3D finite element simulation of the opening movement of the mandible in healthy and pathologic situations

One of the essential causes of disk disorders is the pathologic change in the ligamentous attachments of the disk-condyle complex. In this paper, the response of the soft components of a human temporomandibular joint during mouth opening in healthy and two pathologic situations was studied. A three-dimensional finite element model of this joint comprising the bone components, the articular disk, and the temporomandibular ligaments was developed from a set of medical images. A fiber reinforced porohyperelastic model was used to simulate the behavior of the articular disk, taking into account the orientation of the fibers in each zone of this cartilage component. The condylar movements during jaw opening were introduced as the loading condition in the analysis. In the healthy joint, it was obtained that the highest stresses were located at the lateral part of the intermediate zone of the disk. In this case, the collateral ligaments were subject to high loads, since they are responsible of the attachment of the disk to the condyle during the movement of the mandible. Additionally, two pathologic situations were simulated: damage of the retrodiscal tissue and disruption of the lateral discal ligament. In both cases, the highest stresses moved to the posterior part of the disk since it was displaced in the anterior-medial direction. In conclusion, in the healthy joint, the highest stresses were located in the lateral zone of the disk where perforations are found most often in the clinical experience. On the other hand, the results obtained in the damaged joints suggested that the disruption of the disk attachments may cause an anterior displacement of the disk and instability of the joint.     

In situ mechanical behavior of posterior spinal ligaments in the lumbar region. An in vitro study

The posterior ligaments: ligamentum flavum, articular, interspinous and supraspinous ligaments of twenty five fresh cadaveric intervertebral segments, from T11-T12 to L4-L5, extracted from fourteen spines were tested in tension. A progressive dissection method was used, that is, each segment was tested after first resecting the disk with the ligaments intact and a force-elongation curve obtained. Then one ligament was cut and the test repeated, and so on. The most restrictive ligament was found to be the ligamentum flavum followed by the articular, interspinous, and supraspinous ligaments.     

Anterior displacement of the TMJ disk: repositioning of the disk using a Mitek system. A 3D finite element study

In this paper the behaviors of the temporomandibular joint (TMJ) with an anteriorly displaced disk without reduction and with a surgically repositioned one were compared with the response of a healthy disk during jaw opening. The movement of each joint was obtained imposing the same opening path between incisors and assuming that the movement of the condyle is determined by the passive action of the masticatory muscles and the restrictions imposed by the articulating surfaces and the ligaments. A fiber-reinforced porohyperelastic model was used to simulate the behavior of the articular disk. The influence of the friction coefficient in the diseased joint was also analyzed, finding that the final displacement of the complex condyle-disk was smaller as the friction coefficient increased. On the other hand, its displacement in the repositioned joint was different than in the healthy case because the artificial sutures used in the surgery do not fully stabilize the disk posteriorly as the retrodiscal tissue does. The stress response of the disk changed in both pathologic cases: in the displaced joint the highest stresses moved from the intermediate zone (healthy case) to the posterior band, and in the reconstructed one the most loaded zone moved posteriorly at total opening. Besides, local stress concentrations appeared in the neighborhood of the artificial sutures and therefore damage of the disk and releasing of the sutures might be possible postoperatively.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construction

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials: the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

Nonlinear gross response analysis of a lumbar motion segment in combined sagittal loadings

A 3-D nonlinear mathematical model is used to analyze the mechanical response of a lumbar L2-3 motion segment including the posterior elements when subjected to combined sagittal plane loads. The loadings consist of axial compression force, anterior and posterior shear forces, and flexion and extension moments. The facet articulation is modelled as a general moving contact problem and the ligaments as a collection of uniaxial elements. The disk nucleus is considered as an inviscid fluid and the annulus as a composite of collagenous fibers embedded in a matrix of ground substance. The presence of axial compression force reduces the segmental stiffness in flexion whereas a reverse trend is predicted in extension. In the presence of axial compression with and without sagittal shear force, flexion considerably increases the intradiscal pressure while extension reduces it. In other words, under an identical compression force, disk pressure is predicted to be noticeably larger in flexion than in extension. The segmental mechanical response in extension loadings is markedly influenced by the changes in the relative geometry of the articular surfaces at the lower regions. Finally, the deformation of the bony structures plays a significant role in the segmental mechanics under relatively large loads.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 1: Theoretical Construct

