Sensitivity of subject-specific models to Hill muscle–tendon model parameters in simulations of gait

Psoas force recruitment in full-body musculoskeletal movement simulations is restored with a geometrically informed cost function weighting

Simulations of musculoskeletal models are useful for estimating internal muscle and joint forces. However, predicted forces rely on optimization and modeling formulations. Geometric detail is important to predict muscle forces, and greater geometric complexity is required for muscles that have broad attachments or span many joints, as in the torso. However, the extent to which optimized muscle force recruitment is sensitive to these geometry choices is unclear. We developed level, uphill and downhill sloped walking simulations using a standard (uniformly weighted, "fatigue-like") cost function with lower limb and full-body musculoskeletal models to evaluate hip muscle recruitment with different geometric representations of the psoas muscle under walking conditions with varying hip moment demands. We also tested a novel cost function formulation where muscle activations were weighted according to the modeled geometric detail in the full-body model. Total psoas force was less and iliacus, rectus femoris, and other hip flexors' force was greater when psoas was modeled with greater geometric detail compared to other hip muscles for all slopes. The proposed weighting scheme restored hip muscle force recruitment without sacrificing detailed psoas geometry. In addition, we found that lumbar, but not hip, joint contact forces were influenced by psoas force recruitment. Our results demonstrate that static optimization dependent simulations using models comprised of muscles with different amounts of geometric detail bias force recruitment toward muscles with less geometric detail. Muscle activation weighting that accounts for differences in geometric complexity across muscles corrects for this recruitment bias.

The biomechanical influence of transtibial Bone-Anchored limbs during walking

Individuals with unilateral transtibial amputation (TTA) using socket prostheses demonstrate asymmetric joint biomechanics during walking, which increases the risk of secondary comorbidities (e.g., low back pain (LBP), osteoarthritis (OA)). Bone-anchored limbs are an alternative to socket prostheses, yet it remains unknown how they influence multi-joint loading. Our objective was to determine the influence of bone-anchored limb use on multi-joint biomechanics during walking. Motion capture data (kinematics, ground reaction forces) were collected during overground walking from ten participants with unilateral TTA prior to (using socket prostheses) and 12-months after bone-anchored limb implantation. Within this year, each participant completed a rehabilitation protocol that guided progression of loading based on patient pain response and optimized biomechanics. Musculoskeletal models were developed at each testing timepoint (baseline or 12-months after implantation) and used to calculate joint kinematics, internal joint moments, and joint reaction forces (JRFs). Analyses were performed during three stance periods on each limb. The between-limb normalized symmetry index (NSI) was calculated for joint moments and JRF impulses. Discrete (range of motion (ROM), impulse NSI) dependent variables were compared before and after implantation using paired t-tests with Bonferroni-Holm corrections while continuous (ensemble averages of kinematics, moments, JRFs) were compared using statistical parametric mapping (p < 0.05). When using a bone-anchored limb, frontal plane pelvic (residual: pre = 9.6 ± 3.3°, post = 6.3 ± 2.5°, p = 0.004; intact: pre = 10.2 ± 3.9°, post = 7.9 ± 2.6°, p = 0.006) and lumbar (residual: pre = 15.9 ± 7.0°, post = 10.6 ± 2.5°, p = 0.024, intact: pre = 17.1 ± 7.0°, post = 11.4 ± 2.8°, p = 0.014) ROM was reduced compared to socket prosthesis use. The intact limb hip extension moment impulse increased (pre = -11.0 ± 3.6 Nm*s/kg, post = -16.5 ± 4.4 Nm*s/kg, p = 0.005) and sagittal plane hip moment impulse symmetry improved (flexion: pre = 23.1 ± 16.0 %, post = -3.9 ± 19.5 %, p = 0.004, extension: pre = 29.2 ± 20.3 %, post = 8.7 ± 22.9 %, p = 0.049). Residual limb knee extension moment impulse decreased compared to baseline (pre = 15.7 ± 10.8 Nm*s/kg, post = 7.8 ± 3.9 Nm*s/kg, p = 0.030). These results indicate that bone-anchored limb implantation alters multi-joint biomechanics, which may impact LBP or OA risk factors in the TTA population longitudinally.

Moment arm and torque generating capacity of semitendinosus following tendon harvesting for anterior cruciate ligament reconstruction: A simulation study

Altered semitendinosus (ST) morphology and distal tendon insertion following anterior cruciate ligament reconstruction (ACLR) may reduce knee flexion torque generating capacity of the hamstrings via impaired ST force generation and/or moment arm. This study used a computational musculoskeletal model to simulate mechanical consequences of tendon harvest for ACLR on ST function by modeling changes in ST muscle tendon insertion point, moment arm, and torque generating capacity across a physiological range of motion. Simulated ST function was then compared between ACLR and uninjured contralateral limbs. Magnetic resonance imaging from 18 individuals with unilateral history of ACLR involving a hamstring autograft was used to analyse bilateral hamstring muscle (ST, semimembranosus, bicep femoris long head and short head) morphology and distal ST tendon insertion. The ACLR cohort was sub-grouped into those with and without ST regeneration. For each participant with ST regeneration (n = 7), a personalized musculoskeletal model was created including postoperative remodeling of ST using OpenSim 4.1. Knee flexion and internal rotation moment arms and torque generating capacities of hamstrings were evaluated. Bilateral differences were calculated with an asymmetry index (%) ([unaffected limb-affected limb]/[unaffected limb + affected limb]*100%). Smaller moment arms or knee torques within injured compared to uninjured contralateral limbs were considered a deficit. Compared to uninjured contralateral limbs, ACLR limbs with tendon regeneration (n = 7) had minor reductions in knee flexion (5.80% [95% confidence interval (CI) = 3.97-7.62]) and internal rotation (4.92% [95% CI = 2.77-7.07]) moment arms. Decoupled from muscle morphology, altered ST moment arms in ACLR limbs with tendon regeneration resulted in negligible deficits in knee flexion (1.20% [95% CI = 0.34-2.06]) and internal rotation (0.24% [95% CI = 0.22-0.26]) torque generating capacity compared to uninjured contralateral limbs. Coupled with muscle morphology, ACLR limbs with tendon regeneration had substantial deficits in knee flexion (19.32% [95% CI = 18.35-20.28]) and internal rotation (15.49% [95% CI = 14.56-16.41]) torques compared to uninjured contralateral limbs. Personalized musculoskeletal models with measures of ST distal insertion and muscle morphology provided unique insights into post-ACLR ST and hamstring function. Deficits in knee flexor and internal rotation moment arms and torque generating capacities were evident in those with ACLR even when tendon regeneration occurred. Future studies may wish to implement this framework in personalized musculoskeletal models following ACLR to better understand individual muscle function for injury prevention and treatment evaluation.

