RESEARCH

Volume 8 Issue 1 | Spring 2015

The relationship between trunk muscle strength and flexibility, intervertebral disc wedging, and human lumbar lordosis Connie Hsu1, Eric Castillo2, and Daniel Lieberman3 1

Harvard College ‘16 Department of Human Evolutionary Biology, Harvard University 3 Department of Human Evolutionary Biology, Harvard University 2

Introduction

Functions of various trunk muscles Lumbar lordosis not only stabilizes the spine by maintaining sagittal balance of the upper body’s center of mass, but it also allows for greater sagittal flexion and extension of the trunk due to the orientation of lumbar zygapophyseal joints (Berlemann et al., 1999; Hildebrand, 1974; Guan et al., 2007). Agonist-antagonist muscle groups control sagittal movements of the trunk. The extensor muscles of the lower back, including the Multifidus muscle of the Transversospinalis group and the Erector Spinae muscles, provide mechanical stability and play an important role in controlling movement of the lumbar spine (Hansen et al., 2006; Macintosh & Bogduk, 1986). Other muscles in the lower back include the Psoas Major – which connects the transverse processes of lumbar vertebrae to the lesser trochanter of the femur and contributes to flexion of the trunk, and the Quadratus Lumborum – which primarily functions to brace the lower ribs and provide a steady base for thoracic muscle fibers. The Quadratus Lumborum may also assist in support and movement in lateral bending (Adams et al., 2006). The degree of lordosis in the lumbar spine induces the conversion of power - or a transfer of strength – developed in the back extensor muscles to transfer axial torsion forces, the twisting motion of a torque around

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Physiology

Human axial skeletons possess many derived adaptations for bipedalism, including a posteriorly concave curvature of the lumbar spine known as lordosis (Whitcome et al., 2007). Although humans are morphologically and genetically similar to the African great apes, chimpanzees and gorillas are knuckle-walking quadrupeds, lacking the lordotic curve derived in humans. This may partly be explained by variations in regional vertebral numbers between great apes and humans. Although the total number of vertebrae remains consistent, great apes possess fewer (three to four) lumbar vertebrae and an average of 13 thoracic vertebrae as opposed to an average of five lumbar and 12 thoracic vertebrae in humans. The greater number of lumbar vertebrae in humans likely contributes to the greater range of motion and curvature in human lower backs (Whitcome, 2012). Lumbar lordosis is essential for balancing the human body in an upright posture, and it develops early on in ontogeny when infants begin learning how to walk (Abitol, 1987). However, lordosis is not a uniquely human trait. For example, Japanese macque monkeys trained to walk bipedally also demonstrate a lumbar lordosis, suggesting that lordosis serves an important biomechanical function (Preuschoft et al., 1988). In addition to lumbar lordosis, the the range of motion of the spine differentiates human and non-human primate lower backs (Sparrey et al., 2014). The orientation of the vertebrae that shape the short, flat lumbar spines of great apes are less flexible than human spines, and offer very little mobility, suggesting that changes in lumbar curvature and range of motion were adaptive (Lovejoy, 2005). Indeed, the evolution of human lumbar lordosis required reorganization of the spinal musculature to support bipedal locomotion while maintaining stability and strength in the lower back (Lovejoy, 2005). The mobility of the lumbar spine is especially important because the lumbar region tends to experience the greatest weightbearing loads in the spine, and it is a common site of low-back pain (Battie et al., 2009). While it is unclear how lumbar mobility and lordosis contribute to low back pain, previous studies have discovered that both spinal muscle strength and intervertebral disc morphology are associated with the degree of lordotic curvature (Sinaki et al., 1996; Whitcomb et al., 2007; Sparrey et al., 2014). The aims of this study attempt to investigate whether strength of relative trunk muscles – specifically, the ratio of hypaxial (front) and epaxial (back) muscles – and degree of disc wedging , which is likely involved in stability and flexibility of the lower back, are associated with lumbar lordosis curvature.

