Nanoscale integrin cluster dynamics controls cellular mechanosensing via FAKY397 phosphorylation

Transduction of extracellular matrix mechanics affects cell migration, proliferation, and differentiation. While this mechanotransduction is known to depend on the regulation of focal adhesion kinase phosphorylation on Y397 (FAKpY397), the mechanism remains elusive. To address this, we developed a mathematical model to test the hypothesis that FAKpY397-based mechanosensing arises from the dynamics of nanoscale integrin clustering, stiffness-dependent disassembly of integrin clusters, and FAKY397 phosphorylation within integrin clusters. Modeling results predicted that integrin clustering dynamics governs how cells convert substrate stiffness to FAKpY397, and hence governs how different cell types transduce mechanical signals. Existing experiments on MDCK cells and HT1080 cells, as well as our new experiments on 3T3 fibroblasts, confirmed our predictions and supported our model. Our results suggest a new pathway by which integrin clusters enable cells to calibrate responses to their mechanical microenvironment.

Programmable and robust static topological solitons in mechanical metamaterials

Solitary, persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems. Mechanical solitons characteristically emerge either as a single wave packet or uncorrelated propagating topological entities through space and/or time, but these are notoriously difficult to control. Here, we report a theoretical framework for programming static periodic topological solitons into a metamaterial, and demonstrate its implementation in real metamaterials computationally and experimentally. The solitons are excited by deformation localizations under quasi-static compression, and arise from buckling-induced kink-antikink bands that provide domain separation barriers. The soliton number and wavelength demonstrate a previously unreported size-dependence, due to intrinsic length scales. We identify that these unanticipated solitons stem from displacive phase transitions with periodic topological excitations captured by the well-known [Formula: see text] theory. Results reveal pathways for robust regularizations of stochastic responses of metamaterials.

Cryoprotectant enables structural control of porous scaffolds for exploration of cellular mechano-responsiveness in 3D

Despite the wide applications, systematic mechanobiological investigation of 3D porous scaffolds has yet to be performed due to the lack of methodologies for decoupling the complex interplay between structural and mechanical properties. Here, we discover the regulatory effect of cryoprotectants on ice crystal growth and use this property to realize separate control of the scaffold pore size and stiffness. Fibroblasts and macrophages are sensitive to both structural and mechanical properties of the gelatin scaffolds, particularly to pore sizes. Interestingly, macrophages within smaller and softer pores exhibit pro-inflammatory phenotype, whereas anti-inflammatory phenotype is induced by larger and stiffer pores. The structure-regulated cellular mechano-responsiveness is attributed to the physical confinement caused by pores or osmotic pressure. Finally, in vivo stimulation of endogenous fibroblasts and macrophages by implanted scaffolds produce mechano-responses similar to the corresponding cells in vitro, indicating that the physical properties of scaffolds can be leveraged to modulate tissue regeneration.

Cellular responses to mechanical stimulation have emerged as an important area of research. Here, the authors use cryoprotectant to control the pore size and mechanical properties of porous scaffolds without changing the scaffold composition to allow for the study of cellular mechano-responsiveness in 3D.

Regulation of Cell Behavior by Hydrostatic Pressure

Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.

Atomic force microscopy of phase separation on ruptured, giant unilamellar vesicles, and a mechanical pathway for the co-existence of lipid gel phases

Giant unilamellar vesicles (GUVs) and supported lipid bilayers (SLBs) are synthetic model systems widely used in biophysical studies of lipid membranes. Although SLBs are advantageous for biophysical analysis, phase separation behaviors of lipid species in these two model systems can differ due to the lipid-substrate interactions that are present only for SLBs. In the present study, we report that in binary systems, certain phase domains on GUVs retain their original shapes and patterns after the GUVs rupture on glass surfaces. This enabled atomic force microscopy (AFM) experiments on phase domains, a procedure difficult to perform and interpret when applied to GUVs. Unusual phase behavior was evident in binary GUVs containing DLPC and either DPPC or DSPC. These DLPC/DSPC and DLPC/DPPC GUVs both presented the thermodynamic anomaly of having two co-existing gel phases. One phase (a bright phase) included a relatively high concentration of DiI-C20 but excluded Bodipy-HPC, and the other (dark phase) excluded both probes. The bright phases are of interest because they seem to stabilize dark phases against coalescence. Results suggested that the gel phases labeled by DiIC20 in the DLPC/DSPC membrane, which surround the dark gel phase, is an extra layer of membrane, indicating a highly curved structure that might stabilize the interior dark domains, thereby enabling the co-existence of two different gel phases. Results show the utility of AFM on collapsed GUVs, and suggest a possible mechanism for stabilization of lipid domains.

Translation of a Coated Rigid Spherical Inclusion in an Elastic Matrix: Exact Solution, and Implications for Mechanobiology

The displacement of relatively rigid beads within a relatively compliant, elastic matrix can be used to measure the mechanical properties of the matrix. For example, in mechanobiological studies, magnetic or reflective beads can be displaced with a known external force to estimate the matrix modulus. Although such beads are generally rigid compared to the matrix, the material surrounding the beads typically differs from the matrix in one or two ways. The first case, as is common in mechanobiological experimentation, is the situation in which the bead must be coated with materials such as protein ligands that enable adhesion to the matrix. These layers typically differ in stiffness relative to the matrix material. The second case, common for uncoated beads, is the situation in which the beads disrupt the structure of the hydrogel or polymer, leading to a region of enhanced or reduced stiffness in the neighborhood of the bead. To address both cases, we developed the first analytical solution of the problem of translation of a coated, rigid spherical inclusion displaced within an isotropic elastic matrix by a remotely applied force. The solution is applicable to cases of arbitrary coating stiffness and size of the coating. We conclude by discussing applications of the solution to mechanobiology.

A preliminary study of the local biomechanical environment of liver tumors in vivo

PURPOSE

Biomechanical properties can be used as biomarkers to diagnose tumors, monitor tumor development, and evaluate treatment efficacy. The purpose of this preliminary study is to characterize the biomechanical environment of two typical liver tumors, hemangiomas (HEMs) and hepatocellular carcinomas (HCCs), and to investigate the potential of using strain metrics as biomarkers for tumor diagnosis, based on a limited clinical dataset.

