Control of Tension-Compression Asymmetry in Ogden Hyperelasticity with Application to Soft Tissue Modelling

This paper discusses tension-compression asymmetry properties of Ogden hyperelastic formulations. It is shown that if all negative or all positive Ogden coefficients are used, tension-compression asymmetry occurs the degree of which cannot be separately controlled from the degree of non-linearity. A simple hybrid form is therefore proposed providing separate control over the tension-compression asymmetry. It is demonstrated how this form relates to a newly introduced generalised strain tensor class which encompasses both the tension-compression asymmetric Seth-Hill strain class and the tension-compression symmetric Ba\v{z}ant strain class. If the control parameter is set to q=0.5 a tension-compression symmetric form involving Ba\v{z}ant strains is obtained with the property {\Psi}({\lambda}_1,{\lambda}_2,{\lambda}_3 )={\Psi}(1/{\lambda}_1 ,1/{\lambda}_2 ,1/{\lambda}_3 ). The symmetric form may be desirable for the definition of ground matrix contributions in soft tissue modelling allowing all deviation from the symmetry to stem solely from fibrous reinforcement. Such an application is also presented demonstrating the use of the proposed formulation in the modelling of the non-linear elastic and transversely isotropic behaviour of skeletal muscle tissue in compression (the model implementation and fitting procedure have been made freely available). The presented hyperelastic formulations may aid researchers in independently controlling the degree of tension-compression asymmetry from the degree of non-linearity, and in the case of anisotropic materials may assist in determining the role played by, either the ground matrix, or the fibrous reinforcing structures, in generating asymmetry.Comment: 20 page

A continuum model for tension-compression asymmetry in skeletal muscle

[EN] Experiments on passive skeletal muscle on different species show a strong asymmetry in the observed tension-compression mechanical behavior. This asymmetry shows that the tension modulus is two orders of magnitude higher than the compression modulus. Until now, traditional analytical constitutive models have been unable to capture that strong asymmetry in anisotropic solids using the same material parameters. In this work we present a model which is able to accurately capture five experimental tests in chicken pectoralis muscle, including the observed tension-compression asymmetry. However, aspects of the anisotropy of the tissue are not captured by the model.Partial financial support for this work has been given by grant DPI2015-69801-R from the Direccion General de Proyectos de Investigacion of the Ministerio de Economia y Competitividad of Spain. FJM also acknowledges the support of the Department of Mechanical and Aerospace Engineering of University of Florida during the sabbatical period in which this paper was completed and Ministerio de Educacion, Cultura y Deporte of Spain for the financial support for that stay under grant PRX15/00065Latorre, M.; Mohammadkhah, M.; Simms, CK.; Montáns, FJ. (2018). A continuum model for tension-compression asymmetry in skeletal muscle. Journal of the Mechanical Behavior of Biomedical Materials. 77:455-460. https://doi.org/10.1016/j.jmbbm.2017.09.0124554607

Concussion in Rugby Union and the Role of Biomechanics

Due to the physical and high-impact nature of rugby, head impacts can occur within the game which can result in concussion injuries as well as other moderate-to-severe head injuries 1. Concussion has been defined as “a complex pathophysiological process affecting the brain, induced by traumatic biomechanical forces”1 and was found to be one of the more common brain injuries throughout the world.2 This is particularly true in sport; it has been estimated that over half of all concussions are sports related.3 A systematic review of the incidence of concussion in contact sports found that rugby union has a higher incidence rate compared with other sports such as American football and soccer.4 Unlike other sports injuries, detecting a concussion is difficult as the neuropathological changes cannot be recognized on standard neuroimaging technology.5,6 \Therefore, if a player is suspected of having a concussion, they are removed from play for a Head Injury Assessment (HIA). The HIA is a standardized tool for the medical assessment of concussion injuries in rugby and aims to improve detection and patient education.7 The HIA assesses a range of degenerative concussive symptoms including memory, cognitive ability, balance and player discomfort. This concussion diagnosis protocol therefore relies heavily on side-line medical staff to identify if a player is exhibiting concussive symptoms. A major disadvantage to this is that concussion has a variable natural history, with transient, fluctuating, delayed and evolving signs or symptoms.8) This means that symptoms can take up to 48 hours to become apparent.8 It has therefore been acknowledged that the content of the HIA will be modified as the research around concussion diagnosis evolves.8 The reliance on side-line medical staff to accurately identify concussive symptoms means that there is a possibility a concussed player may remain on the field; this is one problem that biomechanical research into concussion is trying to overcome.  This study will give an overview of concussion in rugby union with a focus on incidence, severity and protection strategies. It will discuss current biomechanical research and further biomechanical research required in the area of concussion injuries in rugby union

Analysis of ball carrier head motion during a rugby union tackle without direct head contact: A case study

Rugby union players can be involved in many tackles per game. However, little is known of the regular head loading environment associated with tackling in rugby union. In particular, the magnitude and influencing factors for head kinematics during the tackle are poorly understood. Accordingly, the goal of this study was to measure head motion of a visually unaware ball carrier during a real game tackle to the upper trunk with no direct head contact, and compare the kinematics with previously reported concussive events. Model-Based Image-Matching was utilised to measure ball carrier head linear and angular velocities. Ball carrier componential maximum change in head angular velocities of 38.1, 20.6 and 13.5 rad/s were measured for the head local X (coronal plane), Y (sagittal plane) and Z (transverse plane) axes respectively. The combination of a high legal tackle height configuration and visually unaware ball carrier can lead to kinematics similar to average values previously reported for concussive direct head impacts

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 tissu