Combining position and acceleration measurements for joint force estimation

The calculation of joint forces in biomechanics is usually based on the measurements of the kinematics of a given body segment, the estimation of the inertial properties of that segment and the solution of the ‘inverse dynamics problem’. Such a process results in estimates of the joint forces and moments needed to sustain the monitored motion. This paper presents a new approach that combines position and acceleration measurements for the purpose of deriving high-quality joint force estimates. An experimental system that is based on an instrumented compound pendulum was designed and tested. The joint forces necessary to maintain a swinging motion of the pendulum were measured by an array of strain gauges, and were compared to the forces estimated by the integrated kinematic segment that measured the position and acceleration of the pendulum. The joint force measurements were also compared to the force estimates that were based on the calculated segmental acceleration generated by the differentiation of the segmental position alone. The results show a high degree of correlation between the forces estimated by the integrated segment and those measured by the strain gauges. The force estimates based on the position measurements alone were less accurate and noisier. The application of the integrated segment to the study of human kinetics is discussed and illustrated by the ankle and knee forces during slow walking. The results suggest that the use of accelerometers is necessary for the estimation of transients and high-frequency components of joint forces.     

Estimation of foot joint kinetics in three and four segment foot models using an existing proportionality scheme: Application in paediatric barefoot walking

Recent studies which estimated foot segment kinetic patterns were found to have inconclusive data on one hand, and did not dissociate the kinetics of the chopart and lisfranc joint. The current study aimed therefore at reproducing independent, recently published three-segment foot kinetic data (Study 1) and in a second stage expand the estimation towards a four-segment model (Study 2).Concerning the reproducibility study, two recently published three segment foot models (Bruening et al., 2014; Saraswat et al., 2014) were reproduced and kinetic parameters were incorporated in order to calculate joint moments and powers of paediatric cohorts during gait. Ground reaction forces were measured with an integrated force/pressure plate measurement set-up and a recently published proportionality scheme was applied to determine subarea total ground reaction forces. Regarding Study 2, moments and powers were estimated with respect to the Instituto Ortopedico Rizzoli four-segment model. The proportionality scheme was expanded in this study and the impact of joint centre location on kinetic data was evaluated.Findings related to Study 1 showed in general good agreement with the kinetic data published by Bruening et al. (2014). Contrarily, the peak ankle, midfoot and hallux powers published by Saraswat et al. (2014) are disputed. Findings of Study 2 revealed that the chopart joint encompasses both power absorption and generation, whereas the Lisfranc joint mainly contributes to power generation.The results highlights the necessity for further studies in the field of foot kinetic models and provides a first estimation of the kinetic behaviour of the Lisfranc joint.     

Muscle work is biased toward energy generation over dissipation in non-level running

This study tested the hypothesis that skeletal muscles generate more mechanical energy in gait tasks that raise the center of mass compared to the mechanical energy they dissipate in gait tasks that lower the center of mass despite equivalent changes in total mechanical energy. Thirteen adults ran on a 10° decline and incline surface at a constant average velocity. Three-dimensional (3D) joint powers were calculated from ground force and 3D kinematic data using inverse dynamics. Joint work was calculated from the power curves and assumed to be due to skeletal muscle–tendon actuators. External work was calculated from the kinematics of the pelvis through the gait cycle. Incline vs. decline running was characterized with smaller ground forces that operated over longer lever arms causing larger joint torques and work from these torques. Total lower extremity joint work was 28% greater in incline vs. decline running (1.32 vs. −1.03 J/kg m, p<0.001). Total lower extremity joint work comprised 86% and 71% of the total external work in incline (1.53 J/kg m) and decline running (−1.45 J/kg m), which themselves were not significantly different (p<0.180). We conjectured that the larger ground forces in decline vs. incline running caused larger accelerations of all body tissues and initiated a greater energy-dissipating response in these tissues compared to their response in incline running. The runners actively lowered themselves less during decline stance and descended farther as projectiles than they lifted themselves during incline stance and ascended as projectiles. These data indicated that despite larger ground forces in decline running, the reduced displacement during downhill stance phases limited the work done by muscle contraction in decline compared to incline running.     

