Sensitivity of temporomandibular joint force calculations to errors in muscle force measurements

A two-dimensional, five-muscle model was used to determine the degree of precision required for accurate calculation of temporomandibular joint force magnitude and direction. The sensitivity of the calculations to each variable were assessed by incrementing each variable through its presumed biological range and were expressed as rate of change in the joint force per unit change in each variable. Sensitivity of the calculations to variables depends upon both bite force direction and bite position. The bite force direction with maximum precision for joint force magnitude produced minimal precision for joint force direction. The accuracy needed for each muscle force varied greatly. The effect of error for each muscle parameter depended upon the magnitude, direction, and moment arm length of the muscle force relative to those of the resultant muscle force. If each of the five muscle forces was known to the nearest 1% of total muscle force magnitude, 1 degree of muscle force direction, and 1 mm of moment arm length, temporomandibular joint force magnitude could be calculated to the nearest 4 kg and joint force direction to the nearest 7 degrees. It is not known whether this precision for the muscle forces is possible.     

Influence of IMU position and orientation placement errors on ground reaction force estimation

Wearable inertial measurement units (IMU) have been proposed to estimate GRF outside of specialized laboratories, however the precise influence of sensor placement error on accuracy is unknown. We investigated the influence of IMU position and orientation placement errors on GRF estimation accuracy. Methods: Kinematic data from twelve healthy subjects based on marker trajectories were used to simulate 1848 combinations of sensor position placement errors (range ± 100 mm) and orientation placement errors (range ± 25°) across eight body segments (trunk, pelvis, left/right thighs, left/right shanks, and left/right feet) during normal walking trials for baseline cases when a single sensor was misplaced and for the extreme cases when all sensors were simultaneously misplaced. Three machine learning algorithms were used to estimate GRF for each placement error condition and compared with the no placement error condition to evaluate performance. Results: Position placement errors for a single misplaced IMU reduced vertical GRF (VGRF), medio-lateral GRF (MLGRF), and anterior-posterior GRF (APGRF) estimation accuracy by up to 1.1%, 2.0%, and 0.9%, respectively and for all eight simultaneously misplaced IMUs by up to 4.9%, 6.0%, and 4.3%, respectively. Orientation placement errors for a single misplaced IMU reduced VGRF, MLGRF, and APGRF estimation accuracy by up to 4.8%, 7.3%, and 1.5%, respectively and for all eight simultaneously misplaced IMUs by up to 20.8%, 23.4%, and 12.3%, respectively. Conclusion: IMU sensor misplacement, particularly orientation placement errors, can significantly reduce GRF estimation accuracy and thus measures should be taken to account for placement errors in implementations of GRF estimation via wearable IMUs.     

An induced acceleration index for examining joint couplings

A muscle produces moments at the joints it crosses, but these moments can also cause accelerations at joints not crossed by the muscle. This phenomenon, the acceleration of a joint caused by a muscle not crossing the joint, is referred to as induced acceleration. For a system of rigid bodies this study examines how system configuration, and segmental inertial properties dictate the potential of one joint to cause the acceleration of other joints in the system. From the equations of motion for a series of rigid bodies, an induced acceleration index (IAI) was developed. The IAI permits quantification of the relative potential of moments produced at joints in the kinematic chain to accelerate other joints in the kinematic chain. The IAI is a function of system orientation, segment lengths, and inertial properties. The IAI was used to examine the roles of the ankle and hip joints in quiet standing. The ankle joint had over 12 times the ability to accelerate the hip joint, than the hip had to accelerate the ankle joint. These results in part explain the relative merits of the two strategies predominantly used to maintain upright stance: the ankle and hip strategies. This index permits an understanding of how the induced accelerations are dependent on system configuration and inertial properties. The IAI is also useful in situations where the inertial properties of the system under investigation changes, for example due to the fitting of a new prostheses to a trans-tibial amputee.     

