 29.2 29.7 29.2 30.0 30.1

178.6 165.3 178.4 164.9 178.1 166.1

84.5 76.7 85.1 77.2 84.7 74.4

L3/L4 L4/L5 L5/S1 L3/L4

14% 16% — —

0.001 0.001 — —

G: gender (0 for female and 1 for male); A: age (yr); H: height (cm); W: weight (kg); TD: trunk depth (cm); TW: trunk width (cm); TWI: trunk width at iliac crest; TWX: trunk width at xiphoid process; IC: trunk circumference at ilium; ARM: circumference of upper arm (straight); CHW: width at chest; ABLW: abdominal’s least width; XIPSPL: vertical length the xiphoid process to the symphysis pubis; IF: index of fat; TA: torso area (cm2).

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present study, and this, along with relatively small sample size, may have impeded their ability to find a relationship with weight. Chaffin et al. [4] indicated that the size of ESMs may not correlate with body weight because the size of the muscles depends more on the physical requirements placed on the muscle during normal manual activities and not on simple gross body weight. The absolute error percentages for regression models were 11%, 12%, and 15% at the L3/L4, L4/L5, and L5/S1 levels, respectively. The minimum and maximum values (in Table 7) indicate that the maximum difference was 20.93 cm2 at the L3/L4 level. This large difference may suggest that the model does not work well for all circumstances. However, the difference between the measured and estimated values was primarily less than 10 cm2 and only one subject had such a large absolute difference. It is known by researchers that this subject was a weight lifting enthusiast with significant musculature. It could be interpreted that the current predictor variables (gender, height, and weight) are not sufficient to explain the variability among subjects. Future studies should investigate further subject characteristics such as the frequency, intensity, and duration of physical exercise. For example, lean body mass may be a good predictor of subject muscularity. Trunk circumference [1], trunk depth and width [8], and trunk area [4] had been studied in previous studies. The relationships between these measurements and the ESM CSA could not be investigated in the present study. Future studies may investigate these relationships and include more anthropometric measurements. Finally, anthropometrics of a subject sample should be considered before using these regression equations. The regression equations provided in the present study may not be applicable for adolescent or older subjects, obese subjects, or trained athletes. Since MRI scans were taken with subjects in a relax, supine posture, they do not reflect the loading associated with standing posture. The subjects in the historical dataset were medical patients and possibly had low back symptoms; therefore, the results of the present study may differ for healthy subjects. Future studies may determine whether the results of this study are applicable for asymptomatic subject populations.

5

Conclusion

The present study showed that an individual’s ESM CSA could be estimated with easily collected individual variables: gender, height, and weight. Validation of regression models showed that the measured and estimated ESM CSAs were not statistically different. An average absolute error of 11%, 12%, and 15% is expected from the regression model at the L3/L4, L4/L5, and L5/S1 levels, respectively. Future studies with larger sample sizes and additional independent variables may provide better estimates. The coefficients of multiple correlation, R2’s, were relatively low in the present study. To address this, future studies may investigate the relationships between the ESM CSA and additional independent variables (such as anthropometric measurements such as lean body mass, subject criteria such as exercise/activity level, and subject medical conditions). In addition, subject body part dimensions vary not only among subjects but also within subjects (e.g., nobody is perfectly “proportional”). Race/ethnicity, occupation, genetics, medical history, lifestyle, geographic region, climate, among other confounding factors may affect body dimensions and proportions. “Natural variation” in anthropometrics introduces some error in predicting body dimensions, particularly internal sizes such as the ESM CSA. We believe that collecting additional personal characteristics may help improve regression fitting and improve R2 values.

071012-8 / Vol. 137, JULY 2015

Acknowledgment This project was partially supported by the National Institute for Occupational Safety and Health (NIOSH) Pilot Project Research Training Grant (CDC-T42OH008414-06).

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