Validation of vibration testing for the assessment of the mechanical properties of human lumbar motion segments

Experimental modal analysis is a non-destructive measurement technique, which applies low forces and small deformations to assess the integrity of a structure. It is therefore a promising method to study the mechanical properties of the spine in vivo. Previously, modal parameters successfully revealed artificially induced spinal injuries. The question remains however, whether experimental modal analysis can be applied successfully in human spinal segments with mechanical changes due to physiological processes. Since quasi-static mechanical testing is considered the "gold standard" for assessing intervertebral stiffness, the purpose of our study was to examine if the mechanical properties derived from vibration testing and quasi-static testing correlate. Six cadaver human spines (L1-L5) were loaded quasi-statically in bending and torsion, while an optical system measured the angular rotations of the individual motion segments. Subsequently, the polysegmental spines were divided into L2-L3 and L4-L5 segments and a shaker was used to vibrate the upper vertebra, while its response was obtained from accelerometers in anteroposterior and mediolateral directions. From the resulting frequency response function the eigenfrequencies (ratio between stiffness and mass) and vibration modes (pattern of motion) were determined. The vibration results showed clear eigenfrequencies for flexion-extension (mean 121.83Hz, SD 40.05Hz), lateroflexion (mean 132.17, SD 34.80Hz) and axial rotation (mean 236.17Hz, SD 81.45Hz). Furthermore, the correlation between static and dynamic tests was significant (r=0.73, p=0.01). In conclusion, the findings from this study show that experimental modal analysis is a valid method to assess the mechanical properties of human lumbar motion segments.     

Personalised mechanical properties of scoliotic vertebrae determined in vivo using tomodensitometry

This in vivo study investigated the mechanical properties of apical scoliotic vertebrae using computed tomography (CT) and finite element (FE) meshing. CT examination was performed on seven scoliotic girls. FE meshing of each vertebral body allowed automatic mapping of the CT scan and the visualisation of the bone density distribution. Centroids and mass centres were compared to analyse the mechanical properties distribution. Compared to the centroid, the mass centre migrated into the concavity of the curvature. The three vertebrae of a same patient had the same body migration behaviour because they were located at the curvature apex. This observation was verified in the coronal plane, but not in the sagittal plane. These results represent new data over few geometrical analyses of scoliotic vertebrae. Same in vivo personalisation of mechanical properties should be performed on intervertebral discs or ligaments to personalise stiffness properties of the spine for the biomechanical modelling of human torso. Moreover, do this mechanical deformation of scoliotic vertebrae, that appears before the vertebral wedging, could be a predictive tool in scoliosis treatment?     

Personalised Mechanical Properties of Scoliotic Vertebrae Determined In Vivo Using Tomodensitometry

This in vivo study investigated the mechanical properties of apical scoliotic vertebrae using computed tomography (CT) and finite element (FE) meshing. CT examination was performed on seven scoliotic girls. FE meshing of each vertebral body allowed automatic mapping of the CT scan and the visualisation of the bone density distribution. Centroids and mass centres were compared to analyse the mechanical properties distribution. Compared to the centroid, the mass centre migrated into the concavity of the curvature. The three vertebrae of a same patient had the same body migration behaviour because they were located at the curvature apex. This observation was verified in the coronal plane, but not in the sagittal plane. These results represent new data over few geometrical analyses of scoliotic vertebrae. Same in vivo personalisation of mechanical properties should be performed on intervertebral discs or ligaments to personalise stiffness properties of the spine for the biomechanical modelling of human torso. Moreover, do this mechanical deformation of scoliotic vertebrae, that appears before the vertebral wedging, could be a predictive tool in scoliosis treatment?     

Presurgical finite element simulation of scoliosis correction

For surgical correction of scoliotic spinal deformity, internal fixation systems apply lateral and distractive corrective forces. In order to gain maximal correction, a finite-element analysis of the spinal deformity correction technique has been carried out preoperatively, after first employing the spinal deformity correction finite-element model to determine the in vivo spinal stiffness. The presurgical analysis also gives us an appreciation of how the parameters of deformity, stiffness and corrective forces jointly contribute to the value of the correction index. The paper presents the methodology and clinical application. It also summarizes the results for ten patients, whereby the efficacy of presurgical analysis is assessed by comparing the corrective index values by presurgical simulation with the surgical results for equivalent levels of corrective forces.     