Ground reaction force estimation using an insole-type pressure mat and joint kinematics during walking

Kinetic analysis of walking requires joint kinematics and ground reaction force (GRF) measurement, which are typically obtained from a force plate. GRF is difficult to measure in certain cases such as slope walking, stair climbing, and track running. Nevertheless, estimating GRF continues to be of great interest for simulating human walking. The purpose of the study was to develop reaction force models placed on the sole of the foot to estimate full GRF when only joint kinematics are provided (Type-I), and to estimate ground contact shear forces when both joint kinematics and foot pressure are provided (Type-II and Type-II-val). The GRF estimation models were attached to a commercial full body skeletal model using the AnyBody Modeling System, which has an inverse dynamics-based optimization solver. The anterior–posterior shear force and medial–lateral shear force could be estimated with approximate accuracies of 6% BW and 2% BW in all three methods, respectively. Vertical force could be estimated in the Type-I model with an accuracy of 13.75% BW. The accuracy of the force estimation was the highest during the mid-single-stance period with an average RMS for errors of 3.10% BW, 1.48% BW, and 7.48% BW for anterior–posterior force, medial–lateral force, and vertical force, respectively. The proposed GRF estimation models could predict full and partial GRF with high accuracy. The design of the contact elements of the proposed model should make it applicable to various activities where installation of a force measurement system is difficult, including track running and treadmill walking.     

Bone position estimation from skin marker co-ordinates using global optimisation with joint constraints

Widespread use of gait or motion analysis in the diagnosis of patients with locomotor pathology and the subsequent planning and assessment of treatment has been limited because of its reliability, particularly in evaluating frontal and transverse plane components. This is because spatial reconstruction of the musculoskeletal system and calculation of its kinematics and kinetics via a skin marker-based multi-link model are subject to marker skin movement artefacts. Traditional methods treat each body segment separately without imposing joint constraints, resulting in apparent dislocations at joints predominantly because of skin movement artefacts. An optimisation method for the determination of the positions and orientations of multi-link musculoskeletal models from marker co-ordinates is presented. It is based on the minimisation of the weighted sum of squared distances between measured and model-determined marker positions. The model imposes joint constraints. Numerical experiments were performed to show that the new method is capable of eliminating joint dislocations and giving more accurate model position and orientation estimations. It is suggested that, with joint constraints and a global error compensation scheme, the effects of measurement errors on the reconstruction of the musculoskeletal system and subsequent mechanical analyses can be reduced globally. The proposed method minimises errors in axial rotation and ab/adduction at the joints and may extend the applicability of gait analysis to clinical problems.     

Biomolecular force measurements and the atomic force microscope

The atomic force microscope (AFM) is a surface-sensitive instrument capable of imaging biological samples at nanometer resolution in all environments including liquids. The sensitivity of the AFM cantilever, to forces in the pico Newton range, has been exploited to measure breakaway forces between biomolecules and to measure folding-unfolding forces within single proteins. By attaching specific antibodies to cantilevers the simultaneous imaging of target antigens and identification of antigen-antibody interactions have been demonstrated.     

Individual-specific muscle maximum force estimation using ultrasound for ankle joint torque prediction using an EMG-driven Hill-type model

EMG-driven models can be used to estimate muscle force in biomechanical systems. Collected and processed EMG readings are used as the input of a dynamic system, which is integrated numerically. This approach requires the definition of a reasonably large set of parameters. Some of these vary widely among subjects, and slight inaccuracies in such parameters can lead to large model output errors. One of these parameters is the maximum voluntary contraction force (F^om). This paper proposes an approach to find F^om by estimating muscle physiological cross-sectional area (PCSA) using ultrasound (US), which is multiplied by a realistic value of maximum muscle specific tension. Ultrasound is used to measure muscle thickness, which allows for the determination of muscle volume through regression equations. Soleus, gastrocnemius medialis and gastrocnemius lateralis PCSAs are estimated using published volume proportions among leg muscles, which also requires measurements of muscle fiber length and pennation angle by US. F^om obtained by this approach and from data widely cited in the literature was used to comparatively test a Hill-type EMG-driven model of the ankle joint. The model uses 3 EMGs (Soleus, gastrocnemius medialis and gastrocnemius lateralis) as inputs with joint torque as the output. The EMG signals were obtained in a series of experiments carried out with 8 adult male subjects, who performed an isometric contraction protocol consisting of 10 s step contractions at 20% and 60% of the maximum voluntary contraction level. Isometric torque was simultaneously collected using a dynamometer. A statistically significant reduction in the root mean square error was observed when US-obtained F^om was used, as compared to F^om from the literature.     

