Reliable Method for Fabricating Tissue‐Mimicking Materials With Designated Relative Permittivity and Conductivity at 128 MHz

Artificial materials that can simultaneously mimic the relative permittivity and conductivity of various human tissues are usually used in medical applications. However, the method of precisely designing these materials with designated values of both relative permittivity and conductivity at 3 T MRI resonance frequency is lacking. In this study, a reliable method is established to determine the compositions of artificial dielectric materials with designated relative permittivity and conductivity at 128 MHz. Sixty dielectric materials were produced using oil, sodium chloride, gelatin, and deionized water as the main raw materials. The dielectric properties of these dielectric materials were measured using the open‐ended coaxial line method at 128 MHz. Nonlinear least‐squares Marquardt–Levenberg algorithm was used to obtain the formula, establishing the relationship between the compositions of the dielectric materials and their dielectric properties at 128 MHz. The dielectric properties of the blood, gall bladder, muscle, skin, lung, and bone at 128 MHz were selected to verify the reliability of the obtained formula. For the obtained formula, the coefficient of determination and the expanded uncertainties with a coverage factor of k = 2 were 0.991% and 4.9% for relative permittivity and 0.992% and 6.4% for conductivity. For the obtained artificial materials measured using the open‐ended coaxial line method, the maximal difference of relative permittivity and conductivity were 1.0 and 0.02 S/m, respectively, with respect to the designated values. In conclusion, the compositions of tissue‐mimicking material can be quickly determined after the establishment of the formulas with the expanded uncertainties of less than 10%. Bioelectromagnetics. 2021;42:86–94. © 2020 Bioelectromagnetics Society.     

Instrumental noise estimates stabilize and quantify endothelial cell micro-impedance barrier function parameter estimates

A novel transcellular micro-impedance biosensor, referred to as the electric cell-substrate impedance sensor or ECIS, has become increasingly applied to the study and quantification of endothelial cell physiology. In principle, frequency dependent impedance measurements obtained from this sensor can be used to estimate the cell–cell and cell–matrix impedance components of endothelial cell barrier function based on simple geometric models. Few studies, however, have examined the numerical optimization of these barrier function parameters and established their error bounds. This study, therefore, illustrates the implementation of a multi-response Levenberg–Marquardt algorithm that includes instrumental noise estimates and applies it to frequency dependent porcine pulmonary artery endothelial cell impedance measurements. The stability of cell–cell, cell–matrix and membrane impedance parameter estimates based on this approach is carefully examined, and several forms of parameter instability and refinement illustrated. Including frequency dependent noise variance estimates in the numerical optimization reduced the parameter value dependence on the frequency range of measured impedances. The increased stability provided by a multi-response non-linear fit over one-dimensional algorithms indicated that both real and imaginary data should be used in the parameter optimization. Error estimates based on single fits and Monte Carlo simulations showed that the model barrier parameters were often highly correlated with each other. Independently resolving the different parameters can, therefore, present a challenge to the experimentalist and demand the use of non-linear multivariate statistical methods when comparing different sets of parameters.     

Extraction and optimization of exopolysaccharide from Lactobacillus sp. using response surface methodology and artificial neural networks

Abstract

The microbial polysaccharides secreted and produced from various microbes into their extracellular environment is known as exopolysaccharide. These polysaccharides can be secreted from the microbes either in a soluble or insoluble form.Lactobacillus sp. is one of the organisms that have been found to produce exopolysaccharide. Exo-polysaccharides (EPS) have various applications such as drug delivery, antimicrobial activity, surgical implants and many more in different fields. Medium composition is one of the major aspects for the production of EPS from Lactobacillus sp., optimization of medium components can help to enhance the synthesis of EPS . In the present work, the production of exopolysaccharide with different medium composition was optimized by response surface methodology (RSM) followed by tested for fitting with artificial neural networks (ANN). Three algorithms of ANN were compared to investigate the highest yeild of EPS. The highest yeild of EPS production in RSM was achieved by the medium composition that consists of (g/L) dextrose 15, sodium dihydrogen phosphate 3, potassium dihydrogen phosphate 2.5, triammonium citrate 1.5, and, magnesium sulfate 0.25. The output of 32 sets of RSM experiments were tested for fitting with ANN with three algorithms viz. Levenberg–Marquardt Algorithm (LMA), Bayesian Regularization Algorithm (BRA) and Scaled Conjugate Gradient Algorithm (SCGA) among them LMA found to have best fit with the experiments as compared to the SCGA and BRA.     

