The authors have no conflict of interest

Research Article

# Loss of Regularity in the Curvature of the Thoracolumbar Spine: A Measure of Structural Failure^{†}

Article first published online: 22 MAR 2004

DOI: 10.1359/JBMR.040320

Copyright © 2004 ASBMR

Additional Information

#### How to Cite

Zebaze, R. M., Maalouf, G., Maalouf, N. and Seeman, E. (2004), Loss of Regularity in the Curvature of the Thoracolumbar Spine: A Measure of Structural Failure. J Bone Miner Res, 19: 1099–1104. doi: 10.1359/JBMR.040320

^{†}

#### Publication History

- Issue published online: 2 DEC 2009
- Article first published online: 22 MAR 2004
- Manuscript Accepted: 22 MAR 2004
- Manuscript Revised: 10 FEB 2004
- Manuscript Received: 7 NOV 2003

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### Keywords:

- vertebral fracture;
- thoracolumbar curvature irregularity

### Abstract

**Departure from regularity (smoothness) in the curvature of the spine was quantified and correlated with the number of fractures, deficits in height, BMD, and identified women with vertebral fractures.**

**Introduction:** Differences in anterior and posterior vertebral heights (VHs) form the thoracolumbar curvature needed for stability in bipedal gait. Modest differences in VHs within and between adjacent vertebrae allow the spine curve to change its trajectory gently. Large differences in VHs, as occur following a fracture, produce abrupt changes in the direction of the curve, producing a departure from regularity (i.e., irregularity or loss of smoothness).

**Materials and Methods:** VHs and BMD were measured using DXA in 697 Lebanese women 20-87 years of age. Regularity of the spinal curvature was measured by comparing the ratio of the anterior to the posterior VHs of one vertebra to this ratio of adjacent vertebrae. If these ratios are similar, there is a smooth transition in the trajectory of the spinal curve. Departure from this regularity (smoothness) was measured at each pair of adjacent vertebrae in each individual and expressed as the spinal curvature irregularity index (SCII) for the entire thoracolumbar spine.

**Results and Conclusions:** In premenopausal women, the mean SCII was 8.5% (range, 4-15%); that is, regularity was 91.5%. Only 0.8% of women had a SCII >17%. In postmenopausal women, the mean SCII was 10% (range, 4-36%) and was correlated with age (*r* = 0.25), height (*r* = −0.21), BMD (*r* = −0.13), and the number of deformities assessed by quantitative vertebral morphometry (QVM; *r* = 0.31-0.60; all *p* < 0.001). About 5% of women had an SCII >17%, and this group had 3- to 9-fold more deformities (as defined by QVM) than women with SCII <17%, reduced lumbar spine BMD (−1.01 SD), and 2- to 4-fold greater height deficits (−0.5 SD) than women with deformities (by QVM). The SCII is a robust method of identifying structural failure that is easy to compute and does not require controls.

### INTRODUCTION

QUADRUPEDALISM IS ASSOCIATED with only small differences in anterior and posterior vertebral heights (VHs) and narrowing in the vertebral body cross-sectional area (CSA) more caudally.^{(1)} The acquisition of upright posture produced greater mobility and freed the upper limbs but killed the stability of quadrupedal gait, by raising the body's center of gravity, and increased the compressive and torsional forces on more caudal vertebrae. This loss of stability may have resulted in the selection for species that could form spinal curvatures, an anatomical feature conferring stability in the upright posture by reducing bending moments and reduce energy expenditure during walking.^{(1–10)}

Spinal curvatures can be produced by enforcing bipedalism in monkeys.^{(5,7,11)} These curvatures are produced by differences in anterior and posterior VHs within a vertebra and between adjacent vertebrae.^{(1,9)} For the midthoracic vertebrae, slower anterior than posterior growth produces the “wedging” necessary for concavity, whereas faster anterior than posterior growth in the lower lumbar regions produces convexity. More rapid growth of caudal vertebrae produces larger vertebral bodies so that greater loads are distributed over a large CSA, reducing compressive stresses (load/area).^{(5,7,12)}

Differences in anterior and posterior VHs of a vertebra and between VHs in adjacent vertebrae are also used to define vertebral “fracture.” The distinction between “fracture” and anatomical variation is often difficult because there is no gold standard to distinguish anatomical variation from fracture. To identify a fracture, ratios of VHs for individual vertebrae are compared with a reference population range for that vertebra. However, VH ratios vary greatly within a population, and this normal variability may produce misclassification and false positives in a system using a reference population and fixed cut-offs.^{(13,14)}

Unlike differences in VHs between individuals, differences in VHs between adjacent vertebrae in an individual are minimal, ensuring a smooth change in the trajectory of the spinal curve. Departure from this smoothness or regularity in the curvatures, produced by a fracture, can be quantified using the ratio of anterior to posterior heights of adjacent vertebral bodies. We hypothesized that the extent of deviation from regularity (i.e., irregularity) correlates with age, height, and BMD deficits and with vertebral deformity assessed by quantitative vertebral morphometry (QVM).

