Three-dimensional Musculoskeletal Model Research Articles

Estimation of Muscle Response Using Three-Dimensional Musculoskeletal Models Before Impact Situation: A Simulation Study

When car crash experiments are performed using cadavers or dummies, the active muscles' reaction on crash situations cannot be observed. The aim of this study is to estimate muscles' response of the major muscle groups using three-dimensional musculoskeletal model by dynamic simulations of low-speed sled-impact. The three-dimensional musculoskeletal models of eight subjects were developed, including 241 degrees of freedom and 86 muscles. The muscle parameters considering limb lengths and the force-generating properties of the muscles were redefined by optimization to fit for each subject. Kinematic data and external forces measured by motion tracking system and dynamometer were then input as boundary conditions. Through a least-squares optimization algorithm, active muscles' responses were calculated during inverse dynamic analysis tracking the motion of each subject. Electromyography for major muscles at elbow, knee, and ankle joints was measured to validate each model. For low-speed sled-impact crash, experiment and simulation with optimized and unoptimized muscle parameters were performed at 9.4 m/h and 10 m/h and muscle activities were compared among them. The muscle activities with optimized parameters were closer to experimental measurements than the results without optimization. In addition, the extensor muscle activities at knee, ankle, and elbow joint were found considerably at impact time, unlike previous studies using cadaver or dummies. This study demonstrated the need to optimize the muscle parameters to predict impact situation correctly in computational studies using musculoskeletal models. And to improve accuracy of analysis for car crash injury using humanlike dummies, muscle reflex function, major extensor muscles' response at elbow, knee, and ankle joints, should be considered.

Effect of hip angle on anterior hip joint force during gait

Anterior hip or groin pain is a common complaint for which people are referred for physical therapy. We have observed that people with anterior hip pain often walk in greater hip extension than people without anterior hip pain, and that the pain is reduced when they walk in less hip extension. Therefore, we investigated anterior hip joint forces which may contribute to anterior hip pain and examined the effect of end range hip extension on the anterior hip joint force during gait. To do this, we used a 6 degree of freedom, three-dimensional musculoskeletal model to estimate hip joint forces during gait. Within subjects, the maximum anterior hip joint force for gait trials with the most hip extension was compared to the anterior hip joint force for gait trials with the least hip extension. The musculoskeletal model indicated that increasing the maximum end range hip extension when walking results in an increase in the anterior hip joint force when compared to walking in less hip extension. Walking in greater hip extension may result in an increase in the anterior hip joint force, and thereby contribute to anterior hip pain. The findings of this study provide some evidence supporting the use of gait modification to reduce anterior hip force when treating people with anterior hip pain.

Hamstring muscle forces prior to and immediately following an acute sprinting-related muscle strain injury

A thorough understanding of the biomechanics of the hamstrings during sprinting is required to optimise injury rehabilitation and prevention strategies. The main aims of this study were to compare hamstrings load across different modes of locomotion as well as before and after an acute sprinting-related muscle strain injury. Bilateral kinematic and ground reaction force data were captured from a single subject whilst walking, jogging and sprinting prior to and immediately following a significant injury involving the right semitendinosis and biceps femoris long head muscles. Experimental data were input into a three-dimensional musculoskeletal model of the body and used, together with optimisation theory, to determine lower-limb muscle forces for each locomotor task. Hamstrings load was found to be greatest during terminal swing for sprinting. The hamstrings contributed the majority of the terminal swing hip extension and knee flexion torques, whilst gluteus maximus contributed most of the stance phase hip extension torque. Gastrocnemius contributed little to the terminal swing knee flexion torque. Peak hamstrings force was also substantially greater during terminal swing compared to stance for sprinting, but not for walking and jogging. Immediately following the muscle strain injury, the hamstrings demonstrated an intolerance to perform an eccentric-type contraction. Whilst peak hamstrings force during terminal swing did not decrease post-injury, both peak hamstrings length and negative work during terminal swing were considerably reduced. These results lend support to the paradigm that the hamstrings are most susceptible to muscle strain injury during the terminal swing phase of sprinting when they are contracting eccentrically.

Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking

A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.

