Uniaxial and biaxial mechanical properties of porcine linea alba.

Incisional hernia is a severe complication post-laparoscopic/laparotomy surgery that is commonly associated with the linea alba. However, the few studies on the mechanical properties of the linea alba in the literature appear contradictory, possible due to challenges with the physical dimensions of samples and variations in protocol. This study focuses on the tensile mechanical characterisation of the porcine linea alba, as determined by uniaxial and equi-load biaxial testing using image-based strain measurement methods. Results show that the linea alba demonstrated a non-linear elastic, anisotropic behaviour which is often observed in biological soft tissues. The transverse direction (parallel to fibres) was found to be approximately eight times stiffer than the longitudinal (cross-fibre) direction under both uniaxial and equi-load biaxial loading. The equi-load biaxial tensile tests revealed that contraction could occur in the transverse direction despite increasing load, probably due to the anisotropy of the tissue. Optical surface marker tracking and digital image correlation methods were found to greatly improve the accuracy of stretch measurement, resulting in a 75% change in the apparent stiffness compared to using strain derived from machine cross-head displacement. Additionally, a finite element model of the experiments using a combination of an Ogden and fibre exponential power law model for the linea alba was implemented to quantify the effect of clamping and tissue dimensions (which are suboptimal for tensile testing) on the results. The preliminary model results were used to apply a correction factor to the uniaxial experimental data prior to inverse optimisation to derive best fit material parameters for the fibre reinforced Ogden model. Application of the model to the equi-load biaxial case showed some differences compared to the experimental data, suggesting a more complex anisotropic model may be necessary to capture biaxial behaviour. These results provide an improved assessment of the mechanical properties of the porcine linea alba for wound closure and other studies.

Assessing the microstructural response to applied deformation in porcine passive skeletal muscle.

The passive micro-structural mechanical response of muscle tissue is important for numerous medical applications. However, the recently observed tension/compression asymmetry in porcine muscle remains poorly explained. In particular there remains a lack of understanding of how external tension or compression applied in the fibre or cross-fibre direction translates internally to deformation of muscle fibres and the extra-cellular matrix. Accordingly, fresh porcine skeletal muscle tissue was harvested, deformed by 30% in uniaxial tension or compression in both the fibre and cross-fibre directions and prepared for optical microscope, polarised light microscope and SEM analysis. The average deformed specimen results were compared to the average control results in each case. For compressive or tensile stretch applied in the muscle fibre direction the average measured muscle fibre cross-sectional area changes are in close correspondence with predictions based on global Poisson's ratio measurements and these deformation modes did not cause shape changes in the muscle fibre cross-sections. However, muscle tissue reacted to the applied cross-fibre direction deformations as follows: compression flattened muscle fibre cross-sections, aligning them perpendicular to the direction of the applied deformation while tensile deformations stretched the cross-sections of muscle fibres, aligning them parallel to the direction of applied deformation. No evidence of structural reorganisation of endomysium collagen fibres in response to applied stretch was observed. The observed micro-structural responses do not appear to be influenced by the surrounding endomysium, but appear to be significantly influenced by proximity to the perimysium network. It is hypothesised that the perimysium and its interaction with the surrounding muscle fibres is therefore likely to be predominantly responsible for the tension/compression asymmetry observed in macroscopic tests of passive skeletal muscle stress strain behaviour.

Passive skeletal muscle response to impact loading: experimental testing and inverse modelling.

Appropriate mechanical representation of passive muscle tissue is crucial for human body impact modelling. In this paper the experimental and modelling results of compressive loading of freshly slaughtered porcine muscle samples using a drop-tower testing rig are reported. Fibre and cross-fibre compression tests at strain rates varying from 11,600%/s to 37,800%/s were performed. Experimental results show a nonlinear stress-stretch relationship as well as a clear rate dependency of the stress. The mean (standard deviation) engineering stress in the fibre direction at a stretch of 0.7 was 22.47 kPa (5.34 kPa) at a strain rate of 22,000%/s and 38.11k Pa (5.41 kPa) at a strain rate of 37,800%/s. For the cross-fibre direction, the engineering stresses were 5.95 kPa (1.12 kPa) at a strain rate of 11,600%/s, 25.52 kPa (5.12 kPa) at a strain rate of 22,000%/s and 43.66 kPa (6.62 kPa) at a strain rate of 37,800%/s. Significant local strain variations were observed, as well as an average mass loss of 8% due to fluid exudation, highlighting the difficulties in these kinds of tests. The inverse analysis shows for the first time that the mechanical response in terms of both applied load and tissue deformation for each of the strain rates can be captured using a 1st order Ogden hyperelastic material law extended with a three-term quasilinear viscoelastic (QVL) expansion to model viscoelastic effects. An optimisation procedure was used to derive optimal material parameters for which the error in the predicted boundary condition force at maximum compression was less than 3% for all three rates of testing (11,600%/s, 22,000%/s and 37,800%/s). This model may be appropriate for whole body impact modelling at these rates.

