Topological transformability and reprogrammability of multistable mechanical metamaterials.

Concepts from quantum topological states of matter have been extensively utilized in the past decade to create mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized elasticity. Maxwell lattices represent a class of topological mechanical metamaterials that exhibit distinct robust mechanical properties at edges/interfaces when they are topologically polarized. Realizing topological phase transitions in these materials would enable on-and-off switching of these edge states, opening opportunities to program mechanical response and wave propagation. However, such transitions are extremely challenging to experimentally control in Maxwell topological metamaterials due to mechanical and geometric constraints. Here we create a Maxwell lattice with bistable units to implement synchronized transitions between topological states and demonstrate dramatically different stiffnesses as the lattice transforms between topological phases both theoretically and experimentally. By combining multistability with topological phase transitions, this metamaterial not only exhibits topologically protected mechanical properties that swiftly and reversibly change, but also offers a rich design space for innovating mechanical computing architectures and reprogrammable neuromorphic metamaterials. Moreover, we design and fabricate a topological Maxwell lattice using multimaterial 3D printing and demonstrate the potential for miniaturization via additive manufacturing. These design principles are applicable to transformable topological metamaterials for a variety of tasks such as switchable energy absorption, impact mitigation, wave tailoring, neuromorphic metamaterials, and controlled morphing systems.

Abiotic tooth enamel.

Tooth enamel comprises parallel microscale and nanoscale ceramic columns or prisms interlaced with a soft protein matrix. This structural motif is unusually consistent across all species from all geological eras. Such invariability-especially when juxtaposed with the diversity of other tissues-suggests the existence of a functional basis. Here we performed ex vivo replication of enamel-inspired columnar nanocomposites by sequential growth of zinc oxide nanowire carpets followed by layer-by-layer deposition of a polymeric matrix around these. We show that the mechanical properties of these nanocomposites, including hardness, are comparable to those of enamel despite the nanocomposites having a smaller hard-phase content. Our abiotic enamels have viscoelastic figures of merit (VFOM) and weight-adjusted VFOM that are similar to, or higher than, those of natural tooth enamels-we achieve values that exceed the traditional materials limits of 0.6 and 0.8, respectively. VFOM values describe resistance to vibrational damage, and our columnar composites demonstrate that light-weight materials of unusually high resistance to structural damage from shocks, environmental vibrations and oscillatory stress can be made using biomimetic design. The previously inaccessible combinations of high stiffness, damping and light weight that we achieve in these layer-by-layer composites are attributed to efficient energy dissipation in the interfacial portion of the organic phase. The in vivo contribution of this interfacial portion to macroscale deformations along the tooth's normal is maximized when the architecture is columnar, suggesting an evolutionary advantage of the columnar motif in the enamel of living species. We expect our findings to apply to all columnar composites and to lead to the development of high-performance load-bearing materials.

Ogden material calibration via magnetic resonance cartography, parameter sensitivity and variational system identification.

Contemporary material characterization techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully three-dimensional displacement fields acquired in silicone elastomers with our recently developed magnetic resonance cartography (MR-u) technique on the order of greater than [Formula: see text], we leverage partial differential equation-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric and discuss the implications for experimental design. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

The Role of the Non-Collagenous Extracellular Matrix in Tendon and Ligament Mechanical Behavior: A Review.

Tendon is a connective tissue that transmits loads from muscle to bone, while ligament is a similar tissue that stabilizes joint articulation by connecting bone to bone. The 70-90% of tendon and ligament's extracellular matrix (ECM) is composed of a hierarchical collagen structure that provides resistance to deformation primarily in the fiber direction, and the remaining fraction consists of a variety of non-collagenous proteins, proteoglycans, and glycosaminoglycans (GAGs) whose mechanical roles are not well characterized. ECM constituents such as elastin, the proteoglycans decorin, biglycan, lumican, fibromodulin, lubricin, and aggrecan and their associated GAGs, and cartilage oligomeric matrix protein (COMP) have been suggested to contribute to tendon and ligament's characteristic quasi-static and viscoelastic mechanical behavior in tension, shear, and compression. The purpose of this review is to summarize existing literature regarding the contribution of the non-collagenous ECM to tendon and ligament mechanics, and to highlight key gaps in knowledge that future studies may address. Using insights from theoretical mechanics and biology, we discuss the role of the non-collagenous ECM in quasi-static and viscoelastic tensile, compressive, and shear behavior in the fiber direction and orthogonal to the fiber direction. We also address the efficacy of tools that are commonly used to assess these relationships, including enzymatic degradation, mouse knockout models, and computational models. Further work in this field will foster a better understanding of tendon and ligament damage and healing as well as inform strategies for tissue repair and regeneration.

