Membrane Elastic Modulus Research Articles

Nonlinear vibrations of a flexible membrane under periodic load

A finite element solution procedure is proposed, and the nonlinear vibrations of a flexible membrane under periodic load are investigated numerically. First, a simplified model is proposed for the flow-induced vibration of a membrane wing at higher angles of attack and the corresponding governing equation is derived briefly. Then, a solution procedure based on the Galerkin finite element method, Generalized- $$\upalpha $$ method and Newton–Raphson method is developed to solve the governing equation and its accuracy and stability are examined by a steady problem with exact solution. Finally, using the numerical method proposed, the forced vibration of a flexible membrane under periodic load is simulated, and the effects of the membrane density, elastic modulus and pre-strain are investigated in detail. In addition, the change in the vibration state along the membrane is also analysed to examine whether the centre point can reflect correctly the vibration state of the whole structure.

Conformability of a Thin Elastic Membrane Laminated on a Soft Substrate With Slightly Wavy Surface

When laminating a thin elastic membrane on a substrate with surface roughness, three scenarios can happen: fully conformed (FC), i.e., the membrane completely follows the surface morphology of the substrate without any interfacial gap, nonconformed (NC), i.e., the membrane remains flat if gravity is not concerned, and partially conformed (PC). Good conformability can enhance effective membrane-to-substrate adhesion strength and can facilitate signal/heat/mass transfer across the interface, which are of great importance to soft electronics laminated on rough bio-tissues. To reveal governing parameters in this problem and to predict conformability, energy minimization is implemented after successfully finding the substrate elastic energy under partially conformable contact. Four dimensionless governing parameters involving the substrate roughness, membrane thickness, membrane and substrate elastic moduli, and membrane-to-substrate intrinsic work of adhesion have been identified to analytically predict the conformability status and the area of contact. The analytical prediction has found excellent agreement with experimental observations. In summary, an experimentally validated quantitative guideline for the conformability of elastic membrane on soft corrugated substrate has been established in the four-parameter design space.

Experimental and numerical studies of a microfluidic device with compliant chambers for flow stabilization

This paper reports experimental and numerical studies of a passive microfluidic device that stabilizes a pulsating incoming flow and delivers a steady flow at the outlet. The device employs a series of chambers along the flow direction with a thin polymeric membrane (of thickness 75–250 µm) serving as the compliant boundary. The deformation of the membrane allows accumulation of fluid during an overflow and discharge of fluid during an underflow for flow stabilization. Coupled fluid-structure simulations are performed using Mooney–Rivlin formulations to account for a thin hyperelastic membrane material undergoing large deformations to accurately predict the device performance. The device was fabricated with PDMS as the substrate material and thin PDMS membrane as the compliant boundary. The performance of the device is defined in terms of a parameter called ‘Attenuation Factor (AF)’. The effect of various design parameters including membrane thickness, elastic modulus, chamber size and number of chambers in series as well as operating conditions including the outlet pressure, mean input flow rate, fluctuation amplitude and frequency on the device performance were studied using experiments and simulations. The simulation results successfully confront the experimental data (within 10%) which validates the numerical simulations. The device was used at the exit of a PZT actuated valveless micropump to take pulsating flow at the upstream and deliver steady flow downstream. The amplitude of the pulsating flow delivered by the micropump was significantly reduced (AF = 0.05 for a device with three 4 mm chambers) but at the expense of a reduction in the pressure capability (<20%). The proposed device could potentially be used for reducing flow pulsations in practical microfluidic circuits.

Effects of Phyllanthus sellowianus Müll Arg. extracts on the rheological properties of human erythrocytes.