A structural model of passive skeletal muscle shows two reinforcement processes in resisting deformation.

Passive skeletal muscle derives its structural response from the combination of the titin filaments in the muscle fibres, the collagen fibres in the connective tissue and incompressibility due to the high fluid content. Experiments have shown that skeletal muscle tissue presents a highly asymmetrical three-dimensional behaviour when passively loaded in tension or compression, but structural models predicting this are not available. The objective of this paper is to develop a mathematical model to study the internal mechanisms which resist externally applied deformation in skeletal muscle bulk. One cylindrical muscle fibre surrounded by connective tissue was considered. The collagenous fibres of the endomysium and perimysium were grouped and modelled as tension-only oriented wavy helices wrapped around the muscle fibre. The titin filaments are represented as non-linear tension-only springs. The model calculates the force developed by the titin molecules and the collagen network when the muscle fibre undergoes an isochoric along-fibre stretch. The model was evaluated using a range of literature based input parameters and compared to the experimental fibre-direction stress-stretch data available. Results show the fibre direction non-linearity and tension/compression asymmetry are partially captured by this structural model. The titin filament load dominates at low tensile stretches, but for higher stretches the collagen network was responsible for most of the stiffness. The oblique and initially wavy collagen fibres account for the non-linear tensile response since, as the collagen fibres are being recruited, they straighten and re-orient. The main contribution of the model is that it shows that the overall compression/tension response is strongly influenced by a pressure term induced by the radial component of collagen fibre stretch acting on the incompressible muscle fibre. Thus for along-fibre tension or compression the model predicts that the collagen network contributes to overall muscle stiffness through two different mechanisms: (1) a longitudinal force directly opposing tension and (2) a pressure force on the muscle fibres resulting in an indirect longitudinal load. Although the model presented considers only a single muscle fibre and evaluation is limited to along-fibre loading, this is the first model to propose these two internal mechanisms for resisting externally applied deformation of skeletal muscle tissue.

The anisotropic mechanical behaviour of passive skeletal muscle tissue subjected to large tensile strain.

The passive mechanical properties of muscle tissue are important for many biomechanics applications. However, significant gaps remain in our understanding of the three-dimensional tensile response of passive skeletal muscle tissue to applied loading. In particular, the nature of the anisotropy remains unclear and the response to loading at intermediate fibre directions and the Poisson's ratios in tension have not been reported. Accordingly, tensile tests were performed along and perpendicular to the muscle fibre direction as well as at 30°, 45° and 60° to the muscle fibre direction in samples of Longissimus dorsi muscle taken from freshly slaughtered pigs. Strain was measured using an optical non-contact method. The results show the transverse or cross fibre (TT') direction is broadly linear and is the stiffest (77 kPa stress at a stretch of 1.1), but that failure occurs at low stretches (approximately λ=1.15). In contrast the longitudinal or fibre direction (L) is nonlinear and much less stiff (10 kPa stress at a stretch of 1.1) but failure occurs at higher stretches (approximatelyλ=1.65). An almost sinusoidal variation in stress response was observed at intermediate angles. The following Poisson's ratios were measured: VLT=VLT'=0.47, VTT'=0.28 and VTL=0.74. These observations have not been previously reported and they contribute significantly to our understanding of the three dimensional deformation response of skeletal muscle tissue.

The fracture toughness of soft tissues.

Fracture toughness is important for any material, but to date there have been few investigations of this mechanical property in soft mammalian tissues. This paper presents new data on porcine muscle tissue and a detailed analysis of all previous work. The conclusion is that, in most cases, fracture toughness has not in fact been measured for these tissues. Reanalysis of the previous work shows that failure of the test specimens generally occurred at the material's ultimate strength, implying that no information about toughness can be obtained from the results. This finding applied to work on cartilage, artificial neocartilage, muscle and the TMJ disc. Our own data, which was also found to be invalid, gave measured fracture toughness values which were highly variable and showed a strong dependence on the crack growth increment. The net-section failure stress and failure energy were relatively constant in large specimens, independent of crack length, whilst for smaller specimens they showed a strong size effect. These findings are explained by the fact that the process zone size, estimated here using the critical distance parameter L, was similar to, or larger than, critical specimen dimensions (crack length and specimen width). Whilst this analysis casts doubt on much of the published literature, a useful finding is that soft tissues are highly tolerant of defects, able to withstand the presence of cracks several millimetres in length without significant loss of strength.