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Nölle LV, Alfaro EH, Martynenko OV, Schmitt S. An investigation of tendon strains in jersey finger injury load cases using a finite element neuromuscular human body model. Front Bioeng Biotechnol 2023; 11:1293705. [PMID: 38155925 PMCID: PMC10752991 DOI: 10.3389/fbioe.2023.1293705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Accepted: 12/01/2023] [Indexed: 12/30/2023] Open
Abstract
Introduction: A common hand injury in American football, rugby and basketball is the so-called jersey finger injury (JFI), in which an eccentric overextension of the distal interphalangeal joint leads to an avulsion of the connected musculus flexor digitorum profundus (FDP) tendon. In the field of automotive safety assessment, finite element (FE) neuromuscular human body models (NHBMs) have been validated and are employed to evaluate different injury types related to car crash scenarios. The goal of this study is to show, how such a model can be modified to assess JFIs by adapting the hand of an FE-NHBM for the computational analysis of tendon strains during a generalized JFI load case. Methods: A jersey finger injury criterion (JFIC) covering the injury mechanisms of tendon straining and avulsion was defined based on biomechanical experiments found in the literature. The hand of the Total Human Model for Safety (THUMS) version 3.0 was combined with the musculature of THUMS version 5.03 to create a model with appropriate finger mobility. Muscle routing paths of FDP and musculus flexor digitorum superficialis (FDS) as well as tendon material parameters were optimized using literature data. A simplified JFI load case was simulated as the gripping of a cylindrical rod with finger flexor activation levels between 0% and 100%, which was then retracted with the velocity of a sprinting college football player to forcefully open the closed hand. Results: The optimization of the muscle routing node positions and tendon material parameters yielded good results with minimum normalized mean absolute error values of 0.79% and 7.16% respectively. Tendon avulsion injuries were detected in the middle and little finger for muscle activation levels of 80% and above, while no tendon or muscle strain injuries of any kind occurred. Discussion: The presented work outlines the steps necessary to adapt the hand model of a FE-NHBM for the assessment of JFIs using a newly defined injury criterion called the JFIC. The injury assessment results are in good agreement with documented JFI symptoms. At the same time, the need to rethink commonly asserted paradigms concerning the choice of muscle material parameters is highlighted.
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Affiliation(s)
- Lennart V. Nölle
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Eduardo Herrera Alfaro
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Oleksandr V. Martynenko
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Syn Schmitt
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
- Stuttgart Center for Simulation Science, University of Stuttgart, Stuttgart, Germany
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2
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Martynenko OV, Kempter F, Kleinbach C, Nölle LV, Lerge P, Schmitt S, Fehr J. Development and verification of a physiologically motivated internal controller for the open-source extended Hill-type muscle model in LS-DYNA. Biomech Model Mechanobiol 2023; 22:2003-2032. [PMID: 37542621 PMCID: PMC10613192 DOI: 10.1007/s10237-023-01748-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 07/06/2023] [Indexed: 08/07/2023]
Abstract
Nowadays, active human body models are becoming essential tools for the development of integrated occupant safety systems. However, their broad application in industry and research is limited due to the complexity of incorporated muscle controllers, the long simulation runtime, and the non-regular use of physiological motor control approaches. The purpose of this study is to address the challenges in all indicated directions by implementing a muscle controller with several physiologically inspired control strategies into an open-source extended Hill-type muscle model formulated as LS-DYNA user-defined umat41 subroutine written in the Fortran programming language. This results in increased usability, runtime performance and physiological accuracy compared to the standard muscle material existing in LS-DYNA. The proposed controller code is verified with extensive experimental data that include findings for arm muscles, the cervical spine region, and the whole body. Selected verification experiments cover three different muscle activation situations: (1) passive state, (2) open-loop and closed-loop muscle activation, and (3) reflexive behaviour. Two whole body finite element models, the 50th percentile female VIVA OpenHBM and the 50th percentile male THUMS v5, are used for simulations, complemented by the simplified arm model extracted from the 50th percentile male THUMS v3. The obtained results are evaluated additionally with the CORrelation and Analysis methodology and the mean squared error method, showing good to excellent biofidelity and sufficient agreement with the experimental data. It was shown additionally how the integrated controller allows simplified mimicking of the movements for similar musculoskeletal models using the parameters transfer method. Furthermore, the Hill-type muscle model presented in this paper shows better kinematic behaviour even in the passive case compared to the existing one in LS-DYNA due to its improved damping and elastic properties. These findings provide a solid evidence base motivating the application of the enhanced muscle material with the internal controller in future studies with Active Human Body Models under different loading conditions.
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Affiliation(s)
- Oleksandr V Martynenko
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Nobelstr. 15, 70569, Stuttgart, Germany.
| | - Fabian Kempter
- Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany
| | - Christian Kleinbach
- Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany
| | - Lennart V Nölle
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Nobelstr. 15, 70569, Stuttgart, Germany
| | - Patrick Lerge
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Nobelstr. 15, 70569, Stuttgart, Germany
| | - Syn Schmitt
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Nobelstr. 15, 70569, Stuttgart, Germany.
| | - Jörg Fehr
- Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany
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Meszaros-Beller L, Hammer M, Schmitt S, Pivonka P. Effect of neglecting passive spinal structures: a quantitative investigation using the forward-dynamics and inverse-dynamics musculoskeletal approach. Front Physiol 2023; 14:1135531. [PMID: 37324394 PMCID: PMC10264677 DOI: 10.3389/fphys.2023.1135531] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2023] [Accepted: 04/28/2023] [Indexed: 06/17/2023] Open
Abstract
Purpose: Inverse-dynamics (ID) analysis is an approach widely used for studying spine biomechanics and the estimation of muscle forces. Despite the increasing structural complexity of spine models, ID analysis results substantially rely on accurate kinematic data that most of the current technologies are not capable to provide. For this reason, the model complexity is drastically reduced by assuming three degrees of freedom spherical joints and generic kinematic coupling constraints. Moreover, the majority of current ID spine models neglect the contribution of passive structures. The aim of this ID analysis study was to determine the impact of modelled passive structures (i.e., ligaments and intervertebral discs) on remaining joint forces and torques that muscles must balance in the functional spinal unit. Methods: For this purpose, an existing generic spine model developed for the use in the demoa software environment was transferred into the musculoskeletal modelling platform OpenSim. The thoracolumbar spine model previously used in forward-dynamics (FD) simulations provided a full kinematic description of a flexion-extension movement. By using the obtained in silico kinematics, ID analysis was performed. The individual contribution of passive elements to the generalised net joint forces and torques was evaluated in a step-wise approach increasing the model complexity by adding individual biological structures of the spine. Results: The implementation of intervertebral discs and ligaments has significantly reduced compressive loading and anterior torque that is attributed to the acting net muscle forces by -200% and -75%, respectively. The ID model kinematics and kinetics were cross-validated against the FD simulation results. Conclusion: This study clearly shows the importance of incorporating passive spinal structures on the accurate computation of remaining joint loads. Furthermore, for the first time, a generic spine model was used and cross-validated in two different musculoskeletal modelling platforms, i.e., demoa and OpenSim, respectively. In future, a comparison of neuromuscular control strategies for spinal movement can be investigated using both approaches.
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Affiliation(s)
- Laura Meszaros-Beller
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Biomedical Technologies, Queensland University of Technology, Brisbane, QLD, Australia
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Maria Hammer
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
- Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, Stuttgart, Germany
| | - Syn Schmitt
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD, Australia
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
- Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, Stuttgart, Germany
| | - Peter Pivonka
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD, Australia
- Centre for Biomedical Technologies, Queensland University of Technology, Brisbane, QLD, Australia
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4
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Izzi F, Mo A, Schmitt S, Badri-Spröwitz A, Haeufle DFB. Muscle prestimulation tunes velocity preflex in simulated perturbed hopping. Sci Rep 2023; 13:4559. [PMID: 36941316 PMCID: PMC10027857 DOI: 10.1038/s41598-023-31179-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 03/07/2023] [Indexed: 03/23/2023] Open
Abstract
Muscle fibres possess unique visco-elastic properties, which generate a stabilising zero-delay response to unexpected perturbations. This instantaneous response-termed "preflex"-mitigates neuro-transmission delays, which are hazardous during fast locomotion due to the short stance duration. While the elastic contribution to preflexes has been studied extensively, the function of fibre viscosity due to the force-velocity relation remains unknown. In this study, we present a novel approach to isolate and quantify the preflex force produced by the force-velocity relation in musculo-skeletal computer simulations. We used our approach to analyse the muscle response to ground-level perturbations in simulated vertical hopping. Our analysis focused on the preflex-phase-the first 30 ms after impact-where neuronal delays render a controlled response impossible. We found that muscle force at impact and dissipated energy increase with perturbation height, helping reject the perturbations. However, the muscle fibres reject only 15% of step-down perturbation energy with constant stimulation. An open-loop rising stimulation, observed in locomotion experiments, amplified the regulatory effects of the muscle fibre's force-velocity relation, resulting in 68% perturbation energy rejection. We conclude that open-loop neuronal tuning of muscle activity around impact allows for adequate feed-forward tuning of muscle fibre viscous capacity, facilitating energy adjustment to unexpected ground-level perturbations.
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Affiliation(s)
- Fabio Izzi
- Hertie Institute for Clinical Brain Research and Center for Integrative Neuroscience, University of Tübingen, Tübingen, Germany.
