Variations in Posteroanterior Stiffness in the Thoracolumbar Spine: Preliminary Observations and Proposed Mechanisms.

The application of posteroanterior (PA) force over the spinous processes of a prone patient and evaluation of the PA response is a common assessment procedure used by physical therapists.[1-4] Despite the widespread use of this technique, however, the normal PA response has not been well described. In addition, it is not clear which tissues are most responsible for variations in the PA response. The degree to which the PA response reflects the behavior of intervertebral joints adjacent to the target vertebra compared with more distal intervertebral joints, the rib cage, muscles, skin, and other tissues has not been established.

Lee and Svensson[5] found that, when a vertical PA force was applied to the spinous process of the L3 vertebra of a prone subject, the force-displacement response comprised a nonlinear region followed by a linear zone. They described each subject's force-displacement response with 2 variables: the gradient and the X-intercept of a least-squares regression line fitted to the linear zone. Both the gradient and the X-intercept of the linear-phase regression line showed good test-retest consistency (intraclass correlation coefficient [ICC(2,1)]=.88 tot both) when measured at L3.[5] Subsequently, the gradient of the linear region, designated the stiffness coefficient K, has been commonly used to characterize the PA response pattern in the lumbar spine[6-13] and, in one case, the thoracic spine.[14]

Judgments about a patient's response to a PA force are often made by clinicians comparing the response with their memories of the responses of other subjects, as well as with the response at other vertebral levels in the patient being examined.[15] Both of these comparisons require an awareness of the normal variation in PA responses along the nondegenerated thoracolumbar spine of subjects without low back impairments. Three studies of variations of the PA response variables among different locations along the thoracolumbar spine have been reported.[8,9,14] Lee and Liversidge[8] applied PA forces to the L3, L4, and L5. They found that the mean PA stiffness coefficient K was greatest at L5 (18.4 N/mm), smaller at L4 (15.5 N/mm), and least at L3 (12.7 N/mm). Viner et al[9] applied a PA force at each lumbar spinous process. They found a linear trend of decreasing PA stiffness from L5 (16.4 N/mm) to L1 (14.1 N/mm), supporting and extending the findings of Lee and Liversidge.[8] A third study demonstrated that the PA stiffness was greater at T5 (14.8 N/mm) than at T4 (13.6 N/mm),[14] but the investigators did not examine the responses at other thoracic or lumbar levels.

The response to PA force at particular locations has been shown to be highly variable among subjects without low back problems,[6-8] but the source of this variation has not been studied. We believe it has been generally assumed that the PA response reflects the intervertebral joint properties, especially at those joints immediately adjacent to the vertebrae to which the force is applied. Recent evidence, however, challenges this assumption.[6,9,10,15] Lee and Svensson[6] observed that when cyclical loads were applied over the L3 spinous process, there were measurable displacements as far away as T8. Viner et al[9] observed that both the skinfold thickness over the anterior superior iliac spine (ASIS) and the body mass index (BMI = mass / [height[2]) were predictors of PA stiffness in the lumbar spine, with the greatest influence on stiffness at more caudal lumbar levels. At L5, the ASIS skinfold thickness accounted for a high proportion (50%) of the variance in PA stiffness, with smaller proportions accounted for at other vertebral levels (41% at L4, 28% at L3, 7% at L2, and 0.4% at L1).

A computer model of the spine's response to lumbar PA loading was developed by Lee and colleagues,[15] and its predictions of average spinal movements in response to low lumbar loads were found to be consistent with observations of the responses of living human subjects. Using the model, Lee et al[15] predicted that, at the lower lumbar levels, the PA stiffness would be sensitive to the manner in which a subject's pelvis was supported by the table on which he or she lay. In another study using this computer model,[10] Lee and colleagues found that the amount of displacement in adjacent intervertebral joints was typically less than 10% of the total PA displacement felt by the therapist. That is, when 10 mm of PA movement of the skin surface occurred under the therapist's hands, less than 1 mm of intervertebral movement had occurred at each intervertebral joint immediately adjacent to the target spinous process. Thus, abnormalities in motion of an intervertebral joint may be a minor factor in determination of PA movement,[10]

The findings of these studies cast doubt on the traditional view that PA stiffness is primarily a measure of intervertebral joint stiffness adjacent to the point of load application. The behavior of tissues outside the spine may also influence the PA response. Lee et al[11] have proposed that the movement of a vertebra in response to a lumbar PA force involves intervertebral displacements at many intervertebral joints, anterior rotation of the pelvis, compression of the anterior and posterior superficial soft tissues, deformation of the rib cage, and compression of the abdominal contents. The relative importance of each possible source of resistance to displacement, however, has not yet been established.