### MATERIALS AND METHODS

#### Subjects, BMD, and QVM

Study subjects were recruited from all parts of Lebanon by advertisement and from the Red Cross and health organizations. There were 120 premenopausal women (20-49 years of age) and 577 postmenopausal women (50-87 years of age). All subjects were ambulatory, free of chronic disease, and not taking medications known to affect skeletal metabolism. The study was approved by the Lebanese Osteoporosis Prevention Society Ethics Committee. Lumbar spine, femoral neck BMD, and VHs were measured using the GE Lunar Expert-XL (Lunar, Madison, WI, USA). Scans were analyzed using the software supplied by the manufacturer that allowed placement of points on the vertebral body to define the anterior (A), middle (M), and posterior heights (P) of vertebrae. The precision error for this measurement was ∼2%. The reference range for QVM was derived using a statistical trimming algorithm described by Melton et al.^{(15)} Vertebral deformities were classified according to Eastell et al.^{(16)} into wedge (A/P), biconcavity (M/P), and crush deformities (P/P_{±1}; ±1 indicates the vertebra above or below), using cut-offs of 3 and 4 SD and 15%, 20%, and 30% below the mean.^{(15,16)}

#### Spinal regularity and irregularity

A curve is regular when its direction, given by the tangent at each successive point, changes by the same degree. An abrupt change in the direction of the curve produces a sudden change in the trajectory of the curve and constitutes an irregularity. Adjacent vertebrae in any part of the spine are aligned to form a structure defined by two curves: one formed by the anterior vertebral heights (inner curve) and the other by the posterior vertebral heights (outer curve; Fig. 1, left and middle panels). If the degree of curvature (bending) at two adjacent vertebrae is the same, the center and the radius of the curvature of the inner (and outer curves) will be the same; therefore, there is regularity (Fig. 1, left and middle panels). If there is a vertebral fracture, the amount of bending of the curves at the level of the fracture will change abruptly, resulting in a change in the center and/or radius forming the new curves (Fig. 1, right panel); this change is defined as an irregularity.

The detection of irregularity does not require knowledge of the radius or the location of the center of the curvature. The irregularity is determined by examining the ratio of the anterior/posterior VH of one vertebral body to the anterior/posterior VH of the adjacent vertebrae, that is, the ratio of the VH ratios of adjacent vertebrae. The ratio of VH ratios (not the absolute heights) determines the radius and the center of the curvature. (If anterior equals posterior height, the structure is regular, but the radius of the virtual circle is infinite. The radius of curvature of a straight line is infinite because as a circle gets bigger and bigger, it looks more and more like a straight line at a local level—just as the Earth appears flat to us.) A fracture alters the VHs, which then alters the radius and/or center of the virtual circle so that criteria for regularity and smoothness are violated (Fig. 1, right panel; *V*_{i + 2} and *V*_{i + 3}).

The anterior and posterior VHs of any two adjacent vertebrae (*V*_{i} and *V*_{i + 1}) are sectors of the perimeters of two virtual circles (Fig. 1, right panel). The following equations hold without any assumptions:

- (1)

- (2)

where *A*_{i}, *P*_{i}, and *D*_{i} are, respectively, the anterior and posterior VHs and depth of vertebra i (*V*_{i}); *A*_{i + 1}, *P*_{i + 1}, and *D*_{i + 1} are the corresponding parameters for *V*_{i + 1}; angles α and β are measured in radians; *R*_{i} is the radius of the sector of the circle defined by the anterior heights (inner curve). From *Eqs.*1 and 2, *Eqs.*3 and 4 are determined:

- (3)

- (4)

If the center of the two virtual circles is the same (*O*_{i}), radii forming sectors of the inner circle (*R*_{i} and *R*_{i + 1}) are the same, and radii forming sectors of the outer circle (*R*_{i}+ *D*_{i} = *R*_{i + 1} + *D*_{i + 1}) are the same (adjacent vertebrae can be assumed to have the same depth), the criteria for curve regularity are fulfilled. In such circumstances,

- (5)

so that

- (6)

That is, if the ratio of anterior/posterior heights of two adjacent vertebrae are the same (e.g., say 0.9, then the ratio of these ratios [*Eq.*6] is unity). If they differ, this term differs from unity, and the more the term differs from unity, the more irregular the curve. This ratio of adjacent vertebral body height ratios can be expressed as:

- (7)

where *Re*_{i,i + 1} is the regularity of curves produced by the heights of vertebrae *i* and *i* + 1.