The robustness of a second order sliding mode approach to human gait simulation

Nonlinear control techniques such as the sliding mode approach can provide a useful alternative to computationally intensive optimisation strategies in the simulation of human gait. Application of the sliding mode approach has the added advantage that it can provide estimates of internal parameters/signals and can be used to measure and/or monitor the deviation from normal gait in patients who are suffering from conditions such as osteoarthritis, for example. Effectively the principle of the equivalent injection that has been long used for fault detection and diagnostics in engineering machinery can be seen to provide a useful new dimension to gait analysis. Any such model, however, requires apriori estimates to be made of the physical dimensions and muscle characteristics of an individual. The fidelity of any resulting gait analysis will be dependent upon the degree to which the system is sensitive to the selection of such parameters. This paper investigates the effect of inducing errors in the mass, scale and proportions of the individual when simulating the gait cycle of ten normal subjects using a second order sliding mode approach. Seven experiments were carried out to examine the influence of errors up to 50% in the assumed parameters of a three-dimensional musculoskeletal lower body model. The second order sliding mode based simulated gait process was concluded to be sufficiently robust to body segment parameter variation that the use of scaled default parameters can be justified in the gait simulator.

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.

Biomechanical capabilities influence postural control strategies in the cat hindlimb

During postural responses to perturbations, horizontal plane forces generated by the cat hindlimb are stereotypically directed either towards or away from the animal's center of mass, independent of perturbation direction. We used a static, three-dimensional musculoskeletal model of the hindlimb to investigate possible biomechanical determinants of this “force constraint strategy.” We hypothesized that directions in which the hindlimb can produce large forces are preferentially used in postural control. We computed feasible force sets (FFSs) based on hindlimb configurations of three cats during postural equilibrium tasks and compared them to horizontal plane postural force directions. The grand mean FFS was bimodal, with maxima near the posterior–anterior axis (−86±8° and 71±4°), and minima near the medial–lateral axis (177±8° and 8±8°). Experimental postural force directions clustered near both maxima; there were no medial postural forces near the absolute minimum. However, the medians of the anterior and posterior postural force direction histograms in the right hindlimb were rotated counter-clockwise from the FFS maxima ( p<0.05; Wilcoxon signed-rank test). Because the posterior–anterior alignment of the FFS is consistent with a hindlimb structure optimized for locomotion, we conclude that the biomechanical capabilities of the hindlimb strongly influence, but do not uniquely determine the force directions observed in the force constraint strategy. Forces used in postural control may reflect a balance between a neural preference for using forces in the directions of large feasible forces and other criteria, such as the stabilization of the center of mass, and muscular coordination strategies.

A model for the prediction of the forces at the glenohumeral joint

The design, validation, and application of a three-dimensional musculoskeletal model of the upper limb is presented here, for the study of joint, muscle, and ligament forces during selected tasks of daily living. Much of the model was constructed using data gathered from real cadavers, including the extensive 'visible human' data set, together with information gathered from published post mortem studies on cadavers. Validation was carried out through comparison of model outcomes with available data in the literature. The model was then used to examine the glenohumeral joint loading during ten previously selected activities of daily living. The predicted glenohumeral joint contact forces during everyday activities were found to range from 23 to 75 per cent body weight. A linear regression method for estimating the joint load from externally measured kinetics was developed, giving a 95 per cent confidence interval in predicted joint forces of 8 per cent body weight. The model presented here, namely the Newcastle shoulder model, provides a basis for future studies into biomechanical problems relating to the understanding of musculoskeletal pathology and implant design and performance.

Analysis of hindlimb muscle moment arms in Tyrannosaurus rex using a three-dimensional musculoskeletal computer model: implications for stance, gait, and speed

