Tomáš Mareš

Role of phospholipid asymmetry in the stability of inverted hexagonal mesoscopic phases.

The role of phospholipid asymmetry in the transition from the lamellar (L(alpha)) to the inverted hexagonal (H(II)) phase upon the temperature increase was considered. The equilibrium configuration of the system was determined by the minimum of the free energy including the contribution of the isotropic and deviatoric bending and the interstitial energy of phospholipid monolayers. The shape and local interactions of a single lipid molecule were taken into account. The minimization with respect to the configuration of the lipid layers was performed by a numerical solution of the system of the Euler-Lagrange differential equations and by the Monte Carlo simulated annealing method. At high enough temperature, the lipid molecules attain a shape exhibiting higher intrinsic mean and deviatoric curvatures, which fits better into the H(II) phase than into the L(alpha) phase. Furthermore, the orientational ordering of lipid molecules in the curvature field expressed as the deviatoric bending provides a considerable negative contribution to the free energy, which stabilizes the nonlamellar H(II) phase. The nucleation configuration for the L(alpha)-H(II) phase transition is tuned by the isotropic and deviatoric bending energies and the interstitial energy.

Artificial neural networks in the calibration of nonlinear mechanical models

Last decades witness rapid development in numerical modelling of structures as well as materials and the complexity of models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models from noisy experimental data remains a nontrivial and often computational exhaustive task. The layered neural networks thus represent a robust and effi cient technique to overcome the timeconsuming simulations of a calibrated model. The potential of neural networks consists in simple implementation and high versatility in approximating nonlinear relationships. Therefore, there were several approaches proposed to accelerate the calibration of nonlinear models by neural networks. This contribution reviews and compares three possible strategies based on approximating (i) model response, (ii) inverse relationship between the model response and its parameters and (iii) error function quantifying how well the model fits the d ata. The advantages and drawbacks of particular strategies are demonstrated on calibration o f four parameters of affi nity hydration model from simulated data as well as from experimental measurements. This model is highly nonlinear, but computationally cheap thus allowing its calibration without any approximation and better quantification of results obtained by the examine d calibration strategies.Paper reviews applications of artificial neural networks in model calibration.Neural network-based calibration strategies are classified into three groups.Identification strategies are compared on calibration of affinity hydration model.The most precise strategy uses an ANN-based surrogate of each response component.Principal component-based inverse mapping is the best for a repeated use on new data. Rapid development in numerical modelling of materials and the complexity of new models increase quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models from noisy experimental data remains a nontrivial and often computationally intensive task. Layered neural networks provide a robust and efficient technique for overcoming the time-consuming simulations of calibrated models. The potential advantages of neural networks include simple implementation and high versatility in approximating nonlinear relationships. Therefore, there were several approaches proposed in literature for accelerating the calibration of nonlinear models by neural networks. This contribution reviews and compares three possible strategies based on approximating (i) the model response, (ii) the inverse relationship between the model response and its parameters and (iii) an error function quantifying how well the model fits the data. The advantages and drawbacks of particular strategies are demonstrated with the calibration of four parameters of an affinity hydration model from simulated data as well as from experimental measurements. The affinity hydration model is highly nonlinear but computationally cheap, thus allowing its calibration without any approximation and better quantification of results obtained by the examined calibration strategies. This paper can be viewed as a guide for engineers to help them develop an appropriate strategy for their particular calibration problems.

Elastic Properties of Human Osteon and Osteonal Lamella Computed by a Bidirectional Micromechanical Model and Validated by Nanoindentation

Knowledge of the anisotropic elastic properties of osteon and osteonal lamellae provides a better understanding of various pathophysiological conditions, such as aging, osteoporosis, osteoarthritis, and other degenerative diseases. For this reason, it is important to investigate and understand the elasticity of cortical bone. We created a bidirectional micromechanical model based on inverse homogenization for predicting the elastic properties of osteon and osteonal lamellae of cortical bone. The shape, the dimensions, and the curvature of osteon and osteonal lamellae are described by appropriately chosen curvilinear coordinate systems, so that the model operates close to the real morphology of these bone components. The model was used to calculate nine orthotropic elastic constants of osteonal lamellae. The input values have the elastic properties of a single osteon. We also expressed the dependence of the elastic properties of the lamellae on the angle of orientation. To validate the model, we performed nanoindentation tests on several osteonal lamellae. We compared the experimental results with the calculated results, and there was good agreement between them. The inverted model was used to calculate the elastic properties of a single osteon, where the input values are the elastic constants of osteonal lamellae. These calculations reveal that the model can be used in both directions of homogenization, i.e., direct homogenization and also inverse homogenization. The model described here can provide either the unknown elastic properties of a single lamella from the known elastic properties at the level of a single osteon, or the unknown elastic properties of a single osteon from the known elastic properties at the level of a single lamella.

Determination of the Strength of Adhesion between Lipid Vesicles

A commonly used method to determine the strength of adhesion between adhering lipid vesicles is measuring their effective contact angle from experimental images. The aim of this paper is to estimate the interobserver variations in vesicles effective contact angle measurements and to propose a new method for estimating the strength of membrane vesicle adhesion. Theoretical model shows for the old and for the new measure a monotonic dependence on the strength of adhesion. Results obtained by both measuring techniques show statistically significant correlation and high interobserver reliability for both methods. Therefore the conventional method of measuring the effective contact angle gives qualitatively relevant results as the measure of the lipid vesicle adhesion. However, the new measuring technique provides a lower variation of the measured values than the conventional measures using the effective contact angle. Moreover, obtaining the adhesion angle can be automatized more easily than obtaining the effective contact angle.

