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An FE investigation simulating intra-operative corrective forces applied to correct scoliosis deformity
© Little et al.; licensee BioMed Central Ltd. 2013
- Received: 3 December 2012
- Accepted: 6 May 2013
- Published: 16 May 2013
Adolescent idiopathic scoliosis (AIS) is a deformity of the spine, which may require surgical correction by attaching a rod to the patient’s spine using screws implanted in the vertebral bodies. Surgeons achieve an intra-operative reduction in the deformity by applying compressive forces across the intervertebral disc spaces while they secure the rod to the vertebra. We were interested to understand how the deformity correction is influenced by increasing magnitudes of surgical corrective forces and what tissue level stresses are predicted at the vertebral endplates due to the surgical correction.
Patient-specific finite element models of the osseoligamentous spine and ribcage of eight AIS patients who underwent single rod anterior scoliosis surgery were created using pre-operative computed tomography (CT) scans. The surgically altered spine, including titanium rod and vertebral screws, was simulated. The models were analysed using data for intra-operatively measured compressive forces – three load profiles representing the mean and upper and lower standard deviation of this data were analysed. Data for the clinically observed deformity correction (Cobb angle) were compared with the model-predicted correction and the model results investigated to better understand the influence of increased compressive forces on the biomechanics of the instrumented joints.
The predicted corrected Cobb angle for seven of the eight FE models were within the 5° clinical Cobb measurement variability for at least one of the force profiles. The largest portion of overall correction was predicted at or near the apical intervertebral disc for all load profiles. Model predictions for four of the eight patients showed endplate-to-endplate contact was occurring on adjacent endplates of one or more intervertebral disc spaces in the instrumented curve following the surgical loading steps.
This study demonstrated there is a direct relationship between intra-operative joint compressive forces and the degree of deformity correction achieved. The majority of the deformity correction will occur at or in adjacent spinal levels to the apex of the deformity. This study highlighted the importance of the intervertebral disc space anatomy in governing the coronal plane deformity correction and the limit of this correction will be when bone-to-bone contact of the opposing vertebral endplates occurs.
- Finite element
- Surgical forces
The anterior single rod correction procedure is one possible surgical technique  (Figure 1B) for treating scoliosis. This procedure involves removing the deformed intervertebral discs, implanting material to promote fusion of the intervertebral joint space and securing metal rods to the spinal vertebra using screws . The surgeon achieves an intra-operative reduction in the patient’s deformity by applying compressive forces across the fused intervertebral disc spaces via pairs of adjacent screws, while securing the rod to the vertebra.
Previous researchers have demonstrated the potential of computational methods  and in particular finite element (FE) models to investigate the mechanics of the scoliotic spine during surgery [6–8]. FE models which are personalized to include representations for the individual patient’s soft and osseous anatomy and spinal loading conditions, have the potential to assist surgeons in planning the patient’s surgery and in optimizing their treatment in order to obtain the best possible surgical outcomes. Irrespective of the aetiology of the spinal deformity, surgical treatment involves applying biomechanical corrective forces to the spine using implants attached to the spinal anatomy. Implant related complications involve mechanical failure of the spinal tissues, thus an investigation of the biomechanics of the surgically corrected spine lends itself to the use of the FE method which is able to predict stresses and strains in both implants and spinal tissues.
The aim of this study is to use FE models derived from computed tomography data for the thoracolumbar spine and ribcage of AIS patients, to investigate the biomechanics of the surgically corrected spine during single rod anterior scoliosis surgery. The question of interest is how the AIS deformity – specifically the coronal Cobb angle and disc space deformity - is reduced with increasing magnitudes of surgical corrective force. The ability of the FE model to predict tissue-level stresses was also used to predict the surgically induced contact stresses between adjacent vertebral endplates.
Patient demographics for AIS patients
Pre-operative major Cobb angle (degrees)
Post-operative major Cobb angle (degrees)
Instrumented vertebral levels
Disc at the apex of the curve
Patient-specific anatomy and finite element (FE) models for AIS patients
Our method for generating three-dimensional patient-specific osseo-ligamentous anatomy and FE model geometry for the thoracolumbar spine and ribcage has been described elsewhere [8, 11], so will only be briefly presented here.
