Local-to-non-local transition laws for stiffness-tuneable monoatomic chains preserving springs mass.

Recently, non-local configurations have been proposed by adding beyond nearest neighbour couplings among elements in lattices to obtain roton-like dispersion relations and phase and group velocities with opposite signs. Even though the introduction of non-local elastic links in metamaterials has unlocked unprecedented possibilities, literature models and prototypes seem neither to provide criteria to compare local and non-local lattices nor to discuss any related rules governing the transition between the two configurations. A physically reasonable principle that monoatomic one-dimensional chains must obey to pass from single- to multi-connected systems is here proposed through a mass conservation law for elastic springs thereby introducing a suitable real dimensionless parameter [Formula: see text] to tune stiffness distribution. Therefore, the dispersion relations as a function of [Formula: see text] and of the degree of non-locality [Formula: see text] are derived analytically, demonstrating that the proposed principle can be rather interpreted as a general mechanical consistency condition to preserve proper dynamics, involving the spring-to-bead mass ratio. Finally, after discussing qualitative results and deriving some useful inequalities, numerical simulations and two-dimensional FFTs are performed for some paradigmatic examples to highlight key dynamics features exhibited by chains with finite length as the parameters [Formula: see text] and [Formula: see text] vary.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Effects of a nonlocal microstructure on peeling of thin films.

In this work, starting from an approach previously proposed by the Authors, we put forward an extension to the large deformation regime of the dimensionally-reduced formulation for peridynamic thin plates, including both hyperelasticity and fracture. In particular, the model, validated against numerical simulations, addresses the problem of the peeling in nonlocal thin films, which when attached to a soft substrate highlights how nonlocality of the peeled-off layer might greatly influence the whole structural response and induce some unforeseen mechanical behaviours that could be useful for engineering applications. Through a key benchmark example, we in fact demonstrate that de-localization of damage and less destructive failure modes take place, these effects suggesting the possibility of ad hoc conceiving specific networks of nonlocal interactions between material particles, corresponding to lattice-equivalent structure of the nonlocal model treated, of interest in designing new material systems and interfaces with enhanced toughness and adhesive properties.

Modelling lipid rafts formation through chemo-mechanical interplay triggered by receptor-ligand binding.

Cell membranes, mediator of many biological mechanisms from adhesion and metabolism up to mutation and infection, are highly dynamic and heterogeneous environments exhibiting a strong coupling between biochemical events and structural re-organisation. This involves conformational changes induced, at lower scales, by lipid order transitions and by the micro-mechanical interplay of lipids with transmembrane proteins and molecular diffusion. Particular attention is focused on lipid rafts, ordered lipid microdomains rich of signalling proteins, that co-localise to enhance substance trafficking and activate different intracellular biochemical pathways. In this framework, the theoretical modelling of the dynamic clustering of lipid rafts implies a full multiphysics coupling between the kinetics of phase changes and the mechanical work performed by transmembrane proteins on lipids, involving the bilayer elasticity. This mechanism produces complex interspecific dynamics in which membrane stresses and chemical potentials do compete by determining different morphological arrangements, alteration in diffusive walkways and coalescence phenomena, with a consequent influence on both signalling potential and intracellular processes. Therefore, after identifying the leading chemo-mechanical interactions, the present work investigates from a modelling perspective the spatio-temporal evolution of raft domains to theoretically explain co-localisation and synergy between proteins' activation and raft formation, by coupling diffusive and mechanical phenomena to observe different morphological patterns and clustering of ordered lipids. This could help to gain new insights into the remodelling of cell membranes and could potentially suggest mechanically based strategies to control their selectivity, by orienting intracellular functions and mechanotransduction.

Bimodal buckling governs human fingers' luxation.

Equilibrium bifurcation in natural systems can sometimes be explained as a route to stress shielding for preventing failure. Although compressive buckling has been known for a long time, its less-intuitive tensile counterpart was only recently discovered and yet never identified in living structures or organisms. Through the analysis of an unprecedented all-in-one paradigm of elastic instability, it is theoretically and experimentally shown that coexistence of two curvatures in human finger joints is the result of an optimal design by nature that exploits both compressive and tensile buckling for inducing luxation in case of traumas, so realizing a unique mechanism for protecting tissues and preventing more severe damage under extreme loads. Our findings might pave the way to conceive complex architectured and bio-inspired materials, as well as next generation artificial joint prostheses and robotic arms for bio-engineering and healthcare applications.

