Determining a musculoskeletal system's pre-stretched state using continuum-mechanical forward modelling and joint range optimization

The subject-specific range of motion (RoM) of a musculoskeletal joint system is balanced by pre-tension levels of individual muscles, which affects their contraction capability. Such an inherent pre-tension or pre-stretch of muscles is not measureable with in vivo experiments. Using a 3D continuum mechanical forward simulation approach for motion analysis of the musculoskeletal system of the forearm with 3 flexor and 2 extensor muscles, we developed an optimization process to determine the muscle fibre pre-stretches for an initial arm position, which is given human dataset. We used RoM values of a healthy person to balance the motion in extension and flexion. The performed sensitivity study shows that the fibre pre-stretches of the m. brachialis, m. biceps brachii and m. triceps brachii with 91 % dominate the objective flexion ratio, while m. brachiradialis and m. anconeus amount 7.8 % and 1.2 % . Within the multi-dimensional space of the surrogate model, 3D sub-spaces of primary variables, namely the dominant muscles and the global objective, flexion ratio, exhibit a path of optimal solutions. Within this optimal path, the muscle fibre pre-stretch of two flexors demonstrate a negative correlation, while, in contrast, the primary extensor, m. triceps brachii correlates positively to each of the flexors. Comparing the global optimum with four other designs along the optimal path, we saw large deviations, e.g., up to 15∘ in motion and up to 40% in muscle force. This underlines the importance of accurate determination of fibre pre-stretch in muscles, especially, their role in pathological muscular disorders and surgical applications such as free muscle or tendon transfer.

3D ultrasound-based determination of skeletal muscle fascicle orientations

Architectural parameters of skeletal muscle such as pennation angle provide valuable information on muscle function, since they can be related to the muscle force generating capacity, fiber packing, and contraction velocity. In this paper, we introduce a 3D ultrasound-based workflow for determining 3D fascicle orientations of skeletal muscles. We used a custom-designed automated motor driven 3D ultrasound scanning system for obtaining 3D ultrasound images. From these, we applied a custom-developed multiscale-vessel enhancement filter-based fascicle detection algorithm and determined muscle volume and pennation angle. We conducted trials on a phantom and on the human tibialis anterior (TA) muscle of 10 healthy subjects in plantarflexion (157 ± 7∘ ), neutral position (109 ± 7∘ , corresponding to neutral standing), and one resting position in between (145 ± 6∘ ). The results of the phantom trials showed a high accuracy with a mean absolute error of 0.92 ± 0.59∘ . TA pennation angles were significantly different between all positions for the deep muscle compartment; for the superficial compartment, angles are significantly increased for neutral position compared to plantarflexion and resting position. Pennation angles were also significantly different between superficial and deep compartment. The results of constant muscle volumes across the 3 ankle joint angles indicate the suitability of the method for capturing 3D muscle geometry. Absolute pennation angles in our study were slightly lower than recent literature. Decreased pennation angles during plantarflexion are consistent with previous studies. The presented method demonstrates the possibility of determining 3D fascicle orientations of the TA muscle in vivo.

Postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents: A simulation study

Postinhibitory excitation is a transient overshoot of a neuron's baseline firing rate following an inhibitory stimulus and can be observed in vivo in human motoneurons. However, the biophysical origin of this phenomenon is still unknown and both reflex pathways and intrinsic motoneuron properties have been proposed. We hypothesized that postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents (h-currents). Using an electrical circuit model, we investigated how h-currents can modulate the postinhibitory response of motoneurons. Further, we analyzed the spike trains of human motor units from the tibialis anterior muscle during reciprocal inhibition. The simulations revealed that the activation of h-currents by an inhibitory postsynaptic potential can cause a short-term increase in a motoneuron's firing probability. This result suggests that the neuron can be excited by an inhibitory stimulus. In detail, the modulation of the firing probability depends on the time delay between the inhibitory stimulus and the previous action potential. Further, the postinhibitory excitation's strength correlates with the inhibitory stimulus's amplitude and is negatively correlated with the baseline firing rate as well as the level of input noise. Hallmarks of h-current activity, as identified from the modeling study, were found in 50% of the human motor units that showed postinhibitory excitation. This study suggests that h-currents can facilitate postinhibitory excitation and act as a modulatory system to increase motoneuron excitability after a strong inhibition.

High-density magnetomyography is superior to high-density surface electromyography for motor unit decomposition: a simulation study

OBJECTIVE

Studying motor units (MUs) is essential for understanding motor control, the detection of neuromuscular disorders and the control of human-machine interfaces. Individual motor unit firings are currently identified in vivo by decomposing electromyographic (EMG) signals. Due to our body's properties and anatomy, individual motor units can only be separated to a limited extent with surface EMG. Unlike electrical signals, magnetic fields do not interact with human tissues. This physical property and the emerging technology of quantum sensors make magnetomyography (MMG) a highly promising methodology. However, the full potential of MMG to study neuromuscular physiology has not yet been explored.

APPROACH

In this work, we perform in silico trials that combine a biophysical model of EMG and MMG with state-of-the-art algorithms for the decomposition of motor units. This allows the prediction of an upper-bound for the motor unit decomposition accuracy.

MAIN RESULTS

It is shown that non-invasive high-density MMG data is superior over comparable high-density surface EMG data for the robust identification of the discharge patterns of individual motor units. Decomposing MMG instead of EMG increased the number of identifiable motor units by 76%. Notably, MMG exhibits a less pronounced bias to detect superficial motor units.

SIGNIFICANCE

The presented simulations provide insights into methods to study the neuromuscular system non-invasively and in vivo that would not be easily feasible by other means. Hence, this study provides guidance for the development of novel biomedical technologies.

