- Email: [email protected]
Sagittal plane segmental motion of the cervical spine. A new precision measurement protocol and normal motion data of healthy adults
Clinical Biomechanics 17 (2002) 21–31 www.elsevier.com/locate/clinbiomech
Sagittal plane segmental motion of the cervical spine. A new precision measurement protocol and normal motion data of healthy adults W. Frobin a
a,*
, G. Leivseth b, M. Biggemann c, P. Brinckmann
a
Institut f€ur Experimentelle Biomechanik, Universit€atsklinikum M€unster, Domagkstrasse 3, D-48129 M€unster, Germany b Department of Clinical Neurosciences, Norwegian University of Science and Technology, Trondheim, Norway c Radiologische Klinik, Krankenhaus Bethesda, Duisburg, Germany Received 4 June 2001; accepted 23 October 2001
Abstract Objective. (1) Precise documentation of sagittal plane segmental rotational and posteroanterior translational motion of segments C0/C1–C6/C7 of the human cervical spine from lateral radiographic views. (2) Compilation of a database describing normal motion. (3) Comparison of individual motion patterns with the normal database. Design. Descriptive study based on computer-aided measurements from lateral radiographic views taken in flexion and extension. Background. Previous studies concentrated on segmental rotational motion of the cervical spine. Normal data for translational motion were not available. Description of cervical spine motion patterns thus remained incomplete. Methods. Based on computer-aided measurements from lateral radiographic views taken in flexion and extension, a new protocol determines rotational and translational motion for all segments (C0/C1–C6/C7) imaged on the radiographic views. Measured results are corrected for radiographic magnification and variation in stature; they are virtually uninfluenced by radiographic distortion and patient alignment errors. A database describing normal motion was compiled from 137 sets of lateral views of healthy adults taken in active flexion and extension. A specimen study as well as inter- and intra-observer studies quantify measurement errors. Results. The error study demonstrated the error (SD) of a rotational motion measurement to amount to slightly less than 2°. The error (SD) of a translational motion measurement amounts to less than 5% of vertebral depth; for a vertebra of 15 mm depth this corresponds to 0.7 mm. A normal database for rotational and translational motion was compiled. There was a linear relation between rotational and translational motion. This finding agrees qualitatively with results from previous studies; quantitative comparisons are not possible due to divergent definitions for translational motion. The relation between rotation and translation can be employed in individual cases to predict translational motion, in dependence on the rotation actually performed. A comparison of the rotational motion with the normal database and the difference between predicted and actual translational motion allow segmental hypo-, normal or hypermobility to be quantified. Conclusions. The new protocol measures segmental motion with high precision and corrects for radiographic distortion, variation in stature and alignment errors of patients. Thus, archive studies using existing radiographs are feasible. Relevance Flexion–extension radiographs of the cervical spine are performed to explore potential damage to the bony or ligamentous structure resulting in abnormal, segmental motion patterns. Determining rotational motion gives only an incomplete picture. The new protocol allows for precise quantification of translational motion and classification of segments as hypo- or hypermobile by comparison with normal motion data. Ó 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction Segmental motion of the cervical spine is analysed from lateral radiographs taken in flexion and extension in order to document abnormal motion caused by injury to the ligamentous structure, as a result of congenital
*
Corresponding author.
anomalies like basilar impression, os odontoideum and spondylolisthesis, to detect and monitor progress of rheumatoid arthritis and check the effect of surgical fusion. Previous studies concentrated mainly on documenting ranges of rotational motion; for a recent review see [1]. The rationale of these studies was to provide normal data as a basis for detection of abnormalities, i.e. segmental, rotational hypo- or hypermobility. Save for the work of Dvorak et al. [2] and Lind et al. [3] these
0268-0033/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 1 ) 0 0 1 0 5 - X
22
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
past studies did not, however, state SDs of the ranges of motion communicated nor inter- or intra-observer errors. The pioneering work of Penning [4] drew attention to the fact that segmental motion of cervical vertebrae is not simply a rocking about a pivot located at the centre of the disc but a complex motion composed of rotation and posteroanterior translation of the vertebrae relative to each other. Penning chose to describe this motion by a pure rotation. The construction of rotation centres provides insight into the functional anatomy and into the deformation of discs and ligaments resulting from the motion. The appertaining centres of rotation were located by means of a superposition procedure of the vertebral images in flexion and extension. Starting from segment C2/C3, Penning found the centres of rotation to be located generally below the endplate of the caudal vertebrae. This means that a backwards bend of a cervical motion segment is accompanied by displacement of the cranial vertebra into posterior direction. Amevo et al. [5,6] reconsidered Penning’s concept and analysed error sources of his procedure. Their results were in qualitative agreement with Penning’s findings. Describing relative, plane motion of two objects (here: two neighbouring vertebrae) by a pure rotation is not compulsory. Alternatively, the identical motion can be described by translation in combination with rotation, this rotation occurring about a centre different from that in the case of a pure rotation. Which of the two descriptions is adopted depends on the problem being dealt with. Angles of rotation prove to be equal in both descriptions (not self evident, but a mathematical special case). The translation data obviously differ: zero in the case of a pure rotation and with a specified magnitude and into a specified direction in the second case. While both descriptions are equivalent in mathematical terms, three properties are associated with the description of segmental motion as pure rotation. For anatomical reasons, one might be interested in translational motion in a specific direction, for example in the relative posteroanterior motion of two neighbouring vertebrae in the plane of the intervening disc. A pure rotation does not vividly describe this component of the motion. Secondly it may occur in pathologic cases that the actual motion is purely translational. In such a case the centre of rotation moves to infinity if the ‘‘pure rotation’’ description is adopted. In addition it holds that centres of rotation far away from the moving object can be determined with low precision only. Thirdly, it is difficult to scale the location of a centre of rotation determined in one spine to the given geometry of another spine. Dvorak et al. [7] and Lin et al. [8] partitioned the relative movement of cervical vertebrae into rotational and translational components. Translation measure-
ments were, however, done in mm from the films. This prohibits collection of normal data as differences in radiographic magnification and stature cannot be corrected for. For these reasons, and guided by a previous study of segmental motion in the lumbar spine [9], the present study chose to describe segmental motion in the cervical spine by a combination of rotation and posteroanterior translation, the latter being measured in the plane of the disc and quoted in relative units. A new protocol for documenting segmental motion from lateral radiographic views in flexion and extension was developed with special emphasis on minimising measurement errors and on excluding subjective influence. Normal data for rotational and translational motion are presented which will serve in future studies for documenting segmental motion abnormalities.
2. Methods The new protocol documents segmental motion of segments C0/C1–C6/C7 from sets of two lateral radiographic views taken in extension and flexion. The protocol is based on landmarks identified on the skull and computer-aided location of objective landmarks on vertebrae C1–C7. The parameters describing rotational and translational motion are derived from these landmarks in such a fashion that the result is virtually uninfluenced by radiographic distortion and magnification. Special control of patient alignment with respect to radiographic film and tube is not required; normal positioning suffices. Thus retrospective studies using existing radiographs are feasible. The definition of rotational and translational motion is outlined first for segments C3/C4–C6/C7 (Fig. 1). For segments C0/C1–C2/C3, the definitions require logical modifications. Corners 1–4 are located on the outer contours of the vertebral bodies by a computerised algorithm (see Appendix A). The centre point is the geometric centre of corners 1–4. The vertebral midplane is defined as a line running through the midpoints between corners 1, 3 and corners 2, 4, respectively. The angle between two vertebrae is given by the angle between their midplanes. The angle is counted positive if the wedge opens anteriorly. (The angle shown in Fig. 1 thus bears a positive sign.) Rotational motion of a segment is defined as the difference of the angle in extension minus the angle in flexion. Rotational motion is quoted in degrees. Perpendiculars are constructed from the centre points of adjacent vertebrae onto the bisectrix between the midplanes. Posteroanterior displacement is defined as the distance between those points where the perpendiculars intersect the bisectrix. Thus, displacement (and consequently translational motion) is measured along a
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
23
Fig. 2. Definition of the angle for the segment C0/C1.