Muscle moment arms are important determinants of muscle function; however, it is challenging to determine moment arms by inspecting bone specimens alone, as muscles have curvilinear paths that change as joints rotate. The goals of this study were to (1) develop a three-dimensional graphics-based model of the musculoskeletal system of the Cretaceous theropod dinosaur Tyrannosaurus rex that predicts muscle-tendon unit paths, lengths, and moment arms for a range of limb positions; (2) use the model to determine how the T. rex hindlimb muscle moment arms varied between crouched and upright poses; (3) compare the predicted moment arms with previous assessments of muscle function in dinosaurs; (4) evaluate how the magnitudes of these moment arms compare with those in other animals; and (5) integrate these findings with previous biomechanical studies to produce a revised appraisal of stance, gait, and speed in T. rex. The musculoskeletal model includes ten degrees of joint freedom (flexion/extension, ab/adduction, or medial/lateral rotation) and 33 main muscle groups crossing the hip, knee, ankle, and toe joints of each hindlimb. The model was developed by acquiring and processing bone geometric data, defining joint rotation axes, justifying muscle attachment sites, and specifying muscle-tendon geometry and paths. Flexor and extensor muscle moment arms about all of the main limb joints were estimated, and limb orientation was statically varied to characterize how the muscle moment arms changed. We used sensitivity analysis of uncertain parameters, such as muscle origin and insertion centroids, to deterimine how much our conclusions depend on the muscle reconstruction we adopted. This shows that a specific amount of error in the reconstruction (e.g., position of muscle origins) can have a greater, lesser, similar, or no effect on the moment arms, depending on complex interactions between components of the musculoskeletal geometry. We found that more upright poses would have improved mechanical advantage of the muscles considerably. Our analysis shows that previously assumed moment arm values were generally conservatively high. Our results for muscle moment arms are generally lower than the values predicted by scaling data from extant taxa, suggesting that T. rex did not have the allometrically large muscle moment arms that might be expected in a proficient runner. The information provided by the model is important for determining how T. rex stood and walked, and how the muscles of a 4000–7000 kg biped might have worked in comparison with extant bipeds such as birds and humans. Our model thus strengthens the conclusion that T. rex was not an exceptionally fast runner, and supports the inference that more upright (although not completely columnar) poses are more plausible for T. rex. These results confirm general principles about the relationship between size, limb orientation, and locomotor mechanics: exceptionally big animals have a more limited range of locomotor abilities and tend to adopt more upright poses that improve extensor muscle effective mechanical advantage. This model builds on previous phylogenetically based muscle reconstructions and so moves closer to a fully dynamic, three-dimensional model of stance, gait, and speed in T. rex.

Identifying the time of occurrence of a hamstring strain injury during treadmill running: A case study

While hamstring strain injuries are common during sprinting, the mechanisms of injury are not well understood. In this study, we analyzed the running kinematics of an athlete obtained at the time of an acute hamstring strain injury. The purpose was to identify the period of the gait cycle during which the hamstring was likely injured, as well as to characterize the biomechanical conditions associated with the injury. A male professional skier injured his right biceps femoris long head while running at 5.36 m/s on a treadmill with a 15% incline. Whole body kinematics were recorded at the time of injury. A linear periodic prediction model was used to determine when individual marker trajectories deviated from a cyclic periodic pattern, indicating the mechanical response to injury. A three-dimensional musculoskeletal model was used to compute joint angles and hamstring musculotendon lengths during the injurious running trial. These data were used with estimates of neuromuscular latencies and electromechanical delays to identify the most likely time period of injury. Based upon the earliest indications in marker trajectories, a 130 ms period during the late swing phase of the gait cycle was identified as the period of injury. During this period, the biceps femoris reached a peak musculotendon length that was estimated to be 12% beyond the length seen in an upright posture and exceeded the normalized peak length of the medial hamstrings. This case provides quantitative data suggesting that the biceps femoris muscle is susceptible to an lengthening contraction injury during the late swing phase of the running gait cycle.

Analysis of hindlimb muscle moment arms in Tyrannosaurus rex using a three-dimensional musculoskeletal computer model: implications for stance, gait, and speed

Analysis of hindlimb muscle moment arms in Tyrannosaurus rex using a three-dimensional musculoskeletal computer model: implications for stance, gait, and speed

Three-dimensional model of the feline hindlimb.

This article describes a three-dimensional musculoskeletal model of the feline hindlimb based on digitized musculoskeletal anatomy. The model consists of seven degrees of freedom: three at the hip and two each at the knee and ankle. Lines of action and via points for 32 major muscles of the limb are described. Interspecimen variability of muscle paths was surprisingly low; most via points displayed a scatter of only a few millimeters. Joint axes identified by mechanical techniques as noncoincident and nonorthogonal were further honed to yield moment arms consistent with previous reports. Interspecimen variability in joint axes was greater than that of muscle paths and highlights the importance of joint axes in kinematic models. The contribution of specific muscles to the direction of endpoint force generation is discussed.