Phyllanthus sellowianus extracts have been used in Argentina since colonial times in the treatment of diabetes. The in vitro biorheological and hemoagglutinant action of different extracts of P. sellowianus bark on human erythrocytes (RBC) were studied. RBCs were incubated in vitro with four aqueous extracts: Maceration; Controlled Digestion (PD); Decoction; and Infusion. Biorheological parameters (deformability, membrane surface viscosity, elastic modulus, and dynamic viscolelasticity) were determined with an Erythrodeformeter, and erythrocyte adhesion was characterized by image digital analysis. Immunohematological assays in RBC incubated with all the extracts showed large globular aggregates and agglutination in human ABO blood group system. Isolated cell coefficient showed the increase of cell adhesion. Aggregated shape parameters were significantly higher than normal and they changed with the concentration, particularly of PD extracts. Rheological results showed that the extract biorheological action varies with the temperature used in the extract preparations. The results obtained are useful to study the action mechanism of extracts from P. sellowianus bark in order to evaluate its use as therapeutic agent in diabetes. Immunohematological Tests using ABO system showed its agglutinant power, which is of special interest in Immunohematology to be used as hemoclassifier.

Microscale modeling of coupled water transport and mechanical deformation of fruit tissue during dehydration

Water loss of fruit typically results in fruit tissue deformation and consequent quality loss. To better understand the mechanism of water loss, a model of water transport between cells and intercellular spaces coupled with cell deformation was developed. Pear (Pyrus communis L. cv. Conference) was chosen as a model system as this fruit suffers from shriveling with excessive water loss. A 2D geometric model of cortex tissue was obtained by a virtual fruit tissue generator that is based on cell growth modeling. The transport of water in the intercellular space, the cell wall network and cytoplasm was predicted using transport laws using the chemical potential as the driving force for water exchange between different microstructural compartments. The different water transport properties of the microstructural components were obtained experimentally or from literature. An equivalent microscale model that incorporates the dynamics of mechanical deformation of the cellular structure was implemented. The model predicted the apparent tissue conductivity of pear cortex tissue to be 9.42±0.40×10−15kgm−1s−1Pa−1, in the same range as those measured experimentally. The largest gradients in water content were observed across the cell walls and cell membranes. A sensitivity analysis of membrane permeability and elastic modulus of the wall on the water transport properties and deformation showed that the membrane permeability has the largest influence. The model can be improved further by taking into account 3-D connectivity of cells and intercellular pore spaces. It will then become feasible to evaluate measures to reduce water loss of fruit during storage and distribution using the microscale model in a multiscale modeling framework.

A computational study of a capsule lateral migration in microchannel flow

A numerical method is used to model a capsule migration in a microchannel with small Reynolds number Re ≈ 0.01. The capsule is modeled as a liquid drop surrounded by a neo-Hookean elastic membrane. The numerical model combines immersed boundary with lattice Boltzmann method (IB-LBM). The LBM is used to simulate fixed Cartesian grid while the IBM is utilized to implement the fluid-structure interaction by a set of Lagrangian moving grids for the membrane. The effect of shear elasticity and bending stiffness are both considered. The results show the significance of elastic modulus and initial lateral position on deformation and morphological properties of a circular capsule. The wall effect becomes stronger as the capsule initial position gets closer to the channel wall. As the elastic modulus of membrane increases, the capsule undergoes less pronounced deformation and velocity in direction x is decreased, thus, the capsule motion is slower than the background flow. The best agreement between the present model and experiments for migration velocity takes place for the capsule with normal to moderate membrane elastic modulus. The results are in good agreement with experiment study of Coupier et al. and previous numerical studies. Therefore, the IB-LBM can be employed to make prediction in vitro and in vivo studies of capsule deformation.

The Quantum Casimir Effect May Be a Universal Force Organizing the Bilayer Structure of the Cell Membrane

A mathematic–physical model of the interaction between cell membrane bilayer leaflets is proposed based on the Casimir effect in dielectrics. This model explains why the layers of a lipid membrane gently slide one past another rather than penetrate each other. The presented model reveals the dependence of variations in the free energy of the system on the membrane thickness. This function is characterized by the two close minima corresponding to the different levels of interdigitation of the lipids from neighbor layers. The energy barrier of the compressing transition between the predicted minima is estimated to be 5.7 kT/lipid, and the return energy is estimated to be 3.1 kT/lipid. The proposed model enables estimation of the value of the membrane elastic thickness modulus of compressibility, which is 1.7 × 109 N/m2, and the value of the interlayer friction coefficient, which is 1.9 × 108 Ns/m3.