Fig. 1. Definition of angle and displacement for motion segments C3/ C4–C6/C7.
direction coinciding in good approximation with the midplane of the disc. Displacement is counted positive if the projection of the cranial centre point is located anteriorly from the projection of the caudal centre point. (The displacement shown in Fig. 1 thus bears a negative sign.) To correct for radiographic magnification and variation in stature, displacement measured in millimeters is divided by the mean depth of the caudal vertebra. The mean depth is the mean of the distance of corners 1, 2 and 3, 4, respectively. Posteroanterior translational motion is given by the difference of the displacement in extension minus the displacement in flexion. As quotients of lengths, displacement and translational motion are dimensionless quantities. Previous work [9–11] ascertained that in lumbar vertebrae relative location of midpoints between the anterior and posterior vertebral corners, location of centre points, mean depth as well as location and orientation of midplanes and their bisectrix are virtually independent of distortion in central projection and of small alignment errors of the patients. As the definition of landmarks and derived parameters is similar for cervical and lumbar vertebrae, rotational and translational motion, as defined here, are virtually uninfluenced by distortion and patient alignment errors as well. For segment C0/C1 (Fig. 2), the angle is given by the angle between the McGregor line, i.e. the tangent from the posterior rim of the palatum durum onto the contour of the occiput, and a line connecting the centres of
area of the medullary cavities of the anterior and posterior arch of C1. Rotational motion of a segment is defined as the difference of the angle in extension minus the angle in flexion. It is to be added that the McGregor line will shift if the head is tilted sideways. Thus the C0/ C1 angle will depend on patient alignment. Posteroanterior displacement and translational motion are not defined for C0/C1. For segment C1/C2 (Fig. 3) definition of angle and displacement are based on the landmarks of C1 (centres of the marrow cavities) and the caudal corners 3 and 4 of C2. The unique shape of dens and corpus axis prohibits definition of four vertebral corners; a landmark placed at the tip of the dens proved to be unreliable. Objective location of caudal corners 3 and 4 is described in Appendix A. The angle between C1 and C2 is given by the angle between the line running through the centres of the marrow cavities of C1 and the line through corners 3 and 4 of C2. Posteroanterior displacement is given by the distance between the projection of the midpoint of the line connecting the marrow cavities of C1 and the projection of the midpoint of the line connecting corners 3 and 4 of C2 onto the bisectrix between the two lines. Rotational and translational motion are then defined as above. The value of translational motion measured in millimeters is divided by the distance between corners 3 and 4 of C2. For seg-
Fig. 3. Definition of angle and displacement for segment C1/C2.
24
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
ment C2/C3 (Fig. 4) analogous definitions for angle, displacement, rotational and translational motion are chosen. The distance between the dens and the inner surface of the anterior arch of the atlas, in the following termed ‘‘dens–atlas gap’’, is defined as the distance between those points where the line connecting the centres of the marrow cavities of C1 intersects the contours of the dens and the anterior arch of the atlas (Fig. 3). To correct for differences in radiographic magnification, this distance is divided by the distance between corners 3 and 4 of C2. The change in the dens–atlas gap is given by its value in extension minus its value in flexion. The technical procedure for measuring rotational and translational motion consists in identifying the posterior rim of the palatum durum, the contour of the occiput, the contours of the anterior and posterior arch of C1 and the contours of the marrow cavities of the arches, the contour of the dens and corpus axis, and the contours of vertebral bodies C3–C7 in both the flexion and the extension radiographs. The location of the posterior rim of the palatum durum, all contours and handmarked corners, serving as starting points for the iterative corner-locating algorithm, are mapped onto transparent foils. Points and contours are digitised (point density 5 per mm, precision 0.125 mm). Series of computer programs check geometric properties of the contours, locate corners, and calculate derived geometric measures as well as rotational and translational
motion for all segments imaged on each set of radiographs.
3. Material Sets of lateral radiographs of the cervical spine taken in active maximum flexion and extension were collected from archives of five medical institutions in Iceland, Norway, the Netherlands and Germany. From the total number of 137 sets, 101 stemmed from female and 36 from male, skeletally mature subjects in the age range between 16 and 58 yr (mean age 33 yr for both genders). The majority of radiographs stemmed from healthy volunteers who had participated in previous studies conducted by other authors. The remaining radiographs had been taken to rule out a variety of diseases. These sets had all been inspected by radiologists and classified as exhibiting no pathological findings. Not all of the 137 sets imaged the occiput and the palatum durum on both the flexion and the extension views. Furthermore, a portion of the sets imaged only vertebrae distal to C2. C7 was imaged in only a few sets. For these reasons, the number of entries in the result tables varies for the different segments and is generally lower than 137. From a sub-set of 40 subjects, radiographs imaging C3–C7 and taken at intermediate postures (erect and medium flexion) were available in addition to the views taken in maximum extension and flexion.
4. Error study
Fig. 4. Definition of angle and displacement for C2/C3.
As stated above, a previous study on segmental motion of the lumbar spine served as a guide on how to minimise errors resulting from radiographic distortion and patient alignment. Nevertheless, it seemed desirable to re-assess measurement precision in view of the fact that dimensions of cervical vertebrae are small compared with lumbar ones, while the radiographic magnification is approximately identical for lateral views of the cervical and lumbar spine. The small dimensions of the cervical vertebrae decrease distortion effects on the one hand but tend to increase identification and mapping errors of the bony contours on the other. Six deepfrozen cervical spine specimens comprising vertebrae C1–C7 were each radiographed in nine different projections, longitudinally aligned as well as tilted by 5° and axially rotated through 5° with respect to the film. All 54 views were evaluated independently by two observers. In the absence of measurement errors, the angle, displacement and dens–atlas gap should yield identical values within each set of the nine views of each specimen. The actual scatter of the results directly quantifies measurement precision.
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
For determination of segmental motion, the 137 sets of flexion–extension views were processed in approximately equal parts by two observers. To assess reproducibility in the measurement of rotational and translational motion, seven sets were evaluated by both observers and seven sets were evaluated twice by one observer, but at a 6-month interval. In both cases, evaluation comprised identification and mapping of contours on transparent foils (in no case had marks been placed on the radiographs), digitisation and computation of the motion parameters. The two-sided t-test for paired measurements, level of significance 0.05, was employed to evaluate the inter- and intra-observer tests. The additional radiographs in the sub-set of the material, taken at intermediate extension and flexion angles, were used to verify the assumption of a linear dependence of posteroanterior displacement on the angle of rotation. For this purpose the deviation of the posteroanterior displacement observed at the intermediate angles from those values calculated from the maximum extension and flexion data under the assumption of a strictly linear dependence was computed and averaged, and compared with the measurement precision.
25
5. Results 5.1. Measurement errors Measurement precision of the segmental angle determined from the sets of specimen radiographs ranged for segments C1/C2–C6/C7 between 1.1° and 1.9° with negligible differences between the two observers (Table 1). For rotational motion determined from in vivo flexion–extension views, inter- and intra-observer tests resulted in SDs of 1.98° and 1.91°, respectively (Tables 2 and 3). Comparison shows the error in rotational motion (i.e. for angle differences) to be slightly inferiorpto the error of an angle measurement multiplied by 2. This is due to the fact that the simultaneous availability of both an extension and a flexion radiograph assists the observer in correctly identifying the relevant bony contours. (The contours themselves are usually differently shaped due to projection differences between the two views.) The error of displacement determined from specimen radiographs ranged among segments between 0.0181 and 0.0312 (Table 1). Inter- and intra-observer SDs for translational motion determined from in vivo flexion–extension views amounted to 0.0473 and 0.0330, respectively, equivalent to approx. 4.7% or 3.3% of
Table 1 Measurement precision (SD), determined from radiographs of six cervical spine specimens each radiographed in nine different projections Segment
Angle, observer 1
Angle, observer 2
Displacement, observer 1
Displacement, observer 2
Dens–atlas gap, observer 1
Dens–atlas gap, observer 2
C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7
1.1123 1.9347 1.6867 1.7658 1.4551 1.2228
1.2384 1.7253 1.3778 1.3793 1.2955 1.2138
0.0297 0.0268 0.0290 0.0309 0.0181 0.0195
0.0312 0.0204 0.0208 0.0248 0.0208 0.0194
0.0149 – – – – –
0.0135 – – – – –
Mean
1.5296
1.3717
0.0257
0.0229
Measurement of angle (degrees), displacement and dens–atlas gap (both in units of vertebral depth) performed by two observers. Variances were computed for each segment of each specimen and then averaged over the six specimens. The table quotes the square root of these variances.
Table 2 Inter-observer error for rotational and translational motion determined from n pairs of flexion–extension radiographs Level C0/C1 C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7 All segments
n 7 7 7 7 7 6 1 42
Rotational motion mean deviation and SD
n
0.3660 )0.3080 0.3010 0.8437 0.6004 )1.4299 3.6401
–
(1.7282) (1.5739) (1.7104) (1.1048) (2.7072) (2.2821) –
0.1829 (1.9849)
Translational motion mean deviation and SD 7 7 7 7 6 1
Not defined )0.0111 (0.0821) 0.0196 (0.0339) )0.0002 (0.0288) )0.0131 (0.0376) )0.0073 (0.0359) )0.0659 –
35
)0.0041 (0.0473)
Rotational motion in degrees, translational motion in units of the depth of the caudal vertebra. SD in parentheses. Translational motion not defined for C0/C1. All mean deviations are not significantly different from zero ða ¼ 0:05Þ.
