An improved OpenSim gait model with multiple degrees of freedom knee joint and knee ligaments

Musculoskeletal models are widely used to investigate joint kinematics and predict muscle force during gait. However, the knee is usually simplified as a one degree of freedom joint and knee ligaments are neglected. The aim of this study was to develop an OpenSim gait model with enhanced knee structures. The knee joint in this study included three rotations and three translations. The three knee rotations and mediolateral translation were independent, with proximodistal and anteroposterior translations occurring as a function of knee flexion/extension. Ten elastic elements described the geometrical and mechanical properties of the anterior and posterior cruciate ligaments (ACL and PCL), and the medial and lateral collateral ligaments (MCL and LCL). The three independent knee rotations were evaluated using OpenSim to observe ligament function. The results showed that the anterior and posterior bundles of ACL and PCL (aACL, pACL and aPCL, pPCL) intersected during knee flexion. The aACL and pACL mainly provided force during knee flexion and adduction, respectively. The aPCL was slack throughout the range of three knee rotations; however, the pPCL was utilised for knee abduction and internal rotation. The LCL was employed for knee adduction and rotation, but was slack beyond 20° of knee flexion. The MCL bundles were mainly used during knee adduction and external rotation. All these results suggest that the functions of knee ligaments in this model approximated the behaviour of the physical knee and the enhanced knee structures can improve the ability to investigate knee joint biomechanics during various gait activities.     

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.     

On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Gender differences exist in the hip joint moments of healthy older walkers

Gender differences in the incidence of symptomatic hip osteoarthritis (OA), changes in hip cartilage volume and hip joint space and rates hip arthroplasty of older people are reported in the literature. As the rate of progression of OA is in part mechanically modulated it is possible that this gender bias may be related to inherent differences (if they exist) in walking mechanics between older males and females. The purpose of this study was to examine potential mechanisms for gender differences in hip joint mechanics during walking by testing the hypotheses that females would exhibit higher hip flexion, adduction and internal rotation moments but not significantly greater normalized ground reaction forces (GRFs). Forty-two healthy subjects (21 male, 21 female), ages 50–79 yr were recruited for gait analysis. In support of the hypotheses, greater external hip adduction and internal rotation along with hip extension moments were found for females compared to males after normalizing for body size for all self-selected walking speeds. Differences in walking style (kinematics) were the main determinants in the joint kinetic differences as no differences in the normalized GRFs were found. As external joint moments are surrogate measures of the joint contact forces, the results of this study suggest the hip joint stress for the female population is higher compared to male population. This is in favor of a hypothesis that the increased joint contact stress in a female population could contribute to a greater joint degeneration at the hip in females as compared with males.     

Cruciate coupling and screw-home mechanism in passive knee joint during extension--flexion

The screw-home mechanism and coupling between forces in cruciate ligaments during passive knee joint flexion were investigated for various boundary conditions, flexion axis alignments and posterior cruciate ligaments (PCL)/anterior cruciate ligament (ACL) conditions. A developed non-linear 3D finite element model was used to perform detailed elasto-static response analyses of the human tibiofemoral joint as a function of flexion angle varying from 10 degrees hyper-extension to 90 degrees flexion. The tibia rotated internally as the femur flexed and externally as the femur extended. The re-alignment of the flexion axis by +/-5 degrees rotation about the axial (distal-proximal) axis, transection of the ACL and changes in cruciate ligament initial strains substantially influenced the 'screw-home' motion. On the other hand, restraint on this coupled rotation diminished ACL forces in flexion. A remarkable coupling was predicted between ACL and PCL forces in flexion; forces in both cruciate ligaments increased as the initial strain or pretension in one of them increased whereas they both diminished as one of them was cut or became slack. This has important consequences in joint functional biomechanics following a ligament injury or replacement surgery and, hence, in the proper management of joint disorders.     

Analysis of simulated single ligament transection on the mechanical behaviour of a lumbar functional spinal unit.

The influence of the different lumbar spinal ligaments on intersegmental rotation is not fully understood. In order to explore this effect, a finite element model of the functional spinal unit L3/L4 was loaded with pure moments in the three main anatomic planes. The two extremes--minimum and maximum--ligament stiffness values reported in the literature were applied. After virtual transection of each of the spinal ligaments in turn, the intersegmental rotation and forces in the remaining ligaments were calculated. On flexion, the highest force was found for the posterior longitudinal ligament; on extension and lateral bending for the anterior longitudinal ligament; and on axial rotation for the facet capsular ligament. The strongest influence on intersegmental rotation is exerted by the interspinous ligament on flexion, by the anterior longitudinal ligament on extension and lateral bending, and by the facet capsular ligaments on axial rotation. Ligament stiffness has a strong influence on intersegmental rotation and forces in the ligaments, so that finite element models of spinal segments must be validated by experimental data. This study should help to elucidate the role of the various ligaments.     

