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Deng Z, Zhang Y, Yan S. Mechanism of elastic energy storage of honey bee abdominal muscles under stress relaxation. JOURNAL OF INSECT SCIENCE (ONLINE) 2023; 23:7176136. [PMID: 37220090 DOI: 10.1093/jisesa/iead026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Revised: 03/30/2023] [Accepted: 04/08/2023] [Indexed: 05/25/2023]
Abstract
Energy storage of passive muscles plays an important part in frequent activities of honey bee abdomens due to the muscle distribution and open circulatory system. However, the elastic energy and mechanical properties of structure in passive muscles remain unclear. In this article, stress relaxation tests on passive muscles from the terga of the honey bee abdomens were performed under different concentrations of blebbistatin and motion parameters. In stress relaxation, the load drop with the rapid and slow stages depending on stretching velocity and stretching length reflects the features of myosin-titin series structure and cross-bridge-actin cyclic connections in muscles. Then a model with 2 parallel modules based on the 2 feature structures in muscles was thus developed. The model described the stress relaxation and stretching of passive muscles from honey bee abdomen well for a good fitting in stress relaxation and verification in loading process. In addition, the stiffness change of cross-bridge under different concentrations of blebbistatin is obtained from the model. We derived the elastic deformation of cross-bridge and the partial derivatives of energy expressions on motion parameters from this model, which accorded the experimental results. This model reveals the mechanism of passive muscles from honey bee abdomens suggesting that the temporary energy storage of cross-bridge in terga muscles under abdomen bending provides potential energy for springback during the periodic abdomen bending of honey bee or other arthropod insects. The finding also provides an experimental and theoretical basis for the novel microstructure and material design of bionic muscle.
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Affiliation(s)
- Zhizhong Deng
- Division of Intelligent and Biomechanical Systems, State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, PR China
| | - Yuling Zhang
- Division of Intelligent and Biomechanical Systems, State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, PR China
| | - Shaoze Yan
- Division of Intelligent and Biomechanical Systems, State Key Laboratory of Tribology in Advanced Equipment, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, PR China
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Böl M, Kohn S, Leichsenring K, Morales-Orcajo E, Ehret AE. On multiscale tension-compression asymmetry in skeletal muscle. Acta Biomater 2022; 144:210-220. [PMID: 35339701 DOI: 10.1016/j.actbio.2022.03.034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 03/11/2022] [Accepted: 03/17/2022] [Indexed: 11/17/2022]
Abstract
Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.
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Affiliation(s)
- Markus Böl
- Institute of Mechanics and Adaptronics, Technische Universität Braunschweig, D-38106 Braunschweig, Germany.
| | - Stephan Kohn
- Institute of Mechanics and Adaptronics, Technische Universität Braunschweig, D-38106 Braunschweig, Germany
| | - Kay Leichsenring
- Institute of Mechanics and Adaptronics, Technische Universität Braunschweig, D-38106 Braunschweig, Germany
| | - Enrique Morales-Orcajo
- Institute of Mechanics and Adaptronics, Technische Universität Braunschweig, D-38106 Braunschweig, Germany
| | - Alexander E Ehret
- Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600 Dübendorf, Switzerland; Institute for Mechanical Systems, ETH Zurich, CH-8092, Zürich, Switzerland
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Kohn S, Leichsenring K, Kuravi R, Ehret AE, Böl M. Direct measurement of the direction-dependent mechanical behaviour of skeletal muscle extracellular matrix. Acta Biomater 2021; 122:249-262. [PMID: 33444799 DOI: 10.1016/j.actbio.2020.12.050] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Revised: 12/22/2020] [Accepted: 12/28/2020] [Indexed: 12/19/2022]
Abstract
This paper reports the first comprehensive data set on the anisotropic mechanical properties of isolated endo- and perimysial extracellular matrix of skeletal muscle, and presents the corresponding protocols for preparing and testing the samples. In particular, decellularisation of porcine skeletal muscle is achieved with caustic soda solution, and mechanical parameters are defined based on compressive and tensile testing in order to identify the optimal treatment time such that muscle fibres are dissolved whereas the extracellular matrix remains largely intact and mechanically functional. At around 18 h, a time window was found and confirmed by histology, in which axial tensile experiments were performed to characterise the direction-dependent mechanical response of the extracellular matrix samples, and the effect of lateral pre-compression was studied. The typical, large variability in the experimental stress response could be largely reduced by varying a single scalar factor, which was attributed to the variation of the fraction of extracellular matrix within the tissue. While experimental results on the mechanical properties of intact muscle tissue and single muscle fibres are increasingly available in literature, there is a lack of information on the properties of the collagenous components of skeletal muscle. The present work aims at closing this gap and thus contributes to an improved understanding of the mechanics of skeletal muscle tissue and provides a missing piece of information for the development of corresponding constitutive and computational models.