26
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
Table 3 Intra-observer error for rotational and translational motion determined from n pairs of flexion–extension radiographs Level
n
C0/C1 C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7 All segments
7 7 7 7 7 5 2 42
Rotational motion mean deviation and SD
n
0.0429 )0.2426 0.3021 0.4464 0.1111 )0.0681 )1.5717
–
(0.8588) (1.5096) (1.8113) (2.8810) (2.4639) (2.0781) (0.3078)
0.0271 (1.9054)
Translational motion mean deviation and SD 7 7 7 7 6 1
Not defined )0.0095 (0.0505) 0.0036 (0.0324) )0.0154 (0.0220) )0.0107 (0.0346) )0.0282 ð0:0200Þ )0.0159 (0.0239)
35
)0.0113 (0.0330)
Rotational motion in degrees, translational motion in units of the depth of the caudal vertebra. SD in parentheses. Translational motion not defined for C0/C1. All mean deviations, save the one marked with *, are not significantly different from zero ða ¼ 0:05Þ.
vertebral depth (Tables 2 and 3). For a vertebra of 15 mm depth, this corresponds to approximately 0.7 mm. For comparison, Johnsson et al. [12] using RSA reported errors (SD) between 0.16 and 0.22 mm for translation measurements. RSA is, however, in general not adapted to measure translation in specific anatomic directions (here: the plane of the disc) but rather along the axes of a laboratory coordinate system. The magnitude of the dens–atlas gap was determined from specimen radiographs by the two observers with errors of 0.0149 and 0.0135, respectively (Table 1) and from single in vivo extension- or flexion views with inter- or intra-observer SDs of 0.0235 and 0.0257, respectively (Table 4). The change in the dens–atlas gap (Table 4) was determined from in vivo flexion–extension views with inter-observer or intra-observer SDs of 0.0262 and 0.0121, respectively, equivalent to approx. 2.6% and 1.2% of the depth of C2 (Table 4). Assuming a depth of C2 of 15 mm, this corresponds to less than 0.4 mm.
5.2. Rotational motion The range of rotational motion observed in the present cohort as well as its SD are compiled in Table 5. 5.3. Translational motion As translational motion occurs simultaneously with rotational motion, ranges of translational motion are not quoted. Rather the measured magnitude of translational motion of each individual segment is divided by its rotational range of motion to obtain the slope of translation vs. rotation. Table 6 lists average values of the ‘‘translational motion per degree of rotation’’. Only those segments contribute to the data in Table 6 where the rotational motion amounted to at least 7.5° (approx. 4 SD of the measurement error of rotational motion). Inclusion of data from segments exhibiting very small rotational motion would induce imprecision due to the measurement errors both of angle and of displacement.
Table 4 Inter- and intra-observer error for the magnitude of the dens–atlas gap in flexion or extension as well as for its change in the course of rotational motion
Magnitude of dens–atlas gap Change in dens–atlas gap
n
Inter-observer error
Intra-observer error
14 7
0.0177 ð0:0235Þ )0.0149 (0.0262)
)0.0061 (0.0257) )0.0020 (0.0121)
Magnitude and change in dens–atlas gap change in units of the depth of C2. SD in parentheses. Mean deviations marked * are significantly different from zero ða ¼ 0:05Þ. Table 5 Range of rotational motion observed in the cohort investigated Level
n
Range (°) females
n
Range (°) males
C0/C1 C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7
23 61 57 92 95 92 23
12.6 10.9 8.4 15.2 17.0 17.9 11.4
18 36 34 34 33 27 10
14.5 11.6 7.8 11.6 14.4 12.2 9.8
(6.83) (4.87) (3.43) (4.72) (5.46) (6.60) (6.82)
SD in parentheses. n denotes the number of segments measured.
(7.65) (4.57) (3.09) (3.57) (4.55) (5.19) (5.73)
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
27
Table 6 Magnitude and direction of posteroanterior translational motion per degree of rotation in a healthy, adult cohort Level
Females, n
Females, change in posteroanterior displacement per degree of rotation
Males, n
Males, change in posteroanterior displacement per degree of rotation
C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7
46 33 86 89 84 15
+0.01435 (0.00680) )0.00826 (0.00457) )0.00970 (0.00341) )0.00886 (0.00294) )0.00490 (0.00212) )0.00151 (0.00274)
30 17 31 31 21 6
+0.01232 (0.00800) )0.00827 (0.00375) )0.00708 (0.00266) )0.00702 (0.00221) )0.00599 (0.00363) )0.00230 (0.00179)
Translational motion is measured in units of the mean depth (or in case of C1/C2: of the depth) of the caudal vertebra of each segment; translation is thus a dimensionless number. SD in parentheses. Data from only those sets of flexion–extension views contribute, where the angular range of motion amounted to at least 7.5°. Translation per degree of rotation is significantly different between females and males for segments C3/C4 and C4/C5 (twosided t-test, a ¼ 0:05).
The analysis of those sets of radiographs where, in addition to views in maximum flexion and extension, two intermediate views in erect posture and medium flexion were processed, showed that deviation of the measured displacement at the intermediate postures from a straight line connecting the data points of maximum flexion and extension was virtually equal to the measurement error for displacement. In consideration of the measurement precision of the protocol presented in this study, this justifies the assumption of a linear relation between rotation and translation. 5.4. Dens–atlas gap As in the case of translational motion, the change in the dens–atlas gap was expected to depend on the magnitude of the rotational motion. Table 7 lists the change in the gap size per degree of rotational motion. Again, only those segments contribute to the data in Table 7 where the rotational motion of C1/C2 amounted to at least 7.5°.
reported [3] when measuring rotational motion from lateral flexion–extension views, using a protocol different from the one employed in this study. Ryd et al. [13] determined the precision (SD) of radiostereometric analysis (RSA) when measuring rotational motion in the cervical spine in a cohort of fusion patients to range between 0.18° and 2.26°. While RSA is generally more precise than measurements from plain radiographs, the authors showed that RSA accuracy depends critically on the geometric configuration of the implanted markers. In unfavourable configurations [12], measurement accuracy at the cervical spine may fall substantially short of the values previously obtained from the lumbar spine or from rigid-body RSA laboratory studies. The range of rotational motion observed in the present cohort complies with results of previous studies [2,3,14]. Fig. 5 gives an example of individual rotational motion data compared with the normal range. The data of this subject reveal no pathological findings. However, not much importance would probably even be attached to cases where rotational motion of all segments
6. Discussion Using the new protocol, the measurement error (SD) for rotational motion, determined from specimen experiments as well as from inter- and intra-observer tests, is slightly less than 2°. This complies well with intra- and inter-observer errors (SD) of 1.8° and 1.2°, respectively, Table 7 Dependence of the magnitude of the dens–atlas gap on the angle between C1 and C2 n
Change in dens–atlas gap per degree of rotation, females
n
Change in dens–atlas gap per degree of rotation, males
46
)0.00281 (0.00415)
30
)0.00268 (0.00474)
The gap is measured in units of the depth of C2. Data from only those sets of flexion–extension views contribute, where the angular range of motion amounted to at least 7.5°; SD in parentheses. The two-sided ttest with a ¼ 0:05 indicates no significant gender-related difference.
Fig. 5. Example of documentation of rotational motion in the individual case and its comparison with normal values. In this as well as in the following figures: solid line: normal mean; error bars: measurement errors (1 SD). The graph shows no pathological deviation from normal rotational motion.
28
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
deviated in the same sense from normal. The reason is that 95% confidence limits for rotational motion are broad and individual motion is influenced by motivation or pain. Only cases where all segments save one exhibit virtually normal ranges of rotational motion, while one segment exhibits a substantial deviation from normal, might point to an abnormality (Fig. 6). More important than comparisons with the normal range, the precise measurement of rotational motion offers a precise tool to investigate and document effects of conservative or operative treatment. Examples are the measurement of suspected residual motion in fused segments or potential changes in the motion pattern of segments adjacent to a fused one. While measurement accuracy for rotational motion is on average inferior to RSA, the new protocol is (in contrast to RSA) not restricted to postoperative investigations. As demonstrated before [2,8] rotational motion in cervical segments is always linked with simultaneous translational motion. As this study determines translational motion along the midplane of the disc, there are no previous studies available for quantitative comparison. Translational motion per degree of rotation (Table 6) amounts to slightly less than 0.01 (i.e. less than 1% of vertebral depth) per degree of rotation. It differs among genders and levels and exhibits a considerable biological variation. A positive sign of translational motion per degree of rotation means that when moving in extension the cranial vertebra of the segment translates in anterior direction. This is the case for the segment C1/C2. In all other segments the negative sign indicates that when moving in extension the cranial vertebra translates into posterior direction. This complies qualitatively with Penning’s [4] earlier findings for the location of the
Fig. 6. Example of documentation of rotational motion where motion of one single segment (C5/C6) deviates substantially from normal while the motion of the other segments is well within the normal range. The case shown exhibited no radiological abnormality. Clinical significance of such isolated deviations from normal remains to be shown in future studies.
centre of rotation. The direction of segmental motion is explained by the shape of the cervical spine articulations. For a recent review see [1]. Knowledge of ‘‘translational motion per degree of rotation’’ permits a comparison of individual translation data with normal ones. An individual range of translational motion cannot be directly compared with a norm, because the individual rotational motion may (for any reasons whatever) deviate uncontrollably from normal. For the purpose of comparison, the normal value of ‘‘translational motion per degree of rotation’’ (Table 6) is multiplied by the individual, actually performed range of rotational motion. This predicts the normal translational motion to be expected for the individual under investigation. Comparison of the actually measured translational motion with the predicted one permits individual segments to be classified as normal, hyper- or hypomobile with respect to translation. It is unlikely that comparing actual translation with its predicted value will be confounded by motivation or pain, as the magnitude of rotational segmental motion can be voluntarily controlled, but not the accompanying translational motion. Fig. 7 shows an example of comparing individual translational motion with the values predicted from the normal database of ‘‘translational motion per degree’’, thus allowing for the given range of rotational motion when inspecting translation. The range of variation of 1:96 SD about the predicted norm is calculated from the variation of translational motion per degree and the error of the rotation measurement. The error bars of the data points designate the measurement error (1 SD) of the translation measurement. The data shown in Fig. 7 reveal no pathological findings. Fig. 8 shows an example where translational motion in one segment (C3/C4) deviates by approx. 3 SD from normal. It remains to be shown what clinical significance can be attached to such findings.