Effect of simulated joint instability and bracing on ankle and subtalar joint flexibility

It is clinically challenging to distinguish between ankle and subtalar joints instability in vivo. Understanding the changes in load-displacement at the ankle and subtalar joints after ligament injuries may detect specific changes in joint characteristics that cannot be detected by investigating changes in range of motion alone. The effect of restricting joints end range of motion with ankle braces was already established, but little is known about the effect of an ankle brace on the flexibility of the injured ankle and subtalar joints. Therefore, the purposes of this study were to (1) understand how flexibility is affected at the ankle and subtalar joints after sectioning lateral and intrinsic ligaments during combined sagittal foot position and inversion and during internal rotation and (2) investigate the effect of a semi-rigid ankle brace on the ankle and subtalar joint flexibility. Kinematics and kinetics were collected from nine cadaver feet during inversion through the range of ankle flexion and during internal rotation. Motion was applied with and without a brace on an intact foot and after sequentially sectioning the calcaneofibular ligament (CFL) and the intrinsic ligaments. Segmental flexibility was defined as the slope of the angle-moment curve for each 1 Nm interval. Early flexibility significantly increased at the ankle and subtalar joint after CFL sectioning during inversion. The semi-rigid ankle brace significantly decreased early flexibility at the subtalar joint during inversion and internal rotation for all ligament conditions and at the ankle joint after all ligaments were cut.     

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.     

Computational modeling to predict mechanical function of joints: application to the lower leg with simulation of two cadaver studies

Computational models of musculoskeletal joints and limbs can provide useful information about joint mechanics. Validated models can be used as predictive devices for understanding joint function and serve as clinical tools for predicting the outcome of surgical procedures. A new computational modeling approach was developed for simulating joint kinematics that are dictated by bone/joint anatomy, ligamentous constraints, and applied loading. Three-dimensional computational models of the lower leg were created to illustrate the application of this new approach. Model development began with generating three-dimensional surfaces of each bone from CT images and then importing into the three-dimensional solid modeling software SOLIDWORKS and motion simulation package COSMOSMOTION. Through SOLIDWORKS and COSMOSMOTION, each bone surface file was filled to create a solid object and positioned necessary components added, and simulations executed. Three-dimensional contacts were added to inhibit intersection of the bones during motion. Ligaments were represented as linear springs. Model predictions were then validated by comparison to two different cadaver studies, syndesmotic injury and repair and ankle inversion following ligament transection. The syndesmotic injury model was able to predict tibial rotation, fibular rotation, and anterior/posterior displacement. In the inversion simulation, calcaneofibular ligament extension and angles of inversion compared well. Some experimental data proved harder to simulate accurately, due to certain software limitations and lack of complete experimental data. Other parameters that could not be easily obtained experimentally can be predicted and analyzed by the computational simulations. In the syndesmotic injury study, the force generated in the tibionavicular and calcaneofibular ligaments reduced with the insertion of the staple, indicating how this repair technique changes joint function. After transection of the calcaneofibular ligament in the inversion stability study, a major increase in force was seen in several of the ligaments on the lateral aspect of the foot and ankle, indicating the recruitment of other structures to permit function after injury. Overall, the computational models were able to predict joint kinematics of the lower leg with particular focus on the ankle complex. This same approach can be taken to create models of other limb segments such as the elbow and wrist. Additional parameters can be calculated in the models that are not easily obtained experimentally such as ligament forces, force transmission across joints, and three-dimensional movement of all bones. Muscle activation can be incorporated in the model through the action of applied forces within the software for future studies.     

Quantitative evaluation of the major determinants of human gait

Accurate knowledge of the isolated contributions of joint movements to the three-dimensional displacement of the center of mass (COM) is fundamental for understanding the kinematics of normal walking and for improving the treatment of gait disabilities. Saunders et al. (1953) identified six kinematic mechanisms to explain the efficient progression of the whole-body COM in the sagittal, transverse, and coronal planes. These mechanisms, referred to as the major determinants of gait, were pelvic rotation, pelvic list, stance knee flexion, foot and knee mechanisms, and hip adduction. The aim of the present study was to quantitatively assess the contribution of each major gait determinant to the anteroposterior, vertical, and mediolateral displacements of the COM over one gait cycle. The contribution of each gait determinant was found by applying the concept of an ‘influence coefficient’, wherein the partial derivative of the COM displacement with respect to a prescribed determinant was calculated. The analysis was based on three-dimensional measurements of joint angular displacements obtained from 23 healthy young adults walking at slow, normal and fast speeds. We found that hip flexion, stance knee flexion, and ankle-foot interaction (comprised of ankle plantarflexion, toe flexion and the displacement of the center of pressure) are the major determinants of the displacements of the COM in the sagittal plane, while hip adduction and pelvic list contribute most significantly to the mediolateral displacement of the COM in the coronal plane. Pelvic rotation and pelvic list contribute little to the vertical displacement of the COM at all walking speeds. Pelvic tilt, hip rotation, subtalar inversion, and back extension, abduction and rotation make negligible contributions to the displacements of the COM in all three anatomical planes.     

