A Simplified Scheme for Piezoelectric Anisotropic Analysis in Human Vertebrae Using Integral Methods

Duarte, Vannessa; Thoeni, Klaus; Garzón‐Alvarado, Diego Alexander; Cerrolaza, M.

doi:10.1155/2018/2783867

Cited by 4 publications

(4 citation statements)

References 20 publications

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“…Recently, a computational model was developed to analyze the matrix piezoelectric behavior of the lumbar vertebral body in the remodeling process [125]. They particularly focused on the algorithms for the distribution of the density in bone and the simulation of the strain energy density for each point of the geometry.…”

Section: The Clinical Relevance Of Computational Studies Of Bone Piezmentioning

confidence: 99%

A review on computer modeling of bone piezoelectricity and its application to bone adaptation and regeneration

Mohammadkhah

Marinković

Zehn

et al. 2019

Bone

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Bone is a hierarchical, multiphasic and anisotropic structure which in addition posses piezoelectric properties. The generation of piezoelectricity in bone is a complex process which has been shown to play a key role both in bone adaptation and regeneration. In order to understand the complex biological, mechanical and electrical interactions that take place during these processes, several computer models have been developed and used to test hypothesis on potential mechanisms behind experimental observations. This paper aims to review the available literature on computer modeling of bone piezoelectricity and its application to bone adaptation and healing. We first provide a brief overview of the fundamentals of piezoelectricity and bone piezoelectric effects. We then review how these properties have been used in computational models of bone adaptation and electromechanical behaviour of bone. In addition, in the last section, we summarize current limitations and potential directions for future work.

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Section: The Clinical Relevance Of Computational Studies Of Bone Piezmentioning

confidence: 99%

A review on computer modeling of bone piezoelectricity and its application to bone adaptation and regeneration

Mohammadkhah

Marinković

Zehn

et al. 2019

Bone

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“…However, the exact mechanisms for the piezoelectricity of bone tissue have not been understood completely so far (Wieland et al 2015 ). Several mathematical and computational models of bone remodelling have been proposed but only a few of them have considered the piezoelectric properties of bone (Cerrolaza et al 2017 ; Fernández et al 2012a ; Garzón-Alvarado et al 2012 ; Qu et al 2006 ; Beheshtiha et al 2015 ; Duarte et al 2018 ) and are recently reviewed in (Mohammadkhah et al 2019 ).…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bansod

Kebbach

Kluess

et al. 2021

Biomech Model Mechanobiol

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Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

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“…When subjected to mechanical loading, bone generates an electric charge (direct piezoelectric effect), and conversely, when an electrical charge is applied, strains/stresses can appear in bone (converse piezoelectric effect) ( Fernández et al, 2012a ; Fernández et al, 2012c ) (see Figure 1B ). Similar to other studies ( Fotiadis et al, 1999 ; Qin and Ye, 2004 ; Fernández et al, 2012a , Fernández et al, 2012c ; Duarte et al, 2018 ), the bone was assumed to behave like a crystal with hexagonal symmetry, i.e., the third-order piezoelectric stress tensor ℰ is defined by four values and the electric permittivity tensor (dielectric tensor)

is a diagonal matrix with two constants. These tensors can be written in the following matrix form:

where the third principal direction represents the longitudinal direction of the tibia bone ( Fernández et al, 2012c ).…”

Section: Methodsmentioning

confidence: 99%

“…Until now, the specific mechanisms for bone piezoelectricity remain unclear. However, there are few computational models of bone remodeling that take the piezoelectricity of bone into account ( Qu et al, 2006 ; Fernández et al, 2012a ; Garzón-Alvarado et al, 2012 ; Beheshtiha and Nackenhorst, 2015 ; Cerrolaza et al, 2017 ; Duarte et al, 2018 ) and have been summarized in recent review by Mohammadkhah et al (2019) .…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of Bone Remodeling in the Proximal Tibia Under Electrical Stimulation Considering the Piezoelectric Properties

Bansod

Kebbach

Kluess

et al. 2021

Front. Bioeng. Biotechnol.

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The piezoelectricity of bone is known to play a crucial role in bone adaptation and remodeling. The application of an external stimulus such as mechanical strain or electric field has the potential to enhance bone formation and implant osseointegration. Therefore, in the present study, the objective is to investigate bone remodeling under electromechanical stimulation as a step towards establishing therapeutic strategies. For the first time, piezoelectric bone remodeling in the human proximal tibia under electro-mechanical loads was analyzed using the finite element method in an open-source framework. The predicted bone density distributions were qualitatively and quantitatively assessed by comparing with the computed tomography (CT) scan and the bone mineral density (BMD) calculated from the CT, respectively. The effect of model parameters such as uniform initial bone density and reference stimulus on the final density distribution was investigated. Results of the parametric study showed that for different values of initial bone density the model predicted similar but not identical final density distribution. It was also shown that higher reference stimulus value yielded lower average bone density at the final time. The present study demonstrates an increase in bone density as a result of electrical stimulation. Thus, to minimize bone loss, for example, due to physical impairment or osteoporosis, mechanical loads during daily physical activities could be partially replaced by therapeutic electrical stimulation.

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A Simplified Scheme for Piezoelectric Anisotropic Analysis in Human Vertebrae Using Integral Methods

Cited by 4 publications

References 20 publications

A review on computer modeling of bone piezoelectricity and its application to bone adaptation and regeneration

A review on computer modeling of bone piezoelectricity and its application to bone adaptation and regeneration

Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Computational Analysis of Bone Remodeling in the Proximal Tibia Under Electrical Stimulation Considering the Piezoelectric Properties

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