Eur Spine J (1992) 1:178-184

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Viscoelasticity of the alar and transverse ligaments j. M611er 1,2, L.-P. Nolte 3, H. Visarius 3, R. Willburger 1, J. J. Crisco 4, and M. M. Panjabi 3 1Department of Orthopaedic Surgery, St. Josef Hospital, Ruhr University Bochum, Federal Republic of Germany 2Department of Surgery, Augusta-Krankenanstalten, Ruhr University Bochum, Federal Republic of Germany 3Bioengineering Center at Wayne State University, Detroit, Michigan, USA 4Biomechanics Laboratory Yale School of Medicine, Connecticut, USA

Visco-61asticit6 des ligaments alaires et transverse R6sum6. L'articulation occipito-atlanto-axo'/dienne est l'une des plus complexes du rachis humain. Les ldsions traumatiques ou inflammatoires de cette r6gion peuvent conduire ~ l'instabilit6 et 5 des troubles neurologiques importants. Cette 6tude rapporte les r6sultats d'une 6tude anatomique et biom6canique de 13 spdcimens de rachis cervical sup6rieur et met l'accent sur le comportement visco-dlastique des ligaments alaires et transverse. Des essais de mise en tension ont 6t6 r6alisds sur 25 ligaments alaires et 11 ligaments transverses, en restant en de95 du point de rupture. Ils ont 6t6 effectu6s sur un appareil monoaxial, selon trois niveaux de charge diffdrents: 0.1 ram/s, 1.0 mm/s et 10.0 mm/s. La d6tente ligamentaire a 6t6 en outre 6tudi6e pendant 300 s. Chaque ligament a montr6 une zone neutre initiale (NZ) dans laquelle aucune force de tension ne pouvait Otre mesurde au cours du cycle d'essai. Cette zone neutre 6tait plus importante pour les ligaments alaires que pour les ligaments transverses, compte tenu de la longueur ligamentaire mesur6e in situ (11.2 contre 18.1ram en moyenne). L'augmentation de la ddformation axiale a conduit & une augmentation des contraintes dans tousles ligaments. L'hyst6r6sis, c'est ~ dire la perte d'6nergie prdsent6e par le matdriel visco-61astique soumis 5 des cycles de mise en charge et d6charge, augmentait avec l'amplitude du d6placement et l'intensit6 des forces de tension. En position neutre, les ligaments alaires 6taient d6tendus sur t o u s l e s sp6cimens. Lors de la rotation axiale, les deux ligaments alaires se sont mis en tension. La r6sistance du ligament 5 la rotation s'est trouv6e accrue en fin d'amplitude. La zone neutre explique la laxit6 des ligaments en position interm6diaire et permet la mobilit6 du rachis cervical supdrieur avec un minimum de ddpense d'6nergie. Les ligaments se tendent sous des charges plus 61ev6es et par consdquent contribuent ~ la limitation de R O M dans l'articulation occipito-atlanto-axo'fdienne. Correspondence to: Dr. J. M611er, Department of Surgery, Augusta-Krankenanstalten, Ruhr University Bochum, Bergstrasse 26, W-4630 Bochum 1, FRG