Capturing the elasticity and morphology of live fibroblast cell cultures during degradation with atomic force microscopy

Atomic force microscopy, in a liquid environment, was used to capture in vitro the morphological and mechanical changes that cultured fibroblasts undergo as time elapses from the completion of the cell culture. Topography images illustrated that initially, the nucleus had a height of 1.18 ± 0.2 μm, and after 48 h it had decreased to 550 ± 60 nm; similarly, the cell membrane exhibited significant shrinkage from 34 ± 4 to 23 ± 2 μm. After each image scan, atomic force microscopy indentation was performed on the centre of the nucleus, to measure the changes in the cell elasticity. Examination of the force-distance curves indicated that the membrane elastic modulus at the nucleus remained the same within the time frame of 48 h, even though the cell morphology had significantly changed.

The morphological characterization of the forewing of the Manduca sexta species for the application of biomimetic flapping wing micro air vehicles

To properly model the structural dynamics of the forewing of the Manduca sexta species, it is critical that the material and structural properties of the biological specimen be understood. This paper presents the results of a morphological study that has been conducted to identify the material and structural properties of a sample of male and female Manduca sexta specimens. The average mass, area, shape, size and camber of the wing were evaluated using novel measurement techniques. Further emphasis is placed on studying the critical substructures of the wing: venation and membrane. The venation cross section is measured using detailed pathological techniques over the entire venation of the wing. The elastic modulus of the leading edge veins is experimentally determined using advanced non-contact structural dynamic techniques. The membrane elastic modulus is randomly sampled over the entire wing to determine global material properties for the membrane using nanoindentation. The data gathered from this morphological study form the basis for the replication of future finite element structural models and engineered biomimetic wings for use with flapping wing micro air vehicles.

The development of collagen-GAG scaffold-membrane composites for tendon tissue engineering

Current tissue engineering approaches for tendon defects require improved biomaterials to balance microstructural and mechanical design criteria. Collagen-glycosaminoglycan (CG) scaffolds have shown considerable success as in vivo regenerative templates and in vitro constructs to study cell behavior. While these scaffolds possess many advantageous qualities, their mechanical properties are typically orders of magnitude lower than orthopedic tissues such as tendon. Taking inspiration from mechanically efficient core–shell composites in nature such as plant stems and porcupine quills, we have created core–shell CG composites that display high bioactivity and improved mechanical integrity. These composites feature integration of a low density, anisotropic CG scaffold core with a high density, CG membrane shell. CG membranes were fabricated via an evaporative process that allowed separate tuning of membrane thickness and elastic moduli and were found to be isotropic in-plane. The membranes were then integrated with an anisotropic CG scaffold core via freeze-drying and subsequent crosslinking. Increasing the relative thickness of the CG membrane shell was shown to increase composite tensile elastic modulus by as much as a factor of 36 in a manner consistent with predictions from layered composites theory. CG scaffold-membrane composites were found to support tendon cell viability, proliferation, and metabolic activity in vitro, suggesting they maintain sufficient permeability while demonstrating improved mechanical strength. This work suggests an effective, biomimetic approach for balancing strength and bioactivity requirements of porous scaffolds for tissue engineering.