Growth of a flexible fibre in a deformable ring.

We study the equilibrium configurations related to the growth of an elastic fibre in a confining flexible ring. This system represents a paradigm for a variety of biological, medical, and engineering problems. We consider a simplified geometry in which initially the container is a circular ring of radius R. Quasi-static growth is then studied by solving the equilibrium equations as the fibre length l increases, starting from l = 2R. Considering both the fibre and the ring as inextensible and unshearable, we find that beyond a critical length, which depends on the relative bending stiffness, the fibre buckles. Furthermore, as the fibre grows further it folds, distorting the ring until it induces a break in mirror symmetry at l > 2πR. We get that the equilibrium shapes depend only on two dimensionless parameters: the length ratio µ = l/R and the bending stiffnesses ratio κ. These findings are also supported by finite element simulation. Finally we experimentally validate the theoretical results showing a very good quantitative prediction of the observed buckling and folding regimes at variable geometrical parameters.

Ultrasound waves in tumors via needle irradiation for precise medicine.

Grounded in the interdisciplinary crosstalk among physics and biological sciences, precision medicine-based diagnosis and treatment strategies have recently gained great attention for the actual applicability of new engineered approaches in many medical fields, particularly in oncology. Within this framework, the use of ultrasounds employed to attack cancer cells in tumors to induce possible mechanical damage at different scales has received growing attention from scholars and scientists worldwide. With these considerations in mind, on the basis of ad hoc elastodynamic solutions and numerical simulations, we propose a pilot study for in silico modeling of the propagation of ultrasound waves inside tissues, with the aim of selecting proper frequencies and powers to be irradiated locally through a new teragnostic platform based on Lab-on-Fiber technology, baptized as a hospital in the needle and already the object of a patent. It is felt that the outcomes and the related biophysical insights gained from the analyses could pave the way for envisaging new integrated diagnostic and therapeutic approaches that might play a central role in future applications of precise medicine, starting from the growing synergy among physics, engineering and biology.

Multiscale geometry and mechanics of lipid monolayer collapse.

Langmuir monolayers at gas/liquid interfaces provide a rich framework to investigate the interplay between multiscale geometry and mechanics. Monolayer collapse is investigated at a topological and geometric level by building a scale space M from experimental imaging data. We present a general lipid monolayer collapse phase diagram, which shows that wrinkling, folding, crumpling, shear banding, and vesiculation are a continuous set of mechanical states that can be approached by either tuning monolayer composition or temperature. The origin of the different mechanical states can be understood by investigating the monolayer geometry at two scales: fluorescent vs atomic force microscopy imaging. We show that an interesting switch in continuity occurs in passing between the two scales, CAFM∈MAFM≠CFM∈M. Studying the difference between monolayers that fold vs shear band, we show that shear banding is correlated to the persistence of a multi-length scale microstructure within the monolayer at all surface pressures. A detailed analytical geometric formalism to describe this microstructure is developed using the theory of structured deformations. Lastly, we provide the first ever finite element simulation of lipid monolayer collapse utilizing a direct mapping from the experimental image space M into a simulation domain P. We show that elastic dissipation in the form of bielasticity is a necessary and sufficient condition to capture loss of in-plane stability and shear banding.

A lesson from earthquake engineering for selectively damaging cancer cell structures.

