Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models.

In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality, rendering them infeasible if the parameter domain of the function is higher-dimensional (four or more parameters). Sparse grids constitute a discretization method that drastically eases the curse, while the approximation quality deteriorates only insignificantly. However, conventional basis functions such as piecewise linear functions are not smooth (continuously differentiable). Hence, these basis functions are unsuitable for applications in which gradients are required. One example for such an application is gradient-based optimization, in which the availability of gradients greatly improves the speed of convergence and the accuracy of the results. This thesis demonstrates that hierarchical B-splines on sparse grids are well-suited for obtaining smooth interpolants for higher dimensionalities. The thesis is organized in two main parts: In the first part, we derive new B-spline bases on sparse grids and study their implications on theory and algorithms. In the second part, we consider three real-world applications in optimization: topology optimization, biomechanical continuum-mechanics, and dynamic portfolio choice models in finance. The results reveal that the optimization problems of these applications can be solved accurately and efficiently with hierarchical B-splines on sparse grids.

Marker-based Optical Motion Capture (OMC) systems and associated musculoskeletal (MSK) modelling predictions offer non-invasively obtainable insights into muscle and joint loading at an in vivo level, aiding clinical decision-making. However, an OMC system is lab-based, expensive, and requires a line of sight. Inertial Motion Capture (IMC) techniques are widely-used alternatives, which are portable, user-friendly, and relatively low-cost, although with lesser accuracy. Irrespective of the choice of motion capture technique, one typically uses an MSK model to obtain the kinematic and kinetic outputs, which is a computationally expensive tool increasingly well approximated by machine learning (ML) methods. Here, an ML approach is presented that maps experimentally recorded IMC input data to the human upper-extremity MSK model outputs computed from ('gold standard') OMC input data. Essentially, this proof-of-concept study aims to predict higher-quality MSK outputs from the much easier-to-obtain IMC data. We use OMC and IMC data simultaneously collected for the same subjects to train different ML architectures that predict OMC-driven MSK outputs from IMC measurements. In particular, we employed various neural network (NN) architectures, such as Feed-Forward Neural Networks (FFNNs) and Recurrent Neural Networks (RNNs) (vanilla, Long Short-Term Memory, and Gated Recurrent Unit) and a comprehensive search for the best-fit model in the hyperparameters space in both subject-exposed (SE) as well as subject-naive (SN) settings. We observed a comparable performance for both FFNN and RNN models, which have a high degree of agreement (ravg,SE,FFNN=0.90±0.19, ravg,SE,RNN=0.89±0.17, ravg,SN,FFNN=0.84±0.23, and ravg,SN,RNN=0.78±0.23) with the desired OMC-driven MSK estimates for held-out test data. The findings demonstrate that mapping IMC inputs to OMC-driven MSK outputs using ML models could be instrumental in transitioning MSK modelling from 'lab to field'.

Total knee replacement (TKR) is one of the most performed orthopedic surgeries to treat knee joint diseases in the elderly population. Although the survivorship of knee implants may extend beyond two decades, the poor outcome rate remains considerable. A recent computational approach used to better understand failure modes and improve TKR outcomes is based on the combination of musculoskeletal (MSK) and finite element models. This combined multiscale modeling approach is a promising strategy in the field of computational biomechanics; however, some critical aspects need to be investigated. In particular, the identification and quantification of the uncertainties related to the boundary conditions used as inputs to the finite element model due to a different definition of the MSK model are crucial. Therefore, the aim of this study is to investigate this problem, which is relevant for the model credibility assessment process. Three different generic MSK models available in the OpenSim platform were used to simulate gait, based on the experimental data from the fifth edition of the “Grand Challenge Competitions to Predict in vivo Knee Loads.” The outputs of the MSK analyses were compared in terms of relative kinematics of the knee implant components and joint reaction (JR) forces and moments acting on the tibial insert. Additionally, the estimated knee JRs were compared with those measured by the instrumented knee implant so that the “global goodness of fit” was quantified for each model. Our results indicated that the different kinematic definitions of the knee joint and the muscle model implemented in the different MSK models influenced both the motion and the load history of the artificial joint. This study demonstrates the importance of examining the influence of the model assumptions on the output results and represents the first step for future studies that will investigate how the uncertainties in the MSK models propagate on disease-specific finite element model results.

