Effect of density grading on the mechanical behaviour of advanced functionally graded lattice structures

Lattice structures have found significant applications in the biomedical field due to their interesting combination of mechanical and biological properties. Among these, functionally graded structures sparked interest because of their potential of varying their mechanical properties throughout the volume, allowing the design of biomedical devices able to match the characteristics of a graded structure like human bone. The aim of this works is the study of the effect of the density grading on the mechanical response and the failure mechanisms of a novel functionally graded lattice structure, namely Triply Arranged Octagonal Rings (TAOR). The mechanical behaviour was compared with the same lattice structures having constant density ratio. Electron Beam Melting technology was used to manufacture titanium alloy specimens with global relative densities from 10% to 30%. Functionally graded structures were obtained by increasing the relative density along the specimen, by individually designing the lattice's layers. Scanning electron and a digital microscopy were used to evaluate the dimensional mismatch between actual and designed structures. Compressive tests were carried out to obtain the mechanical properties and to evaluate the collapse modes of the structures in relation to their average relative density and lattice grading. Open-source Digital Image Correlation algorithm was applied to evaluate the deformation behaviour of the structures and to calculate their elastic moduli. The results showed that uniform density structures provide higher mechanical properties than functionally graded ones. The Digital Image Correlation results showed the possibility of effectively designing the different layers of functionally graded structures selecting desired local mechanical properties to mimic the different characteristics of cortical and cancellous bone.

Strain-dependent elastography of cancer cells reveals heterogeneity and stiffening due to attachment

Because cells vary in thickness and in biomechanical properties, the use of a constant force trigger during atomic force microscopy (AFM) stiffness mapping produces a varied nominal strain that can obfuscate the comparison of local material properties. In this study, we measured the biomechanical spatial heterogeneity of ovarian and breast cancer cells by using an indentation-dependent pointwise Hertzian method. Force curves and surface topography were used together to determine cell stiffness as a function of nominal strain. By recording stiffness at a particular strain, it may be possible to improve comparison of the material properties of cells and produce higher contrast representations of cell mechanical properties. Defining a linear region of elasticity that corresponds to a modest nominal strain, we were able to clearly distinguish the mechanics of the perinuclear region of cells. We observed that, relative to the lamelopodial stiffness, the perinuclear region was softer for metastatic cancer cells than their nonmetastatic counterparts. Moreover, contrast in the strain-dependent elastography in comparison to conventional force mapping with Hertzian model analysis revealed a significant stiffening phenomenon in the thin lamellipodial region in which the modulus scales inversely and exponentially with cell thickness. The observed exponential stiffening is not affected by relaxation of cytoskeletal tension, but finite element modeling indicates it is affected by substrate adhesion. The novel cell mapping technique explores cancer cell mechanical nonlinearity that results from regional heterogeneity, which could help explain how metastatic cancer cells can show soft phenotypes while simultaneously increasing force generation and invasiveness.

Hierarchical modeling of elastic moduli of equine hoof wall

This study predicts analytically effective elastic moduli of substructures within an equine hoof wall. The hoof wall is represented as a composite material with a hierarchical structure comprised of a sequence of length scales. A bottom-up approach is employed. Thus, the outputs from a lower spatial scale serve as the inputs for the following scale. The models include the Halpin-Tsai model, composite cylinders model, a sutured interface model, and classical laminate theory. The length scales span macroscale, mesoscale, sub-mesoscale, microscale, sub-microscale, and nanoscale. The macroscale represents the hoof wall, consisting of tubules within a matrix at the mesoscale. At the sub-mesoscale, a single hollow tubule is reinforced by a tubule wall made of lamellae; the surrounding intertubular material also has a lamellar structure. The lamellae contain sutured and layered cells at the microscale. A single cell is made of crystalline macrofibrils arranged in an amorphous matrix at the sub-microscale. A macrofibril contains aligned crystalline rod-like intermediate filaments at the nanoscale. Experimentally obtained parameters are used in the modeling as inputs for geometry and nanoscale properties. The predicted properties of the hoof wall material agree with experimental measurements at the mesoscale and macroscale. We observe that the hierarchical structure of the hoof wall leads to a decrease in the elastic modulus with increasing scale, from the nanoscale to the macroscale. Such behavior is an intrinsic characteristic of hierarchical biological materials. This study can serve as a framework for designing impact-resistant hoof-inspired materials and structures.

