The Meshless Methods in the Bone Tissue Remodelling Analysis

Belinha, J.; Dinis, L.M.J.S.; Jorge, R.M. Natal

doi:10.1016/j.proeng.2015.07.009

Cited by 34 publications

(134 citation statements)

References 43 publications

Supporting

Mentioning

132

Contrasting

Order By: Relevance

“…The c and p variables are the MQ-RBF shape parameters, which are fixed values determined in previous works [15][16][17]. The variation of these parameters can affect the performance of the MQ-RBFs.…”

Section: Rpi Shape Functionsmentioning

confidence: 99%

“…Comparing the NNRPIM formulation with the classic meshless method formulation, some notorious advantages [15,17] are verified. Since the background integration mesh of the NNRPIM is constructed respecting the Delaunay triangulation geometric concept [21], the geometric definition of the integration mesh depends exclusively on the computational nodal distribution.…”

Section: Introductionmentioning

confidence: 97%

“…Combining the natural neighbour concept and the radial point interpolator technique, it was possible to enhance the RPIM and develop the Natural Neighbour Radial Point Interpolation Method (NNRPIM) [15][16][17]. More recently, another highly efficient radial point interpolation meshless method was developed and applied to computational mechanics, the Natural Radial Element Method (NREM) [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…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%

See 3 more Smart Citations

Crack path prediction using the natural neighbour radial point interpolation method

Azevedo

Belinha

Dinis

et al. 2015

Engineering Analysis with Boundary Elements

Self Cite

View full text Add to dashboard Cite

Section: Rpi Shape Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Crack path prediction using the natural neighbour radial point interpolation method

Azevedo

Belinha

Dinis

et al. 2015

Engineering Analysis with Boundary Elements

Self Cite

View full text Add to dashboard Cite

“…Recently, Belinha et al [22,23] presented a new bone tissue remodelling algorithm relying on the meshless method accuracy. The methodology was capable to obtain numerical solutions very close with the clinical X-ray images of natural bones [22][23][24], Figure 2a, and natural bones with implants, Figure 2b [25,26]. The methodology was applied also to predict the bone biological behaviour dental biomechanics, with and without the presence of implants [27][28][29][30].…”

mentioning

confidence: 99%

Meshless Methods: The Future of Computational Biomechanical Simulation

Belinha¹

2016

J Biom Biostat

View full text Add to dashboard Cite

IntroductionIn computational biomechanics there are three important phases: the modulation, the simulation and the analysis. In order to perform them, it is necessary to use a discretization technique. This design process is naturally recurrent and strongly depends on the selected numerical methodology. The research community continuously seeks the best numerical approach to reproduce in-silico the studied biological phenomenon.Presently, there are many numerical methods available and capable to successfully handle the previously mentioned phases of the bioengineering design.However, the different numerical approaches described in the literature are fundamentally very dissimilar, which lead to distinct numerical performances.Nowadays, the finite element method (FEM) is the most popular discretization technique available in the literature [1]. The FEM replicates the physical domain with a geometrical model constructed with finite elements that do not overlap each other and do not present any gap disrupting the model continuum. In Figure 1a is represented the geometric model of a half human head, which was obtained directly from a CAT scan, and in Figure 1b is shown the corresponding 3D element mesh. This discretization technique requires a heavy pre-processing phase to build a balanced element mesh. The FEM performance relies strongly on the model's mesh quality. Additionally, any mesh modification or mesh refinement during the analysis represent an extra (heavy) computational cost, which is a significant drawback in biomechanics.Recently, within the computational mechanics scientific community, meshless methods became a focus of interest for solving partial differential equations. Since in meshless methods the rigid concept of element, in meshless methods the solid domain can be discretized with an unstructured cloud of nodes [2][3][4][5][6]. In Figure 1c is represented the nodal discretization of a half human head. Truly meshless methods [5][6][7][8][9][10][11] allow to acquire the nodal cloud directly from the CAT scan or the MRI by considering the pixels (or voxels) position and then obtain the nodal connectivity, the integration points and the shape functions using only the nodal spatial information [5]. Using the grey tones of medical images, truly meshless methods are even capable of recognizing distinct biomaterial and then affecting directly to the nodes the corresponding material properties, Figure 1c. Meshless Methods in BiomechanicsMeshless methods possess several advantages over the FEM, such as the remeshing efficiency, which permits to simulate explicitly fluid flow (the hemodynamics, the swallow, the respiration, etc.) and to deal with the large distortions of soft materials (internal organs, muscles, tendons, skin, etc.). Furthermore, the smoothness and the accuracy of the solution fields (displacements, stresses, strain, etc.) obtained with meshless methods are very useful to predict the remodelling process of biological tissues and the rupture or damage of such biomaterials. Additionally, recen...

show abstract

A preliminary study of endothelial cell migration during angiogenesis using a meshless method approach

Guerra

Belinha

Jorge

2020

Numer Methods Biomed Eng

View full text Add to dashboard Cite

Angiogenesis, the development of new blood capillaries, is crucial for the wound healing process. This biological process allows the proper blood supply to the tissue, essential for cell proliferation and viability. Several biological factors modulate angiogenesis, however the vascular endothelial growth factor (VEGF) is the main one. Given the complexity of angiogenesis, in the last years, computational modelling aroused the interest of scientists since it allows to model this process with different, more economic and faster methodologies, comparatively to experimental approaches. In this work, a mathematical model motivated by the analysis of the effect of VEGF diffusion gradient in endothelial cell migration is presented. This is the process that allows capillary formation and it is essential for angiogenesis. The proposed mathematical model is combined with the Radial Point Interpolation Method, being the area discretized considering an unorganized nodal cloud and a background mesh of integration points, without predefined relations. The nodal connectivity was achieved using the “influence‐domain” approach. The interpolation functions were constructed using the Radial Point Interpolators techniques. This method combines a radial basis functions with a polynomial functions to obtain the approximation. This preliminary work does not account for the whole complexity of cell and tissue biology, and numerical results are presented for an idealised two‐dimensional setting. Nevertheless, the developed RPIM software is a valid numerical tool that can be adjusted to biological problems and may also be able to complement the biological and medical subjects.

show abstract

The Meshless Methods in the Bone Tissue Remodelling Analysis

Cited by 34 publications

References 43 publications

Crack path prediction using the natural neighbour radial point interpolation method

Crack path prediction using the natural neighbour radial point interpolation method

Meshless Methods: The Future of Computational Biomechanical Simulation

A preliminary study of endothelial cell migration during angiogenesis using a meshless method approach

Contact Info

Product

Resources

About