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Affiliation(s)
- Stephan Kohn
- Institute of Mechanics and Adaptronics, Technische Universität Braunschweig, Braunschweig D-38106, Germany
| | - Kay Leichsenring
- Institute of Mechanics and Adaptronics, Technische Universität Braunschweig, Braunschweig D-38106, Germany
| | - Ramachandra Kuravi
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Dübendorf CH-8600, Switzerland; Institute for Mechanical Systems, ETH Zurich, Zürich CH-8092, Switzerland
| | - Alexander E Ehret
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Dübendorf CH-8600, Switzerland; Institute for Mechanical Systems, ETH Zurich, Zürich CH-8092, Switzerland
| | - Markus Böl
- Institute of Mechanics and Adaptronics, Technische Universität Braunschweig, Braunschweig D-38106, Germany.
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Wheatley BB, Odegard GM, Kaufman KR, Haut Donahue TL. Modeling Skeletal Muscle Stress and Intramuscular Pressure: A Whole Muscle Active-Passive Approach. J Biomech Eng 2019; 140:2682436. [PMID: 30003256 DOI: 10.1115/1.4040318] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Indexed: 11/08/2022]
Abstract
Clinical treatments of skeletal muscle weakness are hindered by a lack of an approach to evaluate individual muscle force. Intramuscular pressure (IMP) has shown a correlation to muscle force in vivo, but patient to patient and muscle to muscle variability results in difficulty of utilizing IMP to estimate muscle force. The goal of this work was to develop a finite element model of whole skeletal muscle that can predict IMP under passive and active conditions to further investigate the mechanisms of IMP variability. A previously validated hypervisco-poroelastic constitutive approach was modified to incorporate muscle activation through an inhomogeneous geometry. Model parameters were optimized to fit model stress to experimental data, and the resulting model fluid pressurization data were utilized for validation. Model fitting was excellent (root-mean-square error or RMSE <1.5 kPa for passive and active conditions), and IMP predictive capability was strong for both passive (RMSE 3.5 mmHg) and active (RMSE 10 mmHg at in vivo lengths) conditions. Additionally, model fluid pressure was affected by length under isometric conditions, as increases in stretch yielded decreases in fluid pressurization following a contraction, resulting from counteracting Poisson effects. Model pressure also varied spatially, with the highest gradients located near aponeuroses. These findings may explain variability of in vivo IMP measurements in the clinic, and thus help reduce this variability in future studies. Further development of this model to include isotonic contractions and muscle weakness would greatly benefit this work.
