Influence of Porosity on Fracture Toughness and Fracture Behavior of Antibiotic-Loaded PMMA Bone Cement.

Aseptic loosening is the most common reason for the long-term revision of cemented arthroplasties with fracture of the cement being a postulated cause or contributing factor. In our previous studies we showed that adding an antibiotic to a polymethylmethacrylate (PMMA) bone cement led to detrimental effects on various mechanical properties of the cement such as bending strength, compressive strength and fracture toughness (KIC). This finding implied that the mechanical failure of antibiotic-loaded PMMA bone cement was influenced by its pore volume fraction. Up to now this aspect has not been studied. Hence the purposes of this study were to determine (1) the influence of antibiotic (telavancin) loading on the KIC of a widely used PMMA bone cement brand (Palacos®R) and (2) the influence of pore size and pore distribution on the fracture behavior of the KIC specimens. For (2) both experimental and numerical methods (extended finite element method [XFEM]) were used allowing a comparison between the two sets of results. We found that: (1) KIC decreased with increased porosity with the drop (relative to the value for the control cement) being significant when the telavancin loading was 4.8 wt/wt % (2 g of telavancin added to 40 g of control cement powder); (2) there was a critical pore size above which there was a significant decrease in KIC and is 1 mm; (3) crack propagation was strongly influenced by pore size and pore locations (pore-pore interactions); and, (4) there was good agreement between the experimental and XFEM results. The implications of these findings for the use of a telavancin-loaded PMMA bone cement in cemented total joint arthroplasties are commented upon.

A Numerical Investigation of Dimensionless Numbers Characterizing Meltpool Morphology of the Laser Powder Bed Fusion Process.

Microstructure evolution in metal additive manufacturing (AM) is a complex multi-physics and multi-scale problem. Understanding the impact of AM process conditions on the microstructure evolution and the resulting mechanical properties of the printed component remains an active area of research. At the meltpool scale, the thermo-fluidic governing equations have been extensively modeled in the literature to understand the meltpool conditions and the thermal gradients in its vicinity. In many phenomena governed by partial differential equations, dimensional analysis and identification of important dimensionless numbers can provide significant insights into the process dynamics. In this context, we present a novel strategy using dimensional analysis and the linear least-squares regression method to numerically investigate the thermo-fluidic governing equations of the Laser Powder Bed Fusion AM process. First, the governing equations are solved using the Finite Element Method, and the model predictions are validated by comparing with experimentally estimated cooling rates, and with numerical results from the literature. Then, through dimensional analysis, an important dimensionless quantity interpreted as a measure of heat absorbed by the powdered material and the meltpool, is identified. This dimensionless measure of absorbed heat, along with classical dimensionless quantities such as Péclet, Marangoni, and Stefan numbers, are employed to investigate advective transport in the meltpool for different alloys. Further, the framework is used to study variations in the thermal gradients and the solidification cooling rate. Important correlations linking meltpool morphology and microstructure-evolution-related variables with classical dimensionless numbers are the key contribution of this work.

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework.

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff-Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a 'phase diagram' for its symmetric and broken-symmetry states.

A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth.

Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates' exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify to form a new incremental layer of the exoskeleton. Most of the existing literature on the morphology of mollusks is descriptive. The mathematical understanding of the underlying coupling between pre-existing shell morphology, de novo surface deposition and morpho-elastic volume growth is at a nascent stage, primarily limited to reduced geometric representations. Here, we propose a general, three-dimensional computational framework coupling pre-existing morphology, incremental surface growth by accretion, and morpho-elastic volume growth. We exercise this framework by applying it to explain the stepwise morphogenesis of seashells during growth: new material surfaces are laid down by accretive growth on the mantle whose form is determined by its morpho-elastic growth. Calcification of the newest surfaces extends the shell as well as creates a new scaffold that constrains the next growth step. We study the effects of surface and volumetric growth rates, and of previously deposited shell geometries on the resulting modes of mantle deformation, and therefore of the developing shell's morphology. Connections are made to a range of complex shells ornamentations.

Coordination of signaling and tissue mechanics during morphogenesis of murine intestinal villi: a role for mitotic cell rounding.

Efficient digestion and absorption of nutrients by the intestine requires a very large apical surface area, a feature that is enhanced by the presence of villi, fingerlike epithelial projections that extend into the lumen. Prior to villus formation, the epithelium is a thick pseudostratified layer. In mice, villus formation begins at embryonic day (E)14.5, when clusters of mesenchymal cells form just beneath the thick epithelium. At this time, analysis of the flat lumenal surface reveals a regular pattern of short apical membrane invaginations that form in regions of the epithelium that lie in between the mesenchymal clusters. Apical invaginations begin in the proximal intestine and spread distally, deepening with time. Interestingly, mitotically rounded cells are frequently associated with these invaginations. These mitotic cells are located at the tips of the invaginating membrane (internalized within the epithelium), rather than adjacent to the apical surface. Further investigation of epithelial changes during membrane invagination reveals that epithelial cells located between mesenchymal clusters experience a circumferential compression, as epithelial cells above each cluster shorten and widen. Using a computational model, we examined whether such forces are sufficient to cause apical invaginations. Simulations and in vivo data reveal that proper apical membrane invagination involves intraepithelial compressive forces, mitotic cell rounding in the compressed regions and apico-basal contraction of the dividing cell. Together, these data establish a new model that explains how signaling events intersect with tissue forces to pattern apical membrane invaginations that define the villus boundaries.

Elastic free energy drives the shape of prevascular solid tumors.

It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors in vivo and is an important step in understanding the processes underlying solid tumor growth.