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{"title"=>"A fibre-reinforced poroviscoelastic model accurately describes the biomechanical behaviour of the rat achilles tendon", "type"=>"journal", "authors"=>[{"first_name"=>"Hanifeh", "last_name"=>"Khayyeri", "scopus_author_id"=>"35113357400"}, {"first_name"=>"Anna", "last_name"=>"Gustafsson", "scopus_author_id"=>"7102201056"}, {"first_name"=>"Ashley", "last_name"=>"Heuijerjans", "scopus_author_id"=>"56708833400"}, {"first_name"=>"Marko K.", "last_name"=>"Matikainen", "scopus_author_id"=>"35610152400"}, {"first_name"=>"Petro", "last_name"=>"Julkunen", "scopus_author_id"=>"13612636200"}, {"first_name"=>"Pernilla", "last_name"=>"Eliasson", "scopus_author_id"=>"24068298600"}, {"first_name"=>"Per", "last_name"=>"Aspenberg", "scopus_author_id"=>"56249800800"}, {"first_name"=>"Hanna", "last_name"=>"Isaksson", "scopus_author_id"=>"35784623000"}], "year"=>2015, "source"=>"PLoS ONE", "identifiers"=>{"pmid"=>"26030436", "sgr"=>"84934894995", "doi"=>"10.1371/journal.pone.0126869", "scopus"=>"2-s2.0-84934894995", "pui"=>"604922783", "isbn"=>"1939-005X (Electronic)\\r1939-005X (Linking)", "issn"=>"19326203"}, "id"=>"8084bf2e-89d9-3109-8c30-e9afbab8ad1f", "abstract"=>"BACKGROUND: Computational models of Achilles tendons can help understanding how healthy tendons are affected by repetitive loading and how the different tissue constituents contribute to the tendon's biomechanical response. However, available models of Achilles tendon are limited in their description of the hierarchical multi-structural composition of the tissue. This study hypothesised that a poroviscoelastic fibre-reinforced model, previously successful in capturing cartilage biomechanical behaviour, can depict the biomechanical behaviour of the rat Achilles tendon found experimentally.\\n\\nMATERIALS AND METHODS: We developed a new material model of the Achilles tendon, which considers the tendon's main constituents namely: water, proteoglycan matrix and collagen fibres. A hyperelastic formulation of the proteoglycan matrix enabled computations of large deformations of the tendon, and collagen fibres were modelled as viscoelastic. Specimen-specific finite element models were created of 9 rat Achilles tendons from an animal experiment and simulations were carried out following a repetitive tensile loading protocol. The material model parameters were calibrated against data from the rats by minimising the root mean squared error (RMS) between experimental force data and model output.\\n\\nRESULTS AND CONCLUSIONS: All specimen models were successfully fitted to experimental data with high accuracy (RMS 0.42-1.02). Additional simulations predicted more compliant and soft tendon behaviour at reduced strain-rates compared to higher strain-rates that produce a stiff and brittle tendon response. Stress-relaxation simulations exhibited strain-dependent stress-relaxation behaviour where larger strains produced slower relaxation rates compared to smaller strain levels. Our simulations showed that the collagen fibres in the Achilles tendon are the main load-bearing component during tensile loading, where the orientation of the collagen fibres plays an important role for the tendon's viscoelastic response. In conclusion, this model can capture the repetitive loading and unloading behaviour of intact and healthy Achilles tendons, which is a critical first step towards understanding tendon homeostasis and function as this biomechanical response changes in diseased tendons.", "link"=>"http://www.mendeley.com/research/fibrereinforced-poroviscoelastic-model-accurately-describes-biomechanical-behaviour-rat-achilles-ten", "reader_count"=>36, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>1, "Researcher"=>7, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>13, "Student > Master"=>7, "Other"=>1, "Student > Bachelor"=>2, "Lecturer > Senior Lecturer"=>1}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>1, "Researcher"=>7, "Student > Doctoral Student"=>3, "Student > Ph. D. Student"=>13, "Student > Master"=>7, "Other"=>1, "Student > Bachelor"=>2, "Lecturer > Senior Lecturer"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>18, "Unspecified"=>2, "Biochemistry, Genetics and Molecular Biology"=>1, "Nursing and Health Professions"=>1, "Materials Science"=>3, "Agricultural and Biological Sciences"=>2, "Medicine and Dentistry"=>5, "Sports and Recreations"=>2, "Physics and Astronomy"=>1, "Earth and Planetary Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>18}, "Materials Science"=>{"Materials Science"=>3}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>5}, "Sports and Recreations"=>{"Sports and Recreations"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>2}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Unspecified"=>{"Unspecified"=>2}}, "reader_count_by_country"=>{"Finland"=>1}, "group_count"=>0}

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• http://doi.org/10.1016/j.jmbbm.2019.04.041
• http://doi.org/10.1016/j.jbiomech.2019.02.028
• http://doi.org/10.1016/j.jmbbm.2016.04.007
• http://doi.org/10.1007/s10237-016-0774-5
• http://doi.org/10.1038/s41598-018-20739-w
• http://doi.org/10.1016/j.actbio.2018.01.041
• http://doi.org/10.1177/0954411917692010