Studies using models have the potential to give detailed information about tissue deformations and loads during PA mobilization, information that would be difficult to obtain by other means. Adequate validation of the models used, however, is essential. Validation of computer models of mobilization has previously been conducted by considering responses to loads applied only to the lower lumbar spine.[15] If a model provides an accurate prediction of responses to forces in the low lumbar region, but not in the upper lumbar and thoracic regions, then there is doubt about whether the model is appropriately simulating the roles of upper lumbar and thoracic structures. Thus, the mechanism that is suggested by the model to be underlying the PA response may not be accurate. Additional information about the response of human subjects to loads in the upper lumbar and thoracic regions is needed to allow comparison between model predictions and observed behavior in these regions and therefore provide more evidence of model validity.

Our study was designed to document the variations of PA stiffness among a group of young subjects without known low back impairments at 5 locations throughout the thoracolumbar spine and to investigate the possible relationship between PA stiffness and subject characteristics. Knowledge about these variations in PA stiffness could provide information of clinical relevance that could be used to help identify those variables that are important determinants of thoracolumbar PA stiffness in patients and to provide data for model-validation studies.

Method

Subjects

Twenty-one volunteer subjects (10 male, 11 female) were recruited from the population of students and staff of the Faculty of Health Sciences of The University of Sydney. All subjects had no back pain at the time of testing and had never sought medical attention or been absent from work due to back pain. Each subject's sex, age, height, and mass were recorded, and the BMI was calculated. The subjects had a mean age of 26.6 years (SD=7.5), a mean height of 173.0 cm (SD=9.1), a mean mass of 71.9 kg (SD=16.3), and a mean BMI of 23.8 kg/[m.sup.2] (SD=3.5). Detailed subject data are given in the Table. Each subject gave written informed consent to participate.

Table. Subject Data: Age, Sex, Height, Mass, Calculated Body Mass Index (BMI, Where BMI = Mass / Height[2]), Distances Between Spinous Process Markers, Anteroposterior (AP) and Transverse Chest Diameters, and Skinfold Dimensions

                              Height   Mass    BMI
Subject No.   Age (y)   Sex   (cm)     (kg)    (kg/[m.sup.2])

1             40        M     171.5    63       21.42
2             23        M     186      91       26.3
3             18        M     180      75.5     23.3
4             19        M     180      66       20.37
5             22        F     170      60       20.76
6             18        F     173      70       23.39
7             30        F     160.5    61       23.68
8             31        F     164      50       18.59
9             24        M     184.5   105       30.85
10            27        M     183      85.5     25.54
11            19        M     183.5    72       21.38
12            32        F     165      75       27.55
13            20        M     172      63       21.3
14            27        F     162      61       23.24
15            27        F     162      63       24.01
16            20        M     187     115       32.89
17            34        F     168      63       22.32
18            41        F     162.5    57       21.59
19            19        F     164      67       24.91
20            27        F     173      61       20.38
21            40        M     182      86       25.96
[bar]X        26.57           173      71.9     23.8
SD             7.52             9.11   16.30     3.5
Maximum       41              187     115       32.88
Minimum       18              160.5    50       18.59

                                              Length
                        Chest Diameter        Between
                        (mm)                  Markers (cm)
Subject No.   Age (y)   AP       Transverse   T1-S1   T1-L4

1             40        204      308          46      31
2             23        235      350          53      45
3             18        209      288          48.5    42
4             19        185      293          49.8    44
5             22        160      285          43.5    39.5
6             18        205      290          48      42
7             30        215      270          42.5    38.3
8             31        167      237          42      30.5
9             24        232      324          52      44
10            27        228      350          53      44.5
11            19        198      280          53.5    47
12            32        184      303          43.5    38.5
13            20        188      276          48      41.5
14            27        188      251          52      43
15            27        176      287          49      38
16            20        232      375          57.5    44.5
17            34        178      261          47      40
18            41        198      248          49      42
19            19        186      288          49      40
20            27        202      265          48.5    41
21            40        213      306          53      45.5
[bar]X        26.57     199.19   292.1        48.97   41.04
SD             7.52      21.55    35.03        4.04    4.24
Maximum       41        235      375          57.5    47
Minimum       18        160      237          42      30.5

                         Skinfold Thickness
                         (mm)
Subject No.   Age (y)    Iliac crest   Midaxilla