How mechanics of individual muscle-tendon units define knee and ankle joint function in health and cerebral palsy-a narrative review

This study reviews the relationship between muscle-tendon biomechanics and joint function, with a particular focus on how cerebral palsy (CP) affects this relationship. In healthy individuals, muscle size is a critical determinant of strength, with muscle volume, cross-sectional area, and moment arm correlating with knee and ankle joint torque for different isometric/isokinetic contractions. However, in CP, impaired muscle growth contributes to joint pathophysiology even though only a limited number of studies have investigated the impact of deficits in muscle size on pathological joint function. As muscles are the primary factors determining joint torque, in this review two main approaches used for muscle force quantification are discussed. The direct quantification of individual muscle forces from their relevant tendons through intraoperative approaches holds a high potential for characterizing healthy and diseased muscles but poses challenges due to the invasive nature of the technique. On the other hand, musculoskeletal models, using an inverse dynamic approach, can predict muscle forces, but rely on several assumptions and have inherent limitations. Neither technique has become established in routine clinical practice. Nevertheless, identifying the relative contribution of each muscle to the overall joint moment would be key for diagnosis and formulating efficient treatment strategies for patients with CP. This review emphasizes the necessity of implementing the intraoperative approach into general surgical practice, particularly for joint correction operations in diverse patient groups. Obtaining in vivo data directly would enhance musculoskeletal models, providing more accurate force estimations. This integrated approach can improve the clinicians' decision-making process and advance treatment strategies by predicting changes at the muscle and joint levels before interventions, thus, holding the potential to significantly enhance clinical outcomes.

Predictions of thumb, hand, and arm muscle parameters derived using force measurements of varying complexity and neural networks

Subject-specific musculoskeletal models are a promising avenue for personalized healthcare. However, current methods for producing personalized models require dense, biomechanical datasets that include expensive and time-consuming physiological measurements. For personalized models to be clinically useful, we must be able to rapidly generate models from simple, easy to collect data. In this context, the objective of this paper is to evaluate if and how simple data, namely height/weight and pinch force data, can be used to achieve model personalization via machine learning. Using simulated lateral pinch force measurements from a synthetic population of 40,000 randomly generated subjects, we train neural networks to estimate four Hill-type muscle model parameters and bone density. We compare parameter estimates to the true parameters of 10,000 additional synthetic subjects. We also generate new personalized models using the parameter estimates and perform new lateral pinch simulations to compare predicted forces using these personalized models to those generated using a baseline model. We demonstrate that increasing force measurement complexity reduces the root-mean-square error in the majority of parameter estimates. Additionally, musculoskeletal models using neural network-based parameter estimates provide up to an 80% reduction in absolute error in simulated forces when compared to a generic model. Thus, easily obtained force measurements may be suitable for personalizing models of the thumb, although extending the method to more tasks and models involving other joints likely requires additional measurements.

Digital twin-driven dynamic monitoring system of the upper limb force

Digital twin represents the core technology to realize the dynamic monitoring of complex industrial systems. However, the human body, as the most complex system in the physical world, digital twin is rarely applied in it. In this study, we successfully demonstrated a digital twin in the human biomedical application by proposing a dynamic monitoring system of the upper limb force. In this system, the real upper limb drives the motion of the virtual one in real-time and dynamically updates the force. Meanwhile, the virtual upper limb feeds back the monitoring-results of the force to the controller of the real upper limb via immersive virtual reality interaction. Experimental results of the typical motions of the upper limb revealed that the proposed system functioned interactively in real-time in a non-invasive manner, while ensuring the accurate solving of the muscle force. In conclusion, our digital twin-driven system is of great importance for rehabilitation medicine, biomechanical scientific research and physical training, promoting the application of the digital twin in the human biomedical field.

Neuromuscular control: from a biomechanist's perspective

Understanding neural control of movement necessitates a collaborative approach between many disciplines, including biomechanics, neuroscience, and motor control. Biomechanics grounds us to the laws of physics that our musculoskeletal system must obey. Neuroscience reveals the inner workings of our nervous system that functions to control our body. Motor control investigates the coordinated motor behaviours we display when interacting with our environment. The combined efforts across the many disciplines aimed at understanding human movement has resulted in a rich and rapidly growing body of literature overflowing with theories, models, and experimental paradigms. As a result, gathering knowledge and drawing connections between the overlapping but seemingly disparate fields can be an overwhelming endeavour. This review paper evolved as a need for us to learn of the diverse perspectives underlying current understanding of neuromuscular control. The purpose of our review paper is to integrate ideas from biomechanics, neuroscience, and motor control to better understand how we voluntarily control our muscles. As biomechanists, we approach this paper starting from a biomechanical modelling framework. We first define the theoretical solutions (i.e., muscle activity patterns) that an individual could feasibly use to complete a motor task. The theoretical solutions will be compared to experimental findings and reveal that individuals display structured muscle activity patterns that do not span the entire theoretical solution space. Prevalent neuromuscular control theories will be discussed in length, highlighting optimality, probabilistic principles, and neuromechanical constraints, that may guide individuals to families of muscle activity solutions within what is theoretically possible. Our intention is for this paper to serve as a primer for the neuromuscular control scientific community by introducing and integrating many of the ideas common across disciplines today, as well as inspire future work to improve the representation of neural control in biomechanical models.