A nanomechanical strategy involving focal adhesion kinase for overcoming drug resistance in breast cancer

Despite implementation of nanomechanical studies in cancer research, studies on the nanomechanical aspects of drug resistance in cancer are lacking. Here, we established the mechanical signatures of drug-resistant breast cancer cells using atomic force microscopy-based indentation techniques and functionalized nanopatterned substrates (NPS). Additionally, we examined the expression of proteins pertinent to focal adhesions in order to elucidate the molecular signatures responsible for the acquisition of drug resistance in breast cancer cells. Drug-resistant breast cancer cells exhibited mechanical reinforcement, increased actin stress fibers, dysfunctional mechano-reciprocal interaction with the NPS, vinculin overexpression, and improved focal adhesion kinase (FAK) activity. Owing to differences in FAK activation upon co-treatment with a FAK inhibitor, the drug-resistant breast cancer cells were eradicated more efficiently than invasive breast cancer cells having pro-survival activity. These findings demonstrated the potential of a novel co-treatment regimen using FAK inhibitors for overcoming drug resistance in breast cancer cells.

Modeling of the human mandibular periosteum material properties and comparison with the calvarial periosteum

Knowledge of mandibular periosteum mechanical properties is fundamental for understanding its role in craniofacial growth, in trauma and bone regeneration. There is a lack in the literature regarding mechanical behavior of the human periosteum, including both experimental and modeling aspects. The proposed study involves tensile tests of periosteum samples from different locations including two locations of human mandibular periosteum: lingual and vestibular, compared with samples from various locations of the calvarial periosteum. We propose to analyze the tensile response of the mandibular periosteum using a model, initially applied on the skin, and based on a structural approach involving the mechanical properties of the corrugation of the collagen. Two different approaches for the model parameters' identification are proposed: (1) identification from experimental curve fitting and (2) identification from histological study. This approach allows us to compare parameters extracted from the traction test fitting to structural parameters measured on periosteum histological slices. Concerning experimental aspects, we showed significant differences, in terms of stiffness, between calvarial and mandibular periostea. (The mean final stiffness is [Formula: see text] for the mandible versus [Formula: see text] for the calvaria.) About modeling, we succeed to capture the correct mechanical behavior for the periosteum, and the statistical analysis showed that certain parameters from the geometric data and traction data are significantly comparable (e.g., [Formula: see text] for [Formula: see text]). However, we also observed a discrepancy between these two approaches for the elongation at which the fibril has become straight ([Formula: see text]).

Elastic, electronic, chemical bonding and thermodynamic properties of the ternary nitride Ca4TiN4: Ab initio predictions

In order to shed light on the unexplored properties of the ternary nitride Ca₄TiN₄, we report for the first time the results of an ab initio study of its structural, electronic, elastic, chemical bonding and thermodynamic properties. Calculated equilibrium structural parameters are in excellent concordance with available experimental data. Electronic properties were explored through the calculation of the energy band dispersions and density of states. It is found that Ca₄TiN₄ has an indirect band gap (Z-Γ) of 1.625 (1.701) eV using LDA (GGA). Nature of the chemical bonding was studied via Mulliken population analysis and charge density distribution map. It is found that the Ca-N bond is dominantly ionic, whereas the Ti-N one is dominantly covalent. Elastic properties of both single-crystal and polycrystalline phases of the title compound were explored in details using the stain-stress approach. Analysis of the calculated elastic moduli reveals that the title compound is mechanically stable, ductile and elastically anisotropic. Temperature and pressure dependencies of the unit-cell volume, bulk modulus, heat capacities, volume thermal expansion coefficient, Grüneisen parameter and Debye temperature were investigated based on the quasiharmonic Debye model.