Mots-cl6s: Rachis cervical supdrieur - Ligament alaire Ligament transverse - Anatomie - Biom6canique Summary. The occipito-atlanto-axial joint is the most complex one of the human spine. Traumatic or inflammatory lesions in this region may lead to instability and neurological symptoms of clinical importance. This study reports the results of anatomical and biomechanical examination of 13 human upper cervical spine specimens and focuses on the viscoelastic behavior of the alar and transverse ligaments. Non-destructive tensile testing was performed on a uniaxial testing machine with 25 alar and 11 transverse ligaments at three different load rates of 0.1 ram/s, 1.0 ram/s, and 10.0 mm/s. The ligaments were further tested for relaxation over 300 s. Each ligament exhibited an initial neutral zone in which no tensile force could be measured during cyclic testing. This neutral zone was more significant in the alar ligaments than in the transverse ligaments with respect to the measured in situ length of the ligaments ( l l . 2 v s 18.1mm on average). Increasing axial deformation led to increased load in all ligaments. Hysteresis, i.e., the energy loss exhibited by viscoelastic material subjected to loading and unloading cycles, increased with higher displacement rates and higher tensile forces. In neutral position the alar ligaments were lax in all specimens. During axial rotation both alars tightened. Ligamentous resistance increased as the end of the range of motion (ROM) was approchaed during rotation. The neutral zone explains the laxity of the ligaments in midposition and allows mobility of the upper cervical spine with minimum expenditure of muscular energy. The ligaments become stiffer under higher loads and therefore contribute to a limitation of the R O M in the occipitio-atlanto-axial joint. Key words: Upper cervical spine - Alar ligament - Transverse ligament - Anatomy - Biomechanics

As regards anatomy and kinematics, the occipital-atlantoaxial joints are the most complex in the human axial

179 skeleton [24]. Because of the particular anatomical and biomechanical situation, injuries of the occipito-atlantoaxial region are significantly different from other cervical lesions. As c o m p u t e d t o m o g r a p h y (CT) and magnetic resonance imaging ( M R I ) have allowed m o r e precise visualization of soft tissue injuries, these lesions have gained in clinical importance. In studies of 427 cervical spines o b t a i n e d f r o m accident victims Saternus [21] detected ligamentous lesions in nearly 80% of cases. In p o s t m o r t e m examinations and experimental in vitro studies, hidden soft-tissue injuries of the u p p e r cervical spine were f o u n d m o r e often than expected [11, 13, 14]. T h e ligamentous structures of the occipito-atlantoaxial joint are of i m p o r t a n c e for the clinical stability of the u p p e r cervical spine. L i g a m e n t o u s lesions m a y lead to hypermobility and instability of the u p p e r cervical spine, resulting in clinical s y m p t o m s such as pain, vertigo neurologic deficits, cervical nystagmus [12], and vertebral artery insufficiency. Nevertheless, despite its clinical i m p o r t a n c e , there are only a few anatomical and biomechanical studies of this region, with s o m e w h a t controversial findings. Several hypotheses exist on the descriptive and functional a n a t o m y of the alar and transverse ligaments. While a majority of the studies f o u n d the alar ligaments to c o n n e c t the lateral parts of the dens axis with the condyles of the occiput [3, 9, 24], other authors described some parts of the alar fibers as inserting on the pars lateralis of the atlas [1, 4, 15, 17]. Investigations of the biomechanical function of the alar ligaments are similarly controversial [2]. With the lack of an intervertebral disc in the C0/C1 and the C1/C2 joints and a relatively flat facet joint at C1/C2, the alar ligaments limit axial rotation at C1/C2 [2, 24]. P r o b a b l y the m o s t c o m m o n hypothesis is the limitation of rotation by the contralateral alar ligament, i.e., rotation to the right is limited by the left alar ligament and vice versa [4, 9, 23, 24]. H o w e v e r , in an experimental in vitro study Panjabi et al. [18] f o u n d a significantly increased range of m o t i o n ( R O M ) in axial rotation in both directions after dissection of a single alar ligament. Crisco et al. [2] developed a m a t h e m a t i c a l m o d e l to explain these experimental findings. T h e biomechanical function of the transverse ligament is less a subject of controversy: this ligament is widely believed to p r e v e n t anterior atlanto-axial luxation or fixation of the dens during axial rotation [5, 9, 17, 19, 24]. T h e p u r p o s e of this experimental in vitro study was an examination of the functional a n a t o m y and the viscoelastic b e h a v i o r of two i m p o r t a n t ligamentous structures of the occipito-axial joints: the alar and transverse ligaments. T h e experimental data were used for the develo p m e n t of a m a t h e m a t i c a l m o d e l of the e x a m i n e d ligaments [22].