METHODS

Magnetic resonance (MR) tagging was used to quantify the motion and deformation of the two types of liver tumors. Displacements of the tumors arising from a heartbeat were measured over one cardiac cycle. Local biomechanical conditions of the tumors were characterized by estimating two principal strains (ε₁ and ε₂ ) and an octahedral shear strain (ε_soct ) of the tumor and its peripheral region. Biomechanical conditions of the tumors were compared with those of the arbitrarily selected regions from healthy volunteers.

RESULTS

We observed that the HCCs had significantly smaller strain values compared to their peripheral tissues. However, the HEMs did not have significantly different strains from those of the peripheral tissues, and were similar to healthy liver regions. The sensitivity of using ε₁ , ε₂ , and ε_soct to diagnose HCC were all 1, while the sensitivity of using ε₁ , ε₂ , and ε_soct to diagnose HEM were 0.67, 0.17, and 0.67, respectively.

CONCLUSIONS

Lagrangian strain metrics provide insight into the biomechanical conditions of certain liver tumors in the human body and may provide another perspective for tumor characterization and diagnosis.

The multiscale structural and mechanical effects of mouse supraspinatus muscle unloading on the mature enthesis

The musculoskeletal system is sensitive to its loading environment; this is of particular concern under conditions such as disuse, paralysis, and extended-duration space flight. Although structural and mechanical changes to tendon and bone following paralysis and disuse are well understood, there is a pressing need to understand how this unloading affects the bone-tendon interface (enthesis); the location most prone to tears and injury. We therefore elucidated these effects of unloading in the entheses of adult mice shoulders that were paralyzed for 21 days by treatment with botulinum toxin A. Unloading significantly increased the extent of mechanical failure and was associated with structural changes across hierarchical scales. At the millimeter scale, unloading caused bone loss. At the micrometer scale, unloading decreased bioapatite crystal size and crystallographic alignment in the enthesis. At the nanometer scale, unloading induced compositional changes that stiffened the bioapatite/collagen composite tissue. Mathematical modeling and mechanical testing indicated that these factors combined to increase local elevations of stress while decreasing the ability of the tissue to absorb energy prior to failure, thereby increasing injury risk. These first observations of the multiscale effects of unloading on the adult enthesis provide new insight into the hierarchical features of structure and composition that endow the enthesis with increased resistance to failure. STATEMENT OF SIGNIFICANCE: The musculoskeletal system is sensitive to its loading environment; this is of particular concern under conditions such as disuse, paralysis, and extended-duration space flight. Although changes to tendon and bone following paralysis are understood, there is a pressing need to clarify how unloading affects the bone-tendon interface (enthesis), which is the location most prone to tears and injury. We elucidated the effects of enthesis unloading in adult mice shoulders showing, for the first time, that unloading significantly increased the risk and extent of mechanical failure and was associated with structural changes across hierarchical scales. These observations provide new insight into the hierarchical features of structure and composition that endow the enthesis with resilience. This knowledge can be used to develop more targeted treatments to improve mobility and function.

Regularization-Free Strain Mapping in Three Dimensions, With Application to Cardiac Ultrasound

Quantifying dynamic strain fields from time-resolved volumetric medical imaging and microscopy stacks is a pressing need for radiology and mechanobiology. A critical limitation of all existing techniques is regularization: because these volumetric images are inherently noisy, the current strain mapping techniques must impose either displacement regularization and smoothing that sacrifices spatial resolution, or material property assumptions that presuppose a material model, as in hyperelastic warping. Here, we present, validate, and apply the first three-dimensional (3D) method for estimating mechanical strain directly from raw 3D image stacks without either regularization or assumptions about material behavior. We apply the method to high-frequency ultrasound images of mouse hearts to diagnose myocardial infarction. We also apply the method to present the first ever in vivo quantification of elevated strain fields in the heart wall associated with the insertion of the chordae tendinae. The method shows promise for broad application to dynamic medical imaging modalities, including high-frequency ultrasound, tagged magnetic resonance imaging, and confocal fluorescence microscopy.

The relationship between thiol-acrylate photopolymerization kinetics and hydrogel mechanics: An improved model incorporating photobleaching and thiol-Michael addition

Biocompatible hydrogels with defined mechanical properties are critical to tissue engineering and regenerative medicine. Thiol-acrylate photopolymerized hydrogels have attracted special interest for their degradability and cytocompatibility, and for their tunable mechanical properties through controlling factors that affect reaction kinetics (e.g., photopolymerization, stoichiometry, temperature, and solvent choice). In this study, we hypothesized that the mechanical property of these hydrogels can be tuned by photoinitiators via photobleaching and by thiol-Michael addition reactions. To test this hypothesis, a multiscale mathematical model incorporating both photobleaching and thiol-Michael addition reactions was developed and validated. After validating the model, the effects of thiol concentration, light intensity, and pH values on hydrogel mechanics were investigated. Results revealed that hydrogel stiffness (i) was maximized at a light intensity-specific optimal concentration of thiol groups; (ii) increased with decreasing pH when synthesis occurred at low light intensity; and (iii) increased with decreasing light intensity when synthesis occurred at fixed precursor composition. The multiscale model revealed that the latter was due to higher initiation efficiency at lower light intensity. More broadly, the model provides a framework for predicting mechanical properties of hydrogels based upon the controllable kinetics of thiol-acrylate photopolymerization.