Fig. 7. Example of documentation of translational motion in the individual case; data for the same subject as in Fig. 5. No deviation from normal translational motion.
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
In our material investigated there was a trend for the dens–atlas gap to be smaller in extension than in flexion. This is reflected by the negative sign of the ‘‘change in gap size per degree of rotational motion’’ (Table 7). There was, however, a considerable biological variation. In a fraction of the cohort the gap size actually increased in extension. In the material investigated, no uniform prescriptions how to flex or extend had been prescribed. Thus, part of the variation may be due to different motion patterns, i.e. performing forward flexion more via a ‘‘nodding’’ motion of the head or more by a forward bending of the cervical spine. In addition, measurement errors may confound the relation between rotational motion and gap size, as gap size is small and minute errors in locating and mapping the opposing contours of dens and atlas contribute to the observed variation. As an example Fig. 9 shows the change of the dens–atlas gap together with the appertaining predicted normal value. Like in the case of translation, the prediction is given by the product of the ‘‘change of gap size per degree’’ of normals and the ‘‘C1/C2 rotation’’ actually performed.
29
To summarise, a new protocol for documenting segmental motion of segments C0/C1–C6/C7 is presented and validated. Measurements are based on lateral flexion–extension radiographic views taken in normal clinical settings using computer-aided, objective algorithms. The error (SD) of a rotational motion measurement amounts to slightly less than 2°. The error (SD) of a translational motion measurement amounts to slightly less than 5% of vertebral depth; for a vertebra of 15 mm depth this corresponds to an error of 0.75 mm. Normal data for rotational and posteroanterior translational motion of cervical motion segments are presented, permitting comparison of individual motion data with the normal database. While rotational motion, influenced by age, pain and patient compliance, usually varies widely, the new protocol permits precise inspection of translational motion independent of the aforementioned factors. The new protocol can be employed to diagnose motion abnormalities like translational hypo- or hypermobility and to monitor conservative or operative treatment of the cervical spine.
Acknowledgements The authors thank E. Kristjansson, Reykjavik, Iceland, K. Dale M.D. Ph.D., Rikshospitalet, University Hospital of Oslo, Norway, and Dr. D.H.W. Sch€ onfeld, Sint Maartenskliniek, Nijmegen, The Netherlands, for their most valuable assistance in the collection of the radiographs of normal subjects.
Appendix A. Definition of landmarks
Fig. 8. Example of documentation of translational motion, where motion of one single segment (C3/C4) deviates by approximately 3 SD from the norm. The clinical significance of such deviations from normal remains to be shown in future studies.
Fig. 9. Example of the change of the dens–atlas gap size when moving from extension to flexion. The solid line and the shaded area depict the normal range 1:96 SD of the change of gap size, predicted from the normal gap size change per degree of rotation and the actual range of rotation of this subject (same subject as in Figs. 5 and 7). No pathological deviation from normal.
The essential aspect of landmark (‘‘corner’’) location is to minimise subjective observer influence. Instead of using hand-marked locations, landmarks are defined by applying mathematical procedures based on objective geometric properties of vertebral contours. Corner location is first described for vertebrae C3–C7. Due to the divergent shape of C2, definitions are appropriately modified. C0 (skull) and C1 require specific definitions. C3–C7. Starting from hand-marked corners 1h to 4h (Fig. 10), the vertebral midplane is constructed through the midpoints between corners 1h, 3h and 2h, 4h respectively. Reference lines at predefined angles a with respect to the midplane are drawn through the centre point P (geometric centre of points 1h to 4h). Corners are defined as points of maximum distance from these reference lines. Fig. 10 illustrates the procedure with the example of corner 4. 4h denotes the hand marked and 4c the computed corner location. Once corners 1c–4c have been located according to this algorithm, the procedure is repeated four times in an iterative fashion. Angles a were previously determined from a preparatory study on
30
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
Fig. 11. Computer-aided location of corners on the contour of vertebra C2.
Fig. 10. Computer-aided location of corners on the contours of vertebrae C3–C7.
cervical spine specimens radiographed in nine slightly different projections as those angles which permit ‘‘aiming’’ to be done from the reference line ‘‘perpendicularly into the corner region’’ and provide the best reproducibility of corner location within sets of radiographs of identical specimens. Table 8 lists the set of angles used. (If the images of the vertebral bodies approximated a square, the angles would be close to +45° or +135°. Their deviation from these values actually reflects the rhomboid shape of cervical vertebral body contours.) C2. Due to the biological variance of the shape of C2, its tip (the cranial corner) proved to be an unreliable landmark for segmental motion measurements. Measurement of motion is thus based only on its caudal corners 3 and 4 (Fig. 11). In C2, the line connecting corners 3h and 4h substitutes the midplane; a point on the perpendicular bisector at 1/2 the distance 3h–4h above this line substitutes the centre point P. Again, reference lines at a predefined angles a are drawn through P and the computed corner points 3c and 4c are defined as points of maximum distance from these lines. Fig. 11 illustrates this for corner 4 where 4h denotes the initial hand-marked and 4c the computed corner location. After corners 3c and 4c have been determined, the procedure is repeated four times in an iterative fashion. The angles a employed are listed in Table 8. C1. The shape of the outer cortex of the arches, especially of the posterior one, depends critically on the Table 8 Set of angles a employed for corner location on the contours of vertebrae C2–C7 Vertebra
Corner 1 (°)
Corner 2 (°)
Corner 3 (°)
Corner 4 (°)
C2 C3–C7
– +40
– +133
+157 +149
+31 +47
projection. Thus, points selected on the outer cortex of the arches proved to be unsuitable for precise determination of rotational and translational motion. Instead, the geometric centres of the areas of the marrow cavities of the anterior and posterior arch of C1 (cf. Fig. 2), computed from their digitised periphery, are used as landmarks. C0. The posterior rim of the palatum durum is used as a landmark for construction of the McGregor line, i.e. the tangent from this point onto the occiput.
References [1] Bogduk N, Mercer S. Biomechanics of the cervical spine. I: normal kinematics. Clin Biomech 2000;15:633–48. [2] Dvorak J, Froehlich D, Penning L, Baumgartner H, Panjabi MM. Functional radiographic diagnosis of the cervical spine: flexion/extension. Spine 1988;13:748–55. [3] Lind B, Sihlbom H, Nordall A, Malchau H. Normal range of motion of the cervical spine. Arch Med Phys Rehabil 1989;70:692–5. [4] Penning L. Normal movements of the cervical spine. Am J Roentgenol 1978;130:317–26. [5] Amevo B, Worth D, Bogduk N. Instantaneous axes of rotation of the typical cervical motion segments: II. Optimization of technical errors. Clin Biomech 1991;6:38–46. [6] Amevo B, Worth D, Bogduk N. Instantaneous axes of rotation of the typical cervical motion segments: a study in normal volunteers. Clin Biomech 1991;6:111–7. [7] Dvorak J, Panjabi MM, Novotny JE, Antinnes JA. In vivo flexion/extension of the normal cervical spine. J Orthop Res 1991;9:828–34. [8] Lin RM, Tsai KH, Chu LP, Chang PQ. Characteristics of sagittal vertebral alignment in flexion determined by dynamic radiographs of the cervical spine. Spine 2001;26:256–61. [9] Frobin W, Brinckmann P, Leivseth G, Biggemann M, Reikeras O. Precision measurement of segmental motion from flexion– extension radiographs of the lumbar spine. Clin Biomech 1996;11:457–65. [10] Brinckmann P, Frobin W, Biggemann M, Hilweg D, Seidel S, Burton K, et al. Quantification of overload injuries to thoracolumbar vertebrae and discs in persons exposed to heavy physical exertions or vibration at the work place. Part I. The shape of vertebrae and intervertebral discs – study of a young healthy population and a middle aged control group. Clin Biomech 1994;9(Suppl 1):S1–S83.
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31 [11] Frobin W, Brinckmann P, Biggemann M, Tillotson M, Burton K. Precision measurement of disc height, vertebral height and sagittal plane displacement from lateral radiographic views of the lumbar spine. Clin Biomech 1997;12(Suppl 1): S1–S63. [12] Johnsson R, Axelson P, Str€ omqvist B. Mobility provocation of lumbar fusion evaluated by radiostereometric analysis. Acta Orthop Scand 1996;67(Suppl):45–6.
31
[13] Ryd L,Yuan X, L€ ofgren H. Methods to determine the accuracy of radiostereometric analysis. In: L€ ofgren H, editor. Outcome and bone grafts in surgical treatment of cervical disc disease. Link€ oping Univ. Med. Diss. No. 621, Link€ oping, 2000. [14] Van Mameren H, Drukker J, Sanches H, Beursgens J. Cervical spine motion in the sagittal plane (I). Range of motion of actually performed movements, an X-ray cinematographic study. Eur J Morphology 1990;28:47–68.
