Objective: Accurate estimation of stiffness across anatomical levels (i.e., joint, muscle, and tendon) in vivo has long been a challenge in biomechanics. Recent advances in electromyography (EMG)-driven musculoskeletal modeling have allowed the non-invasive estimation of stiffness during dynamic joint rotations. Nevertheless, validation has been limited to the joint level due to a lack of simultaneous in vivo experimental measurements of muscle and tendon stiffness. Methods: With a focus on the triceps surae, we employed a novel perturbation-based experimental technique informed by dynamometry and ultrasonography to derive reference stiffness at the joint, muscle, and tendon levels simultaneously. Here, we propose a new EMG-driven model-based approach that does not require external joint perturbation, nor ultrasonography, to estimate multi-level stiffness. We present a novel set of closed-form equations that enables the person-specific tuning of musculoskeletal parameters dictating biological stiffness, including passive force-length relationships in modeled muscles and tendons. Results: Calibrated EMG-driven musculoskeletal models estimated the reference data with average normalized root-mean-square error ≈ 20%. Moreover, only when calibrated tendons were approximately four times more compliant than typically modeled, our approach could estimate multi-level reference stiffness. Conclusion: EMG-driven musculoskeletal models can be calibrated on a larger set of reference data to provide more realistic values for the biomechanical variables across multiple anatomical levels. Moreover, the tendon models that are typically used in musculoskeletal modeling are too stiff. Significance: Calibrated musculoskeletal models informed by experimental measurements give access to an augmented range of biomechanical variables that might not be easily measured with sensors alone.

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The simultaneous modulation of joint torque and stiffness enables humans to perform large repertoires of movements, while versatilely adapting to external mechanical demands. Multi-muscle force control is key for joint torque and stiffness modulation. However, the inability to directly measure muscle force in the intact moving human prevents understanding how muscle force causally links to joint torque and stiffness. Joint stiffness is predominantly estimated via joint perturbation-based experiments in combination with system identification techniques. However, these techniques provide joint-level stiffness estimations with no causal link to the underlying muscle forces. Moreover, the need for joint perturbations limits the generalizability and applicability to study natural movements. Here, we present an electromyography (EMG)-driven musculoskeletal modeling framework that can be calibrated to match reference joint torque and stiffness profiles simultaneously via a multi-term objective function. EMG-driven models calibrated on <2 s of reference torque and stiffness data could blindly estimate reference profiles across 100 s of data not used for calibration. Model calibrations using an objective function comprising torque and stiffness terms always provided less feasible solutions than an objective function comprising solely a torque term, thereby reducing the space of feasible muscle–tendon parameters. Results also showed the proposed framework's ability to estimate joint stiffness in unperturbed conditions, while capturing differences against stiffness profiles derived during perturbed conditions. The proposed framework may provide new ways for studying causal relationships between muscle force and joint torque and stiffness during movements in interaction with the environment, with broad implications across biomechanics, rehabilitation and robotics.

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Quantifying human joint stiffness in vivo during movement remains challenging. Well established stiffness estimation methods include system identification and the notion of quasi-stiffness, with experimental and conceptual limitations, respectively. Joint stiffness computation via biomechanical models is an emerging solution to overcome such limitations. However, these models make assumptions that hamper their generalization across muscle architectures. Here we present a stiffness formulation that considers the muscle’s pennation angle, and its comparison to a simpler formulation that does not. Model-based stiffness estimates are evaluated against joint-perturbation-based system identification. Results on muscles with different pennation angle show that our formulation seamlessly adjusts the muscle-tendon units’ stiffness depending on their architecture. At the joint level, our new model improved the stiffness estimations. Our study’s relevance is the creation and validation of a modeling formulation that does not require joint perturbation. This will enable better estimations and understanding of stiffness properties and human movement.@en

