Loss of Regularity in the Curvature of the Thoracolumbar Spine: A Measure of Structural Failure

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1 JOURNAL OF BONE AND MINERAL RESEARCH Volume 19, Number 7, 2004 Published online on March 22, 2004; doi: /JBMR American Society for Bone and Mineral Research Loss of Regularity in the Curvature of the Thoracolumbar Spine: A Measure of Structural Failure Roger MD Zebaze, 1 Ghassan Maalouf, 2 Naim Maalouf, 3 and Ego Seeman 1 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 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 ; 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. J Bone Miner Res 2004;19: Published online on March 22, 2004; doi: /JBMR Key words: vertebral fracture, thoracolumbar curvature irregularity 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 The authors have no conflict of interest. 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 1 Department of Endocrinology, Austin and Repatriation Medical Centre, University of Melbourne, Melbourne, Australia; 2 Saint George University Hospital, Faculty of Medicine, Balamand University, Beirut, Lebanon; 3 Center for Mineral and Clinical Research, University of Texas Southwestern Medical Center, Dallas, Texas, USA. 1099

2 1100 DJOUMESSI ET AL. FIG. 1. (Left and middle panels) Anterior and posterior heights of two adjacent vertebrae form sectors of two circles with definable features. (Right panel) A fracture modifies these features (see the Materials and Methods section). 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: A i R i P i R i D i (1) A i 1 R i 1 P i 1 R i 1 D i 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

3 SPINAL STRUCTURAL FAILURE 1101 TABLE 1. CORRELATIONS (r) OF SCII AND AGE, HEIGHT, WEIGHT, LUMBAR SPINE (LS), AND FEMORAL NECK (FN) BMD IN PRE- AND POSTMENOPAUSAL WOMEN SCII (premenopausal women) SCII (postmenopausal women) Age * Height * Weight LS BMD 0.22* 0.13* FN BMD 0.20* 0.13* * p FIG. 2. Distribution of SCII (%) in pre- and postmenopausal women. The frequency distribution of SCII was similar in pre- and postmenopausal women. Values 17% were uncommon in premenopausal women but common in postmenopausal women. D i 1 are the corresponding parameters for V i 1 ; angles and 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: A i /P i R i / R i D i (3) A i 1 /P i 1 R i 1 / R i 1 D i 1. (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, so that A i /P i A i 1 /P i 1 (5) A i P i 1 /P i A i 1 1. (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: Re i,i 1 A i P i 1 P i A i 1 (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: SCII i,i 1 % 1 Re i,i (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): SCII % i 1 i n 1 SCII i,i 1 n 1 i 1 i n 1 1 Re i,i (9) n 1 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

4 1102 DJOUMESSI ET AL. FIG. 3. (A) The SCII does not change in premenopausal women. In postmenopausal women, the SCII increases with age. (B) The mean SCII increases with the increasing number of deformities (by QVM) in an individual. (C) The SCII is higher among women with deformities (by QVM) defined by more stringent thresholds than in those with less stringent thresholds. (D) The prevalence of women with vertebral deformities defined by SCII increases exponentially with age. *p TABLE 2. CORRELATIONS (r) OF SCII AND THE NUMBER OF DEFORMITIES AS DEFINED BY DIFFERENT QVM CUT-OFFS * p Cut-offs SCII 3 SD 0.60* 4 SD 0.54* 15% 0.39* 20% 0.45* 30% 0.31* 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 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 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 SD, which is 2-fold lower than in women with no structural failure (SCII 17%; 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 dif-

5 SPINAL STRUCTURAL FAILURE 1103 TABLE 3. MULTIPLE REGRESSION EQUATION SHOWING THE RELATIONSHIP BETWEEN SCII VALUES, HEIGHT, AND AGE FOR SCII VALUES 17% AND 17% Independent variable Dependent variables SCII 17% SCII 17% Coefficient p Coefficient p Height (intercept) (intercept) SCII Age FIG. 4. Trace showing the distribution of the SCII subvalues per spine level. (A) A 56-year-old postmenopausal woman with a lumbar spine T-score of 0.4 and an average SCII value of 3.5%. The trace of the SCII subvalues is relatively constant with no abrupt changes in the spine trajectory. (B) A 67-year-old postmenopausal woman with a lumbar spine T-score of 2 and an average SCII value of 36%. The trace shows generally high values and a peak at the T 12 L 1 region, indicative of an abrupt change in the trajectory of the spine (i.e., a vertebral fracture). fers 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 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

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