Determining a Suitable Material to Simulate the Tympanic Membrane Based on Quantitative Linear Elasticity

Objective: Find a material to simulate the quantitative, as well as qualitative, qualities of the tension and compliance of a tympanic membrane based on published values of the elastic modulus for a tympanic membrane. Method: Prospective study that took place from August to December 2009. Using the Instron Testing Instrument, an elastic modulus was calculated for various materials. Based on these values, 3 materials were chosen. Seven physicians performed a myringotomy and completed a survey to rank subjective qualities of the materials. Results: Nitrile gloves, Kimwipes, and laboratory stretch film all had an elastic modulus that fell within the previously published range of the tympanic membrane elastic modulus and were chosen to undergo further evaluation. Kimwipes scored the highest in terms of compliance, tension, and texture compared with an actual TM during blunt palpation. Nitrile gloves scored the highest in terms of compliance, tension, and texture while making the myringotomy incision. Nitrile gloves scored best when comparing how the incision split open, responded to suction, and felt during introduction of the PE tube. Overall Nitrile gloves scored the highest. Conclusion: As competency-based teaching and evaluation becomes a bigger part of resident-training, the utility of training models will also likely become more widespread. Nitrile gloves represent a material that is inexpensive, is widely available, and displays a quantitative and qualitative linear elasticity similar to that of a true tympanic membrane.

Homogenization of the elastic behavior of a layer-to-layer angle-interlock composite

Composite materials reinforced with 3D layer-to-layer angle-interlock fabrics are increasingly employed due to their significant resistance to delamination and impact damage, which is not observed in classical 2D laminated composites. However, the prediction of the mechanical behavior of such composites is challenging due to the intricate fibrous architecture. The structure is intimately linked to its history of manufacturing which induces changes in the reinforcement geometry. The purpose of this work is to assess the equivalent membrane and bending elastic moduli of the shell-type structure by an asymptotic homogenization procedure on a periodic unit cell, in the framework of the Love–Kirchhoff plate theory. A specific Python program using Abaqus software package is developed, allowing for parameterized geometrical modeling and mechanical analysis in a systematic and efficient way. This modeling and simulation tool enables to consider the real composite architecture after infusion and the yarn damage during weaving. The effective properties are finally validated using numerical computations on 3D heterogeneous plates and by comparison with experimental tests.

Effect of membrane mechanics on charge transfer by the membrane protein prestin

Prestin was found in the membrane of outer hair cells (OHCs) located in the cochlea of the mammalian inner ear. These cells convert changes in the membrane potential into dimensional changes and (if constrained) to an active electromechanical force. The OHCs provide the ear with the mechanism of amplification and frequency selectivity that is effective up to tens of kHz. Prestin is a crucial part of the motor complex driving OHCs. Other cells transfected with prestin acquire electromechanical properties similar to those in the native cell. While the mechanism of prestin has yet to be fully understood, the charge transfer is its critical component. Here we investigate the effect of the mechanics of the surrounding membrane on electric charge transfer by prestin. We simulate changes in the membrane mechanics via the corresponding changes in the free energy of the prestin system. The free energy gradient enters a Fokker-Planck equation that describes charge transfer in our model. We analyze the effects of changes in the membrane tension and membrane elastic moduli. In the case of OHC, we simulate changes in the longitudinal and/or circumferential stiffness of the cell's orthotropic composite membrane. In the case of cells transfected with prestin, we vary the membrane areal modulus. As a result, we show the effects of the membrane mechanics on the probabilistic characteristics of prestin-associated charge transfer for both stationary and high-frequency conditions. We compare our computational results with the available experimental data and find good agreement with the experiment.

Adhesion Kinetics between a Membrane and a Flat Substrate. An Ideal Upper Bound to the Spreading Rate of an Adhesive Patch

A semiquantitative theory to describe the adhesion mechanism between an elastic membrane and a solid substrate (or another membrane) was developed. Since the membrane bending deformation requires a relatively small energy cost, thermally excited fluctuations may give rise to a local protrusion connecting the membrane to the substrate. This transient adhesion site is stabilized by short-range adhesion forces and it is destabilized by repulsion and elastic deformation energy. Above a critical radius of the contact site, adhesion forces prevail, enabling the contact site to expand until complete membrane-substrate adhesion is attained. This represents a typical nucleation mechanism involving both growth and dissolution processes. However, here we prove that also in the barrierless region, well beyond the critical radius, the spreading rate of a membrane still remains rather small, even under the favorable assumption of strong, sudden, and irreversible membrane-substrate adhesion. A detailed analysis of the membrane vibrational behavior near the adhesion patch rim suggests a reasonable mechanism for the spreading rate that has been analyzed by nonequilibrium statistical mechanics approaches. In relevant limiting cases, the model yields simple analytical formulas. Approximate relationships between the spreading rate and parameters like membrane elastic bending modulus, membrane-substrate interaction, temperature, and solvent viscosity have been found.