Blood flow restricted resistance exercise (BFR-RE) is a novel method that is effective at increasing strength and hypertrophy using much lower loads than the higher loads typical in progressive resistance exercise. However, the effects of BFR-RE on skeletal muscle fatigue, mitochondrial response, and activation are still being explored. This dissertation will discuss the impacts of BFR-RE, how it affects college-aged individuals that are trained and untrained, and the effects of BFR-RE on skeletal muscle fatigue, mitochondrial response, and activation. The first study examined the effects of 6-weeks of low load blood flow restricted resistance exercise (LLBFR) on muscular strength, mass, and mitochondrial response. These measures were compared to low load resistance exercise (LLRE) and a control group. In the LLBFR group, there were significant increases in knee extension strength, power, and bone-free lean mass. There was an increase in leg press strength for the LLRE group and a trend to increased knee extension strength. Although there were no increases in mitochondrial response for either group, the LLRE group did see a trend. These results suggest that LLBFR effectively increases strength, endurance, and muscular hypertrophy. The second study examined the differences between trained and untrained individuals’ muscular activation and fatigue rates during and after two different intensities of acute bouts of BFR-RE compared to a bout of HLRE. We saw significant decreases in MVIC in the trained group after HLRE and LLBFR 30sec post exercise that returned to baseline at 90sec. The untrained participants had a significant decrease in their MVIC 90sec after the HLRE condition. The trained participants had greater pre-exercise activation than the untrained participants and in the HLRE and LLBFR conditions post-exercise and remained for the 90sec mark. The untrained participants had a decrease in muscle activation at the 90sec time point for the MLBFR condition. In pooled data, muscle activation was significantly lower after all 3 conditions at 30sec and 90sec post-exercise. Our data showed that relative activation is lower in the LLBFR condition than in HLRE and MLBFR. This suggests that LLBFR may not initiate neural activation as much as HLRE or MLBFR.

BackgroundAccurate interpretation of electromyography (EMG) signals is essential for reliable control of musculoskeletal (MS) models in biomechanics and rehabilitation applications. Conventional preprocessing methods may not account for subject-specific signal characteristics and task-related muscle function.ObjectiveThis study aimed to develop and validate an adaptive and personalized EMG preprocessing pipeline to enhance the physiological accuracy of EMG-driven musculoskeletal models during elbow flexion-extension tasks.MethodsEMG signals from six upper limb muscles were recorded using a Delsys system while participants performed elbow flexion-extension movements. The signals were preprocessed using individualized spectral filtering and a dual-stage normalization approach. First, dynamic maximum voluntary contraction (MVC) based min-max normalization was applied to standardize signal amplitudes. Second, functional weighting was used to scale each muscle's activation based on its biomechanical contribution to the movement. The processed signals were used as input to an OpenSim elbow model, and resulting joint kinematics were compared to reference motion data captured by an Xsens system.ResultsThe EMG-driven OpenSim model showed strong agreement with the Xsens data, with correlation coefficients exceeding 0.98 and root mean square error (RMSE) values below 8°. While a minor systematic offset was observed, joint angle trajectories remained consistent and physiologically plausible across trials.ConclusionThe proposed subject-specific EMG preprocessing pipeline enhances the accuracy and interpretability of biomechanical models. Future research should explore adaptive signal alignment techniques and AI-based processing methods to improve model robustness in dynamic and wearable scenarios.