Three-dimensional geometry for the vertebral bodies was interpolated between the vertebral endplates  and similarly, the intervertebral disc geometry was interpolated from the adjacent vertebral endplates. The curved transverse profile for the articulating surfaces of the facet joints was described using a sinusoidal curve and the curvatures of the ribs were defined using 5th order polynomials, with both derived from user-selected bony landmarks. Interfacial contact between the articulating surfaces of the facet joints was modelled using exponential softened contact (normal contact) and zero-friction tangential sliding.
The costo-vertebral joints were represented in detail, since these structures are of key importance in governing the biomechanics of the spine [13, 14]. Both the costo-vertebral and costo-transverse connections were represented and our method for simulating this joint has been described and validated in a previous study .
Details of the element types and material parameters (with references) included in the FE models
- Cortical shell
Linear elastic E = 11,300 MPa, ν = 0.2
- Cancellous bone
Linear elastic E = 140 MPa, ν = 0.2
Vertebral posterior elements
As for cortical bone, with exponential softened contact between adjacent facet surfaces
- Anulus fibrosus
Hyperelastic, Mooney-Rivlin C10 = 0.7, C01 = 0.2
- Collagen fibres
Tension-only, ABAQUS ‘rebar’ elements
Linear elastic E = 500 MPa, ν = 0.3
- Nucleus pulposus
4-node, hydrostatic fluid
Linear elastic E = 9,860 MPa, ν = 0.3
Linear elastic E = 49 MPa, ν = 0.4
Linear elastic E = 9,860 MPa, ν = 0.3
Linear elastic Ecompr = 245 N/mm; Torsional stiffness, kt = 4167Nmm/rad; Bending stiffness, kb = 6706Nmm/rad (average antero-posterior and cranio-caudal flexion stiffness)
- Ligamentum flava, supra-/inter-spinous, capsular, inter-transverse
2-node, tension-only connector
Piecewise, non-linear elastic
- Anterior/posterior longitudinal ligament
Piecewise, non-linear elastic
- Inter-costal connections
2-node, tension-only connector
Linear elastic, E = 25 MPa
Linear elastic, E = 108,000 MPa, ν = 0.3
8-node brick and 2-node rigid beam
Linear elastic, perfectly plastic E = 108,000 MPa, ν = 0.3 Yield Stress = 390 MPa
Modelling the surgically altered spine
The eight patients modeled in the study had previously undergone a single rod, anterior scoliosis procedure and clinical follow-up data was available. In carrying out this procedure the surgeon produces an immediate (intra-operative) reduction in the spinal deformity by attaching a metal rod to the anterior spinal column. The surgery firstly involves the insertion of screws into the vertebral bodies within the primary structural curve. Screws are inserted on the convex side of the primary structural curve, directly into the lateral side each vertebral body. Following this, the discs within the limits of this curve are partially removed (within the limits of endoscopic surgical accesss) and the disc spaces are packed with bone graft to promote bony fusion after surgery. In a step-wise manner, the surgeon then applies compressive forces between the screw heads of adjacent pairs of vertebrae (starting at the most-caudal motion segment in the structural curve), to reduce the level-wise deformity at each motion segment, and then locks the screws onto the rod. Thus, these level-wise corrections produce a cumulative reduction in the overall spinal deformity, which is held in place by the screw heads being locked onto the rod.