1             40           9.20          8.8
2             23          22            16.5
3             18          13.2           8.2
4             19           9.3           9.3
5             22          10.2          12.7
6             18          15.1          15
7             30          12.5          12.2
8             31           6             6.2
9             24          17            22
10            27           4.5           6.5
11            19           8.2          10.2
12            32          10.5          16
13            20          11.75         10.25
14            27          11.25          9.5
15            27           5             7.2
16            20          20            22
17            34           7             7.4
18            41           5.5           7.75
19            19          13            18
20            27           6.4           8.6
21            40           7.6           8.2
[bar]X        26.57       10.72         11.55
SD             7.52        4.81          4.87
Maximum       41          22            22
Minimum       18           4.5           6.2

Equipment

The PA force-displacement response at each of the 5 thoracolumbar locations was measured using the "Spinal Physiotherapy Simulator" (SPS) (Fig. 1). This device is described in detail elsewhere,[5] but it is described briefly here. The device contains a padded indenter that applies a force to the body surface of a subject who lies prone on a rigid table. The line of movement of the indenter can be tilted to a desired orientation in the sagittal plane. The indenter moves up and down at a rate of up to 2 Hz, determined by the rotation of a motor-driven cam. The upper limit of force that can be applied to the subject is determined by a weight that produces downward movement of the indenter. The applied force and skin-surface displacement are measured by the device, and the force and displacement data are sampled at 100 Hz and passed to a 12-bit analog-to-digital converter (Data Translation model DT2801A(*)). Good reliability (ICC[2,1]=.88) has been observed for repeated measurement of PA stiffness at L3 when using the SPS to test 11 subjects without low back problems.[5] The error of the SPS when making stiffness measurements of an aluminum beam (with a stiffness of the same order of magnitude as lumbar PA stiffness) has been established as less than 1%.[5]

[Figure 1 ILLUSTRATION OMITTED]

Procedure

The subject lay in the prone position while the spinous processes from C7 to S1 were identified by palpation by one of the researchers (ML). The C7 spinous process was identified on the basis of its prominence in an extended position. The lumbosacral junction was identified on the basis of its relative prominence compared with the region immediately caudal, its association with a point of discontinuity in surface curvature, and the appropriate number of palpable spinous processes caudad up to the C7 spinous process. The S1 spinous process was assumed to be the first prominence caudad to the palpated lumbosacral junction, and the L5 spinous process was identified as a relatively small, deep spinous process immediately cephalad to the lumbosacral junction. The levels T1, T4, T7, T10, L1, L4, and S1 were marked. The magnitude of the error in location of any spinous process when using this procedure is not known. Similarly, the sensitivity of PA stiffness to small variations in the location of the PA force has not been studied. The horizontal distances between the centers of the T1, L4, and S1 spinous processes were measured with a metric rule to the nearest 5 mm (Table).

Chest diameters and skinfold thicknesses were measured to explore their possible relationship with PA stiffness. With the subject in a standing position, the anteroposterior (AP) and transverse chest diameters and the iliac crest and midaxillary skinfold thicknesses were measured using a standard procedure[16] (although measured at nonstandard locations). The AP and transverse chest diameters were measured (to the nearest 5 mm) at the level of the xiphisternal junction using an anthropometer.([dagger]) The skinfold thicknesses were measured to the nearest 0.2 mm using skinfold calipers.([dagger]) Three readings were taken, and the average value was recorded. The iliac crest skinfold reading was taken superficial to the anterior superior iliac crest. The midaxillary skinfold reading was made in the midaxillary line at the level of the xiphisternal junction. The mean AP chest diameter was 199.2 mm (SD=21.6), the mean transverse chest diameter was 292.1 mm (SD=35.0), the mean iliac crest skinfold thickness was 10.7 mm (SD=4.8), and the midaxillary skinfold thickness was 11.6 mm (SD=4.9) (see Table for details). The intraexaminer reliability coefficients for similar skinfold and chest measurements of subjects without low back problems have been found to be good (ICC=.99 for both).[17]

When a lumbar PA load is applied to a prone-lying subject, the pelvis rotates anteriorly toward the table,[18] causing compression of the anterior abdominal soft tissues and thus resisting the movement. We wanted to investigate the possible role of this resistance in determining the overall PA resistance. To measure the resistance to rotation offered by compression of the abdominal soft tissues, we rotated part of the table toward the pelvis, assuming that the resistance would be similar to the case in which the pelvis rotated toward the table. This approach was used because it involved only small movements of the pelvis and spine, and therefore the independent resistance of the abdominal tissues could be assessed without resistance from movements of the spine.