- Dynamic Locomotion Group, Max Planck Institute for Intelligent Systems, Stuttgart, Germany.
| | - An Mo
- Dynamic Locomotion Group, Max Planck Institute for Intelligent Systems, Stuttgart, Germany
| | - Syn Schmitt
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Alexander Badri-Spröwitz
- Dynamic Locomotion Group, Max Planck Institute for Intelligent Systems, Stuttgart, Germany
- Department of Mechanical Engineering, KU Leuven, Leuven, Belgium
| | - Daniel F B Haeufle
- Hertie Institute for Clinical Brain Research and Center for Integrative Neuroscience, University of Tübingen, Tübingen, Germany
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
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5
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Meszaros-Beller L, Hammer M, Riede JM, Pivonka P, Little JP, Schmitt S. Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution. Biomech Model Mechanobiol 2023; 22:669-694. [PMID: 36602716 PMCID: PMC10097810 DOI: 10.1007/s10237-022-01673-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Accepted: 12/08/2022] [Indexed: 01/06/2023]
Abstract
In spine research, two possibilities to generate models exist: generic (population-based) models representing the average human and subject-specific representations of individuals. Despite the increasing interest in subject specificity, individualisation of spine models remains challenging. Neuro-musculoskeletal (NMS) models enable the analysis and prediction of dynamic motions by incorporating active muscles attaching to bones that are connected using articulating joints under the assumption of rigid body dynamics. In this study, we used forward-dynamic simulations to compare a generic NMS multibody model of the thoracolumbar spine including fully articulated vertebrae, detailed musculature, passive ligaments and linear intervertebral disc (IVD) models with an individualised model to assess the contribution of individual biological structures. Individualisation was achieved by integrating skeletal geometry from computed tomography and custom-selected muscle and ligament paths. Both models underwent a gravitational settling process and a forward flexion-to-extension movement. The model-specific load distribution in an equilibrated upright position and local stiffness in the L4/5 functional spinal unit (FSU) is compared. Load sharing between occurring internal forces generated by individual biological structures and their contribution to the FSU stiffness was computed. The main finding of our simulations is an apparent shift in load sharing with individualisation from an equally distributed element contribution of IVD, ligaments and muscles in the generic spine model to a predominant muscle contribution in the individualised model depending on the analysed spine level.
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Affiliation(s)
- Laura Meszaros-Beller
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, Australia.,Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Maria Hammer
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany.,Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, Stuttgart, Germany
| | - Julia M Riede
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Peter Pivonka
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, Australia
| | - J Paige Little
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, Australia
| | - Syn Schmitt
- School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, Australia. .,Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany. .,Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, Stuttgart, Germany.
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6
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Design and Scaling of Exoskeleton Power Units Considering Load Cycles of Humans. ROBOTICS 2022. [DOI: 10.3390/robotics11050107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
Exoskeletons are powerful tools for aiding humans with pathological conditions, in dangerous environments or in manually exhausting tasks. Typically, they are designed for specific maximum scenarios without taking into account the diversity of tasks and the individuality of the user. To address this discrepancy, a framework was developed for personalizing an exoskeleton by scaling the components, especially the electrical machine, based on different simulated human muscle forces. The main idea was to scale a numerical arm model based on body mass and height to predict different movements representing both manual labor and daily activities. The predicted torques necessary to produce these movements were then used to generate a load/performance cycle for the power unit design. Considering these torques, main operation points of this load cycle were defined and a reference power unit was scaled and optimized. Therefore, a scalability model for an electrical machine is introduced. This individual adaptation and scaling of the power unit for different users leads to a better performance and a lighter design.
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7
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Putra IPA, Iraeus J, Sato F, Svensson MY, Thomson R. Finite element human body models with active reflexive muscles suitable for sex based whiplash injury prediction. Front Bioeng Biotechnol 2022; 10:968939. [PMID: 36246354 PMCID: PMC9557094 DOI: 10.3389/fbioe.2022.968939] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 09/12/2022] [Indexed: 11/24/2022] Open
Abstract
Previous research has not produced a satisfactory resource to study reflexive muscle activity for investigating potentially injurious whiplash motions. Various experimental and computational studies are available, but none provided a comprehensive biomechanical representation of human response during rear impacts. Three objectives were addressed in the current study to develop female and male finite element human body models with active reflexive neck muscles: 1) eliminate the buckling in the lower cervical spine of the model observed in earlier active muscle controller implementations, 2) evaluate and quantify the influence of the individual features of muscle activity, and 3) evaluate and select the best model configuration that can be used for whiplash injury predictions. The current study used an open-source finite element model of the human body for injury assessment representing an average 50th percentile female anthropometry, together with the derivative 50th percentile male morphed model. Based on the head-neck kinematics and CORelation and Analyis (CORA) tool for evaluation, models with active muscle controller and parallel damping elements showed improved head-neck kinematics agreement with the volunteers over the passive models. It was concluded that this model configuration would be the most suitable for gender-based whiplash injury prediction when different impact severities are to be studied.
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Affiliation(s)
- I Putu Alit Putra
- Injury Prevention Unit, Division of Vehicle Safety, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden
- *Correspondence: I Putu Alit Putra, ; Johan Iraeus,
| | - Johan Iraeus
- Injury Prevention Unit, Division of Vehicle Safety, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden
- *Correspondence: I Putu Alit Putra, ; Johan Iraeus,
| | - Fusako Sato
- Injury Prevention Unit, Division of Vehicle Safety, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden
- Japan Automobile Research Institute (JARI), Tsukuba, Japan
| | - Mats Y. Svensson
- Injury Prevention Unit, Division of Vehicle Safety, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden
| | - Robert Thomson
- Injury Prevention Unit, Division of Vehicle Safety, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden
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8
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Nölle LV, Mishra A, Martynenko OV, Schmitt S. Evaluation of muscle strain injury severity in active human body models. J Mech Behav Biomed Mater 2022; 135:105463. [PMID: 36137370 DOI: 10.1016/j.jmbbm.2022.105463] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Revised: 11/04/2021] [Accepted: 09/09/2022] [Indexed: 10/31/2022]
Abstract
Even though significant efforts in the field of injury detection with finite element active human body models (FE AHBMs) have been made, injuries of the muscle-tendon unit (MTU) have not yet been taken into consideration. Therefore, the goal of this study was to define a muscle strain injury criterion (MSIC) to evaluate the damage sustained by the musculature during muscle driven movement scenarios. The MSIC was derived from biomechanical tests found in the literature and the proposed threshold values were substantiated through a comparison to an estimate of the ultimate tensile strength of human skeletal muscle and the forces acting on the biceps femoris long head muscle during one sprinting gait cycle. The application of the MSIC to state-of-the-art FE AHBMs was demonstrated by evaluating the strain injury severity of selected neck muscles of a full-body AHBM during two seat rotation load cases. The results of the MSIC substantiation suggest that all three injury threshold values proposed in this work fall in a plausible corridor of forces acting on the MTU. The combined results of the AHBM simulations indicate that neither of the two examined seat rotations are likely to cause strain injury to the neck muscles and that the proposed MSIC can easily be applied to current AHBMs without further modification of the model architecture or the muscle parameters. The MSIC was also used to formulate a hypothesis on the aetiology of muscle strain injuries, through which it was demonstrated that material inhomogeneities in the MTU might be the cause for strain injuries sustained during otherwise physiological movements. This work is a first step in the direction of the definition of a wholistic injury criterion for the human skeletal muscle fibre.
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Affiliation(s)
- Lennart V Nölle
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany.
| | - Atul Mishra
- Mercedes-Benz Research and Development, Bangalore, India
| | - Oleksandr V Martynenko
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Syn Schmitt
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
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Wochner I, Nölle LV, Martynenko OV, Schmitt S. ‘Falling heads’: investigating reflexive responses to head–neck perturbations. Biomed Eng Online 2022; 21:25. [PMID: 35429975 PMCID: PMC9013062 DOI: 10.1186/s12938-022-00994-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 03/29/2022] [Indexed: 11/10/2022] Open
Abstract
Abstract
Background
Reflexive responses to head–neck perturbations affect the injury risk in many different situations ranging from sports-related impact to car accident scenarios. Although several experiments have been conducted to investigate these head–neck responses to various perturbations, it is still unclear why and how individuals react differently and what the implications of these different responses across subjects on the potential injuries might be. Therefore, we see a need for both experimental data and biophysically valid computational Human Body Models with bio-inspired muscle control strategies to understand individual reflex responses better.
Methods
To address this issue, we conducted perturbation experiments of the head–neck complex and used this data to examine control strategies in a simulation model. In the experiments, which we call ’falling heads’ experiments, volunteers were placed in a supine and a prone position on a table with an additional trapdoor supporting the head. This trapdoor was suddenly released, leading to a free-fall movement of the head until reflexive responses of muscles stopped the downwards movement.
Results
We analysed the kinematic, neuronal and dynamic responses for all individuals and show their differences for separate age and sex groups. We show that these results can be used to validate two simple reflex controllers which are able to predict human biophysical movement and modulate the response necessary to represent a large variability of participants.
Conclusions
We present characteristic parameters such as joint stiffness, peak accelerations and latency times. Based on this data, we show that there is a large difference in the individual reflexive responses between participants. Furthermore, we show that the perturbation direction (supine vs. prone) significantly influences the measured kinematic quantities. Finally, ’falling heads’ experiments data are provided open-source to be used as a benchmark test to compare different muscle control strategies and to validate existing active Human Body Models directly.
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10
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Ross SA, Wakeling JM. The energy of muscle contraction. IV. Greater mass of larger muscles decreases contraction efficiency. J R Soc Interface 2021; 18:20210484. [PMID: 34583567 PMCID: PMC8479364 DOI: 10.1098/rsif.2021.0484] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 08/31/2021] [Indexed: 11/12/2022] Open
Abstract
While skeletal muscle mass has been shown to decrease mass-specific mechanical work per cycle, it is not yet known how muscle mass alters contraction efficiency. In this study, we examined the effect of muscle mass on mass-specific metabolic cost and efficiency during cyclic contractions in simulated muscles of different sizes. We additionally explored how tendon and its stiffness alters the effects of muscle mass on mass-specific work, mass-specific metabolic cost and efficiency across different muscle sizes. To examine contraction efficiency, we estimated the metabolic cost of the cycles using established cost models. We found that for motor contractions in which the muscle was primarily active during shortening, greater muscle mass resulted in lower contraction efficiency, primarily due to lower mass-specific mechanical work per cycle. The addition of a tendon in series with the mass-enhanced muscle model improved the mass-specific work and efficiency per cycle with greater mass for motor contractions, particularly with a shorter excitation duty cycle, despite higher predicted metabolic cost. The results of this study indicate that muscle mass is an important determinant of whole muscle contraction efficiency.