This surgical procedure was simulated for the eight patients included in this study, by adding the screws and rod to each patient-specific model, and by removing disc material from the models in the same manner as the surgically performed discectomies. Clinical data for the surgical procedure carried out on each patient was used to simulate the surgery in each patient FE model – the portion of intervertebral disc elements removed from each simulated joint space was representative of the amount of disc material extracted clinically; the clinical spinal levels fused were used to define the vertebrae in which screws were simulated; and the geometry for the simulated surgical instruments was representative of the screw diameters and rod diameter implanted for each patient. As such, eight patient-specific surgically altered spines were simulated. The screws were assumed to be perfectly bonded to the surrounding vertebral bone, so the contact mechanics of the bone-implant interface was not considered in the models. In modelling the discectomies, the fused intervertebral levels were simulated by removing approximately two-thirds of the brick elements representing the anulus fibrosus and by removing the entire hydrostatic fluid cavity representing the nucleus pulposus for these discs. The bone graft material was not simulated in this study, since bony fusion does not occur until 3–6 months after surgery and the material offers minimal mechanical resistance during surgery. The contact interaction between the exposed vertebral endplates at the discectomy levels was modelled using an exponential, softened contact relationship for normal contact and Coulomb friction (μ = 0.3) for tangential sliding. This softened contact relationship simulated a cartilaginous endplate thickness of 0.1 mm, being the distance at which the contact pressure between adjacent endplates became non-zero.
Simulating the intra-operative loadcase and boundary conditions
There is limited biomechanical data available in the literature describing the surgical forces applied intra-operatively during anterior spinal deformity surgery. As such, in a recent in vivo biomechanical study by members of our group, Fairhurst et al.  presented intra-operatively measured force data for a series of 15 AIS patients who underwent the single rod anterior corrective procedure. This study presented descriptive mechanical data (mean and standard deviation) for the surgical corrective forces applied intra-operatively at each intervertebral level, normalized by vertebral level relative to the apex of the curve. (This study was performed with approval from the Mater Children’s Hospital Ethics Committee). Due to the timing of the two studies, the 15 patients in this previous biomechanical study were not included in the patient series for the current study. While these biomechanical data could not be used to provide personalized force data for the eight AIS patient FE models in the current study, the data was still invaluable in providing representative values for intra-operatively applied forces in a comparable patient data set – data which was heretofore unavailable in the literature.
Three separate force profiles simulated for each patient-specific FE model - based on the mean and standard deviation in vivo measurements of Fairhurst et al. (2011)
To simulate the guided sliding movement of the screws along the rod during surgery, a ‘no separation’ normal contact and frictionless tangential contact definition were defined between the screw head and the surface of the rod. After the surgical force loading step had been applied for each pair of adjacent screws, this tangential contact definition was changed to roughened (bonded) contact to simulate the surgical procedure for locking the screws onto the rod. During the simulations the spine was fully constrained from rigid body motion at the inferior-most vertebral level (L5) and stabilized in the lateral direction at the superior-most vertebra to simulate the constraint provided by the operating table (since the patient is positioned in the lateral decubitus position on the operating table).
Intra-operatively, the rod is pre-bent manually prior to being attached to the vertebrae . The angle of rod pre-bend varies from patient to patient based on the surgeon’s judgement of the achievable deformity correction and is not measured clinically. In the absence of measured values for the rod pre-bend angle in each case, the simulated pre-bend in the models was based on the pre-operative coronal Cobb angle for each patient. In this study, a ‘prebend’ load step was performed in which the screw heads were fixed in space, and then the connector elements between the rod and the screw heads were reduced to zero length (these elements provide an axial link between the connected nodes on the rod and screw and have no associated stiffness), in order to bend the rod to conform to the pre-operative profile of the spine. Following the prebend load step, the fixed boundary constraint on the screw heads was removed in the second loadstep allowing elastic springback of the rod prior to the actual surgery simulation steps.
As described above, each of the eight patient-specific models were analyzed using three separate intra-operative force profiles (Force profiles A, B and C in Table 3). These 24 analyses were performed using a quasi-static solver (no inertial effects) with the ABAQUS nonlinear geometry capability enabled.
The predicted corrected Cobb angle for the instrumented curve was calculated for each analysis and compared with the clinically measured post-operative Cobb angle for each patient (using the 1 week post-operative standing x-ray). In comparing model predictions with clinical measurements, the accepted clinical radiograph measurement variability of ±5o,  was taken into account.