A three-dimensional model of the knee is developed to study the interactions between the muscles, ligaments, and bones during activity. The geometry of the distal femur, proximal tibia, and patella is based on cadaver data reported for an average-size knee. The shapes of the femoral condyles are represented by high-order polynomials; the tibial plateaux and patellar facets are approximated as flat surfaces. The contacting surfaces of the femur and tibia are modeled as deformable, while those of the femur and patella are assumed to be rigid. Interpenetration of the femur and tibia is taken into account by modeling cartilage as a thin, linear, elastic layer, mounted on rigid bone. Twelve elastic elements describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit modeled as a three-element muscle in series with tendon. The path of each muscle is approximated as a straight line, except where it contacts and wraps around bone and other muscles; changes in muscle paths are taken into account using data obtained from MRI. In the first part of this paper, the model is used to simulate passive knee flexion. Quantitative comparisons of the model results with experimental data reported in the literature indicate that the relative movements of the bones and the geometry of the ligaments and muscles in the model are similar to those evident in the real knee. In Part II, the model is used to describe knee-ligament function during anterior-posterior draw, axial rotation, and isometric knee-extension and knee-flexion exercises.     

The retaining ligaments of the cheek

The zygomatic ligaments (McGregor's patch) anchor the skin of the cheek to the inferior border of the zygoma just posterior to the origin of the zygomaticus minor muscle. The mandibular ligaments tether the overlying skin to the anterior mandible. Both these ligaments are obstacles to surgical maneuvers intended to advance the overlying skin. They also restrain the facial skin against gravitational changes, and they delineate the anterior border of the "jowl" area. The platysma-auricular ligament is a thin fascial sheet that extends from the posterosuperior border of the platysma and that is intimately attached to the periauricular skin; it serves as a surgical guide to the posterosuperior border of the platysma. The anterior platysma-cutaneous ligaments are variable fascial condensations that anchor the SMAS and platysma to the dermis. They can cause anatomic disorientation with dissection of false planes into the dermis. These four ligaments are useful as anatomic landmarks during facial dissections. The tethering effects of the zygomatic and mandibular ligaments must be interrupted if a maximum upward movement of the facial skin is desired.     

Correlations of calcium accumulations in arteries, veins, cartilages, ligaments, and bones in single humans

To show the relationships of calcium accumulation in the thoracic aorta to the other tissues, calcium contents were determined with a microwave-induced plasma-atomic emission spectrometer on arteries, veins, cartilages, ligaments, and bones. These tissues were resected from 18 individuals, consisting of 11 men and 7 women who died in the age range 59–91 yr. As thoracic and abdominal aortas are routinely used for radiographic examination of arterial calcification, they appear to be standard tissues of the calcium accumulation. The calcium accumulations were determined in the femoral artery, the superior and inferior venae cavae, the internal jugular vein, cartilages of the articular disk of the temporomandibular joint and the intervertebral disk, both the ligaments of the anterior cruciate ligament and the ligamentum capitis femoris, and the calcaneus, in contrast with the thoracic aorta. As calcium increased in the thoracic aorta, it increased in the femoral artery, the articular disk of the temporomandibular joint, the intervertebral disk, both ligaments of the anterior cruciate ligament, and the ligamentum capitis femoris, but it did not increase in veins, such as the superior and inferior venae cavae and the internal jugular vein. In contrast, it decreased in the calcaneus.     

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.     