Intervertebral disc morphology and flexibility of the lower spine The morphology of intervertebral discs affects the amount of lordosis and mobility of the lumbar region. Intervertebral discs separate adjacent vertebrae, allow for movement, and resist loading between vertebrae (Adams et al., 2006). Previous studies have indicated that loading of the spine significantly compresses the discs especially in the L4-5 and L5-S1 lumbar regions, which have greatest sagittal, or vertical, range of motion (Shymon et al., 2014). Compression and shearing of discs (See Figure 1 for descriptions) may be related to a higher risk of disc disease and instability in the lower spine (Shymon et al., 2014). Since intervertebral discs provide most of the spine’s intrinsic resistance to small movements (including compression, torsion, and shearing forces), discs are likely locations of instability. Conditions such as degenerative disc disease are correlated with reduced lordosis in the lumbar spine (Barrey et al., 2007), likely due to an inability of the diseased disc to allow for the same range of motion as a healthy disc. It is possible that certain morphological features of the disc, such as disc height, are associated with variations in flexibility of the lumbar spine, which may be crucial for determining rehabilitation methods for disc-related lower back pain targeted at particular disc levels for strengthening the back without sacrificing flexibility.

RESEARCH

Physiology

a vertical axis, that are necessary to rotate the pelvis while walking (Sparrey et al., 2014). The abdominal muscles in the trunk that are antagonistic to the back muscles include the Rectus Abdominus, Transversus Abdominus, Internal Abdominal Oblique, and External Abdominal Oblique. The Rectus Abdominus, the muscle commonly targeted in abdominal workouts, originates on the pubis and inserts on the xiphoid process of the sternum and the costal cartilages of the ribs and is responsible for flexion of the spine in the sagittal plane (See Figure 2 for a visual of the muscle groups). Trunk muscles and stability in the lower spine The strength of agonist-antagonist trunk muscles is important for postural stability. In general, the cross-sectional area of a muscle correlates with its strength because the capacity of a muscle to generate force is directly proportional to the number and size of the muscle fibers within it (Akagi et al., 2009, Blazevich et al., 2009). Mathematical modeling predicts that larger muscle forces are required for lumbar stability, which depends on the degree of lumbar curvature (Meakin & Aspden, 2012). This suggests a relationship between muscle size and sagittal lumbar curvature. Previous studies have indeed found that the volume of the lumbar extensor muscles (including the Multifidus and Erector Spinae muscles) are positively correlated with the magnitude of lordosis curvature in the lumbar regions, indicating that larger muscle forces are required for stabilization in populations with greater lumbar lordosis (Meakin et al., 2013). In addition, decreased trunk extensor muscle volume is correlated with back pain (Danneels et al., 2000; Kamaz et al., 2007). However, the relationship between strength of the antagonistic trunk flexor muscles, such as Rectus Abdominis, with flexibility and curvature of the lower back has not yet been thoroughly investigated.

Figure 1: Degree of lumbar lordosis and forces acting on the lower spine (Castillo et al., 2015). Shearing forces represent horizontal forces acting on the spine. Compression refers to perpendicular forces acting on the spine. Trunk weight refers to the vector sum of the weight-bearing forces acting on the spine.