A continuum mechanical porous media model for vertebroplasty: Numerical simulations and experimental validation

The outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A reliable simulation could predict the patient-specific outcome preoperatively and avoid the risk of cement leakage. Therefore, the aim of this work was to introduce a computationally feasible and experimentally validated model for simulating vertebroplasty. The developed model is a multiphase continuum-mechanical macro-scale model based on the Theory of Porous Media. The related governing equations were discretized using a combined finite element-finite volume approach by the so-called Box discretization. Three different rheological upscaling methods were used to compare and determine the most suitable approach for this application. For validation, a benchmark experiment was set up and simulated using the model. The influence of bone marrow and parameters like permeability, porosity, etc., was investigated to study the effect of varying conditions on vertebroplasty. The presented model could realistically simulate the injection of bone cement in porous materials when used with the correct rheological upscaling models, of which the semi-analytical averaging of the viscosity gave the best results. The marrow viscosity is identified as the crucial reference to categorize bone cements as 'high- 'or 'low-' viscosity in the context of vertebroplasty. It is confirmed that a cement with higher viscosity than the marrow ensures stable development of the injection and a proper cement interdigitation inside the vertebra.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

Optimizing NV magnetometry for Magnetoneurography and Magnetomyography applications

Magnetometers based on color centers in diamond are setting new frontiers for sensing capabilities due to their combined extraordinary performances in sensitivity, bandwidth, dynamic range, and spatial resolution, with stable operability in a wide range of conditions ranging from room to low temperatures. This has allowed for its wide range of applications, from biology and chemical studies to industrial applications. Among the many, sensing of bio-magnetic fields from muscular and neurophysiology has been one of the most attractive applications for NV magnetometry due to its compact and proximal sensing capability. Although SQUID magnetometers and optically pumped magnetometers (OPM) have made huge progress in Magnetomyography (MMG) and Magnetoneurography (MNG), exploring the same with NV magnetometry is scant at best. Given the room temperature operability and gradiometric applications of the NV magnetometer, it could be highly sensitive in the pT / Hz -range even without magnetic shielding, bringing it close to industrial applications. The presented work here elaborates on the performance metrics of these magnetometers to the state-of-the-art techniques by analyzing the sensitivity, dynamic range, and bandwidth, and discusses the potential benefits of using NV magnetometers for MMG and MNG applications.

Mapping the role of oral cavity physiological factors into the viscoelastic model of denture adhesives for numerical implementation

Physiological parameters of the oral cavity have a profound impact on any restorative solutions designed for edentulous patients including denture adhesives. This study aims to mathematically quantify the influence of three such variables, namely: the temperature, pH, and the swelling of such adhesives under the influence of saliva on its mechanical behavior. The mathematical quantification is further aimed to implement a material model for such adhesives which considers the impact of such physiological factors. The denture adhesive is experimentally investigated by means of rheological steady state frequency sweep tests to obtain the relaxation spectrum of the material. The relaxation behavior is measured for a wide range of oral cavity temperatures and pH. Also, the adhesive is hydrated and upon swelling to different levels again tested to understand the impact of swelling on the mechanical behavior. The experimentally measured continuous relaxation spectrum is modeled as a viscoelastic material using a discrete set of points based on the Prony series discretization technique. The relaxation spectrums for various temperatures are compared and the possibility of a time-temperature superposition is explored for the model. Similarly, the measured values of Storage and loss modulus are investigated to understand the role of pH and swelling. The results in this study clearly indicated a horizontal shift in the relaxation behavior with increase in temperature. And hence, the time-temperature shift factor was calculated for the adhesive. The relaxation spectrum also showed a strong correlation with swelling of the adhesive and the pH. The influence of these two parameters were captured into the model based on the relaxation time parameter in the Prony series approach. Based on this study the impact of these parameters could be appreciated on the performance and mechanical behavior of denture adhesives and implemented into a Prony series based viscoelastic material model which can be used with numerical simulations.

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

A biophysically guided constitutive law of the musculotendon-complex: modelling and numerical implementation in Abaqus

BACKGROUND AND OBJECTIVE

Many biomedical, clinical, and industrial applications may benefit from musculoskeletal simulations. Three-dimensional macroscopic muscle models (3D models) can more accurately represent muscle architecture than their 1D (line-segment) counterparts. Nevertheless, 3D models remain underutilised in academic, clinical, and commercial environments. Among the reasons for this is a lack of modelling and simulation standardisation, verification, and validation. Here, we strive towards a solution by providing an open-access, characterised, constitutive relation (CR) for 3D musculotendon models.

METHODS

The musculotendon complex is modelled following the state-of-the-art active stress approach and is treated as hyperelastic, transversely isotropic, and nearly incompressible. Furthermore, force-length and -velocity relationships are incorporated, and muscle activation is derived from motor-unit information. The CR was implemented within the commercial finite-element software package Abaqus as a user-subroutine. A masticatory system model with left and right masseters was used to demonstrate active and passive movement.

RESULTS

The CR was characterised by various experimental data sets and was able to capture a wide variety of passive and active behaviours. Furthermore, the masticatory simulations revealed that joint movement was sensitive to the muscle's in-fibre passive response.

CONCLUSIONS

This user-material provides a "plug and play" template for 3D neuro-musculoskeletal finite element modelling. We hope that this reduces modelling effort, fosters exchange, and contributes to the standardisation of such models.

Multi-scale mechanobiological model for skeletal muscle hypertrophy

Skeletal muscle adaptation is correlated to training exercise by triggering different signaling pathways that target many functions; in particular, the IGF1-AKT pathway controls protein synthesis and degradation. These two functions regulate the adaptation in size and strength of muscles. Computational models for muscle adaptation have focused on: the biochemical description of signaling pathways or the mechanical description of muscle function at organ scale; however, an interrelation between these two models should be considered to understand how an adaptation in muscle size affects the protein synthesis rate. In this research, a dynamical model for the IGF1-AKT signaling pathway is linked to a continuum-mechanical model describing the active and passive mechanical response of a muscle; this model is used to study the impact of the adaptive muscle geometry on the protein synthesis at the fiber scale. This new computational model links the signaling pathway to the mechanical response by introducing a growth tensor, and links the mechanical response to the signaling pathway through the evolution of the protein synthesis rate. The predicted increase in cross sectional area (CSA) due to an 8 weeks training protocol excellently agreed with experimental data. Further, our results show that muscle growth rate decreases, if the correlation between protein synthesis and CSA is negative. The outcome of this study suggests that multi-scale models coupling continuum mechanical properties and molecular functions may improve muscular therapies and training protocols.