A 3D elastic micropolar model of vertebral trabecular bone from lattice homogenization of the bone microstructure

A 3D anisotropic micropolar continuum model of vertebral trabecular bone is presently developed accounting for the influence of microstructure-related scale effects on the macroscopic effective properties. Vertebral trabecular bone is modeled as a cellular material with an idealized periodic structure made of open 3D cells. The micromechanical approach relies on the discrete homogenization technique considering lattice microrotations as additional degrees of freedom at the microscale. The effective elastic properties of 3D lattices made of articulated beams taking into account axial, transverse shearing, flexural, and torsional deformations of the cell struts are derived as closed form expressions of the geometrical and mechanical microparameters. The scaling laws of the effective moduli versus density are determined in situations of low and high effective densities to assess the impact of the transverse shear deformation. The classical and micropolar effective moduli and the internal flexural and torsional lengths are identified versus the same microparameters. A finite element model of the local architecture of the trabeculae gives values of the effective moduli that are in satisfactory agreement with the homogenized moduli.     

On stiffness of scaffolds for bone tissue engineering—a numerical study

Tissue scaffolds are typically designed and fabricated to match native bone properties. However, it is unclear if this would lead to the best tissue ingrowth outcome within the scaffold as neo-tissue keeps changing the stiffness of entire construct. This paper presents a numerical method to address this issue for design optimization and assessment of tissue scaffolds. The elasticity tensors of two different types of bones are weighted by different multipliers before being used as the targets in scaffold design. A cost function regarding the difference between the effective elasticity tensor, calculated by the homogenization technique, and the target tensor, is minimized by using topology optimization procedure. It is found that different stiffnesses can lead to different remodeling results. The comparison confirms that bone remodeling is at its best when the scaffold elastic tensor matches or is slightly higher than the elastic properties of the host bone.     

Prediction of nonlinear elastic behaviour of vaginal tissue: experimental results and model formulation

The mechanical properties of the vaginal tissue need to be characterised to perform accurate simulations of prolapse and other pelvic disorders that commonly affect women. This is also a fundamental step towards the improvement of therapeutic techniques such as surgery. Issues like the efficiency of using autologous tissue in pelvic reconstruction may be addressed. The goal of this study was to characterise the elastic behaviour of vaginal tissue. For this purpose, prolapsed vaginal tissue from eight different post-menopausal patients, excised during prolapse corrective surgery, was mechanically tested. The mechanical testing of vaginal tissue, consisting of uniaxial tension tests performed along the longitudinal axis of the vagina, revealed the nonlinear mechanical behaviour of the tissue. The material model parameters were fit to the experimental data using the Levenberg–Marquardt optimisation algorithm. All the curve fittings showed a good agreement between experimental and theoretical results, evidenced by R ² values close to 1 and by very low ? values.     

On the mechanical characterization of compact bone structure using the homogenization theory

In a previous paper (Crolet et al., 1993, J. Biomechanics 26, 677–687), a modelling of the mechanical behavior of compact bone was presented, in which the homogenization theory was the basic tool of computation. In this simulation, approximations were used for the modelling of the lamellae and the osteons: the lamella and the osteon were divided into cylindrical sectors, each sector being approximated as a parallelepiped having a periodic structure (fibrous composite for the lamella, superimposition of plates for the osteon). The present study deals with a new model without these approximations. First, it can be proved that the homogenized elasticity tensor for a lamella, which has a non-periodic structure, is obtained at each geometrical point as a homogenized tensor of a periodic problem. Similarly, for the osteonal structure, the components of the homogenized tensor are determined at each point as the result of a periodic homogenization.