Energy dissipation in mammalian collagen fibrils: Cyclic strain-induced damping, toughening, and strengthening

As the fundamental structural protein in mammals, collagen transmits cyclic forces that are necessary for the mechanical function of tissues, such as bone and tendon. Although the tissue-level mechanical behavior of collagenous tissues is well understood, the response of collagen at the nanometer length scales to cyclical loading remains elusive. To address this major gap, we cyclically stretched individual reconstituted collagen fibrils, with average diameter of 145 ± 42 nm, to small and large strains in the partially hydrated conditions of 60% relative humidity. It is shown that cyclical loading results in large steady-state hysteresis that is reached immediately after the first loading cycle, followed thereafter by limited accumulation of inelastic strain and constant initial elastic modulus. Cyclic loading above 20% strain resulted in 70% increase in tensile strength, from 638 ± 98 MPa to 1091 ± 110 MPa, and 70% increase in toughness, while maintaining the ultimate tensile strain of collagen fibrils not subjected to cyclic loading. Throughout cyclic stretching, the fibrils maintained a steady-state hysteresis, yielding loss coefficients that are 5-10 times larger than those of known homogeneous materials in their modulus range, thus establishing damping of nanoscale collagen fibrils as a major component of damping in tissues. STATEMENT OF SIGNIFICANCE: It is shown that steady-state energy dissipation occurs in individual collagen fibrils that are the building blocks of hard and soft tissues. To date, it has been assumed that energy dissipation in tissues takes place mainly at the higher length scales of the tissue hierarchy due to interactions between collagen fibrils and fibers, and in limited extent inside collagen fibrils. It is shown that individual collagen fibrils need only a single loading cycle to assume a highly dissipative, steady-state, cyclic mechanical response. Mechanical cycling at large strains leads to 70% increase in mechanical strength and values exceeding those of engineering steels. The same cyclic loading conditions also lead to 70% increase in toughness and loss properties that are 5-10 times higher than those of engineering materials with comparable stiffness.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Enhanced tendon-to-bone repair through adhesive films

Tendon-to-bone surgical repairs have unacceptably high failure rates, possibly due to their inability to recreate the load transfer mechanisms of the native enthesis. Instead of distributing load across a wide attachment footprint area, surgical repairs concentrate shear stress on a small number of suture anchor points. This motivates development of technologies that distribute shear stresses away from suture anchors and across the enthesis footprint. Here, we present predictions and proof-of-concept experiments showing that mechanically-optimized adhesive films can mimic the natural load transfer mechanisms of the healthy attachment and increase the load tolerance of a repair. Mechanical optimization, based upon a shear lag model corroborated by a finite element analysis, revealed that adhesives with relatively high strength and low stiffness can, theoretically, strengthen tendon-to-bone repairs by over 10-fold. Lap shear testing using tendon and bone planks validated the mechanical models for a range of adhesive stiffnesses and strengths. Ex vivo human supraspinatus repairs of cadaveric tissues using multipartite adhesives showed substantial increase in strength. Results suggest that adhesive-enhanced repair can improve repair strength, and motivate a search for optimal adhesives.

STATEMENT OF SIGNIFICANCE

Current surgical techniques for tendon-to-bone repair have unacceptably high failure rates, indicating that the initial repair strength is insufficient to prevent gapping or rupture. In the rotator cuff, repair techniques apply compression over the repair interface to achieve contact healing between tendon and bone, but transfer almost all force in shear across only a few points where sutures puncture the tendon. Therefore, we evaluated the ability of an adhesive film, implanted between tendon and bone, to enhance repair strength and minimize the likelihood of rupture. Mechanical models demonstrated that optimally designed adhesives would improve repair strength by over 10-fold. Experiments using idealized and clinically-relevant repairs validated these models. This work demonstrates an opportunity to dramatically improve tendon-to-bone repair strength using adhesive films with appropriate material properties.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

Integrated Multiscale Biomaterials Experiment and Modeling

The integration of modeling and experimentation is an integral component of all engineering design. Developing the technologies to achieve this represents a critical challenge in biomaterials because of the hierarchical structures that comprise them and the spectra of timescales upon which they operate. Progress in integrating modeling and experiment in biomaterials represents progress towards harnessing them for engineering application. We present here a summary of the state of the art, and outlooks for the field as a whole.

Functional and Biomimetic Materials for Engineering of the Three-Dimensional Cell Microenvironment

The cell microenvironment has emerged as a key determinant of cell behavior and function in development, physiology, and pathophysiology. The extracellular matrix (ECM) within the cell microenvironment serves not only as a structural foundation for cells but also as a source of three-dimensional (3D) biochemical and biophysical cues that trigger and regulate cell behaviors. Increasing evidence suggests that the 3D character of the microenvironment is required for development of many critical cell responses observed in vivo, fueling a surge in the development of functional and biomimetic materials for engineering the 3D cell microenvironment. Progress in the design of such materials has improved control of cell behaviors in 3D and advanced the fields of tissue regeneration, in vitro tissue models, large-scale cell differentiation, immunotherapy, and gene therapy. However, the field is still in its infancy, and discoveries about the nature of cell-microenvironment interactions continue to overturn much early progress in the field. Key challenges continue to be dissecting the roles of chemistry, structure, mechanics, and electrophysiology in the cell microenvironment, and understanding and harnessing the roles of periodicity and drift in these factors. This review encapsulates where recent advances appear to leave the ever-shifting state of the art, and it highlights areas in which substantial potential and uncertainty remain.

Toughening of fibrous scaffolds by mobile mineral deposits

Partially mineralized fibrous tissue situated between tendon and bone is believed to be tougher than either tendon or bone, possibly serving as a compliant, energy absorptive, protective barrier between the two. This tissue does not reform following surgical repair (e.g., rotator cuff tendon-to-bone re-attachment) and might be a factor in the poor outcomes following such surgeries. Towards our long-term goal of tissue engineered solutions to functional tendon-to-bone re-attachment, we tested the hypotheses that partially mineralized fibrous matrices can derive toughness from mobility of mineral along their fibers, and that in such cases toughness is maximized at levels of mineralization sufficiently low to allow substantial mobility. Nanofibrous electrospun poly(lactic-co-glycolic acid) (PLGA) scaffolds mineralized for prescribed times were fabricated as model systems to test these hypotheses. Tensile tests performed at varying angles relative to the dominant fiber direction confirmed that mineral cross-linked PLGA nanofibers without adhering to them. Peel tests revealed that fracture toughness increased with mineralization time up to a peak value, then subsequently decreased with increasing mineralization time back to the baseline toughness of unmineralized scaffolds. These experimental results were predicted by a theoretical model combining mineral growth kinetics with fracture energetics, suggesting that toughness increased with mineralization time until mineral mobility was attenuated by steric hindrance, then returned to baseline levels following the rigid percolation threshold. Results supported our hypotheses, and motivate further study of the roles of mobile mineral particles in toughening the tendon-to-bone attachment.

