The Mandible Remodeling Induced by Dental Implants: A Meshless Approach

This paper presents simulations of a three-dimensional model of the bone remodelling process. The model consists of a set of variable order partial differential equations, in which the varying order depends on the presence of tumour cells. The simulations are of a two-dimensional bone, to make visualisation simpler. They show that this model corresponds to the known evolution of bone remodelling, and is simpler than integer order models found in the literature.

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“…They too could be simplified using variable order derivatives. • Mechanical solicitations also affect bone remodelling [2,3].…”

Section: Discussionmentioning

confidence: 99%

Bulletin of the Polish Academy of Sciences: Technical Sciences

Valério

Neto

Vinga

2019

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“…Furthermore, Belinha et al [144][145][146] predicted bone density distributions on the mandible and maxillary bones as a result of the presence of dental implants, by means of a topology optimization model built on the deformation energy method using Carter's remodeling algorithm [147] within the NNRPIM meshless technique framework. Also, using the NNRPIM meshless method, Duarte et al [148,149] studied a prosthetic system consisting of two implants connected with a bar using a 2D linear elastic stress-strain model.…”

Section: Bone Remodeling and Dental Studiesmentioning

confidence: 99%

Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

Zhang

Ademiloye

Liew

2018

Arch Computat Methods Eng

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The use of meshfree and particle methods in the field of bioengineering and biomechanics has significantly increased. This may be attributed to their unique abilities to overcome most of the inherent limitations of mesh-based methods in dealing with problems involving large deformation and complex geometry that are common in bioengineering and computational biomechanics in particular. This review article is intended to identify, highlight and summarize research works on topics that are of substantial interest in the field of computational biomechanics in which meshfree or particle methods have been employed for analysis, simulation or/and modeling of biological systems such as soft matters, cells, biological soft and hard tissues and organs. We also anticipate that this review will serve as a useful resource and guide to researchers who intend to extend their work into these research areas. This review article includes 333 references. Highlights  We present an up to date review of meshfree and particle methods, including their advantages and limitations.  We comprehensively discuss past and recent applications of meshfree and particle methods in bioengineering and biomechanics.  We identify research areas, directions, and opportunities for the application of meshfree and particle methods in bioengineering and biomechanics.

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“…The NNRPIM was successfully extended to the non-linear analysis considering large deformations and elastoplasticity [24,25], to the dynamic analysis [26][27][28], to the analysis of laminated shell-like structures [29,30] and to the analysis of functionally graded plates [31]. Additionally, it is possible to find in the literature demanding non-linear biomechanical applications using the NNRPIM [17,[32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%