To evaluate the resistance to pelvic rotation, the SPS was modified from its standard configuration. Instead of applying forces and measuring movements over the spine, the SPS configuration was altered to produce movements and measure responses, as shown in Figure 2. The table surface on which the subject lay was altered to provide a hinged flap that could be rotated up toward the subject's pelvis while the subject lay on top of the table. The weight of the subject, combined with the stiffness of the abdominal region, provided resistance to upward movement of the flap. No additional force was applied to prevent posterior trunk movement during rotation of the flap into the abdominal region, but any small posterior rotations of the pelvis were measured so that the amount of relative rotation between the pelvis and the table flap could be determined. The oscillating motion (provided by the modified SPS) was applied via a load cell to the free edge of the flap to produce angular motion of the flap under the subject's pelvis. The subject's pubic symphysis was assumed to be the approximate location of the axis for pelvic rotation; thus, the hinge edge of the table flap was located under the pubic symphysis. The flap rotations produced by the SPS were such that the maximum inclination of the flap was approximately 5 degrees. Flap inclination was measured using an inclinometer (Lucas Accustar Sensing Clinometer, model 02383-09([double dagger])). The inclination of the subject's pelvis was measured by strapping another inclinometer over the subject's sacrum.

[Figure 2 ILLUSTRATION OMITTED]

The relative angular displacement between the flap and the pelvis was then calculated by subtracting any angular displacement of the pelvis from the angular displacement of the flap. The force required to lift the flap was multiplied by the moment arm between the lifting cable and the flap hinge to give the size of the torque applied to the flap. The torque due to the weight of the cable, flap, and inclinometer was experimentally determined (by measuring the force required to lift the flap and inclinometer with no subject in place) and subtracted from the values measured when a subject was lying on the table to obtain the true resisting torque applied by the subject. Thus, the relationship between resisting torque and the relative angular displacement between the table flap and the pelvis could be established for each subject.

Before the measurements were made, at least 3 preconditioning cycles were performed. At least 3 cycles were used in an attempt to ensure that most of the preconditioning occurred before data collection.[19] Preconditioning was performed to help ensure that the measured responses were repeatable. The rotation occurred slowly, at a rate of 0.05 Hz. This frequency was chosen to estimate the quasi-static responses to allow comparison with other studies of living subjects[6,8,13] and model predictions.[15] The force and inclination data for 1.5 cycles (including 2 loading phases) were collected over a 30-second period and stored on diskette for subsequent analysis. No reliability studies were conducted to determine the reliability of the data collected during this procedure.

The raw pelvic data were converted to torque-angle data as described. Using SigmaPlot software,([sections]) linear regression was carried out over the range of relative angular displacements up to 3 degrees (a range of angles likely to be involved during PA loading[18]) for one selected loading phase. In all cases except one, the first loading phase was used for analysis. In one case, the start of the loading phase was obscured by an artifact; therefore, the second loading phase was analyzed. The analysis of the pelvic rotation data, in our opinion, showed that the straight line fitted acceptably well to the torque-angle data, with a mean re value of .925 (SD=.024). The mean stiffness opposing pelvic rotation was 0.86 N [multiplied by]-m/degree (SD=0.41).

Following the pelvic rotation test, the SPS was restored to its standard configuration for the application of force to the spinous processes. The 5 selected vertebral levels (T4, T7, T10, L1, and L4) were chosen to indicate the trend of response variations throughout the thoracolumbar spine and were tested in a controlled order that was randomly allocated to subjects. Again, at least 3 preconditioning cycles were done at each location before the responses were recorded. When measuring the force-displacement responses, the force was applied in the sagittal plane at angles corresponding to the tilt of the vertebrae due to the average sagittal curve of the spine in the standing position.[20] The angles from vertical that were used in the lumbar spine were consistent with those that are used in clinical practice.[21] The angles used were 4.5 degrees from vertical (caudad) at L4, -12.5 degrees (cephalad) at L1, -8.5 degrees (cephalad) at T10, 4.5 degrees (caudad) at T7, and 11.0 degrees (caudad) at T4. The weight on the SPS was set to provide a maximum force to the subject of approximately 110 N. Again, the force was applied at 0.05 Hz with 1.5 cycles of force, and displacement data were collected over a 30-second period and stored for subsequent analysis. For spinal loading, it has been previously established that there is an initial nonlinear region in the lumbar spine continuing up to 20 to 30 N of applied force.[6,12-14] Thus, only the range above 30 N was considered for the linear regression. In view of the SPS force being limited to a little over 100 N, a maximum of 100 N of applied force was used for all spinal loading analyses. If the maximum applied load did not reach 100 N due to low subject stiffness, then the regression was performed up to the level of the maximum force applied. For the spinal loading, only the first loading phase was used for the analysis, except where the range of forces was equal or greater in the second loading phase and the second phase showed substantially greater linearity in the range of 30 to 100 N. These criteria determined that the second loading phase was used for 7 of the 105 cases. Due to the prior application of preconditioning cycles, it would be expected that there would be only small differences between the first and second loading phases, as repeated testing of preconditioned subjects has been found to have no systematic effect on the PA response.[12]