STATEMENT OF SIGNIFICANCE

Effective surgical repair of interfaces between tendon and bone remains an unmet clinical need, in part due to a lack of understanding of how toughness is achieved in the healthy tissue. Using combined synthesis, experiment, and modeling approaches, the current work supported the hypothesis that toughening of a fibrous scaffold arises from brittle mineral particles that crosslink the fibers, but only if the particles are free to slide relative to the fibers. In the case of the tendon-to-bone interface, this suggests that partially mineralized tissue between tendon and bone, with mobile mineral but relatively low stiffness, may serve as a compliant, energy-absorbing barrier that guards against injury. These results suggest an opportunity for fabrication of tough and strong fibrous scaffolds for tissue engineering applications.

Micro-mechanical properties of the tendon-to-bone attachment

The tendon-to-bone attachment (enthesis) is a complex hierarchical tissue that connects stiff bone to compliant tendon. The attachment site at the micrometer scale exhibits gradients in mineral content and collagen orientation, which likely act to minimize stress concentrations. The physiological micromechanics of the attachment thus define resultant performance, but difficulties in sample preparation and mechanical testing at this scale have restricted understanding of structure-mechanical function. Here, microscale beams from entheses of wild type mice and mice with mineral defects were prepared using cryo-focused ion beam milling and pulled to failure using a modified atomic force microscopy system. Micromechanical behavior of tendon-to-bone structures, including elastic modulus, strength, resilience, and toughness, were obtained. Results demonstrated considerably higher mechanical performance at the micrometer length scale compared to the millimeter tissue length scale, describing enthesis material properties without the influence of higher order structural effects such as defects. Micromechanical investigation revealed a decrease in strength in entheses with mineral defects. To further examine structure-mechanical function relationships, local deformation behavior along the tendon-to-bone attachment was determined using local image correlation. A high compliance zone near the mineralized gradient of the attachment was clearly identified and highlighted the lack of correlation between mineral distribution and strain on the low-mineral end of the attachment. This compliant region is proposed to act as an energy absorbing component, limiting catastrophic failure within the tendon-to-bone attachment through higher local deformation. This understanding of tendon-to-bone micromechanics demonstrates the critical role of micrometer scale features in the mechanics of the tissue.

STATEMENT OF SIGNIFICANCE

The tendon-to-bone attachment (enthesis) is a complex hierarchical tissue with features at a numerous scales that dissipate stress concentrations between compliant tendon and stiff bone. At the micrometer scale, the enthesis exhibits gradients in collagen and mineral composition and organization. However, the physiological mechanics of the enthesis at this scale remained unknown due to difficulty in preparing and testing micrometer scale samples. This study is the first to measure the tensile mechanical properties of the enthesis at the micrometer scale. Results demonstrated considerably enhanced mechanical performance at the micrometer length scale compared to the millimeter tissue length scale and identified a high-compliance zone near the mineralized gradient of the attachment. This understanding of tendon-to-bone micromechanics demonstrates the critical role of micrometer scale features in the mechanics of the tissue.

An Integrated Stochastic Model of Matrix-Stiffness-Dependent Filopodial Dynamics

The ways that living cells regulate their behavior in response to their local mechanical environment underlie growth, development, and healing and are important to critical pathologies such as metastasis and fibrosis. Although extensive experimental evidence supports the hypothesis that this regulation is governed by the dependence of filopodial dynamics upon extracellular matrix stiffness, the pathways for this dependence are unclear. We therefore developed a model to relate filopodial focal adhesion dynamics to integrin-mediated Rho signaling kinetics. Results showed that focal adhesion maturation, i.e., focal adhesion links reinforcement and integrin clustering, dominates over filopodial dynamics. Downregulated focal adhesion maturation leads to the biphasic relationship between extracellular matrix stiffness and retrograde flow that has been observed in embryonic chick forebrain neurons, whereas upregulated maturation leads to the monotonically decreasing relationship that has been observed in mouse embryonic fibroblasts. When integrin-mediated Rho activation and stress-dependent focal adhesion maturation are combined, the model shows how filopodial dynamics endows cells with exquisite mechanosensing. Taken together, the results support the hypothesis that mechanical and structural factors combine with signaling kinetics to enable cells to probe their environments via filopodial dynamics.

Investigation of Nanoscopic Phase Separations in Lipid Membranes Using Inverse FCS

Measurement of the sizes of nanoscopic particles is a difficult challenge, especially in two-dimensional systems such as cell membranes. We have extended inverse fluorescence correlation spectroscopy (iFCS) to endow it with unique advantages for measuring particle size from the nano- to the microscale. We have augmented iFCS with an analysis of moments of fluorescence fluctuations and used it to measure stages of phase separation in model lipid bilayer membranes. We observed two different pathways for the growth of phase domains. In one, nanoscopic gel domains appeared first and then gradually grew to micrometer size. In the other, the domains reached micrometer size quickly, and their number gradually increased. These measurements demonstrate the value of iFCS measurements through their ability, to our knowledge, to provide new information about the mechanism of lipid phase separation and potentially about the physical basis of naturally occurring nanodomains such as lipid rafts.

The tendon-to-bone attachment: Unification through disarray

High-resolution imaging, composition analysis and mechanical testing reveal a disordered transitional material within the Achilles tendon-to-bone attachment, structured as a fibrous network to enable force transfer and maximize structural integrity.

The Arabidopsis trichome is an active mechanosensory switch

Trichomes ('hair cells') on Arabidopsis thaliana stem and leaf surfaces provide a range of benefits arising from their shape and disposition. These include tempting herbivores to sample constitutive toxins before they reach the bulk of the tissue. We asked whether, in addition, small mechanical disturbances such as an insect can make elicit signals that might help the plant respond to herbivory. We imaged, pressed and brushed trichomes in several ways, most notably with confocal microscopy of trichomes transgenically provided with apoplastic pH reporter apo-pHusion and cytosolic Ca²⁺ reporter cameleon. In parallel, we modelled trichome wall mechanics with finite element analysis. The stimulated trichome focuses force on a pliant zone and the adjoining podium of the stalk. A buckling instability can further focus force on a skirt of cells surrounding the podium, eliciting oscillations of cytosolic Ca²⁺ and shifts in apoplastic pH. These observations represent active physiological response. Modelling establishes that the effectiveness of force focusing and buckling is due to the peculiar tapering wall structure of the trichome. Hypothetically, these active mechanosensing functions enhance toxin synthesis above constitutive levels, probably via a priming process, thus minimizing the costly accumulation of toxins in the absence of herbivore attack but assuring rapid build-up when needed.