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Affiliation(s)
- Stephanie A. Ross
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6
| | - James M. Wakeling
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6
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11
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Guo J, Guo W, Ren G. Embodiment of intra-abdominal pressure in a flexible multibody model of the trunk and the spinal unloading effects during static lifting tasks. Biomech Model Mechanobiol 2021; 20:1599-1626. [PMID: 34050846 DOI: 10.1007/s10237-021-01465-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 05/07/2021] [Indexed: 11/28/2022]
Abstract
The role of intra-abdominal pressure (IAP) in spinal load reduction has remained controversial, partly because previous musculoskeletal models did not introduce the pressure generating mechanism. In this study, an integrated computational methodology is proposed to combine the IAP change with core muscle activations. An ideal gas relationship was introduced to calculate pressure distribution within the abdominal cavity. Additionally, based on flexible multibody dynamics, a muscle membrane element was developed by incorporating the muscular fiber deformation, inter-fiber stiffness, and volume constancy. This element was then utilized in discretizing the diaphragm and transversus abdominis, forming an IAP-muscle coupling system of the abdominal cavity. Based on this methodology, a forward dynamic simulation of spinal flexion was presented to examine the unloading effect of abdominal breathing. The results confirm that core muscle contraction during the abdominal breathing cycle can substantially reduce the forces of spinal compression together with trunk extensor muscles, and this effect is more pronounced when the IAP increase is produced by contraction of the transversus abdominis. This unloading effect still holds even with the co-activation of other abdominal muscles, providing a potential choice when designing trunk movements during weight-lifting tasks.
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Affiliation(s)
- Jianqiao Guo
- MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China.
| | - Wei Guo
- Air Force Medical Center, PLA, Beijing, 100142, China
| | - Gexue Ren
- Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China
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12
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Günther M, Rockenfeller R, Weihmann T, Haeufle DFB, Götz T, Schmitt S. Rules of nature's Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed. J Theor Biol 2021; 523:110714. [PMID: 33862096 DOI: 10.1016/j.jtbi.2021.110714] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Revised: 03/24/2021] [Accepted: 04/08/2021] [Indexed: 10/21/2022]
Abstract
The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.
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Affiliation(s)
- Michael Günther
- Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, Universität Stuttgart, Nobelstraße 15, 70569 Stuttgart, Germany; Friedrich-Schiller-Universität, 07737 Jena, Germany.
| | - Robert Rockenfeller
- Mathematisches Institut, Universität Koblenz-Landau, Universitätsstraße 1, 56070 Koblenz, Germany
| | - Tom Weihmann
- Institut für Zoologie, Universität zu Köln, Zülpicher Straße 47b, 50674 Köln, Germany
| | - Daniel F B Haeufle
- Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, Universität Stuttgart, Nobelstraße 15, 70569 Stuttgart, Germany; Multi-level Modeling in Motor Control and Rehabilitation Robotics, Hertie-Institute for Clinical Brain Research, Eberhard-Karls-Universität, Hoppe-Seyler-Straße 3, 72076 Tübingen, Germany
| | - Thomas Götz
- Mathematisches Institut, Universität Koblenz-Landau, Universitätsstraße 1, 56070 Koblenz, Germany
| | - Syn Schmitt
- Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, Universität Stuttgart, Nobelstraße 15, 70569 Stuttgart, Germany; Stuttgart Center for Simulation Science (SC SimTech), Universität Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
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13
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Bishop PJ, Falisse A, De Groote F, Hutchinson JR. Predictive Simulations of Musculoskeletal Function and Jumping Performance in a Generalized Bird. ACTA ACUST UNITED AC 2021; 3:obab006. [PMID: 34377939 PMCID: PMC8341896 DOI: 10.1093/iob/obab006] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
Jumping is a common, but demanding, behavior that many animals employ during everyday activity. In contrast to jump-specialists such as anurans and some primates, jumping biomechanics and the factors that influence performance remains little studied for generalized species that lack marked adaptations for jumping. Computational biomechanical modeling approaches offer a way of addressing this in a rigorous, mechanistic fashion. Here, optimal control theory and musculoskeletal modeling are integrated to generate predictive simulations of maximal height jumping in a small ground-dwelling bird, a tinamou. A three-dimensional musculoskeletal model with 36 actuators per leg is used, and direct collocation is employed to formulate a rapidly solvable optimal control problem involving both liftoff and landing phases. The resulting simulation raises the whole-body center of mass to over double its standing height, and key aspects of the simulated behavior qualitatively replicate empirical observations for other jumping birds. However, quantitative performance is lower, with reduced ground forces, jump heights, and muscle–tendon power. A pronounced countermovement maneuver is used during launch. The use of a countermovement is demonstrated to be critical to the achievement of greater jump heights, and this phenomenon may only need to exploit physical principles alone to be successful; amplification of muscle performance may not necessarily be a proximate reason for the use of this maneuver. Increasing muscle strength or contractile velocity above nominal values greatly improves jump performance, and interestingly has the greatest effect on more distal limb extensor muscles (i.e., those of the ankle), suggesting that the distal limb may be a critical link for jumping behavior. These results warrant a re-evaluation of previous inferences of jumping ability in some extinct species with foreshortened distal limb segments, such as dromaeosaurid dinosaurs. Simulations prédictives de la fonction musculo-squelettique et des performances de saut chez un oiseau généralisé Sauter est un comportement commun, mais exigeant, que de nombreux animaux utilisent au cours de leurs activités quotidiennes. Contrairement aux spécialistes du saut tels que les anoures et certains primates, la biomécanique du saut et les facteurs qui influencent la performance restent peu étudiés pour les espèces généralisées qui n’ont pas d’adaptations marquées pour le saut. Les approches de modélisation biomécanique computationnelle offrent un moyen d’aborder cette question de manière rigoureuse et mécaniste. Ici, la théorie du contrôle optimal et la modélisation musculo-squelettique sont intégrées pour générer des simulations prédictives du saut en hauteur maximal chez un petit oiseau terrestre, le tinamou. Un modèle musculo-squelettique tridimensionnel avec 36 actionneurs par patte est utilisé, et une méthode numérique nommée “direct collocation” est employée pour formuler un problème de contrôle optimal rapidement résoluble impliquant les phases de décollage et d’atterrissage. La simulation qui en résulte élève le centre de masse du corps entier à plus du double de sa hauteur debout, et les aspects clés du comportement simulé reproduisent qualitativement les observations empiriques d’autres oiseaux sauteurs. Cependant, les performances quantitatives sont moindres, avec une réduction des forces au sol, des hauteurs de saut et de la puissance musculo-tendineuse. Une manœuvre de contre-mouvement prononcée est utilisée pendant le lancement. Il a été démontré que l’utilisation d’un contre-mouvement est essentielle à l’obtention de hauteurs de saut plus importantes, et il se peut que ce phénomène doive exploiter uniquement des principes physiques pour réussir; l’amplification de la performance musculaire n’est pas nécessairement une raison immédiate de l’utilisation de cette manœuvre. L’augmentation de la force musculaire ou de la vitesse de contraction au-dessus des valeurs nominales améliore grandement la performance de saut et, fait intéressant, a le plus grand effet sur les muscles extenseurs des membres plus distaux (c'est-à-dire ceux de la cheville), ce qui suggère que le membre distal peut être un lien critique pour le comportement de saut. Ces résultats justifient une réévaluation des déductions précédentes de la capacité de sauter chez certaines espèces éteintes avec des segments de membres distaux raccourcis, comme les dinosaures droméosauridés. Voorspellende simulaties van musculoskeletale functie en springprestaties bij een gegeneraliseerde vogel Springen is een veel voorkomend, maar veeleisend, gedrag dat veel dieren toepassen tijdens hun dagelijkse bezigheden. In tegenstelling tot de springspecialisten zoals de anura en sommige primaten, is de biomechanica van het springen en de factoren die de prestaties beïnvloeden nog weinig bestudeerd voor algemene soorten die geen uitgesproken adaptaties voor het springen hebben. Computationele biomechanische modelbenaderingen bieden een manier om dit op een rigoureuze, mechanistische manier aan te pakken. Hier worden optimale controle theorie en musculoskeletale modellering geïntegreerd om voorspellende simulaties te genereren van maximale hoogtesprong bij een kleine grondbewonende vogel, een tinamou. Een driedimensionaal musculoskeletaal model met 36 actuatoren per poot wordt gebruikt, en directe collocatie wordt toegepast om een snel oplosbaar optimaal controleprobleem te formuleren dat zowel de opstijg-als de landingsfase omvat. De resulterende simulatie verhoogt het lichaamszwaartepunt tot meer dan het dubbele van de stahoogte, en belangrijke aspecten van het gesimuleerde gedrag komen kwalitatief overeen met empirische waarnemingen voor andere springende vogels. De kwantitatieve prestaties zijn echter minder, met verminderde grondkrachten, spronghoogtes en spierpeeskracht. Tijdens de lancering wordt een uitgesproken tegenbewegingsmanoeuvre gebruikt. Aangetoond is dat het gebruik van een tegenbeweging van cruciaal belang is voor het bereiken van grotere spronghoogten, en dit fenomeen hoeft alleen op fysische principes te berusten om succesvol te zijn; versterking van de spierprestaties hoeft niet noodzakelijk een proximate reden te zijn voor het gebruik van deze manoeuvre. Het verhogen van de spierkracht of van de contractiesnelheid boven de nominale waarden verbetert de sprongprestatie aanzienlijk, en heeft interessant genoeg het grootste effect op de meer distale extensoren van de ledematen (d.w.z. die van de enkel), wat suggereert dat de distale ledematen een kritieke schakel kunnen zijn voor het springgedrag. Deze resultaten rechtvaardigen een herevaluatie van eerdere conclusies over springvermogen bij sommige uitgestorven soorten met voorgekorte distale ledematen, zoals dromaeosauride dinosauriërs. Prädiktive Simulationen der muskuloskelettalen Funktion und Sprungleistung bei einem generalisierten Vogel Springen ist ein übliches jedoch anstrengendes Verhalten, das viele Tiere bei ihren täglichen Aktivitäten einsetzen. Im Gegensatz zu Springspezialisten, wie Fröschen und einigen Primaten, sind bei allgemeinen Arten, welche keine ausgeprägten Anpassung für Sprungverhalten aufweisen, die Biomechanik beim Springen und die Faktoren, welche die Leistungsfähigkeit beeinflussen, noch wenig untersucht. Computergestützte biomechanische Modellierungsverfahren bieten hier eine Möglichkeit, dies in einer gründlichen, mechanistischen Weise anzugehen. In dieser Arbeit werden die optimale Steuerungstheorie und Muskel-Skelett-Modellierung zusammen eingesetzt, um die maximale Sprunghöhe eines kleinen bodenlebenden Vogels, eines Perlsteisshuhns, zu simulieren und zu prognostizieren. Es wird ein dreidimensionales Muskel-Skelett-Modell mit 36 Aktuatoren pro Bein verwendet, und durch direkte Kollokation wird ein schnell lösbares optimales Steuerungsproblem formuliert, das sowohl die Abstoss- als auch die Landephase umfasst. Die daraus folgende Simulation bringt den Ganzkörperschwerpunkt auf mehr als das Doppelte seiner Standhöhe und entscheidende Aspekte des simulierten Verhaltens entsprechen qualitativ empirischen Beobachtungen für andere springende Vögel. Allerdings ist die quantitative Leistungsfähigkeit geringer, mit reduzierten Bodenkräften, Sprunghöhen und Muskel-Sehnen-Kräften. Beim Abstossen wird ein ausgeprägtes Gegenbewegungsmanöver durchgeführt. Die Durchführung einer Gegenbewegung ist nachweislich entscheidend für das Erreichen grösserer Sprunghöhen, wobei dieses Phänomen möglicherweise nur physikalische Prinzipien auszuschöpfen braucht, um erfolgreich zu sein. Die Verstärkung der Muskelleistung ist daher möglicherweise nicht zwingend ein unmittelbarer Grund für die Verwendung dieses Manövers. Eine Erhöhung der Muskelkraft oder der Kontraktionsgeschwindigkeit über die Nominalwerte hinaus führt zu einer erheblichen Zunahme der Sprungleistung und hat interessanterweise den grössten Effekt bei den weiter distal gelegenen Streckmuskeln der Beine (d.h. bei denjenigen des Sprunggelenks), was darauf hindeutet, dass die distale Gliedmasse ein entscheidendes Element für das Sprungverhalten sein könnte. Diese Ergebnisse geben Anlass zur Überprüfung früherer Schlussfolgerungen hinsichtlich der Sprungfähigkeit einiger ausgestorbener Arten mit verkürzten distalen Gliedmassen, wie beispielsweise bei dromaeosauriden Dinosauriern.