Neuromusculoskeletal model calibration accounts for differences in electromechanical delay and maximum isometric muscle force

Electromechanical delay (EMD) and maximum isometric muscle force (F_o^M) are important parameters for joint contact force calculation with EMG-informed neuromusculoskeletal (NMS) models. These parameters can vary between tasks (EMD) and individuals (EMD and F_o^M), making it challenging to establish representative values. One promising approach is to personalise candidate parameters to the participant (e.g., F_o^M by regression equation) and then adjust all parameters within a calibration (i.e., numerical optimisation) to minimise error between corresponding pairs of experimental measures and model-predicted values. The purpose of this study was to determine whether calibration of an NMS model resulted in consistent joint contact forces, regardless of EMD value or personalisation of F_o^M. Hip, knee, and ankle contact forces were predicted for 28 participants using EMG-informed NMS models. Differences in joint contact forces with EMD were examined in six models, calibrated with EMD from 15 to 110 ms. Differences in joint contact forces with personalisation of F_o^M were examined in two models, both calibrated with the same initial EMD (50 ms), one with generic and one with personalised values for F_o^M. For all models, joint contact force peaks during the first and second halves of stance were extracted and compared using a repeated-measures analysis of variance. Calibrated models with EMD set between 35 and 70 ms produced similar magnitude and timing of peak joint contact forces. Compared with generic values, personalising and then calibrating F_o^M resulted in comparable peak contact forces at hip, but not knee or ankle, while also producing muscle-specific tensions similar to reported literature. Overall, EMD between 35 and 70 ms and personalised initial values of F_o^M before calibration are advised for EMG-informed NMS modelling.

Leveraging Multivariable Linear Regression Analysis to Identify Patients with Anterior Cruciate Ligament Deficiency Using a Composite Index of the Knee Flexion and Muscle Force

Patients with anterior cruciate ligament (ACL) deficiency (ACLD) tend to have altered lower extremity kinematics and dynamics. Clinical diagnosis of ACLD requires more objective and convenient evaluation criteria. Twenty-five patients with ACLD before ACL reconstruction and nine healthy volunteers were recruited. Five experimental jogging data sets of each participant were collected and calculated using a musculoskeletal model. The resulting knee flexion and muscle force data were analyzed using a t-test for characteristic points, which were the time points in the gait cycle when the most significant difference between the two groups was observed. The data of the characteristic points were processed with principal component analysis to generate a composite index for multivariable linear regression. The accuracy rate of the regression model in diagnosing patients with ACLD was 81.4%. This study demonstrates that the multivariable linear regression model and composite index can be used to diagnose patients with ACLD. The composite index and characteristic points can be clinically objective and can be used to extract effective information quickly and conveniently.

Numerical instability of Hill-type muscle models

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

The functional role of hip muscles during gait in patients with increased femoral anteversion

BACKGROUND

Femoral anteversion affects the lever arm and moment-generating capacity of the hip abductors, while an increased hip internal rotation during walking was proposed to be a compensatory mechanism to restore the abductive lever arm. Children with isolated increased femoral anteversion, however, do not always present a deficit in the net hip abduction moment during gait, suggesting that a more comprehensive understanding of the effect of morphology and motion on muscle forces and moments is needed to aid clinical decision making.

RESEARCH QUESTION

Are muscle contributions to hip joint moments and muscle forces altered in patients with increased femoral anteversion and internally rotated gait pattern compared to a control group of typically developing children? And how would the functional role of the muscle be altered if the patients walked straight?

METHODS

This follow-up study compared patients with increased femoral anteversion (n = 42, 12.8 ± 1.9 years, femoral anteversion: 39.6 ± 6.9°) to controls (n = 9, 12.0 ± 3.0 years, femoral anteversion: 18.7 ± 4.1°). Muscle forces and moment contributions were calculated using personalized musculoskeletal models. Additionally, a hypothetical scenario, in which the gait of the controls was modelled with an anteverted femoral morphology, was used to understand what would happen if the patients walked straight.

RESULTS

Gluteus medius abductive contribution was lower in patients compared to controls, despite a comparable net abduction moment around the hip. Patients presented lower muscle forces. However, if modelled to walk straight, they would require higher forces as well as a larger co-contraction of both hip internal and external rotators in the transversal plane.

SIGNIFICANCE

This study suggests that patients with increased femoral anteversion walking with an internally rotated gait pattern present lower muscle forces, but when modelled to walk straight muscle forces increase. The current results provide important information to better understand this condition and improve treatment recommendations in these patients.

On the estimation of hip joint loads through musculoskeletal modeling

Noninvasive estimation of joint loads is still an open challenge in biomechanics. Although musculoskeletal modeling represents a solid resource, multiple improvements are still necessary to obtain accurate predictions of joint loads and to translate such potential into practical utility. The present study, focused on the hip joint, is aimed at reviewing the state-of-the-art literature on the estimation of hip joint reaction forces through musculoskeletal modeling. Our literature inspection, based on well-defined selection criteria, returned seventeen works, which were compared in terms of methods and results. Deviations between predicted and in vivo measured hip joint loads, taken from the OrthoLoad database, were assessed through quantitative deviation indices. Despite the numerous modeling and computational improvements made over the last two decades, predicted hip joint loads still deviate from their experimental counterparts and typically overestimate them. Several critical aspects have emerged that affect muscle force estimation, hence joint loads. Among them, the physical fidelity of the musculoskeletal model, with its parameters and geometry, plays a crucial role. Also, predicted joint loads are markedly affected by the selected muscle recruitment strategy, which reflects the underlying motor control policy. Practical guidelines for researchers interested in noninvasive estimation of hip joint loads are also provided.