The progressive falling of barriers among disciplines is opening unforeseen scenarios in diagnosis and treatment of cancer diseases. By sharing models and mature knowledge in physics, engineering, computer sciences and molecular biology, synergistic efforts have in fact contributed in the last years to re-think still unsolved problems, shedding light on key roles of mechanobiology in tumors and envisaging new effective strategies for a precise medicine. The use of ultrasounds for altering cancer cells' program is one of the most attracting grounds to be explored in oncophysics, although how to administer mechanical energy to impair selected cell structures and functions simultaneously overcoming the critical trade-off between the impact of the cure and the patient risk still remains an open issue. Within this framework, by starting from the theoretical possibility of selectively attacking malignant cells by exploiting the stiffness discrepancies between tumor and healthy single cells, first proposed by Fraldi et al. (2015), we here investigate the in-frequency response of an overall spherical close-packing of geometrically equal polyhedral cells to gain insights into how mechanical resonance and vibration-induced failure phenomena can be oriented to destroy specific target units when both the cell populations coexist, as it happens for in vivo cases. Inspired by the dynamic action of earthquakes - which fracture only selected elements among adjacent ones in the same structure or damage individual constructions in contiguous buildings - we study the harmonic response of hierarchically architectured cell agglomerates, inhabited by both tumor and healthy cells that interact mutually throughout the extra-cellular matrix and whose cytoskeleton is modeled as a nonlinear soft-tensegrity structure. Numerical Finite Element results show that, at frequencies compatible with low intensity therapeutic ultrasounds, mechanical resonance and possible fatigue cycles of the pre-stressed actin filaments and microtubules can be selectively induced in cancer cells as a function of the global volume fraction of the cell species, paving the way for future engineered treatment protocols.

Three dimensional bone mineral density changes in the femur over 1 year in primary total hip arthroplasty patients.

BACKGROUND: The aim of the study was to compare the bone mineral density changes between unmatched patients undergoing total hip arthroplasty receiving uncemented and cemented type of implants. Previous studies have used DEXA or a two dimensional analysis to estimate the bone quality following total joint replacement, whereas this study presents the changes in three dimensions. METHODS: Fifty subjects both male and females receiving both cemented and uncemented type of implant were recruited. Two CT scans were taken of each subject, the first at 24 h post surgery and the second one 1 year after surgery. The scans were calibrated using a phantom converting the Hounsfield units to bone mineral density values in g/cm3. The two scans were registered together using anatomical landmarks and resliced to compare the two femurs in the identical frame of reference. The bone density gain and loss was calculated by comparing density values between the two sets of scans. FINDINGS: The results showed that most of the bone loss was located around the Lesser Trochanter and some bone density gain at the distal tip of the implant. The three dimensional density changes occur differently between individuals and the study showed no correlation of bone loss with age. INTERPRETATION: The bone loss occurred mostly at the proximal femur, which is in agreement with previously presented studies. By carrying out three dimensional analysis on the bone gain and loss on the femur, it is possible to identify the patients that are showing high degree of bone loss.

Mechanobiology predicts raft formations triggered by ligand-receptor activity across the cell membrane.

Clustering of ligand-binding receptors of different types on thickened isles of the cell membrane, namely lipid rafts, is an experimentally observed phenomenon. Although its influence on cell's response is deeply investigated, the role of the coupling between mechanical processes and multiphysics involving the active receptors and the surrounding lipid membrane during ligand-binding has not yet been understood. Specifically, the focus of this work is on G-protein-coupled receptors (GPCRs), the widest group of transmembrane proteins in animals, which regulate specific cell processes through chemical signalling pathways involving a synergistic balance between the cyclic Adenosine Monophosphate (cAMP) produced by active GPCRs in the intracellular environment and its efflux, mediated by the Multidrug Resistance Proteins (MRPs) transporters. This paper develops a multiphysics approach based on the interplay among energetics, multiscale geometrical changes and mass balance of species, i.e. active GPCRs and MRPs, including diffusion and kinetics of binding and unbinding. Because the obtained energy depends upon both the kinematics and the changes of species densities, balance of mass and of linear momentum are coupled and govern the space-time evolution of the cell membrane. The mechanobiology involving remodelling and change of lipid ordering of the cell membrane allows to predict dynamics of transporters and active receptors -in full agreement with experimentally observed cAMP levels- and how the latter trigger rafts formation and cluster on such sites. Within the current scientific debate on Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2) and on the basis of the ascertained fact that lipid rafts often serve as an entry port for viruses, it is felt that approaches accounting for strong coupling among mechanobiological aspects could even turn helpful in better understanding membrane-mediated phenomena such as COVID-19 virus-cell interaction.

Burrowing below ground: interaction between soil mechanics and evolution of subterranean mammals.