Volume 8 Issue 1 | Spring 2015

Variation in lumbar lordosis vs. strength and flexibility There is a considerable range of variation in lumbar sagittal curvature in humans (Berthonnaud et al., 2005; Boulay et al., 2006), possibly due to factors such as change in posture or intrinsic bony anatomy (Meakin et al., 2012). Previous studies have shown this variability to be correlated with variation in back extensor size and strength (Danneels et al., 2000; Kamaz et al., 2007; Hides et al., 2008; Wallwork et al., 2009). Even though abdominal flexor muscles and back extensor muscles require coactivation in order to provide mechanical stability in the spine, the extent to which they are activated differs between individuals, implying that different individuals use different patterns of flexor or extensor muscle coactivation to stabilize the lumbar spine (Cholewicki et al., 1997), which may explain some variations in lumbar curvature. Little is known about how sagittal spinal range of motion relates to variations in lordosis and trunk stability. Previous interventions aimed at increasing spinal stabilization while maintaining flexibility and mobility in patients after surgery have been plagued by complications and failures, perhaps indicating evidence for a trade-off between flexibility and range of motion with stability and strength in the lumbar spine (Shymon et al., 2014). Variations in lumbar lordosis are hypothesized to be correlated with a tradeoff between trunk muscle strength and sagittal lumbar flexibility, since muscle strength functions to maintain stability and stiffness of structures, while flexibility increases range of motion in joints but is often associated with structural instability in the trunk. There is also evidence that improving core muscle balance may be an effective intervention in correcting posture problems in young subjects as a prevention measure for back pain, possibly due to increased stability, but the outcomes of such an intervention are unknown (Scannell & McGill, 2003). This study tests the hypothesis that there is an underlying tradeoff between strength of the Rectus Abdominus and back (Erector Spinae, Multifidus, Quadratus Lumborum, or Psoas) muscle strength, which leads to variations in lumbar lordosis. The study also tests the hypothesis that lumbar lordodsis is associated with decreased rostral (back) disc height. A sample of magnetic resonance image (MRI) scans from healthy, young adult volunteers were analyzed to investigate factors affecting lumbar lordosis variations. In contrast to previous studies that found an association between lumbar extensor muscle volume lumbar lordosis (Meakin et al., 2013), we hypothesize that lumbar lordosis will covary with the relative strength of agonistantagonist trunk muscle groups. Thus, we predict that subjects with larger, and thus stronger, Rectus Abdominis muscles relative to lumbar extensor muscles have decreased lumbar curvature in the lower back due to the antagonistic role of the Rectus Abdominis in lower back movement (flexion, instead of extension). We also expect that subjects with larger lumbar extensors relative to trunk flexors will show increased lumbar curvature. In addition to trunk strength, we also test the hypothesis that soft-tissue factors, such as increased posterior wedging of the vertebral discs (as indicated from the rostral (back) disc height relative to the max disc height of that level) will be positively associated with an increased lumbar curvature. Testing the hypothesized trade-off between hypaxial and epaxial trunk strength in the lordotic spine will lead to a better understanding of how stability and range of motion interact to moderate variations in lumbar lordosis, which has important implications for the intervention and prevention of biomechanical risk factors for back pain.

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RESEARCH 400mm, and 300mm respectively, with a resolution of 1.280 pixels per mm for a slice thickness of 7mm. Axial imaging involved a FLASH scan consisting of scans with a height, width, and depth of 218mm, 350mm, and 250mm respectively, with a resolution of 1.463 pixels per mm for a slice thickness of 5mm.

Figure 2: This image is a FLASH scan of an axial view of the spinal musculature just above the L4/L5 disc. This image was selected randomly in order to avoid bias. This study targeted the Rectus Abdominus (blue), Erector Spinae (green), Multifidus (purple), Quadratus Lumborum (red), and Psoas (orange) muscle groups.

Subject Recruitment and Consent Thirty-one subjects (n=15 females and 16 males) were recruited from the greater Boston area. Subjects were young adults (18-35 years old) in good health to minimize age-related degenerative changes in the spine, such as arthritis, disc degeneration, or other spinal pathology. Potential subjects were screened using a health questionnaire, and any subjects who reported a history of back pain or diagnosed spinal pathology were excluded. The Committee of Use of Human Subjects on Institutional Review Board at Harvard University approved this study, and all subjects gave their written informed consent. Data Acquisition Magnetic Resonance Imaging (MRI) data from subjects was collected, along with their age, height, and body mass. Scans were conducted at the Center for Brain Science Neuroimaging lab (at Harvard University) with a 3-Tesla Siemens Tim Trio MRI scanner. Subjects were scanned in the supine position with their legs laying flat during the scan. To minimize image artifact due to diaphragm movement, FLASH scans were implemented with the subject holding their breath for 30 seconds. These scans were used in the analysis of the lumbar spine from an axial view. A single-slice localizer scan was used for analyses of the spine in the mid-sagittal plane. The standard protocol of the MRI scans consisted of sagittal and axial T1-weighted images [repetition time/echo times of 8.6/4 ms and 7.4/4 ms respectively]. The sagittal imaging involved a localizer single-slice with height, width, and depth of 400mm,