Contributions of individual muscle forces to hip, knee, and ankle contact forces during the stance phase of running: a model-based study

Knowledge of muscle forces' contributions to the joint contact forces can assist in the evaluation of muscle function, joint injury prevention, treatment of gait disorders, and arthroplasty planning. This study's objective was to evaluate the contributions of human lower limb muscles to the hip, knee, and ankle joint contact forces during the stance phase of running. A total of 25 muscles (or groups) were investigated based on the OpenSim framework along the anterior-posterior, superoinferior, and mediolateral components of each joint coordinate system. It was revealed that, during the running stance phase, the gluteus medius, gluteus maximus, and iliopsoas mainly contributed to the hip contact force. The soleus, vastus group, and rectus femoris primarily contributed to the knee contact force, while the peroneus, soleus, gluteus medius, and gastrocnemius mainly contributed to the ankle joint force; some muscles simultaneously offloaded the joints during the stance phase. The distributive pattern of the individual muscle functions contributing to the joint load may substantially differ during the running and walking stance phases. This study's findings may further provide suggestive information for the design of lower limb joint prosthesis, the study of the biomechanics of pathologic walking and running, and the progression of joint osteoarthritis.

Personalisation of Plantarflexor Musculotendon Model Parameters in Children with Cerebral Palsy

Neuromusculoskeletal models can be used to evaluate aberrant muscle function in cerebral palsy (CP), for example by estimating muscle and joint contact forces during gait. However, to be accurate, models should include representative musculotendon parameters. We aimed to estimate personalised parameters that capture the mechanical behaviour of the plantarflexors in children with CP and typically developing (TD) children. Ankle angle (using motion capture), torque (using a load-cell), and medial gastrocnemius fascicle lengths (using ultrasound) were measured during slow passive ankle dorsiflexion rotation for thirteen children with spastic CP and thirteen TD children. Per subject, the measured rotation was input to a scaled OpenSim model to simulate the torque and fascicle length output. Musculotendon model parameters were personalised by the best match between simulated and experimental torque–angle and fascicle length-angle curves according to a least-squares fit. Personalised tendon slack lengths were significantly longer and optimal fibre lengths significantly shorter in CP than model defaults and than in TD. Personalised tendon compliance was substantially higher in both groups compared to the model default. The presented method to personalise musculotendon parameters will likely yield more accurate simulations of subject-specific muscle mechanics, to help us understand the effects of altered musculotendon properties in CP.

Hamstrings force-length relationships and their implications for angle-specific joint torques: a narrative review

Temporal biomechanical and physiological responses to physical activity vary between individual hamstrings components as well as between exercises, suggesting that hamstring muscles operate differently, and over different lengths, between tasks. Nevertheless, the force-length properties of these muscles have not been thoroughly investigated. The present review examines the factors influencing the hamstrings’ force-length properties and relates them to in vivo function. A search in four databases was performed for studies that examined relations between muscle length and force, torque, activation, or moment arm of hamstring muscles. Evidence was collated in relation to force-length relationships at a sarcomere/fiber level and then moment arm-length, activation-length, and torque-joint angle relations. Five forward simulation models were also used to predict force-length and torque-length relations of hamstring muscles. The results show that, due to architectural differences alone, semitendinosus (ST) produces less peak force and has a flatter active (contractile) fiber force-length relation than both biceps femoris long head (BFlh) and semimembranosus (SM), however BFlh and SM contribute greater forces through much of the hip and knee joint ranges of motion. The hamstrings’ maximum moment arms are greater at the hip than knee, so the muscles tend to act more as force producers at the hip but generate greater joint rotation and angular velocity at the knee for a given muscle shortening length and speed. However, SM moment arm is longer than SM and BFlh, partially alleviating its reduced force capacity but also reducing its otherwise substantial excursion potential. The current evidence, bound by the limitations of electromyography techniques, suggests that joint angle-dependent activation variations have minimal impact on force-length or torque-angle relations. During daily activities such as walking or sitting down, the hamstrings appear to operate on the ascending limbs of their force-length relations while knee flexion exercises performed with hip angles 45–90° promote more optimal force generation. Exercises requiring hip flexion at 45–120° and knee extension 45–0° (e.g. sprint running) may therefore evoke greater muscle forces and, speculatively, provide a more optimum adaptive stimulus. Finally, increases in resistance to stretch during hip flexion beyond 45° result mainly from SM and BFlh muscles.

Increased Femoral Anteversion Does Not Lead to Increased Joint Forces During Gait in a Cohort of Adolescent Patients

Orthopedic complications were previously reported for patients with increased femoral anteversion. A more comprehensive analysis of the influence of increased femoral anteversion on joint loading in these patients is required to better understand the pathology and its clinical management. Therefore, the aim was to investigate lower-limb kinematics, joint moments and forces during gait in adolescent patients with increased, isolated femoral anteversion compared to typically developing controls. Secondly, relationships between the joint loads experienced by the patients and different morphological and kinematic features were investigated. Patients with increased femoral anteversion (n = 42, 12.8 ± 1.9 years, femoral anteversion: 39.6 ± 6.9°) were compared to typically developing controls (n = 9, 12.0 ± 3.0 years, femoral anteversion: 18.7 ± 4.1°). Hip and knee joint kinematics and kinetics were calculated using subject-specific musculoskeletal models. Differences between patients and controls in the investigated outcome variables (joint kinematics, moments, and forces) were evaluated through statistical parametric mapping with Hotelling T2 and t-tests (α = 0.05). Canonical correlation analyses (CCAs) and regression analyses were used to evaluate within the patients’ cohort the effect of different morphological and kinematic predictors on the outcome variables. Predicted compressive proximo-distal loads in both hip and knee joints were significantly reduced in patients compared to controls. A gait pattern characterized by increased knee flexion during terminal stance (KneeFlex_tSt) was significantly correlated with hip and knee forces, as well as with the resultant force exerted by the quadriceps on the patella. On the other hand, hip internal rotation and in-toeing, did not affect the loads in the joints. Based on the finding of the CCAs and linear regression analyses, patients were further divided into two subgroups based KneeFlex_tSt. Patients with excessive KneeFlex_tSt presented a significantly higher femoral anteversion than those with normal KneeFlex_tSt. Patients with excessive KneeFlex_tSt presented significantly larger quadriceps forces on the patella and a larger posteriorly-oriented shear force at the knee, compared to patients with normal KneeFlex_tSt, but both patients’ subgroups presented only limited differences in terms of joint loading compared to controls. This study showed that an altered femoral morphology does not necessarily lead to an increased risk of joint overloading, but instead patient-specific kinematics should be considered.