剛体ばねモデルによる腰椎固定インプラントの力学的解析

Pedicle screw fixation is a typical surgical method for lumbar scoliosis using spinal instruments such as metal screws, connectors, and rods. In correcting scoliosis, this method is stronger than other methods. However, screw loosening or rod breaking happens occasionally.In this study, a whole lumbar and instruments were modeled by rigid bodies and springs in three dimensions. An abdominal pressure and muscle forces acted on this model. Inserted pedicle loads and corrected lumbar postures were estimated using this model.Five lumbar vertebrae and ten screws are modeled as rigid bodies, and soft tissues and rods are represented as springs. A ligament is modeled by a linear spring for a tensile deformation, and an intervertebral disc is simplified as three axial springs and three torsional springs.A screw and a connector are combined as one rigid body. The 40-mm-long screw passes through 29 mm of cancellous bone in the vertebral body, 9 mm of subcortical bone in the pedicle, and 2 mm of cortical bone on the surface of the vertebra. These three kinds of bone are replaced with pullout, radial, and torsional springs, respectively. Each spring constant is obtained from experimental data in the literature. The spring constant of the rod is assumed to be equivalent to the uniform column beam.Muscle forces in daily simple motions are obtained from the three-dimensional musculoskeletal model developed in the previous study. The simple motions are represented by a flexion of 30 degrees, a right lateral bending of 20 degrees, and a counterclockwise rotation of 10 degrees.The relative displacements (3 D.O.F. times 15 rigid bodies) and angles (3 times 15) are calculated applying the Runge-Kutta-Gill method. The initial load of the calculation is the gross weight of the upper body (0.25 kN) .The following three types of fixation for scoliosis with a Cobb’s angle of 30 degrees were simulated: (a) screws inserted into both sides of L1-5; (b) both sides of L1, 3, and 5; and (c) only the right side of L1-5. In the case of (a) and (b), the relative displacements and rotation angles are almost the same values, but pullout forces on L3 in (b) are close to the maximum limitation (1.0 kN) . In (c), the radial forces are very large. These estimates indicate that only case (a) can correct the scoliosis without loosening the screws. Additionally, since all the corrected postures are lumbar coupled motions, the above results show that three-dimensional models are available.The force of the connection along the rod between the connector and the rod needs 1.2 kN, and the moment around the rod needs 1.8 Nm in simple motions. In order to prevent this force and moment from exceeding a fatigue stress (Ti-6Al-4V: 0.54 GPa), the diameter of the rod should be at least 4.2 mm. This design is given only by modeling of the instruments and of the in vivo conditions such as an abdominal pressure and muscle forces.

The influence of orthotic devices and vastus medialis strength and timing on patellofemoral loads during running

Objective. To use a musculoskeletal model and simulation of running to examine: (1) the influence of two commonly prescribed treatments for patellofemoral pain (vastus medialis oblique strengthening and orthoses) and (2) the functional significance of timing differences between vastus medialis oblique and vastus lateralis on lateral patellofemoral joint loads. Design. A three-dimensional musculoskeletal model of the lower extremity was used to simulate running at 4 m/s. Background. Repetitive and excessive joint loading is often associated with overuse injuries that require clinical treatments to reduce pain and restore function. Affecting one in four runners, patellofemoral pain is one of the most common injuries in running. Although conservative treatments have been reported to successfully treat patellofemoral pain, the effectiveness is often based on subjective or empirical data, which have generated disagreement on the most effective treatment. Methods. Nine subject specific running simulations were generated and experiments were performed by applying the treatments and timing differences to the nominal simulations. Results. Both treatments significantly reduced the average patellofemoral joint load and the vastus medialis strengthening also significantly reduced the peak patellofemoral joint load. In addition, when the vastus medialis oblique timing was delayed and advanced relative to the vastus lateralis timing, a significant increase and decrease in the joint load was observed, respectively, during the loading response. Conclusions. Increasing vastus medialis oblique strength yielded more consistent results across subjects than the orthosis in reducing patellofemoral joint loads during running. The effect of orthoses was highly variable and sensitive to the individual subject's running mechanics. Vastus medialis oblique activation timing is an important determinant of lateral patellofemoral joint loading during the impact phase. Relevance These findings indicate that a reduction in patellofemoral pain may be achieved through techniques that selectively increase the vastus medialis oblique strength. Therefore, future studies should be directed towards identifying such techniques. Additionally, the functional significance of timing differences between the vastus medialis oblique and vastus lateralis is an important consideration in patellofemoral pain treatment and orthoses may be beneficial for some patients depending on their running mechanics.