Force transmission via axial tendons in undulating fish: a dynamic analysis

Sonomicrometrics of in vivo axial strain of muscle has shown that the swimming fish body bends like a homogenous, continuous beam in all species except tuna. This simple beam-like behavior is surprising because the underlying tendon structure, muscle structure and behavior are complex. Given this incongruence, our goal was to understand the mechanical role of various myoseptal tendons. We modeled a pumpkinseed sunfish, Lepomis gibbosus, using experimentally-derived physical and mechanical attributes, swimming from rest with steady muscle activity. Axially oriented muscle-tendons, transverse and axial myoseptal tendons, as suggested by current morphological knowledge, interacted to replicate the force and moment distribution. Dynamic stiffness and damping associated with muscle activation, realistic muscle force generation, and force distribution following tendon geometry were incorporated. The vertebral column consisted of 11 rigid vertebrae connected by joints that restricted bending to the lateral plane and endowed the body with its passive viscoelasticity. In reaction to the acceleration of the body in an inviscid fluid and its internal transmission of moment via the vertebral column, the model predicted the kinematic response. Varying only tendon geometry and stiffness, four different simulations were run. Simulations with only intrasegmental tendons produced unstable axial and lateral tail forces and body motions. Only the simulation that included both intra- and intersegmental tendons, muscle-enhanced segment stiffness, and a stiffened caudal joint produced stable and large lateral and axial forces at the tail. Thus this model predicts that axial tendons function within a myomere to (1) convert axial force to moment (moment transduction), (2) transmit axial forces between adjacent myosepta (segment coupling), and, intersegmentally, to (3) distribute axial forces (force entrainment), and (4) stiffen joints in bending (flexural stiffening). The fact that all four functions are needed to produce the most realistic swimming motions suggests that axial tendons are essential to the simple beam-like behavior of fish.     

Spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation

This paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation. The objective is to test the hypothesis that the type of spinal instrumentation system (Cotrel-Dubousset versus Colorado) does not influence these motion parameters. Intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre- and post-operative radiographs of 82 patients undergoing spinal correction. The three-dimensional (3D) reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae. A least-squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters. Average centers of rotation for all intervertebral levels are located in the neural canal at the mid-sagittal plane and approximately at the superior endplate level of the inferior vertebra. Intervertebral rotations have components in all planes: 6.7 degrees (frontal), 5.5 degrees (sagittal) and 4.5 degrees (transverse) RMS for all intervertebral levels. Nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems. Various intervertebral rotations and 3D reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method. Intervertebral rotation errors were 1.7 degrees when simulating 3D errors of 3mm on the position of the landmarks. Maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2.5 degrees (most cases), but were larger (38 mm) for small intervertebral rotations (<1 degrees ). The type of instrumentation system did not influence intervertebral rotations and centers of rotation. These results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis.     

Biomechanical characterization of the native porcine aortic root

A thorough understanding of the well-functioning, native aortic root is pivotal in an era, where valve sparing surgical techniques are developed and used with increasing frequency. The objective of this study was to characterize the local structural stiffness of the native aortic root, to create a baseline for understanding how different surgical interventions affect the dynamics of the aortic root. In this acute porcine study (N = 10), two dedicated force transducers were implanted to quantify the forces acting on both the annular plane and on the sinotubular junction (STJ). To assess the changes in geometry, eleven sonomicrometry crystals were implanted within the aortic root. The combination of force and length measurements yields the radial structural stiffness for each segment of the aortic root.The least compliant segment at the annular plane was the right-left interleaflet triangle with a stiffness modulus of 1.1 N mm⁻¹ (SD0.4). At the sinotubular junction the same segment (right-left) was most compliant, compared with the two other segments, however not statistically significant different.The elastic energy storage was derived from the aortic root pressure volume relationship; the mean elastic energy storage was 826 µJ (SD529). In conclusion, the aortic root has been characterized in terms of both segmental forces, segmental change in length and elastic energy storage. This study is the first to assess the radial structural stiffness of different segments of the aortic root. The presented data is reference for further studies regarding the impact of surgical interventions on the aortic root.     

