A Review on Recent Advances in the Constitutive Modeling of Bone Tissue

Pahr, Dieter H.; Reisinger, Andreas

doi:10.1007/s11914-020-00631-1

Cited by 28 publications

(20 citation statements)

References 54 publications

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“…Тут слід зауважити, що кісткова тканина є неоднорідною і має анізотропію механічних характеристик [9,10]. Однак у більшості робіт, пов'язаних із вивченням напружено-деформованого стану систем "кісткафіксатор", вона розглядається як однорідне, ізотропне, пружне середовище [11][12][13][14]. Цей факт обумовлений тим, що з одного боку, існують певні складнощі при дослідженні механічних характеристик кісткової тканини і, як наслідок, відсутній достатній обсяг експериментальних даних, а з іншоготрудомісткість або навіть неможливість призначення цих властивостей розрахунковим моделям у програмних комплексах через особливості геометрії кісток.…”

Section: вступunclassified

Study of the Stress-Strain State of the "Bone–Fixation Plate" System in Conjunction With Cortical Tissue Mechanical Properties

Panchenko

Kolosov

Onyshchenko

et al. 2022

Innov Biosyst Bioeng

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Background. Bone osteosynthesis is considered one of the most efficient methods of treating fractures of long tubular bones. Development of modern computer technology and specialized software makes it possible for a traumatologist to perform preliminary efficiency estimation of osteosynthesis using fixation plates of various designs. Results of such studies can significantly depend on calculation model parameters. In most papers related to the study of a stress-strain state of “bone–fixator” systems, bone tissue is considered as a homogeneous, isotropic, elastic medium. However, in fact it is heterogeneous and has an anisotropy of mechanical characteristics. Accordingly in a case of using a simplified isotropic model of bone tissue, when performing calculations, there is a possibility of obtaining inaccurate results. Objective. Estimation of influence of orthotropy of the bone tissue physical and mechanical properties on a stress-strain state of the “bone–fixator” system. Methods. The study is performed in the software environment based on the finite element method. Osteosynthesis of a low transverse fracture of a fibula using a smooth plate is selected as a computational case. Two computational models simplified in terms of geometry are constructed to solve the problem. These models are different only in properties of cortical bone tissue. Results. Analysis of a stress state in elements of models indicated that normal stresses reached the highest values, and tangential stresses are relatively small. In addition, the character of stress distribution turned out to be significantly inhomogeneous. However, stress state patterns are qualitatively similar for both computational models. A common feature of the maximum stresses both in the bone and in the plate turned out to be that all the maximum stresses are the result of their concentration. Conclusions. Consideration of orthotropy of elastic parameters of a bone led to significant quantitative changes in the indicators of a stress state. It is established that the minimum safety margins for both models turned out to be considered by the maximum tensile stresses acting in the vertical direction. A similar result in estimating bone strength also occurs in a case when only elastic orthotropy is considered, but the orthotropy of strength indicators is not considered. If the strength orthotropy is considered for the isotropic model of cortical bone, the pattern changes qualitatively. The normal tensile stress directed along the tangent to a circumference of bone cross-section is considered unsafe. Calculations results indicate a possibility of using an isotropic model of cortical tissue when performing comparative estimations in order to identify the most efficient, in terms of strength, fixation plate designs.

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Section: вступunclassified

Study of the Stress-Strain State of the "Bone–Fixation Plate" System in Conjunction With Cortical Tissue Mechanical Properties

Panchenko

Kolosov

Onyshchenko

et al. 2022

Innov Biosyst Bioeng

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“…However, another question remains open: How are the load-displacement, apparent stress-strain, and effective stress-strain dependencies related? To answer this question, we need a corresponding computational model, an acceptable version of which could not be found in the review [4] or in other articles [12,13,19,[30][31][32][33]. The answers to these questions are presented below.…”

Section: Bone As a Biomechanical System Of Interacting Structural Unitsmentioning

confidence: 99%

“…Moreover, bone cells are periodically, but not synchronously, updated, which determines the dependence of the strength of structural units on the stage of renewal. In most cases, bone tissue is a very complex object, the study of which will not stop for a long time [3,4].…”

Section: Introductionmentioning

confidence: 99%

A Damage Model to Trabecular Bone and Similar Materials: Residual Resource, Effective Elasticity Modulus, and Effective Stress under Uniaxial Compression