Protein-free formation of bone-like apatite: New insights into the key role of carbonation

The nanometer-sized plate-like morphology of bone mineral is necessary for proper bone mechanics and physiology. However, mechanisms regulating the morphology of these mineral nanocrystals remain unclear. The dominant hypothesis attributes the size and shape regulation to organic-mineral interactions. Here, we present data supporting the hypothesis that physicochemical effects of carbonate integration within the apatite lattice control the morphology, size, and mechanics of bioapatite mineral crystals. Carbonated apatites synthesized in the absence of organic molecules presented plate-like morphologies and nanoscale crystallite dimensions. Experimentally-determined crystallite size, lattice spacing, solubility and atomic order were modified by carbonate concentration. Molecular dynamics (MD) simulations and density functional theory (DFT) calculations predicted changes in surface energy and elastic moduli with carbonate concentration. Combining these results with a scaling law predicted the experimentally observed scaling of size and energetics with carbonate concentration. The experiments and models describe a clear mechanism by which crystal dimensions are controlled by carbonate substitution. Furthermore, the results demonstrate that carbonate substitution is sufficient to drive the formation of bone-like crystallites. This new understanding points to pathways for biomimetic synthesis of novel, nanostructured biomaterials.

Discrete quasi-linear viscoelastic damping analysis of connective tissues, and the biomechanics of stretching

The time- and frequency-dependent properties of connective tissue define their physiological function, but are notoriously difficult to characterize. Well-established tools such as linear viscoelasticity and the Fung quasi-linear viscoelastic (QLV) model impose forms on responses that can mask true tissue behavior. Here, we applied a more general discrete quasi-linear viscoelastic (DQLV) model to identify the static and dynamic time- and frequency-dependent behavior of rabbit medial collateral ligaments. Unlike the Fung QLV approach, the DQLV approach revealed that energy dissipation is elevated at a loading period of ∼10s. The fitting algorithm was applied to the entire loading history on each specimen, enabling accurate estimation of the material's viscoelastic relaxation spectrum from data gathered from transient rather than only steady states. The application of the DQLV method to cyclically loading regimens has broad applicability for the characterization of biological tissues, and the results suggest a mechanistic basis for the stretching regimens most favored by athletic trainers.

Fibroblasts Slow Conduction Velocity in a Reconstituted Tissue Model of Fibrotic Cardiomyopathy

Myocardial function deteriorates over the course of fibrotic cardiomyopathy, due to electrophysiological and mechanical effects of myofibroblasts that are not completely understood. Although a range of experimental model systems and associated theoretical treatments exist at the levels of isolated cardiomyocytes and planar co-cultures of myofibroblasts and cardiomyocytes, interactions between these cell types at the tissue level are less clear. We studied these interactions through an engineered heart tissue (EHT) model of fibrotic myocardium and a mathematical model of the effects of cellular composition on EHT impulse conduction velocity. The EHT model allowed for modulation of cardiomyocyte and myofibroblast volume fractions, and observation of cell behavior in a three-dimensional environment that is more similar to native heart tissue than is planar cell culture. The cardiomyocyte and myofibroblast volume fractions determined the retardation of impulse conduction (spread of the action potential) in EHTs as measured by changes of the fluorescence of the Ca²⁺ probe, Fluo-2. Interpretation through our model showed retardation far in excess of predictions by homogenization theory, with conduction ceasing far below the fibroblast volume fraction associated with steric percolation. Results point to an important multiscale structural role of myofibroblasts in attenuating impulse conduction in fibrotic cardiomyopathy.

A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials

The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress-relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's 'box'-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress-relaxation data in an unbiased way. Our 'discrete QLV' (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress-relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.

Multi-scale Modeling in Clinical Oncology: Opportunities and Barriers to Success

Hierarchical processes spanning several orders of magnitude of both space and time underlie nearly all cancers. Multi-scale statistical, mathematical, and computational modeling methods are central to designing, implementing and assessing treatment strategies that account for these hierarchies. The basic science underlying these modeling efforts is maturing into a new discipline that is close to influencing and facilitating clinical successes. The purpose of this review is to capture the state-of-the-art as well as the key barriers to success for multi-scale modeling in clinical oncology. We begin with a summary of the long-envisioned promise of multi-scale modeling in clinical oncology, including the synthesis of disparate data types into models that reveal underlying mechanisms and allow for experimental testing of hypotheses. We then evaluate the mathematical techniques employed most widely and present several examples illustrating their application as well as the current gap between pre-clinical and clinical applications. We conclude with a discussion of what we view to be the key challenges and opportunities for multi-scale modeling in clinical oncology.

Allometry of the Tendon Enthesis: Mechanisms of Load Transfer Between Tendon and Bone

Several features of the tendon-to-bone attachment were examined allometrically to determine load transfer mechanisms. The humeral head diameter increased geometrically with animal mass. Area of the attachment site exhibited a near isometric increase with muscle physiological cross section. In contrast, the interfacial roughness as well as the mineral gradient width demonstrated a hypoallometric relationship with physiologic cross-sectional area (PCSA). The isometric increase in attachment area indicates that as muscle forces increase, the attachment area increases accordingly, thus maintaining a constant interfacial stress. Due to the presence of constant stresses at the attachment, the micrometer-scale features may not need to vary with increasing load.

On the accuracy and fitting of transversely isotropic material models

Fiber reinforced structures are central to the form and function of biological tissues. Hyperelastic, transversely isotropic material models are used widely in the modeling and simulation of such tissues. Many of the most widely used models involve strain energy functions that include one or both pseudo-invariants (I4 or I5) to incorporate energy stored in the fibers. In a previous study we showed that both of these invariants must be included in the strain energy function if the material model is to reduce correctly to the well-known framework of transversely isotropic linear elasticity in the limit of small deformations. Even with such a model, fitting of parameters is a challenge. Here, by evaluating the relative roles of I4 and I5 in the responses to simple loadings, we identify loading scenarios in which previous models accounting for only one of these invariants can be expected to provide accurate estimation of material response, and identify mechanical tests that have special utility for fitting of transversely isotropic constitutive models. Results provide guidance for fitting of transversely isotropic constitutive models and for interpretation of the predictions of these models.