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Figshare

• {"files"=>["https://ndownloader.figshare.com/files/2089770"], "description"=>"<p><i>E</i>₁, <i>E</i>₂, <i>k</i>₁, <i>k</i>₂ and <i>η</i> are system constants, <i>ε</i>_<i>f</i> stands for the total fibre strain, <i>ε</i>_<i>v</i> is the strain in the dash pot and <i>ε</i>_<i>e</i> is the strain in the spring in the Maxwell element.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431988, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g001", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_An_illustration_of_the_viscoelastic_model_representing_the_collagen_fibres_/1431988", "title"=>"An illustration of the viscoelastic model representing the collagen fibres.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089771"], "description"=>"<p>A) Mesh and boundary conditions. B) The experimental loading protocol cycles 1–3 for all 9 tendons interpolated over 2π for each load cycle (grey). The average loading protocol for cycles 1–3 (red). C) The loading protocols for cycle 1–3 for all 9 tendons in the time-domain (grey) illustrate the variability among experimental specimens. The average loading protocol for cycles 1–3 in time-domain (red).</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431989, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g002", "stats"=>{"downloads"=>5, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_illustrations_/1431989", "title"=>"Model illustrations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089772"], "description"=>"<p>A schematic picture showing the optimisation procedure.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431990, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g003", "stats"=>{"downloads"=>0, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_schematic_picture_showing_the_optimisation_procedure_/1431990", "title"=>"A schematic picture showing the optimisation procedure.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089773"], "description"=>"<p>The new poroviscoelastic model fitted to experimental data from cycle 1–3 of the tensile tests on rat Achilles tendons. The best (A) material model fit (RMS = 0.42) and the worst (B) material model fit (RMS = 1.02).</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431991, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g004", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_calibration_/1431991", "title"=>"Model calibration.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089774"], "description"=>"<p>The optimised result when the material model is fitted to the average tendon model and the average loading protocol. A) Loading cycle 1–3, RMS = 0.84 and B) during later loading cycles (cycle 10–12), RMS = 0.41.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431992, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g005", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_tendon_model_/1431992", "title"=>"Average tendon model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089775"], "description"=>"<p>The strain-stiffening behaviour captured by the poroviscoelastic model where the Achilles tendons subjected to higher strain-rates exhibit a stiffer and more brittle behaviour than when subjected to slower strain-rates.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431993, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g006", "stats"=>{"downloads"=>0, "page_views"=>17, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Strain_stiffening_test_/1431993", "title"=>"Strain-stiffening test.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089777"], "description"=>"<p>Stress-relaxation response of the Achilles tendon, as predicted by the material model. Higher strains result in reduced relaxation compared to lower strain magnitudes (A), and demonstrate a slower relaxation rate, as illustrated in the log-log plot (B).</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431995, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g007", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Stress_relaxation_test_/1431995", "title"=>"Stress-relaxation test.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089778"], "description"=>"<p>A) Model prediction of the creep behaviour in Achilles tendons when subjected to different stress magnitudes. B) The log-log plot shows almost no stress-dependent creep rate behaviour.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431996, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g008", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Creep_test_/1431996", "title"=>"Creep test.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089779"], "description"=>"<p>A) The stress in the collagen fibres and B) the stress in the non-fibrillar matrix, during one load cycle. C) Fluid velocities in the tendon during one load cycle (output from highlighted element at the centre edge of the tendon mesh, see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0126869#pone.0126869.g002\" target=\"_blank\">Fig 2A</a>). The dip in fluid velocity is an effect of the boundary condition, which creates a propagating wave through the tendon.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431997, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.g009", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Contribution_of_tissue_constituents_/1431997", "title"=>"Contribution of tissue constituents.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089780"], "description"=>"<p>The mean (of the 9 optimised tendon models), the standard deviations (SD) and the coefficients of variation (CV) of the specimens are calculated.</p><p>The optimised model parameters for all 9 specimen-specific finite element models based on cycle 1–3.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431998, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.t001", "stats"=>{"downloads"=>6, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_optimised_model_parameters_for_all_9_specimen_specific_finite_element_models_based_on_cycle_1_8211_3_/1431998", "title"=>"The optimised model parameters for all 9 specimen-specific finite element models based on cycle 1–3.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-06-01 02:45:41"}
• {"files"=>["https://ndownloader.figshare.com/files/2089781"], "description"=>"<p>The optimised model parameters for the average tendon model based on cycle 1–3 and 10–12.</p>", "links"=>[], "tags"=>["Achilles tendons", "loading", "material model parameters", "Achilles tendon", "rat Achilles tendon", "collagen fibres", "Rat Achilles Tendon BackgroundComputational models", "simulation", "9 rat Achilles tendons", "proteoglycan matrix", "rms", "ConclusionsAll specimen models", "biomechanical response changes", "understanding tendon homeostasis", "cartilage biomechanical behaviour"], "article_id"=>1431999, "categories"=>["Biological Sciences"], "users"=>["Hanifeh Khayyeri", "Anna Gustafsson", "Ashley Heuijerjans", "Marko K. Matikainen", "Petro Julkunen", "Pernilla Eliasson", "Per Aspenberg", "Hanna Isaksson"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0126869.t002", "stats"=>{"downloads"=>4, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_optimised_model_parameters_for_the_average_tendon_model_based_on_cycle_1_8211_3_and_10_8211_12_/1431999", "title"=>"The optimised model parameters for the average tendon model based on cycle 1–3 and 10–12.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2015-06-01 02:45:41"}

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{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}

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