Overall and segmental coronal Cobb correction
Using patient-specific FE models of the osseoligamentous thoracolumbar spine, this study investigates the biomechanical response of eight AIS patients to surgical corrective forces applied during single rod, anterior scoliosis surgery. Each FE model was subjected to three corrective force profiles in the range of experimentally measured values, and the resulting model response was investigated with particular focus on the predicted coronal plane correction occurring in the intervertebral disc spaces following partial discectomy and single anterior rod instrumentation.
A limitation of this study is that the passive osseo-ligamentous models of the spine and ribcage used herein do not provide biomechanical insights on the response of the spine to post-operative loading conditions which involve muscle activation. While the spinal muscles may play a role in passively resisting loads applied to the spine while the patient is anaesthetized , the current study assumes this contribution to spinal flexibility is minimal in comparison to that of the ligamentous and cartilaginous tissues of the spine.
Post-operatively, the corrected Cobb angle is normally measured clinically using standing radiographs obtained one week after surgery. However, the comparison between the clinical and predicted corrected Cobb angle in the current study (Figure 4) was based on model predictions which were analysed for the surgical loadcase only, thus assumed the patient was still supine. Ideally, supine radiographs obtained immediately after surgery, while the patient is still recovering and so is not yet load-bearing, would provide a better clinical comparison for the predicted post-operative Cobb angle from the patient-specific models. However, these radiographs were not available for the patients in the current study. Once the rod is surgically attached to the vertebra, it is reasonable to assume that the instrumented region of the spine would experience only small intervertebral motions (< 1o), since the main purpose of the surgery is to ensure that motion is sufficiently restricted such that bony fusion can occur between adjacent vertebral bodies. Therefore, the difference in the clinically measured corrected Cobb angle from supine compared to standing radiographs is not expected to be of the magnitude which is observed prior to surgery in the uninstrumented spine.
The use of tissue mechanical properties derived from adult data to simulate adolescent spinal tissues is another limitation of the study, and is a necessary consequence of the paucity of paediatric and adolescent tissue mechanical data available in the literature. However, we note that tissue stiffness (e.g. the force-displacement for a whole ligament) is a result of both the inherent mechanical response of the ligament tissue itself, and the dimensions (in this case length and cross-sectional area) of the ligament. By including patient-specific anatomical landmarks as the ligament attachment points in the models, the patient-specific modeling approach used in the current study incorporates variations in ligament length between patients, and therefore goes some way to simulating patient-specific tissue properties.
Another limitation of the current study is that the angle of rod prebend which is introduced prior to attaching the rod to the patient’s spine is not measured clinically and is based on the surgeon’s judgement. In the current study, this angle of prebend for the simulated surgery was estimated using the pre-operative Cobb angle, however, future studies using this patient series will focus on investigating the sensitivity of model predictions to the prebend angle and plastic prestrain in the rod.
With regard to model validation, Figure 4 showed that the predicted Cobb angles after surgical correction were within 5° agreement with the clinical values for seven of the eight patients in the study. However it is important to keep in mind that the surgery force profiles used in the study were not ‘patient specific’, since average surgery force data for an experimental measurement series  were used to define the model load profiles for all eight patients in the current study. The results from the current study show that increasing the simulated intra-operative forces, resulted in a reduction in the predicted corrected Cobb angle.
Measurement variability from clinical radiographs results in a wide range of error (±5o), and furthermore, there was large variability in the intra-operatively measured surgical forces which resulted in a similarly wide range of variation in the predicted corrected Cobb angle. It should be noted that the inter-relationship between these sources of variability may have the potential to obscure patterns in the predicted outputs. For instance, the results for patient five suggest that the average surgery forces applied to the model were higher than those applied intra-operatively for this patient. While the descriptive data for surgical forces were measured for a series of AIS patients from the same study population as patients simulated in the current study, the use of intra-operative force data measured for each individual patient would provide a more ideal simulation for individual patient loading. This reflects a limitation of the future clinical application of patient-specific modeling approaches for all such virtual spine models, in that patient-specific surgically applied forces can only be measured at the time of surgery, therefore actual patient force data can only be simulated retrospectively post-surgery. Aside from modeling considerations, the substantial variation in surgically applied corrective forces warrants further study, and there may be a case for developing technology to provide force feedback to surgeons during implant insertion.