Change in knee contact force with simulated change in body weight

The relationship between obesity, weight gain and progression of knee osteoarthritis is well supported, suggesting that excessive joint loading may be a mechanism responsible for cartilage deterioration. Examining the influence of weight gain on joint compressive forces is difficult, as both muscles and ground reaction forces can have a significant impact on the forces experienced during gait. While previous studies have examined the relationship between body weight and knee forces, these studies have used models that were not validated using experimental data. Therefore, the objective of this study was to evaluate the relationship between changes in body weight and changes in knee joint contact forces for an individual's gait pattern using musculoskeletal modeling that is validated against known internal compressive forces. Optimal weighting constants were determined for three subjects to generate valid predictions of knee contact forces (KCFs) using in vivo data collection with instrumented total knee arthroplasty. A total of five simulations per walking trial were generated for each subject, from 80% to 120% body weight in 10% increments, resulting in 50 total simulations. The change in peak KCF with respect to body weight was found to be constant and subject-specific, predominantly determined by the peak force during the baseline condition at 100% body weight. This relationship may be further altered by any change in kinematics or body mass distribution that may occur as a result of a change in body weight or exercise program.     

Coordination of leg muscles during speed skating

Five speed skaters of elite performance level and six speed skaters of trained level were subjected to an inverse dynamical analysis during speed skating. Push-off forces were registered by means of special skates. Myoelectric activity (EMG) of ten leg muscles and cinematographic data were recorded. Linked segment modelling yielded net joint moments and joint powers. The speed skating technique is characterized by a typical horizontal position of the trunk and a suppression of a plantar flexion during the push-off. This technique, necessary to reduce external friction, constrains the transfer of rotation in joints to translation of the mass center of the body. In spite of constrained push-off, the EMG levels of the leg muscles show a proximo-distal temporal order which to a certain extent is comparable to that previously found in an unconstrained vertical jump. This proximo-distal sequence is also reflected by the time courses of the net moment and net power output in hip, knee and ankle joints. The temporal sequence in activation levels of activated muscles is not different between elite and trained speed skaters. The difference in performance level between these groups obviously has an origin in the ability of the elite speed skaters to realise larger net joint moments. Differences in net joint moments and in kinematics result in a higher power output and a lower air frictional force for the elite than for the trained speed skaters.     

MRI-derived body segment parameters of children differ from age-based estimates derived using photogrammetry

Body segment parameters are required when researching joint kinetics using inverse dynamics models. However, the only regression equations for estimating pediatric body segment parameters across a wide age range were developed, using photogrammetry, based on 12 boys and have not been validated to date (Jensen, R.K., 1986. Body segment mass, radius and radius of gyration proportions of children. Journal of Biomechanics 19, 359–368). To assess whether these equations could validly be applied to girls, we asked whether body segment parameters estimated by the equations differ from parameters measured using a validated magnetic resonance imaging (MRI) method. If so, do the differences cause significant differences in joint kinetics during normal gait? Body segment parameters were estimated from axial MRIs of the left thigh and shank of 10 healthy girls (9.6±0.9 years) and compared to those from Jensen's equations. Kinematics and kinetics were collected for 10 walking trials. Extrema in hip and knee moments and powers were compared between the two sets of body segment parameters. With the exception of the shank mass center and radius of gyration, body segment parameters measured using MRI were significantly different from those estimated using regression equations. These systematic differences in body segment parameters resulted in significant differences in sagittal-plane joint moments and powers during gait. Nevertheless, it is doubtful that even the greatest differences in kinetics are practically meaningful (0.3%BW×HT and 0.7%BW×HT/s for moments and power at the hip, respectively). Therefore, body segment parameters estimated using Jensen's regression equations are a suitable substitute for more detailed anatomical imaging of 8–10-year-old girls when quantifying joint kinetics during gait.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--II. Movement of the multi-link chain model

Movement of a multi-link chain model is treated using the 'sources' and 'fractions' concept introduced earlier (part I of this series, J. Biomechanics 19, 287-293). 'The energy balance equations', i.e. the relations between the powers of the sources and the time rate of change of the total energy of the links are obtained. It is shown that the action of joint forces can promote energy transfers between links and energy transformations of the energy fractions of the links but it cannot change the total energy of the system. A formula for the mechanical energy expenditure for the control moments is deduced. 'External' and 'internal' energy balance equations are derived. 'External' energy is the energy of the general center of mass, 'internal' energy is the energy of the links in their motion relative to the general center of mass. It is shown that 'external' and 'internal' work depend on each other and their sum is not equal to the mechanical energy expenditure which occurs during movement of the body. This is because of the possibility of some source powers to change the external and internal energy of the system simultaneously out of phase with each other.     

