Image‐Based Multiscale Modeling of Porous Bone Materials

Abstract

Bones comprise about one-fifth of an individual body weight, with the main functions in supporting and protecting organs, performing movements, and producing the blood cells, among others. Based on the microstructural composition, bones can be classified as cortical bone (compact bone) and trabecular bone (cancellous bone or spongy bone). With reference to Figure 20.1a for a femur long bone, the cortical bone constitutes about 80% of the human skeleton mass and forms an outer layer of bones, while the trabecular bone fills the interior with a porous and cancellous structure; see the microstructure of the femur long bone shown in Figure 20.1b. In general, the cortical bone is stiffer, harder, and denser than the trabecular bone so that it has the ability to protect organs and support the body movement, in addition to its ability to transmit chemical components. In contrast, the trabecular bone has a larger surface area, lower density and stiffness, and higher porosity than those of the cortical bone. Owing to the porous nature of the trabecular bone, there exists space for the blood vessels and bone marrow to flow inside the spongy structure, as can be seen from the computed tomography (CT) scan of the trabecular bone microstructure in Figure 20.2. As such, the bone materials can be characterized as porous media of solid skeleton with the pores filled with fluid. Consequently, the fluid-saturated porous material has been introduced to describe the constitutive behavior of bone materials.Homogenization methods have been introduced to provide a multiscale paradigm for analysis of poroelastic materials, and yield macroscopic balance laws that resemble the Biot's theory [1] while embedding microscopic features [2][3][4]. This work is motivated by the fact that as high-resolution digital imaging techniques emerge, such as the advancement of micro-CT and micro-magnetic resonance imaging (micro-MRI), the investigation of mechanical properties of cortical and trabecular bones can Multiscale Simulations and Mechanics of Biological Materials, First Edition. Edited by Shaofan Li and Dong Qian.

Image-based Modeling of Coupled Electro-Chemo-Mechanical Behavior of Li-ion Battery Cathode Using an Interface-Modified Reproducing Kernel Particle Method

“…Using backward Euler for time integration of the lithium transport equation, and considering the nonlinearities of 𝑫 with respect to 𝑐 and of 𝐽 ̅ with respect to 𝑐 and 𝛷, the incremental form of the coupled electrochemistry equations in (31) and (33) at iteration 𝜈 of time step (𝑛 + 1) is given as:…”

“…To alleviate the aforementioned difficulties, an enhancement of the reproducing kernel particle method (RKPM) is introduced in this work for image-based modeling of coupled electro-chemomechanical behavior of Li-ion battery cathodes. RKPM [25][26][27][28][29] has shown to be effective for adaptive refinement [30], modeling as-built material microstructures [31][32][33][34], and for incorporating strong and weak discontinuities into the approximation [35][36][37][38]34].…”

Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

“…They also analyzed the nonlinear Fisher transient diffusion equation[134] for the 2D modeling of a fractured bone by incorporating initial cell concentrations at the periosteum, the marrow, and between the bone and the callus (at the fractured end). Yang[135,136] utilized high-resolution medical images to develop an imagebased strong form collocation procedure using a gradient reproducing kernel approximation, for the biomaterial modeling of bone fracture, the bone remodeling process and the design of bone-implant systems, as well as the microstructure modeling of trabecular bone.More recently, interest in the application of various numerical methods (meshfree methods included) to dentistry and food processing has grown significantly. Cleary and his colleagues[137][138][139] modeled the process of fluid flow and the breakage of various kinds and shapes of food by teeth in the oral cavity using a coupled SPH-biomechanical model.…”