The results of this study highlight the importance of the intervertebral disc space anatomy in governing the coronal plane deformity correction which may be achieved in the instrumented curve. Since the partially cleared intervertebral disc spaces are the primary anatomy in the anterior column of the spine imparting flexibility, the maximum correction which may be achieved surgically will be governed by the anatomy of the discs in terms of disc wedge angle and disc height. The limit of this achievable deformity correction will be when bone-to-bone contact of the opposing vertebral endplates occurs, and for different patients, this limit will be achieved with varying magnitudes of surgical corrective forces. One of the strengths of the patient-specific model geometry used here is the ability to capture endplate to endplate contact during the surgical correction, and thus to predict the diminishing return between applied corrective force and segmental correction.
Results for the predicted corrected Cobb angle indicate that there is an inverse relationship between the magnitude of the total corrective force and the decrease in corrected Cobb angle and this is a proportional relationship for all except patient two. By increasing the total corrective force by as much as 120% (comparing the total force applied in Profile A to the total for Profile C), this resulted in a reduction in the corrected Cobb angle. For example, for patient three, the corrected Cobb angle for Profile C was 19.1o and for Profile A was 6.9o (Figure 4), which represented a 64% reduction in the corrected Cobb angle with increasing corrective force. This percentage reduction in corrected Cobb angle ranged from 32 to 84% when comparing the results for Profile A to Profile C for the eight patients (Figure 4). Moreover, as stated above, the anatomy of the discs will strongly influence the maximum achievable correction and for some patients, applying increasing magnitude corrective forces will result in bone-to-bone contact in the disc space and unnecessarily load the vertebral bone with a comparatively minor improvement in deformity correction. As such, the interaction of these key biomechanical factors of force, geometry (patient anatomy) and tissue stresses is of key importance in achieving an optimal correction for a patient, with the least risk of excessive loads on the spinal tissues causing possible implant related complications. Herein lies a key advantage of use of patient-specific FE models as tools to assist surgeons in pre-operative planning for deformity surgery.
Attempts to improve the outcomes of spinal deformity surgery using patient-specific computer models depend strongly on the ability of the models to correctly capture the anatomy, tissue mechanical properties, and applied loading in individual patients for their validity. The simulations presented in this study are an initial step in the development of computational tools to predict surgical deformity correction. This study demonstrated a direct relationship between the surgically applied corrective forces and the deformity correction achieved, showing that the majority of deformity correction occurs in the intervertebral disc spaces at or near the apex of the deformity. The study results highlighted the importance of the intervertebral disc space anatomy in influencing the coronal plane deformity correction. By better understanding how the mechanics of a patient’s spine is altered during scoliosis corrective surgery, patient-specific models such as these can potentially provide an improved understanding of how to achieve an optimum correction for an individual patient’s spine.
