Osteoblasts infill irregular pores under curvature and porosity controls: a hypothesis-testing analysis of cell behaviours

The geometric control of bone tissue growth plays a significant role in bone remodelling, age-related bone loss, and tissue engineering. However, how exactly geometry influences the behaviour of bone-forming cells remains elusive. Geometry modulates cell populations collectively through the evolving space available to the cells, but it may also modulate the individual behaviours of cells. To factor out the collective influence of geometry and gain access to the geometric regulation of individual cell behaviours, we develop a mathematical model of the infilling of cortical bone pores and use it with available experimental data on cortical infilling rates. Testing different possible modes of geometric controls of individual cell behaviours consistent with the experimental data, we find that efficient smoothing of irregular pores only occurs when cell secretory rate is controlled by porosity rather than curvature. This porosity control suggests the convergence of a large scale of intercellular signalling to single bone-forming cells, consistent with that provided by the osteocyte network in response to mechanical stimulus. After validating the mathematical model with the histological record of a real cortical pore infilling, we explore the infilling of a population of randomly generated initial pore shapes. We find that amongst all the geometric regulations considered, the collective influence of curvature on cell crowding is a dominant factor for how fast cortical bone pores infill, and we suggest that the irregularity of cement lines thereby explains some of the variability in double labelling data as well as the overall speed of osteon infilling.     

A Mechanobiology-based Algorithm to Optimize the Microstructure Geometry of Bone Tissue Scaffolds

Complexity of scaffold geometries and biological mechanisms involved in the bone generation process make the design of scaffolds a quite challenging task. The most common approaches utilized in bone tissue engineering require costly protocols and time-consuming experiments. In this study we present an algorithm that, combining parametric finite element models of scaffolds with numerical optimization methods and a computational mechano-regulation model, is able to predict the optimal scaffold microstructure. The scaffold geometrical parameters are perturbed until the best geometry that allows the largest amounts of bone to be generated, is reached. We study the effects of the following factors: (1) the shape of the pores; (2) their spatial distribution; (3) the number of pores per unit area. The optimal dimensions of the pores have been determined for different values of scaffold Young''s modulus and compression loading acting on the scaffold upper surface.Pores with rectangular section were predicted to lead to the formation of larger amounts of bone compared to square section pores; similarly, elliptic pores were predicted to allow the generation of greater amounts of bone compared to circular pores. The number of pores per unit area appears to have rather negligible effects on the bone regeneration process. Finally, the algorithm predicts that for increasing loads, increasing values of the scaffold Young''s modulus are preferable.The results shown in the article represent a proof-of-principle demonstration of the possibility to optimize the scaffold microstructure geometry based on mechanobiological criteria.     

Soluble and insoluble signals sculpt osteogenesis in angiogenesis

The basic tissue engineering paradigm is tissue induction and morphogenesis by combinatorial molecular protocols whereby soluble molecular signals are combined with insoluble signals or substrata. The insoluble signal acts as a three-dimensional scaffold for the initiation of de novo tissue induction and morphogenesis. The osteogenic soluble molecular signals of the transforming growth factor-β (TGF-β) supergene family, the bone morphogenetic/osteogenic proteins (BMPs/OPs) and, uniquely in the non-human primate Papio ursinus (P. ursinus), the three mammalian TGF-β isoforms induce bone formation as a recapitulation of embryonic development. In this paper, I discuss the pleiotropic activity of the BMPs/OPs in the non-human primate P. ursinus, the induction of bone by transitional uroepithelium, and the apparent redundancy of molecular signals initiating bone formation by induction including the three mammalian TGF-β isoforms. Amongst all mammals tested so far, the three mammalian TGF-β isoforms induce endochondral bone formation in the non-human primate P. ursinus only. Bone tissue engineering starts by erecting scaffolds of biomimetic biomaterial matrices that mimic the supramolecular assembly of the extracellular matrix of bone. The molecular scaffolding lies at the hearth of all tissue engineering strategies including the induction of bone formation. The novel concept of tissue engineering is the generation of newly formed bone by the implantation of "smart" intelligent biomimetic matrices that per se initiate the ripple-like cascade of bone differentiation by induction without exogenously applied BMPs/OPs of the TGF-β supergene family. A comprehensive digital iconographic material presents the modified tissue engineering paradigm whereby the induction of bone formation is initiated by intelligent smart biomimetic matrices that per se initiate the induction of bone formation without the exogenous application of the soluble osteogenic molecular signals. The driving force of the intrinsic induction of bone formation by bioactive biomimetic matrices is the shape of the implanted substratum. The language of shape is the language of geometry; the language of geometry is the language of a sequence of repetitive concavities, which biomimetizes the remodelling cycle of the primate osteonic bone.     