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Affiliation(s)
- P J Bishop
- Structure and Motion Laboratory, Department of Comparative Biomedical Sciences, Royal Veterinary College, Hatfield, UK.,Geosciences Program, Queensland Museum, Brisbane, Australia.,Museum of Comparative Zoology, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
| | - A Falisse
- Department of Movement Sciences, KU Leuven, Leuven, Belgium.,Department of Bioengineering, Stanford University, Stanford, CA 94305, USA
| | - F De Groote
- Department of Movement Sciences, KU Leuven, Leuven, Belgium
| | - J R Hutchinson
- Structure and Motion Laboratory, Department of Comparative Biomedical Sciences, Royal Veterinary College, Hatfield, UK
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14
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Ross SA, Rimkus B, Konow N, Biewener AA, Wakeling JM. Added mass in rat plantaris muscle causes a reduction in mechanical work. J Exp Biol 2020; 223:jeb224410. [PMID: 32737211 PMCID: PMC7561483 DOI: 10.1242/jeb.224410] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2020] [Accepted: 07/24/2020] [Indexed: 11/20/2022]
Abstract
Most of what we know about whole muscle behaviour comes from experiments on single fibres or small muscles that are scaled up in size without considering the effects of the additional muscle mass. Previous modelling studies have shown that tissue inertia acts to slow the rate of force development and maximum velocity of muscle during shortening contractions and decreases the work and power per cycle during cyclic contractions; however, these results have not yet been confirmed by experiments on living tissue. Therefore, in this study we conducted in situ work-loop experiments on rat plantaris muscle to determine the effects of increasing the mass of muscle on mechanical work during cyclic contractions. We additionally simulated these experimental contractions using a mass-enhanced Hill-type model to validate our previous modelling work. We found that greater added mass resulted in lower mechanical work per cycle relative to the unloaded trials in which no mass was added to the muscle (P=0.041 for both 85 and 123% increases in muscle mass). We additionally found that greater strain resulted in lower work per cycle relative to unloaded trials at the same strain to control for length change and velocity effects on the work output, possibly due to greater accelerations of the muscle mass at higher strains. These results confirm that tissue mass reduces muscle mechanical work at larger muscle sizes, and that this effect is likely amplified for lower activations.
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Affiliation(s)
- Stephanie A Ross
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
| | - Barbora Rimkus
- Department of Biological Sciences, University of Massachusetts Lowell, Lowell, MA 01854, USA
| | - Nicolai Konow
- Department of Biological Sciences, University of Massachusetts Lowell, Lowell, MA 01854, USA
- Concord Field Station, Museum of Comparative Zoology and Department of Organismic and Evolutionary Biology, Harvard University, Bedford, MA 01730, USA
| | - Andrew A Biewener
- Concord Field Station, Museum of Comparative Zoology and Department of Organismic and Evolutionary Biology, Harvard University, Bedford, MA 01730, USA
| | - James M Wakeling
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
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15
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Rockenfeller R, Müller A, Damm N, Kosterhon M, Kantelhardt SR, Frank R, Gruber K. Muscle-driven and torque-driven centrodes during modeled flexion of individual lumbar spines are disparate. Biomech Model Mechanobiol 2020; 20:267-279. [PMID: 32939615 PMCID: PMC7892748 DOI: 10.1007/s10237-020-01382-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 08/24/2020] [Indexed: 11/25/2022]
Abstract
Lumbar spine biomechanics during the forward-bending of the upper body (flexion) are well investigated by both in vivo and in vitro experiments. In both cases, the experimentally observed relative motion of vertebral bodies can be used to calculate the instantaneous center of rotation (ICR). The timely evolution of the ICR, the centrode, is widely utilized for validating computer models and is thought to serve as a criterion for distinguishing healthy and degenerative motion patterns. While in vivo motion can be induced by physiological active structures (muscles), in vitro spinal segments have to be driven by external torque-applying equipment such as spine testers. It is implicitly assumed that muscle-driven and torque-driven centrodes are similar. Here, however, we show that centrodes qualitatively depend on the impetus. Distinction is achieved by introducing confidence regions (ellipses) that comprise centrodes of seven individual multi-body simulation models, performing flexion with and without preload. Muscle-driven centrodes were generally directed superior–anterior and tail-shaped, while torque-driven centrodes were located in a comparably narrow region close to the center of mass of the caudal vertebrae. We thus argue that centrodes resulting from different experimental conditions ought to be compared with caution. Finally, the applicability of our method regarding the analysis of clinical syndromes and the assessment of surgical methods is discussed.
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Affiliation(s)
- Robert Rockenfeller
- Mathematical Institute, University Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz, Germany.
| | - Andreas Müller
- Institute for Medical Engineering and Information Processing (MTI Mittelrhein), University Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz, Germany
- Mechanical Systems Engineering Laboratory, EMPA-Swiss Federal Laboratories for Materials Science and Technology, Ueberlandstr. 129, 8600 Dübendorf, Switzerland
| | - Nicolas Damm
- Institute for Medical Engineering and Information Processing (MTI Mittelrhein), University Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz, Germany
| | - Michael Kosterhon
- Department of Neurosurgery, University Medical Centre, Johannes Gutenberg-University, Langenbeckstr. 1, 55131, Mainz, Germany
| | - Sven R Kantelhardt
- Department of Neurosurgery, University Medical Centre, Johannes Gutenberg-University, Langenbeckstr. 1, 55131, Mainz, Germany
| | - Rolfdieter Frank
- Mathematical Institute, University Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz, Germany
| | - Karin Gruber
- Institute for Medical Engineering and Information Processing (MTI Mittelrhein), University Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz, Germany
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16
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Rockenfeller R, Herold JL, Götz T. Parameter estimation and experimental design for Hill-type muscles: Impulses from optimization-based modeling. Math Biosci 2020; 327:108432. [PMID: 32710903 DOI: 10.1016/j.mbs.2020.108432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Revised: 07/07/2020] [Accepted: 07/20/2020] [Indexed: 10/23/2022]
Abstract
The benefits of optimization-based modeling for parameter estimation of Hill-type muscle models are demonstrated. Therefore, we examined the model and data of Günther et al. (2007), who analyzed isometric, concentric, and quick-release contractions of a piglet calf muscle. We found that the isometric experiments are suitable for derivative-based parameter estimation while the others did not provide any additional value. During the estimation process, certain parameters had to be fixed. We give possible reasons and provide impulses for modelers. Subsequently, unnecessarily complex or deprecated model parts were exchanged and the new model was fitted to the data. In order to be able to provide a reliable estimation of the whole parameter set, we propose two isometric and two quick-release experiments, which are real-life feasible and together allow an identification of all parameters based on a local sensitivity analysis. These experiments can be used as qualitative guidelines for practitioners to reduce the experimental effort when estimating parameters for macroscopic muscle models.
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Affiliation(s)
- R Rockenfeller
- Mathematical Institute, University of Koblenz-Landau, Universitätsstr. 1, 56070 Koblenz, Germany.
| | - J L Herold
- Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany
| | - T Götz
- Mathematical Institute, University of Koblenz-Landau, Universitätsstr. 1, 56070 Koblenz, Germany
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17
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Haeufle DFB, Siegel J, Hochstein S, Gussew A, Schmitt S, Siebert T, Rzanny R, Reichenbach JR, Stutzig N. Energy Expenditure of Dynamic Submaximal Human Plantarflexion Movements: Model Prediction and Validation by in-vivo Magnetic Resonance Spectroscopy. Front Bioeng Biotechnol 2020; 8:622. [PMID: 32671034 PMCID: PMC7332772 DOI: 10.3389/fbioe.2020.00622] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 05/21/2020] [Indexed: 11/30/2022] Open
Abstract
To understand the organization and efficiency of biological movement, it is important to evaluate the energy requirements on the level of individual muscles. To this end, predicting energy expenditure with musculoskeletal models in forward-dynamic computer simulations is currently the most promising approach. However, it is challenging to validate muscle models in-vivo in humans, because access to the energy expenditure of single muscles is difficult. Previous approaches focused on whole body energy expenditure, e.g., oxygen consumption (VO2), or on thermal measurements of individual muscles by tracking blood flow and heat release (through measurements of the skin temperature). This study proposes to validate models of muscular energy expenditure by using functional phosphorus magnetic resonance spectroscopy (31P-MRS). 31P-MRS allows to measure phosphocreatine (PCr) concentration which changes in relation to energy expenditure. In the first 25 s of an exercise, PCr breakdown rate reflects ATP hydrolysis, and is therefore a direct measure of muscular enthalpy rate. This method was applied to the gastrocnemius medialis muscle of one healthy subject during repetitive dynamic plantarflexion movements at submaximal contraction, i.e., 20% of the maximum plantarflexion force using a MR compatible ergometer. Furthermore, muscle activity was measured by surface electromyography (EMG). A model (provided as open source) that combines previous models for muscle contraction dynamics and energy expenditure was used to reproduce the experiment in simulation. All parameters (e.g., muscle length and volume, pennation angle) in the model were determined from magnetic resonance imaging or literature (e.g., fiber composition), leaving no free parameters to fit the experimental data. Model prediction and experimental data on the energy supply rates are in good agreement with the validation phase (<25 s) of the dynamic movements. After 25 s, the experimental data differs from the model prediction as the change in PCr does not reflect all metabolic contributions to the energy expenditure anymore and therefore underestimates the energy consumption. This shows that this new approach allows to validate models of muscular energy expenditure in dynamic movements in vivo.