Biomechanical modeling of posterior instrumentation of the scoliotic spine

Scoliosis is a three-dimensional deformation of the spine that can be treated by vertebral fusion using surgical instrumentation. However, the optimal configuration of instrumentation remains controversial. Simulating the surgical maneuvers with personalized biomechanical models may provide an analytical tool to determine instrumentation configuration during the pre-operative planning. Finite element models used in surgical simulations display convergence difficulties as a result of discontinuities and stiffness differences between elements. A kinetic model using flexible mechanisms has been developed to address this problem, and this study presents its use in the simulation of Cotrel-Dubousset Horizon surgical maneuvers. The model of the spine is composed of rigid bodies corresponding to the thoracic and lumbar vertebrae, and flexible elements representing the intervertebral structures. The model was personalized to the geometry of three scoliotic patients (with a thoracic Cobb angle of 45 degrees, 49 degrees and 39 degrees ). Binary joints and kinematic constraints were used to represent the rod-implant-vertebra joints. The correction procedure was simulated using three steps: (1) Translation of hooks and screws on the first rod; (2) 90 degrees rod rotation; (3) Hooks and screws look-up on the rod. After the simulation, slight differences of 0-6 degrees were found for the thoracic spine scoliosis and the kyphosis, and of 1-8 degrees for the axial rotation of the apical vertebra and for the orientation of the plane of maximum deformity, compared to the real post-operative shape of the patient. Reaction loads at the vertebra-implant link were mostly below 1000 N, while reaction loads at the boundary conditions (representing the overall action of the surgeon) were in the range 7-470 N and maximum torque applied to the rod was 1.8 Nm. This kinetic modeling approach using flexible mechanisms provided a realistic representation of the surgical maneuvers. It may offer a tool to predict spinal geometry correction and assist in the pre-operative planning of surgical instrumentation of the scoliotic spine.     

Finite element analysis of moment-rotation relationships for human cervical spine

A comprehensive, geometrically accurate, nonlinear C0-C7 FE model of head and cervical spine based on the actual geometry of a human cadaver specimen was developed. The motions of each cervical vertebral level under pure moment loading of 1.0 Nm applied incrementally on the skull to simulate the movements of the head and cervical spine under flexion, tension, axial rotation and lateral bending with the inferior surface of the C7 vertebral body fully constrained were analysed. The predicted range of motion (ROM) for each motion segment were computed and compared with published experimental data. The model predicted the nonlinear moment-rotation relationship of human cervical spine. Under the same loading magnitude, the model predicted the largest rotation in extension, followed by flexion and axial rotation, and least ROM in lateral bending. The upper cervical spines are more flexible than the lower cervical levels. The motions of the two uppermost motion segments account for half (or even higher) of the whole cervical spine motion under rotational loadings. The differences in the ROMs among the lower cervical spines (C3-C7) were relatively small. The FE predicted segmental motions effectively reflect the behavior of human cervical spine and were in agreement with the experimental data. The C0-C7 FE model offers potentials for biomedical and injury studies.     

Contribution of vertebral [corrected] bodies, endplates, and intervertebral discs to the compression creep of spinal motion segments

Spinal segments show non-linear behavior under axial compression. It is unclear to what extent this behavior is attributable to the different components of the segment. In this study, we quantified the separate contributions of vertebral bodies and intervertebral discs to creep of a segment. Secondly, we investigated the contribution of bone and osteochondral endplate (endplates including cartilage) to the deformation of the vertebral body. From eight porcine spines a motion segment, a disc and a vertebral body were dissected and subjected to mechanical testing. In an additional test, cylindrical samples, machined from the lowest thoracic vertebrae of 11 porcine spines, were used to compare the deformation of vertebral bone and endplate. All specimens were subjected to three loading cycles, each comprising a loading phase (2.0 MPa, 15 min) and a recovery phase (0.001 MPa, 30 min). All specimens displayed substantial time-dependent height changes. Average creep was the largest in motion segments and smallest in vertebral bodies. Bone samples with endplates displayed substantially more creep than samples without. In the early phase, behavior of the vertebra was similar to that of the disc. Visco-elastic deformation of the endplate therefore appeared dominant. In the late creep phase, behavior of the segment was similar to that of isolated discs, suggesting that in this phase the disc dominated creep behavior, possibly by fluid flow from the nucleus. We conclude that creep deformation of vertebral bodies contributes substantially to creep of motion segments and that within a vertebral body endplates play a major role.     