Uncertainty in Muscle–Tendon Parameters can Greatly Influence the Accuracy of Knee Contact Force Estimates of Musculoskeletal Models

Understanding the sources of error is critical before models of the musculoskeletal system can be usefully translated. Using in vivo measured tibiofemoral forces, the impact of uncertainty in muscle–tendon parameters on the accuracy of knee contact force estimates of a generic musculoskeletal model was investigated following a probabilistic approach. Population variability was introduced to the routine musculoskeletal modeling framework by perturbing input parameters of the lower limb muscles around their baseline values. Using ground reaction force and skin marker trajectory data collected from six subjects performing body-weight squat, the knee contact force was calculated for the perturbed models. The combined impact of input uncertainties resulted in a considerable variation in the knee contact force estimates (up to 2.1 BW change in the predicted force), especially at larger knee flexion angles, hence explaining up to 70% of the simulation error. Although individual muscle groups exhibited different contributions to the overall error, variation in the maximum isometric force and pathway of the muscles showed the highest impacts on the model outcomes. Importantly, this study highlights parameters that should be personalized in order to achieve the best possible predictions when using generic musculoskeletal models for activities involving deep knee flexion.

Altering the strength of the muscles crossing the lower limb joints only affects knee joint reaction forces

BACKGROUND

Generic musculoskeletal models based on literature data are often used to estimate joint reaction forces (JRFs) that otherwise could only be measured invasively. Estimated JRFs are sensitive to changes in maximum isometric force (F_iso) of the muscles, but these are normally simply scaled using a multiplicative coefficient. The impact of varying F_iso, or strength, of muscles crossing each lower limb joint on estimated JRFs has not been systematically explored in musculoskeletal models of the lower limb.

RESEARCH QUESTION

How do alterations in the strength of joint-crossing muscles influence the lower limb JRF magnitudes computed through a generic musculoskeletal model?

METHODS

By modifying F_iso of muscles crossing hip, knee, ankle, or all joints at once up to ± 40% in 10% increments, thirty-two models were created to simulate the gait of a patient with an instrumented tibial prosthesis (5^th Grand Challenge dataset). A standard workflow (inverse kinematics, static optimization, joint reaction analysis) was utilized to calculate JRFs. Both alterations in JRF magnitudes due to joint crossing muscles' strength modifications and their accuracy against in vivo knee loading measurements were quantified.

RESULTS

The knee JRF was the most sensitive force to changes in the joint-crossing muscles' strength (variations ranging from -37.9 ± 0.5% to +37.9 ± 3.2%), while the hip and ankle JRFs were almost unaffected (maximum variation: +6.1%). Reducing the strength of knee and ankle-crossing muscles and intensifying the strength of hip-crossing muscles lowered the knee JRF. The knee JRF was best estimated (peak error: 0.42 ± 0.15 body weight, root mean squared error: 0.37 ± 0.06 body weight, coefficient of determination: 0.76 ± 0.10) by the model with -40% weakened knee-crossing muscles.

SIGNIFICANCE

Altering strengths mainly affects knee JRF estimated with generic musculoskeletal models, suggesting that personalization of strength of joint-crossing muscles is required for accurate knee JRF estimations. Rehabilitation regimes meant to strengthen muscles crossing a joint should be carefully designed to avoid undesired effects on the other joints.

The relationship between quantitative magnetic resonance imaging of the ankle plantar flexors, muscle function during walking and maximal strength in people with neuromuscular diseases

BACKGROUND

Progression of plantar flexor weakness in neuromuscular diseases is usually monitored by muscle strength measurements, although they poorly relate to muscle function during walking. Pathophysiological changes such as intramuscular adipose tissue affect dynamic muscle function independent from isometric strength. Diffusion tensor imaging and T2 imaging are quantitative MRI measures reflecting muscular pathophysiological changes, and are therefore potential biomarkers to monitor plantar flexor functioning during walking in people with neuromuscular diseases.

METHODS

In fourteen individuals with plantar flexor weakness diffusion tensor imaging and T2 scans of the plantar flexors were obtained, and the diffusion indices fractional anisotropy and mean diffusivity calculated. With a dynamometer, maximal isometric plantar flexor strength was measured. 3D gait analysis was used to assess maximal ankle moment and power during walking.

FINDINGS

Fractional anisotropy, mean diffusivity and T2 relaxation time all moderately correlated with maximal plantar flexor strength (r > 0.512). Fractional anisotropy and mean diffusivity were not related with ankle moment or power (r < 0.288). T2 relaxation time was strongly related to ankle moment (r = -0.789) and ankle power (r = -0.798), and moderately related to maximal plantar flexor strength (r < 0.600).

INTERPRETATION

In conclusion, T2 relaxation time, indicative of multiple pathophysiological changes, was strongly related to plantar flexor function during walking, while fractional anisotropy and mean diffusivity, indicative of fiber size, only related to maximal plantar flexor strength. This indicates that these measures may be suitable to monitor muscle function and gain insights into the pathophysiological changes underlying a poor plantar flexor functioning during gait in people with neuromuscular diseases.