- Patient and Family: Surgical Treatment. http://www.srs.org/patient_and_family/what_are_my_treatment_options/surgical_treatment.htm Access Date: 03/04/2013
- Hawes MC, O'Brien JP: A century of spine surgery: what can patients expect?. Disab rehab. 2008, 30: 808-817. 10.1080/09638280801889972.View ArticleGoogle Scholar
- Lowe TG, Betz R, Lenke L, Clements D, Harms J, Newton P, Haher T, Merola A, Wenger D: Anterior single-rod instrumentation of the thoracic and lumbar spine: saving levels. Spine (Phila Pa 1976). 2003, 28: S208-S216. 10.1097/01.BRS.0000092483.10776.2A.View ArticleGoogle Scholar
- Lenke LG: Anterior endoscopic discectomy and fusion for adolescent idiopathic scoliosis. Spine. 2003, 28: S36-S43.View ArticlePubMedGoogle Scholar
- Aubin CE, Petit Y, Stokes IA, Poulin F, Gardner-Morse M, Labelle H: Biomechanical modeling of posterior instrumentation of the scoliotic spine. Comput methods biomech biomed eng. 2003, 6: 27-32. 10.1080/1025584031000072237.View ArticleGoogle Scholar
- Rohlmann A, Richter M, Zander T, Klockner C, Bergmann G: Effect of different surgical strategies on screw forces after correction of scoliosis with a VDS implant. Eur Spine J. 2006, 15: 457-464. 10.1007/s00586-005-0923-5.View ArticlePubMedGoogle Scholar
- Dumas R, Lafage V, Lafon Y, Steib JP, Mitton D, Skalli W: Finite element simulation of spinal deformities correction by in situ contouring technique. Comput methods biomech biomed eng. 2005, 8: 331-337. 10.1080/10255840500309653.View ArticleGoogle Scholar
- Little JP, Adam C: Patient-specific computational biomechanics for simulating adolescent scoliosis surgery: Predicted vs clinical correction for a preliminary series of six patients. Int J Num Methods Biomed Eng. 2011, 27: 347-356. 10.1002/cnm.1422.View ArticleGoogle Scholar
- Kamimura M, Kinoshita T, Itoh H, Yuzawa Y, Takahashi J, Hirabayashi H, Nakamura I: Preoperative CT examination for accurate and safe anterior spinal instrumentation surgery with endoscopic approach. J Spinal Disord Tech. 2002, 15: 47-51. 10.1097/00024720-200202000-00008. discussion 51–42View ArticlePubMedGoogle Scholar
- Fairhurst H, Little JP, Adam CJ: Annual meeting of the spine society of australia; 15–17 april. The measurement of applied forces during anterior single rod correction of adolescent idiopathic scoliosis (AIS). 2011, Melbourne, AustraliaGoogle Scholar
- Little JP, Adam CJ: Patient-specific modelling of scoliosis. Patient-specific modelling in Tomorrow's medicine. Edited by: Gefen A. 2012, Berlin: SpringerGoogle Scholar
- Little JP, Pearcy MJ, Pettet GJ: Parametric equations to represent the profile of the human intervertebral disc in the transverse plane. Med biol eng comput. 2007, 45: 939-945. 10.1007/s11517-007-0242-6.View ArticlePubMedGoogle Scholar
- Oda I, Abumi K, Cunningham BW, Kaneda K, McAfee PC: An in vitro human cadaveric study investigating the biomechanical properties of the thoracic spine. Spine. 2002, 27: E64-E70. 10.1097/00007632-200202010-00007.View ArticlePubMedGoogle Scholar
- Watkins R, 3rd Watkins R, Williams L, Ahlbrand S, Garcia R, Karamanian A, Sharp L, Vo C, Hedman T: Stability provided by the sternum and rib cage in the thoracic spine. Spine. 2005, 30: 1283-1286. 10.1097/01.brs.0000164257.69354.bb.View ArticlePubMedGoogle Scholar
- Little JP, Adam CJ: Effects of surgical joint destabilization on load sharing between ligamentous structures in the thoracic spine: a finite element investigation. Clin Biomech (Bristol, Avon). 2011, 26: 895-903. 10.1016/j.clinbiomech.2011.05.004.View ArticleGoogle Scholar
- Reutlinger C, Hasler C, Scheffler K, Buchler P: Intraoperative determination of the load-displacement behavior of scoliotic spinal motion segments: preliminary clinical results. Eur Spine J. 2012, 21 (Suppl 6): S860-867.View ArticlePubMedGoogle Scholar