Joint impedance is a common way of representing human joint dynamics. Since ankle joint impedance varies within the gait cycle, time-varying system identification techniques can be used to estimate it. Commonly, time-varying system identification techniques assume repeatably of joint impedance over cyclic motions, without taking into consideration the inherent variability of human behavior. In this paper, a method that assumes smooth, cyclic joint impedance, yet allows for cycle-to-cycle variability, is proposed. The method was tested on isometric, cyclic experimental data from the ankle under conditions with a time variation comparable to the expected one during the gait cycle. The estimated model could describe the data with high accuracy (VAF of 94.96%) and retrieve realistic inertia, damping and stiffness parameters. The results provide motivation to further apply the method on experiments under dynamic conditions and to employ the proposed method as a tool for investigating the human joint dynamics during cyclic movements.

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In vivo joint stiffness estimation during time-varying conditions remains an open challenge. Multiple communities, e.g. system identification and biomechanics, have tackled the problem from different perspectives and using different methods, each of which entailing advantages and limitations, often complementary. System identification formulations provide data-driven estimates of stiffness at the joint level, while biomechanics often relies on musculoskeletal models to estimate stiffness at multiple levels, i.e. joint, muscle, and tendon. Collaboration across these two scientific communities seems to be a logical step toward a reliable multi-level understanding of joint stiffness. However, differences at the theoretical, computational, and experimental levels have limited inter-community interaction. In this article we present a roadmap to achieve a unified framework for the estimation of time-varying stiffness in the composite human neuromusculoskeletal system during movement. We present our perspective on future developments to obtain data-driven system identification and musculoskeletal models that are compatible at the theoretical, computational, and experimental levels. Moreover, we propose a novel combined closed-loop paradigm, in which reference estimates of joint stiffness via system identification are decomposed into underlying muscle and tendon contribution via high-density-electromyography-driven musculoskeletal modeling. We highlight the need for aligning experimental requirements to be able to compare both joint stiffness formulations. Unifying both biomechanics' and system identification's formulations is a necessary step for truly generalizing stiffness estimation across individuals, movement conditions, training and impairment levels. From an application point of view, this is central for enabling patient-specific neurorehabilitation therapies, as well as biomimetic control of assistive robotic technologies. The roadmap we propose could serve as an inspiration for future collaborations across broadly different scientific communities to truly understand joint stiffness bio- and neuromechanics.

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Joint stiffness estimation under dynamic conditions still remains a challenge. Current stiffness estimation methods often rely on the external perturbation of the joint. In this study, a novel 'perturbation-free' stiffness estimation method via electromyography (EMG)-driven musculoskeletal modeling was validated for the first time against system identification techniques. EMG signals, motion capture, and dynamic data of the ankle joint were collected in an experimental setup to study the ankle joint stiffness in a controlled way, i.e. at a movement frequency of 0.6 Hz as well as in the presence and absence of external perturbations. The model-based joint stiffness estimates were comparable to system identification techniques. The ability to estimate joint stiffness at any instant of time, with no need to apply joint perturbations, might help to fill the gap of knowledge between the neural and the muscular systems and enable the subsequent development of tailored neurorehabilitation therapies and biomimetic prostheses and orthoses.

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An important goal in the design of next-generation exoskeletons and limb prostheses is to replicate human limb dynamics. Joint impedance determines the dynamic relation between joint displacement and torque. Joint stiffness is the position-dependent component of joint impedance and is key in postural control and movement. However, the mechanisms to modulate joint stiffness are not fully understood yet. The goal of this study is to conduct a systematic analysis on how humans modulate ankle stiffness. Time-varying stiffness was estimated for six healthy subjects under isometric, as well as quick and slow dynamic conditions via system identification techniques; specifically, an ensemble-based algorithm using short segments of ankle torque and position recordings. Our results show that stiffness had the lowest magnitude under quick dynamic conditions. Under isometric conditions, with fixed position and varying muscle activity, stiffness exhibited a higher magnitude. Finally, under slow dynamic conditions, stiffness was found to be the highest. Our results highlight, for the first time, the variability in stiffness modulation strategies across conditions, especially across movement velocity.

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