An optimal control model for determining articular contact forces at the human knee during rising from a static squat position

A two-dimensional dynamic model of the knee joint was incorporated into a four-segment, eight-muscle model of the human body to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans stand up from a static squatting position. Our optimal control model predicted peak tibiofemoral contact forces 8 times as high as body weight. Furthermore, ligament forces, especially those in the anterior-cruciate, were nearly body weight as knee flexion approached 90 degrees. Ligament and tibiofemoral contact loads were dominated by the forces exerted by muscles during the movement.     

Trunk and lower extremity muscle activity in seated weight-moving tasks: Three-dimensional analyses of intersubject and intertask differences

A three-dimensional musculoskeletal model was used to predict the trunk and lower extremity muscle activity required to stabilize the body while performing dynamic tasks in the seated posture. We studied seven subjects performing four tasks consisting of cyclic or single-directional movements of a hand-held weight in the sagittal plane. Five different optimization schemes involving the minimization of muscle forces, muscle stresses, or joint force components were used to predict the 64 muscle force-time histories. A quantitative method was used to compare prediction schemes by correlating predicted muscle forces with measured myoelectric data and ranking the efficacy of each scheme for different tasks and subjects. The results showed that (1) the trunk and lower extremity muscles play an important role in stabilizing the seated posture in these tasks. (2) the most successful muscle force prediction scheme was not the same for all seven subjects performing a given task, or for a given subject performing all four tasks, and (3) these linear optimization techniques successfully predicted activity in up to 10 of the 15 muscles whose myoelectric signals were actually monitored.     

A musculoskeletal lumbar and thoracic model for calculation of joint kinetics in the spine

The objective of this study was to develop a musculoskeletal spine model that allows relative movements in the thoracic spine for calculation of intra-discal forces in the lumbar and thoracic spine. The thoracic part of the spine model was composed of vertebrae and ribs connected with mechanical joints similar to anatomical joints. Three different muscle groups around the thoracic spine were inserted, along with eight muscle groups around the lumbar spine in the original model from AnyBody. The model was tested using joint kinematics data obtained from two normal subjects during spine flexion and extension, axial rotation and lateral bending motions beginning from a standing posture. Intra-discal forces between spine segments were calculated in a musculoskeletal simulation. The force at the L4-L5 joint was chosen to validate the model’s prediction against the lumbar model in the original AnyBody model, which was previously validated against clinical data.

     

Muscle forces analysis in the shoulder mechanism during wheelchair propulsion

This study combines an ergometric wheelchair, a six-camera video motion capture system and a prototype computer graphics based musculoskeletal model (CGMM) to predict shoulder joint loading, muscle contraction force per muscle and the sequence of muscular actions during wheelchair propulsion, and also to provide an animated computer graphics model of the relative interactions. Five healthy male subjects with no history of upper extremity injury participated. A conventional manual wheelchair was equipped with a six-component load cell to collect three-dimensional forces and moments experienced by the wheel, allowing real-time measurement of hand/rim force applied by subjects during normal wheelchair operation. An ExpertVision six-camera video motion capture system collected trajectory data of markers attached on anatomical positions. The CGMM was used to simulate and animate muscle action by using an optimization technique combining observed muscular motions with physiological constraints to estimate muscle contraction forces during wheelchair propulsion. The CGMM provides results that satisfactorily match the predictions of previous work, disregarding minor differences which presumably result from differing experimental conditions, measurement technologies and subjects. Specifically, the CGMM shows that the supraspinatus, infraspinatus, anterior deltoid, pectoralis major and biceps long head are the prime movers during the propulsion phase. The middle and posterior deltoid and supraspinatus muscles are responsible for arm return during the recovery phase. CGMM modelling shows that the rotator cuff and pectoralis major play an important role during wheelchair propulsion, confirming the known risk of injury for these muscles during wheelchair propulsion. The CGMM successfully transforms six-camera video motion capture data into a technically useful and visually interesting animated video model of the shoulder musculoskeletal system. The CGMM further yields accurate estimates of muscular forces during motion, indicating that this prototype modelling and analysis technique will aid in study, analysis and therapy of the mechanics and underlying pathomechanics involved in various musculoskeletal overuse syndromes.     

