How linear tension converts to curvature: geometric control of bone tissue growth

This study investigated how substrate geometry influences in-vitro tissue formation at length scales much larger than a single cell. Two-millimetre thick hydroxyapatite plates containing circular pores and semi-circular channels of 0.5 mm radius, mimicking osteons and hemi-osteons respectively, were incubated with MC3T3-E1 cells for 4 weeks. The amount and shape of the tissue formed in the pores, as measured using phase contrast microscopy, depended on the substrate geometry. It was further demonstrated, using a simple geometric model, that the observed curvature-controlled growth can be derived from the assembly of tensile elements on a curved substrate. These tensile elements are cells anchored on distant points of the curved surface, thus creating an actin "chord" by generating tension between the adhesion sites. Such a chord model was used to link the shape of the substrate to cell organisation and tissue patterning. In a pore with a circular cross-section, tissue growth increases the average curvature of the surface, whereas a semi-circular channel tends to be flattened out. Thereby, a single mechanism could describe new tissue growth in both cortical and trabecular bone after resorption due to remodelling. These similarities between in-vitro and in-vivo patterns suggest geometry as an important signal for bone remodelling.     

Quantification of fluid shear stress in bone tissue engineering scaffolds with spherical and cubical pore architectures

Recent studies have shown that mechanical stimulation, in the form of fluid perfusion and mechanical compression, can enhance osteogenic differentiation of mesenchymal stem cells and bone cells within tissue engineering scaffolds in vitro. The precise nature of mechanical stimulation within tissue engineering scaffolds is not only dictated by the exogenously applied loading regime, but also depends on the geometric features of the scaffold, in particular architecture, pore size and porosity. However, the precise contribution of each geometric feature towards the resulting mechanical stimulation within a scaffold is difficult to characterise due to the wide range of interacting parameters. In this study, we have applied a fluid–structure interaction model to investigate the role of scaffold geometry (architecture, pore size and porosity) on pore wall shear stress (WSS) under a range of different loading scenarios: fluid perfusion, mechanical compression and a combination of perfusion and compression. It is found that scaffold geometry (spherical and cubical pores), in particular the pore size, has a significant influence on the stimulation within scaffolds. Furthermore, we observed an amplified WSS within scaffolds under a combination of fluid perfusion and mechanical compression, which exceeded that caused by individual fluid perfusion or mechanical compression approximately threefold. By conducting this comprehensive parametric variation study, an expression was generated to allow the design and optimisation of 3D TE scaffolds and inform experimental loading regimes so that a desired level of mechanical stimulation, in terms of WSS is generated within the scaffold.     

Geometric Dependence of 3D Collective Cancer Invasion

Metastasis of mesenchymal tumor cells is traditionally considered as a single-cell process. Here, we report an emergent collective phenomenon in which the dissemination rate of mesenchymal breast cancer cells from three-dimensional tumors depends on the tumor geometry. Combining experimental measurements and computational modeling, we demonstrate that the collective dynamics is coordinated by the mechanical feedback between individual cells and their surrounding extracellular matrix (ECM). We find the tissue-like fibrous ECM supports long-range physical interactions between cells, which turn geometric cues into regulated cell dissemination dynamics. Our results suggest that migrating cells in three-dimensional ECM represent a distinct class of an active particle system in which the collective dynamics is governed by the remodeling of the environment rather than direct particle-particle interactions.     

Porosity-geometry interaction in the conservation of bone strength

Automated image analysis of a small sample of femoral cross-section radiographs has revealed a consistent difference in bone porosity relative to geometry. Two sub-periosteal fields were assessed microscopically, with field location determined with reference to the principal moment axes (Imax, Imin). The data indicate that: (1) porosity is greatest in the direction of maximum geometric resistance to bending, along the Imin axis; and (2) porosity differences between the Imax and Imin fields decrease as the bone becomes more circular in cross-sectional shape.     

Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone

Mechanical properties of bones are largely determined by their microstructure. The latter comprises a large number of diverse pores. The present paper analyzes a connection between structure of the porous space of the osteonal cortical bone and bone's overall anisotropic elastic moduli. The analysis is based on recent developments in the theory of porous materials that predict the anisotropic effective moduli of porous solids in terms of pores' shapes, orientations and densities. Bone's microstructure is modeled using available micrographs. The calculated anisotropic elastic constants for porous cortical bone are, mostly, in agreement with available experimental data. The influence of each of the pore types on the overall moduli is examined. The results of the analysis can also be used to estimate the extent of mineralization (hydroxyapatite content) if the overall porosity and the effective moduli are known and, vice versa, to estimate porosity from the measured moduli and the extent of mineralization.     