Joint forces and torques when walking in shallow water

This study reports for the first time an estimation of the internal net joint forces and torques on adults' lower limbs and pelvis when walking in shallow water, taking into account the drag forces generated by the movement of their bodies in the water and the equivalent data when they walk on land. A force plate and a video camera were used to perform a two-dimensional gait analysis at the sagittal plane of 10 healthy young adults walking at comfortable speeds on land and in water at a chest-high level. We estimated the drag force on each body segment and the joint forces and torques at the ankle, knee, and hip of the right side of their bodies using inverse dynamics. The observed subjects' apparent weight in water was about 35% of their weight on land and they were about 2.7 times slower when walking in water. When the subjects walked in water compared with walking on land, there were no differences in the angular displacements but there was a significant reduction in the joint torques which was related to the water's depth. The greatest reduction was observed for the ankle and then the knee and no reduction was observed for the hip. All joint powers were significantly reduced in water. The compressive and shear joint forces were on average about three times lower during walking in water than on land. These quantitative results substantiate the use of water as a safe environment for practicing low-impact exercises, particularly walking.     

Dynamics and energetics of impacts in crutch walking

The impulsive dynamics associated with the impact of the crutch with the ground is an important topic of research, since this is known to be the main cause of energy loss during crutch gait. In this article, a four-segmental 2D model based on anthropometric body segment parameters is used to analyze various dynamics aspects of such impact. For this purpose, a novel formulation based on the decomposition of the tangent space of the biomechanical system to two subspaces associated with the constrained and admissible motions is developed. Detailed numerical analysis is presented to discuss the effects of body configuration and crutch length on the kinetic energy redistribution, velocity change and impulsive contact forces generated. The conclusions reached via this analysis give guidelines for optimal crutch selection or crutch-use teaching that can be applied to injured subjects. For instance, to reduce energy consumption which leads to a reduction of muscular fatigue.     

Understanding muscle coordination of the human leg with dynamical simulations

Muscles coordinate multijoint motion by generating forces that cause reaction forces throughout the body. Thus, a muscle can redistribute existing segmental energy by accelerating some segments and decelerating others. In the process, a muscle may also produce or absorb energy, in which case its summed energetic effect on the segments is positive or negative, respectively. This Borelli Lecture shows how dynamical simulations derived from musculoskeletal models reveal muscle-induced segmental energy redistribution and muscle co-functions and synergies. Synergy occurs when co-excited muscles distribute segmental energy differently to execute the motor task. In maximum height jumping, high vertical velocity at lift-off occurs desirably at full body extension because biarticular leg muscles redistribute the energy produced by the uniarticular leg muscles. In pedaling, synergistic ankle plantarflexor force generation during leg extension allows the high energy produced by the uniarticular hip and knee extensors to be delivered to the crank. An analogous less-powerful flexor synergy exists during leg flexion. Hamstrings reduce crank deceleration during the leg extension-to-flexion transition by not only producing energy but delivering it to the crank through its contribution to the tangential (accelerating) crank force, though this hamstrings function occurs at the opposite (flexion-extension) transition when pedaling backwards. In walking, the eccentric quadriceps activity in early stance not only decelerates the leg but also accelerates the trunk. In mid-stance, the uni- and biarticular plantarflexors, by having opposite segmental energetic effects, act in synergy to support the whole body, so segmental potential and kinetic energy exchange can occur. To conclude, the extraction of unmeasurable variables from dynamical simulations emulating task kinematics, kinetics, and EMGs shows how the production of force and energy by individual muscles contribute to the energy flow among the individual segments during task execution.     

The impact of adding trunk motion to the interpretation of the role of joint moments during normal walking

Biomechanical model assumptions affect the interpretation of the role of the muscle or joint moments to the segmental power estimated by induced acceleration analysis (IAA). We evaluated the effect of modeling the pelvis and trunk segments as two separate segments (8 SM) versus as a single segment (7 SM) on the segmental power, support of the body, knee and hip extension acceleration produced by the joint moments during the stance phase of normal walking. Significant differences were observed in the contribution of the stance hip abductor and extensor moments to support, ipsilateral knee and hip acceleration, and ipsilateral thigh and upper body power. The primary finding was that the role of the stance hip moment in generating ipsilateral thigh and upper body power differed based on degrees of freedom in the model. Secondarily, the magnitude of contributions also differed. For example, the hip abductor and extensor moments showed greater contribution to support, hip and knee acceleration in the 8 SM. IAA and segment power analysis are sensitive to the degrees of freedom between the pelvis and trunk. There is currently no gold standard by which to evaluate the accuracy of IAA predictions. However, modeling the pelvis and trunk as separate segments is closer to the anatomical architecture of the body. An 8 SM appears to be more appropriate for estimating the role of joint moments, particularly to motion of more proximal segments during normal walking.     