Investigation of Fiber-Driven Mechanical Behavior of Human and Porcine Bladder Tissue Tested Under Identical Conditions.

The urinary bladder is a highly dynamic organ that undergoes large deformations several times per day. Mechanical characteristics of the tissue are crucial in determining the function and dysfunction of the organ. Yet, literature reporting on the mechanical properties of human bladder tissue is scarce and, at times, contradictory. In this study, we focused on mechanically testing tissue from both human and pig bladders using identical protocols to validate the use of pigs as a model for the human bladder. Furthermore, we tested the effect of two treatments on tissue mechanical properties. Namely, elastase to digest elastin fibers, and oxybutynin to reduce smooth muscle cell spasticity. Additionally, mechanical properties based on the anatomical direction of testing were evaluated. We implemented two different material models to aid in the interpretation of the experimental results. We found that human tissue behaves similarly to pig tissue at high deformations (collagen-dominated behavior) while we detected differences between the species at low deformations (amorphous matrix-dominated behavior). Our results also suggest that elastin could play a role in determining the behavior of the fiber network. Finally, we confirmed the anisotropy of the tissue, which reached higher stresses in the transverse direction when compared to the longitudinal direction.

The Influence of Anterior Cruciate Ligament Matrix Mechanical Properties on Simulated Whole-Knee Biomechanics.

Knee finite element (FE) models are used to study tissue deformation in response to complex loads. Typically, ligaments are modeled using transversely isotropic, hyperelastic material models fitted to tension data along the predominant fiber direction (longitudinal) and, less commonly, to tension data orthogonal to the fiber direction (transverse). Currently, the shear and bulk responses of the anterior cruciate ligament (ACL) are not fitted to experimental data. In this study, a newly proposed material model was fitted to longitudinal tension, transverse tension, and shear experimental data. The matrix transverse tensile, shear, and bulk stiffnesses were then varied independently to determine the impact of each property on knee kinematics and tissue deformation in a whole-knee FE model. The range of values for each parameter was chosen based on published FE studies of the knee. For a knee at full extension under 134 N anterior tibial force (ATF), increasing matrix transverse tensile stiffness, shear stiffness, or bulk stiffness decreased anterior tibial translation (ATT), ACL longitudinal strain, and ACL shear strain. For a knee under 134 N ATF and 1600 N compression, changing the ACL matrix mechanical properties caused variations in ATT and thus changed cartilage deformation contours by changing the point of contact between the femoral and the tibial cartilage. These findings indicate that material models for the ACL must describe matrix material properties to best predict the in vivo response to applied loads.

The Effect of Articular Cartilage Focal Defect Size and Location in Whole Knee Biomechanics Models.

Articular cartilage focal defects are common soft tissue injuries potentially linked to osteoarthritis (OA) development. Although several defect characteristics likely contribute to osteoarthritis, their relationship to local tissue deformation remains unclear. Using finite element models with various femoral cartilage geometries, we explore how defects change cartilage deformation and joint kinematics assuming loading representative of the maximum joint compression during the stance phase of gait. We show how defects, in combination with location-dependent cartilage mechanics, alter deformation in affected and opposing cartilages, as well as joint kinematics. Small and average sized defects increased maximum compressive strains by approximately 50% and 100%, respectively, compared to healthy cartilage. Shifts in the spatial locations of maximum compressive strains of defect containing models were also observed, resulting in loading of cartilage regions with reduced initial stiffnesses supporting the new, elevated loading environments. Simulated osteoarthritis (modeled as a global reduction in mean cartilage stiffness) did not significantly alter joint kinematics, but exacerbated tissue deformation. Femoral defects were also found to affect healthy tibial cartilage deformations. Lateral femoral defects increased tibial cartilage maximum compressive strains by 25%, while small and average sized medial defects exhibited decreases of 6% and 15%, respectively, compared to healthy cartilage. Femoral defects also affected the spatial distributions of deformation across the articular surfaces. These deviations are especially meaningful in the context of cartilage with location-dependent mechanics, leading to increases in peak contact stresses supported by the cartilage of between 11% and 34% over healthy cartilage.