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.     

Bone remodelling in Neanderthal mandibles from the El Sidrón site (Asturias, Spain)

Skull morphology results from the bone remodelling mechanism that underlies the specific bone growth dynamics. Histological study of the bone surface from Neanderthal mandible specimens of El Sidrón (Spain) provides information about the distribution of the remodelling fields (bone remodelling patterns or BRP) indicative of the bone growth directions. In comparison with other primate species, BRP shows that Neanderthal mandibles from the El Sidrón (Spain) sample present a specific BRP. The interpretation of this map allows inferences concerning the growth directions that explain specific morphological traits of the Neanderthal mandible, such as its quadrangular shape and the posterior location of the mental foramen.     

Remodelling of skeletal tissues bone and structural specialisations in an elasmosaurid (Sauropterygia: Plesiosauroidea) from the Upper Cretaceous of Patagonia,Argentina

Elasmosauridae were cosmopolitan Late Cretaceous plesiosaurs with conspicuous morphological diversity. Within this group, vertebral morphology is a criterion for estimating relative age in plesiosaur. On the other hand, the microstructure of plesiosaur bone is considered as indicative of ontogenetic stage. However, knowledge about ontogenetic tissue transformation in different elements of the skeleton is poorly known. Resorption and remodelling of skeletal tissues are required for development and growth, mechanical adaptation, repair and mineral homeostasis of the vertebrate skeleton. This contribution analyses different postcranial elements of a Late Cretaceous elasmosaurid from Patagonia. Characterisation of bone microstructure indicates the presence of compact bone inner organisation in an adult derived plesiosaur from the Cretaceous and that the distribution of bone specialisations depicts conspicuous variations within a single skeleton depending on the skeletal element considered. Bone compactness or degree of remodelling in elasmosaurids is not necessarily correlated with the ontogenetic age of the animal or to costal versus pelagic lifestyles. The available data are still scarce, but we propose a topic of discussion: perhaps the degree of remodelling and compactness also may be related to the activity level and increased mechanical load in different skeletal elements.     

Prediction of shape and internal structure of the proximal femur using a modified level set method for structural topology optimisation

A computational framework was developed to simulate the bone remodelling process as a structural topology optimisation problem. The mathematical formulation of the Level Set technique was extended and then implemented into a coronal plane model of the proximal femur to simulate the remodelling of internal structure and external geometry of bone into the optimal state. Results indicated that the proposed approach could reasonably mimic the major geometrical and material features of the natural bone. Simulation of the internal bone remodelling on the typical gross shape of the proximal femur, resulted in a density distribution pattern with good consistency with that of the natural bone. When both external and internal bone remodelling were simulated simultaneously, the initial rectangular design domain with a regularly distributed mass reduced gradually to an optimal state with external shape and internal structure similar to those of the natural proximal femur.     

Prediction of shape and internal structure of the proximal femur using a modified level set method for structural topology optimisation

A computational framework was developed to simulate the bone remodelling process as a structural topology optimisation problem. The mathematical formulation of the Level Set technique was extended and then implemented into a coronal plane model of the proximal femur to simulate the remodelling of internal structure and external geometry of bone into the optimal state. Results indicated that the proposed approach could reasonably mimic the major geometrical and material features of the natural bone. Simulation of the internal bone remodelling on the typical gross shape of the proximal femur, resulted in a density distribution pattern with good consistency with that of the natural bone. When both external and internal bone remodelling were simulated simultaneously, the initial rectangular design domain with a regularly distributed mass reduced gradually to an optimal state with external shape and internal structure similar to those of the natural proximal femur.     

A multiscale optimisation method for bone growth scaffolds based on triply periodic minimal surfaces

Tissue engineered bone scaffolds are potential alternatives to bone allografts and autografts. Porous scaffolds based on triply periodic minimal surfaces (TPMS) are good candidates for tissue growth because they offer high surface-to-volume ratio, have tailorable stiffness, and can be easily fabricated by additive manufacturing. However, the range of TPMS scaffold types is extensive, and it is not yet clear which type provides the fastest cell or tissue growth while being sufficiently stiff to act as a bone graft. Nor is there currently an established methodology for TPMS bone scaffold design which can be quickly adopted by medical designers or biologists designing implants. In this study, we examine six TPMS scaffold types for use as tissue growth scaffolds and propose a general methodology to optimise their geometry. At the macro-scale, the optimisation routine ensures a scaffold stiffness within suitable limits for bone, while at the micro-scale it maximises the cell growth rate. The optimisation procedure also ensures the scaffold pores are of sufficient diameter to allow oxygen and nutrient delivery via capillaries. Of the examined TPMS structures, the Lidinoid and Split P cell types provide the greatest cell growth rates and are therefore the best candidates for bone scaffolds.