The evolution of species is governed by complex phenomena in which biological and environmental features may interact dynamically. Subterranean mammals dig tunnels whose diameter minimizes energetic costs during excavations and display anatomical adaptations in order to burrow structurally stable tunnels according to specific features of the soil. These animals weight from less than 50 g up to 1-2 kg, and dig tunnels with diameters from 3 to 15 cm. The use of allometric laws has enabled these data to be correlated. However, since tunnels need to be stable with respect to the geomechanical characteristics of the resident soils, a mathematical treatment linking the admissible dimensions of tunnels to the environment here suggests a mechanically grounded correlation between the body mass of subterranean mammals and the maximum dimensions of tunnels. Remarkably, such theoretical findings reflect very well the empirical allometric relationship and contribute to explain the wide differences observed in body sizes of subterranean mammals. In this respect, a far from ancillary role of environmental mechanics on the morphological evolution of subterranean mammals can be hypothesized.

Competition between delamination and tearing in multiple peeling problems.

Adhesive attachment systems consisting of multiple tapes or strands are commonly found in nature, for example in spider web anchorages or in mussel byssal threads, and their structure has been found to be ingeniously architected in order to optimize mechanical properties: in particular, to maximize dissipated energy before full detachment. These properties emerge from the complex interplay between mechanical and geometric parameters, including tape stiffness, adhesive energy, attached and detached lengths and peeling angles, which determine the occurrence of three main mechanisms: elastic deformation, interface delamination and tape fracture. In this paper, we introduce a formalism to evaluate the mechanical performance of multiple tape attachments in different parameter ranges, where an optimal (not maximal) adhesion energy emerges. We also introduce a numerical model to simulate the multiple peeling behaviour of complex structures, illustrating its predictions in the case of the staple-pin architecture. Finally, we present a proof-of-principle experiment to illustrate the predicted behaviour. We expect the presented formalism and the numerical model to provide important tools for the design of bioinspired adhesive systems with tuneable or optimized detachment properties.

Euler's Elastica-Based Biomechanics of the Papillary Muscle Approximation in Ischemic Mitral Valve Regurgitation: A Simple 2D Analytical Model.

Ischemic mitral regurgitation (IMR) occurs as an adverse consequence of left ventricle remodeling post-myocardial infarction. A change in mitral valve configuration with an imbalance between closing and tethering forces underlie this pathological condition. These abnormalities lead to impaired leaflet coaptation and a variable degree of mitral regurgitation, which can in turn influence the ventricular filling status, the heart rhythm and the afterload regardless of the residual ischemic insult. The IMR correction can be pursued through under-sizing mitral annuloplasty and papillary muscle approximation to restore the mitral valve and left ventricle physiological geometry to, consequently, achieve normalization of the engaged physical forces. Because the structures involved undergo extremely large deformations, a biomechanics model based on the Euler's Elastica -the mitral leaflet- interlaced with nonlinear chordae tendineae anchored on papillary muscles has been constructed to elucidate the interactions between closing and tethering forces. The model takes into account the actual updated geometrical and mechanical features of the valvular and subvalvular apparatuses in physiological and IMR conditions, as well as in case of papillary muscle approximation, finally furnishing ad hoc geometry-based mathematical relations that could be utilised to support-and optimize-the relevant choices in cardiac surgery.

Patient-specific mobility assessment to monitor recovery after total hip arthroplasty.

Total hip arthroplasty is a ubiquitously successful orthopedic surgical procedure, whose prevalence is rising worldwide. While many investigations focus on characterizing periprosthetic pathophysiology, the objective of our research is to develop and describe multi-metric assemblies as a first step toward creating a patient-specific mobility index that rehabilitators and orthopedic surgeons can utilize for prescribing their respective procedures. In total, 48 total hip arthroplasty patients (both cemented and uncemented) undergoing unilateral, primary surgery went through computed tomographic scans and gait analysis measurements both before and 1 year following their surgery. Altogether, the reported quantitative metrics include 11 spatial and temporal gait parameters, muscle density, and electromyography signals from the rectus femoris, vastus lateralis, and vastus medialis, and bone mineral density values from bioimage analysis around the implant stem. We found that measured parameters from a subgroup were sensitive to changes observed during patient recovery, implicating the predictive sensitivity of these patient conditions. Most post-operative gait parameters changed significantly, while electromyography data indicated few significant differences. Moreover, results from bioimage analyses indicate a general reduction of periprosthetic bone mineral density after 1 year, in association with increasing density of the quadriceps muscles. Furthermore, this work identifies which quantitative metrics undergo the greatest variation after total hip arthroplasty and demonstrates the clinical feasibility of a multimodal approach to mobility assessment that may ultimately support decision-making for post-surgical rehabilitation protocols.