Potential Use of Porous Titanium–Niobium Alloy in Orthopedic Implants: Preparation and Experimental Study of Its Biocompatibility In Vitro

Background

The improvement of bone ingrowth into prosthesis and enhancement of the combination of the range between the bone and prosthesis are important for long-term stability of artificial joints. They are the focus of research on uncemented artificial joints. Porous materials can be of potential use to solve these problems.

Objectives/Purposes

This research aims to observe the characteristics of the new porous Ti-25Nb alloy and its biocompatibility in vitro, and to provide basic experimental evidence for the development of new porous prostheses or bone implants for bone tissue regeneration.

Methods

The Ti-25Nb alloys with different porosities were fabricated using powder metallurgy. The alloys were then evaluated based on several characteristics, such as mechanical properties, purity, pore size, and porosity. To evaluate biocompatibility, the specimens were subjected to methylthiazol tetrazolium (MTT) colorimetric assay, cell adhesion and proliferation assay using acridine staining, scanning electron microscopy, and detection of inflammation factor interleukin-6 (IL-6).

Results

The porous Ti-25Nb alloy with interconnected pores had a pore size of 200 µm to 500 µm, which was favorable for bone ingrowth. The compressive strength of the alloy was similar to that of cortical bone, while with the elastic modulus closer to cancellous bone. MTT assay showed that the alloy had no adverse reaction to rabbit bone marrow mesenchymal stem cells, with a toxicity level of 0 to 1. Cell adhesion and proliferation experiments showed excellent cell growth on the surface and inside the pores of the alloy. According to the IL-6 levels, the alloy did not cause any obvious inflammatory response.

Conclusion

All porous Ti-25Nb alloys showed good biocompatibility regardless of the percentage of porosity. The basic requirement of clinical orthopedic implants was satisfied, which made the alloy a good prospect for biomedical application. The alloy with 70% porosity had the optimum mechanical properties, as well as suitable pore size and porosity, which allowed more bone ingrowth.     

Transbilayer Pores Induced by Thickness Fluctuations

Thermally-induced fluctuations of individual phospholipids in a bilayer lipid membrane (BLM) are converted into collective motions due to the intermolecular interactions. Here, we demonstrate that transbilayer stochastic pores can be generated via collective thermal movements (CTM). Using the elastic theory of continuous media applied to smectic-A liquid crystals, we estimate the pore radius and the energetic requirements for pore appearance. Three types of thermally-induced transbilayer pores could be formed through BLMs: open and stable, open and unstable, and closed. In most of the situations, two open and stable pores with different radii could be generated. Notably, the two pores have the same generation probability. Unstable pores are possible to appear across thin bilayers that contain phospholipids with a large polar headgroup. Closed pores are present throughout the cases that we have inspected. The effects of hydrophobic thickness, polar headgroup size of phospholipids, temperature, surface tension, and elastic compression on the pore formation and pore stability have been examined as well.     

Prediction of cortical bone elastic constants by a two-level micromechanical model using a generalized self-consistent method

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.     

Modeling the Effect of Curvature on the Collective Behavior of Cells Growing New Tissue

The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue’s evolution. Understanding the cellular basis of this control is highly significant for bioscaffold tissue engineering, the evolution of bone microarchitecture, wound healing, and tumor growth. Although previous models have proposed geometrical relationships between tissue growth and curvature, the role of cell density and cell vigor remains poorly understood. We propose a cell-based mathematical model of tissue growth to investigate the systematic influence of curvature on the collective crowding or spreading of tissue-synthesizing cells induced by changes in local tissue surface area during the motion of the interface. Depending on the strength of diffusive damping, the model exhibits complex growth patterns such as undulating motion, efficient smoothing of irregularities, and the generation of cusps. We compare this model with in vitro experiments of tissue deposition in bioscaffolds of different geometries. By including the depletion of active cells, the model is able to capture both smoothing of initial substrate geometry and tissue deposition slowdown as observed experimentally.     