Sagittal plane segmental motion of the cervical spine. A new precision measurement protocol and normal motion data of healthy adults W. Frobin a
a,*
, G. Leivseth b, M. Biggemann c, P. Brinckmann
a
Institut f€ur Experimentelle Biomechanik, Universit€atsklinikum M€unster, Domagkstrasse 3, D-48129 M€unster, Germany b Department of Clinical Neurosciences, Norwegian University of Science and Technology, Trondheim, Norway c Radiologische Klinik, Krankenhaus Bethesda, Duisburg, Germany Received 4 June 2001; accepted 23 October 2001
Abstract Objective. (1) Precise documentation of sagittal plane segmental rotational and posteroanterior translational motion of segments C0/C1–C6/C7 of the human cervical spine from lateral radiographic views. (2) Compilation of a database describing normal motion. (3) Comparison of individual motion patterns with the normal database. Design. Descriptive study based on computer-aided measurements from lateral radiographic views taken in flexion and extension. Background. Previous studies concentrated on segmental rotational motion of the cervical spine. Normal data for translational motion were not available. Description of cervical spine motion patterns thus remained incomplete. Methods. Based on computer-aided measurements from lateral radiographic views taken in flexion and extension, a new protocol determines rotational and translational motion for all segments (C0/C1–C6/C7) imaged on the radiographic views. Measured results are corrected for radiographic magnification and variation in stature; they are virtually uninfluenced by radiographic distortion and patient alignment errors. A database describing normal motion was compiled from 137 sets of lateral views of healthy adults taken in active flexion and extension. A specimen study as well as inter- and intra-observer studies quantify measurement errors. Results. The error study demonstrated the error (SD) of a rotational motion measurement to amount to slightly less than 2°. The error (SD) of a translational motion measurement amounts to less than 5% of vertebral depth; for a vertebra of 15 mm depth this corresponds to 0.7 mm. A normal database for rotational and translational motion was compiled. There was a linear relation between rotational and translational motion. This finding agrees qualitatively with results from previous studies; quantitative comparisons are not possible due to divergent definitions for translational motion. The relation between rotation and translation can be employed in individual cases to predict translational motion, in dependence on the rotation actually performed. A comparison of the rotational motion with the normal database and the difference between predicted and actual translational motion allow segmental hypo-, normal or hypermobility to be quantified. Conclusions. The new protocol measures segmental motion with high precision and corrects for radiographic distortion, variation in stature and alignment errors of patients. Thus, archive studies using existing radiographs are feasible. Relevance Flexion–extension radiographs of the cervical spine are performed to explore potential damage to the bony or ligamentous structure resulting in abnormal, segmental motion patterns. Determining rotational motion gives only an incomplete picture. The new protocol allows for precise quantification of translational motion and classification of segments as hypo- or hypermobile by comparison with normal motion data. Ó 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction Segmental motion of the cervical spine is analysed from lateral radiographs taken in flexion and extension in order to document abnormal motion caused by injury to the ligamentous structure, as a result of congenital
*
Corresponding author.
anomalies like basilar impression, os odontoideum and spondylolisthesis, to detect and monitor progress of rheumatoid arthritis and check the effect of surgical fusion. Previous studies concentrated mainly on documenting ranges of rotational motion; for a recent review see [1]. The rationale of these studies was to provide normal data as a basis for detection of abnormalities, i.e. segmental, rotational hypo- or hypermobility. Save for the work of Dvorak et al. [2] and Lind et al. [3] these
0268-0033/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 8 - 0 0 3 3 ( 0 1 ) 0 0 1 0 5 - X
22
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
past studies did not, however, state SDs of the ranges of motion communicated nor inter- or intra-observer errors. The pioneering work of Penning [4] drew attention to the fact that segmental motion of cervical vertebrae is not simply a rocking about a pivot located at the centre of the disc but a complex motion composed of rotation and posteroanterior translation of the vertebrae relative to each other. Penning chose to describe this motion by a pure rotation. The construction of rotation centres provides insight into the functional anatomy and into the deformation of discs and ligaments resulting from the motion. The appertaining centres of rotation were located by means of a superposition procedure of the vertebral images in flexion and extension. Starting from segment C2/C3, Penning found the centres of rotation to be located generally below the endplate of the caudal vertebrae. This means that a backwards bend of a cervical motion segment is accompanied by displacement of the cranial vertebra into posterior direction. Amevo et al. [5,6] reconsidered Penning’s concept and analysed error sources of his procedure. Their results were in qualitative agreement with Penning’s findings. Describing relative, plane motion of two objects (here: two neighbouring vertebrae) by a pure rotation is not compulsory. Alternatively, the identical motion can be described by translation in combination with rotation, this rotation occurring about a centre different from that in the case of a pure rotation. Which of the two descriptions is adopted depends on the problem being dealt with. Angles of rotation prove to be equal in both descriptions (not self evident, but a mathematical special case). The translation data obviously differ: zero in the case of a pure rotation and with a specified magnitude and into a specified direction in the second case. While both descriptions are equivalent in mathematical terms, three properties are associated with the description of segmental motion as pure rotation. For anatomical reasons, one might be interested in translational motion in a specific direction, for example in the relative posteroanterior motion of two neighbouring vertebrae in the plane of the intervening disc. A pure rotation does not vividly describe this component of the motion. Secondly it may occur in pathologic cases that the actual motion is purely translational. In such a case the centre of rotation moves to infinity if the ‘‘pure rotation’’ description is adopted. In addition it holds that centres of rotation far away from the moving object can be determined with low precision only. Thirdly, it is difficult to scale the location of a centre of rotation determined in one spine to the given geometry of another spine. Dvorak et al. [7] and Lin et al. [8] partitioned the relative movement of cervical vertebrae into rotational and translational components. Translation measure-
ments were, however, done in mm from the films. This prohibits collection of normal data as differences in radiographic magnification and stature cannot be corrected for. For these reasons, and guided by a previous study of segmental motion in the lumbar spine [9], the present study chose to describe segmental motion in the cervical spine by a combination of rotation and posteroanterior translation, the latter being measured in the plane of the disc and quoted in relative units. A new protocol for documenting segmental motion from lateral radiographic views in flexion and extension was developed with special emphasis on minimising measurement errors and on excluding subjective influence. Normal data for rotational and translational motion are presented which will serve in future studies for documenting segmental motion abnormalities.
2. Methods The new protocol documents segmental motion of segments C0/C1–C6/C7 from sets of two lateral radiographic views taken in extension and flexion. The protocol is based on landmarks identified on the skull and computer-aided location of objective landmarks on vertebrae C1–C7. The parameters describing rotational and translational motion are derived from these landmarks in such a fashion that the result is virtually uninfluenced by radiographic distortion and magnification. Special control of patient alignment with respect to radiographic film and tube is not required; normal positioning suffices. Thus retrospective studies using existing radiographs are feasible. The definition of rotational and translational motion is outlined first for segments C3/C4–C6/C7 (Fig. 1). For segments C0/C1–C2/C3, the definitions require logical modifications. Corners 1–4 are located on the outer contours of the vertebral bodies by a computerised algorithm (see Appendix A). The centre point is the geometric centre of corners 1–4. The vertebral midplane is defined as a line running through the midpoints between corners 1, 3 and corners 2, 4, respectively. The angle between two vertebrae is given by the angle between their midplanes. The angle is counted positive if the wedge opens anteriorly. (The angle shown in Fig. 1 thus bears a positive sign.) Rotational motion of a segment is defined as the difference of the angle in extension minus the angle in flexion. Rotational motion is quoted in degrees. Perpendiculars are constructed from the centre points of adjacent vertebrae onto the bisectrix between the midplanes. Posteroanterior displacement is defined as the distance between those points where the perpendiculars intersect the bisectrix. Thus, displacement (and consequently translational motion) is measured along a
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
23
Fig. 2. Definition of the angle for the segment C0/C1.
Fig. 1. Definition of angle and displacement for motion segments C3/ C4–C6/C7.
direction coinciding in good approximation with the midplane of the disc. Displacement is counted positive if the projection of the cranial centre point is located anteriorly from the projection of the caudal centre point. (The displacement shown in Fig. 1 thus bears a negative sign.) To correct for radiographic magnification and variation in stature, displacement measured in millimeters is divided by the mean depth of the caudal vertebra. The mean depth is the mean of the distance of corners 1, 2 and 3, 4, respectively. Posteroanterior translational motion is given by the difference of the displacement in extension minus the displacement in flexion. As quotients of lengths, displacement and translational motion are dimensionless quantities. Previous work [9–11] ascertained that in lumbar vertebrae relative location of midpoints between the anterior and posterior vertebral corners, location of centre points, mean depth as well as location and orientation of midplanes and their bisectrix are virtually independent of distortion in central projection and of small alignment errors of the patients. As the definition of landmarks and derived parameters is similar for cervical and lumbar vertebrae, rotational and translational motion, as defined here, are virtually uninfluenced by distortion and patient alignment errors as well. For segment C0/C1 (Fig. 2), the angle is given by the angle between the McGregor line, i.e. the tangent from the posterior rim of the palatum durum onto the contour of the occiput, and a line connecting the centres of
area of the medullary cavities of the anterior and posterior arch of C1. Rotational motion of a segment is defined as the difference of the angle in extension minus the angle in flexion. It is to be added that the McGregor line will shift if the head is tilted sideways. Thus the C0/ C1 angle will depend on patient alignment. Posteroanterior displacement and translational motion are not defined for C0/C1. For segment C1/C2 (Fig. 3) definition of angle and displacement are based on the landmarks of C1 (centres of the marrow cavities) and the caudal corners 3 and 4 of C2. The unique shape of dens and corpus axis prohibits definition of four vertebral corners; a landmark placed at the tip of the dens proved to be unreliable. Objective location of caudal corners 3 and 4 is described in Appendix A. The angle between C1 and C2 is given by the angle between the line running through the centres of the marrow cavities of C1 and the line through corners 3 and 4 of C2. Posteroanterior displacement is given by the distance between the projection of the midpoint of the line connecting the marrow cavities of C1 and the projection of the midpoint of the line connecting corners 3 and 4 of C2 onto the bisectrix between the two lines. Rotational and translational motion are then defined as above. The value of translational motion measured in millimeters is divided by the distance between corners 3 and 4 of C2. For seg-
Fig. 3. Definition of angle and displacement for segment C1/C2.
