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Anssari-Benam A, Saccomandi G. Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue. J Biomech Eng 2024; 146:091009. [PMID: 38581377 DOI: 10.1115/1.4065271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Accepted: 04/03/2024] [Indexed: 04/08/2024]
Abstract
The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.
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Affiliation(s)
- Afshin Anssari-Benam
- Cardiovascular Engineering Research Lab (CERL), School of Mechanical and Design Engineering, University of Portsmouth, Anglesea Road, Portsmouth PO1 3DJ, UK
| | - Giuseppe Saccomandi
- Dipartimento di Ingegneria, Universita degli studi di Perugia, Via G. Duranti, Perugia 06125, Italy
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Liu Q, Zhang HL, Zhang YL, Wang S, Feng XQ, Li K, Zhang CQ. Strain rate-dependent failure mechanics of the intervertebral disc under tension/compression and constitutive analysis. Med Eng Phys 2024; 127:104158. [PMID: 38692761 DOI: 10.1016/j.medengphy.2024.104158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Revised: 03/17/2024] [Accepted: 03/22/2024] [Indexed: 05/03/2024]
Abstract
BACKGROUND The intervertebral disc exhibits not only strain rate dependence (viscoelasticity), but also significant asymmetry under tensile and compressive loads, which is of great significance for understanding the mechanism of lumbar disc injury under physiological loads. OBJECTIVE In this study, the strain rate sensitive and tension-compression asymmetry of the intervertebral disc were analyzed by experiments and constitutive equation. METHOD The Sheep intervertebral disc samples were divided into three groups, in order to test the strain rate sensitive mechanical behavior, and the internal displacement as well as pressure distribution. RESULTS The tensile stiffness is one order of magnitude smaller than the compression stiffness, and the logarithm of the elastic modulus is approximately linear with the logarithm of the strain rate, showing obvious tension-compression asymmetry and rate-related characteristics. In addition, the sensitivity to the strain rate is the same under these two loading conditions. The stress-strain curves of unloading and loading usually do not coincide, and form a Mullins effect hysteresis loop. The radial displacement distribution is opposite between the anterior and posterior region, which is consistent with the stress distribution. By introducing the damage factor into ZWT constitutive equation, the rate-dependent viscoelastic and weakening behavior of the intervertebral disc can be well described.
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Affiliation(s)
- Qing Liu
- Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China; National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China; Department of Mechanics, Tianjin University, Tianjin, 300354, China; Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, 300354, China
| | - Han-Lin Zhang
- Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China; National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China
| | - Yu-Lin Zhang
- Sinopec Zhenhai Refining & Chemical Company, Ningbo, 315200, China
| | - Shuo Wang
- Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China; National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China
| | - Xiao-Qing Feng
- Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China; National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China
| | - Kun Li
- Tianjin Key Laboratory of Film Electronic and Communication Device, Tianjin University of Technology, Tianjin, 300384, China.
| | - Chun-Qiu Zhang
- Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China; National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China.
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Durcan C, Hossain M, Chagnon G, Perić D, Girard E. Characterization of the layer, direction and time-dependent mechanical behaviour of the human oesophagus and the effects of formalin preservation. J R Soc Interface 2024; 21:20230592. [PMID: 38593841 PMCID: PMC11003784 DOI: 10.1098/rsif.2023.0592] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 03/05/2024] [Indexed: 04/11/2024] Open
Abstract
The mechanical characterization of the oesophagus is essential for applications such as medical device design, surgical simulations and tissue engineering, as well as for investigating the organ's pathophysiology. However, the material response of the oesophagus has not been established ex vivo in regard to the more complex aspects of its mechanical behaviour using fresh, human tissue: as of yet, in the literature, only the hyperelastic response of the intact wall has been studied. Therefore, in this study, the layer-dependent, anisotropic, visco-hyperelastic behaviour of the human oesophagus was investigated through various mechanical tests. For this, cyclic tests, with increasing stretch levels, were conducted on the layers of the human oesophagus in the longitudinal and circumferential directions and at two different strain rates. Additionally, stress-relaxation tests on the oesophageal layers were carried out in both directions. Overall, the results show discrete properties in each layer and direction, highlighting the importance of treating the oesophagus as a multi-layered composite material with direction-dependent behaviour. Previously, the authors conducted layer-dependent cyclic experimentation on formalin-embalmed human oesophagi. A comparison between the fresh and embalmed tissue response was carried out and revealed surprising similarities in terms of anisotropy, strain-rate dependency, stress-softening and hysteresis, with the main difference between the two preservation states being the magnitude of these properties. As formalin fixation is known to notably affect the formation of cross-links between the collagen of biological materials, the differences may reveal the influence of cross-links on the mechanical behaviour of soft tissues.