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Affiliation(s)
- Benjamin B Wheatley
- Department of Mechanical Engineering, Bucknell University, 1 Dent Drive, Lewisburg, PA 17837 e-mail:
| | - Gregory M Odegard
- Department of Mechanical Enginering- Engineering Mechanics, Department of Materials Science and Engineering, Michigan Technological University, , Houghton, MI 49931
| | - Kenton R Kaufman
- Department of Orthopedic Surgery, Department of Physiology and Biomedical Engineering Mayo Clinic, , Rochester, MN 55906
| | - Tammy L Haut Donahue
- Department of Mechanical Engineering, School of Biomedical Engineering, Colorado State University, , Fort Collins, CO 80523
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Tamura A, Hongu JI, Matsumoto T. Theoretical elastic tensile behavior of muscle fiber bundles in traumatic loading events. Clin Biomech (Bristol, Avon) 2019; 69:184-190. [PMID: 31376809 DOI: 10.1016/j.clinbiomech.2019.07.021] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/20/2018] [Revised: 07/09/2019] [Accepted: 07/22/2019] [Indexed: 02/07/2023]
Abstract
BACKGROUND The mechanical characterization of skeletal muscle under high-rate loading regimes is important for predicting traumatic injuries due to traffic accidents and contact sports. However, it is difficult to perform dynamic mechanical tests at rates relevant to such rapid loading events. METHODS In the present study, a series of stress relaxation tests were conducted on rabbit hind-limb muscle fiber bundles using a custom tensile tester. Using relatively moderate loading conditions compared to those typically associated with traumatic injuries, the passive stress-decaying mechanical properties of muscle fiber bundles were characterized. In addition, stress relaxation responses to various ramp-hold stretches were theoretically predicted by a custom-built code. FINDINGS The results showed that the muscle fiber bundles exhibit greater stress relaxation at higher loading rates and greater stretch magnitudes. Based on these results, the data points representing the "elastic" stress-strain tensile behavior typical of traumatic injury were extrapolated using curve fitting. The theoretical model revealed rate-dependent characteristics of the muscle fiber bundles under traumatic loading conditions, which would result in tensile strengths of 300-500 kPa at the maximum engineering strain of 54%. This strength is on the order of magnitude as the maximum isometric stress of an active muscle contraction. INTERPRETATION The proposed numerical model is expected to serve as a powerful research tool to investigate injury mechanisms of the skeletal muscle. Moreover, the elastic response that was theoretically predicted here will be useful in the development of effective countermeasures to prevent traumatic injuries due to rapid loading events.
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Affiliation(s)
- Atsutaka Tamura
- Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan; Tottori University, Koyama-minami, Tottori, Tottori 680-8552, Japan.
| | - Jun-Ichi Hongu
- Tottori University, Koyama-minami, Tottori, Tottori 680-8552, Japan
| | - Takeo Matsumoto
- Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan; Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
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6
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Mechanical and microstructural changes of skeletal muscle following immobilization and/or stroke. Biomech Model Mechanobiol 2019; 19:61-80. [DOI: 10.1007/s10237-019-01196-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Accepted: 06/26/2019] [Indexed: 11/27/2022]
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Jalal N, Zidi M. Influence of experimental conditions on visco-hyperelastic properties of skeletal muscle tissue using a Box-Behnken design. J Biomech 2019; 85:204-209. [PMID: 30732908 DOI: 10.1016/j.jbiomech.2019.01.020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2018] [Revised: 01/01/2019] [Accepted: 01/08/2019] [Indexed: 10/27/2022]
Abstract
The Mechanical characterization of skeletal muscles is strongly dependent on numerous experimental design factors. Nevertheless, significant knowledge gaps remain on the characterization of muscle mechanics and a large number of experiments should be implemented to test the influence of a large number of factors. In this study, we propose a design of experiment method (DOE) to study the parameter sensitivity while minimizing the number of tests. A Box-Behnken design was then implemented to study the influence of strain rate, preconditioning and preloading conditions on visco-hyperelastic mechanical parameters of two rat forearm muscles. The results show that the strain rate affects the visco-hyperelastic parameters for both muscles. These results are consistent with previous work demonstrating that stiffness and viscoelastic contributions increase with strain rate. Thus, DOE has been shown to be a valid method to determine the effect of the experimental conditions on the mechanical behaviour of biological tissues such as skeletal muscle. This method considerably reduces the number of experiments. Indeed, the presented study using 3 parameters at 3 levels would have required at least 54 tests per muscle against 14 for the proposed DOE method.