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Affiliation(s)
- Daniel F B Haeufle
- Multi-level Modeling in Motor Control and Rehabilitation Robotics, Hertie Institute for Clinical Brain Research, University of Tübingen, Tübingen, Germany
| | - Johannes Siegel
- Multi-level Modeling in Motor Control and Rehabilitation Robotics, Hertie Institute for Clinical Brain Research, University of Tübingen, Tübingen, Germany.,Department of Motion and Exercise Science, Institute of Sport and Movement Science, University of Stuttgart, Stuttgart, Germany
| | - Stefan Hochstein
- Motion Science, Institute of Sport Science, Martin-Luther-University Halle, Halle, Germany
| | - Alexander Gussew
- Department of Radiology, University Hospital Halle (Saale), Halle, Germany
| | - Syn Schmitt
- Computational Biophysics and Biorobotics, Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany.,Stuttgart Center of Simulation Science, University of Stuttgart, Stuttgart, Germany
| | - Tobias Siebert
- Department of Motion and Exercise Science, Institute of Sport and Movement Science, University of Stuttgart, Stuttgart, Germany
| | - Reinhard Rzanny
- Medical Physics Group, Institute of Diagnostic and Interventional Radiology, Jena University Hospital - Friedrich Schiller University, Jena, Germany
| | - Jürgen R Reichenbach
- Medical Physics Group, Institute of Diagnostic and Interventional Radiology, Jena University Hospital - Friedrich Schiller University, Jena, Germany
| | - Norman Stutzig
- Department of Motion and Exercise Science, Institute of Sport and Movement Science, University of Stuttgart, Stuttgart, Germany
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18
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Wochner I, Driess D, Zimmermann H, Haeufle DFB, Toussaint M, Schmitt S. Optimality Principles in Human Point-to-Manifold Reaching Accounting for Muscle Dynamics. Front Comput Neurosci 2020; 14:38. [PMID: 32499691 PMCID: PMC7242656 DOI: 10.3389/fncom.2020.00038] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2019] [Accepted: 04/14/2020] [Indexed: 11/26/2022] Open
Abstract
Human arm movements are highly stereotypical under a large variety of experimental conditions. This is striking due to the high redundancy of the human musculoskeletal system, which in principle allows many possible trajectories toward a goal. Many researchers hypothesize that through evolution, learning, and adaption, the human system has developed optimal control strategies to select between these possibilities. Various optimality principles were proposed in the literature that reproduce human-like trajectories in certain conditions. However, these studies often focus on a single cost function and use simple torque-driven models of motion generation, which are not consistent with human muscle-actuated motion. The underlying structure of our human system, with the use of muscle dynamics in interaction with the control principles, might have a significant influence on what optimality principles best model human motion. To investigate this hypothesis, we consider a point-to-manifold reaching task that leaves the target underdetermined. Given hypothesized motion objectives, the control input is generated using Bayesian optimization, which is a machine learning based method that trades-off exploitation and exploration. Using numerical simulations with Hill-type muscles, we show that a combination of optimality principles best predicts human point-to-manifold reaching when accounting for the muscle dynamics.
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Affiliation(s)
- Isabell Wochner
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
| | - Danny Driess
- Machine Learning and Robotics Lab, University of Stuttgart, Stuttgart, Germany
| | - Heiko Zimmermann
- Khoury College of Computer Sciences, Northeastern University, Boston, MA, United States
| | - Daniel F B Haeufle
- Hertie Institute for Clinical Brain Research, and Werner Reichard Centre for Integrative Neuroscience, University of Tübingen, Tübingen, Germany
| | - Marc Toussaint
- Machine Learning and Robotics Lab, University of Stuttgart, Stuttgart, Germany
| | - Syn Schmitt
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
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19
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Rockenfeller R, Günther M, Stutzig N, Haeufle DFB, Siebert T, Schmitt S, Leichsenring K, Böl M, Götz T. Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model. Front Physiol 2020; 11:306. [PMID: 32431619 PMCID: PMC7214688 DOI: 10.3389/fphys.2020.00306] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 03/19/2020] [Indexed: 12/01/2022] Open
Abstract
Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.
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Affiliation(s)
| | - Michael Günther
- Institute for Modelling and Simulation of Biomechanical Systems, Computational Biophysics and Biorobotics, University of Stuttgart, Stuttgart, Germany
- Friedrich-Schiller-University, Jena, Germany
| | - Norman Stutzig
- Department of Motion and Exercise Science, University of Stuttgart, Stuttgart, Germany
| | - Daniel F. B. Haeufle
- Hertie-Institute for Clinical Brain Research and Center for Integrative Neuroscience, Eberhard-Karls-University, Tübingen, Germany
| | - Tobias Siebert
- Department of Motion and Exercise Science, University of Stuttgart, Stuttgart, Germany
| | - Syn Schmitt
- Institute for Modelling and Simulation of Biomechanical Systems, Computational Biophysics and Biorobotics, University of Stuttgart, Stuttgart, Germany
| | - Kay Leichsenring
- Institute of Solid Mechanics, Technical University Braunschweig, Braunschweig, Germany
| | - Markus Böl
- Institute of Solid Mechanics, Technical University Braunschweig, Braunschweig, Germany
| | - Thomas Götz
- Mathematical Institute, University of Koblenz-Landau, Koblenz, Germany
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20
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Mörl F, Günther M, Riede JM, Hammer M, Schmitt S. Loads distributed in vivo among vertebrae, muscles, spinal ligaments, and intervertebral discs in a passively flexed lumbar spine. Biomech Model Mechanobiol 2020; 19:2015-2047. [DOI: 10.1007/s10237-020-01322-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2020] [Accepted: 03/18/2020] [Indexed: 01/09/2023]
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21
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A systems-theoretic analysis of low-level human motor control: application to a single-joint arm model. J Math Biol 2019; 80:1139-1158. [PMID: 31768630 DOI: 10.1007/s00285-019-01455-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2017] [Revised: 05/31/2019] [Indexed: 12/26/2022]
Abstract
Continuous control using internal models appears to be quite straightforward explaining human motor control. However, it demands both, a high computational effort and a high model preciseness as the whole trajectory needs to be converted. Intermittent control shows great promise for avoiding these drawbacks of continuous control, at least to a certain extent. In this contribution, we study intermittency at the motoneuron level. We ask: how many different, but constant muscle stimulation sets are necessary to generate a stable movement for a specific motor task? Intermittent control, in our perspective, can be assumed only if the number of transitions is relatively small. As application case, a single-joint arm movement is considered. The muscle contraction dynamics is described by a Hill-type muscle model, for the muscle activation dynamics both Hatze's and Zajac's approach are considered. To actuate the lower arm, up to four muscle groups are implemented. A systems-theoretic approach is used to find the smallest number of transitions between constant stimulation sets. A method for a stability analysis of human motion is presented. A Lyapunov function candidate is specified. Thanks to sum-of-squares methods, the presented procedure is generally applicable and computationally feasible. The region-of-attraction of a transition point, and the number of transitions necessary to perform stable arm movements are estimated. The results support the intermittent control theory on this level of motor control, because only very few transitions are necessary.
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22
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Röhrle O, Yavuz UŞ, Klotz T, Negro F, Heidlauf T. Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2019; 11:e1457. [PMID: 31237041 DOI: 10.1002/wsbm.1457] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2019] [Revised: 05/13/2019] [Accepted: 05/14/2019] [Indexed: 01/10/2023]
Abstract
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.
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Affiliation(s)
- Oliver Röhrle
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany.,Stuttgart Center for Simulation Sciences (SC SimTech), University of Stuttgart, Stuttgart, Germany
| | - Utku Ş Yavuz
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany.,Biomedical Signals and Systems, Universiteit Twente, Enschede, The Netherlands
| | - Thomas Klotz
- Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany.,Stuttgart Center for Simulation Sciences (SC SimTech), University of Stuttgart, Stuttgart, Germany
| | - Francesco Negro
- Department of Clinical and Experimental Sciences, Universià degli Studi di Brescia, Brescia, Italy
| | - Thomas Heidlauf
- EPS5 - Simulation and System Analysis, Hofer pdc GmbH, Stuttgart, Germany
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23
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Hwang IS, Hu CL, Yang ZR, Lin YT, Chen YC. Improving Precision Force Control With Low-Frequency Error Amplification Feedback: Behavioral and Neurophysiological Mechanisms. Front Physiol 2019; 10:131. [PMID: 30842742 PMCID: PMC6391708 DOI: 10.3389/fphys.2019.00131] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2018] [Accepted: 02/01/2019] [Indexed: 11/13/2022] Open
Abstract
Although error amplification (EA) feedback has been shown to improve performance on visuomotor tasks, the challenge of EA is that it concurrently magnifies task-irrelevant information that may impair visuomotor control. The purpose of this study was to improve the force control in a static task by preclusion of high-oscillatory components in EA feedback that cannot be timely used for error correction by the visuomotor system. Along with motor unit behaviors and corticomuscular coherence, force fluctuations (Fc) were modeled with non-linear SDA to contrast the reliance of the feedback process and underlying neurophysiological mechanisms by using real feedback, EA, and low-frequency error amplification (LF-EA). During the static force task in the experiment, the EA feedback virtually potentiated the size of visual error, whereas the LF-EA did not channel high-frequency errors above 0.8 Hz into the amplification process. The results showed that task accuracy was greater with the LF-EA than with the real and EA feedback modes, and that LF-EA led to smaller and more complex Fc. LF-EA generally led to smaller SDA variables of Fc (critical time points, critical point of Fc, the short-term effective diffusion coefficient, and short-term exponent scaling) than did real feedback and EA. The use of LF-EA feedback increased the irregularity of the ISIs of MUs but decreased the RMS of the mean discharge rate, estimated with pooled MU spike trains. Beta-range EEG–EMG coherence spectra (13–35 Hz) in the LF-EA condition were the greatest among the three feedback conditions. In summary, amplification of low-frequency errors improves force control by shifting the relative significances of the feedforward and feedback processes. The functional benefit arises from the increase in the common descending drive to promote a stable state of MU discharges.