Modelling intra-muscular contraction dynamics using in silico to in vivo domain translation

BACKGROUND

Advances in sports medicine, rehabilitation applications and diagnostics of neuromuscular disorders are based on the analysis of skeletal muscle contractions. Recently, medical imaging techniques have transformed the study of muscle contractions, by allowing identification of individual motor units' activity, within the whole studied muscle. However, appropriate image-based simulation models, which would assist the continued development of these new imaging methods are missing. This is mainly due to a lack of models that describe the complex interaction between tissues within a muscle and its surroundings, e.g., muscle fibres, fascia, vasculature, bone, skin, and subcutaneous fat. Herein, we propose a new approach to overcome this limitation.

METHODS

In this work, we propose to use deep learning to model the authentic intra-muscular skeletal muscle contraction pattern using domain-to-domain translation between in silico (simulated) and in vivo (experimental) image sequences of skeletal muscle contraction dynamics. For this purpose, the 3D cycle generative adversarial network (cycleGAN) models were evaluated on several hyperparameter settings and modifications. The results show that there were large differences between the spatial features of in silico and in vivo data, and that a model could be trained to generate authentic spatio-temporal features similar to those obtained from in vivo experimental data. In addition, we used difference maps between input and output of the trained model generator to study the translated characteristics of in vivo data.

RESULTS

This work provides a model to generate authentic intra-muscular skeletal muscle contraction dynamics that could be used to gain further and much needed physiological and pathological insights and assess and overcome limitations within the newly developed research field of neuromuscular imaging.

Numerical study of the stress state on the oral mucosa and abutment tooth upon insertion of partial dentures in the mandible

The introduction of a removable partial denture onto the dental arch significantly influences the mechanical stress characteristics of both the jawbone and oral mucosa. The aim of this study was to analyze the stress state caused by biting forces upon insertion of partial dentures into the assembly, and to understand the influence of the resulting contact pressure on its retention behavior. For this purpose, a numerical model of a removable partial denture is proposed based on 3D models developed using computer tomography data of the jawbone and the removable partial denture. The denture system rests on the oral mucosa surface and three abutment teeth. The application of bite forces on the denture generated a stick condition on the loaded regions of the denture-oral mucosa interface, which indicates positive retention of the denture onto the oral mucosa surface. Slip and negative retention were observed in the regions of the contact space that were not directly loaded. The contact pressures observed in the regions of the oral mucosa in contact with the denture were below the clinical pressure pain threshold value for soft tissue, which potentially lowers the risk of pain being experienced by denture users. Further, the variation of the retention behavior and contact pressures across different regions of the denture assembly was observed. Thus, there is a need for adhesives or restraining mechanisms for the denture system in order to avoid bending and deformation of sections of the denture as a consequence of the applied bite force.

Investigating the spatial resolution of EMG and MMG based on a systemic multi-scale model

While electromyography (EMG) and magnetomyography (MMG) are both methods to measure the electrical activity of skeletal muscles, no systematic comparison between both signals exists. Within this work, we propose a novel in silico model for EMG and MMG and test the hypothesis that MMG surpasses EMG in terms of spatial selectivity, i.e. the ability to distinguish spatially shifted sources. The results show that MMG provides a slightly better spatial selectivity than EMG when recorded directly on the muscle surface. However, there is a remarkable difference in spatial selectivity for non-invasive surface measurements. The spatial selectivity of the MMG components aligned with the muscle fibres and normal to the body surface outperforms the spatial selectivity of surface EMG. Particularly, for the MMG’s normal-to-the-surface component the influence of subcutaneous fat is minimal. Further, for the first time, we analyse the contribution of different structural components, i.e. muscle fibres from different motor units and the extracellular space, to the measurable biomagnetic field. Notably, the simulations show that for the normal-to-the-surface MMG component, the contribution from volume currents in the extracellular space and in surrounding inactive tissues, is negligible. Further, our model predicts a surprisingly high contribution of the passive muscle fibres to the observable magnetic field.

A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue

The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.

Variations in Muscle Activity and Exerted Torque During Temporary Blood Flow Restriction in Healthy Individuals

Recent studies suggest that transitory blood flow restriction (BFR) may improve the outcomes of training from anatomical (hypertrophy) and neural control perspectives. Whilst the chronic consequences of BFR on local metabolism and tissue adaptation have been extensively investigated, its acute effects on motor control are not yet fully understood. In this study, we compared the neuromechanical effects of continuous BFR against non-restricted circulation (atmospheric pressure—AP), during isometric elbow flexions. BFR was achieved applying external pressure either between systolic and diastolic (lower pressure—LP) or 1.3 times the systolic pressure (higher pressure—HP). Three levels of torque (15, 30, and 50% of the maximal voluntary contraction—MVC) were combined with the three levels of pressure for a total of 9 (randomized) test cases. Each condition was repeated 3 times. The protocol was administered to 12 healthy young adults. Neuromechanical measurements (torque and high-density electromyography—HDEMG) and reported discomfort were used to investigate the response of the central nervous system to BFR. The investigated variables were: root mean square (RMS), and area under the curve in the frequency domain—for the torque, and average RMS, median frequency and average muscle fibres conduction velocity—for the EMG. The discomfort caused by BFR was exacerbated by the level of torque and accumulated over time. The torque RMS value did not change across conditions and repetitions. Its spectral content, however, revealed a decrease in power at the tremor band (alpha-band, 5–15 Hz) which was enhanced by the level of pressure and the repetition number. The EMG amplitude showed no differences whilst the median frequency and the conduction velocity decreased over time and across trials, but only for the highest levels of torque and pressure. Taken together, our results show strong yet transitory effects of BFR that are compatible with a motor neuron pool inhibition caused by increased activity of type III and IV afferences, and a decreased activity of spindle afferents. We speculate that a compensation of the central drive may be necessary to maintain the mechanical output unchanged, despite disturbances in the afferent volley to the motor neuron pool.