Recruitment of knee joint ligaments

On the basis of earlier reported data on the in vitro kinematics of passive knee-joint motions of four knee specimens, the length changes of ligament fiber bundles were determined by using the points of insertion on the tibia and femur. The kinematic data and the insertions of the ligaments were obtained by using Roentgenstereophotogrammetry. Different fiber bundles of the anterior and posterior cruciate ligaments and the medial and lateral collateral ligaments were identified. On the basis of an assumption for the maximal strain of each ligament fiber bundle during the experiments, the minimal recruitment length and the probability of recruitment were defined and determined. The motions covered the range from extension to 95 degrees flexion and the loading conditions included internal or external moments of 3 Nm and anterior or posterior forces of 30 N. The ligament length and recruitment patterns were found to be consistent for some ligament bundles and less consistent for other ligament bundles. The most posterior bundle of each ligament was recruited in extension and the lower flexion angles, whereas the anterior bundle was recruited for the higher flexion angles. External rotation generally recruited the collateral ligaments, while internal rotation recruited the cruciate ligaments. However, the anterior bundle of the posterior cruciate ligament was recruited with external rotation at the higher flexion angles. At the lower flexion angles, the anterior cruciate and the lateral collateral ligaments were recruited with an anterior force. The recruitment of the posterior cruciate ligament with a posterior force showed that neither its most anterior nor its most posterior bundle was recruited at the lower flexion angles. Hence, the posterior restraint must have been provided by the intermediate fiber bundles, which were not considered in the experiment. At the higher flexion angles, the anterior bundles of the anterior cruciate ligament and the posterior cruciate ligament were found to be recruited with anterior and posterior forces, respectively. The minimal recruitment length and the recruitment probability of ligament fiber bundles are useful parameters for the evaluation of ligament length changes in those experiments where no other method can be used to determine the zero strain lengths, ligament strains and tensions.     

Geometric and mechanical properties of human cervical spine ligaments

This study characterized the geometry and mechanical properties of the cervical ligaments from C2-T1 levels. The lengths and cross-sectional areas of the anterior longitudinal ligament, posterior longitudinal ligament, joint capsules, ligamentum flavum, and interspinous ligament were determined from eight human cadavers using cryomicrotomy images. The geometry was defined based on spinal anatomy and its potential use in complex mathematical models. The biomechanical force-deflection, stiffness, energy, stress, and strain data were obtained from 25 cadavers using in situ axial tensile tests. Data were grouped into middle (C2-C5) and lower (C5-T1) cervical levels. Both the geometric length and area of cross section, and the biomechanical properties including the stiffness, stress, strain, energy, and Young's modulus, were presented for each of the five ligaments. In both groups, joint capsules and ligamentum flavum exhibited the highest cross-sectional area (p < 0.005), while the longitudinal ligaments had the highest length measurements. Although not reaching statistical significance, for all ligaments, cross-sectional areas were higher in the C5-T1 than in the C2-C5 group; and lengths were higher in the C2-C5 than in the C5-T1 group with the exception of the flavum (Table 1 in the main text). Force-deflection characteristics (plots) are provided for all ligaments in both groups. Failure strains were higher for the ligaments of the posterior (interspinous ligament, joint capsules, and ligamentum flavum) than the anterior complex (anterior and posterior longitudinal ligaments) in both groups. In contrast, the failure stress and Young's modulus were higher for the anterior and posterior longitudinal ligaments compared to the ligaments of the posterior complex in the two groups. However, similar tendencies in the structural responses (stiffness, energy) were not found in both groups. Researchers attempting to incorporate these data into stress-analysis models can choose the specific parameter(s) based on the complexity of the model used to study the biomechanical behavior of the human cervical spine.     

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.     