The software OSTEON, which is the computational method associated with this model, allows one to obtain a better understanding of the effects of many bony parameters. The obtained results are in accordance with experimental data.     

PHARMFIT—a Nonlinear Fitting Program for Pharmacology

A new program is presented for nonlinear fitting of data from pharmacological and chronobiological investigations. It contains functions for calculating data from ligand-binding studies and competition experiments, for the analysis of dose-response curves, for pharmacokinetic calculations, and for cosine analysis of harmonic and overlapping rhythms. In addition, it is possible to implement general equations by the user. The program allows data exchange with most spreadsheet, database, and graphics presentation programs, and accepts data from two widely used ambulatory 24-h blood-pressure monitoring systems. The fitting procedure uses the Marquardt–Levenberg algorithm. It calculates the weighted or the unweighted fit together with a great variety of statistics for estimation of goodness of fit. A graphics module permits graphical presentation of the fitted curve. Moreover, fitting of data to different models can be compared for the most likely fit and model discrimination statistics for improvement of further experiments are provided. To demonstrate the chronobiological application of the fitting program PHARMFIT, the analysis of telemetric heart rate data from rats is presented.     

Characterization of structure and properties of bone by spectral measure method

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.     

Robust nonlinear parameter estimation in tracer kinetic analysis using infinity norm regularization and particle swarm optimization

In positron emission tomography (PET) studies, the voxel-wise calculation of individual rate constants describing the tracer kinetics is quite challenging because of the nonlinear relationship between the rate constants and PET data and the high noise level in voxel data. Based on preliminary simulations using a standard two-tissue compartment model, we can hypothesize that it is possible to reduce errors in the rate constant estimates when constraining the overestimation of the larger of two exponents in the model equation. We thus propose a novel approach based on infinity-norm regularization for limiting this exponent. Owing to the non-smooth cost function of this regularization scheme, which prevents the use of conventional Jacobian-based optimization methods, we examined a proximal gradient algorithm and the particle swarm optimization (PSO) through a simulation study. Because it exploits multiple initial values, the PSO method shows much better convergence than the proximal gradient algorithm, which is susceptible to the initial values. In the implementation of PSO, the use of a Gamma distribution to govern random movements was shown to improve the convergence rate and stability compared to a uniform distribution. Consequently, Gamma-based PSO with regularization was shown to outperform all other methods tested, including the conventional basis function method and Levenberg–Marquardt algorithm, in terms of its statistical properties.     

A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties

At its highest level of microstructural organization—the mesoscale or millimeter scale—cortical bone exhibits a heterogeneous distribution of pores (Haversian canals, resorption cavities). Multi-scale mechanical models rely on the definition of a representative volume element (RVE). Analytical homogenization techniques are usually based on an idealized RVE microstructure, while finite element homogenization using high-resolution images is based on a realistic RVE of finite size. The objective of this paper was to quantify the size and content of possible cortical bone mesoscale RVEs. RVE size was defined as the minimum size: (1) for which the apparent (homogenized) stiffness tensor becomes independent of the applied boundary conditions or (2) for which the variance of elastic properties for a set of microstructure realizations is sufficiently small. The field of elastic coefficients and microstructure in RVEs was derived from one acoustic microscopy image of a human femur cortical bone sample with an overall porosity of 8.5%. The homogenized properties of RVEs were computed with a finite element technique. It was found that the size of the RVE representative of the overall tissue is about 1.5 mm. Smaller RVEs (~0.5 mm) can also be considered to estimate local mesoscopic properties that strongly depend on the local pores volume fraction. This result provides a sound basis for the application of homogenization techniques to model the heterogeneity of cortical microstructures. An application of the findings to estimate elastic properties in the case of a porosity gradient is briefly presented.     

