Meshless Methods: The Future of Computational Biomechanical Simulation

Abstract

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...