     

Mechanical properties of pore-spanning lipid bilayers probed by atomic force microscopy

We measure the elastic response of a free-standing lipid membrane to a local indentation by using an atomic force microscope. Starting point is a planar gold-coated alumina substrate with a chemisorbed 3-mercaptopropionic acid monolayer displaying circular pores of very well defined and tunable size, over which bilayers composed of N,N,-dimethyl-N,N,-dioctadecylammonium bromide or 1,2-dioleoyl-3-trimethylammonium-propane chloride were spread. Centrally indenting these "nanodrums" with an atomic force microscope tip yields force-indentation curves, which we quantitatively analyze by solving the corresponding shape equations of continuum curvature elasticity. Since the measured response depends in a known way on the system geometry (pore size, tip radius) and on material parameters (bending modulus, lateral tension), this opens the possibility to monitor local elastic properties of lipid membranes in a well-controlled setting.     

A novel adaptive algorithm for 3D finite element analysis to model extracortical bone growth

Extracortical bone growth with osseointegration of bone onto the shaft of massive bone tumour implants is an important clinical outcome for long-term implant survival. A new computational algorithm combining geometrical shape changes and bone adaptation in 3D Finite Element simulations has been developed, using a soft tissue envelope mesh, a novel concept of osteoconnectivity, and bone remodelling theory. The effects of varying the initial tissue density, spatial influence function and time step were investigated. The methodology demonstrated good correspondence to radiological results for a segmental prosthesis.     

Functional strain in bone tissue as an objective, and controlling stimulus for adaptive bone remodelling

The skeleton consists of a series of elements with a variety of functions. In locations where shape or protection are of prime importance the bone's architecture is achieved during growth under direct genetic control. In locations where resistance to repetitive loading is important only the general form of the bone will be achieved as a result of growth alone, the remaining characteristics result from functional adaptation. This mechanism ensures that bone architecture is modelled and remodelled until prevailing strains match those genetically prescribed for that location. For this match to be established, and subsequently maintained, bone cells must be able to 'assess' feedback derived directly or indirectly from the functional strains produced within the tissue. These strains are therefore the objective of functionally adaptive remodelling, and the stimulus for its control. Evans was the first person to refer to the recording of functional strains from gauges attached to bone in vivo. This technique has allowed quantitative investigations on bone's normal functional strain environment, and its adaptive response to changes in its state of strain. Recent investigations have extended to the immediate effects of dynamic strains on the structure of the bone matrix, and the biochemical behaviour of the resident bone cells. Such studies should reveal the mechanism by which strains within the matrix are transduced into the biochemical signals by which adaptive remodelling is controlled.     

Bacterial cell curvature through mechanical control of cell growth

The cytoskeleton is a key regulator of cell morphogenesis. Crescentin, a bacterial intermediate filament‐like protein, is required for the curved shape of Caulobacter crescentus and localizes to the inner cell curvature. Here, we show that crescentin forms a single filamentous structure that collapses into a helix when detached from the cell membrane, suggesting that it is normally maintained in a stretched configuration. Crescentin causes an elongation rate gradient around the circumference of the sidewall, creating a longitudinal cell length differential and hence curvature. Such curvature can be produced by physical force alone when cells are grown in circular microchambers. Production of crescentin in Escherichia coli is sufficient to generate cell curvature. Our data argue for a model in which physical strain borne by the crescentin structure anisotropically alters the kinetics of cell wall insertion to produce curved growth. Our study suggests that bacteria may use the cytoskeleton for mechanical control of growth to alter morphology.     

Study of cycle of cell wall assembly in Streptococcus faecalis by three-dimensional reconstructions of thin sections of cells.

