Three-dimensional static modeling of the lumbar spine

This paper presents three-dimensional static modeling of the human lumbar spine to be used in the formation of anatomically-correct movement patterns for a fully cable-actuated robotic lumbar spine which can mimic in vivo human lumbar spine movements to provide better hands-on training for medical students. The mathematical model incorporates five lumbar vertebrae between the first lumbar vertebra and the sacrum, with dimensions of an average adult human spine. The vertebrae are connected to each other by elastic elements, torsional springs and a spherical joint located at the inferoposterior corner in the mid-sagittal plane of the vertebral body. Elastic elements represent the ligaments that surround the facet joints and the torsional springs represent the collective effect of intervertebral disc which plays a major role in balancing torsional load during upper body motion and the remaining ligaments that support the spinal column. The elastic elements and torsional springs are considered to be nonlinear. The nonlinear stiffness constants for six motion types were solved using a multiobjective optimization technique. The quantitative comparison between the angles of rotations predicted by the proposed model and in the experimental data confirmed that the model yields angles of rotation close to the experimental data. The main contribution is that the new model can be used for all motions while the experimental data was only obtained at discrete measurement points.     

Are coupled rotations in the lumbar spine largely due to the osseo-ligamentous anatomy?--a modeling study

Prior studies have found that primary rotations in the lumbar spine are accompanied by coupled out-of-plane rotations. However, it is not clear whether these accompanying rotations are primarily due to passive (discs, ligaments and facet joints) or active (muscles) spinal anatomy. The aim of this study was to use a finite element (FE) model of the lumbar spine to predict three-dimensional coupled rotations between the lumbar vertebrae, due to passive spinal structures alone. The FE model was subjected to physiologically observed whole lumbar spine rotations about in vivo centres of rotation. Model predictions were validated by comparison of intra-discal pressures and primary rotations with in vivo measurements and these showed close agreement. Predicted coupled rotations matched in vivo measurements for all primary motions except lateral bending. We suggest that coupled rotations accompanying primary motions in the sagittal (flexion/extension) and transverse (axial rotation) planes are primarily due to passive spinal structures. For lateral bending the muscles most likely play a key role in the coupled rotation of the spine.     

New aspects of the morphology and function of the human hip joint ligaments.

The capsular ligaments of the human hip joint were submitted to exact morphological analysis, and they proved to be multiple and numerous. We have described various ligamentous systems and their interconnections, and have suggested new terminologies and systematics. The ligaments were subjected to functional analysis by means of measuring strips to determine the positions in which the ligaments are taut. The ligament systems were all found to serve a restrictive function, and various parts of the apparatus restricted all possible movements in the hip joint. Extension is restricted by the medial iliofemoral complex, abduction by the pubofemoral ligament, and adduction by the posterior coxal ligaments and by the superior ischiofemoral ligament. Flexion is restricted by the inferior ischiofemoral ligaments, inward rotation by the superior ischiofemoral ligament, and outward rotation by the lateral iliofemoral complex. Only the ligament of the femoral head is unable to exert a restricting function, despite reaching a state of tension in extreme adduction.     

Mechanically simulated muscle forces strongly stabilize intact and injured upper cervical spine specimens

Although muscles are assumed to be capable of stabilizing the spinal column in vivo, they have only rarely been simulated in vitro. Their effect might be of particular importance in unstable segments. The present study therefore tests the hypothesis that mechanically simulated muscle forces stabilize intact and injured cervical spine specimens. In the first step, six human occipito-cervical spine specimens were loaded intact in a spine tester with pure moments in lateral bending (+/- 1.5 N m), flexion-extension (+/- 1.5 N m) and axial rotation (+/- 0.5 N m). In the second step, identical flexibility tests were carried out during constant traction of three mechanically simulated muscle pairs: splenius capitits (5 N), semispinalis capitis (5 N) and longus colli (15 N). Both steps were repeated after unilateral and bilateral transection of the alar ligaments. The muscle forces strongly stabilized C0-C2 in all loading and injury states. This was most obvious in axial rotation, where a reduction of range of motion (ROM) and neutral zone to <50% (without muscles=100%) was observed. With increasing injury the normalized ROM (intact condition=100%) increased with and without muscles approximately to the same extend. With bilateral injury this increase was 125-132% in lateral bending, 112%-119% in flexion-extension and 103-116% in axial rotation. Mechanically simulated cervical spine muscles strongly stabilized intact and injured cervical spine specimens. Nevertheless, it could be shown that in vitro flexibility tests without muscle force simulation do not necessarily lead to an overestimation of spinal instability if the results are normalized to the intact state.     