Flexible device for vertebral body replacement

A novel vertebral prosthesis is presented. The prosthesis was developed for surgical procedures requiring the resection of a complete vertebral body and the adjacent intervertebral discs, the design objective being to develop a flexible implant that would be robust enought to withstand the in vivo stress environment of the human spine. In theory, a flexible implant should preserve a more normal range of motion and apply less stress to surrounding tissue than a rigid implant. A prototype implant was constructed so as to combine a rigid stainless steel structure with flexible silicon rubber elements in order to form an implant with static and dynamic mechanical characteristics similar to those of the anterior spinal column. Implant flexibility characteristics were determined from ex vivo stress-strain behaviour during bending and compressive creep testing. Results from the bending tests indicated good agreement for the lateral and sagittal bending characteristics in comparison with in vitro bending tests of human lumbar motion segments. Comparison of the implant compressive creep responsé with similar in vitro tests on human lumbar intervertebral discs also demonstrated similarities in the time-dependent mechanical parameters.     

Evaluation of frontal radiographs of scoliotic spines—Part II. Relations between lateral deviation, lateral tilt and axial rotation of vertebrae

The shape of scoliotic spines as measured from frontal radiographs (see Part I of this paper) is analysed with respect to interrelations between lateral deviation, lateral tilt and axial rotation of the vertebrae. These parameters are represented by sinusoidal functions of the longitudinal coordinate. The interrelations can, therefore, be expressed in terms of amplitude and phase relations. Two additional functions—‘spinal tilt’ and (local) curvature—are calculated from the first and second derivatives of lateral deviation. The method has been applied to three patient groups with different aetiology: 113 patients with idiopathic scoliosis (478 radiographs, partially follow-up examinations), 23 patients with scoliosis secondary to Wilms' tumour irradiation and 18 patients with scoliosis secondary to poliomyelitis. The amplitude and phase relations of all functions reveal a characteristic pattern which is apparently independent of the specific aetiology. The results show that the available biomechanic explanations of coupling of vertebral motions are questionable.     

The mechanical role of bark

The ability of stem bark to resist bending forces was examined by testing in bending segments of Acer saccharum, Fraxinus americana, and Quercus robur branches with and without their bark. For each species, the bark contributed significantly to the ability of stem segments differing in age to resist bending forces, but its contribution was age-dependent and differed among the three species. The importance of the mechanical role of the bark decreased basipetally with increasing age of F. americana and Q. robur stem segments and was superceded by that of the wood for segments ≥ 6 yr old. A. saccharum bark was as mechanically important as the wood for stem segments 7 yr old but was not a significant stiffening agent for younger or older portions of stems. On average, the stiffness of the bark from all three species was 50% that of the wood. However, the geometric contribution to the flexural rigidity of stems made by the bark (i.e., the bark's second moment of area) was sufficiently large to offset its lower stiffness (Young's modulus) relative to that of the wood. A simple model is presented that shows that the bark must be as mechanically important as the wood when its radial thickness equals 32% that of the wood and its stiffness is 50% that of the wood. Based on this model, which is shown to comply with the data from three species purported to have stiff woods, it is evident that the role of the bark cannot be neglected when considering the mechanical behavior of juvenile woody stems subjected to externally applied bending forces.     