Deconstructing the anterior cruciate ligament: what we know and do not know about function, material properties, and injury mechanics.

Anterior cruciate ligament (ACL) injury is a common and potentially catastrophic knee joint injury, afflicting a large number of males and particularly females annually. Apart from the obvious acute injury events, it also presents with significant long-term morbidities, in which osteoarthritis (OA) is a frequent and debilitative outcome. With these facts in mind, a vast amount of research has been undertaken over the past five decades geared toward characterizing the structural and mechanical behaviors of the native ACL tissue under various external load applications. While these efforts have afforded important insights, both in terms of understanding treating and rehabilitating ACL injuries; injury rates, their well-established sex-based disparity, and long-term sequelae have endured. In reviewing the expanse of literature conducted to date in this area, this paper identifies important knowledge gaps that contribute directly to this long-standing clinical dilemma. In particular, the following limitations remain. First, minimal data exist that accurately describe native ACL mechanics under the extreme loading rates synonymous with actual injury. Second, current ACL mechanical data are typically derived from isolated and oversimplified strain estimates that fail to adequately capture the true 3D mechanical response of this anatomically complex structure. Third, graft tissues commonly chosen to reconstruct the ruptured ACL are mechanically suboptimal, being overdesigned for stiffness compared to the native tissue. The net result is an increased risk of rerupture and a modified and potentially hazardous habitual joint contact profile. These major limitations appear to warrant explicit research attention moving forward in order to successfully maintain/restore optimal knee joint function and long-term life quality in a large number of otherwise healthy individuals.

Cartilage thickness mismatches in patellar osteochondral allograft transplants affect local cartilage stresses.

Osteochondral allograft implantation is a form of cartilage transplant in which a cylindrical graft of cartilage and subchondral bone from a donor is implanted into a patient's prepared articular defect site. No standard exists for matching the cartilage thickness of the donor and recipient. The goal of this study was to use finite element (FE) analysis to identify the effect of cartilage thickness mismatches between donor and recipient cartilage on cartilage stresses in patellar transplants. Two types of FE models were used: patient-specific 3D models and simplified 2D models. 3D models highlighted which geometric features produced high-stress regions in the patellar cartilage and provided ranges for the parameter sweeps that were conducted with 2D models. 2D models revealed that larger thickness mismatches, thicker recipient cartilage, and a donor-to-recipient cartilage thickness ratio (DRCR) < 1 led to higher stresses at the interface between the donor and recipient cartilage. A surface angle between the donor-recipient cartilage interface and cartilage surface normal near the graft boundary increased stresses when DRCR > 1, with the largest increase observed for an angle of 15°. A surface angle decreased stresses when DRCR < 1. Clinical Significance: This study highlights a potential mechanism to explain the high rates of failure of patellar OCAs. Additionally, the relationship between geometric features and stresses explored in this study led to a hypothetical scoring system that indicates which transplanted patellar grafts may have a higher risk of failure.

Engineered Tissue Graft for Repair of Injured Infraspinatus Rotator Cuff Tendon.