Data Analysis

The data were examined to characterize the spinal responses at different locations and to explore the possible contributions of independent variables to the measured responses. Systematic variation of PA force-displacement stiffness coefficients among the vertebral levels tested was examined using an analysis of variance (ANOVA). The contribution of anthropometric variables and the pelvic torque-angle relationship to PA stiffness was examined using stepwise multipleregression analyses (to enter a variable, P=.05; to remove a variable, P=.10). Independent variables used in the multiple-regression analyses were the BMI, the AP chest diameter, the iliac crest skinfold thickness, and the gradient of the line fitted to the pelvic torque-angle relationship. These independent variables were selected on the basis that they were thought to be most likely to be related to PA stiffness, while keeping the number of independent variables to no more than one fifth of the number of subjects studied.[22] One factor considered when selecting independent variables was the desire to be able to interpret the effect of each variable in relation to possible mechanisms involved in providing resistance to PA force. Therefore, the morphometric variables that might be sex-related (ie, skinfold thickness and rib-cage diameter) were selected in preference to sex because its influence would be more difficult to interpret in terms of specific mechanisms. Five multiple-regression analyses were performed, with the 5 dependent variables being the PA stiffness values at the 5 vertebral levels. Statistical tests were conducted using an SPSS software program.([sections]) A level of significance of P [is less than] .05 was used for all statistical tests.

Results

The variation of mean PA stiffness with vertebral location is shown in Figure 3. The mean PA stiffness was greatest at the L4 level (13.3 N/mm). From the level with the lowest mean stiffness (L1 level, 10.4 N/mm), the mean stiffness rose in a cephalad direction (11.6 N/mm at T10, 12.5 N/mm at T7), then fell slightly at T4 (12.2 N/mm). The ANOVA indicated that the mean stiffness varied between vertebral levels (F=4.35, P=.003). Post hoc analysis (Bonferroni) of pair-wise comparisons to determine where the differences lay indicated that the stiffness at L1 (10.4 N/mm) was lower than the stiffness at L4 (13.3 N/mm), T7 (12.5 N/mm), and T4 (12.2 N/mm).

[Figure 3 ILLUSTRATION OMITTED]

The multiple-regression analyses showed that there were predictors of PA stiffness at 3 vertebral levels (L4, T10, and T7). In none of these cases, however, was a major proportion of the PA stiffness variance accounted for by the independent variable. At L4, the skinfold thickness over the iliac crest accounted for 18% of the variance in PA stiffness, with a negative regression coefficient (coefficient=-.418; regression line intercept=17.85 N/mm), indicating that subjects with greater skinfold thickness showed smaller PA stiffness values. At T10, the pelvic rotation stiffness accounted for 22% of the variance in PA stiffness (coefficient=3.32; regression line intercept=8.66 N/mm), showing that greater pelvic rotation stiffness was associated with greater PA stiffness. At T7, the AP chest diameter accounted for 17% of the variance, with subjects who had larger AP chest diameters demonstrating greater PA stiffness (coefficient=.063; regression line intercept=-0.110 N/mm).

Discussion

The major finding of this investigation is that PA stiffness varies along the thoracolumbar spine. Previous research has investigated PA stiffness within the lumbar region[6,8,9] and at 2 upper thoracic levels,[14] but there have been no investigations of the relationship between thoracic and lumbar PA responses. Figure 3 shows the results of our study, together with results of other studies in which there have been tests at more than one level using testing protocols similar to ours. The PA stiffness at L4 found in our study ([bar] X=13.3 N/mm, SD=4.3) compares well with the values obtained by Lee and Liversidge[8] ([bar] X= 13.5 N/mm, SD=3.8), who tested a similar subject group and applied loads using an almost identical protocol. When testing at a higher frequency of loading (0.5 Hz), Lee and Liversidge[8] found that the measured stiffness was an average of 3.0 N/mm higher. The data obtained by Viner et al[9] and Lee et al[14] also generally follow the trends found in our study, with their higher PA stiffness values likely to be partly attributable to a higher frequency of loading.