A Poisson–Boltzmann approach for a lipid membrane in an electric field

The behavior of a non-conductive quasi-planar lipid membrane in an electrolyte and in a static (dc) electric field is investigated theoretically in the nonlinear (Poisson–Boltzmann) regime. Electrostatic effects due to charges in the membrane lipids and in the double layers lead to corrections to the membrane elastic moduli, which are analyzed here. We show that, especially in the low salt limit, (i) the electrostatic contribution to the membrane's surface tension due to the Debye layers crosses over from a quadratic behavior in the externally applied voltage to a linear voltage regime, and (ii) the contribution to the membrane's bending modulus due to the Debye layers saturates for high voltages. Nevertheless, the membrane undulation instability due to an effectively negative surface tension predicted by the linear Debye–Hückel theory is shown to persist in the nonlinear, high-voltage regime.

Nucleation theory with delayed interactions: An application to the early stages of the receptor-mediated adhesion/fusion kinetics of lipid vesicles

A semiquantitative theory aimed to describe the adhesion kinetics between soft objects, such as living cells or vesicles, has been developed. When rigid bodies are considered, the adhesion kinetics is successfully described by the classical Derjaguin, Landau, Verwey, and Overbeek (DLVO) picture, where the energy profile of two approaching bodies is given by a two asymmetrical potential wells separated by a barrier. The transition probability from the long-distance to the short-distance minimum defines the adhesion rate. Conversely, soft bodies might follow a different pathway to reach the short-distance minimum: thermally excited fluctuations give rise to local protrusions connecting the approaching bodies. These transient adhesion sites are stabilized by short-range adhesion forces (e.g., ligand-receptor interactions between membranes brought at contact distance), while they are destabilized both by repulsive forces and by the elastic deformation energy. Above a critical area of the contact site, the adhesion forces prevail: the contact site grows in size until the complete adhesion of the two bodies inside a short-distance minimum is attained. This nucleation mechanism has been developed in the framework of a nonequilibrium Fokker-Planck picture by considering both the adhesive patch growth and dissolution processes. In addition, we also investigated the effect of the ligand-receptor pairing kinetics at the adhesion site in the time course of the patch expansion. The ratio between the ligand-receptor pairing kinetics and the expansion rate of the adhesion site is of paramount relevance in determining the overall nucleation rate. The theory enables one to self-consistently include both thermodynamics (energy barrier height) and dynamic (viscosity) parameters, giving rise in some limiting cases to simple analytical formulas. The model could be employed to rationalize fusion kinetics between vesicles, provided the short-range adhesion transition is the rate-limiting step to the whole adhesion process. Approximate relationships between the experimental fusion rates reported in the literature and parameters such as membrane elastic bending modulus, repulsion strength, temperature, osmotic forces, ligand-receptor binding energy, solvent and membrane viscosities are satisfactory explained by our model. The present results hint a possible role of the initial long-distance-->short-distance transition in determining the whole fusion kinetics.