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Affiliation(s)
- Ing-Shiou Hwang
- Institute of Allied Health Sciences, College of Medicine, National Cheng Kung University, Tainan, Taiwan.,Department of Physical Therapy, College of Medicine, National Cheng Kung University, Tainan, Taiwan
| | - Chia-Ling Hu
- Department of Physical Therapy, College of Medicine, National Cheng Kung University, Tainan, Taiwan
| | - Zong-Ru Yang
- Institute of Allied Health Sciences, College of Medicine, National Cheng Kung University, Tainan, Taiwan
| | - Yen-Ting Lin
- Physical Education Office, Asian University, Taichung, Taiwan
| | - Yi-Ching Chen
- Department of Physical Therapy, College of Medical Science and Technology, Chung Shan Medical University, Taichung, Taiwan.,Physical Therapy Room, Chung Shan Medical University Hospital, Taichung, Taiwan
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24
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Zhang C, Wang W, Anderson D, Guan S, Li G, Xiang H, Zhao H, Cheng B. Effect of Low-Frequency Vibration on Muscle Response under Different Neurointact Conditions. Appl Bionics Biomech 2019; 2019:1971045. [PMID: 30719071 PMCID: PMC6335862 DOI: 10.1155/2019/1971045] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Revised: 07/26/2018] [Accepted: 08/30/2018] [Indexed: 11/17/2022] Open
Abstract
Stretch reflex is an important factor that influences the biomechanical response of the human body under whole-body vibration. However, there is a lack of quantitative evaluation at lower frequencies. Thus, the aim of this study was to investigate the effects of vibration on the stretch reflex and, in particular, to explore the quantitative relationship between dynamic muscle responses and low-frequency vibrations. The gastrocnemius muscle of 45 Sprague-Dawley rats was dissected. Sinusoidal vibrations of five discrete frequencies (2~16 Hz) with peak-to-peak amplitudes of 1 mm were applied to the gastrocnemius muscles with 2 mm or 3 mm prelengthening. Variables including dynamic muscle force, vibration acceleration, and displacement were recorded in two conditions, with and without the stretch reflex. Results showed that the dynamic muscle forces decreased by 20% on average for the 2 mm prelengthening group after the stretch reflex was blocked and by 24% for the 3 mm prelengthening group. Statistical analysis indicated that the amplitude of dynamic muscle force in the "with stretch reflex" condition was significantly larger than that in the "without stretch reflex" condition (p < 0.001). The tension-length curve was found to be a nonlinear hysteresis loop that changed with frequency. The phase difference between the dynamic muscle force and the length change was affected significantly by vibration frequency (p < 0.01), and the minimum frequency was 4-8 Hz. Experimental results of this study could benefit musculoskeletal model by providing a theoretical support to build a stretch reflex model for low-frequency vibration.
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Affiliation(s)
- Chaofei Zhang
- State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China
| | - Wenjun Wang
- State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China
| | - Dennis Anderson
- Center for Advanced Orthopedic Studies, Beth Israel Deaconess Medical Center, Boston, MA 02215, USA
| | - Sishu Guan
- Chongqing Key Laboratory of Vehicle/Biological Crash Security, Department 4th, Institute of Surgery Research, Daping Hospital, Third Military Medical University, Chongqing 400042, China
| | - Guofa Li
- Institute of Human Factors and Ergonomics, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China
| | - Hongyi Xiang
- Chongqing Key Laboratory of Vehicle/Biological Crash Security, Department 4th, Institute of Surgery Research, Daping Hospital, Third Military Medical University, Chongqing 400042, China
| | - Hui Zhao
- Chongqing Key Laboratory of Vehicle/Biological Crash Security, Department 4th, Institute of Surgery Research, Daping Hospital, Third Military Medical University, Chongqing 400042, China
| | - Bo Cheng
- State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China
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25
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The basic mechanical structure of the skeletal muscle machinery: One model for linking microscopic and macroscopic scales. J Theor Biol 2018; 456:137-167. [DOI: 10.1016/j.jtbi.2018.07.023] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Revised: 06/18/2018] [Accepted: 07/19/2018] [Indexed: 11/19/2022]
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26
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Rockenfeller R, Günther M. Inter-filament spacing mediates calcium binding to troponin: A simple geometric-mechanistic model explains the shift of force-length maxima with muscle activation. J Theor Biol 2018; 454:240-252. [DOI: 10.1016/j.jtbi.2018.06.009] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2017] [Revised: 06/03/2018] [Accepted: 06/06/2018] [Indexed: 10/28/2022]
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27
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Valentin J, Sprenger M, Pflüger D, Röhrle O. Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e2965. [PMID: 29427559 DOI: 10.1002/cnm.2965] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2017] [Revised: 01/26/2018] [Accepted: 01/29/2018] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- J Valentin
- Institute for Parallel and Distributed Systems (IPVS), University of Stuttgart, Universitätsstraße 38, 70569 Stuttgart, Germany
- Stuttgart Research Centre for Simulation Technology (SimTech), University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
| | - M Sprenger
- Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany
- Stuttgart Research Centre for Simulation Technology (SimTech), University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
| | - D Pflüger
- Institute for Parallel and Distributed Systems (IPVS), University of Stuttgart, Universitätsstraße 38, 70569 Stuttgart, Germany
- Stuttgart Research Centre for Simulation Technology (SimTech), University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
| | - O Röhrle
- Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany
- Stuttgart Research Centre for Simulation Technology (SimTech), University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
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28
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Kleinbach C, Martynenko O, Promies J, Haeufle DFB, Fehr J, Schmitt S. Implementation and validation of the extended Hill-type muscle model with robust routing capabilities in LS-DYNA for active human body models. Biomed Eng Online 2017; 16:109. [PMID: 28865494 PMCID: PMC5581498 DOI: 10.1186/s12938-017-0399-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2017] [Accepted: 08/21/2017] [Indexed: 11/25/2022] Open
Abstract
BACKGROUND In the state of the art finite element AHBMs for car crash analysis in the LS-DYNA software material named *MAT_MUSCLE (*MAT_156) is used for active muscles modeling. It has three elements in parallel configuration, which has several major drawbacks: restraint approximation of the physical reality, complicated parameterization and absence of the integrated activation dynamics. This study presents implementation of the extended four element Hill-type muscle model with serial damping and eccentric force-velocity relation including [Formula: see text] dependent activation dynamics and internal method for physiological muscle routing. RESULTS Proposed model was implemented into the general-purpose finite element (FE) simulation software LSDYNA as a user material for truss elements. This material model is verified and validated with three different sets of mammalian experimental data, taken from the literature. It is compared to the *MAT_MUSCLE (*MAT_156) Hill-type muscle model already existing in LS-DYNA, which is currently used in finite element human body models (HBMs). An application example with an arm model extracted from the FE ViVA OpenHBM is given, taking into account physiological muscle paths. CONCLUSION The simulation results show better material model accuracy, calculation robustness and improved muscle routing capability compared to *MAT_156. The FORTRAN source code for the user material subroutine dyn21.f and the muscle parameters for all simulations, conducted in the study, are given at https://zenodo.org/record/826209 under an open source license. This enables a quick application of the proposed material model in LS-DYNA, especially in active human body models (AHBMs) for applications in automotive safety.
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Affiliation(s)
- Christian Kleinbach
- Institute for Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Oleksandr Martynenko
- Biomechanics and Biorobotics, Stuttgart Research Centre for Simulation Sciences (SRC SimTech), University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
| | - Janik Promies
- Institute for Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Daniel F. B. Haeufle
- Multi-Level Modeling in Motor Control and Rehabilitation Robotics, Hertie Institute for Clinical Brain Research, University of Tübingen, Otfried-Müller-Strasse 25, 72076 Tübingen, Germany
| | - Jörg Fehr
- Institute for Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
| | - Syn Schmitt
- Biomechanics and Biorobotics, Stuttgart Research Centre for Simulation Sciences (SRC SimTech), University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
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29
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Hill equation and Hatze's muscle activation dynamics complement each other: enhanced pharmacological and physiological interpretability of modelled activity-pCa curves. J Theor Biol 2017; 431:11-24. [PMID: 28755955 DOI: 10.1016/j.jtbi.2017.07.023] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Revised: 07/17/2017] [Accepted: 07/25/2017] [Indexed: 01/03/2023]
Abstract
In pharmacology, particularly receptor theory, the drug dose-effect relation of bio-active substances is frequently described by a sigmoidal function formulated by A.V. Hill. In biomechanics and muscle physiology then again, H. Hatze had elaborated a mathematical model for the stimulation- and length-dependent dynamics of the calcium-induced activation of mammalian skeletal muscle. Here, we prove that muscular activity-pCa curves described by the Hill equation and the equilibrium state predicted by Hatze's activation dynamics are equivalent. Thus, the exponent introduced by Hatze can be directly identified with its counterpart in the Hill equation, by which the former model gains further physiological interpretability. Conversely, the Hill constant can now be interpreted as a function of the fibre length, generally allowing for advanced Hill plots based on model ideas. We derive and examine the complementary relation of both model approaches, highlight the benefits of mutually viewing one approach from the perspective of the other, and address the physiology behind sigmoidal curves.
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30
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Dick TJM, Biewener AA, Wakeling JM. Comparison of human gastrocnemius forces predicted by Hill-type muscle models and estimated from ultrasound images. J Exp Biol 2017; 220:1643-1653. [PMID: 28202584 PMCID: PMC5450802 DOI: 10.1242/jeb.154807] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2016] [Accepted: 02/11/2017] [Indexed: 11/20/2022]
Abstract
Hill-type models are ubiquitous in the field of biomechanics, providing estimates of a muscle's force as a function of its activation state and its assumed force-length and force-velocity properties. However, despite their routine use, the accuracy with which Hill-type models predict the forces generated by muscles during submaximal, dynamic tasks remains largely unknown. This study compared human gastrocnemius forces predicted by Hill-type models with the forces estimated from ultrasound-based measures of tendon length changes and stiffness during cycling, over a range of loads and cadences. We tested both a traditional model, with one contractile element, and a differential model, with two contractile elements that accounted for independent contributions of slow and fast muscle fibres. Both models were driven by subject-specific, ultrasound-based measures of fascicle lengths, velocities and pennation angles and by activation patterns of slow and fast muscle fibres derived from surface electromyographic recordings. The models predicted, on average, 54% of the time-varying gastrocnemius forces estimated from the ultrasound-based methods. However, differences between predicted and estimated forces were smaller under low speed-high activation conditions, with models able to predict nearly 80% of the gastrocnemius force over a complete pedal cycle. Additionally, the predictions from the Hill-type muscle models tested here showed that a similar pattern of force production could be achieved for most conditions with and without accounting for the independent contributions of different muscle fibre types.