We propose that the pattern of PA stiffness that we observed among the vertebral levels tested is likely to be due to the nature of the support of the spine. In our laboratory, we have recently developed a finite-element model of the spine, rib cage, and pelvis subject to lumbar PA loading.[15] The model was found to be a good predictor of average responses, including the movement of the pelvis and thoracolumbar spine.[15] Based on the findings of that study, together with the data from the present study, we developed the simple conceptual model of PA loading shown in Figure 4. The model suggests that the lowest PA stiffness in the thoracolumbar spine would be expected to occur in the mid-lumbar or upper lumbar spine because there is least support for the spine in that region. The lower lumbar spine is supported by the relatively rigid pelvis, whereas the thoracic spine is supported by the rib cage. The degree of support for the thoracic vertebrae from its attachments would be expected to depend on the vertebral level. Less support and thus lower PA stiffness would be expected in the upper thoracic spine because of its proximity to the cervical spine, which is highly mobile[23] and is itself minimally supported by other structures in the prone position. The lower thoracic spine also may be expected to have slightly less support due to the fact that the connected structures, the lower 2 pairs of fibs, are "false" ribs and therefore not connected to the anterior chest. In addition, the lower "true" ribs are relatively long and are connected to the sternum through more compliant costal cartilage.[24]

[Figure 4 ILLUSTRATION OMITTED]

It is unlikely that variations in intervertebral joint stiffness within each subject's spine would have been a major factor in producing the pattern of PA stiffness along the spine that we observed. There is some evidence that intervertebral joint stiffness may be higher at the lumbosacral joint than at joints at more cranial lumbar levels,[25] perhaps contributing to the higher PA stiffness at L4 that we found in our study. Variations in intervertebral joint stiffness, however, are unlikely to explain the higher PA stiffness that we observed in the thoracic spine compared with L1. Previous research[25-27] has shown that thoracic intervertebral joint stiffness is not higher than upper lumbar intervertebral joint stiffness.

The ability of clinicians to detect the observed differences in mean PA stiffness between vertebral levels is not known. Previous research demonstrated that, when palpating linearly elastic springs, a difference in stiffness of 11% could be consistently detected between 2 springs by clinicians? If this result were applicable to lumbar PA stiffness values, a difference of about 24% would be readily detected between mean stiffness values at L1 and L4. Stiffness values at other locations may not be sufficiently different to be detected. The extent to which findings for the palpation of springs can be applied to thoracolumbar PA responses, however, is not clear. The pattern of stiffness variation suggested by Figure 3 indicates that the lower lumbar spine is the region in which interlevel differences in PA stiffness are likely to be the greatest and therefore most easily detectable.

In any individual subject, the pattern of mean stiffness that we observed would not necessarily be manifest. Viner and colleagues[9] found that, although there was a systematic trend of PA stiffness variation within the lumbar spine, there was marked variability among subjects. They concluded that, in young subjects without low back impairments, the variability was such that only relatively large differences in PA stiffness between adjacent lumbar vertebral levels (greater than 3.6 N/mm) could be designated as abnormal. In this context, the variation in stiffness along the spine observed in our study is more significant as an indicator of the possible factors that determine PA stiffness than as a template against which the normality of an individual patient response can be judged.

Multiple regression was used to conduct an exploratory analysis of the factors that may contribute to the variation of PA stiffness among subjects. At 3 vertebral levels (ie, L4, T10, and T7), there was a statistically significant predictor of PA stiffness. It should be noted that at none of these levels did the independent variable account for more than 22% of the between-subject variance in PA stiffness. Furthermore, the relatively small number of subjects involved means that the findings should not be extrapolated to a larger subject group without reservation. Despite these cautionary factors, the results are noteworthy because in each case the independent variable responsible for the variance is not directly related to the spine. The role of variables related to tissues outside the spine in determination of the PA response has been largely ignored by clinical textbooks (eg, Vertebral Manipulation by Maitland[4]). Nonetheless, the following discussion of the role of these nonspinal variables must be seen in the context of the fact that contributors of the remaining variance have not yet been established and therefore the relative importance of these factors is not known.