Retrieving acoustic energy densities and local pressure amplitudes in microfluidics by holographic time-lapse imaging.

The development of techniques able to characterize and map the pressure field is crucial for the widespread use of acoustofluidic devices in biotechnology and lab-on-a-chip platforms. In fact, acoustofluidic devices are powerful tools for driving precise manipulation of microparticles and cells in microfluidics in non-contact modality. Here, we report a full and accurate characterization of the movement of particles subjected to acoustophoresis in a microfluidic environment by holographic imaging. The particle displacement along the direction of the ultrasound wave propagation, coinciding with the optical axis, is observed and investigated. Two resonance frequencies are explored, varying for each the amplitude of the applied signal. The trajectories of individual tracers, accomplished by holographic measurements, are fitted with the theoretical model thus allowing the retrieval of the acoustic energy densities and pressure amplitudes through full holographic analysis. The absence of prior calibration, being independent of the object shape and the possibility of implementing automatic analysis make the use of holography very appealing for applications in devices for biotechnologies.

Simulating the ideal geometrical and biomechanical parameters of the pulmonary autograft to prevent failure in the Ross operation.

OBJECTIVES: Reinforcements for the pulmonary autograft (PA) in the Ross operation have been introduced to avoid the drawback of conduit expansion and failure. With the aid of an in silico simulation, the biomechanical boundaries applied to a healthy PA during the operation were studied to tailor the best implant technique to prevent reoperation. METHODS: Follow-up echocardiograms of 66 Ross procedures were reviewed. Changes in the dimensions and geometry of reinforced and non-reinforced PAs were evaluated. Miniroot and subcoronary implantation techniques were used in this series. Mechanical stress tests were performed on 36 human pulmonary and aortic roots explanted from donor hearts. Finite element analysis was applied to obtain high-fidelity simulation under static and dynamic conditions of the biomechanical properties and applied stresses on the PA root and leaflet and the similar components of the native aorta. RESULTS: The non-reinforced group showed increases in the percentages of the mean diameter that were significantly higher than those in the reinforced group at the level of the Valsalva sinuses (3.9%) and the annulus (12.1%). The mechanical simulation confirmed geometrical and dimensional changes detected by clinical imaging and demonstrated the non-linear biomechanical behaviour of the PA anastomosed to the aorta, a stiffer behaviour of the aortic root in relation to the PA and similar qualitative and quantitative behaviours of leaflets of the 2 tissues. The annulus was the most significant constraint to dilation and affected the distribution of stress and strain within the entire complex, with particular strain on the sutured regions. The PA was able to evenly absorb mechanical stresses but was less adaptable to circumferential stresses, potentially explaining its known dilatation tendency over time. CONCLUSIONS: The absence of reinforcement leads to a more marked increase in the diameter of the PA. Preservation of the native geometry of the PA root is crucial; the miniroot technique with external reinforcement is the most suitable strategy in this context.

Biomechanics raises solution to avoid geometric mitral valve configuration abnormalities in ischemic mitral regurgitation.

Ischemic mitral regurgitation (IMR) is a form of mitral insufficiency that is characterized by papillary muscle (PM) displacement, leaflet tethering, reduced closing forces, and different degree of annular dilatation. Treatment of this condition includes mitral valve replacement or mitral valve repair with restrictive annuloplasty. Recent evidences in mitral valve repair showed that addressing only the annulus and neglecting the subvalvular apparatus provides a suboptimal operation with poor long-term results. However, the complexity of the geometrical aberrances occurring in IMR demands for more accurate analysis also involving the biomechanics underlying the failing mitral valve and subvalvular apparatus. Finite element analysis (FEA) is a powerful tool in this context and we developed a biomechanical model of mitral valve and subvalvular unit using 3D geometry of the leaflets, annulus, chordae and PM. After the application of structural properties of materials to these elements and simulation of systemic pressure loading, FEA could be used to directly determine biomechanical changes and geometry variations. We believe this approach can provide valuable information to better address the surgical treatment of IMR and answer some of the questions still pending in IMR management.