Effect of different walking speeds on joint and muscle force estimation using AnyBody and OpenSim

BACKGROUND

To be able to use muscluloskeletal models in clinical settings, it is important to understand the effect of walking speed on joint and muscle force estimations in different generic musculoskeletal models.

RESEARCH QUESTION

The aim of the current study is to compare estimated joint and muscle forces as a function of walking speed between two standard approaches offered in two different modelling environments (AnyBody and OpenSim).

METHODS

Experimental data of 10 healthy participants were recorded at three different walking speeds (self-selected, 25 % slower, 25 % faster) using a ten-camera motion capture system together with four force plates embedded into a ten-meter walkway. Joint compression forces and muscle forces were calculated with a generic model in AnyBody and OpenSim. Trend analyses, mean absolute error (MAE) and correlation coefficients were used to compare joint compression forces and muscle forces between the two approaches. A one-way and two-way ANOVA with repeated measures were used to compare MAE and trend analysis changes, respectively (α = 0.05, Bonferroni corrected post-hoc tests).

RESULTS

Trend analyses showed the same speed effect for AnyBody and OpenSim. MAEs increased significantly from slow to fast walking for knee joint compression forces, biceps femoris long head, gluteus maximus, gluteus medius and vastus intermedius. Lower correlation coefficients during slower walking were found for quadriceps muscles, gluteus maximus and biceps femoris compared to normal and faster walking.

SIGNIFICANCE

Lower correlation coefficients during slower walking are assumed to be due to a higher amount of solutions solving the muscle recruitment in musculoskeletal models. This indicates that decreasing walking speed is more prone to speed dependent differences regarding variability, while the absolute error increased with increasing walking speed. To conclude, different modelling environments can react differently to changes in walking speed, but overall results are promising regarding the generalization across different generic musculoskeletal models.

An Anatomical Atlas-Based Scaling Study for Quantifying Muscle and Hip Joint Contact Forces in Above and Through-Knee Amputees Using Validated Musculoskeletal Modelling

OBJECTIVE

Customisation of musculoskeletal modelling using magnetic resonance imaging (MRI) significantly improves the model accuracy, but the process is time consuming and computationally intensive. This study hypothesizes that linear scaling to a lower limb amputee model with anthropometric similarity can accurately predict muscle and joint contact forces.

METHODS

An MRI-based anatomical atlas, comprising 18 trans-femoral and through-knee traumatic lower limb amputee models, is developed. Gait data, using a 10-camera motion capture system with two force plates, and surface electromyography (EMG) data were collected. Muscle and hip joint contact forces were quantified using musculoskeletal modelling. The predicted muscle activations from the subject-specific models were validated using EMG recordings. Anthropometry based multiple linear regression models, which minimize errors in force predictions, are presented.

RESULTS

All predictions showed excellent (error interval c = 0-0.15), very good (c = 0.15-0.30) or good (c = 0.30-0.45) similarity to the EMG data, demonstrating accurate computation of muscle activations. The primary predictors of discrepancies in force predictions were differences in pelvis width (p < 0.001), body mass index (BMI, p < 0.001) and stump length to pelvis width ratio (p < 0.001) between the respective individual and underlying dataset.

CONCLUSION

Linear scaling to a model with the most similar pelvis width, BMI and stump length to pelvis width ratio results in modelling outcomes with minimal errors.

SIGNIFICANCE

This study provides robust tools to perform accurate analyses of musculoskeletal mechanics for high-functioning lower limb military amputees, thus facilitating the further understanding and improvement of the amputee's function. The atlas is available in an open source repository.

MRI-based anatomical characterisation of lower-limb muscles in older women

The ability of muscles to produce force depends, among others, on their anatomical features and it is altered by ageing-associated weakening. However, a clear characterisation of these features, highly relevant for older individuals, is still lacking. This study hence aimed at characterising muscle volume, length, and physiological cross-sectional area (PCSA) and their variability, between body sides and between individuals, in a group of post-menopausal women. Lower-limb magnetic resonance images were acquired from eleven participants (69 (7) y. o., 66.9 (7.7) kg, 159 (3) cm). Twenty-three muscles were manually segmented from the images and muscle volume, length and PCSA were calculated from this dataset. Personalised maximal isometric force was then calculated using the latter information. The percentage difference between the muscles of the two lower limbs was up to 89% and 22% for volume and length, respectively, and up to 84% for PCSA, with no recognisable pattern associated with limb dominance. Between-subject coefficients of variation reached 36% and 13% for muscle volume and length, respectively. Generally, muscle parameters were similar to previous literature, but volumes were smaller than those from in-vivo young adults and slightly higher than ex-vivo ones. Maximal isometric force was found to be on average smaller than those obtained from estimates based on linear scaling of ex-vivo-based literature values. In conclusion, this study quantified for the first time anatomical asymmetry of lower-limb muscles in older women, suggesting that symmetry should not be assumed in this population. Furthermore, we showed that a scaling approach, widely used in musculoskeletal modelling, leads to an overestimation of the maximal isometric force for most muscles. This heavily questions the validity of this approach for older populations. As a solution, the unique dataset of muscle segmentation made available with this paper could support the development of alternative population-based scaling approaches, together with that of automatic tools for muscle segmentation.