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Affiliation(s)
- Naïm Jalal
- Bioengineering, Tissues and Neuroplasticity, EA 7377, Université Paris-Est Créteil, Faculté de Médecine, 8 rue du Général Sarrail, 94010 Créteil, France
| | - Mustapha Zidi
- Bioengineering, Tissues and Neuroplasticity, EA 7377, Université Paris-Est Créteil, Faculté de Médecine, 8 rue du Général Sarrail, 94010 Créteil, France.
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Jalal N, Zidi M. Effect of cryopreservation at −80 °C on visco-hyperelastic properties of skeletal muscle tissue. J Mech Behav Biomed Mater 2018; 77:572-577. [DOI: 10.1016/j.jmbbm.2017.10.006] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Revised: 09/25/2017] [Accepted: 10/02/2017] [Indexed: 11/26/2022]
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Wheatley BB, Odegard GM, Kaufman KR, Haut Donahue TL. A validated model of passive skeletal muscle to predict force and intramuscular pressure. Biomech Model Mechanobiol 2016; 16:1011-1022. [PMID: 28040867 DOI: 10.1007/s10237-016-0869-z] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2016] [Accepted: 12/19/2016] [Indexed: 02/02/2023]
Abstract
The passive properties of skeletal muscle are often overlooked in muscle studies, yet they play a key role in tissue function in vivo. Studies analyzing and modeling muscle passive properties, while not uncommon, have never investigated the role of fluid content within the tissue. Additionally, intramuscular pressure (IMP) has been shown to correlate with muscle force in vivo and could be used to predict muscle force in the clinic. In this study, a novel model of skeletal muscle was developed and validated to predict both muscle stress and IMP under passive conditions for the New Zealand White Rabbit tibialis anterior. This model is the first to include fluid content within the tissue and uses whole muscle geometry. A nonlinear optimization scheme was highly effective at fitting model stress output to experimental stress data (normalized mean square error or NMSE fit value of 0.993) and validation showed very good agreement to experimental data (NMSE fit values of 0.955 and 0.860 for IMP and stress, respectively). While future work to include muscle activation would broaden the physiological application of this model, the passive implementation could be used to guide surgeries where passive muscle is stretched.
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Affiliation(s)
- Benjamin B Wheatley
- Department of Mechanical Engineering, Colorado State University, 1374 Campus Delivery, Fort Collins, CO, 80523, USA
| | - Gregory M Odegard
- Department of Mechanical Engineering - Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI, 49931, USA
| | - Kenton R Kaufman
- Department of Orthopedic Surgery, Mayo Clinic, First Street SW, Rochester, MN, 55905, USA
| | - Tammy L Haut Donahue
- Department of Mechanical Engineering, School of Biomedical Engineering, Colorado State University, 1374 Campus Delivery, Fort Collins, CO, 80523, USA.