24
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
ment C2/C3 (Fig. 4) analogous definitions for angle, displacement, rotational and translational motion are chosen. The distance between the dens and the inner surface of the anterior arch of the atlas, in the following termed ‘‘dens–atlas gap’’, is defined as the distance between those points where the line connecting the centres of the marrow cavities of C1 intersects the contours of the dens and the anterior arch of the atlas (Fig. 3). To correct for differences in radiographic magnification, this distance is divided by the distance between corners 3 and 4 of C2. The change in the dens–atlas gap is given by its value in extension minus its value in flexion. The technical procedure for measuring rotational and translational motion consists in identifying the posterior rim of the palatum durum, the contour of the occiput, the contours of the anterior and posterior arch of C1 and the contours of the marrow cavities of the arches, the contour of the dens and corpus axis, and the contours of vertebral bodies C3–C7 in both the flexion and the extension radiographs. The location of the posterior rim of the palatum durum, all contours and handmarked corners, serving as starting points for the iterative corner-locating algorithm, are mapped onto transparent foils. Points and contours are digitised (point density 5 per mm, precision 0.125 mm). Series of computer programs check geometric properties of the contours, locate corners, and calculate derived geometric measures as well as rotational and translational
motion for all segments imaged on each set of radiographs.
3. Material Sets of lateral radiographs of the cervical spine taken in active maximum flexion and extension were collected from archives of five medical institutions in Iceland, Norway, the Netherlands and Germany. From the total number of 137 sets, 101 stemmed from female and 36 from male, skeletally mature subjects in the age range between 16 and 58 yr (mean age 33 yr for both genders). The majority of radiographs stemmed from healthy volunteers who had participated in previous studies conducted by other authors. The remaining radiographs had been taken to rule out a variety of diseases. These sets had all been inspected by radiologists and classified as exhibiting no pathological findings. Not all of the 137 sets imaged the occiput and the palatum durum on both the flexion and the extension views. Furthermore, a portion of the sets imaged only vertebrae distal to C2. C7 was imaged in only a few sets. For these reasons, the number of entries in the result tables varies for the different segments and is generally lower than 137. From a sub-set of 40 subjects, radiographs imaging C3–C7 and taken at intermediate postures (erect and medium flexion) were available in addition to the views taken in maximum extension and flexion.
4. Error study
Fig. 4. Definition of angle and displacement for C2/C3.
As stated above, a previous study on segmental motion of the lumbar spine served as a guide on how to minimise errors resulting from radiographic distortion and patient alignment. Nevertheless, it seemed desirable to re-assess measurement precision in view of the fact that dimensions of cervical vertebrae are small compared with lumbar ones, while the radiographic magnification is approximately identical for lateral views of the cervical and lumbar spine. The small dimensions of the cervical vertebrae decrease distortion effects on the one hand but tend to increase identification and mapping errors of the bony contours on the other. Six deepfrozen cervical spine specimens comprising vertebrae C1–C7 were each radiographed in nine different projections, longitudinally aligned as well as tilted by 5° and axially rotated through 5° with respect to the film. All 54 views were evaluated independently by two observers. In the absence of measurement errors, the angle, displacement and dens–atlas gap should yield identical values within each set of the nine views of each specimen. The actual scatter of the results directly quantifies measurement precision.
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
For determination of segmental motion, the 137 sets of flexion–extension views were processed in approximately equal parts by two observers. To assess reproducibility in the measurement of rotational and translational motion, seven sets were evaluated by both observers and seven sets were evaluated twice by one observer, but at a 6-month interval. In both cases, evaluation comprised identification and mapping of contours on transparent foils (in no case had marks been placed on the radiographs), digitisation and computation of the motion parameters. The two-sided t-test for paired measurements, level of significance 0.05, was employed to evaluate the inter- and intra-observer tests. The additional radiographs in the sub-set of the material, taken at intermediate extension and flexion angles, were used to verify the assumption of a linear dependence of posteroanterior displacement on the angle of rotation. For this purpose the deviation of the posteroanterior displacement observed at the intermediate angles from those values calculated from the maximum extension and flexion data under the assumption of a strictly linear dependence was computed and averaged, and compared with the measurement precision.
25
5. Results 5.1. Measurement errors Measurement precision of the segmental angle determined from the sets of specimen radiographs ranged for segments C1/C2–C6/C7 between 1.1° and 1.9° with negligible differences between the two observers (Table 1). For rotational motion determined from in vivo flexion–extension views, inter- and intra-observer tests resulted in SDs of 1.98° and 1.91°, respectively (Tables 2 and 3). Comparison shows the error in rotational motion (i.e. for angle differences) to be slightly inferiorpto the error of an angle measurement multiplied by 2. This is due to the fact that the simultaneous availability of both an extension and a flexion radiograph assists the observer in correctly identifying the relevant bony contours. (The contours themselves are usually differently shaped due to projection differences between the two views.) The error of displacement determined from specimen radiographs ranged among segments between 0.0181 and 0.0312 (Table 1). Inter- and intra-observer SDs for translational motion determined from in vivo flexion–extension views amounted to 0.0473 and 0.0330, respectively, equivalent to approx. 4.7% or 3.3% of
Table 1 Measurement precision (SD), determined from radiographs of six cervical spine specimens each radiographed in nine different projections Segment
Angle, observer 1
Angle, observer 2
Displacement, observer 1
Displacement, observer 2
Dens–atlas gap, observer 1
Dens–atlas gap, observer 2
C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7
1.1123 1.9347 1.6867 1.7658 1.4551 1.2228
1.2384 1.7253 1.3778 1.3793 1.2955 1.2138
0.0297 0.0268 0.0290 0.0309 0.0181 0.0195
0.0312 0.0204 0.0208 0.0248 0.0208 0.0194
0.0149 – – – – –
0.0135 – – – – –
Mean
1.5296
1.3717
0.0257
0.0229
Measurement of angle (degrees), displacement and dens–atlas gap (both in units of vertebral depth) performed by two observers. Variances were computed for each segment of each specimen and then averaged over the six specimens. The table quotes the square root of these variances.
Table 2 Inter-observer error for rotational and translational motion determined from n pairs of flexion–extension radiographs Level C0/C1 C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7 All segments
n 7 7 7 7 7 6 1 42
Rotational motion mean deviation and SD
n
0.3660 )0.3080 0.3010 0.8437 0.6004 )1.4299 3.6401
–
(1.7282) (1.5739) (1.7104) (1.1048) (2.7072) (2.2821) –
0.1829 (1.9849)
Translational motion mean deviation and SD 7 7 7 7 6 1
Not defined )0.0111 (0.0821) 0.0196 (0.0339) )0.0002 (0.0288) )0.0131 (0.0376) )0.0073 (0.0359) )0.0659 –
35
)0.0041 (0.0473)
Rotational motion in degrees, translational motion in units of the depth of the caudal vertebra. SD in parentheses. Translational motion not defined for C0/C1. All mean deviations are not significantly different from zero ða ¼ 0:05Þ.
26
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
Table 3 Intra-observer error for rotational and translational motion determined from n pairs of flexion–extension radiographs Level
n
C0/C1 C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7 All segments
7 7 7 7 7 5 2 42
Rotational motion mean deviation and SD
n
0.0429 )0.2426 0.3021 0.4464 0.1111 )0.0681 )1.5717
–
(0.8588) (1.5096) (1.8113) (2.8810) (2.4639) (2.0781) (0.3078)
0.0271 (1.9054)
Translational motion mean deviation and SD 7 7 7 7 6 1
Not defined )0.0095 (0.0505) 0.0036 (0.0324) )0.0154 (0.0220) )0.0107 (0.0346) )0.0282 ð0:0200Þ )0.0159 (0.0239)
35
)0.0113 (0.0330)
Rotational motion in degrees, translational motion in units of the depth of the caudal vertebra. SD in parentheses. Translational motion not defined for C0/C1. All mean deviations, save the one marked with *, are not significantly different from zero ða ¼ 0:05Þ.
vertebral depth (Tables 2 and 3). For a vertebra of 15 mm depth, this corresponds to approximately 0.7 mm. For comparison, Johnsson et al. [12] using RSA reported errors (SD) between 0.16 and 0.22 mm for translation measurements. RSA is, however, in general not adapted to measure translation in specific anatomic directions (here: the plane of the disc) but rather along the axes of a laboratory coordinate system. The magnitude of the dens–atlas gap was determined from specimen radiographs by the two observers with errors of 0.0149 and 0.0135, respectively (Table 1) and from single in vivo extension- or flexion views with inter- or intra-observer SDs of 0.0235 and 0.0257, respectively (Table 4). The change in the dens–atlas gap (Table 4) was determined from in vivo flexion–extension views with inter-observer or intra-observer SDs of 0.0262 and 0.0121, respectively, equivalent to approx. 2.6% and 1.2% of the depth of C2 (Table 4). Assuming a depth of C2 of 15 mm, this corresponds to less than 0.4 mm.