Statistical Analysis Statistical analysis of the data was conducted using Microsoft Excel and R statistical software (version 0.98.501). A Shapiro-Wilk test (Shapiro & Wilk, 1965) was completed on each of the independent variables - ratio of Rectus Abdominus muscle over back extensor muscles and disc wedging – as well as the dependent variable (LA) in order to establish whether the data followed a normal distribution. Multiple partial regression models were implemented to determine associations between lordosis angle and the hypaxial / epaxial strength ratio (measured as the cross-sectional areas of Rectus Abdominus to various back muscles), accounting for the effects of age, height, and weight as additional covariates. The multiple regression models with the greatest significance between the hypaxial / epaxial strength ratios and lordosis angles were then normalized to z-scores. Sample size power tests were implemented to determine the ideal sample size for a multiple regression model given the strength of the effect sizes (multiple R2). Cohen’s f2 effect size

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Physiology

Materials and Methods

Image Analysis MRI images were analyzed using ImageJ software (National Institutes of Health). Each measurement on cross-sectional area of the trunk muscles, lordosis angle, and disc heights were completed three times and averaged to ensure intra-individual measurement reliability. Coefficients of variation for intra-individual consistency were calculated for each of three measurements for all of the measured variables. Intervertebral disc wedging was assessed from the mid-sagittal localizer scan. Disc and vertebral wedging were analyzed using the tracing feature of ImageJ by measuring the anterior and posterior disc heights for the T12 through L5 vertebrae, as well as the maximum disc height at the T12-S1 intervertebral levels. Posterior disc wedging at each level was found by dividing the height of the disc in the posterior position by the maximum height of the disc at that level in order to determine the disc shape asymmetry due to wedging from various forces. The same strategy was used to calculate the degree of anterior disc wedging. Vertebral body height measurements were also taken at the above levels using the sagittal scan view. Since the cross-sectional area of a muscle is proportional to the capacity of the muscle to generate force, muscle strength was approximated by measuring the cross-sectional areas of muscle groups in axial view using FLASH breath-hold scans. The muscle groups analyzed included the Multifidus, Erector Spinae, Psoas, Quadratus Lumborum, and Rectus Abdominus muscles. Cross sectional areas of these muscles were traced at the L3/L4 and L4/L5 spinal levels. The cross-sectional areas of the muscles were then corrected for the non-orthogonal orientation of the scan plane relative to the orientation of the muscle cross-section by multiplying the measured cross sectional area by the cosine of the degree of vertebral body tilt at that spinal level (plus 45 degrees to ensure that tilt angles were all positive). The degree of lordosis, analyzed at the mid-sagittal plan using the angle feature in ImageJ, was measured as Cobb’s angle (lordosis angle; LA), which is defined as the intersection of vectors drawn along the superior endplate of the L1 vertebrae and superior endplate of S1 (see Been, 2011).

RESEARCH was calculated and used to estimate statistical power. The desired statistical power level for this test was P = 0.80, and the probability level used in the calculation was p = 0.05.

Physiology

Results Summary statistics and intra-individual measurement errors for anthropometrics and muscle cross-sectional areas are reported in Table 1. Subjects had a mean lumbar curvature of 49.0 degrees with a standard deviation of 9.64. In all models, height was negatively associated with lordosis angle, while weight and age were both positively associated with lordosis angle. Models also suggest that the ratio of the cross-sectional area of the Rectus Abdominus muscle to the cross-sectional area of various back extensor muscles – as a proxy for relative core versus back muscle strength – was negatively associated with lordosis angle for some muscle groups at specific spinal levels after accounting for age, height, and weight (Table 3). The three statistical models with the most significant strength ratios are shown with standardized beta coefficients in Table 3. All independent and dependent variables in these three models passed the Shapiro-Wilk test for normality. Sample size power tests were calculated to be 39, 34, and 35 (See Table 3) for each of the statistical models. The relationship between the ratio of the Rectus Abdominus muscle to the multifidus muscle and lordotic curvature at the L5 level had a coefficient of -0.33 approaching conventional significance levels (p = 0.087). A significant negative association between the ratio of the Rectus Abdominus muscle to the erector spinae