An approach to quantifying 3D responses of cells to extreme strain

The tissues of hollow organs can routinely stretch up to 2.5 times their length. Although significant pathology can arise if relatively large stretches are sustained, the responses of cells are not known at these levels of sustained strain. A key challenge is presenting cells with a realistic and well-defined three-dimensional (3D) culture environment that can sustain such strains. Here, we describe an in vitro system called microscale, magnetically-actuated synthetic tissues (micro-MASTs) to quantify these responses for cells within a 3D hydrogel matrix. Cellular strain-threshold and saturation behaviors were observed in hydrogel matrix, including strain-dependent proliferation, spreading, polarization, and differentiation, and matrix adhesion retained at strains sufficient for apoptosis. More broadly, the system shows promise for defining and controlling the effects of mechanical environment upon a broad range of cells.

Tissue constructs: platforms for basic research and drug discovery

The functions, form and mechanical properties of cells are inextricably linked to their extracellular environment. Cells from solid tissues change fundamentally when, isolated from this environment, they are cultured on rigid two-dimensional substrata. These changes limit the significance of mechanical measurements on cells in two-dimensional culture and motivate the development of constructs with cells embedded in three-dimensional matrices that mimic the natural tissue. While measurements of cell mechanics are difficult in natural tissues, they have proven effective in engineered tissue constructs, especially constructs that emphasize specific cell types and their functions, e.g. engineered heart tissues. Tissue constructs developed as models of disease also have been useful as platforms for drug discovery. Underlying the use of tissue constructs as platforms for basic research and drug discovery is integration of multiscale biomaterials measurement and computational modelling to dissect the distinguishable mechanical responses separately of cells and extracellular matrix from measurements on tissue constructs and to quantify the effects of drug treatment on these responses. These methods and their application are the main subjects of this review.

Tunability of collagen matrix mechanical properties via multiple modes of mineralization

Functionally graded, mineralized collagen tissues exist at soft-to-hard material attachments throughout the body. However, the details of how collagen and hydroxyapatite mineral (HA) interact are not fully understood, hampering efforts to develop tissue-engineered constructs that can assist with repair of injuries at the attachments of soft tissues to bone. In this study, spatial control of mineralization was achieved in collagen matrices using simulated body fluids (SBFs). Based upon previous observations of poor bonding between reconstituted collagen and HA deposited using SBF, we hypothesized that mineralizing collagen in the presence of fetuin (which inhibits surface mineralization) would lead to more mineral deposition within the scaffold and therefore a greater increase in stiffness and toughness compared with collagen mineralized without fetuin. We tested this hypothesis through integrated synthesis, mechanical testing and modelling of graded, mineralized reconstituted collagen constructs. Results supported the hypothesis, and further suggested that mineralization on the interior of reconstituted collagen constructs, as promoted by fetuin, led to superior bonding between HA and collagen. The results provide us guidance for the development of mineralized collagen scaffolds, with implications for bone and tendon-to-bone tissue engineering.

Integrated multiscale biomaterials experiment and modelling: a perspective

Advances in multiscale models and computational power have enabled a broad toolset to predict how molecules, cells, tissues and organs behave and develop. A key theme in biological systems is the emergence of macroscale behaviour from collective behaviours across a range of length and timescales, and a key element of these models is therefore hierarchical simulation. However, this predictive capacity has far outstripped our ability to validate predictions experimentally, particularly when multiple hierarchical levels are involved. The state of the art represents careful integration of multiscale experiment and modelling, and yields not only validation, but also insights into deformation and relaxation mechanisms across scales. We present here a sampling of key results that highlight both challenges and opportunities for integrated multiscale experiment and modelling in biological systems.

Stochastic interdigitation as a toughening mechanism at the interface between tendon and bone

Reattachment and healing of tendon to bone poses a persistent clinical challenge and often results in poor outcomes, in part because the mechanisms that imbue the uninjured tendon-to-bone attachment with toughness are not known. One feature of typical tendon-to-bone surgical repairs is direct attachment of tendon to smooth bone. The native tendon-to-bone attachment, however, presents a rough mineralized interface that might serve an important role in stress transfer between tendon and bone. In this study, we examined the effects of interfacial roughness and interdigital stochasticity on the strength and toughness of a bimaterial interface. Closed form linear approximations of the amplification of stresses at the rough interface were derived and applied in a two-dimensional unit-cell model. Results demonstrated that roughness may serve to increase the toughness of the tendon-to-bone insertion site at the expense of its strength. Results further suggested that the natural tendon-to-bone attachment presents roughness for which the gain in toughness outweighs the loss in strength. More generally, our results suggest a pathway for stochasticity to improve surgical reattachment strategies and structural engineering attachments.

Effective elastic properties of a composite containing multiple types of anisotropic ellipsoidal inclusions, with the application to the attachment of tendon to bone

Estimates of the effective stiffness of a composite containing multiple types of inclusions are needed for the design and study of functionally graded systems in engineering and physiology. While excellent estimates and tight bounds exist for composite systems containing specific classes and distributions of identical inclusions, these are not easily generalized to complex systems with multiple types of inclusions. For example, three-point parameters are known for only a few inclusion shapes and orientations. The best estimate available for a composite containing multiple classes of inclusions arises from the Kanaun-Jeulin approach. However, this method is analogous to a generalized Benveniste approach, and therefore suffers from the same limitations: while excellent for low volume fractions of inclusions, the Kanaun-Jeullin and Benveniste estimates lie outside of three-point bounds at higher volume fractions. Here, we present an estimate for composites containing multiple classes of aligned ellipsoidal inclusions that lies within known three-point bounds at relatively higher volume fractions of inclusions and that is applicable to many engineering and biological composites.