Knee and hip joint forces--sensitivity to the degrees of freedom classification at the knee

Previous research has demonstrated that the number of degrees of freedom (DOF) modelled at a given joint affects the antagonistic muscle activity predicted by inverse dynamics optimization techniques. This higher level of muscle activity in turn results in greater joint contact forces. For instance, modelling the knee as a 3 DOF joint has been shown to result in higher hip and knee joint forces commensurate with a higher level of muscular activity than when the knee is modelled with 1 DOF. In this study, a previously described musculoskeletal model of the lower limb was used to evaluate the sensitivity of the knee and hip joint contact forces to the DOF at the knee during vertical jumping in both a 1 and a 3 DOF knee model. The 3 DOF knee was found to predict higher tibiofemoral and hip joint contact forces and lower patellofemoral joint contact forces. The magnitude of the difference in hip contact force was at least as significant as that found in previous research exploring the effect of subject-specific hip geometry on hip contact force. This study therefore demonstrates a key sensitivity of knee and hip joint contact force calculations to the DOF at the knee. Finally, it is argued that the results of this study highlight an important physiological question with practical implications for the loading of the structures of the knee; that is, the relative interaction of muscular, ligamentous, and articular structures in creating moment equilibrium at the knee.     

Maximum finger force prediction using a planar simulation of the middle finger

Maximum isometric finger-grip forces were predicted using a biomechanical model for plane motion of the middle finger. In the course of this study, mathematical representations of tendon displacement, the moment arm of tendon at the finger joints and muscle force-length relationship were investigated. The information gathered was applied to the model to estimate the maximum grip force of the middle finger gripping cylinders of different sizes. Muscle force per unit physiological cross-section area of 30 N/cm2 resulted in good agreement with measured force. However, for finger postures having an acute proximal interphalangeal joint angle, the estimated force was greater than that measured. Various joint angles were applied to the model to simulate the wrist and finger postures not limited to the cylinder grip. In general the finger force was greatest with the wrist in its extended position and at acute flexion of the proximal interphalangeal joint. The maximum finger force occurred at reduced metacarpophalangeal joint angles as the wrist joint changed from an extended position to a flexed one. It is also postulated that muscle force-length relationship is an important factor in muscle force predictions. The data obtained by this research are useful for the design of handles and the current model is applicable to the analysis of hand postures for workers using hand tools.     

The variation in the orientations and moment arms of the knee extensor and flexor muscle tendons with increasing muscle force: a mathematical analysis

The orientations and moment arms of the knee extensor and flexor muscle tendons are evaluated with increasing values of muscle force during simulated isometric exercises. A four-bar linkage model of the knee in the sagittal plane was used to define the motion of the joint in the unloaded state during 0-120 degrees flexion. The cruciate and collateral ligaments were represented by arrays of elastic fibres, which were recruited sequentially under load or remained buckled when slack. A bi-articular model of the patello-femoral joint was used. Simple straight-line representation was used for the lines of action of the forces transmitted by the model muscle tendons. The effects of tissue deformation with increasing muscle force were considered. During quadriceps contraction resisted by an external flexing load, the maximum change in moment arm of the patellar tendon was found to be 2 per cent at 0 degree flexion when the quadriceps force was increased tenfold, from 250 to 2500 N. The corresponding maximum change in orientation of the tendon was 3 degrees at 120 degrees flexion. During hamstrings contraction resisted by an external extending load, the maximum change in moment arm of the hamstrings tendon was 8 per cent at 60 degrees flexion when the hamstrings force was increased tenfold, from 100 to 1000 N. During gastrocnemious contraction, the corresponding maximum change for the gastrocnemious tendon was 3 per cent at 0 degree. The orientations of the flexor muscle tendons in this range of force either remained constant or changed by 1 degree or less at any flexion angle. The general trend at any flexion angle was that, as the muscle force was increased, the moment arms and the orientations approached nearly constant values, showing asymptotic behaviour. It is concluded that experimental simulations of knee muscle action with low values of the externally applied load, of the order of 50 N, can provide reliable estimates of the relationships between muscle forces and external loads during activity.     

Can extra-articular strains be used to measure facet contact forces in the lumbar spine? An in-vitro biomechanical study

