A novel mathematical model for growth of capillaries and nutrient supply with application to prediction of osteophyte onset

Bednarczyk, Ewa; Lekszycki, Tomasz

doi:10.1007/s00033-016-0687-2

Cited by 33 publications

(21 citation statements)

References 66 publications

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“…11. The reference signal or the set-point is assumed to be regulated by hormone activity or by the presence of oxygen and nutrients (Bednarczyk and Lekszycki 2016;Lu and Lekszycki 2018). 12.…”

Section: Basic Kinematical Fields and Fundamental Modeling Assumptionsmentioning

confidence: 99%

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Giorgio¹,

Dell’Isola²,

Andreaus³

et al. 2019

Biomech Model Mechanobiol

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In the past years, many attempts have been made in order to model the process of bone remodeling. This process is complex, as it is governed by not yet completely understood biomechanical coupled phenomena. It is well known that bone tissue is able to self-adapt to different environmental demands of both mechanical and biological origin. The mechanical aspects are related to the functional purpose of the bone tissue, i.e., to provide support to the body and protection for the vitally important organs in response to the external loads. The many biological aspects include the process of oxygen and nutrients supply. To describe the biomechanical process of functional adaptation of bone tissue, the approach commonly

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Section: Basic Kinematical Fields and Fundamental Modeling Assumptionsmentioning

confidence: 99%

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Giorgio¹,

Dell’Isola²,

Andreaus³

et al. 2019

Biomech Model Mechanobiol

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“…Similar effects may be observed in biological and other natural structures. Bones and other hard tissues are known to respond to loading [66][67][68][69] and the proposed approach can be used for understanding biomaterial structure and function, particularly in relation to their anisotropy [70]. Finally, it is noteworthy that the granular micromechanics can lead to general micromorphic continuum models [35] that exhibit the length scale effects of material microstructure and can lead to further modifications in the optimal design [71].…”

Section: The Four Benchmark Examples Demonstrate Clearly the Effects mentioning

confidence: 99%

Optimal structural topology of materials with micro-scale tension-compression asymmetry simulated using granular micromechanics

et al. 2017

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Material systems derived from particulate precursor exhibit significant micro-scale tensioncompression asymmetry under loading which leads to macro-scale material anisotropy. Topology optimization of structures composed of such materials could suggest new unique topologies as well as material anisotropy distribution. This paper utilizes the granular micromechanics method that relates the micro-scale interactions to the macro-scale for defining material constitutive relationship. The resultant constitutive relationship is implemented in the evolutionary structure optimization algorithm based upon finite element analysis. Benchmark problems are simulated to investigate the influences of degrees of asymmetry on structure topologies and to illustrate how material anisotropy evolves under given boundary conditions.

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“…Historically, bone mechanical behavior was dealt with using classical optimization processes based mainly on the developed mechanical strain energy density (SED) through the material [21][22][23][24][25][26][27][28][29]. However, to be able to obtain a good predictive numerical model, the biological phenomena [30] need to be linked with the surrounding physics [31][32][33][34][35], and account for the growing capillaries and nutrient supply [36][37][38][39]. Lately, a new form of mechanobiological stimulus for bone remodeling has emerged integrating coupled biological and mechanical effects accounting for cell migration and the nutrient supply chain [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Influence of bone microstructure distribution on developed mechanical energy for bone remodeling using a statistical reconstruction method

Sheidaei

Kazempour

Hasanabadi

et al. 2019

Mathematics and Mechanics of Solids

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The development of a predictive model for bone remodeling is becoming increasingly important for medical applications such as bone surgery or bone substitutes like prostheses. However, as bone remodeling is a complex multiphysics phenomenon and difficult to quantify experimentally, predictive numerical models remain, at best, phenomenologically driven. Patient dependency is often ignored as its influence is usually considered secondary, although it is known to play an important role over long periods of time. Another difficulty to study this patient dependency is the availability of experimental samples to carry out extensive analyses. Using our recently developed statistical reconstruction framework, a set of “bone like” microstructures with variety of distributions has been created to study pseudo “patient variabilities.” The method provides similar effective stiffness tensor, equivalent stresses, and strain energy distributions for the original and the statistically reconstructed samples. The main outcome of this study is the correlation of similar effective mechanical properties between samples when bone remodeling will depend on the local strain energy distribution as a function of each bone microstructure. It is expected that two different microstructures with equivalent bone volume fraction will lead to identical bone remodeling in a short period of time, whereas this needs to be proven for long term evolution. This work could be used to develop precise predictive numerical models while developing parametric studies on an infinite number of virtual samples and correlating patient dependency with more precise mechanobiological numerical models.

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A novel mathematical model for growth of capillaries and nutrient supply with application to prediction of osteophyte onset

Cited by 33 publications

References 66 publications

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

On mechanically driven biological stimulus for bone remodeling as a diffusive phenomenon

Optimal structural topology of materials with micro-scale tension-compression asymmetry simulated using granular micromechanics

Influence of bone microstructure distribution on developed mechanical energy for bone remodeling using a statistical reconstruction method

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