An analytical approach to determine the in situ forces in the glenohumeral ligaments.

The purpose of this study was to use an analytical approach to determine the forces in the glenohumeral ligaments during joint motion. Predictions from the analytical approach were validated by comparing them to experimental data. Using a geometric model, the lengths of the four glenohumeral ligaments were determined during anterior-posterior loading simulations and forward flexion-extension. The corresponding force in each structure was subsequently calculated based on length data via load-elongation curves obtained experimentally. During the anterior loading simulation at 0 deg of abduction, the superior glenohumeral ligament carried up to 71 N at the maximally translated position. At 90 deg of abduction, the anterior band of the inferior glenohumeral ligament had the highest force of 45 N during anterior loading. These results correlated well with those found in previous experimental studies. We believe that this validated analytical approach can be used to predict the forces in the glenohumeral ligaments during more complex joint motion as well as assist surgeons during shoulder repair procedures.     

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 instrumented,dynamic test for anterior laxity of the ankle joint complex

Evaluation of anterior laxity of the ankle joint complex is a difficult clinical problem. Currently, the prime determinant for anterolateral ligament function is the subjective manual examination of anterior laxity of the ankle joint complex. An instrumented dynamic test was developed for objective measurement of anterior laxity of the ankle joint complex. The principle of the test was to apply a force-impulse to the calcaneus, within the muscle reflex time, and to measure anterior–posterior and mediolateral rotation. The test was performed on a cadaver specimen and on 15 volunteers of which five subjects suffered from chronic one-sided lateral ankle ligament instability.

In the cadaver test, anterior translation values increased from 5 to 11 mm, after cutting the anterior talofibular ligament and subsequently cutting the calcaneofibular ligament. In the 10 normal subjects, the mean anterior translation value was 6.7 mm (±1.9 mm). The relative variation of the test result within a measurement session was 2.5% (±1.6%). Between the sessions the relative laxity variation was 2.6% (±2.6%). In the ten normal subjects the mean right–left difference was not significantly different from zero. In four out of the five patients it was more than 2 mm. As in the cadaver test in all measurements, the mediolateral rotations were small (<2.5°). The volunteers complained about same pain at the heel after multiple test sessions.

In conclusion the dynamic, functional test appears to be capable of objectively measuring a value for anterior laxity of the ankle joint complex reflecting the functional status of the anterolateral ankle ligaments.     

The effect of three-dimensional postural change on shear elastic modulus of the iliotibial band

To understand and treat iliotibial band (ITB) syndrome, caused by excessive compression between the ITB and lateral femoral condyle, it is important to identify factors contributing to an increase in ITB stiffness. The purpose of this study was to clarify the factors that contribute to an increase in ITB stiffness by examining the relationship between three-dimensional postural changes and ITB stiffness. Fourteen healthy individuals performed one-leg standing under 7 conditions (including normal one-leg standing as a control condition) in which the pelvic position was changed in three planes. The shear elastic modulus in the ITB was measured using shear-wave elastography, as a measure of ITB stiffness. The three-dimensional joint angles and external joint moments in the hip and knee joints were also measured to confirm the changes in joint angles and external load. Compared to the normal one-leg standing condition, ITB stiffness was significantly increased in the pelvic posterior tilted position (i.e. hip extension), contralateral pelvic dropped position (i.e. hip adduction), and contralateral pelvic posterior rotated position (i.e. hip external rotation). The findings suggest that interventions to reduce hip extension, adduction, and external rotation might be useful if these excessive positional changes are detected in patients with ITB syndrome.     