Effect of Cations on the Nanomechanical Response of Phospholipid Model Membranes. A Force Spectroscopy Study

How do metal cations affect the stability and structure of phospholipid bilayers? Which role does ion binding play in the insertion of proteins and in the overall mechanical stability of biological membranes? To characterize such effects, several theoretical and microscopic approaches have been proposed in the past to study the mechanical properties of lipid bilayers. While providing crucial information, molecular dynamics simulations can not completely deal with the extraordinary complexity of biological membranes. Experimental techniques also have problems when it comes to test ion binding to lipid bilayers in an accurate way. Hence, a new perspective from the nanometric scale [1,2], where most of the specific molecular phenomena are sensitive, was introduced being Atomic Force Spectroscopy an essential tool to examine the lipid bilayers structure and behaviour. So, we used Force Spectroscopy to quantitatively characterize the nanomechanical resistance as a function of the electrolyte concentration and composition thanks to a reliable molecular fingerprint that reveals itself as a repetitive jump in the approaching force curve. By systematically testing two model membranes, DPPC and DPPE, immersed in an electrolyte containing a series of either one monovalent (Li+ to Cs+) or divalent cation (Mg2+ and Ca2+) we provide a wealth of information which unambiguously proves an independent contribution of each ion to the gross mechanical resistance, reporting quantitative measurements for the membrane elastic modulus and also for its plastic properties. So, this work deals with the need of assessing the effect of different cations in the structure of phospholipid membranes.[1] Effect of ion-binding and chemical phospholipid structure on the nanomechanics of lipid bilayers studied by force spectroscopy, Biophys J 89 (2005) 1812-1826[2] Nanomechanics of lipid bilayers:heads or tails?, under review (2009)

Statistical Mechanics and Dynamics of Two Supported Stacked Lipid Bilayers

The statistical physics and dynamics of double supported bilayers are studied theoretically. The main goal in designing double supported lipid bilayers is to obtain model systems of biomembranes: the upper bilayer is meant to be almost freely floating, the substrate being screened by the lower bilayer. The fluctuation-induced repulsion between membranes and between the lower membrane and the wall are explicitly taken into account using a Gaussian variational approach. It is shown that the variational parameters, the "effective" adsorption strength, and the average distance to the substrate, depend strongly on temperature and membrane elastic moduli, the bending rigidity, and the microscopic surface tension, which is a signature of the crucial role played by membrane fluctuations. The range of stability of these supported membranes is studied, showing a complex dependence on bare adsorption strengths. In particular, the experimental conditions of having an upper membrane slightly perturbed by the lower one and still bound to the surface are found. Included in the theoretical calculation of the damping rates associated with membrane normal modes are hydrodynamic friction by the wall and hydrodynamic interactions between both membranes.

Use of a Digital Image Correlation Technique for Measuring the Material Properties of Beetle Wing

Beetle wings are very specialized flight organs consisting of the veins and membranes. Therefore it is necessary from a bionic view to investigate the material properties of a beetle wing experimentally. In the present study, we have used a Digital Image Correlation (DIC) technique to measure the elastic modulus of a beetle wing membrane. Specimens were prepared by carefully cutting a beetle hind wing into 3.0 mm by 7.0 mm segments (the gage length was 5 mm). We used a scanning electron microscope for a precise measurement of the thickness of the beetle wing membrane. The specimen was attached to a designed fixture to induce a uniform displacement by means of a micromanipulator. We used an ARAMIS™ system based on the digital image correlation technique to measure the corresponding displacement of a specimen. The thickness of the beetle wing varied at different points of the membrane. The elastic modulus differed in relation to the membrane arrangement showing a structural anisotropy; the elastic modulus in the chordwise direction is approximately 2.65 GPa, which is three times larger than the elastic modulus in the spanwise direction of 0.84 GPa. As a result, the digital image correlation–based ARAMIS system was successfully used to measure the elastic modulus of a beetle wing. In addition to membrane's elastic modulus, we considered the Poisson's ratio of the membrane and measured the elastic modulus of a vein using an Instron universal tensile machine. The result reveals the Poisson's ratio is nearly zero and the elastic modulus of a vein is about 11 GPa.

Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented by D. Lacoste, M. Cosentino Lagomarsino, and J.F. Joanny (EPL 77, 18006 (2007)), by providing a physical explanation for a destabilizing term proportional to [see formula in text] in the fluctuation spectrum, which we relate to a nonlinear (E(2)) electrokinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives the flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a nonequilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.