Figure 3: Partial regression, or added-variable, plots of the relationship between lordosis angle and ratio of Rectus Abdominus to the Multifidus muscle along with all its covariates (weight, height, and age) at the L5 level. All variables are scaled in order to compare strengths of relationships. Ratio.L5.RA.M refers to the ratio of the Rectus Abdominus muscle to the Multifidus muscle at the L5 level. “| others” refers to the partial regression model accounting for all covariates in the model while depicting the relationship between the main coefficient tested and the dependent variable (scaled lordosis angle).

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muscle at the L3/L4 level and lordosis angle was found (coefficient = -0.41; p = 0.04). Furthermore, there was a significant negative association between the ratio of the rectus abdominus muscle to the Quadratus Lumborum muscle at the L3/L4 level and lordosis angle (coefficient = -0.36; p = 0.05). Graphical representations of each of these three statistical models along with their covariates are shown in Figures 3, 4, and 5. Summaries of the mean (SD) of posterior and anterior disc wedging at the L5/S1, L4/L5, L3/L4, L2/L3, and L1/L2 levels can be found in Table 4. Posterior disc wedging was significantly associated with degree of lordosis at the L2/L3, L3/L4, and L4/L5 levels (p<0.05), while anterior disc wedging (also relative to the maximum wedging of that disc) was not significantly associated with the degree of lordosis at any level. All significant associations found passed the Shapiro-Wilk test for normality.

Discussion Summary This study examined the relationship between muscle strength and the degree of curvature in the lumbar spine. We tested the hypothesis by measuring the cross sectional areas of abdominal muscles (which are usually associated with strength and stability of the spine) relative to back muscles (which are usually associated with flexibility and range of motion in the spine), investigating whether these relative relationships could serve as a predictor for lumbar curvature.

Figure 4: Partial regression, or added-variable, plots of the relationship between lordosis angle and ratio of Rectus Abdominus to the Erector Spinae muscle along with all its covariates (weight, height, and age) at the L4 level. All variables are scaled. Ratio.L4.RA.ES refers to the ratio of the Rectus Abdominus muscle to the Erector Spinae muscle at the L4 level. “| others” refers to the partial regression model accounting for all covariates in the model while depicting the relationship between the main coefficient tested and the dependent variable (scaled lordosis angle)

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RESEARCH

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Table 1: Participants and Variables Characteristics Mean

Effects of Relative Trunk Strength on Lordosis Variations We found mixed support for the hypothesis that the ratio of hypaxial to epaxial muscle size is associated with variations in lordosis. Although associations between lordosis curvature and the strength ratios were only statistically significant at certain spinal levels, the direction of association and the effect sizes indicated support for our hypothesis. The strongest and most statistically significant negative association was found between lordosis angle and the ratio of Rectus Abdominus to the Erector Spinae at the L3/L4 level (coefficient = -0.41, p=0.04). This supports our hypothesis of a trade-off between abdominal and back strength, since subjects with either relatively larger Rectus Abdominus muscle cross sectional areas or relatively smaller Erector Spinae muscle cross sectional areas were hypothesized to possess straighter backs. This finding is consistent with previous studies, suggesting that larger extensor muscles caudal to L3/L4 were associated with subjects with greater lumbar curvature (Meakin et al., 2013). Other associations between lordosis curvature and muscle strength in other muscle groups also indicate support for this hypothesis. The ratio of the Rectus Abdominus to the Multifidus muscle had a moderate effect size (coefficient = -0.33; p = 0.08). It is important to note that statistical models would likely have produced results with even greater significance if the sample size of the study had at least 39 subjects. If these findings were significant, the results from this study would support previous studies, which show that larger Multifidus muscles in the L4/L5 region are correlated with a greater degree of lumbar curvature (Meakin et al., 2013).