Kinematics and kinetics of the lower extremities of young and elder women during stairs ascent while wearing low and high-heeled shoes

The effect of the heel height on the temporal, kinematic and kinetic parameters was investigated in 16 young and 11 elderly females. Kinematic and kinetic data were collected when the subjects ascended stairs with their preferred speed in two conditions: wearing low-heeled shoes (LHS), and high-heeled shoes (HHS). The younger adults showed more adjustments in forces and moments at the knee and hip in frontal and transverse planes. Besides a few significantly changes in joint forces and moments, the elder group demonstrated longer cycle duration and double stance phase, larger trunk sideflexion and hip internal rotation, less hip adduction while wearing HHS. Most differences in joint motions between two groups were found at the hip and knee either in LHS or HHS condition. Instead, the differences in moment occurred at the hip joint and only in HHS. The interaction of the heel height and age showed the influences of heel height on trunk rotation, hip abduction/adduction, and knee and hip force and moment at the frontal plane depended on age. These phenomena suggest that younger and elderly women adapt their gait and postural control differently during stair ascent (SA) while wearing HHS.     

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.     

Method for the evaluation of factors influencing the dislocation stability of total hip endoprotheses]

Dislocation of the artificial joint is a serious complication of total hip replacement. Various factors with an influence on dislocation stability were determined clinically. Our goal was to develop a method for evaluating experimentally the parameters implant design, position and the load situation for their influence on joint stability. With the newly developed testing device the range of motion to impingement and to dislocation can be determined at different implant positions. In addition, the rotational moments on subluxation, i.e. the "levering out" of the femoral head, can be determined. By way of example several hip implants were examined during movements associated with dislocation, e.g. (internal-)rotation in 90 degrees flexion and 0 degrees adduction as well as with (external-)rotation in combination with 10 degrees extension and 15 degrees adduction. Irrespective of implant design and position, the following movement phases can be differentiated: undisturbed motion, impingement, subluxation and, finally, complete dislocation of the head. On the basis of the range of motion of the specific phases, the moments occurring and the direction of dislocation, different implant systems can be compared. In this study the influence of the head diameter on the dislocation stability of the hip endoprosthesis is shown. With the aid of the model presented herein, a data set showing the most favourable and/or most dislocation stable implant position can be acquired for different combinations of the implant components. Additionally, useful information for implant design can be deduced and applied to new developments and/or modifications of existing implant components.     

Collateral ligaments of the distal sesamoid bone in the digit of Equus: re-evaluating midstance function

The distal forelimb of the horse has a complex array of ligaments that play a critical role in determining function of the digit and are often associated with the initiation of foot pathologies. The collateral ligaments of the distal sesamoid bone (CLDS) play an important role in digit stabilization near the end of foot contact and there is also limited evidence to suggest that the CLDS stabilize the proximal interphalangeal joint (PIPJ) during weight bearing. By virtue of their anatomical attachments where the ligaments pass dorsal to the axis of rotation of the PIPJ, it is reasonable to assume that the CLDS prevent flexion of the PIPJ during weight bearing or midstance in a moving horse. To test this functional hypothesis, forelimb specimens from three mixed-breed horses were loaded in compression in a materials testing frame. Limb loading was applied with the CLDS intact and following transection. Average PIPJ angle and metacarpophalangeal joint (MCPJ) angle at maximum load (approximately 3000 N) were calculated from angular changes of proximal and middle phalanges and the third metacarpal, which were compared between intact and transected trials. PIPJ angles were found to be the same (175 degrees) at maximum load for intact and transected trials. The proximal and middle phalanges rotated together remaining aligned, regardless of the CLDS condition. Contrary to expectation, however, the combined proximal and middle phalanges unit rotates less relative to the third metacarpal under load after transection, indicating less digit extension at the metacarpophalangeal (fetlock) joint without the influence of CLDS. Since the mechanical properties of the fetlock joint are unchanged by CLDS transection, observed proximal and middle phalanx motion is dependent on increased rotation of the distal phalanx after transection. The original hypothesis was not supported and the results suggest that at midstance the CLDS function primarily to stabilize the articulation of the middle phalanx about the distal phalanx to limit distal interphalangeal joint extension during weight bearing. Establishing the functional role of the CLDS may help to better understand the biomechanical consequences of ligament injuries and diseases of the pastern.     

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 three-dimensional study of the kinematics of the human knee

This paper represents a three-dimensional study of the human knee-joint and studies kinematic effects of the cruciate ligaments. Two methods were used for our studies, one method was preferred. This method used a time lapse photograph and strobe light to give us a plot of reference points to carry out our analysis using the method of Rouleaux applied to three dimensions. Five cadaver joints were used, each of which was used for three series of experiments, including the joint with capsule intact, with one of the ligaments cut and with the remaining ligament cut. Both lateral and medial studies were conducted to provide data for a three-dimensional study.

It was found that the cruciate ligaments had little effect on the kinematics of the knee, and that the knee motion remained unchanged after cutting one or both of the cruciate ligaments. It was concluded that the motion of the knee was due to the geometry of the bones and perhaps the collateral ligaments, and that the joint could be replaced with a prosthesis having a three dimensional axis of rotation with a fixed center.