Rotator cuff tears constitute a vast majority of shoulder-related injuries, occurring in a wide population range and increasing in incidence with age. Current treatments for full thickness tears use suture to secure the ruptured tendon back to its native attachment site and often retear due to improper enthesis regeneration. To reduce the occurrence of retear, our laboratory developed an engineered tendon graft for rotator cuff repair (ETG-RC) to serve as an underlayment to traditional suture repair. We hypothesize the ETG-RC will aid in the repair of the torn rotator cuff tendon by promoting the regeneration of a functional enthesis. This devitalized graft fabricated from ovine-derived bone marrow stromal cells was evaluated for biomechanical and histomorphology properties in an ovine infraspinatus rotator cuff repair model. Compared with a current standard practice Suture-Only model, the ETG-RC repair showed comparable high strain-to-failure forces, greater fibrocartilage deposition, regeneration of zonal gradients, and Shapey's fibers formation, indicative of enthesis regeneration. Enthesis regeneration after rotator cuff repair should repair mechanical properties and alleviate the need for subsequent surgeries required due to retear. The ETG-RC could potentially be used for repairing other tendon injuries throughout the body.

Fatigue-driven compliance increase and collagen unravelling in mechanically tested anterior cruciate ligament.

Approximately 300,000 anterior cruciate ligament (ACL) tears occur annually in the United States, half of which lead to the onset of knee osteoarthritis within 10 years of injury. Repetitive loading is known to result in fatigue damage of both ligament and tendon in the form of collagen unravelling, which can lead to structural failure. However, the relationship between tissue's structural, compositional, and mechanical changes are poorly understood. Herein we show that repetitive submaximal loading of cadaver knees causes an increase in co-localised induction of collagen unravelling and tissue compliance, especially in regions of greater mineralisation at the ACL femoral enthesis. Upon 100 cycles of 4× bodyweight knee loading, the ACL exhibited greater unravelled collagen in highly mineralized regions across varying levels of stiffness domains as compared to unloaded controls. A decrease in the total area of the most rigid domain, and an increase in the total area of the most compliant domain was also found. The results highlight fatigue-driven changes in both protein structure and mechanics in the more mineralized regions of the ACL enthesis, a known site of clinical ACL failure. The results provide a starting point for designing studies to limit ligament overuse injury.

Prostatic fibrosis is associated with lower urinary tract symptoms.

PURPOSE: Current therapies for male lower urinary tract symptoms secondary to prostate enlargement prevent hormonal effects on prostate growth and inhibit smooth muscle contraction to ease bladder neck and urethral pressure. However, lower urinary tract symptoms can be refractory to these therapies, suggesting that additional biological processes not addressed by them may also contribute to lower urinary tract symptoms. Aging associated fibrotic changes in tissue architecture contribute to dysfunction in multiple organ systems. Thus, we tested whether such changes potentially have a role in impaired urethral function and perhaps in male lower urinary tract symptoms. MATERIALS AND METHODS: Periurethral tissues were obtained from a whole prostate ex vivo and from 28 consecutive men treated with radical prostatectomy. Lower urinary tract symptoms were assessed using the American Urological Association symptom index. Prostate tissues were subjected to mechanical testing to assess rigidity and stiffness. Fixed sections of these tissues were evaluated for collagen and elastin content, and glandularity to assess fibrosis. Statistical analysis included the Student t test and calculation of Pearson correlation coefficients to compare groups. RESULTS: Periurethral prostate tissues demonstrated nonlinear viscoelastic mechanical behavior. Tissue from men with lower urinary tract symptoms was significantly stiffer (p = 0.0016) with significantly higher collagen content (p = 0.0038) and lower glandularity than that from men without lower urinary tract symptoms (American Urological Association symptom index 8 or greater vs 7 or less). CONCLUSIONS: Findings show that extracellular matrix deposition and fibrosis characterize the periurethral prostate tissue of some men with lower urinary tract symptoms. They point to fibrosis as a factor contributing to lower urinary tract symptom etiology.

Reactive oxygen species on bone mineral density and mechanics in Cu,Zn superoxide dismutase (Sod1) knockout mice.