Bottom-up estimation of joint moments during manual lifting using orientation sensors instead of position sensors

L5/S1, hip and knee moments during manual lifting tasks are, in a laboratory environment, frequently established by bottom-up inverse dynamics, using force plates to measure ground reaction forces (GRFs) and an optoelectronic system to measure segment positions and orientations. For field measurements, alternative measurement systems are being developed. One alternative is the use of small body-mounted inertial/magnetic sensors (IMSs) and instrumented force shoes to measure segment orientation and GRFs, respectively. However, because IMSs measure segment orientations only, the positions of segments relative to each other and relative to the GRFs have to be determined by linking them, assuming fixed segment lengths and zero joint translation. This will affect the estimated joint positions and joint moments. This study investigated the effect of using segment orientations only (orientation-based method) instead of using orientations and positions (reference method) on three-dimensional joint moments. To compare analysis methods (and not measurement methods), GRFs were measured with a force plate and segment positions and/or orientations were measured using optoelectronic marker clusters for both analysis methods. Eleven male subjects lifted a box from floor level using three lifting techniques: a stoop, a semi-squat and a squat technique. The difference between the two analysis methods remained small for the knee moments: <4%. For the hip and L5/S1 moments, the differences were more substantial: up to 8% for the stoop and semi-squat techniques and up to 14% for the squat technique. In conclusion, joint moments during lifting can be estimated with good accuracy at the knee joint and with reasonable accuracy at the hip and L5/S1 joints using segment orientation and GRF data only.     

Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command

This paper provides an overview of forward dynamic neuromusculoskeletal modeling. The aim of such models is to estimate or predict muscle forces, joint moments, and/or joint kinematics from neural signals. This is a four-step process. In the first step, muscle activation dynamics govern the transformation from the neural signal to a measure of muscle activation-a time varying parameter between 0 and 1. In the second step, muscle contraction dynamics characterize how muscle activations are transformed into muscle forces. The third step requires a model of the musculoskeletal geometry to transform muscle forces to joint moments. Finally, the equations of motion allow joint moments to be transformed into joint movements. Each step involves complex nonlinear relationships. The focus of this paper is on the details involved in the first two steps, since these are the most challenging to the biomechanician. The global process is then explained through applications to the study of predicting isometric elbow moments and dynamic knee kinetics.     

Development of software for human muscle force estimation

Muscle force estimation (MFE) has become more and more important in exploring principles of pathological movement, studying functions of artificial muscles, making surgery plan for artificial joint replacement, improving the biomechanical effects of treatments and so on. At present, existing software are complex for professionals, so we have developed a new software named as concise MFE (CMFE). CMFE which provides us a platform to analyse muscle force in various actions includes two MFE methods (static optimisation method and electromyographic-based method). Common features between these two methods have been found and used to improve CMFE. A case studying the major muscles of lower limb of a healthy subject walking at normal speed has been presented. The results are well explained from the effect of the motion produced by muscles during movement. The development of this software can improve the accuracy of the motion simulations and can provide a more extensive and deeper insight in to muscle study.     

Development of software for human muscle force estimation

Muscle force estimation (MFE) has become more and more important in exploring principles of pathological movement, studying functions of artificial muscles, making surgery plan for artificial joint replacement, improving the biomechanical effects of treatments and so on. At present, existing software are complex for professionals, so we have developed a new software named as concise MFE (CMFE). CMFE which provides us a platform to analyse muscle force in various actions includes two MFE methods (static optimisation method and electromyographic-based method). Common features between these two methods have been found and used to improve CMFE. A case studying the major muscles of lower limb of a healthy subject walking at normal speed has been presented. The results are well explained from the effect of the motion produced by muscles during movement. The development of this software can improve the accuracy of the motion simulations and can provide a more extensive and deeper insight in to muscle study.     

Gait posture estimation using wearable acceleration and gyro sensors

A method for gait analysis using wearable acceleration sensors and gyro sensors is proposed in this work. The volunteers wore sensor units that included a tri-axis acceleration sensor and three single axis gyro sensors. The angular velocity data measured by the gyro sensors were used to estimate the translational acceleration in the gait analysis. The translational acceleration was then subtracted from the acceleration sensor measurements to obtain the gravitational acceleration, giving the orientation of the lower limb segments. Segment orientation along with body measurements were used to obtain the positions of hip, knee, and ankle joints to create stick figure models of the volunteers. This method can measure the three-dimensional positions of joint centers of the hip, knee, and ankle during movement. Experiments were carried out on the normal gait of three healthy volunteers. As a result, the flexion–extension (F–E) and the adduction–abduction (A–A) joint angles of the hips and the flexion–extension (F–E) joint angles of the knees were calculated and compared with a camera motion capture system. The correlation coefficients were above 0.88 for the hip F–E, higher than 0.72 for the hip A–A, better than 0.92 for the knee F–E. A moving stick figure model of each volunteer was created to visually confirm the walking posture. Further, the knee and ankle joint trajectories in the horizontal plane showed that the left and right legs were bilaterally symmetric.     

Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics

Recent work on joint kinematics indicates that the finite centroid (centre of rotation) and the finite helical axis (axis of rotation, screw axis, twist axis) are highly susceptible to measurement errors when they are experimentally determined from landmark position data. This paper presents an analytical model to describe these effects, under isotropic conditions for the measurement errors and for the spatial landmark distribution. It appears that the position and direction errors are inversely proportional to the rotation magnitude, and that they are much more error-prone than the relatively well-determined rotation and translation magnitudes. Furthermore, the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius, and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis. For the planar centroid, the use of rigid-body constraints results in considerable precision improvement relative to the classical, finite Reuleaux method for centroid reconstruction. These analytical results can be used to define suitable measurement configurations, and they are used in this paper to explain experimental results on R?ntgenphotogrammetrically acquired in vitro wrist joint movement.     

Direct force measurements between siRNA and chitosan molecules using force spectroscopy

Information on the interaction strength between small interfering RNA (siRNA) and chitosan can contribute to the understanding of the formation and stability of chitosan/siRNA nanoparticles used as siRNA delivery systems for gene silencing. In this study, we utilize atomic force microscopy to obtain force spectroscopy results of the interaction strengths between siRNA and chitosan measured in physiological phosphate buffered saline buffer at different pH. The force measurements revealed that the adhesive interactions decreased in force strength and force frequency as the pH was increased from 4.1 to 6.1, 7.4, and 9.5, exhibiting distinct multimodal distributions of the interaction forces between siRNA and chitosan molecules at acidic pH and only negligible adhesive forces were observed at neutral or high pH. The strong pH dependence of siRNA-chitosan interactions can provide a convincing rationale for siRNA/chitosan complex formation and nanoparticle stability under low acidic conditions. These findings demonstrate that the use of force spectroscopy for the adhesive force measurements allows an evaluation of the complexing ability between siRNA and chitosan that can be utilized to predict nanoparticle stability.     

Effect of ankle joint position and electrode placement on the estimation of the antagonistic moment during maximal plantarflexion.

During maximal efforts, antagonistic activity can significantly influence the joint moment. During maximal voluntary "isometric" contractions, certain joint rotation can not be avoided. This can influence the estimation of the antagonistic moment from the EMG activity. Our study aimed to quantify the influence on the calculated agonistic moment produced during maximal voluntary isometric plantarflexions (a) when estimating antagonistic moments at different ankle angles and (b) when placing the EMG electrodes at different portions over the m. tibialis anterior. Ten subjects performed maximal voluntary isometric plantarflexions at 90 degrees ankle angle. In order to estimate the antagonistic moment, submaximal isometric dorsiflexions were performed at various ankle angles. Moment and EMG signals from mm. triceps surae and tibialis anterior were measured. The RMS differences between plantarflexors moment calculated considering the antagonistic cocontraction estimated at the same ankle angle at which the maximal plantarflexion moment was achieved and at different ankle angles ranged from 0.10 to 2.94 Nm. The location of the electrodes led to greater RMS differences (2.35-5.18 Nm). In conclusion, an angle 10 degrees greater than the initial plantarflexion angle is enough to minimize the effect of the change in length of the m. tibialis anterior during the plantarflexion on the estimation of the plantarflexors moment. The localisation of the electrodes over the m. tibialis anterior can influence the estimation of its cocontraction during maximal plantarflexion efforts.     

Correlation between ground reaction force and tibial acceleration in vertical jumping

Modern electronics allow for the unobtrusive measurement of accelerations outside the laboratory using wireless sensor nodes. The ability to accurately measure joint accelerations under unrestricted conditions, and to correlate them with jump height and landing force, could provide important data to better understand joint mechanics subject to real-life conditions. This study investigates the correlation between peak vertical ground reaction forces, as measured by a force plate, and tibial axial accelerations during free vertical jumping. The jump heights calculated from force-plate data and accelerometer measurements are also compared. For six male subjects participating in this study, the average coefficient of determination between peak ground reaction force and peak tibial axial acceleration is found to be 0.81. The coefficient of determination between jump height calculated using force plate and accelerometer data is 0.88. Data show that the landing forces could be as high as 8 body weights of the jumper. The measured peak tibial accelerations ranged up to 42 g. Jump heights calculated from force plate and accelerometer sensors data differed by less than 2.5 cm. It is found that both impact accelerations and landing forces are only weakly correlated with jump height (the average coefficient of determination is 0.12). This study shows that unobtrusive accelerometers can be used to determine the ground reaction forces experienced in a jump landing. Whereas the device also permitted an accurate determination of jump height, there was no correlation between peak ground reaction force and jump height.