Aggregative cycles evolve as a solution to conflicts in social investment

Multicellular organization is particularly vulnerable to conflicts between different cell types when the body forms from initially isolated cells, as in aggregative multicellular microbes. Like other functions of the multicellular phase, coordinated collective movement can be undermined by conflicts between cells that spend energy in fuelling motion and ‘cheaters’ that get carried along. The evolutionary stability of collective behaviours against such conflicts is typically addressed in populations that undergo extrinsically imposed phases of aggregation and dispersal. Here, via a shift in perspective, we propose that aggregative multicellular cycles may have emerged as a way to temporally compartmentalize social conflicts. Through an eco-evolutionary mathematical model that accounts for individual and collective strategies of resource acquisition, we address regimes where different motility types coexist. Particularly interesting is the oscillatory regime that, similarly to life cycles of aggregative multicellular organisms, alternates on the timescale of several cell generations phases of prevalent solitary living and starvation-triggered aggregation. Crucially, such self-organized oscillations emerge as a result of evolution of cell traits associated to conflict escalation within multicellular aggregates.     

Geometry Design Optimization of Functionally Graded Scaffolds for Bone Tissue Engineering: A Mechanobiological Approach

Functionally Graded Scaffolds (FGSs) are porous biomaterials where porosity changes in space with a specific gradient. In spite of their wide use in bone tissue engineering, possible models that relate the scaffold gradient to the mechanical and biological requirements for the regeneration of the bony tissue are currently missing. In this study we attempt to bridge the gap by developing a mechanobiology-based optimization algorithm aimed to determine the optimal graded porosity distribution in FGSs. The algorithm combines the parametric finite element model of a FGS, a computational mechano-regulation model and a numerical optimization routine. For assigned boundary and loading conditions, the algorithm builds iteratively different scaffold geometry configurations with different porosity distributions until the best microstructure geometry is reached, i.e. the geometry that allows the amount of bone formation to be maximized. We tested different porosity distribution laws, loading conditions and scaffold Young’s modulus values. For each combination of these variables, the explicit equation of the porosity distribution law–i.e the law that describes the pore dimensions in function of the spatial coordinates–was determined that allows the highest amounts of bone to be generated. The results show that the loading conditions affect significantly the optimal porosity distribution. For a pure compression loading, it was found that the pore dimensions are almost constant throughout the entire scaffold and using a FGS allows the formation of amounts of bone slightly larger than those obtainable with a homogeneous porosity scaffold. For a pure shear loading, instead, FGSs allow to significantly increase the bone formation compared to a homogeneous porosity scaffolds. Although experimental data is still necessary to properly relate the mechanical/biological environment to the scaffold microstructure, this model represents an important step towards optimizing geometry of functionally graded scaffolds based on mechanobiological criteria.     

Engineering porous scaffolds using gas-based techniques

Scaffolds are used in tissue engineering as a matrix for the seeding and attachment of human cells. The creation of porosity in three-dimensional (3D) structures of scaffolds plays a critical role in cell proliferation, migration, and differentiation into the specific tissue while secreting extracellular matrix components. These pores are used to transfer nutrients and oxygen and remove wastes produced from the cells. The lack of oxygen and nutrient supply impedes the cell migration more than 500μm from the surface. The physical properties of scaffolds such as porosity and pore interconnectivity can improve mass transfer and have a great impact on the cell adhesion and penetration into the scaffolds to form a new tissue. Various techniques such as electrospinning, freeze-drying, and solvent casting/salt leaching have been used to create porosity in scaffolds. The major issues in these methods include lack of 3D structure, control on pore size, and pore interconnectivity. In this review, we provide a brief overview of gas-based techniques that have been developed for creating porosity in scaffolds.     

Understanding the effect of mean pore size on cell activity in collagen-glycosaminoglycan scaffolds

Mean pore size is an essential aspect of scaffolds for tissue-engineering. If pores are too small cells cannot migrate in towards the center of the construct limiting the diffusion of nutrients and removal of waste products. Conversely, if pores are too large there is a decrease in specific surface area available limiting cell attachment. However the relationship between scaffold pore size and cell activity is poorly understood and as a result there are conflicting reports within the literature on the optimal pore size required for successful tissue-engineering. Previous studies in bone tissue-engineering have indicated a range of mean pore sizes (96–150 µm) to facilitate optimal attachment. Other studies have shown a need for large pores (300–800 µm) for successful bone growth in scaffolds. These conflicting results indicate that a balance must be established between obtaining optimal cell attachment and facilitating bone growth. In this commentary we discuss our recent investigations into the effect of mean pore size in collagen-glycosaminoglycan (CG) scaffolds with pore sizes ranging from 85–325 μm and how it has provided an insight into the divergence within the literature.     