in 0.9% sodium chloride solution-soaked gauze, and frozen immediately at -25~ Specimens from individuals with a history of rheumatoid arthritis or head or cervical spine injuries were excluded. After thawing at room temperature the posterior vertebral arch C1 was cut and taken away by means of an electrical power saw. Then the tectorial membrane and the cranial part of the cruciform ligament were removed. After preparation of the alar and transverse ligaments, close-up photographs of the ligaments in neutral position with a fade-in scale were taken with a reflex camera (Nikon FE1, Nikon Ltd., Japan). The neutral position of each specimen was defined according to White and Panjabi [24] by construction of an instantaneous axis of rotation for every specific movement and segment. Subsequent digitization of the close-up pictures allowed nondestructive, in situ determination of ligament length, fiber orientation, and insertion area. To remove the ligaments, finally, a midline incision of the anterior arch of the atlas was made and the joint capsules of atlas and axis were cut. The ligaments were taken for biomechanical testing in a bone-ligament-bone preparation. Immediately after preparation, the ligaments were embedded in a quick-setting polyester resin (Plastic Padding, Gothenburg, Sweden) using a specially developed molding device allowing exact fiber alignment according to the previously determined in situ position. During the whole preparation and testing cycle the ligaments were kept moist with 0.9% sodium chloride solution.

Testing device and control program The experiments were performed on a uniaxial testing device (Fig. l) driven by a precision stepper motor (Berger-Lahr Co., Lahr, Germany). The rotational motion of this motor was transformed into a translational motion to stretch the ligaments. A special molding technique was developed to align the load direction to be collateral to the ligament fibers. This procedure, in combination with variable grips to carry out necessary corrections, resulted in controlled axial attachment of the specimen to the testing device. The setup was controlled by a custom-made program allowing the tests to be driven under either load or deformation control. The actual loads were measured using a precision Ioad cell (Hottinger Co., Germany). The axial deformation was controlled form the gear relating factors (translational/rotational) and checked with a linear variable-differential transducer (LVDT, Hottinger Co., Germany). Using this setup, discrete relations between the actual force in the ligament and the corresponding deformation were obtained. These relations were used in the data analysis to determine the free coefficients in the above-mentioned functions.

Materials and methdos

Specimens and preparation Thirteen C0-C2 specimens were obtained from fresh human cadavers with a mean age of 63.2 years (range 36-75 years), wrapped

Fig.1. The uniaxial testing machine on which the biomechanical experiments were peformed. The arrow points to a ligament prepared for testing

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Test protocol The ligaments were fitted on the uniaxial testing machine with exact alignment and an initial length identical to that in situ. After preconditioning over 10 cycles up to 20 N at a displacement rate of 1.0ram/s, nondestructive tensile testing over 10 cycles up to a predetermined displacement was performed with each ligament in a randomized order of three displacement rates (0.1 mm/s, 1.0 mm/s and 10.0 mm/s). The ligaments were then tested for relaxation over 300 s with a load reading taken every 0.25 s. Relaxation testing was undertaken at the same maximum tensile force as used during the cyclic testing.

Results

Anatomy Twenty-five alar and 11 transverse ligaments were obtained from 13 C 0 - C 2 specimens. One alar and two transverse ligaments were damaged during preparation and were excluded. The average length of the alar ligaments was 11.2 mm (range 9.6-12.4 ram). Ligament length was measured exactly in the midportion of the ligaments by digitization of the macrophotographs. Comparison of length between left and right alar ligaments showed no significant difference. The cross-sectional diameter, determined at the midsection of the ligaments with a caliper, was 6.0 • 3.8ram (range 4.0-8.7 x 3.16.6mm). The mean angle between the two alar ligaments was 166 ~ (range 143~176 The existence of the anterior atlantodental ligament, as described by Dvorfik and Panjabi [4], could not be definitely confirmed, but in four cases there was connective tissue between the dens and the anterior arch of the atlas. Dvorfik and Panjabi found a ligamentous connection between the dens and the lateral mass of the atlas as part of the alar ligament in 61% of their examined specimens. In our studies we saw this part insertion at the lateral mass of C1 in four