Knee medial and lateral contact forces in a musculoskeletal model with subject-specific contact point trajectories

Human movement is an instinctive yet challenging task that involves complex interactions between the neuromusculoskeletal system and its interaction with the surrounding environment. One key obstacle in the understanding of human locomotion is the availability and validity of experimental data or computational models. Corresponding measurements describing the relationships of the nervous and musculoskeletal systems and their dynamics are highly variable. Likewise, computational models and musculoskeletal models in particular are vitally dependent on these measurements to define model behavior and mechanics. These measurements are often sparse and disparate due to unsystematic data collection containing variable methodologies and reporting conventions. To date, there is not a framework to concatenate and manage musculoskeletal data (muscle moment arms and lengths). These morphological measurements need to be assembled to manage, compare, and analyze these data to develop comprehensive musculoskeletal models. Such a framework would enable researchers to select and update the posture-dependent relationships necessary to describe musculoskeletal dynamics, which are essential for simulation of muscle and joint torques in movement. Analogous to all simulations, these models require rigorous validation to ensure their accuracy. This is particularly important for musculoskeletal models that represent high-dimensional, posture-dependent relationships developed from limited and variable datasets. Here, I developed a computational workflow to collect and manage moment arm datasets from available published literature for the development of a human lower-limb musculoskeletal model. The moment arm relationships from multiple datasets were then used to create complete moment arm descriptions for all major leg muscles and were validated within a generic musculoskeletal model. These developments are crucial in advancing musculoskeletal modeling by providing standardized software and workflows for managing high-dimensional and posture-dependent morphological data to creating realistic and robust musculoskeletal models.

Musculoskeletal finite element modeling is used to estimate mechanical responses of knee joint tissues but involves uncertainties in muscle activations, marker locations, cartilage stiffness, maximum isometric forces, and gait parameter personalization. This study investigates how these uncertainties affect cartilage mechanical responses in knee joint finite element models during walking. We selected three subjects and constructed five musculoskeletal models for each, representing different variations of modeling assumptions, along with a reference model using conventional assumptions. We then ran finite element simulations of knee joints using both personalized gait inputs (motion and loading boundary conditions) and non-personalized gait inputs from literature. Our results demonstrated that varying modeling assumptions, such as optimization function for muscle activation patterns, knee marker position, knee cartilage stiffness, and maximum isometric force, produced highly subject-specific effects. Differences between the reference and altered models ranged from 3% to 30% in musculoskeletal modeling and from 1% to 61% in finite element modeling results. The largest effects occurred with non-personalized gait data, resulting in up to 6- and 2-fold changes in musculoskeletal and finite element modeling results, respectively. This study highlights the sensitivity of knee mechanics to different modeling assumptions and underscores the importance of applying personalized gait parameters for accurate finite element simulations.

Piano playing is one of the most complex human activities, involving an intricate interplay between the cognitive, neural, and musculoskeletal systems. Understanding the biomechanics of piano playing could have important implications for evidence-based pedagogy, optimizing skill acquisition, increasing practice efficiency, and minimizing the risk of performance-related injuries. This systematic review synthesizes existing literature in piano biomechanics. A comprehensive search across five databases (MEDLINE, PsycINFO, SCOPUS, Music Index, and ERIC) yielded 7,671 studies, of which 53 met inclusion criteria. These studies utilized kinematic, kinetic, and electromyographic measurements during piano performance under varying task conditions, including isolated keystrokes, novel excerpts, self-selected repertoire, and standard piano literature. The results were synthesized to address (1) how variations in pianistic technique (e.g., type of touch, finger independence) influence kinematics, kinetics, and muscle activation, and (2) how task demands (e.g., tempo, loudness), and performance demands (e.g., fatigue, ergonomics) affect pianists’ biomechanical characteristics. Together, current biomechanical evidence indicates that touch type, finger independence, intersegmental kinematics, and muscular activation are modulated by pianists’ skill level, anthropometry, task demands, and muscular fatigue. We further discuss and link the existing literature to pedagogy, practice, and performance, thereby demonstrating that biomechanical parameters are not merely abstract descriptors of motion but are integral to pedagogy, musical expression, and sustainable performance. While there is an accumulating wealth of biomechanical data involving piano playing, its integration into standardized pedagogy remains limited. Interdisciplinary collaboration in piano biomechanics is therefore essential to advance our understanding of musical expression, communication, and wellbeing, ultimately supporting the development of sustainable playing techniques that can be effectively translated into pedagogical frameworks.Systematic review registration: Unique Identifier: 10.17605/OSF.IO/TSNY8