The degree to which adjacent vertebrae fail to form sectors of the same circle, that is, the degree to which *Re*_{i,i + 1} differs from unity, is a measure of irregularity. For two adjacent vertebrae (*i* and *i* + 1) a spinal curvature irregularity index (SCII_{i,i + 1}) can be calculated as an absolute value expressed as a percentage:

- (8)

The average of all of the SCII_{i, i + 1} values for pairs of adjacent vertebrae (calculated in a caudocephalic direction) from the spine of an individual gives the mean irregularity of the curvatures of that spine, designated as SCII. SCII is expressed as a percentage (*Eq.*9):

- (9)

where *n* is the number of vertebrae investigated. The properties of the SCII are such that the greater the SCII, the greater the level of irregularity in the spine.

#### Statistical analyses

We examined the distribution of SCII in pre- and postmenopausal women and expressed the SCII as mean ± SE. Correlations and linear regression were used to assess the relationship between the SCII and age, height, weight, femoral neck and lumbar spine BMD, and the number of deformities. After examining SCII as a continuous variable, a threshold of this parameter was determined to define structural failure (deformity). BMD was expressed as Z-scores adjusted for age, height, and weight. BMD was compared in subjects with and without a deformity defined using either the SCII or QVM. BMD was also expressed as T-scores comparing women with to those without deformity as defined by SCII. Height was also expressed as Z-scores adjusted for age comparing subjects with deformities (defined by QVM and SCII) to subjects with no deformities. One-sample *t*-tests were used to determine whether the mean Z-score differed from the population mean (of zero). Two-sample *t*-tests were used to compare the mean SCII according to number of deformities (by QVM) and age. Results were regarded as significant at the level of 0.05 (two-tailed).

### RESULTS

In premenopausal women, the distribution of the SCII was Gaussian, with a mean SCII of 8.2% (range, 4-15%; Fig. 2). Only one value exceeded 17%. The SCII was independent of age, height, and weight, and correlated negatively with spine and hip BMD (Table 1; Fig. 3A). In postmenopausal women, the distribution remained Gaussian, with only a modest increase in the mean to 10.06%. However, there was an increase in irregularity, and 32 women had values >17% (Figs. 2 and 3A). The SCII correlated negatively with age, height, and BMD (Table 1). The SCII correlated with the number of deformities as assessed by QVM (*r* = 0.3-0.6 depending on the cut-off; Table 2). The greater the SCII, the greater the number and the severity of the deformities (Figs. 3B and 3C). The SCII was 0.7-2 SD higher in women with deformities identified by QVM than those without (*p* < 0.001).

In a multiple regression analysis (including age, height, and SCII) of data, in women with a SCII >17%, the SCII became correlated with height reduction independently of age (Table 3). Thus, the value of SCII of 17% was chosen as a deformity threshold (Fig. 2; Table 3). The prevalence of vertebral deformity assessed using SCII >17% increased exponentially with age from 0.8% in premenopausal women to 15% in women ≥80 years of age (Fig. 3D). Women with spinal deformities as defined by SCII had (1) 2- to 4-fold greater reduction in height (−0.5 SD) than women defined as having vertebral deformities using QVM; (2) lower lumbar spine BMD z-score (−1.01 SD), while no consistent reduction in spine BMD was present in women with deformities as defined by QVM (range, 0.6 SD at 3 SD cut-off to −0.2 at 30% cut-off); (3) a t-score of −2.6 ± 0.28 SD, which is 2-fold lower than in women with no structural failure (SCII < 17%; −1.3 ± 0.08 SD); and (4) three to nine times more deformities (by QVM; depending on the cut-off) than their age-matched peers with SCII <17%.

The middle heights were not included in this analysis. However, the SCII may capture these abnormalities. SCII was 30% higher in women with biconcavity deformity than their age-matched peers with no deformity, and ∼30% of women with structural failure as defined by SCII had isolated biconcavity deformity at the 3 SD cut-off with no wedge or crush deformities.

The distribution of the SCII subvalues within an individual can be plotted as a graph; the general pattern and the presence of a peak are indicative of a VF and the level of the VF (Fig. 4).