Low-Profile Electromagnetic Field Sensors in the Measurement and Modelling of Three-Dimensional Jaw Kinematics and Occlusal Loading

Dynamic occlusal loading during mastication is clinically relevant in the design and functional assessment of dental restorations and removable dentures, and in evaluating temporomandibular joint dysfunction. The aim of this study was to develop a modelling framework to evaluate subject-specific dynamic occlusal loading during chewing and biting over the entire dental arch. Measurements of jaw motion were performed on one healthy male adult using low-profile electromagnetic field sensors attached to the teeth, and occlusal anatomy quantified using an intra-oral scanner. During testing, the subject chewed and maximally compressed a piece of rubber between both second molars, first molars, premolars and their central incisors. The occlusal anatomy, rubber geometry and experimentally measured rubber material properties were combined in a finite element model. The measured mandibular motion was used to kinematically drive model simulations of chewing and biting of the rubber sample. Three-dimensional dynamic bite forces and contact pressures across the occlusal surfaces were then calculated. Both chewing and biting on the first molars produced the highest bite forces across the dental arch, and a large amount of anterior shear force was produced at the incisors and the second molars. During chewing, the initial tooth-rubber contact evolved from the buccal sides of the molars to the lingual sides at full mouth closure. Low-profile electromagnetic field sensors were shown to provide a clinically relevant measure of jaw kinematics with sufficient accuracy to drive finite element models of occlusal loading during chewing and biting. The modelling framework presented provides a basis for calculation of physiological, dynamic occlusal loading across the dental arch.

A Systematic Review and Meta-Analysis on the Longitudinal Effects of Unilateral Knee Extension Exercise on Muscle Strength

The aim of the study was to investigate the time-dependent increase in the knee extensors' isometric strength as a response to voluntary, unilateral, isometric knee extension exercise (UIKEE). To do so, a systematic review was carried out to obtain data for a Bayesian longitudinal model-based meta-analysis (BLMBMA). For the systematic review, PubMed, Web of Science, SCOPUS, Chochrane Library were used as databases. The systematic review included only studies that reported on healthy, young individuals performing UIKEE. Studies utilizing a bilateral training protocol were excluded as the focus of this review lied on unilateral training. Out of the 3,870 studies, which were reviewed, 20 studies fulfilled the selected inclusion criteria. These 20 studies were included in the BLMBMA to investigate the time-dependent effects of UIKEE. If compared to the baseline strength of the trained limb, these data reveal that UKIEE can increase the isometric strength by up to 46%. A meta-analysis based on the last time-point of each available study was employed to support further investigations into UIKEE-induced strength increase. A sensitivity analysis showed that intensity of training (%MVC), fraction of male subjects and the average age of the subject had no significant influence on the strength gain. Convergence of BLMBMA revealed that the peak strength increase is reached after ~4 weeks of UIKEE training.

A NanoFE simulation-based surrogate machine learning model to predict mechanical functionality of protein networks from live confocal imaging

Sub-cellular mechanics plays a crucial role in a variety of biological functions and dysfunctions. Due to the strong structure-function relationship in cytoskeletal protein networks, light can be shed on their mechanical functionality by investigating their structures. Here, we present a data-driven approach employing a combination of confocal live imaging of fluorescent tagged protein networks, in silico mechanical experiments and machine learning to investigate this relationship. Our designed image processing and nanoFE mechanical simulation framework resolves the structure and mechanical behaviour of cytoskeletal networks and the developed gradient boosting surrogate models linking network structure to its functionality. In this study, for the first time, we perform mechanical simulations of Filamentous Temperature Sensitive Z (FtsZ) complex protein networks with realistic network geometry depicting its skeletal functionality inside organelles (here, chloroplasts) of the moss Physcomitrella patens. Training on synthetically produced simulation data enables predicting the mechanical characteristics of FtsZ network purely based on its structural features (R2⩾0.93), therefore allowing to extract structural principles enabling specific mechanical traits of FtsZ, such as load bearing and resistance to buckling failure in case of large network deformation.

A class of analytic solutions for verification and convergence analysis of linear and nonlinear fluid-structure interaction algorithms

Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of applicationspecific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

Decoding rejuvenating effects of mechanical loading on skeletal aging using in vivo μCT imaging and deep learning

Throughout the process of aging, dynamic changes of bone material, micro- and macro-architecture result in a loss of strength and therefore in an increased likelihood of fragility fractures. To date, precise contributions of age-related changes in bone (re)modeling and (de)mineralization dynamics to this fragility increase are not completely understood. Here, we present an image-based deep learning approach to quantitatively describe the effects of short-term aging and adaptive response to cyclic loading applied to proximal mouse tibiae and fibulae. Our approach allowed us to perform an end-to-end age prediction based on μCT imaging to determine the dynamic biological process of aging during a two week period, therefore permitting short-term bone aging analysis with 95% accuracy in predicting time points. In a second application, our deep learning analysis reveals that two weeks of in vivo mechanical loading are associated with an underlying rejuvenating effect of 5 days. Additionally, by quantitatively analyzing the learning process, we could, for the first time, identify the localization of the age-relevant encoded information and demonstrate 89% load-induced similarity of these locations in the loaded tibia with younger control bones. These data therefore suggest that our method enables identifying a general prognostic phenotype of a certain skeletal age as well as a temporal and localized loading-treatment effect on this apparent skeletal age for the studied mouse tibia and fibula. Future translational applications of this method may provide an improved decision-support method for osteoporosis treatment at relatively low cost. STATEMENT OF SIGNIFICANCE: Bone is a highly complex and dynamic structure that undergoes changes during the course of aging as well as in response to external stimuli, such as loading. Automatic assessment of "age" and "state" of the bone may lead to early prognosis of deceases such as osteoporosis and enables evaluating the effects of certain treatments. Here, we present an artificial intelligence-based method capable of automatically predicting the skeletal age from μCT images with 95% accuracy. Additionally, we utilize it to demonstrate the rejuvenation effects of in-vivo loading treatment on bones. We further, for the first time, break down aging-related local changes in bone by quantitatively analyzing "what the age assessment model has learned" and use this information to investigate the structural details of rejuvenation process.