Comparative role of disc degeneration and ligament failure on functional mechanics of the lumbar spine

Understanding spinal kinematics is essential for distinguishing between pathological conditions of spine disorders, which ultimately lead to low back pain. It is of high importance to understand how changes in mechanical properties affect the response of the lumbar spine, specifically in an effort to differentiate those associated with disc degeneration from ligamentous changes, allowing for more precise treatment strategies. To do this, the goals of this study were twofold: (1) develop and validate a finite element (FE) model of the lumbar spine and (2) systematically alter the properties of the intervertebral disc and ligaments to define respective roles in functional mechanics. A three-dimensional non-linear FE model of the lumbar spine (L3-sacrum) was developed and validated for pure moment bending. Disc degeneration and sequential ligament failure were modelled. Intersegmental range of motion (ROM) and bending stiffness were measured. The prediction of the FE model to moment loading in all three planes of bending showed very good agreement, where global and intersegmental ROM and bending stiffness of the model fell within one standard deviation of the in vitro results. Degeneration decreased ROM for all directions. Stiffness increased for all directions except axial rotation, where it initially increased then decreased for moderate and severe degeneration, respectively. Incremental ligament failure produced increased ROM and decreased stiffness. This effect was much more pronounced for all directions except lateral bending, which is minimally impacted by ligaments. These results indicate that lateral bending may be more apt to detect the subtle changes associated with degeneration, without being masked by associated changes of surrounding stabilizing structures.     

A geometric model of the human ankle joint.

A two-dimensional four-bar linkage model of the ankle joint is formulated to describe dorsi/plantarflexion in unloaded conditions as observed in passive tests on ankle complex specimens. The experiments demonstrated that the human ankle joint complex behaves as a single-degree-of-freedom system during passive motion, with a moving axis of rotation. The bulk of the movement occurred at the level of the ankle. Fibres within the calcaneofibular and tibiocalcaneal ligaments remained approximately isometric. The experiments showed that passive kinematics of the ankle complex is governed only by the articular surfaces and the ligaments. It was deduced that the ankle is a single-degree-of-freedom mechanism where mobility is allowed by the sliding of the articular surfaces upon each other and the isometric rotation of two ligaments about their origins and insertions, without tissue deformation. The linkage model is formed by the tibia/fibula and talus/calcaneus bone segments and by the calcaneofibular and tibiocalcaneal ligament segments. The model predicts the path of calcaneus motion, ligament orientations, instantaneous axis of rotation, and conjugate talus surface profile as observed in the experiments. Many features of ankle kinematics such as rolling and multiaxial rotation are elucidated. The geometrical model is a necessary preliminary step to the study of ankle joint stability in response to applied loads and can be used to predict the effects of changes to the original geometry of the intact joint. Careful reconstruction of the original geometry of the ligaments is necessary after injury or during total ankle replacement.     