Development of a Full Flexion 3D Musculoskeletal Model of the Knee Considering Intersegmental Contact During High Knee Flexion Movements

A musculoskeletal model of the right lower limb was developed to estimate 3D tibial contact forces in high knee flexion postures. This model determined the effect of intersegmental contact between thigh-calf and heel-gluteal structures on tibial contact forces. This model includes direct tracking and 3D orientation of intersegmental contact force, femoral translations from in vivo studies, wrapping of knee extensor musculature, and a novel optimization constraint for multielement muscle groups. Model verification consisted of calculating the error between estimated tibial compressive forces and direct measurements from the Grand Knee Challenge during movements to ∼120° of knee flexion as no high knee flexion data are available. Tibial compression estimates strongly fit implant data during walking (R2 = .83) and squatting (R2 = .93) with a root mean squared difference of .47 and .16 body weight, respectively. Incorporating intersegmental contact significantly reduced model estimates of peak tibial anterior-posterior shear and increased peak medial-lateral shear during the static phase of high knee flexion movements by an average of .33 and .07 body weight, respectively. This model supports prior work in that intersegmental contact is a critical parameter when estimating tibial contact forces in high knee flexion movements across a range of culturally and occupationally relevant postures.

Non-amputated limb muscle coordination of unilateral transfemoral amputees

Unilateral transfemoral amputees rely heavily on non-amputated limb muscles to regulate the prosthetic gait. In this study, we compared the non-amputated limb muscle coordination of eight unilateral transfemoral amputees to eight able-bodied controls. Inverse dynamics approach was conducted via a musculoskeletal model to obtain lower limb joint moments and muscle forces. In addition to the muscle forces at the instants of peak joint moments and the maximum muscle forces, the peak joint moments of the lower limbs were also investigated. The results showed that there were significant differences of muscle forces between the non-amputated limbs and the controls at the instant of peak hip extension moment, although the peak hip extension moments themselves were not significantly different between the two groups. The non-amputated limbs had significantly smaller peak hip flexion moment and peak knee extension moment, with significant differences between the muscle forces of non-amputated limbs and controls at the two instants. There was no significant difference between the muscle forces of the non-amputated limbs and controls at the peak knee flexion moment instant, despite the fact that the non-amputated limbs had significantly higher peak knee flexion moments. In addition, the non-amputated limbs had significantly smaller maximum muscle forces than the controls. These results demonstrate that amputees modify their muscle coordination to adapt to the specific joint requirements of the prosthetic gait. Our findings suggest the possibility of non-amputated limb muscle atrophy due to the decrease in the peak muscle forces during walking.

An EMG-Driven Musculoskeletal Model for Estimating Continuous Wrist Motion

EMG-based continuous wrist joint motion estimation has been identified as a promising technique with huge potential in assistive robots. Conventional data-driven model-free methods tend to establish the relationship between the EMG signal and wrist motion using machine learning or deep learning techniques, but cannot interpret the functional relationship between neuro-commands and relevant joint motion. In this paper, an EMG-driven musculoskeletal model is proposed to estimate continuous wrist joint motion. This model interprets the muscle activation levels from EMG signals. A muscle-tendon model is developed to compute the muscle force during the voluntary flexion/extension movement, and a joint kinematic model is established to estimate the continuous wrist motion. To optimize the subject-specific physiological parameters, a genetic algorithm is designed to minimize the differences of joint motion prediction from the musculoskeletal model and joint motion measurement using motion data during training. Results show that mean root-mean-square-errors are 10.08°, 10.33°, 13.22° and 17.59° for single flexion/extension, continuous cycle and random motion trials, respectively. The mean coefficient of determination is over 0.9 for all the motion trials. The proposed EMG-driven model provides an accurate tracking performance based on user's intention.

Muscular architecture of the popliteus muscle and the basic science implications

BACKGROUND

The function of the popliteus muscle is largely treated as a static stabilizer and has a lack of basic muscular architectural data to enable study of its dynamic function. A large volume of literature supports its static function and the essential need for reconstruction in the posterolateral knee when injured to restore knee stability.

HYPOTHESIS/PURPOSE

We hypothesize that the popliteus muscle is more significant as a dynamic presence in the knee.

METHODS

A collection of popliteus architectural data was collected from 28 cadaver specimens (mean (SD) 76 years (11)). Physiological cross-sectional area of the popliteus and semimembranosus muscles were calculated from muscle volume and fiber length to power future muscle force prediction models. Posterior knee muscle trajectories were measured with respect to the longitudinal axis of the tibia. A 2-tailed T test was performed.

RESULTS

Significant differences between males and females were found for both the popliteus (p = 1.1E-05) and semimembranosus (p = 2.0E-05) muscle volumes. Significant differences between males and females were also found in PCSA for the popliteus (p = 0.005) and semimembranosus (p = 4.1E-05) muscles. There were no significant differences in fiber length, overall muscle length (with tendon removed), age, and orientation.

CONCLUSION

Further consideration should be given to include the popliteus muscle as a dynamic entity in the knee given its mechanical properties, trajectory, and prior biomechanical evidence showing when and how it is activated. The present study provides data that may shape future directions of research and treatment with regard to posterolateral corner injuries and ligamentous balancing of the knee.

The effects of electromyography-assisted modelling in estimating musculotendon forces during gait in children with cerebral palsy

Neuro-musculoskeletal modelling can provide insight into the aberrant muscle function during walking in those suffering cerebral palsy (CP). However, such modelling employs optimization to estimate muscle activation that may not account for disturbed motor control and muscle weakness in CP. This study evaluated different forms of neuro-musculoskeletal model personalization and optimization to estimate musculotendon forces during gait of nine children with CP (GMFCS I-II) and nine typically developing (TD) children. Data collection included 3D-kinematics, ground reaction forces, and electromyography (EMG) of eight lower limb muscles. Four different optimization methods estimated muscle activation and musculotendon forces of a scaled-generic musculoskeletal model for each child walking, i.e. (i) static optimization that minimized summed-excitation squared; (ii) static optimization with maximum isometric muscle forces scaled to body mass; (iii) an EMG-assisted approach using optimization to minimize summed-excitation squared while reducing tracking errors of experimental EMG-linear envelopes and joint moments; and (iv) EMG-assisted with musculotendon model parameters first personalized by calibration. Both static optimization approaches showed a relatively low model performance compared to EMG envelopes. EMG-assisted approaches performed much better, especially in CP, with only a minor mismatch in joint moments. Calibration did not affect model performance significantly, however it did affect musculotendon forces, especially in CP. A model more consistent with experimental measures is more likely to yield more physiologically representative results. Therefore, this study highlights the importance of calibrated EMG-assisted modelling when estimating musculotendon forces in TD children and even more so in children with CP.