Occlusal load modelling significantly impacts the predicted tooth stress response during biting: a simulation study

Computational models of the masticatory system can provide estimates of occlusal loading during (static) biting or (dynamic) chewing and therefore can be used to evaluate and optimize functional performance of prosthodontic devices and guide dental surgery planning. The modelling assumptions, however, need to be chosen carefully in order to obtain meaningful predictions. The objectives of this study were two-fold: (i) develop a computational model to calculate the stress response of the first molar during biting of a rubber sample and (ii) evaluate the influence of different occlusal load models on the stress response of dental structures. A three-dimensional finite element model was developed comprising the mandible, first molar, associated dental structures, and the articular fossa and discs. Simulations of a maximum force bite on a rubber sample were performed by applying muscle forces as boundary conditions on the mandible and computing the contact between the rubber and molars (GS case). The molar occlusal force was then modelled as a single point force (CF1 case), four point forces (CF2 case), and as a sphere compressing against the occlusal surface (SL case). The peak enamel stress for the GS case was 110 MPa and 677 MPa, 270 MPa and 305 MPa for the CF1, CF2 and SL cases, respectively. Peak dentin stress for the GS case was 44 MPa and 46 MPa, 50 MPa and 63 MPa for the CF1, CF2 and SL cases, respectively. Furthermore, the enamel stress distribution was also strongly correlated to the occlusal load model. The way in which occlusal load is modelled has a substantial influence on the stress response of enamel during biting, but has relatively little impact on the behavior of dentin. The use of point forces or sphere contact to model occlusal loading during mastication overestimates enamel stress magnitude and also influences enamel stress distribution.

Characterization of Electromechanical Delay Based on a Biophysical Multi-Scale Skeletal Muscle Model

Skeletal muscles can be voluntary controlled by the somatic nervous system yielding an active contractile stress response. Thereby, the active muscle stresses are transmitted to the skeleton by a cascade of connective tissue and thus enable motion. In the context of joint perturbations as well as the assessment of the complexity of neural control, the initial phase of the muscle-tendon system's stress response has a particular importance and is analyzed by means of electromechanical delay (EMD). EMD is defined as the time lag between the stimulation of a muscle and a measurable change in force output. While EMD is believed to depend on multiple structures / phenomena, it is hard to separate their contributions experimentally. We employ a physiologically detailed, three-dimensional, multi-scale model of an idealized muscle-tendon system to analyze the influence of (i) muscle and tendon length, (ii) the material behavior of skeletal muscle and tendon tissue, (iii) the chemo-electro-mechanical behavior of the muscle fibers and (iv) neural control on EMD. Comparisons with experimental data show that simulated EMD values are within the physiological range, i.e., between 6.1 and 68.6 ms, and that the model is able to reproduce the characteristic EMD-stretch curve, yielding the minimum EMD at optimal length. Simulating consecutive recruitment of motor units increases EMD by more than 20 ms, indicating that during voluntary contractions neural control is the dominant factor determining EMD. In contrast, the muscle fiber action potential conduction velocity is found to influence EMD even of a 27 cm long muscle by not more than 3.7 ms. We further demonstrate that in conditions where only little pre-stretch is applied to a muscle-tendon system, the mechanical behavior of both muscle and tendon tissue considerably impacts EMD. Predicting EMD for different muscle and tendon lengths indicates that the anatomy of a specific muscle-tendon system is optimized for its function, i.e., shorter tendon lengths are beneficial to minimize the neural control effort for muscles primary acting as motor in concentric contractions.

Modelling the electrical activity of skeletal muscle tissue using a multi-domain approach

Electromyography (EMG) can be used to study the behaviour of the motor neurons and thus provides insights into the physiology of the central nervous system. However, due to the high complexity of neuromuscular control, EMG signals are challenging to interpret. While the exact knowledge of the excitation patterns of a specific muscle within an in vivo experimental setting remains elusive, simulations allow to systematically investigate EMG signals in a controlled environment. Within this context, simulations can provide virtual EMG data, which, for example, can be used to validate and optimise signal analysis methods that aim to estimate the relationship between EMG signals and the output of motor neuron pools. However, since existing methods, which are employed to compute EMG signals, exhibit deficiencies with respect to the physical model itself as well as with respect to numerical aspects, we propose a novel homogenised continuum model that closely resolves the electro-physiological behaviour of skeletal muscle tissue. The proposed model is based on an extension of the well-established bidomain model and includes a biophysically detailed description of the electrical activity within the tissue, which is due to the depolarisation of the muscle fibre membranes. In contrast to all other published EMG models, which assume that the electrical potential field for each muscle fibre can be calculated independently, the proposed model assumes that the electrical potential in the muscle fibres is coupled to the electrical potential in the extracellular space. We show that the newly proposed model is able to simulate realistic EMG signals and demonstrate the potential to employ the predicted virtual EMG signal in order to evaluate the goodness of automated decomposition algorithms.

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state-of-the-art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub-models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Extensive eccentric contractions in intact cardiac trabeculae: revealing compelling differences in contractile behaviour compared to skeletal muscles

Force enhancement (FE) is a phenomenon that is present in skeletal muscle. It is characterized by progressive forces upon active stretching-distinguished by a linear rise in force-and enhanced isometric force following stretching (residual FE (RFE)). In skeletal muscle, non-cross-bridge (XB) structures may account for this behaviour. So far, it is unknown whether differences between non-XB structures within the heart and skeletal muscle result in deviating contractile behaviour during and after eccentric contractions. Thus, we investigated the force response of intact cardiac trabeculae during and after isokinetic eccentric muscle contractions (10% of maximum shortening velocity) with extensive magnitudes of stretch (25% of optimum muscle length). The different contributions of XB and non-XB structures to the total muscle force were revealed by using an actomyosin inhibitor. For cardiac trabeculae, we found that the force-length dynamics during long stretch were similar to the total isometric force-length relation. This indicates that no (R)FE is present in cardiac muscle while stretching the muscle from 0.75 to 1.0 optimum muscle length. This finding is in contrast with the results obtained for skeletal muscle, in which (R)FE is present. Our data support the hypothesis that titin stiffness does not increase with activation in cardiac muscle.

People with low back pain show reduced movement complexity during their most active daily tasks

BACKGROUND

Actigraphy is a quantitative method for the investigation of human physical activity and is normally based on accelerometric and/or kinematic data.

METHODS

A multichannel actigraphy system, able to record both acceleration and spine angles, was employed in this study to measure the quality of movement in 17 individuals with chronic low back pain (LBP) and 18 healthy individuals during unrestricted daily activities. An indication of movement complexity was computed by means of non-negative matrix factorization throughout the 24 hr period and in the 60 min of highest activity.

RESULTS

Movement complexity differed only when the 60 min of highest activity was taken into account, with the LBP group showing reduced complexity (e.g., for dimensionality = 8, over 90% of the comparisons showed a significant reduction in the LBP group).