- Little JP, Adam C: Towards determining soft tissue properties for modelling spine surgery: current progress and challenges. Medical & biological engineering & computing. 2012, 50: 199-209. 10.1007/s11517-011-0848-6.View ArticleGoogle Scholar
- Little JP, Adam CJ: The effect of soft tissue properties on spinal flexibility in scoliosis: biomechanical simulation of fulcrum bending. Spine (Phila Pa 1976). 2009, 34: E76-82. 10.1097/BRS.0b013e31818ad584.View ArticleGoogle Scholar
- Andriacchi T, Schultz A, Belytschko T, Galante J:A model for studies of mechanical interactions between the human spine and rib cage. Journal of biomechanics. 1974, 7: 497-507. 10.1016/0021-9290(74)90084-0.View ArticlePubMedGoogle Scholar
- Chazal J, Tanguy A, Bourges M, Gaurel G, Escande G, Guillot M, Vanneuville G:Biomechanical properties of spinal ligaments and a histological study of the supraspinal ligament in traction. Journal of biomechanics. 1985, 18: 167-176. 10.1016/0021-9290(85)90202-7.View ArticlePubMedGoogle Scholar
- Kimpara H, Lee JB, Yang KH, King AI, Iwamoto M, Watanabe I, Miki K:Development of a Three-Dimensional Finite Element Chest Model for the 5(th) Percentile Female. Stapp car crash journal. 2005, 49: 251-269.PubMedGoogle Scholar
- Kumaresan S, Yoganandan N, Pintar FA, Maiman DJ:Finite element modeling of the cervical spine: role of intervertebral disc under axial and eccentric loads. Med Eng Phys. 1999, 21: 689-700. 10.1016/S1350-4533(00)00002-3.View ArticlePubMedGoogle Scholar
- Lemosse D, Le Rue O, Diop A, Skalli W, Marec P, Lavaste F:Characterization of the mechanical behaviour parameters of the costo-vertebral joint. Eur Spine J. 1998, 7: 16-23. 10.1007/s005860050021.View ArticlePubMedPubMed CentralGoogle Scholar
- Little JP: Finite element modelling of anular lesions in the lumbar intervertebral disc. 2004, Queensland University of Technology: School of Mechanical, Manufacturing and Medical EngineeringGoogle Scholar
- Lu YM, Hutton WC, Gharpuray VM:Do bending, twisting, and diurnal fluid changes in the disc affect the propensity to prolapse? A viscoelastic finite element model. Spine. 1996, 21: 2570-2579. 10.1097/00007632-199611150-00006.View ArticlePubMedGoogle Scholar
- Nachemson A:Lumbar Intradiscal Pressure: experimental studies on post-mortem material. Acta Orthopaedica Scandinavica. 1960, 43:Google Scholar
- Nolte LP, Panjabi M, Oxland T:Biomechanical properties of lumbar spinal ligaments. Clinical implant materials. Edited by: Heimke G, Soltesz U, Lee AJC. 1990, Elsevier Science Publishing, 663-668.Google Scholar
- Stokes IA, Laible JP:Three-dimensional osseo-ligamentous model of the thorax representing initiation of scoliosis by asymmetric growth. Journal of biomechanics. 1990, 23: 589-595. 10.1016/0021-9290(90)90051-4.View ArticlePubMedGoogle Scholar
- Natali AN:A hyperelastic and almost incompressible material model as an approach to intervertebral disc analysis. J Biomed Eng. 1991, 13: 163-168. 10.1016/0141-5425(91)90063-D.View ArticlePubMedGoogle Scholar
- Shirazi-Adl A, Ahmed AM, Shrivastava SC:Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine. 1986, 11: 914-927. 10.1097/00007632-198611000-00012.View ArticlePubMedGoogle Scholar
- Vrtovec T, Pernus F, Likar B:A review of methods for quantitative evaluation of spinal curvature. Eur Spine J. 2009, 18: 593-607. 10.1007/s00586-009-0913-0.View ArticlePubMedGoogle Scholar
- Duke K, Aubin CE, Dansereau J, Labelle H:Biomechanical simulations of scoliotic spine correction due to prone position and anaesthesia prior to surgical instrumentation. Clin Biomech (Bristol, Avon). 2005, 20: 923-931. 10.1016/j.clinbiomech.2005.05.006.View ArticleGoogle Scholar
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