Investigation of whiplash injuries in the upper cervical spine using a detailed neck model

Whiplash injuries continue to have significant societal cost; however, the mechanism and location of whiplash injury is still under investigation. Recently, the upper cervical spine ligaments, particularly the alar ligament, have been identified as a potential whiplash injury location. In this study, a detailed and validated explicit finite element model of a 50th percentile male cervical spine in a seated posture was used to investigate upper cervical spine response and the potential for whiplash injury resulting from vehicle crash scenarios. This model was previously validated at the segment and whole spine levels for both kinematics and soft tissue strains in frontal and rear impact scenarios. The model predicted increasing upper cervical spine ligament strain with increasing impact severity. Considering all upper cervical spine ligaments, the distractions in the apical and alar ligaments were the largest relative to their failure strains, in agreement with the clinical findings. The model predicted the potential for injury to the apical ligament for 15.2 g frontal or 11.7 g rear impacts, and to the alar ligament for a 20.7 g frontal or 14.4 g rear impact based on the ligament distractions. Future studies should consider the effect of initial occupant position on ligament distraction.     

Soft tissue structures resisting anterior instability in a computational glenohumeral joint model

The glenohumeral joint is the most dislocated joint in the body due to the lack of bony constraints and the dependence on soft tissue for stability. The roles that various structures provide to joint function are important for understanding injury treatment and orthopaedic device design purposes. The goal of this study was to develop a computational model of the glenohumeral joint whereby joint behaviour was dictated by articular contact, ligamentous constraints, muscle loading and external perturbations. The bone structure of the computational model consisted of assembled computer tomographic images of the scapula, humerus and clavicle. The soft tissue elements were composed of forces and tension-only springs that represented muscles and ligaments. Validation of this model was achieved by comparing computational predictions to the results of a cadaveric experiment in which the relative contribution of muscles and ligaments to anterior joint stability was examined. The computational model predicted an anterior subluxation force that was similar to the cadaveric experimental results in humeral external rotation. The individual structure results showed the subscapularis to be critical to stabilisation in both neutral and external rotations, the biceps stabilised the joint in neutral but not in external rotation, and the inferior glenohumeral ligament resisted anterior displacement only in external rotation. The model's predictions were similar to the conclusions of the cadaveric experiment and the literature. Knowledge gained from this type of model could assist in further understanding the contribution of soft tissue stabilisers to joint function, pre-operative planning or the design of orthopaedic implants.     

An in-vitro study of the kinematics of the normal, injured and stabilized cervical spine

The relative motion between various vertebrae of multi-level cervical ligamentous spinal segments (C2-T2), using Bryant angles, is described. A three-dimensional sonic digitizer was utilized to study the motion in flexion, extension, right lateral bending and right axial rotation. Effects of a number of injuries and stabilization (interspinous wiring and acrylic cement, PMMA) on the motion behavior of C5-C6 (injured) and C4-C5 (superior to injured) levels were investigated. The data were normalized with respect to intact specimens. The injury to capsular ligaments at C5-C6 produced a significant increase in the relative motion at C4-C5. Although the interspinous wiring reduced the motion at C5-C6 the C4-C5 motion was still higher. The application of PMMA made the motion at C4-C5 comparable to the intact specimen.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion-extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion–extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

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.     

Control exerted by ligaments

The function of the ligaments as local controllers, independent of the central nervous system, in maintaining the integrity of the joint is demonstrated by modelling the human knee in the sagittal plane, and studying its anterior-posterior motion. In addition to the ligaments, the model includes the characteristic geometry of the joint surface and some muscle groups. The connecting reaction forces at the point of contact between the tibia and the femur are considered to be constraint forces due to three different surface motions--gliding, rolling and combined gliding and rolling. It is demonstrated that the ligamentous structure maintains these holonomic and nonholonomic constraints that describe the joint motion, and that stability of the knee joint is provided mainly by ligaments. Muscular structures further stabilize and contribute to joint movement. Computer simulation of rolling movement of the knee is presented to illustrate the importance of the ligaments for joint integrity and stability.     

A light and electron microscopic study of spinal ligament innervation

The innervation of the posterior ligamentous structures of the human lumbar spine was studied by light microscopy, scanning electron microscopy and transmission electron microscopy. Three types of nerve endings were recognized: free nerve endings, Paciniform corpuscles and Ruffini corpuscles. The free nerve endings, which are thought to act as nociceptors, were found in the superficial layers of all ligaments. A few free nerve endings were also identified within the supraspinous and interspinous ligaments. The Paciniform corpuscles were predominantly found in the supraspinous ligament. The Ruffini corpuscles were located in the interspinous and flaval ligaments. These findings suggest that the posterior ligamentous structures could be involved in the spinal control system.     