CONCLUSIONS

The results are compatible with the hypothesis that pain induces a reduction in the available kinematic trajectories and degrees of freedom during natural movements, which becomes more evident when more demanding tasks are performed. A reduced movement complexity suggests a persistent alteration of the descending neural pathways and/or a disrupted somatosensory information processing, which could be possibly contrasted by administering highly variable motor tasks.

SIGNIFICANCE

People with chronic pain move differently. Movement quality is difficult to evaluate during daily activities, yet it may prove more informative than quantitative measurements. We proposed a new approach for computing movement complexity and found out that patients' movements get more stereotyped when higher spinal acceleration is required.

An Efficient Modelling-Simulation-Analysis Workflow to Investigate Stump-Socket Interaction Using Patient-Specific, Three-Dimensional, Continuum-Mechanical, Finite Element Residual Limb Models

The lack of an efficient modelling-simulation-analysis workflow for creating and utilising detailed subject-specific computational models is one of the key reasons why simulation-based approaches for analysing socket-stump interaction have not yet been successfully established. Herein, we propose a novel and efficient modelling-simulation-analysis workflow that uses commercial software for generating a detailed subject-specific, three-dimensional finite element model of an entire residual limb from Diffusion Tensor MRI images in <20 min. Moreover, to complete the modelling-simulation-analysis workflow, the generated subject-specific residual limb model is used within an implicit dynamic FE simulation of bipedal stance to predict the potential sites of deep tissue injury. For this purpose, a nonlinear hyperelastic, transversely isotropic skeletal muscle constitutive law containing a deep tissue injury model was implemented in LS-DYNA. To demonstrate the feasibility of the entire modelling-simulation-analysis workflow and the fact that detailed, anatomically realistic, multi-muscle models are superior to state-of-the-art, fused-muscle models, an implicit dynamic FE analysis of 2-h bipedal stance is carried out. By analysing the potential volume of damaged muscle tissue after donning an optimally-fitted and a misfitted socket, i.e., a socket whose volume was isotropically shrunk by 10%, we were able to highlight the differences between the detailed individual- and fused-muscle models. The results of the bipedal stance simulation showed that peak stresses in the fused-muscle model were four times lower when compared to the multi-muscle model. The peak interface stress in the individual-muscle model, at the end of bipedal stance analysis, was 2.63 times lower than that in the deep tissues of the stump. At the end of the bipedal stance analysis using the misfitted socket, the fused-muscle model predicted that 7.65% of the residual limb volume was injured, while the detailed-model predicted 16.03%. The proposed approach is not only limited to modelling residual limbs but also has applications in predicting the impact of plastic surgery, for detailed forward-dynamics simulations of normal musculoskeletal systems.

Enabling Detailed, Biophysics-Based Skeletal Muscle Models on HPC Systems

Realistic simulations of detailed, biophysics-based, multi-scale models often require very high resolution and, thus, large-scale compute facilities. Existing simulation environments, especially for biomedical applications, are typically designed to allow for high flexibility and generality in model development. Flexibility and model development, however, are often a limiting factor for large-scale simulations. Therefore, new models are typically tested and run on small-scale compute facilities. By using a detailed biophysics-based, chemo-electromechanical skeletal muscle model and the international open-source software library OpenCMISS as an example, we present an approach to upgrade an existing muscle simulation framework from a moderately parallel version toward a massively parallel one that scales both in terms of problem size and in terms of the number of parallel processes. For this purpose, we investigate different modeling, algorithmic and implementational aspects. We present improvements addressing both numerical and parallel scalability. In addition, our approach includes a novel visualization environment which is based on the MegaMol framework and is capable of handling large amounts of simulated data. We present the results of a number of scaling studies at the Tier-1 supercomputer HazelHen at the High Performance Computing Center Stuttgart (HLRS). We improve the overall runtime by a factor of up to 2.6 and achieve good scalability on up to 768 cores.

Cytological analysis and structural quantification of FtsZ1-2 and FtsZ2-1 network characteristics in Physcomitrella patens

Although the concept of the cytoskeleton as a cell-shape-determining scaffold is well established, it remains enigmatic how eukaryotic organelles adopt and maintain a specific morphology. The Filamentous Temperature Sensitive Z (FtsZ) protein family, an ancient tubulin, generates complex polymer networks, with striking similarity to the cytoskeleton, in the chloroplasts of the moss Physcomitrella patens. Certain members of this protein family are essential for structural integrity and shaping of chloroplasts, while others are not, illustrating the functional diversity within the FtsZ protein family. Here, we apply a combination of confocal laser scanning microscopy and a self-developed semi-automatic computational image analysis method for the quantitative characterisation and comparison of network morphologies and connectivity features for two selected, functionally dissimilar FtsZ isoforms, FtsZ1-2 and FtsZ2-1. We show that FtsZ1-2 and FtsZ2-1 networks are significantly different for 8 out of 25 structural descriptors. Therefore, our results demonstrate that different FtsZ isoforms are capable of generating polymer networks with distinctive morphological and connectivity features which might be linked to the functional differences between the two isoforms. To our knowledge, this is the first study to employ computational algorithms in the quantitative comparison of different classes of protein networks in living cells.

A novel computational method to determine subject-specific bite force and occlusal loading during mastication

The evaluation of three-dimensional occlusal loading during biting and chewing may assist in development of new dental materials, in designing effective and long-lasting restorations such as crowns and bridges, and for evaluating functional performance of prosthodontic components such as dental and/or maxillofacial implants. At present, little is known about the dynamic force and pressure distributions at the occlusal surface during mastication, as these quantities cannot be measured directly. The aim of this study was to evaluate subject-specific occlusal loading forces during mastication using accurate jaw motion measurements. Motion data was obtained from experiments in which an individual performed maximal effort dynamic chewing cycles on a rubber sample with known mechanical properties. A finite element model simulation of one recorded chewing cycle was then performed to evaluate the deformation of the rubber. This was achieved by imposing the measured jaw motions on a three-dimensional geometric surface model of the subject's dental impressions. Based on the rubber's deformation and its material behaviour, the simulation was used to compute the resulting stresses within the rubber as well as the contact pressures and forces on the occlusal surfaces. An advantage of this novel modelling approach is that dynamic occlusal pressure maps and biting forces may be predicted with high accuracy and resolution at each time step throughout the chewing cycle. Depending on the motion capture technique and the speed of simulation, the methodology may be automated in such a way that it can be performed chair-side. The present study demonstrates a novel modelling methodology for evaluating dynamic occlusal loading during biting or chewing.