Children with cerebral palsy (CP) often use a crouch gait pattern that has disturbances in the knee joint kinematics. Although the length and rate of lengthening of the hamstring musculature have been speculated to be the reason that these disturbances are not adequately dissipated, this relationship has not been adequately explored. The purpose of this exploratory investigation was to use simulations of a musculoskeletal model and Floquet analysis to evaluate how the performance of hamstrings musculature during gait may be related to the knee joint instabilities seen in children with CP. Children with CP and typically developing (TD) children walked on a treadmill as a motion capture system assessed the knee joint kinematics. Floquet analysis was used to quantify the rate that disturbances present at the knee joint were dissipated, and simulations of a musculoskeletal model were used to estimate the in vivo length and velocity of the hamstrings. Pearson correlation coefficients were calculated to determine if there was a relationship between the rate that the disturbances were dissipated and the performance of the hamstring musculature. The children with CP had hamstrings that lengthened more slowly than TD children, and required more strides to dissipate disturbances in the knee joint kinematics. There was negative correlation between the rate that the hamstrings lengthened and the rate that the knee joint disturbances were dissipated. Our results suggest that the ability of children with CP to dissipate the knee joint disturbances may be related to the inability to properly control the hamstring musculature.

A musculoskeletal (MSK) model is a valuable tool for assessing complex biomechanical problems, estimating joint torques during motion, optimizing motion in sports, and designing exoskeletons and prostheses. This study proposes an open-source upper body MSK model that supports biomechanical analysis of human motion. The MSK model of the upper body consists of 8 body segments (torso, head, left/right upper arm, left/right forearm, and left/right hand). The model has 20 degrees of freedom (DoFs) and 40 muscle torque generators (MTGs), which are constructed using experimental data. The model is adjustable for different anthropometric measurements and subject body characteristics: sex, age, body mass, height, dominant side, and physical activity. Joint limits are modeled using experimental dynamometer data within the proposed multi-DoF MTG model. The model equations are verified by simulating the joint range of motion (ROM) and torque; all simulation results have a good agreement with previously published research.

Subject-specific 2D/3D image registration and kinematics-driven musculoskeletal model of the spine

This paper aims to investigate the function of constant feed-forward control from the reticulospinal tract (RST) on improving posture stability during standing from the viewpoint of ability to countering the disturbances. We presented a stance control model considering not only the balance control, a PD controller, from vestibular tract based on vestibular feedback but also the constant feed-forward control u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> by reticulospinal tract. Parameters of PD controller, max muscle isometric force of back extensors and flexors and the constant strength of control from RST were optimized during a 3s forward dynamics simulation and the optimal u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> was obtained. Then, we fixed the value of u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> around the value of optimal one and only optimized other four parameters. After that, the abilities of countering the platform disturbance of the musculoskeletal (MSK) model under the control of different u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> were investigated. As a result, we found that optimal u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> would improve the posture stability and make MSK model more adaptive to the disturbance.

Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles

Weight gain and stretched abdominal muscles from an enlarged gravid uterus are remarkable features during pregnancy. These changes elicit postural instability and place strain on body segments, contributing to lower back pain. In general, the agonist and antagonist muscles act simultaneously to increase joint stabilization; however, this can cause additional muscle stress during movement. Furthermore, this activation can be observed in pregnant women because of their unstable body joints. Hence, physical modalities based on assessments of muscle activation are useful for managing low back pain during pregnancy. Musculoskeletal models are common when investigating muscle load. However, it is difficult to apply such models to pregnant women and estimate the co-contraction of muscles using musculoskeletal models. Therefore, the purpose of this study is to construct a musculoskeletal model for pregnant women that estimates the co-contraction of trunk muscles. First, motion analysis was conducted on a pregnant woman and the muscle activations of the rectus abdominis and erector spinae were measured. Then, the musculoskeletal model was specifically modified for pregnant women. Finally, the co-contraction was estimated from the results of the musculoskeletal model and electromyography data using a genetic algorithm. With the proposed methods, weakened abdominal muscle torque and the co-contraction activation of trunk muscles were estimated successfully.