A Method for Numerical Simulation of Single Limb Ground Contact Events: Application to Heel-Toe Running

The objective of this work was to develop a method to simulate single-limb ground contact events, which may be applied to study musculoskeletal injuries associated with such movements. To achieve this objective, a three-dimensional musculoskeletal model was developed consisting of the equations of motion for the musculoskeletal system, and models for the muscle force generation and ground contact elements. An optimization framework and a weighted least-squares objective function were presented that generated muscle stimulation patterns that optimally reproduced subject-specific movement data. Experimental data were collected from a single subject to provide initial conditions for the simulation and tracking data for the optimization. As an example application, a simulation of the stance phase of running was generated. The results showed that the average difference between the simulation and subject's ground reaction force and joint angle data was less than two inter-trial standard deviations. Further, there was good agreement between the model's muscle excitation patterns and experimentally collected electromyography data. These results give confidence in the model to examine musculoskeletal loading during a variety of landing movements and to study the effects of various factors associated with injury. Limitations were examined and areas of improvement for the model were presented.

生体力学モデルと機械モデルによる絶滅哺乳類デスモスチルスの歩行復元

The Desmostylus was an ungulate mammal as large as a present hippopotamus, that lived approximately 15 million years ago. Although fossil bones of the whole body have been discovered, various postures have been restored because of the creature's unusual skeletal structure. In this study, we attempted to judge the reliability of each proposed restoration and also to investigate the creature's most probable walking style, using three different approaches: biomechanical analysis by computer simulation, comparison with living animals, and synthesis of natural motion by a quadrupedal walking machine. A three-dimensional musculoskeletal model of Desmostylus with 98 muscles and 16 bone segments was developed from the measured data for the whole body's skeletal structure and marks of muscle insertion. Fundamental standing posture was determined so as to minimize change in muscle length while walking and to maximize stride length. The sloth-type posture proposed by Domning and the crocodile-type posture proposed by Inuzuka were simulated using the musculoskeletal model. These were chosen since they are the only two restoration models that avoid dislocation of leg joints. The calculated results for muscle loads and stride length show that the crocodile-type posture is superior to the sloth-type. The results also showed that both postures must be supported by the abdomen because of the lack of muscle force. We concluded that the crocodile posture was the basic posture of the Desmostylus. The toe locus during walking was determined while maintaining an efficient range of muscular length so as to minimize body swaying in the stance phase and to maximize the toe lift in the swing phase. The cycle of leg motion was estimated from pendulum motion of the leg in the swing phase. Restored walking velocity was 36 m/min at a trot gait supported by the abdomen. The posture and walking were visualized using computer graphics techniques in order to confirm the validity of the restoration. In order to verify the restoration method, the posture and walking of an alligator (Caiman) were calculated using the same method, and the results were compared with the actual posture and walking pattern. The results obtained by computer simulation showed good agreement with those of an actual alligator, indicating that this restoration method is valid. The posture and walking of Desmostylus were also evaluated using a musculoskeletal robot. The developed 1/5-scale robot (580mm, 1.8 kg) can generate natural leg motion according to the innate musculoskeletal structures of Desmostylus. Referring to the muscle functions of an alligator, we classified the muscles of Desmostylus into the following three types: driving muscles, such as proximal big muscles; two-joint muscles, which are almost isometric during walking; and distal spring-like muscles with a long tendon. The isometric muscle and the bones parallel to the muscle act as a four-link mechanism and automatically generate coordinated leg motion. The four-link mechanism is extended by proximal driving muscles and flexed by distal spring-like muscles. The leg can therefore be driven only by two actuators for propulsion and by lifting of the toe. The restored posture and walking using the musculoskeletal robot agreed with the simulated results. Consequently, the restored Desmostylus has crocodile-type posture and trot walks supported by its abdomen. The proposed biomechanical restoration method can be easily applied to other extinct animals because it requires only the animal's skeleton and common locomotion principle. In addition, the mechanically imitated musculoskeletal robot is a useful tool for understanding the importance of body construction.

Passive regulation of impact forces in heel-toe running

Objective. the purpose of this study was to determine whether passive mechanisms can account for impact force regulation with changing shoe hardness. Design. A three-dimensional musculoskeletal model of the lower extremity was developed to simulate impact in running with two different shoe hardnesses. Background. Considerable research has focused on developing shoe cushioning to reduce impact forces. However, only minimal changes in peak external impact force have been observed with changes in shoe hardness. It is hypothesized that passive mechanisms can regulate impact forces with changing shoe hardness, without changing muscle activities. Methods. Initial kinematic inputs for the simulations were measured from nine male subjects performing heel-toe running. Simulations were performed with initial conditions and muscle stimulation patterns held constant while shoe hardness was varied between a hard and a soft condition. Results. There was no significant difference between the soft and hard shoe peak impact forces. Peak rates of loading were greater for the hard shoe than the soft shoe. Muscle forces changed with shoe conditions. For some muscles (including the tibialis anterior) the forces were greater for the hard shoe, whereas for other muscles (including the peroneus) forces were greater for the soft shoe condition. Conclusions. Peak impact forces with changing shoe conditions can be regulated by passive mechanical changes without changing muscle activities or kinematics before touchdown.