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Affiliation(s)
- Ciara Durcan
- Zienkiewicz Institute for Modelling, Data and Artificial Intelligence, Faculty of Science and Engineering, Swansea University, Swansea SA1 8EN, UK
- CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, Grenoble Alpes University, Grenoble 38000, France
| | - Mokarram Hossain
- Zienkiewicz Institute for Modelling, Data and Artificial Intelligence, Faculty of Science and Engineering, Swansea University, Swansea SA1 8EN, UK
| | - Grégory Chagnon
- CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, Grenoble Alpes University, Grenoble 38000, France
| | - Djordje Perić
- Zienkiewicz Institute for Modelling, Data and Artificial Intelligence, Faculty of Science and Engineering, Swansea University, Swansea SA1 8EN, UK
| | - Edouard Girard
- CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, Grenoble Alpes University, Grenoble 38000, France
- Laboratoire d’Anatomie des Alpes Françaises, Grenoble Alpes University, Grenoble, France
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Mohammadkhah M, Klinge S. Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues. J Mech Behav Biomed Mater 2023; 148:106203. [PMID: 37879165 DOI: 10.1016/j.jmbbm.2023.106203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Revised: 09/25/2023] [Accepted: 10/17/2023] [Indexed: 10/27/2023]
Abstract
Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.
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Affiliation(s)
- Melika Mohammadkhah
- Technische Universität Berlin, Institute of Mechanics, Chair of Structural Mechanics and Analysis, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany.
| | - Sandra Klinge
- Technische Universität Berlin, Institute of Mechanics, Chair of Structural Mechanics and Analysis, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany
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A Review on Damage and Rupture Modelling for Soft Tissues. Bioengineering (Basel) 2022; 9:bioengineering9010026. [PMID: 35049735 PMCID: PMC8773318 DOI: 10.3390/bioengineering9010026] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2021] [Revised: 01/04/2022] [Accepted: 01/05/2022] [Indexed: 11/16/2022] Open
Abstract
Computational modelling of damage and rupture of non-connective and connective soft tissues due to pathological and supra-physiological mechanisms is vital in the fundamental understanding of failures. Recent advancements in soft tissue damage models play an essential role in developing artificial tissues, medical devices/implants, and surgical intervention practices. The current article reviews the recently developed damage models and rupture models that considered the microstructure of the tissues. Earlier review works presented damage and rupture separately, wherein this work reviews both damage and rupture in soft tissues. Wherein the present article provides a detailed review of various models on the damage evolution and tear in soft tissues focusing on key conceptual ideas, advantages, limitations, and challenges. Some key challenges of damage and rupture models are outlined in the article, which helps extend the present damage and rupture models to various soft tissues.
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Physically-based structural modeling of a typical regenerative tissue analog bridges material macroscale continuum and cellular microscale discreteness and elucidates the hierarchical characteristics of cell-matrix interaction. J Mech Behav Biomed Mater 2021; 126:104956. [PMID: 34930707 DOI: 10.1016/j.jmbbm.2021.104956] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Revised: 10/22/2021] [Accepted: 11/01/2021] [Indexed: 11/20/2022]
Abstract
This paper presents a comprehensive physically-based structural modelling for the passive and active biomechanical processes in a typical engineered tissue - namely, cell-compacted collagen gel. First, it introduces a sinusoidal curve analog for quantifying the mechanical response of the collagen fibrils and a probability distribution function of the characteristic crimp ratio for taking into account the fibrillar geometric entropic effect. The constitutive framework based on these structural characteristics precisely reproduces the nonlinearity, the viscoelasticity, and fairly captures the Poisson effect exhibiting in the macroscale tensile tests; which, therefore, substantially validates the structural modelling for the analysis of the cell-gel interaction during collagen gel compaction. Second, a deterministic molecular clutch model specific to the interaction between the cell pseudopodium and the collagen network is developed, which emphasizes the dependence of traction force on clutch number altering with the retrograde flow velocity, actin polymeric velocity, and the deformation of the stretched fibril. The modelling reveals the hierarchical features of cellular substrate sensing, i.e. a biphasic traction force response to substrate elasticity begins at the level of individual fibrils and develops into the second biphasic sensing by means of the fibrillar number integration at the whole-cell level. Singular in crossing the realms of continuum and discrete mechanics, the methodologies developed in this study for modelling the filamentous materials and cell-fibril interaction deliver deep insight into the temporospatially dynamic 3D cell-matrix interaction, and are able to bridge the cellular microscale and material macroscale in the exploration of related topics in mechanobiology.
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