Experimental measurement of the load-bearing patterns of the facet joints in the lumbar spine remains a challenge, thereby limiting the assessment of facet joint function under various surgical conditions and the validation of computational models. The extra-articular strain (EAS) technique, a non-invasive measurement of the contact load, has been used for unilateral facet joints but does not incorporate strain coupling, i.e. ipsilateral EASs due to forces on the contralateral facet joint. The objectives of the present study were to establish a bilateral model for facet contact force measurement using the EAS technique and to determine its effectiveness in measuring these facet joint contact forces during three-dimensional flexibility tests in the lumbar spine. Specific goals were to assess the accuracy and repeatability of the technique and to assess the effect of soft-tissue artefacts. In the accuracy and repeatability tests, ten uniaxial strain gauges were bonded to the external surface of the inferior facets of L3 of ten fresh lumbar spine specimens. Two pressure-sensitive sensors (Tekscan) were inserted into the joints after the capsules were cut. Facet contact forces were measured with the EAS and Tekscan techniques for each specimen in flexion, extension, axial rotation, and lateral bending under a +/- 7.5 N m pure moment. Four of the ten specimens were tested five times in axial rotation and extension for repeatability. These same specimens were disarticulated and known forces were applied across the facet joint using a manual probe (direct accuracy) and a materials-testing system (disarticulated accuracy). In soft-tissue artefact tests, a separate set of six lumbar spine specimens was used to document the virtual facet joint contact forces during a flexibility test following removal of the superior facet processes. Linear strain coupling was observed in all specimens. The average peak facet joint contact forces during flexibility testing was greatest in axial rotation (71 +/- 25 N), followed by extension (27 +/- 35 N) and lateral bending (25 +/- 28 N), and they were most repeatable in axial rotation (coefficient of variation, 5 per cent). The EAS accuracy was about 20 per cent in the direct accuracy assessment and about 30 per cent in the disarticulated accuracy test. The latter was very similar to the Tekscan accuracy in the same test. Virtual facet loads (r.m.s.) were small in axial rotation (12 N) and lateral bending (20 N), but relatively large in flexion (34 N) and extension (35 N). The results suggested that the bilateral EAS model could be used to determine the facet joint contact forces in axial rotation but may result in considerable error in flexion, extension, and lateral bending.     

Glenohumeral contact forces

Glenohumeral contact forces have only been calculated previously either for simple abduction or for athletic activities. The objective of this study was to determine the glenohumeral contact forces for tasks which are demanding of the shoulder but which would commonly be performed by older people. The functional tasks chosen were using the arms to stand up from and sit down into a chair, walking with a cane, lifting a 5 kg box to shoulder height with both hands, and lifting a 10 kg suitcase. The trunk angles, arm angles and hand loads of six healthy subjects, average age 55 years, were recorded. This information was input into a biomechanical computer model which optimized the muscle force distribution by minimizing the sum of squared muscle stresses subject to constraints on the maximum muscle forces and maintaining the direction of the resultant force within the glenoid fossa. Average contact forces ranged from 1.3 to 2.4 times body weight (930-1720 N), the highest force being for lifting a suitcase. This latter value would be even higher if lifting either a greater load or to a greater height. Thus, contact forces at the shoulder should not be underestimated. This study provides functionally relevant contact forces which can be used for mechanical testing or finite element modelling of shoulder prostheses.     

Use of the pulse transit time trend to relate tidal breathing and central respiratory events

Central sleep apnoea (CSA) is a respiratory event where cessation of breathing effort and airflow occurs. Numerous lumped models have related the physical phenomena in the arterial tree to properties of the arterial wall. However, a limited model is available that describes pulse transit time (PTT) oscillations during CSA and tidal breathing. Data from 28 children (22 males; aged 6.2 +/- 3.6 years) were obtained during overnight polysomnography. Using a lumped-element model, PTT fluctuations during both respiratory events were described and compared with actual experimental data. 222 valid CSA and 222 tidal breathing events were acquired and analysed. For the tidal breathing, undamped PTT oscillations of 3.89 s were predicted while actual data showed a mean value of 3.68 +/- 0.83 s. Conversely, a damped PTT trend was observed during CSA as predicted by the model. The results attained showed that clustered CSA occurrences led to an increase of 7.23 +/- 3.34 per cent in PTT baseline value while the model predicted 7.86 +/- 2.63 per cent. The marginal increase in PTT baseline was expected since the blood pressure and heart rate decreased during such occurrences. The findings herein suggest that the described model has the potential to describe respiratory event characteristics of a sleeping child.     

Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait

Several three-dimensional (3D) lower-limb musculo-skeletal models have been developed for gait analysis and different hip, knee and ankle joint models have been considered in the literature. Conversely to the influence of the musculo-tendon geometry, the influence of the joint models--i.e. number of degrees of freedom and passive joint moments--on the estimated musculo-tendon forces and 3D joint reaction forces has not been extensively examined. In this paper musculo-tendon forces and 3D joint reaction forces have been estimated for one subject and one gait cycle with nine variations of a musculoskeletal model and outputs have been compared to measured electromyographic signals and knee joint contact forces. The model outputs are generally in line with the measured signals. However, the 3D joint reaction forces were higher than published values and the contact forces measured for the subject. The results of this study show that, with more degrees of freedom in the model, the musculo-tendon forces and the 3D joint reaction forces tend to increase but with some redistribution between the muscles. In addition, when taking into account passive joint moments, the 3D joint reaction forces tend to decrease during the stance phase and increase during the swing phase. Although further investigations are needed, a five-degree-of-freedom lower-limb musculo-skeletal model with some angle-dependent joint coupling and stiffness seems to provide satisfactory musculo-tendon forces and 3D joint reaction forces.     

