Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee

E, Bologna; Paola, Mario Di; Dayal, Kaushik; Deseri, Luca; Zingales, Massimiliano

doi:10.1098/rsta.2019.0294

Cited by 18 publications

(12 citation statements)

References 42 publications

(50 reference statements)

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“…Third, the authors characterize the mechanical characteristics of the meniscus as the isotropic single-phase linear elastic material. It is prospected to consider the viscoelasticity of the tissue in the future work [42][43][44]. Hence, future studies with an improved design and…”

Section: Fatigue Analysis Results Of Meniscus Modelmentioning

confidence: 99%

Biomechanical Performance of Menisci under Cyclic Loads

Tseng

Huang

Chen

et al. 2021

Applied Bionics and Biomechanics

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The meniscus, composed of fibrocartilage, is a very important part of the human knee joint that behaves like a buffer. Located in the middle of the femoral condyles and the tibial plateau, it is a necessary structure to maintain normal biomechanical properties of the knee. Whether walking or exercising, the meniscus plays a vital role to protect the articular surface of both the femoral condyles and the tibial plateau by absorbing the conveying shock from body weight. However, modern people often suffer from irreversible degeneration of joint tissue due to exercise-induced harm or aging. Therefore, understanding its dynamic characteristics will help to learn more about the actual state of motion and to avoid unnecessary injury. This study uses reverse engineering equipment, a 3D optical scanner, and a plastic teaching human body model to build the geometry of knee joint meniscus. Then, the finite element method (FEM) is employed to obtain the dynamic characteristics of the meniscus. The results show the natural frequencies, mode shapes, and fatigue life analysis of meniscus, with real human material parameters. The achieved results can be applied to do subsequent knee dynamic simulation analysis, to reduce the knee joint and lower external impacts, and to manufacture artificial meniscus through tissue engineering.

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Section: Fatigue Analysis Results Of Meniscus Modelmentioning

confidence: 99%

Biomechanical Performance of Menisci under Cyclic Loads

Tseng

Huang

Chen

et al. 2021

Applied Bionics and Biomechanics

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“…The approach is readily implementable in numerical form to calculate either stress or strain responses of any fractional system where fractional order may change with time. Finally, Bologna et al [55] propose a nonlinear extension of fractional calculus to tissue biomechanics, in order to handle the time-dependent mechanics of ligaments and tendons of the human knee. The authors point out that fibrous tissues exhibit a marked nonlinear behaviour in terms of relaxation and creep functions with coefficients and orders depending nonlinearly on applied strain and stress, respectively.…”

Section: Materials Hereditariness: Viscoelasticitymentioning

confidence: 99%

“…The theme issue includes several contributions on linear and nonlinear fractional viscoelasticity, as applied to various types of materials [50][51][52][53][54][55]. Atanackovic et al [50] investigate the thermo-dynamical restrictions on constitutive equations for viscoelastic fluids, as following from a weak form of entropy inequality under isothermal conditions.…”

Section: Materials Hereditariness: Viscoelasticitymentioning

confidence: 99%

Advanced materials modelling via fractional calculus: challenges and perspectives

Failla

Zingales

2020

Phil. Trans. R. Soc. A.

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Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced materials modelling via fractional calculus, with a focus on complex phenomena and non-conventional media. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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“…However, investigation of the hereditariness of musculoskeletal tissues subverted the above assumptions. For example, self-similar fractals [2–4] emerge from the micro–nano structures of ligaments and tendons, and their time-dependent viscoelasticity can be described using fractional-order derivatives [5]. Guo et al [6] further showed a relationship between fractional-order viscoelasticity and self-similar micro–nano structures.…”

Section: Introductionmentioning

confidence: 99%

Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals

2021

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Self-similar fractals are widely obtained from biomaterials within the human musculoskeletal system, and their viscoelastic behaviours can be described by fractional-order derivatives. However, existing viscoelastic models neglect the internal correlation between the fractal structure of biomaterials and their fractional-order temporal responses. We further expanded the fractal hyper-cell (FHC) viscoelasticity theory to investigate this spatio-temporal correlation. The FHC element was first compared with other material elements and spring–dashpot viscoelastic models, thereby highlighting its discrete and fractal nature. To demonstrate the utility of an FHC, tree-like, ladder-like and triangle-like FHCs were abstracted from human cartilage, tendons and muscle cross-sections, respectively. The duality and symmetry of the FHC element were further discussed, where operating the duality transformation generated new types of FHC elements, and the symmetry breaking of an FHC altered its fractional-order viscoelastic responses. Thus, the correlations between the staggering patterns of FHCs and their rheological power-law orders were established, and the viscoelastic behaviour of the multi-level FHC elements fitted well in stress relaxation experiments at both the macro- and nano-levels of the tendon hierarchy. The FHC element provides a theoretical basis for understanding the connections between structural degeneration of bio-tissues during ageing or disease and their functional changes.

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Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee

Cited by 18 publications

References 42 publications

Biomechanical Performance of Menisci under Cyclic Loads

Biomechanical Performance of Menisci under Cyclic Loads

Advanced materials modelling via fractional calculus: challenges and perspectives

Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals

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