Analysis of nonlinear responses of adherent epithelial cells probed by magnetic bead twisting: A finite element model based on a homogenization approach

An original homogenization method was used to analyze the nonlinear elastic properties of epithelial cells probed by magnetic twisting cytometry. In this approach, the apparent rigidity of a cell with nonlinear mechanical properties is deduced from the mechanical response of the entire population of adherent cells. The proposed hyperelastic cell model successfully accounts for the variability in probe-cell geometrical features, and the influence of the cell-substrate adhesion. Spatially distributed local secant elastic moduli had amplitudes ranging from 10 to 400 Pa. The nonlinear elastic behavior of cells may contribute to the wide differences in published results regarding cell elasticity moduli.     

Forecasting Ozone Levels and Analyzing Their Dynamics by a Bayesian Multilayer Perceptron Model for Two Air-Monitoring Sites in Hong Kong

Tropospheric ozone (O₃) has adverse effects on human heath and vegetation. Forecasting its daily maximum level and assessing the factors that influence its dynamics are of great importance to Hong Kong and similar metropolitans in the world. In this article, we simulate the daily maximum O₃ level in Hong Kong by applying the multilayer perceptron (MLP) model trained with the automatic relevance determination (ARD) method in a Bayesian evidence framework. The proposed model is named the MLP-ARD. By using the ARD method, the O₃ influential factors, which are the model's input variables, can be ranked according to their relative importance in regard to the model's output variable, that is, the daily maximum O₃ level. The formation and transportation mechanism of O₃ for two selected air-monitoring sites can be grossly explained by the ranking information. Compared with the MLP model trained by the Levenberg–Marquardt algorithm, the predictive performance of the MLP-ARD for the aforementioned air-monitoring sites is more reliable and accurate in both episode and non-episode periods.     

Mimetization of the elastic properties of cancellous bone via a parameterized cellular material

Bone tissue mechanical properties and trabecular microarchitecture are the main factors that determine the biomechanical properties of cancellous bone. Artificial cancellous microstructures, typically described by a reduced number of geometrical parameters, can be designed to obtain a mechanical behavior mimicking that of natural bone. In this work, we assess the ability of the parameterized microstructure introduced by Kowalczyk (Comput Methods Biomech Biomed Eng 9:135–147, 2006. doi: 10.1080/10255840600751473) to mimic the elastic response of cancellous bone. Artificial microstructures are compared with actual bone samples in terms of elasticity matrices and their symmetry classes. The capability of the parameterized microstructure to combine the dominant isotropic, hexagonal, tetragonal and orthorhombic symmetry classes in the proportions present in the cancellous bone is shown. Based on this finding, two optimization approaches are devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of a target natural bone specimen: a Sequential Quadratic Programming algorithm that minimizes the norm of the difference between the elasticity matrices, and a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions. The pattern search approach is found to produce the best results. The performance of the method is demonstrated via analyses for 146 bone samples.     

A global relationship between trabecular bone morphology and homogenized elastic properties.

An alternative concept of the relationship between morphological and elastic properties of trabecular bone is presented and applied to human tissue from several anatomical locations using a digital approach. The three-dimensional morphology of trabecular bone was assessed with a microcomputed tomography system and the method of directed secants as well as the star volume procedure were used to compute mean intercept length (MIL) and average bone length (ABL) of 4 mm cubic specimens. Assuming isotropic elastic properties for the trabecular tissue, the general elastic tensors of the bone specimens were determined using the homogenization method and the closest orthotropic tensors were calculated with an optimization algorithm. The assumption of orthotropy for trabecular bone was found to improve with specimen size and hold within 6.1 percent for a 4 mm cube size. A strong global relationship (r2 = 0.95) was obtained between fabric and the orthotropic elastic tensor with a minimal set of five constants. Mean intercept length and average bone length provided an equivalent power of prediction. These results support the hypothesis that the elastic properties of human trabecular bone from an arbitrary anatomical location can be estimated from an approximation of the anisotropic morphology and a prior knowledge of tissue properties.     