Fig. 3. Site as in Fig. 2. After axiaI rotation to the right both alar ligaments tighten (arrows). Symbols as in Fig. 2.

specimens (16%); in two cases it was found only unilaterally. In neutral position the alar ligaments were lax in all specimens (Fig. 2). During axial rotation both alars tightened (Fig. 3). Ligamentous resistance increased as the end of R O M was approached during rotation. However, a large portion of the R O M could be exploited without appreciable ligamentous resistance. Both alar ligaments became taut during axial rotation, independent of toward which side the rotation was carried out. The average length of the transverse ligaments was 18.1 mm (range 15.4-20.4 mm). In all specimens the transverse ligaments surrounded approximately half the dorsolateral circumference of the dens. The ligaments were flattened out in the contact area with the dens and showed a cartilaginoid consistency in this ara.

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-lO Fig. 2. The occipito-atlanto-axial joint after removal of the tectorial membrane and the posterior vertebral arch of C1. In the neutral position both alar ligaments are lax (arrows). A, left alar ligament; V, right alar ligament; [] transverse ligament; 9 top of dens axis

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Displacement [mml Fig. 4. Load-displacement curves of an alar ligament (no. 86/90) over ten cycles at 50Hz (0.1 mm/s). In the initial neutral zone no tensile force could be measured

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Displacement [mml Fig. 7. Load-displacement curves of a transverse ligament (no. 83/ 90) over ten cycles at 50Hz (0.1mm/s). The initial neutral zone was more significant in the alar than ligaments in the transvese ligaments with respect to the measured in situ length of the ligaments

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Biomechanical testing Five alar and four transverse ligaments from seven different specimens failed during tensile testing. Failure always occurred at the bone-ligament insertion area of the ligaments; no midrupture of the ligaments was seen. Of the remaining 27 ligaments each showed an initial neutral zone in which no tensile force was measured during cyclic testing (Figs. 4-8). This neutral zone was m o r e significant in the alar ligaments than in the transverse ligaments in relation to the measured in situ length of the ligaments. Increasing axial deformation led to increased load in all ligaments, Hysteresis, i.e., the energy loss exhibited by viscoelastic material subjected to loading and unloading cycles, increased with higher displacement rates and higher tensile forces.

Relaxation of the ligaments was highest during the initial 20 s of relaxation testing. Nearly 50% of the relaxation occurred in the first 10s of the test, followed by a slowly asymptotic relaxation curve parallel to the xaxis (Figs.9, 10).

Mathematical modeling To predict the biomechanical behavior of the cervical spine ligaments studied, a mathematical model based on Fung's quasi-linear viscoelastic theory was developed [10, 16]. In this, the history of the stress response is assumed to be constituted by the purely elastic response and a normalized, so-called relaxation function of the

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Cycles Fig. 9. The split-up of ten cycles of an alar ligament (no. 83/90) shows that relaxation of the ligaments also occurred during cyclic testing

Fig.ll. Mathematical modeling ( - , "SIGCAL") of the loaddisplacement curve (. . . . ,50 Hz, "SIGEXP") of an alar ligament (no. 86/90)

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time. In the present study the elastic and relaxation parts were assumed to be of the polynomial and logarithmic types, respectively. Closed-form solutions were derived for a full load cycle, i.e., loading and unloading of a specimen. The free coefficients of the corresponding relations for the viscoelastic stress response were determined using experimental data from proportional loading and relaxation tests and applying a nonlinear least square fit. Numerical prediction of the biomechanical properties were found to be in good agreement with those measured in our experiments. In particular, all characteristics of nonlinear viscoelastic soft tissue behaviour, i.e., significant nonlinearity, strain dependency, strain rate dependency, relaxation, and hysteresis, could be simulated (Fig. 11).