The effects of flexion and rotation on the length patterns of the ligaments of the knee

Measurements have been made of the lengths of the ligaments in human knee joint specimens. The ligaments considered were the lateral collateral, medial collateral, anterior cruciate and posterior cruciate. The ligament length patterns were determined for twelve specimens at flexions of 0, 30, 60, 90 and 120°, in neutral, internal rotation and external rotation at each angle. The collateral ligaments steadily diminished by about 20 per cent in length from 0 to 120° flexion, rotation having little effect. The anterior cruciate gradually increased 10 per cent from 0 to 120° flexion and the posterior cruciate, was 10 per cent longer at 0° flexion than at all other angles for which length was constant. The action of the cruciates was therefore somewhat reciprocal. Rotation had a significant effect on cruciate lengths, affecting the anterior more than the posterior cruciate. Computations were made of the change in length of the anterior and posterior fibres of each cruciate ligament, in relation to the central fibres. Reciprocal functions between fibres were demonstrated.     

Linear and quasi-linear viscoelastic characterization of ankle ligaments

The objective of this study was to produce linear and nonlinear viscoelastic models of eight major ligaments in the human ankle/foot complex for use in computer models of the lower extremity. The ligaments included in this study were the anterior talofibular (ATaF), anterior tibiofibular (ATiF), anterior tibiotalar (ATT), calcaneofibular (CF), posterior talofibular (PTaF), posterior tibiofibular (PTiF), posterior tibiotalar (PTT), and tibiocalcaneal (TiC) ligaments. Step relaxation and ramp tests were performed. Back-extrapolation was used to correct for vibration effects and the error introduced by the finite rise time in step relaxation tests. Ligament behavior was found to be nonlinear viscoelastic, but could be adequately modeled up to 15 percent strain using Fung's quasilinear viscoelastic (QLV) model. Failure properties and the effects of preconditioning were also examined.     

Sensorimotor control of the spine.

The spinal viscoelastic structures including disk, capsule and ligaments were reviewed with special focus on their sensory motor functions. Afferent capable of monitoring proprioceptive and kinesthetic information are abundant in the disc, capsule and ligament. Electrical stimulation of the lumbar afferents in the discs, capsules and ligaments seem to elicit reflex contraction of the multifidus and also longissimus muscles. The muscular excitation is pronounced in the level of excitation and with weaker radiation 1 to 2 levels above and below. Similarly, mechanical stimulation of the spinal viscoelastic tissues excites the muscles with higher excitation intensity when more than one tissue (ligaments and discs for example) is stimulated. Overall, it seems that spinal structures are well suited to monitor sensory information as well as to control spinal muscles and probably also provide kinesthetic perception to the sensory cortex.     

双侧自体腘绳肌腱一期重建前后交叉韧带损伤的临床疗效

目的:探讨关节镜辅助下使用双侧自体腘绳肌腱一期修复膝关节前后交叉韧带损伤的方法和临床疗效。方法:内窥镜微创双侧自体腘绳肌腱修复膝关节内韧带,术后用IKDC分级、影像学IKDC分级、Lysholm功能评分和KT2000TM测量进行关节机能打分。结果:11例患者获得3-5年随访,平均随访3.8年。术前Lysholm功能评分平均(46.8±5.7)分,终末随访时平均(81.3±10.5)分,差异有显著性(P<0.05)。术后关节稳定性测量,在20磅时、30磅和最大拉力时健膝和患膝分别是:6.1±0.3和6.8±0.8;6.3±0.5和7.7±1.3;7.5±0.6和9.6±2.4,统计学上差异无显著性(P>0.05)。主观IKDC分级:A级4例,B级6例,C级1例;影像学IKDC分级:A级8例,B级2例,C级1例。结论:关节镜辅助下使用双侧自体腘绳肌腱一期修复膝关节前后交叉韧带损伤是重建膝关节稳定性的良好有效方法。     

Ligament fibre recruitment at the human ankle joint complex in passive flexion

Knowledge of ligament fibre recruitment at the human ankle joint complex is a fundamental prerequisite for analysing mobility and stability. Previous experimental and modelling studies have shown that ankle motion must be guided by fibres within the calcaneofibular and tibiocalcaneal ligaments, which remain approximately isometric during passive flexion. The purpose of this study was to identify these fibres.