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Affiliation(s)
- Taylor J M Dick
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, Canada V5A 1S6
| | | | - James M Wakeling
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, Canada V5A 1S6
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31
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Bayer A, Schmitt S, Günther M, Haeufle DFB. The influence of biophysical muscle properties on simulating fast human arm movements. Comput Methods Biomech Biomed Engin 2017; 20:803-821. [DOI: 10.1080/10255842.2017.1293663] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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32
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Model-Based Estimation of Ankle Joint Stiffness. SENSORS 2017; 17:s17040713. [PMID: 28353683 PMCID: PMC5421673 DOI: 10.3390/s17040713] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/16/2017] [Revised: 03/22/2017] [Accepted: 03/23/2017] [Indexed: 11/17/2022]
Abstract
We address the estimation of biomechanical parameters with wearable measurement technologies. In particular, we focus on the estimation of sagittal plane ankle joint stiffness in dorsiflexion/plantar flexion. For this estimation, a novel nonlinear biomechanical model of the lower leg was formulated that is driven by electromyographic signals. The model incorporates a two-dimensional kinematic description in the sagittal plane for the calculation of muscle lever arms and torques. To reduce estimation errors due to model uncertainties, a filtering algorithm is necessary that employs segmental orientation sensor measurements. Because of the model's inherent nonlinearities and nonsmooth dynamics, a square-root cubature Kalman filter was developed. The performance of the novel estimation approach was evaluated in silico and in an experimental procedure. The experimental study was conducted with body-worn sensors and a test-bench that was specifically designed to obtain reference angle and torque measurements for a single joint. Results show that the filter is able to reconstruct joint angle positions, velocities and torque, as well as, joint stiffness during experimental test bench movements.
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33
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Röhrle O, Sprenger M, Schmitt S. A two-muscle, continuum-mechanical forward simulation of the upper limb. Biomech Model Mechanobiol 2016; 16:743-762. [DOI: 10.1007/s10237-016-0850-x] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2016] [Accepted: 10/22/2016] [Indexed: 09/03/2023]
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34
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Rockenfeller R, Günther M. Extracting low-velocity concentric and eccentric dynamic muscle properties from isometric contraction experiments. Math Biosci 2016; 278:77-93. [DOI: 10.1016/j.mbs.2016.06.005] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Revised: 05/12/2016] [Accepted: 06/10/2016] [Indexed: 11/28/2022]
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35
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Misgeld BJE, Luken M, Riener R, Leonhardt S. Observer-Based Human Knee Stiffness Estimation. IEEE Trans Biomed Eng 2016; 64:1033-1044. [PMID: 27392340 DOI: 10.1109/tbme.2016.2587841] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
OBJECTIVE We consider the problem of stiffness estimation for the human knee joint during motion in the sagittal plane. METHODS The new stiffness estimator uses a nonlinear reduced-order biomechanical model and a body sensor network (BSN). The developed model is based on a two-dimensional knee kinematics approach to calculate the angle-dependent lever arms and the torques of the muscle-tendon-complex. To minimize errors in the knee stiffness estimation procedure that result from model uncertainties, a nonlinear observer is developed. The observer uses the electromyogram (EMG) of involved muscles as input signals and the segmental orientation as the output signal to correct the observer-internal states. Because of dominating model nonlinearities and nonsmoothness of the corresponding nonlinear functions, an unscented Kalman filter is designed to compute and update the observer feedback (Kalman) gain matrix. RESULTS The observer-based stiffness estimation algorithm is subsequently evaluated in simulations and in a test bench, specifically designed to provide robotic movement support for the human knee joint. CONCLUSION In silico and experimental validation underline the good performance of the knee stiffness estimation even in the cases of a knee stiffening due to antagonistic coactivation. SIGNIFICANCE We have shown the principle function of an observer-based approach to knee stiffness estimation that employs EMG signals and segmental orientation provided by our own IPANEMA BSN. The presented approach makes realtime, model-based estimation of knee stiffness with minimal instrumentation possible.
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Comparative Sensitivity Analysis of Muscle Activation Dynamics. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2015; 2015:585409. [PMID: 26417379 PMCID: PMC4568353 DOI: 10.1155/2015/585409] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2014] [Accepted: 02/05/2015] [Indexed: 11/18/2022]
Abstract
We mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative for a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). These models incorporate parameters that directly represent known physiological properties. Other parameters have been introduced to reproduce empirical observations. We used sensitivity analysis to investigate the influence of model parameters on the ODE solutions. In addition, we expanded an existing approach to treating initial conditions as parameters and to calculating second-order sensitivities. Furthermore, we used a global sensitivity analysis approach to include finite ranges of parameter values. Hence, a theoretician striving for model reduction could use the method for identifying particularly low sensitivities to detect superfluous parameters. An experimenter could use it for identifying particularly high sensitivities to improve parameter estimation. Hatze's nonlinear model incorporates some parameters to which activation dynamics is clearly more sensitive than to any parameter in Zajac's linear model. Other than Zajac's model, Hatze's model can, however, reproduce measured shifts in optimal muscle length with varied muscle activity. Accordingly we extracted a specific parameter set for Hatze's model that combines best with a particular muscle force-length relation.
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Mörl F, Siebert T, Häufle D. Contraction dynamics and function of the muscle-tendon complex depend on the muscle fibre-tendon length ratio: a simulation study. Biomech Model Mechanobiol 2015; 15:245-58. [DOI: 10.1007/s10237-015-0688-7] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2015] [Accepted: 05/21/2015] [Indexed: 11/30/2022]
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A forward dynamics simulation of human lumbar spine flexion predicting the load sharing of intervertebral discs, ligaments, and muscles. Biomech Model Mechanobiol 2015; 14:1081-105. [DOI: 10.1007/s10237-015-0656-2] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Accepted: 01/22/2015] [Indexed: 12/19/2022]
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Schmitt S, Haeufle D. Mechanics and Thermodynamics of Biological Muscle – A Simple Model Approach. Soft Robot 2015. [DOI: 10.1007/978-3-662-44506-8_12] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022] Open
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40
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Hill-type muscle model with serial damping and eccentric force–velocity relation. J Biomech 2014; 47:1531-6. [DOI: 10.1016/j.jbiomech.2014.02.009] [Citation(s) in RCA: 91] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2013] [Revised: 01/25/2014] [Accepted: 02/01/2014] [Indexed: 11/23/2022]
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Haeufle DFB, Günther M, Wunner G, Schmitt S. Quantifying control effort of biological and technical movements: an information-entropy-based approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012716. [PMID: 24580266 DOI: 10.1103/physreve.89.012716] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2012] [Indexed: 06/03/2023]
Abstract
In biomechanics and biorobotics, muscles are often associated with reduced movement control effort and simplified control compared to technical actuators. This is based on evidence that the nonlinear muscle properties positively influence movement control. It is, however, open how to quantify the simplicity aspect of control effort and compare it between systems. Physical measures, such as energy consumption, stability, or jerk, have already been applied to compare biological and technical systems. Here a physical measure of control effort based on information entropy is presented. The idea is that control is simpler if a specific movement is generated with less processed sensor information, depending on the control scheme and the physical properties of the systems being compared. By calculating the Shannon information entropy of all sensor signals required for control, an information cost function can be formulated allowing the comparison of models of biological and technical control systems. Exemplarily applied to (bio-)mechanical models of hopping, the method reveals that the required information for generating hopping with a muscle driven by a simple reflex control scheme is only I=32 bits versus I=660 bits with a DC motor and a proportional differential controller. This approach to quantifying control effort captures the simplicity of a control scheme and can be used to compare completely different actuators and control approaches.
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Affiliation(s)
- D F B Haeufle
- Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Germany and Universität Stuttgart, Institut für Theoretische Physik 1, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
| | - M Günther
- Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Germany and Friedrich Schiller Universität, Institut für Sportwissenschaft, Seidelstrasse 20, D-07743 Jena, Germany
| | - G Wunner
- Universität Stuttgart, Institut für Theoretische Physik 1, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
| | - S Schmitt
- Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Germany and Universität Stuttgart, Stuttgart Research Centre for Simulation Technology (SRC SimTech), Pfaffenwaldring 5a, D-70569 Stuttgart, Germany
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Modeling the chemoelectromechanical behavior of skeletal muscle using the parallel open-source software library OpenCMISS. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2013; 2013:517287. [PMID: 24348739 PMCID: PMC3855958 DOI: 10.1155/2013/517287] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2013] [Revised: 08/28/2013] [Accepted: 09/13/2013] [Indexed: 11/18/2022]
Abstract
An extensible, flexible, multiscale, and multiphysics model for nonisometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-of-the-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum flexibility, reproducibility, and extensibility. The results demonstrate the model's capability of simulating different aspects of nonisometric muscle contraction and efficiently simulating the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle.
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Schmitt S, Günther M, Rupp T, Bayer A, Häufle D. Theoretical Hill-type muscle and stability: numerical model and application. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2013; 2013:570878. [PMID: 24319495 PMCID: PMC3844250 DOI: 10.1155/2013/570878] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/19/2013] [Accepted: 09/19/2013] [Indexed: 12/02/2022]
Abstract
The construction of artificial muscles is one of the most challenging developments in today's biomedical science. The application of artificial muscles is focused both on the construction of orthotics and prosthetics for rehabilitation and prevention purposes and on building humanoid walking machines for robotics research. Research in biomechanics tries to explain the functioning and design of real biological muscles and therefore lays the fundament for the development of functional artificial muscles. Recently, the hyperbolic Hill-type force-velocity relation was derived from simple mechanical components. In this contribution, this theoretical yet biomechanical model is transferred to a numerical model and applied for presenting a proof-of-concept of a functional artificial muscle. Additionally, this validated theoretical model is used to determine force-velocity relations of different animal species that are based on the literature data from biological experiments. Moreover, it is shown that an antagonistic muscle actuator can help in stabilising a single inverted pendulum model in favour of a control approach using a linear torque generator.