The method of measuring ligament dimensions by means of an in situ close-up photograph and subsequent digitization used in this study allows exact and nondestructive determination of the ligament length and fiber orientation. A similar method was used by Panjabi et al. [18], who attached markers with cynoacrylate glue to the ligaments and then took stereophotographs. Other researchers also carried out studies on the dimensions of the alar and transverse ligaments using calipers [4, 5]. In the alar ligaments, they differentiated between the length at the cranial and at the caudal aspect, and, probably due to the oblique orientation found the caudal length slightly longer (Table 1). However, their results for both ligaments show a good correlation with the ligament length examination in our study; the small differences may be attributed to the different method of measurement. Previous studies of the descriptive anatomy confirmed our observation that the transverse ligament surrounds the dorsolateral aspect of the dens axis [17, 25]. The transverse ligament was found to be almost exclusively of collagen fibers [20], with the exception of the portion of the ligament close to the dens, where a transition into fibrocartilage was found on the ventral side of the ligament.

Table 1. Comparison of the ligament dimensions measured in different studies Authors

Mean length of alar ligaments

Dvorak and Panjahi {4]

1l•215 13• 11.3•215 10.3• 11.2•215

Dvorfik et al. [5] Present study Cranial aspect of alar ligament b Caudal aspect of alar ligament

a b ~ b

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Biomechanical function In contradiction of earlier theories [4, 9], Panjabi et al. [18] found, after dissection of one alar ligament, a significant increase of R O M on both sides during axial rotation. Crisco et al. [2] developed a mathematical model explaining these, experimental findings. Furthermore, they predicted that both alar ligaments tighten during axial rotation. In our qualitative anatomical studies we found a laxity of the alar ligaments in midposition; during axial rotation a tightening of both alars was observed. Furthermore, the results of the biomechanical testing support the theory of Crisco et al. [2]: the initial neutral zone according to White and Panjabi [24] is defined as a part of the R O M of a ligament under tensile load, starting from the neutral position up to the point where some resistance begins to be offered by the ligament. The neutral zone, found in all tested ligaments, explains the laxity of the alars in midposition and allows mobility of the upper cervical spine with minimum expenditure of muscular enery. The ligaments become stiffer under higher loads and therefore contribute to a limitation of R O M in the occipito-atlanto-axial joint. As nondestructive tensile testing was performed, the load-displacement curves show typical nonelastic behavior. The fact that earlier studies explained axial rotation at the C1/C2 joint as limited by the contralateral alar ligament may be because they studied the coupled motion of axial rotation and lateral bending. This coupled motion then leads to a tightening of the contralateral ligament. However, this coupled motion is not necessary to tighten boths alars: planar axial rotation alone is sufficient to increase the tension in both alar ligaments [2]. Our observations confirmed the theory of the biomechanical function of the transverse ligaments, that is prevention of anterior atlanto-axial luxation and fixation of the dens in the atlas arch during rotation [9, 17, 19]. Being less lax in the neutral position as compared to the alar ligaments, the transverse ligaments tighten during flexion in the atlanto-axial joint. Similar to ourselves, Yahia et al. [26], found during nondestructive tensile testing of the supraspinous and interspinous ligaments of the lumbar spine that about half of the relaxation occurred during the first few seconds of the relaxation test. These results suggest that due to the relaxation phenomenon, proper biomechanical testing of the spine has to be done under dynamic conditions, since delays of a few seconds during the testing procedure permit the viscoelastic ligaments to relax. This may alter internal loads and lead to changes in the amount of stresses at the bone-ligament interface.