The influence of red cell mechanical properties on flow through single capillary-sized pores

The resistive pulse technique was used to study the influence of specific mechanical properties of the red cell on its ability to enter and flow through single capillary-sized pores with diameters of 3.6, 5.0 and 6.3 micron and lengths of 11 micron. A two-fold increase in membrane shear elasticity resulted in a 40 percent increase in the cell's transit time through a 3.6 micron pore but produced no change in transit time through a 6.3 micron pore. A two-fold increase in membrane shear viscosity produced a 40 percent increase in transit time through the 3.6 micron pore and small but significant increases in transit times through the larger pores. Osmotically dehydrated cells showed no increase in transit time through a 6.3 micron pore, but showed increases in transit times of 50 to 70 percent through 5.0 and 3.6 micron pores. Dense red cells showed increased transit times through both 5.0 micron and 6.0 micron pores. These results indicate that for cells with normal geometric properties, the membrane's shear viscosity and elasticity only influence the cell's transit through pores of 5 micron or less in diameter. However, alterations in the cell's geometric properties can extend the influence of membrane shear properties to larger diameter pores.     

Bax-type apoptotic proteins porate pure lipid bilayers through a mechanism sensitive to intrinsic monolayer curvature

During apoptosis, Bax-type proteins permeabilize the outer mitochondrial membrane to release intermembrane apoptogenic factors into the cytosol via a poorly understood mechanism. We have proposed that Bax and DeltaN76Bcl-x(L) (the Bax-like cleavage fragment of Bcl-x(L)) function by forming pores that are at least partially composed of lipids (lipidic pore formation). Since the membrane monolayer must bend during lipidic pore formation, we here explore the effect of intrinsic membrane monolayer curvature on pore formation. Nonlamellar lipids with positive intrinsic curvature such as lysophospholipids promoted membrane permeabilization, whereas nonlamellar lipids with negative intrinsic curvature such as diacylglycerol and phosphatidylethanolamine inhibited membrane permeabilization. The differential effects of nonlamellar lipids on membrane permeabilization were not correlated with lipid-induced changes in membrane binding or insertion of Bax or DeltaN76Bcl-x(L). Altogether, these results are consistent with a model whereby Bax-type proteins change the bending propensity of the membrane to form pores comprised at least in part of lipids in a structure of net positive monolayer curvature.     

Advancing Edge Speeds of Epithelial Monolayers Depend on Their Initial Confining Geometry

Collective cell migrations are essential in several physiological processes and are driven by both chemical and mechanical cues. The roles of substrate stiffness and confinement on collective migrations have been investigated in recent years, however few studies have addressed how geometric shapes influence collective cell migrations. Here, we address the hypothesis that the relative position of a cell within the confinement influences its motility. Monolayers of two types of epithelial cells—MCF7, a breast epithelial cancer cell line, and MDCK, a control epithelial cell line—were confined within circular, square, and cross-shaped stencils and their migration velocities were quantified upon release of the constraint using particle image velocimetry. The choice of stencil geometry allowed us to investigate individual cell motility within convex, straight and concave boundaries. Cells located in sharp, convex boundaries migrated at slower rates than those in concave or straight edges in both cell types. The overall cluster migration occurred in three phases: an initial linear increase with time, followed by a plateau region and a subsequent decrease in cluster speeds. An acto-myosin contractile ring, present in the MDCK but absent in MCF7 monolayer, was a prominent feature in the emergence of leader cells from the MDCK clusters which occurred every ~125 μm from the vertex of the cross. Further, coordinated cell movements displayed vorticity patterns in MDCK which were absent in MCF7 clusters. We also used cytoskeletal inhibitors to show the importance of acto-myosin bounding cables in collective migrations through translation of local movements to create long range coordinated movements and the creation of leader cells within ensembles. To our knowledge, this is the first demonstration of how bounding shapes influence long-term migratory behaviours of epithelial cell monolayers. These results are important for tissue engineering and may also enhance our understanding of cell movements during developmental patterning and cancer metastasis.     

Living microlens arrays

Both individual cells and sheets of cells exert traction forces on the substrate and these forces have been investigated using a wide range of methods. Here we compare the mechanical properties of fibroblasts and epithelial cells using a novel surface geometry. Living cells are added to a thin film of polystyrene [PS] attached to a substrate of crosslinked poly(dimethyl siloxane) [PDMS] microwells. The contractile nature of the cells attached to the surface and the compliance of the PDMS surface geometry allows the PS thin film to buckle, forming arrays of convex microlenses. The resulting curvature of the microlenses allows us to determine the applied strain of growing cell sheets. We report that a monolayer of epithelial cells exerts more stress on the substrate than fibroblasts and attribute this to the collective behavior of the epithelium. By subsequently adding different chemical triggers to the system, the contractile nature of the cells changes, thus modifying the focal length of the microlenses. Together, these findings demonstrate the importance of studying the mechanics of cell sheets and also introduce a new design paradigm for advanced materials, offering great promise for a range of applications.     