Age (years)

22.8

4.17

Height (cm)

172.3

9.27

Weight (kg)

65.7

11.4

Lordosis Angle (degrees)

48.9

9.64

Multifidus (L5)

682.7

298.

Erector Spinae (L5)

805.0

369

Quadratus Lumborum(L5)

373.8

351.46

Psoas (L5)

1130.2

486.1

Rectus Abdominus (L5)

448.3

188.3

Multifidus (L4)

710.5

323.3

Erector Spinae(L4)

1595.7

726.3

Quadratus Lumborum (L4)

631.8

300.5

Psoas (L4)

1366.7

597.1

Rectus Abdominus (L4)

699.1

283.3

Note: Values for each of the muscle groups are given as cross-sectional areas with units of mm2

A negative association between lordosis curvature and the ratio of the Rectus Abdominus muscle to the Quadratus Lumborum muscle at the L3/L4 level was also found (coefficient = -0.358; p= 0.05). Although the Quadratus Lumborum may not be as important as the Multifidus and Erector Spinae muscles in back extensor movement (antagonistic to the flexion movement produced by the rectus abdominus), the Quadratus Lumborum does play a role in extension of the lumbar vertebrae with bilateral contractions and is a common source of back pain, especially when the lower fibers of the Erector Spinae muscles are weak. These results suggest that the Quadratus Lumborum muscle may also play an important

Table 2: Coefficient of Variation on Repeated Trials Measurement

Coefficient of Variation of Intra-Individual Reliability

Lordosis Angle

.027

Multifidus (L5)

.023

Erector Spinae (L5)

.027

Quadratus Lumborum(L5)

.048

Psoas (L5)

.304

Rectus Abdominus (L5)

.032

Multifidus (L4)

.029

Erector Spinae(L4)

.026

Quadratus Lumborum (L4)

.036

Psoas (L4)

.032

Rectus Abdominus (L4)

.037

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Physiology

Figure 5: Partial regression, or added variable, plots of the relationship between lordosis angle and ratio of Rectus Abdominus to the Quadratus Lumborum muscle along with all its covariates (weight, height, and age) at the L4 level. All variables are scaled. Ratio.L4.RA.ES refers to the ratio of the Rectus Abdominus muscle to the Quadratus Lumborum muscle at the L4 level. “| others” refers to the partial regression model accounting for all covariates in the model while depicting the relationship between the main coefficient tested and the dependent variable (scaled lordosis angle)

SD

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Table 3: Multiple Regression Models (with covariates accounting for age, height, and weight) Ratio (RA/[Back muscle])

Standardized Beta Standard Coefficient Estimate Error

p-value

Multiple R2

Cohen’s effect size (f2)

Minimum Sample Size (Power Test)

RA/Multifidus (L5)

-0.33

0.187

.08’’

0.262

0.355

39

RA/Erector Spinae (L4)

-0.41

0.189

.04*

0.298

0.425

34

RA/Quadratus Lumborum (L4)

-0.36

0.175

.05’’

0.287

0.403

35

* = p-value< .05; ‘’ = p-value <.10

Physiology

Table 4: Relationships between Lordosis Angle and Posterior/ Anterior Disc Wedging

Ratio

Coefficient Estimate

p-value

Posterior/Maximum (L5/S1)

-10.22

0.45

Posterior/Maximum (L4/L5)

-24.1

0.04*

Posterior/Maximum (L3/L4)

-23.7

0.03*

Posterior/Maximum (L2/L3)

-23.5

0.03*

Posterior/Maximum (L1/L2)

1.64

0.34

Anterior/Maximum (L5/S1)

14.3

0.12

Anterior/Maximum (L4/L5)

-1.49

0.92

Anterior/Maximum (L3/L4)

-10.6

0.38

Anterior/Maximum (L2/L3)

-10.5

0.31

Anterior/Maximum (L1/L2)