Determination of elastic moduli from measured acoustic velocities

Methods are evaluated in solution of the inverse problem associated with determination of elastic moduli for crystals of arbitrary symmetry from elastic wave velocities measured in many crystallographic directions. A package of MATLAB functions provides a robust and flexible environment for analysis of ultrasonic, Brillouin, or Impulsive Stimulated Light Scattering datasets. Three inverse algorithms are considered: the gradient-based methods of Levenberg-Marquardt and Backus-Gilbert, and a non-gradient-based (Nelder-Mead) simplex approach. Several data types are considered: body wave velocities alone, surface wave velocities plus a side constraint on X-ray-diffraction-based axes compressibilities, or joint body and surface wave velocities. The numerical algorithms are validated through comparisons with prior published results and through analysis of synthetic datasets. Although all approaches succeed in finding low-misfit solutions, the Levenberg-Marquardt method consistently demonstrates effectiveness and computational efficiency. However, linearized gradient-based methods, when applied to a strongly non-linear problem, may not adequately converge to the global minimum. The simplex method, while slower, is less susceptible to being trapped in local misfit minima. A "multi-start" strategy (initiate searches from more than one initial guess) provides better assurance that global minima have been located. Numerical estimates of parameter uncertainties based on Monte Carlo simulations are compared to formal uncertainties based on covariance calculations.

Experimentally-based multiscale model of the elastic moduli of bovine trabecular bone and its constituents

The elastic moduli of trabecular bone were modeled using an analytical multiscale approach. Trabecular bone was represented as a porous nanocomposite material with a hierarchical structure spanning from the collagen-mineral level to the trabecular architecture level. In parallel, compression testing was done on bovine femoral trabecular bone samples in two anatomical directions, parallel to the femoral neck axis and perpendicular to it, and the measured elastic moduli were compared with the corresponding theoretical results. To gain insights on the interaction of collagen and minerals at the nanoscale, bone samples were deproteinized or demineralized. After such processing, the treated samples remained as self-standing structures and were tested in compression. Micro-computed tomography was used to characterize the hierarchical structure of these three bone types and to quantify the amount of bone porosity. The obtained experimental data served as inputs to the multiscale model and guided us to represent bone as an interpenetrating composite material. Good agreement was found between the theory and experiments for the elastic moduli of the untreated, deproteinized, and demineralized trabecular bone.

Proxy model materials to simulate the elastic properties of digested municipal sludge

The elastic rheological properties of sludge are complex and evolve with time as a result of ageing and microbial activity. Due to the peculiar nature of sludge, this makes the measurement of physical parameters difficul. The challenge is to identify a reference material that can be used as a proxy for industrial process design or optimization. In this study, respectively the mixtures of 0.5%, 0.7% and 1% glass beads suspension in water have been added to 0.5%, 0.7% and 1% carbopol dissolved in water and neutralized with NaOH to prepare gel, at different ratios. Elastic and loss moduli have been determined for different glass bead suspension ratios in the range of 0%-80%. The results showed that there is a critical glass bead suspension/carbopol ratio at which the elastic properties of the mixture changes dramatically. The elastic properties of these model mixtures of different glass bead/carbopol ratio suspensions are compared with the elastic property of municipal sludge sampled from a Melbourne Waste Water Treatment Plant, and similarity established.

Validation of shear wave elastography in skeletal muscle

Skeletal muscle is a very dynamic tissue, thus accurate quantification of skeletal muscle stiffness throughout its functional range is crucial to improve the physical functioning and independence following pathology. Shear wave elastography (SWE) is an ultrasound-based technique that characterizes tissue mechanical properties based on the propagation of remotely induced shear waves. The objective of this study is to validate SWE throughout the functional range of motion of skeletal muscle for three ultrasound transducer orientations. We hypothesized that combining traditional materials testing (MTS) techniques with SWE measurements will show increased stiffness measures with increasing tensile load, and will correlate well with each other for trials in which the transducer is parallel to underlying muscle fibers. To evaluate this hypothesis, we monitored the deformation throughout tensile loading of four porcine brachialis whole-muscle tissue specimens, while simultaneously making SWE measurements of the same specimen. We used regression to examine the correlation between Young's modulus from MTS and shear modulus from SWE for each of the transducer orientations. We applied a generalized linear model to account for repeated testing. Model parameters were estimated via generalized estimating equations. The regression coefficient was 0.1944, with a 95% confidence interval of (0.1463-0.2425) for parallel transducer trials. Shear waves did not propagate well for both the 45° and perpendicular transducer orientations. Both parallel SWE and MTS showed increased stiffness with increasing tensile load. This study provides the necessary first step for additional studies that can evaluate the distribution of stiffness throughout muscle.