A new ultrastructural method was used to study rounds of envelope synthesis that occur in Streptococcus faecalis in "growth zones" found between pairs of naturally occurring surface markers. The technique consists of producing three-dimensional reconstructions of these growth zones from the mathematical rotation, about a central axis, of measurements taken from central, longitudinal thin sections of cells. A cycle of exponential-phase envelope growth was then simulated by arranging a series of these reconstructions in increasing order of the amount of peripheral wall surface area or the amount of cell volume that each was calculated to contain. Using this simulated cycle of growth, the geometry of a single growth zone during a round of synthesis was studied. Based on this analysis, a model was developed for the assembly of the cell wall of S. faecalis. The model states that new cell wall surface is synthesized by the regulated flow of essentially two channels of cell wall precursors into a single growth zone. One channel of precursors would be involved in the assembly of a bilayered cross wall that would proceed at a fairly constant rate until the cross wall closes. The second channel of precursors would be involved in the separation of the bilayered cross wall into two segments of peripheral wall. These precursors would intercalate into and thicken the separating layers of the cross wall. The flow of precursors through this channel would be progressively reduced through a cycle. These decreases, when coupled with internal hydrostatic pressure, apparently would result in the enlarging peripheral wall becoming increasingly more curved and would also promote cell division by reducing the total amount of cell wall that must be assembled in order for septation to occur.     

Modelling external bone adaptation using evolutionary structural optimisation

External remodelling is significant in the bone healing process, and it is essential to predict the bone external shape in the design of artificial bone grafts. This paper demonstrates the effectiveness of the evolutionary structural optimisation (ESO) method for the simulation of bone morphology. A two-dimensional ESO strategy is developed which is capable of finding the modified bone topology beginning with any geometry under any loading conditions. The morphology of bone structure is described by the quantitative bone adaptation theory, which is integrated with the finite element method. The evolutionary topology optimisation process is introduced to find the bone shape. A rectangle, which occupies a larger space than the external shape of the bone structure, is specified as a design domain; the evolutionary process iteratively eliminates and redistributes material throughout the domain to obtain an optimum arrangement of bone materials. The technique has been tested on a wide range of examples. In this paper, the formation of trabecular bone architecture around an implant is studied; as another example, the growth of the coronal section of a vertebral body is predicted. The examples support the assertion that the external shape of bone structure can be successfully predicted by the proposed ESO procedure.     

PROROCENTRUM BELIZEANUM,PROROCENTRUM ELEGANS,AND PROROCENTRUM CARIBBAEUM,THREE NEW BENTHIC SPECIES (DINOPHYCEAE) FROM A MANGROVE ISLAND,TWIN CAYS,BELIZE1

Three new benthic dinoflagellate species, Prorocentrum belizeanum, Prorocentrum elegans, and Prorocentrum caribbaeum, from mangrove floating detritus are described from scanning electron micrographs. Species were identified based on shape, size, surface micromorphology, ornamentation of thecal plates, and architecture of the periflagellar area and intercalary band. Cells of P. belizeanum are round to slightly oval with a cell size of 55–60 μm long and 50–55 μm wide. Areolae are round and numerous (853–1024 per valve) and range from 0.66 to 0.83 μm in size. The periflagellar area of P. belizeanum is a broad V-shaped depression; it accommodates a flagellar and an auxiliary pore and a flared, curved apical collar. The intercalary band of P. belizeanum is horizontally striated. Prorocentrum elegans is a small species 15–20 μm long and 10–14 μm wide, with an ovate cell shape. The thecal surface is smooth. Two sizes of valve pores were recognized: large, round pores (20–22 per valve) arranged in a distinct pattern and smaller pores situated in an array along the intercalary band. The periflagellar area is V-shaped; it accommodates an uneven sized flagellar pore, an auxiliary pore, and an angled protuberant flagellar plate. The intercalary band is transversely striated. It is a bloom-forming species. Prorocentrum caribbaeum cells are heart-shaped with a rounded anterior end and a pointed posterior end. Cells range from 40 to 45 μm long and 30 to 35 μm wide. Thecal surface has two different-sized pores: large, round pores (145–203 per valve) arranged perpendicularly from the posterior margins, and small, round pores unevenly distributed on the thecal surface. The periflagellar area is ornate. It is V-shaped with a curved apical collar located next to the auxiliary pore; a smaller protuberant apical plate is adjacent to the flagellar pore. The intercalary band is transversely striated and sinuous. Cells are active swimmers.     