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10
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Böl M, Leichsenring K, Ernst M, Ehret AE. Long-term mechanical behaviour of skeletal muscle tissue in semi-confined compression experiments. J Mech Behav Biomed Mater 2016; 63:115-124. [DOI: 10.1016/j.jmbbm.2016.06.012] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2016] [Revised: 06/02/2016] [Accepted: 06/09/2016] [Indexed: 10/21/2022]
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11
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Wheatley BB, Odegard GM, Kaufman KR, Donahue TLH. How does tissue preparation affect skeletal muscle transverse isotropy? J Biomech 2016; 49:3056-3060. [PMID: 27425557 DOI: 10.1016/j.jbiomech.2016.06.034] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Revised: 06/27/2016] [Accepted: 06/27/2016] [Indexed: 11/19/2022]
Abstract
The passive tensile properties of skeletal muscle play a key role in its physiological function. Previous research has identified conflicting reports of muscle transverse isotropy, with some data suggesting the longitudinal direction is stiffest, while others show the transverse direction is stiffest. Accurate constitutive models of skeletal muscle must be employed to provide correct recommendations for and observations of clinical methods. The goal of this work was to identify transversely isotropic tensile muscle properties as a function of post mortem handling. Six pairs of tibialis anterior muscles were harvested from Giant Flemish rabbits and split into two groups: fresh testing (within four hours post mortem), and non-fresh testing (subject to delayed testing and a freeze/thaw cycle). Longitudinal and transverse samples were removed from each muscle and tested to identify tensile modulus and relaxation behavior. Longitudinal non-fresh samples exhibited a higher initial modulus value and faster relaxation than longitudinal fresh, transverse fresh, and transverse rigor samples (p<0.05), while longitudinal fresh samples were less stiff at lower strain levels than longitudinal non-fresh, transverse fresh, and transverse non-fresh samples (p<0.05), but exhibited more nonlinear behavior. While fresh skeletal muscle exhibits a higher transverse modulus than longitudinal modulus, discrepancies in previously published data may be the result of a number of differences in experimental protocol. Constitutive modeling of fresh muscle should reflect these data by identifying the material as truly transversely isotropic and not as an isotropic matrix reinforced with fibers.
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Affiliation(s)
- Benjamin B Wheatley
- Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA
| | - Gregory M Odegard
- Department of Mechanical Engineering - Engineering Mechanics, Michigan Technological University, Houghton, MI, USA
| | - Kenton R Kaufman
- Department of Orthopedic Surgery, Mayo Clinic, Rochester, MN, USA
| | - Tammy L Haut Donahue
- Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA; School of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA.
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12
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Wheatley BB, Pietsch RB, Haut Donahue TL, Williams LN. Fully non-linear hyper-viscoelastic modeling of skeletal muscle in compression. Comput Methods Biomech Biomed Engin 2015; 19:1181-9. [PMID: 26652761 DOI: 10.1080/10255842.2015.1118468] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Abstract
Understanding the behavior of skeletal muscle is critical to implementing computational methods to study how the body responds to compressive loading. This work presents a novel approach to studying the fully nonlinear response of skeletal muscle in compression. Porcine muscle was compressed in both the longitudinal and transverse directions under five stress relaxation steps. Each step consisted of 5% engineering strain over 1 s followed by a relaxation period until equilibrium was reached at an observed change of 1 g/min. The resulting data were analyzed to identify the peak and equilibrium stresses as well as relaxation time for all samples. Additionally, a fully nonlinear strain energy density-based Prony series constitutive model was implemented and validated with independent constant rate compressive data. A nonlinear least squares optimization approach utilizing the Levenberg-Marquardt algorithm was implemented to fit model behavior to experimental data. The results suggested the time-dependent material response plays a key role in the anisotropy of skeletal muscle as increasing strain showed differences in peak stress and relaxation time (p < 0.05), but changes in equilibrium stress disappeared (p > 0.05). The optimizing procedure produced a single set of hyper-viscoelastic parameters which characterized compressive muscle behavior under stress relaxation conditions. The utilized constitutive model was the first orthotropic, fully nonlinear hyper-viscoelastic model of skeletal muscle in compression while maintaining agreement with constitutive physical boundaries. The model provided an excellent fit to experimental data and agreed well with the independent validation in the transverse direction.
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Affiliation(s)
- Benjamin B Wheatley
- a Soft Tissue Mechanics Laboratory, Department of Mechanical Engineering , Colorado State University , Fort Collins , CO , USA
| | - Renée B Pietsch
- b Injury Biomechanics Laboratory, Department of Agricultural and Biological Engineering , Mississippi State University , Starkville , MS , USA
| | - Tammy L Haut Donahue
- a Soft Tissue Mechanics Laboratory, Department of Mechanical Engineering , Colorado State University , Fort Collins , CO , USA
| | - Lakiesha N Williams
- b Injury Biomechanics Laboratory, Department of Agricultural and Biological Engineering , Mississippi State University , Starkville , MS , USA
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13
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Wheatley BB, Morrow DA, Odegard GM, Kaufman KR, Haut Donahue TL. Skeletal muscle tensile strain dependence: Hyperviscoelastic nonlinearity. J Mech Behav Biomed Mater 2015; 53:445-454. [PMID: 26409235 DOI: 10.1016/j.jmbbm.2015.08.041] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Revised: 08/21/2015] [Accepted: 08/31/2015] [Indexed: 11/17/2022]
Abstract
INTRODUCTION Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain. MATERIALS AND METHODS Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components. RESULTS Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately. CONCLUSIONS Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model.