Biomechanical analysis of primate bipedal walking by computer simulation

A computer simulation technique was applied to make clear the mechanical characteristics of primate bipedal walking. A primate body and the walking mechanism were modeled mathematically with a set of dynamic equations. Using a digital computer, the following were calculated from these equations by substituting measured displacements and morphological data of each segment of the primate: the acceleration, joint angle, center of gravity, foot force, joint moment, muscular force, transmitted force at the joint, electric activity of the muscle, generated power by the leg and energy expenditure in walking.The model was evaluated by comparing some of the calculated results with the experimental results such as foot force and electromyographic data, and improved in order to obtain the agreement between them.The level bipedal walking of man, chimpanzee and Japanese monkey and several types of synthesized walking were analyzed from the viewpoint of biomechanics.It is concluded that the bipedal walking of chimpanzee is nearer to that of man than to that of the Japanese monkey because of its propulsive mechanism, but it requires large muscular force for supporting the body weight.     

An efficient probabilistic methodology for incorporating uncertainty in body segment parameters and anatomical landmarks in joint loadings estimated from inverse dynamics

Inverse dynamics is a standard approach for estimating joint loadings in the lower extremity from kinematic and ground reaction data for use in clinical and research gait studies. Variability in estimating body segment parameters and uncertainty in defining anatomical landmarks have the potential to impact predicted joint loading. This study demonstrates the application of efficient probabilistic methods to quantify the effect of uncertainty in these parameters and landmarks on joint loading in an inverse-dynamics model, and identifies the relative importance of the parameters and landmarks to the predicted joint loading. The inverse-dynamics analysis used a benchmark data set of lower-extremity kinematics and ground reaction data during the stance phase of gait to predict the three-dimensional intersegmental forces and moments. The probabilistic analysis predicted the 1-99 percentile ranges of intersegmental forces and moments at the hip, knee, and ankle. Variabilities, in forces and moments of up to 56% and 156% of the mean values were predicted based on coefficients of variation less than 0.20 for the body segment parameters and standard deviations of 2 mm for the anatomical landmarks. Sensitivity factors identified the important parameters for the specific joint and component directions. Anatomical landmarks affected moments to a larger extent than body segment parameters. Additionally, for forces, anatomical landmarks had a larger effect than body segment parameters, with the exception of segment masses, which were important to the proximal-distal joint forces. The probabilistic modeling approach predicted the range of possible joint loading, which has implications in gait studies, clinical assessments, and implant design evaluations.     

A sensitivity analysis method for the body segment inertial parameters based on ground reaction and joint moment regressor matrices

This paper presents a method allowing a simple and efficient sensitivity analysis of dynamics parameters of complex whole-body human model. The proposed method is based on the ground reaction and joint moment regressor matrices, developed initially in robotics system identification theory, and involved in the equations of motion of the human body. The regressor matrices are linear relatively to the segment inertial parameters allowing us to use simple sensitivity analysis methods. The sensitivity analysis method was applied over gait dynamics and kinematics data of nine subjects and with a 15 segments 3D model of the locomotor apparatus. According to the proposed sensitivity indices, 76 segments inertial parameters out the 150 of the mechanical model were considered as not influent for gait. The main findings were that the segment masses were influent and that, at the exception of the trunk, moment of inertia were not influent for the computation of the ground reaction forces and moments and the joint moments. The same method also shows numerically that at least 90% of the lower-limb joint moments during the stance phase can be estimated only from a force-plate and kinematics data without knowing any of the segment inertial parameters.     

Biomechanical characterization of the native porcine aortic root

A thorough understanding of the well-functioning, native aortic root is pivotal in an era, where valve sparing surgical techniques are developed and used with increasing frequency. The objective of this study was to characterize the local structural stiffness of the native aortic root, to create a baseline for understanding how different surgical interventions affect the dynamics of the aortic root. In this acute porcine study (N = 10), two dedicated force transducers were implanted to quantify the forces acting on both the annular plane and on the sinotubular junction (STJ). To assess the changes in geometry, eleven sonomicrometry crystals were implanted within the aortic root. The combination of force and length measurements yields the radial structural stiffness for each segment of the aortic root.The least compliant segment at the annular plane was the right-left interleaflet triangle with a stiffness modulus of 1.1 N mm⁻¹ (SD0.4). At the sinotubular junction the same segment (right-left) was most compliant, compared with the two other segments, however not statistically significant different.The elastic energy storage was derived from the aortic root pressure volume relationship; the mean elastic energy storage was 826 µJ (SD529). In conclusion, the aortic root has been characterized in terms of both segmental forces, segmental change in length and elastic energy storage. This study is the first to assess the radial structural stiffness of different segments of the aortic root. The presented data is reference for further studies regarding the impact of surgical interventions on the aortic root.     