Kolesnikov

Meltser

2021

Symmetry

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Experimental research of bone strength remains costly and limited for ethical and technical reasons. Therefore, to predict the mechanical state of bone tissue, as well as similar materials, it is desirable to use computer technology and mathematical modeling. Yet, bone tissue as a bio-mechanical object with a hierarchical structure is difficult to analyze for strength and rigidity; therefore, empirical models are often used, the disadvantage of which is their limited application scope. The use of new analytical solutions overcomes the limitations of empirical models and significantly improves the way engineering problems are solved. Aim of the paper: the development of analytical solutions for computer models of the mechanical state of bone and similar materials. Object of research: a model of trabecular bone tissue as a quasi-brittle material under uniaxial compression (or tension). The new ideas of the fracture mechanics, as well as the methods of mathematical modeling and the biomechanics of bone tissues were used in the work. Compression and tension are considered as asymmetric mechanical states of the material. Results: a new nonlinear function that simulates both tension and compression is justified, analytical solutions for determining the effective and apparent elastic modulus are developed, the residual resource function and the damage function are justified, and the dependences of the initial and effective stresses on strain are obtained. Using the energy criterion, it is proven that the effective stress continuously increases both before and after the extremum point on the load-displacement plot. It is noted that the destruction of bone material is more likely at the inflection point of the load-displacement curve. The model adequacy is explained by the use of the energy criterion of material degradation. The results are consistent with the experimental data available in the literature.

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“…In practice, the complex geometry and heterogeneous/anisotropic material properties of bone necessitate the usage of sophisticated methods like image‐based finite element analysis (FEA) in fracture studies of bone. Three recent comprehensive reviews on the implementation of such methods contain several key papers on this important topic 1–3 …”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, there is a broad consensus that certain issues should be resolved before the clinical usage of these methods becomes quite feasible. For instance, the uncertainties about the definition and usage of appropriate and generally accepted failure measures, 1,3,11 along with the high computational cost of nonlinear analysis methods, are among major concerns 6,13,18,24 …”

Section: Introductionmentioning

confidence: 99%

Fracture analysis of healthy and osteoporotic femora using clinical CT images, phantomless densitometry, and linear FE method

Mirzaei

Jafari

Allaveisi

et al. 2022

Journal Orthopaedic Research

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Computational fracture analysis has become a growing branch of orthopedic research. Particularly, the associated methods provide reliable tools for the analysis of 3D CT-based models of bone. This paper reports the results of such analyses for 15 human femora (healthy and osteoporotic) under different loading orientations (85 different analysis cases). A new method was developed for the calculation of the density distribution in the models from ordinary clinical CT images without calibration phantom. This method, along with a strain-energy-based linear finite element (FE) analysis scheme, was used to predict the fracture strength and pattern of 10 cadaveric femora, for which the mechanical testing results and calibrated FE models were already available. The very good agreement and consistency between different sets of results showed the reliability and accuracy of the new density calibration method, as well as the linear analysis scheme. Accordingly, the method was applied to five new clinical images, gathered from two clinics that used different scanners with different protocols. The strength and fracture pattern of each one of these specimens were analyzed under 15 different loading conditions. A consistent behavior was found for variation of the fracture load and pattern of all specimens with the loading orientations, while very clear contrasts were observed between the strength amplitudes of healthy and osteoporotic specimens. The proposed methods can be easily applied to ordinary daily (even archived) clinical CT scans to conduct fast and reliable fracture analysis of human femora for general bone research and opportunistic studies of osteoporosis and trauma.

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A Review on Recent Advances in the Constitutive Modeling of Bone Tissue

Cited by 28 publications

References 54 publications

Study of the Stress-Strain State of the "Bone–Fixation Plate" System in Conjunction With Cortical Tissue Mechanical Properties

Study of the Stress-Strain State of the "Bone–Fixation Plate" System in Conjunction With Cortical Tissue Mechanical Properties

A Damage Model to Trabecular Bone and Similar Materials: Residual Resource, Effective Elasticity Modulus, and Effective Stress under Uniaxial Compression

Fracture analysis of healthy and osteoporotic femora using clinical CT images, phantomless densitometry, and linear FE method

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