Clinical considerations Severe trauma to the upper cervical spine is frequently seen as a result of vehicle accidents, especially in association with head injuries [13, 20]. Posttraumatic stability largely depends on the integrity of the ligaments of the occipito-atlanto-axial joint. CT and MRI have greatly improved the visualization of soft tissue injuries [3, 6]. However, the detection of lesions of the ligaments of the

upper cervical spine remains a problem. For the clinician it is usually difficult to decide whether there is probably a lesion accompanying clinical instability, defined as the loss of ability of a spinal segment to withstand normal physiologic loads while maintaining the normal relationship between adjacent vertebrae [24]. It has been demonstrated that an isolated rupture of the transverse ligament not associated with rupture of the atar ligaments or with rupture of the anterior and posterior portions of the joint capsule at C1/C2 will only result in minimal atlantoaxial instability [8]. Conversely, in atlanto-axial rotary fixations, the rotary feature of this type of lesion depends on the fact that the transverse ligament remains intact and that the atlas rotates around the dens axis [7]. Keeping in mind our experimental findings showing a initial neutral zone during tensile testing of the ligaments, an atlanto-axial rotary fixation without anterior displacement (type I according to Fielding and Hawkins [7]) need not necessarily go along with rupture of the alar ligaments. However, with respect to the anatomical situation and the possible risk for the patient, traumatic lesions of the occipito-atlanto-axial joint should be regarded as unstable as long as the opposite is not evident. The occipito-atlanto-axial region is the most complex joint of the human axial skeleton. In addition to the alar and transverse ligaments, other bony, cartilaginous, and ligamentous structures influence mobility and stability and R O M in this region. Besides the complexity, there also seem to be some variations, as the varying existence of the anterior atlanto-dental ligament indicates. Further clinical, experimental, and forensic studies are required to reveal more about this region. References

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184 13. Jdnsson H, Bring G, Rauschning W, Sahlstedt B (1991) Hidden cervical spine injuries in traffic accident victims with skull fractures. J Spinal Disord 4 : 251-263 14. Liu YK, Chandran KB, Heath RG, Unterharnscheidt F (1984) Subcortical EEG-changes in rhesus monkeys following experimental hypertension-hyperflexion (whiplash). Spine 9:329338 15. Ludwig K (1952) 121ber das Ligamentum alare dentis. Z Anat Entwickl Gesch 116: 442 16. Nolte LP, Visarius H (1992) Ein mathematisches Modell zur Abbildung uniaxialer endlicher Deformation bioweicher Strukturen. Z Biomed Technik (in press) 17. Oppel U (1989) Funktionelle Computertomographie bei zervikozephalen Beschwerdebildern. In: Kt~gelgen B, Hillemacher A (eds) Problem Halswirbels~ule. Springer, Berlin Heidelberg New York, pp 93-106 18. Panjabi MM, Dvorak J, Crisco JJ, Oda T, Wang P, Grob D (1991) Effects of alar ligament transection on upper cervical spine rotation. J Orthop Res 9: 584-593 19. Roach JW, Duncan D, Wenger DR, Maravilla A, Maravilla K (1984) Atlanto-axial instability and spinal cord compression in

20. 21. 22. 23. 24. 25. 26.

children - diagnosis by computerized tomography. J Bone Joint Surg [Am] 66 : 708-714 Saldinger P, Dvorak J, Rahn BA, Perren SM (1990) Histology of the alar and transverse ligaments, Spine 15 : 257-261 Saternus KS (1982) Zur Mechanik des Schleudertraumas der Halswirbelsgule. Z Rechtsmed 88:1-11 Visarius H (1991) Ein mathematisches Modell zur Abbildung endlicher Deformation bioweicher Strukturen. Thesis, University of Bochum Werne S (1957) Studies in spontaneous atlas dislocation. Acta Orthop Scand (Suppl) 23 : 1-150 White AA, Panjabi MM (1990) Clinical biomechanics of the spine, 2nd edn. Lippincott, Philadelphia Worztman G, Dewar FP (1968) Rotary fixation of the atlantoaxial joint: rotational atlantoaxial subluxation. Radiology 90: 479-487 Yahia LH, Audet J, Drouin G (1991) Rheological properties of the human lumbar spine ligaments. Abstracts, 13th International Congress on Biomechanics, Perth, p 583-584