Fig 1.
Scheme of the constitutive model applied to fibres and bundles.
Separated meshes can better describe both intra- (PE, red finite element regions) and extra- (PECM, blue finite element regions) sarcomeric components of the passive forces in muscle bundles through an extension of the classical Hill’s three-element model. The experimental characterization of the constitutive laws for PE and PECM can be made separately, passively stretching single fibres and small bundles. ECM passive properties can be deduced in an almost physiological situation subtracting from the whole passive tension the single fibre component (see text).
Table 1.
Transversal section areas of bundles.
Transversal section areas of three bundles, estimated from the video camera images assuming a circular cross-sectional area of each fibre and with image analysis on cross cryo-section of the same bundle.
Fig 2.
Fibre stress vs. sarcomere length.
a) Stress vs. sarcomere length experimental data for passive elongation of fast and slow fibres. b) Stress vs. sarcomere length experimental data of pooled fast and slow fibres compared to numerical results obtained by the fitting of Eq (1) proposed in the present work.
Fig 3.
Bundle stress vs. sarcomere length.
Stress vs. sarcomere length experimental data for passive elongation of single fibres and bundles. Fast and slow fibres are grouped together for comparison. Red tones are for fibres, blue ones for bundles (different colour for each sample).
Fig 4.
Cross cryo-section of a bundle.
Cross cryo-section of a bundle not exposed to skinning procedure and mechanical experiment. White colour refers to laminin, blue to slow fibres, green to fast 2A fibres and red to fast 2X fibres.
Fig 5.
Comparison between numerical results and experimental data for bundles.
Comparison between numerical results obtained with Eq (9) and experimental data for bundles in terms of force per unit of bundle area vs. stretch. The contribution of all the fibres (yellow continuous line) and ECM (red continuous line) is shown separately and as combination (dark red continuous line).
Fig 6.
Tangent stiffness vs. sarcomere length.
Tangent stiffness vs. sarcomere length for fibres (sum of fast and slow) and ECM, as obtained by the fitting procedure of Eq (9) to experimental data of bundles. The tangent stiffness is here defined as the slope of the stress vs. sarcomere length curve of the bundles.
Table 2.
Average tangent longitudinal modulus of bundles obtained from Eq (9), fitted to experimental data, at different values of bundle sarcomere length.
Table 3.
Percentage tensile load bearing of ECM and fibres estimated by the fitting of Eq (9) to experimental data.
Fig 7.
Stress vs. sarcomere length experimental data for passive elongation of bundles tested in the present work compared with experimental data on infraspinatus and supraspinatus found by Silldorff et al. [21].