### DISCUSSION

There are large differences in vertebral heights in the population, in part, because of differences in sitting height among individuals, secular trends, and other factors. By contrast, in an individual, VHs within a vertebra and between adjacent vertebrae differ only slightly, allowing the development of a smooth or regularly curving spine. Abrupt changes from this uniformity produce irregularity in the spinal curvature. This irregularity correlated with indicators of spinal fragility (age and BMD) and spinal structural failure (height loss and vertebral deformities). The criteria for regularity were met in the majority of premenopausal women. The averaged abrupt changes were 4-15%, with only 0.8% values for irregularity of >17%. Irregularity of >17% occurred in 5.5% of postmenopausal women, and in these subjects, there was an association with vertebral fractures, height loss (independent of age), and reduced BMD, features consistent with the notion that irregularity in spinal curvature of >17% is likely to reflect structural failure.

The measure of deviation from smoothness is not a measure of increasing spine curvature or an angle as measured during assessment of scoliosis.^{(17–19)} This method also differs from current approaches of quantitative or semiquantitative vertebral morphometry because it treats structural failure as a continuous, not a categorical, variable. As such, it may provide a measure of subtle changes in VB shapes that remain undetected by QVM. For example, 30% of individuals with SCII >17% did not have fracture according to the 4 SD or 20% cut-off, yet these women had reduced BMD and height. This suggests that small deficits in VHs accumulating to produce the SCII of >17% may be insufficient to produce VH ratio differences exceeding the 4 SD or 20% cut-off in any given vertebra. Whether these deviations from regularity are associated with symptoms or an increased risk for fractures will require further study. For similar reasons, the SCII correlated negatively with BMD, not height, in premenopausal women. Bone loss starts well before menopause, but height changes may be subtle at the modest levels of bone fragility in these young women.

The irregularity should be insensitive to anatomical variation considered as “fracture” by other methods. For instance, wedging in vertebral shape is normal and essential in the midthoracic region to produce the smooth curvature, so the resemblance of the VH ratios from vertebra to vertebra reflect this smoothness. The anterior/posterior height difference required to produce the wedge shape may “fit” the definition of fracture, producing false positives.^{(14)} However, of the women with a vertebral fracture based on the 15% or 3 SD cut-off value, ∼70% had an SCII <17%.

The SCII avoids the need for a reference range that itself could introduce false positives.^{(14)} Spinal irregularity is captured in a single measure, whereas 39-54 variables plus cut-offs and reference ranges are needed for QVM.^{(13,16,17)} This makes SCII a simple and fast method of gathering objective and quantitative information on structural integrity of the spine. Once vertebral heights were measured, computing SCII in our 697 women took <1 h compared with the weeks of work with QVM used in trimming to define reference ranges and cut-off values for each ratio and classification of vertebral deformities.

This study focused on an average SCII value. However, an analysis of the distribution of SCII subvalues in an individual spine may complement this average value and improve the performance of the SCII. Information including the level and number of VFs will be signaled by one or more peaks corresponding to sudden changes in the trajectory of the spine. These other applications of the SCII are under investigation.

The SCII is a mathematical computation, so accuracy and reproducibility depends on VH measurements. The likelihood that a 2% error in one VH alters the SCII (a combination of 39) is low. The small error is random and diluted. A 2% error in a vertebral height measurement will be reflected in a 0.16% error in the SCII. The SCII is insensitive to parallax error because changes in heights will be proportional. The regularity of a curve is not a function of the angle from which it is seen.

SCII does not use middle VHs because the regularity of the spine in the lateral view depends on the anterior and posterior, not middle, height. However, a collapse in the middle height is likely to affect the anterior and/or the posterior heights and so the SCII. Women with isolated biconcavity deformities had greater SCII than age-matched peers with no deformities. Irregularity in the spinal curvature caused by intervertebral disk degeneration is overlooked by the SCII because this model focuses on the contribution of vertebral bodies to the irregularity in the spinal curvature ignoring intervertebral disks. Degenerative changes or congenital abnormalities affecting vertebral bodies, a limitation common to all quantitative methods of assessment of spinal structure failure, may affect SCII. However, congenital abnormalities will not increase with age as the SCII does, and degenerative changes are associated with an increase, not decrease, in spine BMD, so vertebral fracture are likely to be the major cause of irregularity in the spinal curvatures.

Minne et al.^{(20)} quantitated the amount of spinal structural failure. Direct comparison with the SDI of Minne et al. was not attempted because normal values of vertebral heights for SDI are based on T_{4}, which is difficult to detect with morphometry X-ray absorptiometry. T_{4} was not visible in 25% of our sample. However, difficulties in visualizing T_{4} do not affect the SCII that was adjusted for the number of vertebrae.

In summary, the level of irregularity in the curvatures of the spine has a narrow distribution consistent with the uniformity of the spine. Changes in the degree of regularity provides a simple, rapid and efficient method of identifying spinal structural failure in an individual. Investigations using this approach offer a complimentary or alternative tool for objective and quantitative assessment of spinal fracture.

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