5.2. Rotational motion The range of rotational motion observed in the present cohort as well as its SD are compiled in Table 5. 5.3. Translational motion As translational motion occurs simultaneously with rotational motion, ranges of translational motion are not quoted. Rather the measured magnitude of translational motion of each individual segment is divided by its rotational range of motion to obtain the slope of translation vs. rotation. Table 6 lists average values of the ‘‘translational motion per degree of rotation’’. Only those segments contribute to the data in Table 6 where the rotational motion amounted to at least 7.5° (approx. 4 SD of the measurement error of rotational motion). Inclusion of data from segments exhibiting very small rotational motion would induce imprecision due to the measurement errors both of angle and of displacement.
Table 4 Inter- and intra-observer error for the magnitude of the dens–atlas gap in flexion or extension as well as for its change in the course of rotational motion
Magnitude of dens–atlas gap Change in dens–atlas gap
n
Inter-observer error
Intra-observer error
14 7
0.0177 ð0:0235Þ )0.0149 (0.0262)
)0.0061 (0.0257) )0.0020 (0.0121)
Magnitude and change in dens–atlas gap change in units of the depth of C2. SD in parentheses. Mean deviations marked * are significantly different from zero ða ¼ 0:05Þ. Table 5 Range of rotational motion observed in the cohort investigated Level
n
Range (°) females
n
Range (°) males
C0/C1 C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7
23 61 57 92 95 92 23
12.6 10.9 8.4 15.2 17.0 17.9 11.4
18 36 34 34 33 27 10
14.5 11.6 7.8 11.6 14.4 12.2 9.8
(6.83) (4.87) (3.43) (4.72) (5.46) (6.60) (6.82)
SD in parentheses. n denotes the number of segments measured.
(7.65) (4.57) (3.09) (3.57) (4.55) (5.19) (5.73)
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
27
Table 6 Magnitude and direction of posteroanterior translational motion per degree of rotation in a healthy, adult cohort Level
Females, n
Females, change in posteroanterior displacement per degree of rotation
Males, n
Males, change in posteroanterior displacement per degree of rotation
C1/C2 C2/C3 C3/C4 C4/C5 C5/C6 C6/C7
46 33 86 89 84 15
+0.01435 (0.00680) )0.00826 (0.00457) )0.00970 (0.00341) )0.00886 (0.00294) )0.00490 (0.00212) )0.00151 (0.00274)
30 17 31 31 21 6
+0.01232 (0.00800) )0.00827 (0.00375) )0.00708 (0.00266) )0.00702 (0.00221) )0.00599 (0.00363) )0.00230 (0.00179)
Translational motion is measured in units of the mean depth (or in case of C1/C2: of the depth) of the caudal vertebra of each segment; translation is thus a dimensionless number. SD in parentheses. Data from only those sets of flexion–extension views contribute, where the angular range of motion amounted to at least 7.5°. Translation per degree of rotation is significantly different between females and males for segments C3/C4 and C4/C5 (twosided t-test, a ¼ 0:05).
The analysis of those sets of radiographs where, in addition to views in maximum flexion and extension, two intermediate views in erect posture and medium flexion were processed, showed that deviation of the measured displacement at the intermediate postures from a straight line connecting the data points of maximum flexion and extension was virtually equal to the measurement error for displacement. In consideration of the measurement precision of the protocol presented in this study, this justifies the assumption of a linear relation between rotation and translation. 5.4. Dens–atlas gap As in the case of translational motion, the change in the dens–atlas gap was expected to depend on the magnitude of the rotational motion. Table 7 lists the change in the gap size per degree of rotational motion. Again, only those segments contribute to the data in Table 7 where the rotational motion of C1/C2 amounted to at least 7.5°.
reported [3] when measuring rotational motion from lateral flexion–extension views, using a protocol different from the one employed in this study. Ryd et al. [13] determined the precision (SD) of radiostereometric analysis (RSA) when measuring rotational motion in the cervical spine in a cohort of fusion patients to range between 0.18° and 2.26°. While RSA is generally more precise than measurements from plain radiographs, the authors showed that RSA accuracy depends critically on the geometric configuration of the implanted markers. In unfavourable configurations [12], measurement accuracy at the cervical spine may fall substantially short of the values previously obtained from the lumbar spine or from rigid-body RSA laboratory studies. The range of rotational motion observed in the present cohort complies with results of previous studies [2,3,14]. Fig. 5 gives an example of individual rotational motion data compared with the normal range. The data of this subject reveal no pathological findings. However, not much importance would probably even be attached to cases where rotational motion of all segments
6. Discussion Using the new protocol, the measurement error (SD) for rotational motion, determined from specimen experiments as well as from inter- and intra-observer tests, is slightly less than 2°. This complies well with intra- and inter-observer errors (SD) of 1.8° and 1.2°, respectively, Table 7 Dependence of the magnitude of the dens–atlas gap on the angle between C1 and C2 n
Change in dens–atlas gap per degree of rotation, females
n
Change in dens–atlas gap per degree of rotation, males
46
)0.00281 (0.00415)
30
)0.00268 (0.00474)
The gap is measured in units of the depth of C2. Data from only those sets of flexion–extension views contribute, where the angular range of motion amounted to at least 7.5°; SD in parentheses. The two-sided ttest with a ¼ 0:05 indicates no significant gender-related difference.
Fig. 5. Example of documentation of rotational motion in the individual case and its comparison with normal values. In this as well as in the following figures: solid line: normal mean; error bars: measurement errors (1 SD). The graph shows no pathological deviation from normal rotational motion.
28
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
deviated in the same sense from normal. The reason is that 95% confidence limits for rotational motion are broad and individual motion is influenced by motivation or pain. Only cases where all segments save one exhibit virtually normal ranges of rotational motion, while one segment exhibits a substantial deviation from normal, might point to an abnormality (Fig. 6). More important than comparisons with the normal range, the precise measurement of rotational motion offers a precise tool to investigate and document effects of conservative or operative treatment. Examples are the measurement of suspected residual motion in fused segments or potential changes in the motion pattern of segments adjacent to a fused one. While measurement accuracy for rotational motion is on average inferior to RSA, the new protocol is (in contrast to RSA) not restricted to postoperative investigations. As demonstrated before [2,8] rotational motion in cervical segments is always linked with simultaneous translational motion. As this study determines translational motion along the midplane of the disc, there are no previous studies available for quantitative comparison. Translational motion per degree of rotation (Table 6) amounts to slightly less than 0.01 (i.e. less than 1% of vertebral depth) per degree of rotation. It differs among genders and levels and exhibits a considerable biological variation. A positive sign of translational motion per degree of rotation means that when moving in extension the cranial vertebra of the segment translates in anterior direction. This is the case for the segment C1/C2. In all other segments the negative sign indicates that when moving in extension the cranial vertebra translates into posterior direction. This complies qualitatively with Penning’s [4] earlier findings for the location of the
Fig. 6. Example of documentation of rotational motion where motion of one single segment (C5/C6) deviates substantially from normal while the motion of the other segments is well within the normal range. The case shown exhibited no radiological abnormality. Clinical significance of such isolated deviations from normal remains to be shown in future studies.
centre of rotation. The direction of segmental motion is explained by the shape of the cervical spine articulations. For a recent review see [1]. Knowledge of ‘‘translational motion per degree of rotation’’ permits a comparison of individual translation data with normal ones. An individual range of translational motion cannot be directly compared with a norm, because the individual rotational motion may (for any reasons whatever) deviate uncontrollably from normal. For the purpose of comparison, the normal value of ‘‘translational motion per degree of rotation’’ (Table 6) is multiplied by the individual, actually performed range of rotational motion. This predicts the normal translational motion to be expected for the individual under investigation. Comparison of the actually measured translational motion with the predicted one permits individual segments to be classified as normal, hyper- or hypomobile with respect to translation. It is unlikely that comparing actual translation with its predicted value will be confounded by motivation or pain, as the magnitude of rotational segmental motion can be voluntarily controlled, but not the accompanying translational motion. Fig. 7 shows an example of comparing individual translational motion with the values predicted from the normal database of ‘‘translational motion per degree’’, thus allowing for the given range of rotational motion when inspecting translation. The range of variation of 1:96 SD about the predicted norm is calculated from the variation of translational motion per degree and the error of the rotation measurement. The error bars of the data points designate the measurement error (1 SD) of the translation measurement. The data shown in Fig. 7 reveal no pathological findings. Fig. 8 shows an example where translational motion in one segment (C3/C4) deviates by approx. 3 SD from normal. It remains to be shown what clinical significance can be attached to such findings.