Iliac crest skinfold thickness was a predictor of PA stiffness at L4 (adjusted [r.sup.2]=.18), with increasing skinfold thickness being associated with decreasing PA stiffness. If the skin and subcutaneous soft tissue can be represented as a spring, then greater initial length of the spring (analogous to greater soft tissue thickness) will normally be associated with lower spring stiffness, in terms of the increase in resisting force per unit change in length. In the model shown in Figure 4, the influence of the iliac crest skinfold thickness would be expected to be exerted through its reflection of overall skinfold thicknesses, as a major contributor to the properties of the spring (B) between the manual force and the patient's spinous process. In addition, the iliac crest skinfold thickness might be influential in determining the properties of 2 of the springs restraining the pelvis: the restraint to anterior movement of the pelvic center of rotation (E) and the restraint to pelvic rotation (F). Thus, the structure of the model is consistent with the observed relationships. That is, if spring B, E, or F has lower stiffness, as would be expected if skinfold thickness was greater, then PA movements of the applied manual force should occur more readily, thus producing lower PA stiffness.

In the model shown in Figure 4, the properties of springs E and F would be expected to exert their greatest influence on lower lumbar PA stiffness, whereas the properties of springs such as B, representing dorsal soft tissues, would be expected to exert a similar influence at all vertebral levels, depending on the cephalocaudal variation of skinfold thickness. The fact that iliac crest skinfold thickness was not a predictor of PA stiffness at every tested level suggests that either the influence on PA stiffness of dorsal skin compressibility (spring B) may have been relatively small (compared with the influence of soft tissue compressibility at the anterior surface via springs E and F) or the dorsal skinfold thickness was substantially greater at the L4 level. The relatively small number of subjects and slightly skewed data for iliac crest skinfold thickness (skewness=0.86) suggest the need for caution in the interpretation of the role of this variable. The midaxillary skinfold thickness was found to be highly correlated with the iliac crest skinfold thickness (r=.83). It is likely, therefore, that use of midaxillary skinfold thickness instead of iliac crest skinfold thickness as an independent variable in the multiple-regression analyses would produce a similar result.

In the conceptual model shown in Figure 4, PA stiffness in the midthoracic spine would be expected to be influenced by the compressibility of the rib cage, represented by the springs (K). The multiple-regression analyses showed that the AP rib-cage diameter was a predictor of PA stiffness at T7. As shown by the positive regression coefficient, increases in rib-cage diameter were associated with increases in the PA stiffness. This result would appear to be the opposite of the expected result because normally an increase in spring length would be associated with a decrease in stiffness. A recent investigation of AP rib-cage stiffness demonstrated that sex-related differences existed, with male subjects having greater rib-cage stiffness than female subjects, despite having greater average AP diameters.[29] That result suggests that there may be sex-based differences in the restraint exerted on the midthoracic spine by the rib cage during mobilization. To explore this possibility, we divided the subjects into 2 groups based on sex and compared male and female subjects, using independent t tests.

A difference between male and female subjects was found for both the PA stiffness values at T7 and the AP chest diameters. The AP chest diameter was greater for male subjects ([bar] X=212 mm, SD=18.7, range=185-235) than for female subjects ([bar] X=187 mm, SD=16.7, range=160-215). The PA stiffness at T7 also was greater for male subjects ([bar] X=13.8 N/mm, SD=2.6, range=10.7-19.9) than for female subjects (X=11.2 N/mm, SD=2.8, range=7.7-15.1). Thus, an explanation of the observed contribution of AP chest diameter to the PA stiffness at T7 is that the difference was attributable to underlying sex-related differences in material properties of the rib cage rather than the AP chest diameter. The reasons for the sex-related differences in rib-cage stiffness have not been established, but they could include differences in quantities and properties of superficial soft tissues (eg, breast tissue) as well as differences in rib and costal cartilage shapes and dimensions or material properties. In our study, there was no difference between male and female subjects in terms of the ratio of AP chest diameter to lateral chest diameter, suggesting little role for overall chest shape in influencing the PA response at T7. To investigate the possible role of sex elsewhere, we also used t tests to examine whether there was a sex-related effect on the other variables used in the multiple-regression analyses. No effects were found (P [is less than].05).

The prediction of PA stiffness at T10 by pelvic rotation stiffness is more difficult to understand. One possible explanation may be that the pelvic rotation stiffness is determined by abdominal compressibility, perhaps mediated by intra-abdominal pressure. In terms of the conceptual model represented in Figure 4, the caudal springs in the group K may have a stiffness that contains a contribution from intra-abdominal pressure. Although the effect of intra-abdominal pressure may also be present at levels L1 and L4, the presence of more dominant variables may mask its effect.