Design characteristics for temporomandibular joint disc tissue engineering: learning from tendon and articular cartilage

Tissue engineering of chondrocytic or fibroblastic musculoskeletal tissues has been relatively well studied compared with that of the temporomandibular joint (TMJ) disc. Early attempts at tissue engineering the disc have been misguided owing to a lack of understanding of the composition and function of the TMJ disc. The objective of this review is to compare the TMJ disc with a chondrocytic tissue (hyaline articular cartilage) and a fibroblastic tissue (tendon) to understand better the properties of this fibrocartilaginous tissue. The TMJ disc has 25 times more glycosaminoglycan (GAG) per dry weight than tendon but half that of articular cartilage. The disc's tensile modulus is six times more than cartilage but orders less than tendon. The GAG content and tensile modulus suggest that the TMJ disc is characterized as a tissue between hyaline cartilage and tendon, but the disc appears more tendon like when considering its collagen make-up and cell content. Like tendon, the TMJ disc contains primarily collagen type I at 85 per cent per dry weight, while articular cartilage has 30 per cent less collagen, which is type II. Knowledge of quantitative comparisons between joint tissues can give extensive insight into how to improve tissue engineering of the TMJ disc.     

Musculoskeletal upper limb modeling with muscle activation for flexible body simulation

The use of digital human models has been increasing rapidly in various fields from medical to engineering applications. Most of the works on human models involving muscle activation have been concentrated on rigid body simulation so far, because the dynamics of human body motion has been primary concern regardless of the effects on human musculoskeletal body. Recently the need for flexible body simulation including muscle activation has been increasing for engineering applications. In this paper, a musculoskeletal model with muscle activation of an upper limb for the dynamic simulation of FE based flexible body is presented. In order to estimate the in vivo forces of muscles in motion, optimization technique is employed to solve multiple solutions problem. The simulated results were compared with the experimental data, EMG for validation. As a result it was found that muscle activation as part of musculoskeletal model can be employed for a FE based flexible body software.     

Estimation of muscle and joint forces in the human lower extremity during rising motion from a seated position

Biomechanical models are often employed to predict in vivo muscle or joint forces in the human body because measuring these forces is difficult. Even though the rising motion from a seated position frequently occurs in daily life and the force acting on the knee joints during the motion is important for aged or infirmed people, limited studies related to the motion have been conducted. This study aims to propose a numerical procedure to estimate the muscle and joint forces in the human lower extremity during rising motion from a seated position. The human lower extremity is idealized as a multibody system in which the Hill-type muscle force model is employed. The multibody system consists of four bodies (shank, thigh, pelvis, and upper body), three revolute joints, and ten forces. The motion of the multibody system is assumed constrained to the sagittal plane, and the muscles in the human lower extremity are idealized by nine action/reaction forces. The nine forces are determined by minimizing the metabolic energy, which is consumed during the rising motion. Metabolic energy consists of the energy consumed by heat generation of muscles and the mechanical work done by muscles. For the accuracy validation of the proposed estimation method, numerical results obtained with the proposed method are compared with existing experimental results.     

Evaluation of synthetic composite tibias for fracture testing using impact loads

Composite synthetic bones are a commercially available substitute for cadaveric specimens, and they have previously been validated to replicate natural bone under quasistatic, non-destructive testing. Synthetic tibias could be used to analyse injury risk to the lower leg during impact events, but their failure mode must be validated by way of comparative tests to human bone. Synthetic tibias were instrumented with strain gauges and subjected to axial impact loading. Two different projectile masses were used for the tests, and the effects of force, momentum, and energy on failure were compared with previous cadaveric data. The composite tibias failed at forces between 37-45 per cent of those from cadavers, and failed via cortical delamination in combination with fracture. A Weibull analysis generated a survivability curve based on axial force at failure, and was shown to be lower than previous cadaveric curves. Failure was dependent on both the momentum and energy applied. Strain distributions through the synthetic tibias were significantly different from those of cadavers. The convex distal articular surface of the synthetic bones may partially account for the lower fracture tolerance. As a result of the many differences in response, these synthetic tibias are not recommended for use in impact fracture studies.     

