Journal: Biomechanics and Modeling in Mechanobiology

Article Title: On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

doi: 10.1007/s10237-022-01664-4

Figure Lengend Snippet: Overview of the number of experiments realised in this study

Article Snippet: To find an optimal parameter set in terms of the parameter vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{p}}{}=(c_1,c_2, c_3)^T$$\end{document} p = ( c 1 , c , c ) T the objective function was minimised, using the Nelder–Mead simplex algorithm ( fminsearch , matlab \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circledR }$$\end{document} ® R2018a) (Nelder and Mead ; Lagarias et al. ).

Techniques:

Journal: Biomechanics and Modeling in Mechanobiology

Article Title: On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

doi: 10.1007/s10237-022-01664-4

Figure Lengend Snippet: Stress–strain curves of the axial compression tests in dependence on the fibre orientation: a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0^\circ$$\end{document} 0 ∘ , b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$45^\circ$$\end{document} 45 ∘ , and c \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$90^\circ$$\end{document} 90 ∘ . Black curves indicate mean values, the shaded areas depict the standard deviation, and grey curves identify the single measurements

Article Snippet: To find an optimal parameter set in terms of the parameter vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{p}}{}=(c_1,c_2, c_3)^T$$\end{document} p = ( c 1 , c , c ) T the objective function was minimised, using the Nelder–Mead simplex algorithm ( fminsearch , matlab \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circledR }$$\end{document} ® R2018a) (Nelder and Mead ; Lagarias et al. ).

Techniques: Standard Deviation

Journal: Biomechanics and Modeling in Mechanobiology

Article Title: On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

doi: 10.1007/s10237-022-01664-4

Figure Lengend Snippet: Material parameters and error measures determined from various experiments/experiment combinations

Article Snippet: To find an optimal parameter set in terms of the parameter vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{p}}{}=(c_1,c_2, c_3)^T$$\end{document} p = ( c 1 , c , c ) T the objective function was minimised, using the Nelder–Mead simplex algorithm ( fminsearch , matlab \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circledR }$$\end{document} ® R2018a) (Nelder and Mead ; Lagarias et al. ).

Techniques:

Journal: Biomechanics and Modeling in Mechanobiology

Article Title: On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

doi: 10.1007/s10237-022-01664-4

Figure Lengend Snippet: Comparison of the data from the axial compression experiments with the model response (with parameters from the experimental set (iii), see Table ) for a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0^\circ$$\end{document} 0 ∘ , b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$45^\circ$$\end{document} 45 ∘ , and c \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$90^\circ$$\end{document} 90 ∘ . Green curves illustrate the model response, black curves indicate the mean value of the experimental data, and the shaded areas depict the standard deviation

Article Snippet: To find an optimal parameter set in terms of the parameter vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{p}}{}=(c_1,c_2, c_3)^T$$\end{document} p = ( c 1 , c , c ) T the objective function was minimised, using the Nelder–Mead simplex algorithm ( fminsearch , matlab \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circledR }$$\end{document} ® R2018a) (Nelder and Mead ; Lagarias et al. ).

Techniques: Comparison, Standard Deviation

Journal: Biomechanics and Modeling in Mechanobiology

Article Title: On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

doi: 10.1007/s10237-022-01664-4

Figure Lengend Snippet: Error \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {O}}({\varvec{p}}{})$$\end{document} O ( p ) of the different material models when compared with the experimental data, model ability to produce higher stresses in mode III than in mode I (✓: distinction between mode III and mode I, ✗: no distinction between mode III and mode I), and the number of material parameters used in the corresponding model

Article Snippet: To find an optimal parameter set in terms of the parameter vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{p}}{}=(c_1,c_2, c_3)^T$$\end{document} p = ( c 1 , c , c ) T the objective function was minimised, using the Nelder–Mead simplex algorithm ( fminsearch , matlab \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circledR }$$\end{document} ® R2018a) (Nelder and Mead ; Lagarias et al. ).

Techniques:

Journal: Biomechanics and Modeling in Mechanobiology

Article Title: On a three–dimensional model for the description of the passive characteristics of skeletal muscle tissue

doi: 10.1007/s10237-022-01664-4

Figure Lengend Snippet: Comparison of the data from the axial compression experiments with existing models for a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0^\circ$$\end{document} 0 ∘ , b \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$45^\circ$$\end{document} 45 ∘ , and c \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$90^\circ$$\end{document} 90 ∘ . Coloured curves illustrate the model responses, black curves indicate the mean value of the experimental data, and the shaded areas depict the standard deviation

Article Snippet: To find an optimal parameter set in terms of the parameter vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{p}}{}=(c_1,c_2, c_3)^T$$\end{document} p = ( c 1 , c , c ) T the objective function was minimised, using the Nelder–Mead simplex algorithm ( fminsearch , matlab \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circledR }$$\end{document} ® R2018a) (Nelder and Mead ; Lagarias et al. ).

Techniques: Comparison, Standard Deviation