The multiple-regression analyses showed that, at some levels, a low proportion (17%-22%) of the variance in PA stiffness was associated with nonspinal independent variables (ie, skinfold thickness, pelvic rotation stiffness, and AP rib-cage diameter). The variance in PA stiffness among subjects not accounted for by the independent variables we measured (from 78% to 100% of the between-subject variance at any given vertebral level) may be partly due to geometric properties (eg, tissue lengths, cross-sectional areas, orientations in space) or to material properties (that is, the elastic modulus or nonelastic properties such as viscosity). These geometric or material properties may be associated with intervertebral joints, or they could be associated with extraspinal structures such as the rib cage and abdomen. Alternatively, errors in the experimental data, introduced through uncertainty in measurements, inaccuracy in methods, and incorrect identification of vertebral locations, would have contributed variability to PA stiffness data that could not be accounted for by any subject variable. The size of this source of variance is not known.

The data in our study relate to slowly applied forces and cannot necessarily be applied to other rates of loading. The data reported by Lee and Liversidge[8] for loads applied over the lower lumbar vertebrae, however, indicate that there is a high correlation (r=.94) between slow and cyclic (0.5 Hz) values of PA stiffness (see Fig. 3 for the patterns of mean values). A similar relationship may exist at other vertebral levels, although Lee and Liversidge[8] found that the effect of loading frequency on PA stiffness was dependent on the vertebral level. Application of our data is also limited to moderate levels of applied force (ie, 30-100 N). At very low levels of force, the responses are known to be highly nonlinear.[5-8] At levels of force above 100 N, the response also shows nonlinearity.[30]

Because all of our subjects were from a relatively young group (age range: 18-41 years), the results may be not applicable to other individuals whose age is outside the range of ages of our subjects. There is some evidence that progressive biochemical and anatomical changes occur in the lumbar spine with increasing age.[31] Such changes may be associated with alterations in the stiffness of the spine and may occur unequally in different spinal regions. Thus, the pattern of PA stiffness variation along the spine and the importance of intervertebral stiffness as a determinant of PA stiffness may change with age.

The data in our study could be useful for the validation of quantitative models of PA responses. Previously, only information about the lower lumbar responses has been available for validation studies, If models are to be useful in explaining the mechanisms determining PA stiffness throughout the thoracolumbar spine, then they must be able to predict variations in PA stiffness that we have observed. There are good prospects that therapists will be able to use models to predict the systematic variations in PA stiffness along the spine that we observed through representation of the restraint of the spine that is provided by the rib cage and pelvis. The variations among individuals may be more difficult to model and, therefore, to understand because of the likelihood that material properties or complex anthropometric factors are important, both of which are difficult to match to individual subjects.

Conclusion

Posteroanterior stiffness was found to vary along the thoracolumbar spine in subjects without low back pain. The PA stiffness was lower at L1 than at L4, T7, and T4. The variation of PA stiffness along the spine was consistent with the nature of the support of the spine by the rib cage, pelvis, and other tissues. Variables related to individual subjects were predictors of PA stiffness at L4, T10, and T7, but none of these variables accounted for more than 22% of the variance in PA stiffness. Further research is needed to determine the factors that are responsible for most of the variation in PA stiffness among individuals.

Acknowledgment

We are grateful to Simone Edwards for her help in the data collection and data analysis phases of this project.

(*) Data Translation Inc, 100 Locke Dr, Marlboro, MA 01752.

([dagger]) Holtain Ltd, Crosswell, Crymmych, Pembrokeshire, United Kingdom.

([double dagger]) Lucas Schaevitz, 5828 S Kenton St, Englewood, CO 80111.

([sections]) SPSS Inc, 444 N Michigan Ave, Chicago, IL 60611.

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M Lee, MBiomedE, is Lecturer, School of Exercise and Sport Science, The University of Sydney, East Street, PO Box 170, Lidcombe, New South Wales, 1825 Australia ([e-mail]), and a graduate student in the Department of Aeronautical Engineering, The University of Sydney. Address all correspondence to Mr Lee.

GP Steven, PhD, is Professor, Department of Aeronautical Engineering, The University of Sydney.

J Crosbie, PhD, is Associate Professor, School of Physiotherapy, The University of Sydney.

RJED Higgs, FRCS, FRACS, FAOrthA, is Associate Professor, Department of Mechanical and Mechatronic Engineering, The. University of Sydney, and Department of Orthopaedic Surgery, Repatriation General Hospital, Concord, New South Wales, Australia.

This study was approved by the Human Ethics Committee of The University of Sydney.

This article was submitted September 18, 1997, and was accepted July 7, 1998.