In vivo tibial stiffness is maintained by whole bone morphology and cross-sectional geometry in growing female mice

Whole bone morphology, cortical geometry, and tissue material properties modulate skeletal stresses and strains that in turn influence skeletal physiology and remodeling. Understanding how bone stiffness, the relationship between applied load and tissue strain, is regulated by developmental changes in bone structure and tissue material properties is important in implementing biophysical strategies for promoting healthy bone growth and preventing bone loss. The goal of this study was to relate developmental patterns of in vivo whole bone stiffness to whole bone morphology, cross-sectional geometry, and tissue properties using a mouse axial loading model. We measured in vivo tibial stiffness in three age groups (6, 10, 16 wk old) of female C57Bl/6 mice during cyclic tibial compression. Tibial stiffness was then related to cortical geometry, longitudinal bone curvature, and tissue mineral density using microcomputed tomography (microCT). Tibial stiffness and the stresses induced by axial compression were generally maintained from 6 to 16 wks of age. Growth-related increases in cortical cross-sectional geometry and longitudinal bone curvature had counteracting effects on induced bone stresses and, therefore, maintained tibial stiffness similarly with growth. Tissue mineral density increased slightly from 6 to 16 wks of age, and although the effects of this increase on tibial stiffness were not directly measured, its role in the modulation of whole bone stiffness was likely minor over the age range examined. Thus, whole bone morphology, as characterized by longitudinal curvature, along with cortical geometry, plays an important role in modulating bone stiffness during development and should be considered when evaluating and designing in vivo loading studies and biophysical skeletal therapies.     

Minimal Network Topologies for Signal Processing during Collective Cell Chemotaxis

Cell-cell communication plays an important role in collective cell migration. However, it remains unclear how cells in a group cooperatively process external signals to determine the group’s direction of motion. Although the topology of signaling pathways is vitally important in single-cell chemotaxis, the signaling topology for collective chemotaxis has not been systematically studied. Here, we combine mathematical analysis and simulations to find minimal network topologies for multicellular signal processing in collective chemotaxis. We focus on border cell cluster chemotaxis in the Drosophila egg chamber, in which responses to several experimental perturbations of the signaling network are known. Our minimal signaling network includes only four elements: a chemoattractant, the protein Rac (indicating cell activation), cell protrusion, and a hypothesized global factor responsible for cell-cell interaction. Experimental data on cell protrusion statistics allows us to systematically narrow the number of possible topologies from more than 40,000,000 to only six minimal topologies with six interactions between the four elements. This analysis does not require a specific functional form of the interactions, and only qualitative features are needed; it is thus robust to many modeling choices. Simulations of a stochastic biochemical model of border cell chemotaxis show that the qualitative selection procedure accurately determines which topologies are consistent with the experiment. We fit our model for all six proposed topologies; each produces results that are consistent with all experimentally available data. Finally, we suggest experiments to further discriminate possible pathway topologies.     

Review of biophysical factors affecting osteogenic differentiation of human adult adipose-derived stem cells

Developing bone is subject to the control of a broad variety of influences in vivo. For bone repair applications, in vitro osteogenic assays are routinely used to test the responses of bone-forming cells to drugs, hormones, and biomaterials. Results of these assays are used to predict the behavior of bone-forming cells in vivo. Stem cell research has shown promise for enhancing bone repair. In vitro osteogenic assays to test the bone-forming response of stem cells typically use chemical solutions. Stem cell in vitro osteogenic assays often neglect important biophysical cues, such as the forces associated with regular weight-bearing exercise, which promote bone formation. Incorporating more biophysical cues that promote bone formation would improve in vitro osteogenic assays for stem cells. Improved in vitro osteogenic stimulation opens opportunities for “pre-conditioning” cells to differentiate towards the desired lineage. In this review, we explore the role of select biophysical factors—growth surfaces, tensile strain, fluid flow and electromagnetic stimulation—in promoting osteogenic differentiation of stem cells from human adipose. Emphasis is placed on the potential for physical microenvironment manipulation to translate tissue engineering and stem cell research into widespread clinical usage.