Biomechanical investigation of two long bone growth modulation techniques by finite element simulations

Implants used to correct pathological varus-valgus deformities (VVD) and leg length discrepancies (LLD) may not be optimized for the specific treatment, as suggested by their off-label use. Detailed analysis of this issue has been limited by the poorly understood mechanical behavior of the growing physis and ignorance of the loads acting on the implants. The aim of this study was to predict and compare the loading conditions of a growth modulation implant in VVD and LLD treatments. Idealized finite element (FE) models of the juvenile distal femur treated with the Eight-Plate implant were developed for VVD and LLD. Bone growth was simulated using thermal strains. The axial force in the plate was compared between the two treatments. Case-specific plate forces were predicted by virtually reproducing the screw deformation visible on radiographs of LLD (N = 4) and VVD (N = 4) clinical cases. The simple FE models reproduced the clinical implant deformations well. The resulting forces ranged from 129 to 580 N for the VVD patients. For LLD, this range was from 295 to 1002 N per plate, that is, 590-2004 N for the entire physis. The higher forces in LLD could be explained by restricted screw divergence in the double-sided implant application. For the first time, the loading conditions of a growth modulation implant were investigated and compared between two treatments by FE analyses, and the range of case-specific loads was predicted. These simulation tools may be utilized for guiding appropriate usage and for efficient development of implants. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:1398-1405, 2018.

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

Investigating the interplay between muscular activity and motion is the basis to improve our understanding of healthy or diseased musculoskeletal systems. To be able to analyze the musculoskeletal systems, computational models are used. Albeit some severe modeling assumptions, almost all existing musculoskeletal system simulations appeal to multibody simulation frameworks. Although continuum-mechanical musculoskeletal system models can compensate for some of these limitations, they are essentially not considered because of their computational complexity and cost. The proposed framework is the first activation-driven musculoskeletal system model, in which the exerted skeletal muscle forces are computed using 3-dimensional, continuum-mechanical skeletal muscle models and in which muscle activations are determined based on a constraint optimization problem. Numerical feasibility is achieved by computing sparse grid surrogates with hierarchical B-splines, and adaptive sparse grid refinement further reduces the computational effort. The choice of B-splines allows the use of all existing gradient-based optimization techniques without further numerical approximation. This paper demonstrates that the resulting surrogates have low relative errors (less than 0.76%) and can be used within forward simulations that are subject to constraint optimization. To demonstrate this, we set up several different test scenarios in which an upper limb model consisting of the elbow joint, the biceps and triceps brachii, and an external load is subjected to different optimization criteria. Even though this novel method has only been demonstrated for a 2-muscle system, it can easily be extended to musculoskeletal systems with 3 or more muscles.

Computational 3D imaging to quantify structural components and assembly of protein networks

Traditionally, protein structures have been described by the secondary structure architecture and fold arrangement. However, the relatively novel method of 3D confocal microscopy of fluorescent-protein-tagged networks in living cells allows resolving the detailed spatial organization of these networks. This provides new possibilities to predict network functionality, as structure and function seem to be linked at various scales. Here, we propose a quantitative approach using 3D confocal microscopy image data to describe protein networks based on their nano-structural characteristics. This analysis is constructed in four steps: (i) Segmentation of the microscopic raw data into a volume model and extraction of a spatial graph representing the protein network. (ii) Quantifying protein network gross morphology using the volume model. (iii) Quantifying protein network components using the spatial graph. (iv) Linking these two scales to obtain insights into network assembly. Here, we quantitatively describe the filamentous temperature sensitive Z protein network of the moss Physcomitrella patens and elucidate relations between network size and assembly details. Future applications will link network structure and functionality by tracking dynamic structural changes over time and comparing different states or types of networks, possibly allowing more precise identification of (mal) functions or the design of protein-engineered biomaterials for applications in regenerative medicine.

STATEMENT OF SIGNIFICANCE

Protein networks are highly complex and dynamic structures that play various roles in biological environments. Analyzing the detailed spatial structure of these networks may lead to new insight into biological functions and malfunctions. Here, we propose a tool set that extracts structural information at two scales of the protein network and allows therefore to address questions such as "how is the network built?" or "how networks grow?".

A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation

Contractions on the descending limb of the total (active + passive) muscle force-length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarcomere-length inhomogeneities. This is however not observed in experiments-vast half-sarcomere-length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sarcomere-length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin-titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force-length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided.

Experiment for validation of fluid-structure interaction models and algorithms

In this paper a fluid-structure interaction (FSI) experiment is presented. The aim of this experiment is to provide a challenging yet easy-to-setup FSI test case that addresses the need for rigorous testing of FSI algorithms and modeling frameworks. Steady-state and periodic steady-state test cases with constant and periodic inflow were established. Focus of the experiment is on biomedical engineering applications with flow being in the laminar regime with Reynolds numbers 1283 and 651. Flow and solid domains were defined using computer-aided design (CAD) tools. The experimental design aimed at providing a straightforward boundary condition definition. Material parameters and mechanical response of a moderately viscous Newtonian fluid and a nonlinear incompressible solid were experimentally determined. A comprehensive data set was acquired by using magnetic resonance imaging to record the interaction between the fluid and the solid, quantifying flow and solid motion.

Validation of a non-conforming monolithic fluid-structure interaction method using phase-contrast MRI

This paper details the validation of a non-conforming arbitrary Lagrangian-Eulerian fluid-structure interaction technique using a recently developed experimental 3D fluid-structure interaction benchmark problem. Numerical experiments for steady and transient test cases of the benchmark were conducted employing an inf-sup stable and a general Galerkin scheme. The performance of both schemes is assessed. Spatial refinement with three mesh refinement levels and fluid domain truncation with two fluid domain lengths are studied as well as employing a sequence of increasing time step sizes for steady-state cases. How quickly an approximate steady-state or periodic steady-state is reached is investigated and quantified based on error norm computations. Comparison of numerical results with experimental phase-contrast magnetic resonance imaging data shows very good overall agreement including governing of flow patterns observed in the experiment.