Shear lag sutures: Improved suture repair through the use of adhesives

Suture materials and surgical knot tying techniques have improved dramatically since their first use over five millennia ago. However, the approach remains limited by the ability of the suture to transfer load to tissue at suture anchor points. Here, we predict that adhesive-coated sutures can improve mechanical load transfer beyond the range of performance of existing suture methods, thereby strengthening repairs and decreasing the risk of failure. The mechanical properties of suitable adhesives were identified using a shear lag model. Examination of the design space for an optimal adhesive demonstrated requirements for strong adhesion and low stiffness to maximize the strength of the adhesive-coated suture repair construct. To experimentally assess the model, we evaluated single strands of sutures coated with highly flexible cyanoacrylates (Loctite 4903 and 4902), cyanoacrylate (Loctite QuickTite Instant Adhesive Gel), rubber cement, rubber/gasket adhesive (1300 Scotch-Weld Neoprene High Performance Rubber & Gasket Adhesive), an albumin-glutaraldehyde adhesive (BioGlue), or poly(dopamine). As a clinically relevant proof-of-concept, cyanoacrylate-coated sutures were then used to perform a clinically relevant flexor digitorum tendon repair in cadaver tissue. The repair performed with adhesive-coated suture had significantly higher strength compared to the standard repair without adhesive. Notably, cyanoacrylate provides strong adhesion with high stiffness and brittle behavior, and is therefore not an ideal adhesive for enhancing suture repair. Nevertheless, the improvement in repair properties in a clinically relevant setting, even using a non-ideal adhesive, demonstrates the potential for the proposed approach to improve outcomes for treatments requiring suture fixation. Further study is necessary to develop a strongly adherent, compliant adhesive within the optimal design space described by the model.

Simple and accurate methods for quantifying deformation, disruption, and development in biological tissues

When mechanical factors underlie growth, development, disease or healing, they often function through local regions of tissue where deformation is highly concentrated. Current optical techniques to estimate deformation can lack precision and accuracy in such regions due to challenges in distinguishing a region of concentrated deformation from an error in displacement tracking. Here, we present a simple and general technique for improving the accuracy and precision of strain estimation and an associated technique for distinguishing a concentrated deformation from a tracking error. The strain estimation technique improves accuracy relative to other state-of-the-art algorithms by directly estimating strain fields without first estimating displacements, resulting in a very simple method and low computational cost. The technique for identifying local elevation of strain enables for the first time the successful identification of the onset and consequences of local strain concentrating features such as cracks and tears in a highly strained tissue. We apply these new techniques to demonstrate a novel hypothesis in prenatal wound healing. More generally, the analytical methods we have developed provide a simple tool for quantifying the appearance and magnitude of localized deformation from a series of digital images across a broad range of disciplines.

Efficient and optimized identification of generalized Maxwell viscoelastic relaxation spectra

Viscoelastic relaxation spectra are essential for predicting and interpreting the mechanical responses of materials and structures. For biological tissues, these spectra must usually be estimated from viscoelastic relaxation tests. Interpreting viscoelastic relaxation tests is challenging because the inverse problem is expensive computationally. We present here an efficient algorithm that enables rapid identification of viscoelastic relaxation spectra. The algorithm was tested against trial data to characterize its robustness and identify its limitations and strengths. The algorithm was then applied to identify the viscoelastic response of reconstituted collagen, revealing an extensive distribution of viscoelastic time constants.

Structures formed by a cell membrane-associated arabinogalactan-protein on graphite or mica alone and with Yariv phenylglycosides

BACKGROUND

Certain membrane-associated arabinogalactan-proteins (AGPs) with lysine-rich sub-domains participate in plant growth, development and resistance to stress. To complement fluorescence imaging of such molecules when tagged and introduced transgenically to the cell periphery and to extend the groundwork for assessing molecular structure, some behaviours of surface-spread AGPs were visualized at the nanometre scale in a simplified electrostatic environment.

METHODS

Enhanced green fluorescent protein (EGFP)-labelled LeAGP1 was isolated from Arabidopsis thaliana leaves using antibody-coated magnetic beads, deposited on graphite or mica, and examined with atomic force microscopy (AFM).

KEY RESULTS

When deposited at low concentration on graphite, LeAGP can form independent clusters and rings a few nanometres in diameter, often defining deep pits; the aperture of the rings depends on plating parameters. On mica, intermediate and high concentrations, respectively, yielded lacy meshes and solid sheets that could dynamically evolve arcs, rings, 'pores' and 'co-pores', and pits. Glucosyl Yariv reagent combined with the AGP to make very large and distinctive rings.

CONCLUSIONS

Diverse cell-specific nano-patterns of native lysine-rich AGPs are expected at the wall-membrane interface and, while there will not be an identical patterning in different environmental settings, AFM imaging suggests protein tendencies for surficial organization and thus opens new avenues for experimentation. Nanopore formation with Yariv reagents suggests how the reagent might bind with AGP to admit Ca(2+) to cells and hints at ways in which AGP might be structured at some cell surfaces.

The freedom to heal: nonrigid immobilization by a halo orthosis

Halo orthoses present a paradox. On the one hand, the nominally rigid immobilization they provide to the head aims to remove loads on the cervical spine following injury or surgery, and the devices are retightened routinely to maintain this. On the other hand, bone growth and remodeling are well known to require mechanical stressing. How are these competing needs balanced? To understand this trade-off in an effective, commercial halo orthosis, the authors quantified the response of a commercial halo orthosis to physiological loading levels, applied symmetrically about the sagittal plane. They showed for the first time that after a few cycles of loading analogous to a few steps taken by a patient, the support presented by a standard commercial halo orthosis becomes nonlinear. When analyzed through straightforward structural modeling, these data revealed that the nonlinearity permits mild head motion while severely restricting larger motion. These observations are useful because they open the possibility that halo orthosis installation could be optimized to transfer mild spinal loads that support healing while blocking pathological loads.