Three below-knee amputated specimens were analysed during passive flexion with combined radiostereometry for bone pose estimation and 3D digitisation for ligament attachment area identification. A procedure based on singular value decomposition enabled matching bone pose with digitised data and therefore reconstructing position in space of ligament attachment areas in each joint position. Eleven ordered fibres, connecting corresponding points on origin and insertion curves, were modelled for each of the following ligaments: posterior talofibular, calcaneofibular, anterior talofibular, posterior tibiotalar, tibiocalcaneal, and anterior tibiotalar.

The measured changes in length for the ligament fibres revealed patterns of tightening and slackening. The most anterior fibre of the calcaneofibular and the medio-anterior fibre of the tibiocalcaneal ligament exhibited the most isometric behaviour, as well as the most posterior fibre of the anterior talofibular ligament. Fibres within the calcaneofibular ligament remain parallel in the transverse plane, while those within the tibiocalcaneal ligament become almost parallel in joint neutral position. For both these ligaments, fibres maintain their relative inclination in the sagittal plane throughout the passive flexion range.

The observed significant change in both shape and orientation of the ankle ligaments suggest that this knowledge is fundamental for future mechanical analysis of their response to external forces.     

Accumulation of calcium in human common iliac artery, aortic valve, xiphoid process, costal cartilage, posterior longitudinal ligament, trigeminal nerve, and rib accompanied by increase of magnesium

To examine whether an accumulation of Ca in the tissues was accompanied by an increase of Mg, the authros investigated the relationships between Ca and Mg contents in the common iliac arteries, aortic valves, xiphoid processes, costal cartilages, posterior longitudinal ligaments, trigeminal nerves, and ribs by inductively coupled plasma-atomic emission spectrometry. After the ordinary dissections by medical students were finished, the common iliac arteries, aortic valves, xiphoid processes, bilateral the fourth costal cartilages, posterior longitudinal ligaments between the fourth and fifth cervical vertebrae, trigeminal nerves, and bilateral the sixth ribs were resected from the subjects and elements were determined. It was found that there were extremely significant direct correlations between Ca and Mg contents in all of the common iliac arteries, aortic valves, costal cartilages, posterior longitudinal ligaments, and trigeminal nerves, whereas there were significant direct correlations in both the xiphoid processes and ribs. As for the tissues containing Ca higher than 20 mg/g, the average mass ratios of Mg/Ca were similar among the seven tissues. As Ca increased in all of the common iliac arteries, aortic valves, xiphoid processes, costal cartilages, posterior longitudinal ligaments, trigeminal nerves, and ribs, Mg increased simultaneously in the seven tissues.     

Biomechanical properties of human lumbar spine ligaments.

Biomechanical properties of the six major lumbar spine ligaments were determined from 38 fresh human cadaveric subjects for direct incorporation into mathematical and finite element models. Anterior and posterior longitudinal ligaments, joint capsules, ligamentum flavum, interspinous, and supraspinous ligaments were evaluated. Using the results from in situ isolation tests, individual force-deflection responses from 132 samples were transformed with a normalization procedure into mean force-deflection properties to describe the nonlinear characteristics. Ligament responses based on the mechanical characteristics as well as anatomical considerations, were grouped into T12-L2, L2-L4, and L4-S1 levels maintaining individuality and nonlinearity. A total of 18 data curves are presented. Geometrical measurements of original length and cross-sectional area for these six major ligaments were determined using cryomicrotomy techniques. Derived parameters including failure stress and strain were computed using the strength and geometry information. These properties for the lumbar spinal ligaments which are based on identical definitions used in mechanical testing and geometrical assay will permit more realistic and consistent inputs for analytical models.