Reactive oxygen species (ROS) play a role in a number of degenerative conditions including osteoporosis. Mice deficient in Cu,Zn-superoxide dismutase (Sod1) (Sod1(-/-) mice) have elevated oxidative stress and decreased muscle mass and strength compared to wild-type mice (WT) and appear to have an accelerated muscular aging phenotype. Thus, Sod1(-/-) mice may be a good model for evaluating the effects of free radical generation on diseases associated with aging. In this experiment, we tested the hypothesis that the structural integrity of bone as measured by bending stiffness (EI; N/mm(2)) and strength (MPa) is diminished in Sod1(-/-) compared to WT mice. Femurs were obtained from male and female WT and Sod1(-/-) mice at 8months of age and three-point bending tests were used to determine bending stiffness and strength. Bones were also analyzed for bone mineral density (BMD; mg/cc) using micro-computed tomography. Femurs were approximately equal in length across all groups, and there were no significant differences in BMD or EI with respect to gender in either genotype. Although male and female mice demonstrated similar properties within each genotype, Sod1(-/-) mice exhibited lower BMD and EI of femurs from both males and females compared with gender matched WT mice. Strength of femurs was also lower in Sod1(-/-) mice compared to WT as well as between genders. These data indicate that increased oxidative stress, due to the deficiency of Sod1 is associated with decreased bone stiffness and strength and Sod1(-/-) mice may represent an appropriate model for studying disease processes in aging bone.

Fiber splay precludes the direct identification of ligament material properties: Implications for ACL graft selection.

Anterior cruciate ligament (ACL) injuries typically require surgical reconstruction to restore adequate knee stability. The middle third of an injured patient's patellar tendon (PT) is a commonly used graft for ACL reconstruction. However, many clinicians and researchers question whether it is the best option, as several studies have suggested that it is a stiffer material than the ACL. Still, there is little to no consensus on even the most basic material property of ligaments/tendons: the tangent modulus in the fiber direction, or slope of the linear portion of the uniaxial stress-strain curve. In this study, we investigate the effect of fiber splay (the tendency of collagen fibers to spread out near the enthesis) on the apparent tangent modulus. Using a simplified theoretical model, we establish a quantity we call the splay ratio, which describes the relationship between splay geometry and the apparent tangent modulus. We then more rigorously investigate the effect of the splay ratio on the apparent tangent modulus of the ovine PT and anteromedial and posterolateral regions of the ACL using experimental and computational methods. Both approaches confirmed that splay geometry significantly affects the apparent material behavior. Because true material properties are independent of geometry, we conclude that the macroscopic response of ligaments and tendons is not sufficient for the characterization of their material properties, but rather is reflective of both material and structural properties. We further conclude that the PT is probably not a stiffer material than ACL, but that the PT graft is likely a stiffer structure than either ACL region.

Robust high resolution strain imaging by alternating pulsed field gradient stimulated echo imaging (APGSTEi) at 7 Tesla.

A novel displacement-encoding spin-echo-stimulated-echo MRI sequence (APGSTEi) was used to obtain full-volume 3D strain fields in samples of two soft materials, a silicone elastomer and an ovine ligament. The samples were stretched cyclically and imaged synchronously. The multi-slice imaging sequence employed a combination of hard and soft spin-echos with bipolar gradient pulses for spatial encoding and decoding, combined with rapid multi-slice spin echo readouts. The sequence minimized undesirable signal loss due to T2∗ and T2 decays, which occur in polymeric materials or in the presence of appreciable air-solid susceptibility contrast, a particular concern for irregularly shaped samples in high magnetic fields. The images' magnitudes were T1-weighted; their phase encoded displacements which occurred during a Δ = 400 ms storage interval separating encoding and decoding pulses. Unwanted residual signals were filtered using a Gaussian filter tailored to attain the desired noise floor. The experiments measured 3D deformation with a nominal resolution of 290 µm × 250 µm × 250 µm in a sample volume of 5.6 cm × 1.6 cm × 1.6 cm, in less than an hour.

Shock wave impact on the viability of MDA-MB-231 cells.