A model for studies of mechanical interactions between the human spine and rib cage

A three-dimensional mathematical model useful for studies of the mechanics of the human skeletal thorax is described. To construct this model, rib cage elements are incorporated into a previously reported model of the thoracolumbar spine. The vertebrae and bony portions of the ribs and sternum are idealized as rigid bodies. The behavior of the discs, ligaments and costal cartilages are modelled by deformable elements. Appropriate geometric and stiffness property data are assigned to the elements of the model. In constructing the model, it was found that the mechanical response of the costo-vertebral joint is strongly influenced by articulation geometry. Although rigid bodies were used to model calcified portions of the ribs, the model predicted rib cage deformations in close agreement with those measured experimentally. These studies indicate that the rigid body motion of calcified portions of the rib makes a major contribution to the deformation of the rib cage in response to certain types of loadings. Quantitative results are also reported on the roles the rib cage plays in bending responses of the spine, the lateral stability of the spine, and the production and correction of several scoliotic deformities.     

Three-Dimensional Vertebral Wedging in Mild and Moderate Adolescent Idiopathic Scoliosis

Background

Vertebral wedging is associated with spinal deformity progression in adolescent idiopathic scoliosis. Reporting frontal and sagittal wedging separately could be misleading since these are projected values of a single three-dimensional deformation of the vertebral body. The objectives of this study were to determine if three-dimensional vertebral body wedging is present in mild scoliosis and if there are a preferential vertebral level, position and plane of deformation with increasing scoliotic severity.

Methodology

Twenty-seven adolescent idiopathic scoliotic girls with mild to moderate Cobb angles (10° to 50°) participated in this study. All subjects had at least one set of bi-planar radiographs taken with the EOS® X-ray imaging system prior to any treatment. Subjects were divided into two groups, separating the mild (under 20°) from the moderate (20° and over) spinal scoliotic deformities. Wedging was calculated in three different geometric planes with respect to the smallest edge of the vertebral body.

Results

Factorial analyses of variance revealed a main effect for the scoliosis severity but no main effect of vertebral Levels (apex and each of the three vertebrae above and below it) (F = 1.78, p = 0.101). Main effects of vertebral Positions (apex and above or below it) (F = 4.20, p = 0.015) and wedging Planes (F = 34.36, p<0.001) were also noted. Post-hoc analysis demonstrated a greater wedging in the inferior group of vertebrae (3.6°) than the superior group (2.9°, p = 0.019) and a significantly greater wedging (p≤0.03) along the sagittal plane (4.3°).

Conclusions

Vertebral wedging was present in mild scoliosis and increased as the scoliosis progressed. The greater wedging of the inferior group of vertebrae could be important in estimating the most distal vertebral segment to be restrained by bracing or to be fused in surgery. Largest vertebral body wedging values obtained in the sagittal plane support the claim that scoliosis could be initiated through a hypokyphosis.     

A new brace treatment similar for adolescent scoliosis and kyphosis based on restoration of thoracolumbar lordosis. Radiological and subjective clinical results after at least one year of treatment

Study design

A prospective treatment study with a new brace was conducted Objective. To evaluate radiological and subjective clinical results after one year conservative brace treatment with pressure onto lordosis at the thoracolumbar joint in children with scoliosis and kyphosis.

Summary of background data

Conservative brace treatment of adolescent scoliosis is not proven to be effective in terms of lasting correction. Conservative treatment in kyphotic deformities may lead to satisfactory correction. None of the brace or casting techniques is based on sagittal forces only applied at the thoracolumbar spine (TLI= thoracolumbar lordotic intervention). Previously we showed in patients with scoliosis after forced lordosis at the thoracolumbar spine a radiological instantaneous reduction in both coronal curves of double major scoliosis.

Methods

A consecutive series of 91 children with adolescent scoliosis and kyphosis were treated with a modified symmetric 30 degrees Boston brace to ensure only forced lordosis at the thoracolumbar spine. Scoliosis was defined with a Cobb angle of at least one of the curves [greater than or equal to] 25 degrees and kyphosis with or without a curve <25 degrees in the coronal plane. Standing radiographs were made i) at start, ii) in brace at beginning and iii) after one year treatment without brace.