Isolation of intact mitochondria from the rat liver using vibration

A method for isolating mitochondria from the rat liver is described. In this method the homogenization step is replaced by vibration with the frequency of 50 Hz realized by a simple device. Mitochondria isolated by vibration demonstrate higher indices of the oxidative phosphorylation with succinate and glutamate + malate used as substrates than those isolated by homogenization do. The method described permits decreasing considerably the isolation medium expenditure remaining the mitochondria yield per gram of the liver unchanged.     

Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale

Cortical bone is a multiscale composite material. Its elastic properties are anisotropic and heterogeneous across its cross-section, due to endosteal bone resorption which might affect bone strength. The aim of this paper was to describe a homogenization method leading to the estimation of the variation of the elastic coefficients across the bone cross-section and along the bone longitudinal axis. The method uses the spatial variations of bone porosity and of the degree of mineralization of the bone matrix (DMB) obtained from the analysis of 3-D synchrotron micro-computed tomography images. For all three scales considered (the foam (100 nm), the ultrastructure (5 μm) and the mesoscale (500 μm)), the elastic coefficients were determined using the Eshelby’s inclusion problem. DMB values were used at the scale of the foam. Collagen was introduced at the scale of the ultrastructure and bone porosity was introduced at the mesoscale. The pores were considered as parallel cylinders oriented along the bone axis. Each elastic coefficient was computed for different regions of interest, allowing an estimation of its variations across the bone cross-section and along the bone longitudinal axis. The method was applied to a human femoral neck bone specimen, which is a site of osteoporotic fracture. The computed elastic coefficients for cortical bone were in good agreement with experimental results, but some discrepancies were obtained in the endosteal part (trabecular bone). These results highlight the importance of accounting for the heterogeneity of cortical bone properties across bone cross-section and along bone longitudinal axis.     

Linear modelling of biopolymer systems and related mechanical properties

A numerical method is proposed to assess the role of random microstructure on the effective Young’s modulus of a two-phase biopolymer composite material. An Ising model coupled to a Monte Carlo (MC) technique is used to generate virtual microstructures representing realistic starch–zein blends having random microstructure. The motivation here was to generate virtual microstructures that can be used in a numerical model to allow a continuous variation of both phase fraction and interface length. From the Pair Correlation Function (PCF), the minimum requirement for the Representative Volume Element (RVE) is established based on geometrical considerations. Finite element analysis allowed the prediction of the effective Young’s modulus as function of the phase ratio for the studied microstructures. The predicted trend is found close to that of Confocal Laser Scanning Microscopy (CLSM) microstructures of starch-based blends used as a case study. The comparison between the predicted results and the most popular analytical expressions points out that only the Hashin–Shrickman bounds are the most close bounds to the evolution of the effective Young’s modulus as function of second phase ratio.When implementing the intrinsic properties of starch and zein and considering virtual microstructures, analytical and numerical models exhibit the same trend. However, the comparison with the 3-p bending results suggests instead, a non-linear trend that can be inferred to the presence of imperfect starch–zein interface properties.     

Human cortical bone: the SiNuPrOs model

Many models that have been developed for cortical bone oversimplify much of the architectural and physical complexity. With SiNuPrOs model, a more complete approach is investigated: it is multiscale because it contains five structural levels and multi physic because it takes into account simultaneously structure (with various properties: elasticity, piezoelectricity, porous medium), fluid and mineralization process modelization. The multiscale aspect is modeled by using 18 structural parameters in a specific application of the mathematical theory of homogenization and 10 other physical parameters are necessary for the multi physic aspect. The modelization of collagen as a piezoelectric medium has needed the development of a new behaviour law allowing a better simulation of the effect of a medium considered as evolving during a mineralization process. Then the main interest of SiNuPrOs deals with the possibility to study, at each level of the cortical architecture, either the elastic properties or the fluid motion or the piezoelectric effects or both of them. All these possibilities constitute a very large work and all this mass of information (fluid aspects, even at the nanoscopic scale, piezoelectric phenomena and simulations) will be presented in several papers. This first one is only devoted to the presentation of this model with an application to the computation of elastic properties at the macroscopic scale. The computational methods have been packed into software also called SiNuPrOs and allowing a large number of predictive simulations corresponding to various different configurations.