-3.78

0.68

* = p-value< .05

antagonistic role to the rectus abdominus muscle, similar to the Multifidus and Erector Spinae muscles. This prediction supports previous findings that suggested similar functions of the Erector Spinae and Quadratus Lumborum muscles in certain movements (Andersson et al., 1996). Other predictors of lumbar lordosis The statistical models used in this study also accounted for other covariates, including age, height, and weight. Likely due to age related degenerative effects, models showed the predicted positive trend between age and lordosis angle. Body weight was also positively correlated to lordosis angle, which supports Euler buckling theory in that greater forces along the column along the column lowers the critical (Euler) buckling force and therefore are likely associated with greater lumbar curvature (Wainwright et al., 1976). Furthermore, Euler buckling theory suggests an inverse relationship between column length2 and critical buckling force (Wainwright et al., 1976). Since our findings reported height having a negative correlation with lordosis angle, Euler buckling theory can likely explain these results as well. Disc Wedging Disc wedging was found to support our hypothesis that soft-tissue morphological features of the intervertebral discs are correlated with lumbar curvature. However, the relationships were only significant with wedging at the posterior end of the spine. This might

be explained because the sagittal wedge shape arises from variations in the posterior vertebral body height rather than anterior body height (Been & Kalichman, 2011; Sparrey et al., 2014). Since disc wedging at the posterior end of the spine tends to occur more frequently with certain behaviors and environmental conditions, these findings also suggest that the degree of lumbar curvature in the lower spine due to disc wedging is likely dependent on behavior and environment throughout an individual’s lifespan. Loading on the spine especially may contribute the increased disc wedging that has implications for possible causes of back pain in the future (Shymon et al., 2014). Limitations There are several limitations of this study. First and foremost, the subject pool was small and narrow. There were only 31 subjects involved in this experiment, and most of the subjects were young, able-bodied college students. Sample size power tests indicated that the minimum sample size should have included 39, 35, or 34 subjects for each of the statistical models in order to produce the most significant results. The active lifestyles of these young individuals may affect spinal curvature and strength of associated muscles. It is likely that more significant associations between variables would have been discovered had the sample size been a larger and less biased in terms of age and lifestyle demographics. Inter-individual variability may also limit the accuracy of the study since this was not tested; however, intra-individual variability was very low, as indicated by low coefficients of variation (Table 2). Furthermore, this study only investigated the relationship between muscle strength (i.e. cross-sectional area), intervertebral disc wedging, and degree of lumbar lordosis; flexibility and range of motion were not directly tested. Since this study is part of a larger series of ongoing experiments, other factors must be included in the analysis before drawing the relevant conclusions, including analyses of a possible tradeoff between muscle strength and flexibility.

Conclusions Although the hypothesis requires further testing, this study provides evidence to suggest that there is a relationship between muscle strength and posterior disc wedging and the degree of lumbar curvature. Intriguingly, these results may also have implications for rehabilitation of the back in clinical settings. Although the derived feature of a lumbar lordosis in humans was important in our evolutionary history, the lower back in humans is a common site for back pain, and the strategies to prevent or rehabilitate lower back pain have been controversial. Unlike our nonhuman primate

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relatives, the anatomy of the vertebrae and muscles in the spine lead to increased range of motion and flexibility in the lower spine with the cost of increased weight bearing. However, if it is true that there is a trade-off between trunk muscle strength and lumbar flexibility, it may be helpful to find where strength and flexibility can be maximized in the lower spine to increase functioning, support, and prevention of back pain. Therapists working with lower back pain patients could construct a treatment plan to target trunk muscles such that patients can achieve optimal strength without sacrificing flexibility, and vice versa. In the meantime, however, this study may provide important evidence regarding the selection pressures operating on the evolution of the human lumbar spine.

Acknowledgements I would like to thank Eric Castillo for allowing me to help out with his project and his many contributions towards the drafting of this report. I would also like to thank our Principal Investigator Daniel Lieberman for allowing us to work in his lab and the Center for Brain Science Neuroimaging lab for allowing us the use of their MRI scanner. Lastly, I would like to thank the reviewers for their insightful comments on an earlier draft of this paper.

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