Results

Before treatment start ??in brace?? radiographs showed a strong reduction of the Cobb angles in different curves in kyphosis and scoliosis groups (sagittal n = 5 all p < 0.001, pelvic obliquity p < 0.001). After one year of brace treatment in scoliosis and kyphosis group the measurements on radiographs made without brace revealed an improvement in 3 Cobb angles each.

Conclusion

Conservative treatment using thoracolumbar lordotic intervention in scoliotic and kyphotic deformities in adolescence demonstrates a marked improvement after one year also in clinical and postural criteria. An effect not obtained with current brace techniques.     

The feasibility of modal testing for measurement of the dynamic characteristics of goat vertebral motion segments

Structural vibration testing might be a promising method to study the mechanical properties of spinal motion segments as an alternative to imaging and spinal manipulation techniques. Structural vibration testing is a non-destructive measurement technique that measures the response of a system to an applied vibration as a function of frequency, and allows determination of modal parameters such as resonance frequencies (ratio between stiffness and mass), vibration modes (pattern of motion) and damping. The objective of this study was to determine if structural vibration testing can reveal the resonance frequencies that correspond to the mode shapes flexion-extension, lateroflexion and axial rotation of lumbar motion segments, and to establish whether resonance frequencies can discriminate specific structural alterations of the motion segment. Therefore, a shaker was used to vibrate the upper vertebra of 16 goat lumbar motion segments, while the response was obtained from accelerometers on the transverse and spinous processes and the anterior side of the upper vertebra. Measurements were performed in three conditions: intact, after dissection of the ligaments and after puncturing the annulus fibrosus. The results showed clear resonance peaks for flexion-extension, lateral bending and axial rotation for all segments. Dissection of the ligaments did not affect the resonance frequencies, but puncturing the annulus reduced the resonance frequency of axial rotation. These results indicate that vibration testing can be utilised to assess the modal parameters of lumbar motion segments, and might eventually be used to study the mechanical properties of spinal motion segments in vivo.     

Analysis of functional scoliosis by means of an anisotropic beam model of the human spine

An upright, muscle-relaxed human spine, suffering from a mild functional scoliosis, caused by a small difference in leg length, is modeled as an anisotropic, elastic beam. The lower end of the beam is built-in in a fixed body, i.e., the laterally tilted pelvis. The upper end is rigidly attached to a rigid body, i.e., the supported upper part of the trunk, which is supposed to move freely in the frontal plane. It is shown that the characteristic scoliotic curvature of the spine, observed on an X-ray picture, can be reproduced by means of buckling analysis of the beam model, using realistic values of geometric and loading parameters and a properly chosen bending stiffness, which is found to be in reasonable agreement with earlier experimental findings. The analysis also shows that the muscle-relaxed upright equilibrium position of the spine is mechanically unstable.     

Structural behavior of human lumbar spinal motion segments

The objectives of this study were to obtain linearized stiffness matrices, and assess the linearity and hysteresis of the motion segments of the human lumbar spine under physiological conditions of axial preload and fluid environment. Also, the stiffness matrices were expressed in the form of an 'equivalent' structure that would give insights into the structural behavior of the spine. Mechanical properties of human cadaveric lumbar L2-3 and L4-5 spinal motion segments were measured in six degrees of freedom by recording forces when each of six principal displacements was applied. Each specimen was tested with axial compressive preloads of 0, 250 and 500 N. The displacements were four slow cycles of +/-0.5mm in anterior-posterior and lateral displacements, +/-0.35 mm axial displacement, +/-1.5 degrees lateral rotation and +/-1 degrees flexion-extension and torsional rotations. There were significant increases with magnitude of preload in the stiffness, hysteresis area (but not loss coefficient) and the linearity of the load-displacement relationship. The mean values of the diagonal and primary off-diagonal stiffness terms for intact motion segments increased significantly relative to values with no preload by an average factor of 1.71 and 2.11 with 250 and 500 N preload, respectively (all eight tests p<0.01). Half of the stiffness terms were greater at L4-5 than L2-3 at higher preloads. The linearized stiffness matrices at each preload magnitude were expressed as an equivalent structure consisting of a truss and a beam with a rigid posterior offset, whose geometrical properties varied with preload. These stiffness properties can be used in structural analyses of the lumbar spine.