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Affiliation(s)
- S. Schmitt
- Department of Sports and Exercise Science, University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
- Stuttgart Research Centre for Simulation Technology, University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
| | - M. Günther
- Department of Sports and Exercise Science, University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
- Institute of Sports Science, Science of Motion, University of Jena, Seidelstraß 20, 07749 Jena, Germany
| | - T. Rupp
- Department of Sports and Exercise Science, University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
- Stuttgart Research Centre for Simulation Technology, University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart, Germany
| | - A. Bayer
- Department of Sports and Exercise Science, University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
| | - D. Häufle
- Department of Sports and Exercise Science, University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany
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Böl M, Leichsenring K, Weichert C, Sturmat M, Schenk P, Blickhan R, Siebert T. Three-dimensional surface geometries of the rabbit soleus muscle during contraction: input for biomechanical modelling and its validation. Biomech Model Mechanobiol 2013; 12:1205-20. [DOI: 10.1007/s10237-013-0476-1] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2012] [Accepted: 01/30/2013] [Indexed: 12/26/2022]
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MÖRL FALK, SIEBERT TOBIAS, SCHMITT SYN, BLICKHAN REINHARD, GÜNTHER MICHAEL. ELECTRO-MECHANICAL DELAY IN HILL-TYPE MUSCLE MODELS. J MECH MED BIOL 2012. [DOI: 10.1142/s0219519412500856] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this study, we investigated to which extent Hill-type muscle models can explain the electro-mechanical delay (EMD). The EMD is a phenomenon that has been well examined in muscle experiments. The EMD is the time lag between a change in muscle stimulation and the subsequent measurable change in muscle force. A variety of processes as, e.g., signal conduction and interaction of contractile and elastic muscle structures contribute to the EMD. The relative contributions of the particular processes have not been fully unveiled so far. Thereto, we simulated isometric muscle contractions using two Hill-type muscle models. Their parameters were extracted from experiments on the cat soleus muscle. In agreement with literature data, predicted EMD values depend on muscle-tendon complex (MTC) length and increase when reducing MTC lengths. The highest EMD values (28 and 27 ms) occur at the lowest MTC length examined (78% of optimal length). Above optimal MTC length, we find EMD saturation (2 ms) in one model. In the other model, the EMD slightly re-increases up to 9 ms at the highest length examined (113% of optimal length). The EMD values predicted by the two models were then compared to EMD values found in the same experiments from which the muscle parameters were extracted. At optimal MTC length, the EMD values, mapping ion release and visco-elastic interactions, predicted by both models (3.5 and 5.5 ms) just partly account for the measured value (15.8 ms). The biggest share (about 9 ms) of the remaining 11 ms can be attributed to signal conduction along the nerve and on the muscle surface. Further potential sources of delayed force generation are discussed.
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Affiliation(s)
- FALK MÖRL
- Forschungsgesellschaft für Angewandte, Systemsicherheit und Arbeitsmedizin mbH, Zentrum für Bewegungstherapie, Dubliner Straße 12, D-99091 Erfurt, Deutschland, Germany
| | - TOBIAS SIEBERT
- Friedrich–Schiller–Universität Jena, Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Seidelstraße 20, D-07749 Jena, Deutschland, Germany
| | - SYN SCHMITT
- Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Deutschland, Germany
| | - REINHARD BLICKHAN
- Friedrich–Schiller–Universität Jena, Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Seidelstraße 20, D-07749 Jena, Deutschland, Germany
| | - MICHAEL GÜNTHER
- Friedrich–Schiller–Universität Jena, Institut für Sportwissenschaft, Lehrstuhl für Bewegungswissenschaft, Seidelstraße 20, D-07749 Jena, Deutschland, Germany
- Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Deutschland, Germany
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Spreading out muscle mass within a Hill-type model: a computer simulation study. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2012; 2012:848630. [PMID: 23227110 PMCID: PMC3512296 DOI: 10.1155/2012/848630] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/24/2012] [Accepted: 08/27/2012] [Indexed: 11/18/2022]
Abstract
It is state of the art that muscle contraction dynamics is adequately
described by a hyperbolic relation between muscle force and
contraction velocity (Hill relation), thereby neglecting muscle
internal mass inertia (first-order dynamics). Accordingly, the
vast majority of modelling approaches also neglect muscle internal
inertia. Assuming that such first-order contraction dynamics yet
interacts with muscle internal mass distribution, this study
investigates two questions: (i) what is the time scale on which the
muscle responds to a force step? (ii) How does this response scale
with muscle design parameters? Thereto, we simulated accelerated
contractions of alternating sequences of Hill-type contractile
elements and point masses. We found that in a typical small muscle the
force levels off after about 0.2 ms, contraction velocity after
about 0.5 ms. In an upscaled version representing bigger mammals'
muscles, the force levels off after about 20 ms, and the
theoretically expected maximum contraction velocity is not
reached. We conclude (i) that it may be indispensable to introduce
second-order contributions into muscle models to understand
high-frequency muscle responses, particularly in bigger
muscles. Additionally, (ii) constructing more elaborate measuring
devices seems to be worthwhile to distinguish viscoelastic and
inertia properties in rapid contractile responses of muscles.
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Schmitt S, Haeufle DFB, Blickhan R, Günther M. Nature as an engineer: one simple concept of a bio-inspired functional artificial muscle. BIOINSPIRATION & BIOMIMETICS 2012; 7:036022. [PMID: 22728876 DOI: 10.1088/1748-3182/7/3/036022] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The biological muscle is a powerful, flexible and versatile actuator. Its intrinsic characteristics determine the way how movements are generated and controlled. Robotic and prosthetic applications expect to profit from relying on bio-inspired actuators which exhibit natural (muscle-like) characteristics. As of today, when constructing a technical actuator, it is not possible to copy the exact molecular structure of a biological muscle. Alternatively, the question may be put how its characteristics can be realized with known mechanical components. Recently, a mechanical construct for an artificial muscle was proposed, which exhibits hyperbolic force-velocity characteristics. In this paper, we promote the constructing concept which is made by substantiating the mechanical design of biological muscle by a simple model, proving the feasibility of its real-world implementation, and checking their output both for mutual consistency and agreement with biological measurements. In particular, the relations of force, enthalpy rate and mechanical efficiency versus contraction velocity of both the construct's technical implementation and its numerical model were determined in quick-release experiments. All model predictions for these relations and the hardware results are now in good agreement with the biological literature. We conclude that the construct represents a mechanical concept of natural actuation, which is suitable for laying down some useful suggestions when designing bio-inspired actuators.
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Affiliation(s)
- S Schmitt
- Department of Sports and Exercise Science, University of Stuttgart, Allmandring 28, 70569 Stuttgart, Germany.
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Haeufle DFB, Günther M, Blickhan R, Schmitt S. Proof of concept of an artificial muscle: theoretical model, numerical model, and hardware experiment. IEEE Int Conf Rehabil Robot 2012; 2011:5975336. [PMID: 22275541 DOI: 10.1109/icorr.2011.5975336] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE), a parallel damper element (PDE), and a serial element (SE) exhibits operating points with hyperbolic force-velocity dependency. In this paper, the contraction dynamics of this CE concept were analyzed in a numerical simulation of quick release experiments against different loads. A hyperbolic force-velocity relation was found. The results correspond to measurements of the contraction dynamics of a technical prototype. Deviations from the theoretical prediction could partly be explained by the low stiffness of the SE, which was modeled analog to the metal spring in the hardware prototype. The numerical model and hardware prototype together, are a proof of this CE concept and can be seen as a well-founded starting point for the development of Hill-type artificial muscles. This opens up new vistas for the technical realization of natural movements with rehabilitation devices.
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Affiliation(s)
- D F B Haeufle
- Universität Stuttgart, Institut für Sport- und Bewegungswissenschaft, Allmandring 28, D-70569 Stuttgart, Germany.
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Kosterina N, Westerblad H, Eriksson A. History effect and timing of force production introduced in a skeletal muscle model. Biomech Model Mechanobiol 2011; 11:947-57. [PMID: 22203363 DOI: 10.1007/s10237-011-0364-5] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2011] [Accepted: 12/08/2011] [Indexed: 11/25/2022]
Abstract
Skeletal muscle modelling requires a detailed description of muscular force production. We have performed a series of experiments on mouse skeletal muscles to give a basis for an improved description of the muscular force production. Our previous work introduced a force modification in isometric phases, which was based on the work performed by or on the muscle during transient-length-varying contractions. Here, state-space diagrams were used to investigate the timing aspects of the force production. These show a dominant exponential nature of the force development in isometric phases of the contractions, reached after a non-exponential phase, assumed as an activation or deactivation stage and not further analysed here. The time constants of the exponential functions describing isometric force redevelopment after length variations appear to be related to the one for an initial isometric contraction, but depending on the previous history. The timing of force production calculated from the state-space diagrams was in agreement with the generally accepted muscle properties, thereby demonstrating the reliability of the method. A macroscopic muscular model consisting of a contractile element, parallel and series elastic elements was developed. The parameters from the experiment analysis, particularly the force modification after non-isometric contractions and the time constants, were reproduced by the simulations. The relationship between time constants introduced in a mechanistic model and the measured macroscale timings is discussed.
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50
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Grazi E. Muscle mechanism: The acceleration of the load. Arch Biochem Biophys 2010; 504:204-9. [PMID: 20836987 DOI: 10.1016/j.abb.2010.09.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2010] [Revised: 08/31/2010] [Accepted: 09/04/2010] [Indexed: 10/19/2022]
Abstract
The load (force/cross-section) determines the response of muscle power output, force and speed of contraction). The force is the product of the mass by the acceleration, thus the same force is generated by an infinite number of mass and acceleration couples and each one of these couples displays different physical and biological effects. Therefore, the load must be defined both by the mass and by the acceleration. Early muscle investigators were well aware of this situation as it is indicated by the work of Hill on the flexion of the arm against the "heavy fly-wheel". By making use of a model of sarcomere contraction we show here that the acceleration of the load is the first determinant of the time course of the process of generation of the isometric tension. We also propose that, in order to reproduce the rapid release, it is not necessary to invoke the presence of a distinct elastic element in the contractile machinery. It is sufficient to assume that the stiffness of the same machinery increases with the contractile force.
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Affiliation(s)
- Enrico Grazi
- Department of Biochemistry and Molecular Biology, Ferrara University, Italy.
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