Filamentous network mechanics and active contractility determine cell and tissue shape

For both cells and tissues, shape is closely correlated with function presumably via geometry-dependent distribution of tension. In this study, we identify common shape determinants spanning cell and tissue scales. For cells whose sites of adhesion are restricted to small adhesive islands on a micropatterned substrate, shape resembles a sequence of inward-curved circular arcs. The same shape is observed for fibroblast-populated collagen gels that are pinned to a flat substrate. Quantitative image analysis reveals that, in both cases, arc radii increase with the spanning distance between the pinning points. Although the Laplace law for interfaces under tension predicts circular arcs, it cannot explain the observed dependence on the spanning distance. Computer simulations and theoretical modeling demonstrate that filamentous network mechanics and contractility give rise to a modified Laplace law that quantitatively explains our experimental findings on both cell and tissue scales. Our model in conjunction with actomyosin inhibition experiments further suggests that cell shape is regulated by two different control modes related to motor contractility and structural changes in the actin cytoskeleton.     

Cell Geometry Guides the Dynamic Targeting of Apoplastic GPI-Linked Lipid Transfer Protein to Cell Wall Elements and Cell Borders in Arabidopsis thaliana

During cellular morphogenesis, changes in cell shape and cell junction topology are fundamental to normal tissue and organ development. Here we show that apoplastic Glycophosphatidylinositol (GPI)-anchored Lipid Transfer Protein (LTPG) is excluded from cell junctions and flat wall regions, and passively accumulates around their borders in the epidermal cells of Arabidopsis thaliana. Beginning with intense accumulation beneath highly curved cell junction borders, this enrichment is gradually lost as cells become more bulbous during their differentiation. In fully mature epidermal cells, YFP-LTPG often shows a fibrous cellulose microfibril-like pattern within the bulging outer faces. Physical contact between a flat glass surface and bulbous cell surface induces rapid and reversible evacuation from contact sites and accumulation to the curved wall regions surrounding the contact borders. Thus, LTPG distribution is dynamic, responding to changes in cell shape and wall curvature during cell growth and differentiation. We hypothesize that this geometry-based mechanism guides wax-carrying LTPG to functional sites, where it may act to “seal” the vulnerable border surrounding cell-cell junctions and assist in cell wall fortification and cuticular wax deposition.     

Local force and geometry sensing regulate cell functions

The shapes of eukaryotic cells and ultimately the organisms that they form are defined by cycles of mechanosensing, mechanotransduction and mechanoresponse. Local sensing of force or geometry is transduced into biochemical signals that result in cell responses even for complex mechanical parameters such as substrate rigidity and cell-level form. These responses regulate cell growth, differentiation, shape changes and cell death. Recent tissue scaffolds that have been engineered at the micro- and nanoscale level now enable better dissection of the mechanosensing, transduction and response mechanisms.     

Guidance of engineered tissue collagen orientation by large-scale scaffold microstructures

The tensile strength and stiffness of load-bearing soft tissues are dominated by their collagen fiber orientation. While microgrooved substrates have demonstrated a capacity to orient cells and collagen in monolayer tissue culture, tissue engineering (TE) scaffolds are structurally distinct in that they consist of a three-dimensional (3-D) open pore network. It is thus unclear how the geometry of these open pores might influence cell and collagen orientation. In the current study we developed an in vitro model system for quantifying the capacity of large scale ( approximately 200 microm), geometrically well-defined open pores to guide cell and collagen orientation in engineered tissues. Non-degradable scaffolds exhibiting a grid of 200 microm wide rectangular pores (1:1, 2:1, 5:1, and 10:1 aspect ratios) were fabricated from a transparent epoxy resin via high-resolution stereolithography. The scaffolds (n=6 per aspect ratio) were surface modified to support cell adhesion by covalently grafting GRGDS peptides, sterilized, and seeded with neonatal rat skin fibroblasts. Following 4 weeks of static incubation, the resultant collagen orientation was assessed quantitatively by small angle light scattering (SALS), and cell orientation was evaluated by laser confocal and scanning electron microscopy. Cells adhered to the struts of the pores and proceeded to span the pores in a generally circumferential pattern. While the cell and collagen orientations within 1:1 aspect ratio pores were effectively random, higher aspect ratio rectangular pores exhibited a significant capacity to guide global cell and collagen orientation. Preferential alignment parallel to the long strut axis and decreased spatial variability were observed to occur with increasing pore aspect ratio. Intra-pore variability depended in part on the spatial uniformity of cell attachment around the perimeter of each pore achieved during seeding. Evaluation of diamond-shaped pores [Sacks, M.S. et al., 1997. J. Biomech. Eng. 119(1), 124-127] suggests that they are less sensitive to initial conditions of cell attachment than rectangular pores, and thus more effective in guiding engineered tissue cell and collagen orientation.