Effect of pre-impact movement strategies on the impact forces resulting from a lateral fall

Approximately 90% of hip fractures in older adults result from falls, mostly from landing on or near the hip. A three-dimensional, 11-segment, forward dynamic biomechanical model was developed to investigate whether segment movement strategies prior to impact can affect the impact forces resulting from a lateral fall. Four different pre-impact movement strategies, with and without using the ipsilateral arm to break the fall, were implemented using paired actuators representing the agonist and antagonist muscles acting about each joint. Proportional-derivative feedback controller controlled joint angles and velocities so as to minimize risk of fracture at any of the impact sites. It was hypothesized that (a) the use of active knee, hip and arm joint torques during the pre-contact phase affects neither the whole body kinetic energy at impact nor the peak impact forces on the knee, hip or shoulder and (b) muscle strength and reaction time do not substantially affect peak impact forces. The results demonstrate that, compared with falling laterally as a rigid body, an arrest strategy that combines flexion of the lower extremities, ground contact with the side of the lower leg along with an axial rotation to progressively present the posterolateral aspects of the thigh, pelvis and then torso, can reduce the peak hip impact force by up to 56%. A 30% decline in muscle strength did not markedly affect the effectiveness of that fall strategy. However, a 300-ms delay in implementing the movement strategy inevitably caused hip impact forces consistent with fracture unless the arm was used to break the fall prior to the hip impact.     

The Roles of Monoarticular and Biarticular Muscles of the Lower Limbs in Terrestrial Locomotion

Specific features of the functioning of mono- and biarticular muscles were studied using a multijoint movement (a high jump) as an example. The powers of the knee and ankle joint extensors are insufficient for a strong and quick movement such as a high jump. Biarticular muscles (m. rectus femoris) transfer forces/powers from one joint to another, thereby compensating for the physiological shortcoming of monoarticular muscles, that is, a decrease in the tractive force with increasing contraction rate. In a high jump, a power of 300 W may be transferred from the hip to the knee joint via the m. rectus femoris; 230 W, from the knee to the hip joint via the hamstring muscle; 210 W, from the knee joint to the ankle via the m. gastrocnemius; and 15 W, from the metatarsophalangeal joint to the ankle via the mm. flexors.     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

The dynamics of quadrupedal locomotion

This paper presents a dynamical analysis of quadrupedal locomotion, with specific reference to an adult Nubian goat. Measurements of ground reaction forces and limb motion are used to assess variations in intersegmental forces, joint moments, and instantaneous power for three discernible gaits: walking, running, and jumping. In each case, inertial effects of the torso are shown to dominate to the extent that lower-extremity contributions may be considered negligible. Footforces generated by the forelimbs exceed those exerted by the hindlimbs; and, in general, ground reactions increase with speed. The shoulder and hip dominate mechanical energy production during walking, while the knee plays a more significant role in running. In both cases, however, the elbow absorbs energy, and by so doing functions primarily as a damping (control) element. As opposed to either walking or running, jumping requires total horizontal retardation of the body's center of mass. In this instance, generating the necessary vertical thrust amounts to energy absorption at all joints of the lower extremities.     

Elbow and wrist joint contact forces during occupational pick and place activities

A three-dimensional, mathematical model of the elbow and wrist joints, including 15 muscle units, 3 ligaments and 4 joint forces, has been developed. A new strain gauge transducer has been developed to measure functional grip forces. The device measures radial forces divided into six components and forces of up to 250N per segment can be measured with an accuracy of +/-1%. Ten normal volunteers were asked to complete four tasks representing occupational activities, during which time their grip force was monitored. Together with kinematic information from the six-camera Vicon data, the moment effect of these loads at the joints was calculated. These external moments are assumed to be balanced by the internal moments, generated by the muscles, passive soft tissue and bone contact. The effectiveness of the body's internal structures in generating joint moments was assessed by studying the geometry of a simplified model of the structures, where information about the lines of action and moment arms of muscles, tendons and ligaments is contained. The assumption of equilibrium between these external and internal joint moments allows formulation of a set of equations from which muscle and joint forces can be calculated. A two stage, linear optimisation routine minimising the overall muscle stress and the sum of the joint forces has been used to overcome the force-sharing problem. Humero-ulnar forces of up to 1600N, humero-radial forces of up to 800N and wrist joint forces of up to 2800N were found for moderate level activity. The model was validated by comparison with other studies.