Shock waves are gaining interests in biological and medical applications. In this work, we investigated the mechanical characteristics of shock waves that affect cell viability. In vitro testing was conducted using the metastatic breast epithelial cell line MDA-MB-231. Shock waves were generated using a high-power pulse laser. Two different coating materials and different laser energy levels were used to vary the peak pressure, decay time, and the strength of subsequent peaks of the shock waves. Within the testing capability of the current study, it is shown that shock waves with a higher impulse led to lower cell viability, a higher detached cell ratio, and a higher cell death ratio, while shock waves with the same peak pressure could lead to different levels of cell damage. The results also showed that the detached cells had a higher cell death ratio compared to the attached cells. Moreover, a critical shock impulse of 5 Pa·s was found to cause the cell death ratio of the detached cells to exceed 50%. This work has demonstrated that, within the testing range shown here, the impulse, rather than the peak pressure, is the governing shock wave parameter for the damage of MDA-MB-231 breast cancer cells. The result suggests that a lower-pressure shock wave with a longer duration, or multiple sequential low amplitude shock waves can be applied over a duration shorter than the fundamental response period of the cells to achieve the same impact as shock waves with a high peak pressure but a short duration. The finding that cell viability is better correlated with shock impulse rather than peak pressure has potential significant implications on how shock waves should be tailored for cancer treatments, enhanced drug delivery, and diagnostic techniques to maximize efficacy while minimizing potential side effects.

Highly ductile multilayered films by layer-by-layer assembly of oppositely charged polyurethanes for biomedical applications.

Multilayered thin films prepared with the layer-by-layer (LBL) assembly technique are typically "brittle" composites, while many applications such as flexible electronics or biomedical devices would greatly benefit from ductile, and tough nanostructured coatings. Here we present the preparation of highly ductile multilayered films via LBL assembly of oppositely charged polyurethanes. Free-standing films were found to be robust, strong, and tough with ultimate strains as high as 680% and toughness of approximately 30 MJ/m(3). These results are at least 2 orders of magnitude greater than most LBL materials presented until today. In addition to enhanced ductility, the films showed first-order biocompatibility with animal and human cells. Multilayered structures incorporating polyurethanes open up a new research avenue into the preparation of multifunctional nanostructured films with great potential in biomedical applications.

Morphological and functional characteristics of three-dimensional engineered bone-ligament-bone constructs following implantation.

The incidence of ligament injury has recently been estimated at 400,000/year. The preferred treatment is reconstruction using an allograft, but outcomes are limited by donor availability, biomechanical incompatibility, and immune rejection. The creation of an engineered ligament in vitro solely from patient bone marrow stromal cells (has the potential to greatly enhance outcomes in knee reconstructions. Our laboratory has developed a scaffoldless method to engineer three-dimensional (3D) ligament and bone constructs from rat bone marrow stem cells in vitro. Coculture of these two engineered constructs results in a 3D bone-ligament-bone (BLB) construct with viable entheses, which was successfully used for medial collateral ligament (MCL) replacement in a rat model. 1 month and 2 month implantations were applied to the engineered BLBs. Implantation of 3D BLBs in a MCL replacement application demonstrated that our in vitro engineered tissues grew and remodeled quickly in vivo to an advanced phenotype and partially restored function of the knee. The explanted 3D BLB ligament region stained positively for type I collagen and elastin and was well vascularized after 1 and 2 months in vivo. Tangent moduli of the ligament portion of the 3D BLB 1 month explants increased by a factor of 2.4 over in vitro controls, to a value equivalent to those observed in 14-day-old neonatal rat MCLs. The 3D BLB 1 month explants also exhibited a functionally graded response that closely matched native MCL inhomogeneity, indicating the constructs functionally adapted in vivo.

Correction to: A study on the role of articular cartilage soft tissue constitutive form in models of whole knee biomechanics.

Based on a reader comment, it has become clear that, in the originally published version of the article, Fig. 1 was published with incorrect anatomical labels.

Can nature's design be improved upon? High strength, transparent nacre-like nanocomposites with double network of sacrificial cross links.

The preparation of a high-strength and highly transparent nacre-like nanocomposite via layer-by-layer assembly technique from poly(vinyl alcohol) (PVA) and Na+-montmorillonite clay nanosheets is reported in this article. We show that a high density of weak bonding interactions between the polymer and the clay particles: hydrogen, dipole-induced dipole, and van der Waals undergoing break-reform deformations, can lead to high strength nanocomposites: sigmaUTS approximately 150 MPa and E' approximately 13 GPa. Further introduction of ionic bonds into the polymeric matrix creates a double network of sacrificial bonds which dramatically increases the mechanical properties: sigmaUTS approximately 320 MPa and E' approximately 60 GPa.