絶滅哺乳類デスモスチルスの生体力学的姿勢復元

The Desmostylus, known to have lateral-type limbs like a reptile, was a large mammal that lived about 15 million years ago. Most of its bones have already been discovered; due to the peculiar shape of its skeleton, however, adequacy of its posture restoration had not been verified, and a paleoecological restoration closely related to the posture had never been attempted. In this study, we constructed a three-dimensional musculo-skeletal model of the Desmostylus based on Inuzuka's restored skeleton, which laterally extending the limbs, and verified the adequacy of the peculiar posture by estimating muscular loads to sustain its posture. The musculo-skeletal model was constructed by referring to data obtained from three-dimensional measurement of the restored skeleton and a whole body model made by Inuzuka. Its body was represented by total of 16 rigid links: 3 links in each leg and 4 in the torso. The rigid link properties, such as mass and center of gravity of each segment, were calculated by representing the body shape as elliptical plates. A total of 49 muscles were modeled, including torso muscles. In order to sustain its body weight efficiently, a nonlinear elastic element, like a ligament, was attached around each joint. Body length of the model was 2.6 meters and its body weight was 1.2 tons. We calculated muscular loads to support the body at posture by varying four parameters defining its posture (height of hip joint; inclination angle of a motion plane composed by scapula, upper and fore limbs; directions of toe tips; and positions of the toe tips). In order to maintain the posture with limbs extending laterally, the elastic element at each joint became very important to reduce the muscular loads, instead of the structural support of the posture by bone. Therefore, we determined the posture so as to minimize the change of supporting moment and to maximize the step length. Constant moment can be easily exerted by passive elements. The results were as follows: 1) The calculated posture of Desmostylus is 0.45 meter hip height, 1.06 meters lateral distance between right and left forelimbs, and 0.7meter for that of hindlimbs; 2) muscle cross-sectional area to support the body weight exceeded its permissible leg thickness, therefore, abdomen should touched the ground during daily locomotion; 3) it is more feasible to extend its forelimbs forward, and hindlimbs backward, and the step length is 0.65 meter; 4) the hindlimbs were able to land at a different position from that of the forelimbs; 5) hands and feet were adapted to scratch backward if they were positioned perpendicular to the ground; 6) by inclining the neck downward about 20 degrees from the estimated posture, it could place its mandible parallel to the ground; 7) when in such a low posture, the total muscular load may be comparable with the load of a rat-type posture. We concluded that the lateral posture of Desmostylus touching its abdomen to the ground was adequate and adapted the mammal to live on tidelands.

Analysis of inter-fragmentary movement as a function of musculoskeletal loading conditions in sheep

It is well accepted that inter-fragmentary movement influences the fracture healing process. Small axial movement can stimulate callus formation whereas larger shear movement delays the healing process. It is, therefore, essential for optimal fracture healing to minimize shear and to control axial movement. Unfortunately, the complex gap movements are mostly unknown under the large variety of clinical as well as experimental conditions of fracture fixation. To further understand the complex interactions of musculoskeletal loading and inter-fragmentary movements in bones and to reduce the need for animal experiments, a three-dimensional (3D) musculoskeletal model of the left hind limb of a sheep was developed. From 3D ground reaction forces and inverse dynamics, resultant joint loading was determined over a gait cycle. Muscle and joint contact forces were derived from an optimization routine and internal loads in the tibia and metatarsus from beam theory. Finally, inter-fragmentary movements were calculated from the bony loading condition and experimentally determined stiffness matrices of monolateral AISF external fixator constructs. Both the joint contact forces at the hip and gap movement of a mid-shaft tibial fracture agree with in vivo data reported in the literature. The bones proved to be mainly axially loaded with slightly increasing shear forces toward their ends. The results suggest that inter-fragmentary movement of metatarsal fractures is fairly independent of the fracture location whereas the movement increases in proximal tibial fractures compared to those in the distal and diaphyseal tibia. Considerable shear movement was found for all locations and external fixator mountings. However, shear movement could be minimized with a cranio-lateral rather than a cranio-medial shift from the cranial fixator plane.

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.