Measurement of pulsatile haemodynamic forces in a model of a bifurcated stent graft for abdominal aortic aneurysm repair

The longitudinal haemodynamic force (LF) acting on a bifurcated stent graft for abdominal aortic aneurysm repair has been estimated previously using a simple one-dimensional analytical model based on the momentum equation which assumes steady flow of an inviscid fluid. Using an instrumented stent-graft model an experimental technique was developed to measure the LF under pulsatile flow conditions. The physical stent-graft model, with main trunk diameter of 30mm and limb diameters of 12 mm, was fabricated from aluminium. Strain gauges were bonded on to the main trunk to determine the longitudinal strain which is related to the LF. After calibration, the model was placed in a pulsatile flow system with 40 per cent aqueous glycerol solution as the circulating fluid. The LF was determined using a Wheatstone bridge signal-conditioning circuit. The signals were averaged over 590 cardiac cycles and saved to a personal computer for subsequent processing. The LF was strongly dependent on the pressure but less so on the flowrate. The measured forces were higher than those predicted by the simplified mathematical model by about 6-18 per cent during the cardiac cycle. The excess measured forces are due to the viscous drag and the effect of pulsatile flow. The peak measured LF in this model of 30 mm diameter may exceed the fixation force of some current clinical endovascular stent grafts.     

A new soft-tissue indentation model for estimating circular indenter 'force-displacement' characteristics

Models that predict soft-tissue indentation forces have many important applications including estimation of interaction forces, palpation simulation, disease diagnosis, and robotic assistance. In many medical applications such as rehabilitation, clinical palpation, and manipulation of organs, characterizing soft-tissue properties mainly depends on the accurate estimation of indentation forces. A new indentation model for estimating circular indenter 'force-displacement' characteristics is presented in this paper. The proposed model is motivated by a 'force-displacement' soil-tool model and is computationally efficient. The main feature of the proposed model is that it can be used to predict the force variations for a variety of tools without the need for retuning the model parameters for each tool. A six-degree-of-freedom robot manipulator with force and position sensors is used to validate the indentation model. Measured force versus tool displacement data for lamb liver and kidney, for a variety of tool diameters, are presented and compared with the forces predicted by the model, showing good agreement (RMS error < 8 per cent).     

Development and validation of a model for quantifying glenohumeral ligament strains during function

Analysis of the function of glenohumeral ligaments (GHLs) during physical joint manipulations is hindered by an inability to adequately image these tissues during the movements. This restricts functional biomechanics studies only to the manoeuvres that may be replicated cadaverically. There is, however, a clinical imperative to be able to investigate complex manoeuvres that exacerbate symptoms but cannot be easily conducted physically in the laboratory. The aim of this study was to develop and validate an algorithm for a computer simulation model that allows the quantification of glenohumeral ligament lengths during function. Datasets of the humerus and scapula pair were segmented to provide individual surface meshes of the bones and insertion points of each glenohumeral ligament on both bones. An algorithm was developed in which the glenohumeral ligament attachment-to-attachment length was divided into two straight lines, plus an arc overlaying the spherical wrapping portions. The model was validated by simulating two classical cadaveric studies from the literature and comparing results. Predictions from the model were qualitatively similar to the results of the two cadaveric studies by a factor of 91.7% and 81.8%, respectively. Algorithm application will allow investigation of functional loading of the glenohumeral ligaments during simulated complex motions. This could then be used to provide diagnostic understanding and thus, inform surgical reconstruction.     

Anatomy and biomechanics of quadratus lumborum

Various actions on the lumbar spine have been attributed to quadratus lumborum, but they have not been substantiated by quantitative data. The present study was undertaken to determine the magnitude of forces and moments that quadratus lumborum could exert on the lumbar spine. The fascicular anatomy of quadratus lumborum was studied in six embalmed cadavers. For each fascicle, the sites of attachment, orientation, and physiological cross-sectional area were determined. The fascicular anatomy varied considerably, between sides and between specimens, with respect to the number of fascicles, their prevalence, and their sizes. Approximately half of the fascicles act on the twelfth rib, and the rest act on the lumbar spine. The more consistently present fascicles were incorporated, as force-equivalents, into a model of quadratus lumborum in order to determine its possible actions. The magnitudes of the compression forces exerted by quadratus lumborum on the lumbar spine, the extensor moment, and the lateral bending moment, were each no greater than 10 per cent of those exerted by erector spinae and multifidus. These data indicate that quadratus lumborum has no more than a modest action on the lumbar spine, in quantitative terms. Its actual role in spinal biomechanics has still to be determined.