Analysis of Bone Remodeling Under Piezoelectricity Effects Using Boundary Elements

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

doi:10.1016/s1672-6529(16)60432-8

Cited by 38 publications

(38 citation statements)

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“…Substituting ρ e (x, r) into Equation 7, fluid velocity can be obtained by integrating Equation 7with the boundary conditions (8)…”

Section: Discussionmentioning

confidence: 99%

“…Wang and Qin [7] studied the healing process of bone fractures using a pulsed electromagnetic field device. Literature [8][9][10][11] showed that piezoelectric potentials can enhance bone regeneration and remodeling. For example, Fonseca et al demonstrated that an external microcurrent (10 µA) can modulate the homeostasis of bone remodeling [12].…”

Section: Introductionmentioning

confidence: 99%

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Variation of Streaming Potentials with Time under Steady Fluid Pressure in Bone

et al. 2019

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This paper investigates the streaming potentials’ behaviors when fluid flows through the micropores in bone. An experimental setup was developed for measuring the streaming potentials between two surfaces of a bone plate specimen. It was found that the streaming potentials measured increased almost linearly with time under a constant fluid pressure gradient, which does not agree with the prediction from the classical theory of streaming potentials. To explain the reasons associated with the results obtained, a theoretical model was proposed in which the electric charge densities on the inner surfaces of the capillary are unevenly distributed. A formula was developed for solving the model, and the solutions demonstrate that nonuniform accumulations of electric charges carried by the fluid on the inner surfaces of the microcanals in bone can induce streaming potentials which linearly increase with time during the driving air pressure holding period. This phenomenon represents the specific characteristics of bone. The solution implies that the streaming potentials in Haversian canals, lacunas and canaliculi are not affected by electro-viscous resistance in the bone fluid.

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“…Substituting ρ e (x, r) into Equation 7, fluid velocity can be obtained by integrating Equation 7with the boundary conditions (8)…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Variation of Streaming Potentials with Time under Steady Fluid Pressure in Bone

et al. 2019

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“…The corresponding piezoelectric boundary integral equation for the boundary Γ can be expressed as follows [16,17]:…”

Section: Boundary Element Formulationmentioning

confidence: 99%

“…No volume discretization is required using this approach. For more details on the formulation and its implementation the reader is referred to [17].…”

Section: Boundary Element Formulationmentioning

confidence: 99%

“…These properties are changed according to the density for each element in the geometry. The fundamental solutions are calculated numerically using the Radon Transformation [14,17,20]. Finally, the density can be computed from the stress energy density at every point in the geometry and all values in the system can be updated, until the end of the simulation time T sim .…”

Section: Algorithm For Piezoelectric Bonementioning

confidence: 99%

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

Duarte

Thoeni

Garzón‐Alvarado

et al. 2018

Mathematical Problems in Engineering

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This paper outlines a computational model for the analysis of the piezoelectric behaviour of the vertebral body remodelling process. Particular attention is paid to the algorithms for the simulation of the stress energy density for each point of the geometry and the distribution of the density in the bone. In addition, the model takes into account the piezoelectric effect and the anisotropy (transversal isotropy) of the bone. A model for internal anisotropic piezoelectric bone remodelling of a human vertebra is discussed in detail. The model consists of the implementation of an algorithm which includes the elastic and electric variables in a single equation using boundary element method. The presented results show a good agreement with biological data and the model does not include any electric additional charge.

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