The mechanics of PLGA nanofiber scaffolds with biomimetic gradients in mineral for tendon-to-bone repair

Attachment of dissimilar materials is prone to failure due to stress concentrations that can arise their interface. A compositionally or structurally graded transition can dissipate these stress concentrations and thereby toughen an attachment. The interface between compliant tendon and stiff bone utilizes a monotonic change in hydroxylapatite mineral ("mineral") content to produce a gradient in mechanical properties and mitigate stress concentrations. Previous efforts to mimic the natural tendon-to-bone attachment have included electrospun nanofibrous polymer scaffolds with gradients in mineral. Mineralization of the nanofiber scaffolds has typically been achieved using simulated body fluid (SBF). Depending on the specific formulation of SBF, mineral morphologies ranged from densely packed small crystals to platelike crystal florets. Although this mineralization of scaffolds produced increases in modulus, the peak modulus achieved remained significantly below that of bone. Missing from these prior empirical approaches was insight into the effect of mineral morphology on scaffold mechanics and on the potential for the approach to ultimately achieve moduli approaching that of bone. Here, we applied two mineralization methods to generate scaffolds with spatial gradations in mineral content, and developed methods to quantify the stiffening effects and evaluate them in the context of theoretical bounds. We asked whether either of the mineralization methods we developed holds potential to achieve adequate stiffening of the scaffold, and tested the hypothesis that the smoother, denser mineral coating could attain more potent stiffening effects. Testing this hypothesis required development of and comparison to homogenization bounds, and development of techniques to estimate mineral volume fractions and spatial gradations in modulus. For both mineralization strategies, energy dispersive X-ray analysis demonstrated the formation of linear gradients in mineral concentration along the length of the scaffolds, and Raman spectroscopic analysis revealed that the mineral produced was hydroxylapatite. Mechanical testing showed that the stiffness gradient using the new method was significantly steeper. By analyzing the scaffolds using micromechanical modeling techniques and extrapolating from our experimental results, we present evidence that the new mineralization protocol has the potential to achieve levels of stiffness adequate to contribute to enhanced repair of tendon-to-bone attachments.

Thermal Pain in Teeth: Electrophysiology Governed by Thermomechanics

Thermal pain arising from the teeth is unlike that arising from anywhere else in the body. The source of this peculiarity is a long-standing mystery that has begun to unravel with recent experimental measurements and, somewhat surprisingly, new thermomechanical models. Pain from excessive heating and cooling is typically sensed throughout the body through the action of specific, heat sensitive ion channels that reside on sensory neurons known as nociceptors. These ion channels are found on tooth nociceptors, but only in teeth does the pain of heating differ starkly from the pain of cooling, with cold stimuli producing more rapid and sharper pain. Here, we review the range of hypotheses and models for these phenomena, and focus on what is emerging as the most promising hypothesis: pain transduced by fluid flowing through the hierarchical structure of teeth. We summarize experimental evidence, and critically review the range of heat transfer, solid mechanics, fluid dynamics, and electrophysiological models that have been combined to support this hypothesis. While the results reviewed here are specific to teeth, this class of coupled thermomechanical and neurophysiological models has potential for informing design of a broad range of thermal therapies and understanding of a range of biophysical phenomena.

Strain Localization in an Oscillating Maxwell Viscoelastic Cylinder

The transient rotation responses of simple, axisymmetric, viscoelastic structures are of interest for interpretation of experiments designed to characterize materials and closed structures such as the brain using magnetic resonance techniques. Here, we studied the response of a Maxwell viscoelastic cylinder to small, sinusoidal displacement of its outer boundary. The transient strain field can be calculated in closed form using any of several conventional approaches. The solution is surprising: the strain field develops a singularity that appears when the wavefront leaves the center of the cylinder, and persists as the wavefront reflects to the outer boundary and back to the center of the cylinder. The singularity is alternately annihilated and reinitiated upon subsequent departures of the wavefront from the center of the cylinder until it disappears in the limit of steady state oscillations. We present the solution for this strain field, characterize the nature of this singularity, and discuss its potential role in the mechanical response and evolved morphology of the brain.

Modelling the mechanics of partially mineralized collagen fibrils, fibres and tissue

Progressive stiffening of collagen tissue by bioapatite mineral is important physiologically, but the details of this stiffening are uncertain. Unresolved questions about the details of the accommodation of bioapatite within and upon collagen's hierarchical structure have posed a central hurdle, but recent microscopy data resolve several major questions. These data suggest how collagen accommodates bioapatite at the lowest relevant hierarchical level (collagen fibrils), and suggest several possibilities for the progressive accommodation of bioapatite at higher hierarchical length scales (fibres and tissue). We developed approximations for the stiffening of collagen across spatial hierarchies based upon these data, and connected models across hierarchies levels to estimate mineralization-dependent tissue-level mechanics. In the five possible sequences of mineralization studied, percolation of the bioapatite phase proved to be an important determinant of the degree of stiffening by bioapatite. The models were applied to study one important instance of partially mineralized tissue, which occurs at the attachment of tendon to bone. All sequences of mineralization considered reproduced experimental observations of a region of tissue between tendon and bone that is more compliant than either tendon or bone, but the size and nature of this region depended strongly upon the sequence of mineralization. These models and observations have implications for engineered tissue scaffolds at the attachment of tendon to bone, bone development and graded biomimetic attachment of dissimilar hierarchical materials in general.

Strong and tough mineralized PLGA nanofibers for tendon-to-bone scaffolds

Engineering complex tissues such as the tendon-to-bone insertion sites require a strong and tough biomimetic material system that incorporates both mineralized and unmineralized tissues with different strengths and stiffnesses. However, increasing strength without degrading toughness is a fundamental challenge in materials science. Here, we demonstrate a promising nanofibrous polymer-hydroxyapatite system, in which, a continuous fibrous network must function as a scaffold for both mineralized and unmineralized tissues. It is shown that the high toughness of this material system could be maintained without compromising on the strength with the addition of hydroxyapatite mineral. Individual electrospun poly (lactide-co-glycolide) (PLGA) nanofibers demonstrated outstanding strain-hardening behavior and ductility when stretched uniaxially, even in the presence of surface mineralization. This highly desirable hardening behavior which results in simultaneous nanofiber strengthening and toughening was shown to depend on the initial cross-sectional morphology of the PLGA nanofibers. For pristine PLGA nanofibers, it was shown that ellipsoidal cross-sections provide the largest increase in fiber strength by almost 200% compared to bulk PLGA. This exceptional strength accompanied by 100% elongation was shown to be retained for thin and strongly bonded conformal mineral coatings, which were preserved on the nanofiber surface even for such very large extensions.