Encapsulation of small spherical liposome into larger flaccid liposome induced by human plasma proteins

We show that human plasma can induce the encapsulation of small spherical liposomes into larger flaccid liposomes. To explain the observed phenomena, it is proposed that the orientational ordering of charged plasma proteins induces attractive interaction between two like-charged liposome surfaces in close contact. It is observed that the encapsulation of the spherical liposome is possible only if the membrane of the target liposome is flexible enough to adapt its shape to the shape of the spherical liposome. In the theoretical model, the shapes of the two agglutinated liposomes are determined by minimisation of the sum of the adhesion energy and the membrane elastic energy. In the simulations, the membrane of liposomes is considered as an elastic structure and discretised via the finite element method using spring elements. It is shown that the observed agglutination of liposomes and encapsulation of smaller spherical liposomes into larger flaccid liposomes may be explained as a competition between the membrane deformation energy and the membrane adhesion energy.

Role of Phospholipid Asymmetry in Stability of Inverted Hexagonal Mesoscopic Phases

The role of phospholipid asymmetry in the transition from the lamellar (Lα) to the in-verted hexagonal (HII) phase upon the temperature increase was considered. The equilibrium configuration of the system was determined by the minimum of the free energy including the contribution of the isotropic and deviatoric bending and the interstitial energy of phos-phospholipid monolayers. The shape and local interactions of a single lipid molecule were taken into account. The minimization with respect to the configuration of the lipid layers was performed by a numerical solution of the system of the Euler-Lagrange differential equations and by the Monte Carlo simulated annealing method. At high enough temperature the lipid molecules attain a shape exhibiting higher intrinsic mean and deviatoric curvatures which fits better into the HII phase than into the Lα phase. Furthermore, the orientational order-ing of lipid molecules in the curvature field expressed as the deviatoric bending provides a considerable negative contribution to the free energy which stabilizes the non-lamellar HII phase. The nucleation configuration for the Lα - HII phase transition is tuned by the isotropic and deviatoric bending energies and the interstitial energy. For the mathematical model the deviations from sphericity of inverted hexagonal phase cross-section were calculated, resulting in lower energy in non-spherical cross-section than in spherical cross-sectin.

Microstructural residual stress in particle-filled dental composite

The main goal of this study is to develop a micromechanical model of a particle-filled dental composite focused on the residual stress (RS) field developed during the curing process in its microstructure. A finite element model of a representative volume element of filler and resin was developed, and volumetric shrinkage was simulated during the curing process. Four material models (von Mises plasticity model, Drucker–Prager plasticity model, von Mises plasticity model with stress relaxation and Drucker–Prager plasticity with stress relaxation) of the polymer resin were built to assess the influence of the material model on the resulting internal stress. The relationship between the curing process and the magnitude of the stress components will be described, and an analysis of the post-curing state of the material in particular microstructure locations will be conducted in this study. Obtained RS is comparable to the stresses developed in the material under the external load. The substantial dependence on the choice of material model for resin is to be observed, and the suitability of particular models is discussed.

Examination of the Microrheology of Intervertebral Disc by Nanoindentation

Micro- and Nanoindentation technique has become a standard method for material testing of mechanical properties recently. Especially, indentation method with Oliver and Pharr theory for an analysis of isotropic elastic materials is very strait forward and become a part of every indenter’s software. Some multidirectional indentation analyses have been successfully applied on bone tissues such as cortical osteons and trabecular lamellae to identify their local elastic orthotropic or transverse isotropic properties. Present nanoindenters make possible an acquisition of creep and relaxation data, for that a model of creep or relaxation function can be found in the literature and the viscoelastic material parameters are derived.

Mathematical model of human osteon and its validation by nanomechanical testing of bone lamella

Knowledge of the anisotropic elastic properties of osteon and osteonal lamellae is the key to a description of the elasticity of cortical bone. Various analytical and computational models have been proposed for predicting the mechanical properties of bone at different structural levels. Hamed et al. (2010) modelled the hierarchical structure of bone at more than one level, using multiple step-by-step micromechanics-based homogenisation to capture the behaviour of bone spanning from nanoto sub-microstructure levels. A feature of ourmodel is that we have developed an inverse homogenisation scheme from the macroscopic scale of cortical bone to the single lamella level. There are also experimental methods for studies of cortical bone at the level of osteon and osteonal lamella, for example instrumented nanoindentation (Lukes and Otahal 2009), atomic force microscopy (Lefevre et al. 2013) and the ultrasound method (Rho 1996). To validate the mathematical model presented here, we determined the mechanical properties of a single lamella in three perpendicular directions using instrumented nanoindentation.

Coalescence of phospholipid vesicles mediated by β2GPI – experiment and modelling

Collective interactions between the giant phospholipid vesicles made of POPC, cardiolipin and cholesterol after the addition of β2GPI may cause the coalescence of membrane buds to the mother cell. Using the discrete elastic model of the vesicle membrane mechanics it was shown that the coalescence of the buds depends on the adhesion strength and rigidity of the biomembrane.