Fig. 7. Example of documentation of translational motion in the individual case; data for the same subject as in Fig. 5. No deviation from normal translational motion.
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
In our material investigated there was a trend for the dens–atlas gap to be smaller in extension than in flexion. This is reflected by the negative sign of the ‘‘change in gap size per degree of rotational motion’’ (Table 7). There was, however, a considerable biological variation. In a fraction of the cohort the gap size actually increased in extension. In the material investigated, no uniform prescriptions how to flex or extend had been prescribed. Thus, part of the variation may be due to different motion patterns, i.e. performing forward flexion more via a ‘‘nodding’’ motion of the head or more by a forward bending of the cervical spine. In addition, measurement errors may confound the relation between rotational motion and gap size, as gap size is small and minute errors in locating and mapping the opposing contours of dens and atlas contribute to the observed variation. As an example Fig. 9 shows the change of the dens–atlas gap together with the appertaining predicted normal value. Like in the case of translation, the prediction is given by the product of the ‘‘change of gap size per degree’’ of normals and the ‘‘C1/C2 rotation’’ actually performed.
29
To summarise, a new protocol for documenting segmental motion of segments C0/C1–C6/C7 is presented and validated. Measurements are based on lateral flexion–extension radiographic views taken in normal clinical settings using computer-aided, objective algorithms. The error (SD) of a rotational motion measurement amounts to slightly less than 2°. The error (SD) of a translational motion measurement amounts to slightly less than 5% of vertebral depth; for a vertebra of 15 mm depth this corresponds to an error of 0.75 mm. Normal data for rotational and posteroanterior translational motion of cervical motion segments are presented, permitting comparison of individual motion data with the normal database. While rotational motion, influenced by age, pain and patient compliance, usually varies widely, the new protocol permits precise inspection of translational motion independent of the aforementioned factors. The new protocol can be employed to diagnose motion abnormalities like translational hypo- or hypermobility and to monitor conservative or operative treatment of the cervical spine.
Acknowledgements The authors thank E. Kristjansson, Reykjavik, Iceland, K. Dale M.D. Ph.D., Rikshospitalet, University Hospital of Oslo, Norway, and Dr. D.H.W. Sch€ onfeld, Sint Maartenskliniek, Nijmegen, The Netherlands, for their most valuable assistance in the collection of the radiographs of normal subjects.
Appendix A. Definition of landmarks
Fig. 8. Example of documentation of translational motion, where motion of one single segment (C3/C4) deviates by approximately 3 SD from the norm. The clinical significance of such deviations from normal remains to be shown in future studies.
Fig. 9. Example of the change of the dens–atlas gap size when moving from extension to flexion. The solid line and the shaded area depict the normal range 1:96 SD of the change of gap size, predicted from the normal gap size change per degree of rotation and the actual range of rotation of this subject (same subject as in Figs. 5 and 7). No pathological deviation from normal.
The essential aspect of landmark (‘‘corner’’) location is to minimise subjective observer influence. Instead of using hand-marked locations, landmarks are defined by applying mathematical procedures based on objective geometric properties of vertebral contours. Corner location is first described for vertebrae C3–C7. Due to the divergent shape of C2, definitions are appropriately modified. C0 (skull) and C1 require specific definitions. C3–C7. Starting from hand-marked corners 1h to 4h (Fig. 10), the vertebral midplane is constructed through the midpoints between corners 1h, 3h and 2h, 4h respectively. Reference lines at predefined angles a with respect to the midplane are drawn through the centre point P (geometric centre of points 1h to 4h). Corners are defined as points of maximum distance from these reference lines. Fig. 10 illustrates the procedure with the example of corner 4. 4h denotes the hand marked and 4c the computed corner location. Once corners 1c–4c have been located according to this algorithm, the procedure is repeated four times in an iterative fashion. Angles a were previously determined from a preparatory study on
30
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31
Fig. 11. Computer-aided location of corners on the contour of vertebra C2.
Fig. 10. Computer-aided location of corners on the contours of vertebrae C3–C7.
cervical spine specimens radiographed in nine slightly different projections as those angles which permit ‘‘aiming’’ to be done from the reference line ‘‘perpendicularly into the corner region’’ and provide the best reproducibility of corner location within sets of radiographs of identical specimens. Table 8 lists the set of angles used. (If the images of the vertebral bodies approximated a square, the angles would be close to +45° or +135°. Their deviation from these values actually reflects the rhomboid shape of cervical vertebral body contours.) C2. Due to the biological variance of the shape of C2, its tip (the cranial corner) proved to be an unreliable landmark for segmental motion measurements. Measurement of motion is thus based only on its caudal corners 3 and 4 (Fig. 11). In C2, the line connecting corners 3h and 4h substitutes the midplane; a point on the perpendicular bisector at 1/2 the distance 3h–4h above this line substitutes the centre point P. Again, reference lines at a predefined angles a are drawn through P and the computed corner points 3c and 4c are defined as points of maximum distance from these lines. Fig. 11 illustrates this for corner 4 where 4h denotes the initial hand-marked and 4c the computed corner location. After corners 3c and 4c have been determined, the procedure is repeated four times in an iterative fashion. The angles a employed are listed in Table 8. C1. The shape of the outer cortex of the arches, especially of the posterior one, depends critically on the Table 8 Set of angles a employed for corner location on the contours of vertebrae C2–C7 Vertebra
Corner 1 (°)
Corner 2 (°)
Corner 3 (°)
Corner 4 (°)
C2 C3–C7
– +40
– +133
+157 +149
+31 +47
projection. Thus, points selected on the outer cortex of the arches proved to be unsuitable for precise determination of rotational and translational motion. Instead, the geometric centres of the areas of the marrow cavities of the anterior and posterior arch of C1 (cf. Fig. 2), computed from their digitised periphery, are used as landmarks. C0. The posterior rim of the palatum durum is used as a landmark for construction of the McGregor line, i.e. the tangent from this point onto the occiput.
References [1] Bogduk N, Mercer S. Biomechanics of the cervical spine. I: normal kinematics. Clin Biomech 2000;15:633–48. [2] Dvorak J, Froehlich D, Penning L, Baumgartner H, Panjabi MM. Functional radiographic diagnosis of the cervical spine: flexion/extension. Spine 1988;13:748–55. [3] Lind B, Sihlbom H, Nordall A, Malchau H. Normal range of motion of the cervical spine. Arch Med Phys Rehabil 1989;70:692–5. [4] Penning L. Normal movements of the cervical spine. Am J Roentgenol 1978;130:317–26. [5] Amevo B, Worth D, Bogduk N. Instantaneous axes of rotation of the typical cervical motion segments: II. Optimization of technical errors. Clin Biomech 1991;6:38–46. [6] Amevo B, Worth D, Bogduk N. Instantaneous axes of rotation of the typical cervical motion segments: a study in normal volunteers. Clin Biomech 1991;6:111–7. [7] Dvorak J, Panjabi MM, Novotny JE, Antinnes JA. In vivo flexion/extension of the normal cervical spine. J Orthop Res 1991;9:828–34. [8] Lin RM, Tsai KH, Chu LP, Chang PQ. Characteristics of sagittal vertebral alignment in flexion determined by dynamic radiographs of the cervical spine. Spine 2001;26:256–61. [9] Frobin W, Brinckmann P, Leivseth G, Biggemann M, Reikeras O. Precision measurement of segmental motion from flexion– extension radiographs of the lumbar spine. Clin Biomech 1996;11:457–65. [10] Brinckmann P, Frobin W, Biggemann M, Hilweg D, Seidel S, Burton K, et al. Quantification of overload injuries to thoracolumbar vertebrae and discs in persons exposed to heavy physical exertions or vibration at the work place. Part I. The shape of vertebrae and intervertebral discs – study of a young healthy population and a middle aged control group. Clin Biomech 1994;9(Suppl 1):S1–S83.
W. Frobin et al. / Clinical Biomechanics 17 (2002) 21–31 [11] Frobin W, Brinckmann P, Biggemann M, Tillotson M, Burton K. Precision measurement of disc height, vertebral height and sagittal plane displacement from lateral radiographic views of the lumbar spine. Clin Biomech 1997;12(Suppl 1): S1–S63. [12] Johnsson R, Axelson P, Str€ omqvist B. Mobility provocation of lumbar fusion evaluated by radiostereometric analysis. Acta Orthop Scand 1996;67(Suppl):45–6.
31
[13] Ryd L,Yuan X, L€ ofgren H. Methods to determine the accuracy of radiostereometric analysis. In: L€ ofgren H, editor. Outcome and bone grafts in surgical treatment of cervical disc disease. Link€ oping Univ. Med. Diss. No. 621, Link€ oping, 2000. [14] Van Mameren H, Drukker J, Sanches H, Beursgens J. Cervical spine motion in the sagittal plane (I). Range of motion of actually performed movements, an X-ray cinematographic study. Eur J Morphology 1990;28:47–68.