Twente Spine Model: A thorough investigation of the spinal loads in a complete and coherent musculoskeletal model of the human spine

Although in vivospinal loads have been previously measured, existing data are limited to certain lumbar and thoracic levels. A detailed investigation of spinal loads would assist with injury prevention and implant design but is unavailable. In this study, we developed a complete and coherent musculoskeletal model of the entire human spine and studied the intervertebral disc compression forces for physiological movements on three anatomical planes. This model incorporates the individual vertebrae at the cervical, thoracic, and lumbar regions, a flexible ribcage, and complete muscle anatomy. Intradiscal pressures were estimated from predicted compressive forces, and these were generally in close agreement with previously measured data. We found that compressive forces at the trunk discs increased during trunk lateral bending and axial rotation of the trunk. During flexion, compressive forces increased in the thoracolumbar and lumbar regions and slightly decreased at the middle thoracic discs. In extension, the forces generally decreased at the thoracolumbar and lumbar discs whereas they slightly increased at the upper and middle thoracic discs. Furthermore, similar to a previous biomechanical model of the cervical spine, our model predicted increased compression forces in neck flexion, lateral bending, and axial rotation, and decreased forces in neck extension.

Improving Musculoskeletal Model Scaling Using an Anatomical Atlas: The Importance of Gender and Anthropometric Similarity to Quantify Joint Reaction Forces

OBJECTIVE

The accuracy of a musculoskeletal model relies heavily on the implementation of the underlying anatomical dataset. Linear scaling of a generic model, despite being time and cost efficient, produces substantial errors as it does not account for gender differences and inter-individual anatomical variations. The hypothesis of this study is that linear scaling to a musculoskeletal model with gender and anthropometric similarity to the individual subject produces similar results to the ones that can be obtained from a subject-specific model.

METHODS

A lower limb musculoskeletal anatomical atlas was developed consisting of ten datasets derived from magnetic resonance imaging of healthy subjects and an additional generic dataset from the literature. Predicted muscle activation and joint reaction force were compared with electromyography and literature data. Regressions based on gender and anthropometry were used to identify the use of atlas.

RESULTS

Primary predictors of differences for the joint reaction force predictions were mass difference for the ankle (p < 0.001) and length difference for the knee and hip (p ≤ 0.017). Gender difference accounted for an additional 3% of the variance (p ≤ 0.039). Joint reaction force differences at the ankle, knee, and hip were reduced by between 50% and 67% (p = 0.005) when using a musculoskeletal model with the same gender and similar anthropometry in comparison with a generic model.

CONCLUSION

Linear scaling with gender and anthropometric similarity can improve joint reaction force predictions in comparison with a scaled generic model.

SIGNIFICANCE

The presented scaling approach and atlas can improve the fidelity and utility of musculoskeletal models for subject-specific applications.

Plantarflexor fiber and tendon slack length are strong determinates of simulated single-leg heel raise height

Achilles tendon ruptures have been linked with detrimental changes in muscle-tendon structure, which may help explain long-term functional deficits. However, the causal effects of muscle-tendon structure on joint function have not been tested in a controlled setting. Therefore, the purpose of this study was to test the implications of muscle-tendon unit parameters on simulated single-leg heel raise height. We hypothesized that muscle fiber length and resting ankle angle - a clinical surrogate measure of tendon slack length - would predict single-leg heel raise height more strongly than other parameters. To test this hypothesis, we developed a two-part simulation paradigm that recreated clinically relevant muscle-tendon scenarios and then tested these parameters on single-leg heel raise height. We found that longer muscle fibers had the greatest positive effect on single-leg heel raise height. However, tendon slack length, determined by simulating resting ankle angles in a secondary analysis, revealed a stronger negative correlation with heel raise height. Our findings support previous clinical observations that both muscle fascicle length and resting tendon length are important muscle-tendon parameters for patient function. In addition to minimizing tendon elongation following rupture, treatment plans should focus on preserving plantarflexor muscle structure to mitigate functional loses following Achilles tendon ruptures.

Effect of hip joint angle at seat-off on hip joint contact force during sit-to-stand movement: a computer simulation study

Background

Sit-to-stand movements are a necessary part of daily life, and excessive mechanical stress on the articular cartilage has been reported to encourage the progression of osteoarthritis. Although a change in hip joint angle at seat-off may affect hip joint contact force during a sit-to-stand movement, the effect is unclear. This study aimed to examine the effect of the hip joint angle at seat-off on the hip joint contact force during a sit-to-stand movement by using a computer simulation.

Methods

A musculoskeletal model was created for the computer simulation, and eight muscles were attached to each lower limb. Various sit-to-stand movements were generated using parameters (e.g., seat height and time from seat-off to standing posture) reported by previous studies. The hip joint contact force for each sit-to-stand movement was calculated. Furthermore, the effect of the hip joint angle at seat-off on the hip joint contact force during the sit-to-stand movement was examined. In this study, as the changes to the musculoskeletal model parameters affect the hip joint contact force, a sensitivity analysis was conducted.

Results and conclusions

The hip joint contact force during the sit-to-stand movement increased approximately linearly as the hip flexion angle at the seat-off increased. Moreover, the normal sit-to-stand movement and the sit-to-stand movement yielding a minimum hip joint contact force were approximately equivalent. The effect of the changes to the musculoskeletal model parameters on the main findings of this study was minimal. Thus, the main findings are robust and may help prevent the progression of hip osteoarthritis by decreasing mechanical stress, which will be explored in future studies.

Electronic supplementary material

The online version of this article (10.1186/s12938-018-0610-5) contains supplementary material, which is available to authorized users.