Structure-function relationship of human spinal ligaments

A combination of light, scanning and transmission electron microscopy was used to investigate the morphology and ultrastructure of normal human spinal ligaments sampled from adult surgical specimens. The ligamenta flava consist mostly of dense elastic fibers, whereas the supraspinous and interspinous ligaments are preponderantly collagenous. In all ligaments, the collagen fascicles are characterized by a regular crimp structure. The inner collagen fibers of interspinous ligaments tend to be oriented parallel to the spinous processes while those of the peripheral layers run in postero-cranial direction. The presence of proteoglycan filaments is clearly demonstrated in all of the ligaments examined. They are mainly located at the d band of the collagen fibrils. These findings are discussed in relation to the function of the posterior ligamentous system. It is suggested that the interspinous ligaments are able to transmit tension from the thoracolumbar fascia to the spine. Finally, the spinal ligaments are thought to be involved in the control mechanism of the spine.     

Effect of muscle wrapping on model estimates of neck muscle strength

Of the computational models of the cervical spine reported in the literature, not one takes into account the changes in muscle paths due to the underlying vertebrae. Instead, all model the individual muscle paths as straight-line segments. The major aim of this study was to quantify the changes in muscle moment arm, muscle force and joint moment due to muscle wrapping in the cervical spine. Five muscles in a straight-line model of the cervical spine were wrapped around underlying vertebrae, and the results obtained from this model were compared against the original. The two models were then validated against experimental and computational data. Results show that muscle wrapping has a significant effect on muscle moment arms and therefore joint moments and should not be neglected.     

A reciprocal connection factor for assessing knee-joint function

In the knee joint, interactions between instantaneous kinetics and kinematics associated with ligamentous and articular tissues are not fully understood. These structures may be represented by the instantaneous screw axis ($) (ISA) and static force vectors ($′). Geometric changes to the joint structure affecting motion have not been fully explained, especially after surgical reconstruction and replacement procedures. The ISA offers a joint-characterisation approach, which is dependent on the combined forces of ligaments, articular contacts and muscles. The standard four-bar linkage model in the sagittal plane demonstrates that the normal contact force and the lines of action of the cruciate ligaments always intersect at the centre of rotation of the joint. A kinematic knee model in which the articular surfaces in the lateral and medial compartments as well as the isometric fascicles in the engaged ligaments may be represented as five constraints in a one-degree-of-freedom parallel spatial mechanism. This study provides a theoretical foundation to elucidate the role of each of these elements in the control of the ISA. A recourse to the principle of virtual work explained through d'Alembert's principle for reducing a dynamics problem to an instantaneous static scenario allows screws to be applied to the biomechanics of human motion. The principle of reciprocity links these approaches together to explain the transmitting load between the tibia and the femur as well as the relative motion within the knee joint. A principal clinical implication of this study is the introduction of the reciprocal connection factor to evaluate knee kinematics and kinetics in one simple term, allowing the quantitative assessment of the outcome of knee-joint treatment and rehabilitation methods.     

Effect of muscle wrapping on model estimates of neck muscle strength

Of the computational models of the cervical spine reported in the literature, not one takes into account the changes in muscle paths due to the underlying vertebrae. Instead, all model the individual muscle paths as straight-line segments. The major aim of this study was to quantify the changes in muscle moment arm, muscle force and joint moment due to muscle wrapping in the cervical spine. Five muscles in a straight-line model of the cervical spine were wrapped around underlying vertebrae, and the results obtained from this model were compared against the original. The two models were then validated against experimental and computational data. Results show that muscle wrapping has a significant effect on muscle moment arms and therefore joint moments and should not be neglected.