Exploring the Use of Non-Image-Based Ultrasound to Detect the Position of the Residual Femur within a Stump

A satisfactorily fitted socket interacts dynamically with the stump in order to support body weight, transmit load effectively, enhance dynamic stability, and enable the control and stabilization of the residual limb. The internal dynamics occurring within a socket is important in determining optimal fit. Many measurement and imaging techniques, such as X-rays, have been utilized to investigate the movement of the residual femur within the stump during gait. However, due to associated health risks and costs, none of the current techniques have been extended to clinical prosthetics. The use of B-mode ultrasound has been suggested as a safe and cheap alternative, and has been utilized in previous studies to monitor the motion of the femur. However, the need to create a duplicate socket and time-consuming analysis of the images were obstacles to the system being applied clinically. This study aims to gauge the effectiveness of a non-image based ultrasound system. Here, we determined errors expected from the measurements. Accuracy errors of 2.9 mm to 8.4 mm and reproducibility measurements within a standard deviation of 3.9 mm are reported. We also estimated errors up to 14.4 mm in in-vivo measurements. We think there is potential in developing this technique, and we hope to reduce some technical difficulties such that it can, one day, be easily incorporated into prosthetic fitting.

The Role of Parvalbumin, Sarcoplasmatic Reticulum Calcium Pump Rate, Rates of Cross-Bridge Dynamics, and Ryanodine Receptor Calcium Current on Peripheral Muscle Fatigue: A Simulation Study

A biophysical model of the excitation-contraction pathway, which has previously been validated for slow-twitch and fast-twitch skeletal muscles, is employed to investigate key biophysical processes leading to peripheral muscle fatigue. Special emphasis hereby is on investigating how the model's original parameter sets can be interpolated such that realistic behaviour with respect to contraction time and fatigue progression can be obtained for a continuous distribution of the model's parameters across the muscle units, as found for the functional properties of muscles. The parameters are divided into 5 groups describing (i) the sarcoplasmatic reticulum calcium pump rate, (ii) the cross-bridge dynamics rates, (iii) the ryanodine receptor calcium current, (iv) the rates of binding of magnesium and calcium ions to parvalbumin and corresponding dissociations, and (v) the remaining processes. The simulations reveal that the first two parameter groups are sensitive to contraction time but not fatigue, the third parameter group affects both considered properties, and the fourth parameter group is only sensitive to fatigue progression. Hence, within the scope of the underlying model, further experimental studies should investigate parvalbumin dynamics and the ryanodine receptor calcium current to enhance the understanding of peripheral muscle fatigue.

Multiscale musculoskeletal modelling, data-model fusion and electromyography-informed modelling

This paper proposes methods and technologies that advance the state of the art for modelling the musculoskeletal system across the spatial and temporal scales; and storing these using efficient ontologies and tools. We present population-based modelling as an efficient method to rapidly generate individual morphology from only a few measurements and to learn from the ever-increasing supply of imaging data available. We present multiscale methods for continuum muscle and bone models; and efficient mechanostatistical methods, both continuum and particle-based, to bridge the scales. Finally, we examine both the importance that muscles play in bone remodelling stimuli and the latest muscle force prediction methods that use electromyography-assisted modelling techniques to compute musculoskeletal forces that best reflect the underlying neuromuscular activity. Our proposal is that, in order to have a clinically relevant virtual physiological human, (i) bone and muscle mechanics must be considered together; (ii) models should be trained on population data to permit rapid generation and use underlying principal modes that describe both muscle patterns and morphology; and (iii) these tools need to be available in an open-source repository so that the scientific community may use, personalize and contribute to the database of models.

A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin-titin interaction

Although recent research emphasises the possible role of titin in skeletal muscle force enhancement, this property is commonly ignored in current computational models. This work presents the first biophysically based continuum-mechanical model of skeletal muscle that considers, in addition to actin-myosin interactions, force enhancement based on actin-titin interactions. During activation, titin attaches to actin filaments, which results in a significant reduction in titin's free molecular spring length and therefore results in increased titin forces during a subsequent stretch. The mechanical behaviour of titin is included on the microscopic half-sarcomere level of a multi-scale chemo-electro-mechanical muscle model, which is based on the classic sliding-filament and cross-bridge theories. In addition to titin stress contributions in the muscle fibre direction, the continuum-mechanical constitutive relation accounts for geometrically motivated, titin-induced stresses acting in the muscle's cross-fibre directions. Representative simulations of active stretches under maximal and submaximal activation levels predict realistic magnitudes of force enhancement in fibre direction. For example, stretching the model by 20 % from optimal length increased the isometric force at the target length by about 30 %. Predicted titin-induced stresses in the muscle's cross-fibre directions are rather insignificant. Including the presented development in future continuum-mechanical models of muscle function in dynamic situations will lead to more accurate model predictions during and after lengthening contractions.

Predicting electromyographic signals under realistic conditions using a multiscale chemo-electro-mechanical finite element model

This paper presents a novel multiscale finite element-based framework for modelling electromyographic (EMG) signals. The framework combines (i) a biophysical description of the excitation-contraction coupling at the half-sarcomere level, (ii) a model of the action potential (AP) propagation along muscle fibres, (iii) a continuum-mechanical formulation of force generation and deformation of the muscle, and (iv) a model for predicting the intramuscular and surface EMG. Owing to the biophysical description of the half-sarcomere, the model inherently accounts for physiological properties of skeletal muscle. To demonstrate this, the influence of membrane fatigue on the EMG signal during sustained contractions is investigated. During a stimulation period of 500 ms at 100 Hz, the predicted EMG amplitude decreases by 40% and the AP propagation velocity decreases by 15%. Further, the model can take into account contraction-induced deformations of the muscle. This is demonstrated by simulating fixed-length contractions of an idealized geometry and a model of the human tibialis anterior muscle (TA). The model of the TA furthermore demonstrates that the proposed finite element model is capable of simulating realistic geometries, complex fibre architectures, and can include different types of heterogeneities. In addition, the TA model accounts for a distributed innervation zone, different fibre types and appeals to motor unit discharge times that are based on a biophysical description of the α motor neurons.