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Affiliation(s)
- Benjamin B Wheatley
- Soft Tissue Mechanics Laboratory, Department of Mechanical Engineering, Colorado State University, 1374 Campus Delivery, Fort Collins, CO 80523, United States
| | - Duane A Morrow
- Motion Analysis Laboratory, Department of Orthopedic Surgery, Mayo Clinic, 200 First Street SW, Rochester, MN 55906, United States
| | - Gregory M Odegard
- Department of Mechanical Engineering - Engineering Mechanics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, United States
| | - Kenton R Kaufman
- Motion Analysis Laboratory, Department of Orthopedic Surgery, Mayo Clinic, 200 First Street SW, Rochester, MN 55906, United States
| | - Tammy L Haut Donahue
- Soft Tissue Mechanics Laboratory, Department of Mechanical Engineering, Colorado State University, 1374 Campus Delivery, Fort Collins, CO 80523, United States; School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, United States.
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14
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Calvo B, Sierra M, Grasa J, Muñoz M, Peña E. Determination of passive viscoelastic response of the abdominal muscle and related constitutive modeling: Stress-relaxation behavior. J Mech Behav Biomed Mater 2014; 36:47-58. [DOI: 10.1016/j.jmbbm.2014.04.006] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2014] [Revised: 04/02/2014] [Accepted: 04/09/2014] [Indexed: 10/25/2022]
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15
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Böl M, Ehret AE, Leichsenring K, Weichert C, Kruse R. On the anisotropy of skeletal muscle tissue under compression. Acta Biomater 2014; 10:3225-34. [PMID: 24636829 DOI: 10.1016/j.actbio.2014.03.003] [Citation(s) in RCA: 62] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2013] [Revised: 02/18/2014] [Accepted: 03/04/2014] [Indexed: 11/28/2022]
Abstract
This paper deals with the role of the muscle fibres and extracellular matrix (ECM) components when muscle tissue is subjected to compressive loads. To this end, dissected tissue samples were tested in compression modes which induced states of fibres in compression (I), in tension (II) or at constant length (III), respectively. A comparison of the stress responses indicated that the tissue behaviour is significantly different for these modes, including differences between the modes (I) and (III). This contradicts the paradigm of many constitutive models that the stress response can be decomposed into an isotropic part relating to the ECM and an anisotropic fibre part the contribution of which can be neglected under compression. Conversely, the results provide experimental evidence that there is an anisotropic contribution of the fibre direction to the compressive stress. Interpreting these results in terms of recent microscopical studies, potential connections between the observed behaviour and the structure of muscle ECM are established.
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Affiliation(s)
- Markus Böl
- Institute of Solid Mechanics, Technische Universität Braunschweig, 38106 Braunschweig, Germany.
| | - Alexander E Ehret
- Institute of Solid Mechanics, Technische Universität Braunschweig, 38106 Braunschweig, Germany; Institute of Mechanical Systems, ETH Zurich, 8092 Zurich, Switzerland
| | - Kay Leichsenring
- Institute of Solid Mechanics, Technische Universität Braunschweig, 38106 Braunschweig, Germany
| | - Christine Weichert
- Institute of Solid Mechanics, Technische Universität Braunschweig, 38106 Braunschweig, Germany
| | - Roland Kruse
- Institute of Solid Mechanics, Technische Universität Braunschweig, 38106 Braunschweig, Germany
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