G. U. Unnikrishnan

Constitutive material modeling of cell: a micromechanics approach.

The variations in mechanical properties of cells obtained from experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work. The proposed model is developed using the Mori-Tanaka method of homogenization by treating the cell as a fiber-reinforced composite medium satisfying the continuum hypothesis. The validation of the constitutive model using finite element analysis on atomic force microscopy (AFM) and magnetic twisting cytometry (MTC) has been carried out and is found to yield good correlation with reported experimental results. It is observed from the study that as the volume fraction of the stress fiber increases, the stiffness of the cell increases and it alters the force displacement behavior for the AFM and MTC experiments. Through this model, we have also been able to find the stress fiber as a likely cause of the differences in the derived mechanical property from the AFM and MTC experiments. The correlation of the mechanical behavior of the cell with the cell composition, as obtained through this study, is an important observation in cell mechanics.

Effect of Permeability on the Performance of Elastographic Imaging Techniques

Elastography is a well-established imaging modality. While a number of studies aimed at evaluating the performance of elastographic techniques are retrievable in the literature, very little information is available on the effects that the presence of an underlying permeability contrast in the tissue may have on the resulting elastograms. Permeability is a fundamental tissue parameter, which characterizes the ease with which fluid can move within a tissue. This parameter plays a central role both biomechanically in the description of the temporal behavior of fluid-filled tissues and clinically in the development of a number of diagnostic and therapeutic modalities. In this paper, we present a simulation study that investigates selected elastographic image quality factors in nonhomogeneous materials, modeled as poroelastic media with different geometries and permeability contrasts. The results of this study indicate that the presence of an underlying permeability contrast may create a new contrast mechanism in the spatial and temporal distributions of the axial strains and the effective Poissons ratios experienced by the tissue and as imaged by the corresponding elastograms. The effect of permeability on the elastographic image quality factors analyzed in this study was found to be a nonsymmetric function of the underlying mechanical contrast between background and target, the geometry of the material and the boundary conditions.

Multiscale Nonlocal Thermo-Elastic Analysis of Graphene Nanoribbons

This paper investigates the effect of interfacial thermal characteristics and nonlocal effects on the overall effective thermal property of graphene nanoribbons embedded in low-density polyethylene matrix. It is widely known that apart from the thermal conductivity, the effect of interfacial thermal resistance is the most important factor that determines the thermal efficiency of nanostructures. In this work, we develop nonlocal thermo-elastic properties coupled with a multiscale strategy by means of properties derived from atomistic simulations. Atomistic based thermal properties of graphene nanoribbons are estimated from molecular dynamics (MD) simulations and the effect of inter-tubular spacing on the interfacial thermal characteristics are also studied. The paper also discusses the effect of the nonlocal parameter on the thermal conduction of the composite system using the developed nonlocal thermo-elastic model.

Tissue-fluid interface analysis using biphasic finite element method.

Numerical studies on fluid–structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid–structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue–fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.

Computational Homogenization of Polymeric Nanofiber Scaffolds and Biological Cells

An understanding of the structure–property relationship is essential for the estimation of mechanical properties of nano-materials like polymeric nanofibers and biological materials like cells and tissues. The properties of these structures are closely related to the internal molecular structure and therefore a multiscale based mathematical modeling is required for the determination of its macroscopic properties. In this investigation, we present multiscale mathematical models to estimate the mechanical properties of polymeric nanofibers from the basic building blocks to the macroscale nanofibrous structures and also study the homogenization of biological cells considering the microcellular constituents.Theoretical analysis of polymeric nanofibers based scaffolds are necessary towards designing novel bio-medical applications, while through homogenization of biological cells new diagnostic tools based on mechanical properties could be developed.

Effect of Interstitial Fluid Pressure on Ultrasound Axial Strain and Axial Shear Strain Elastography

Ultrasound elastography is an imaging modality that has been used to diagnose tumors of the breast, thyroid, and prostate. Both axial strain elastography and axial shear strain elastography (ASSE) have shown significant potentials to differentiate between benign and malignant tumors. Elevated interstitial fluid pressure (IFP) is a characteristic of many malignant tumors and a major barrier in targeted drug delivery therapies. This parameter, however, has not received significant attention in ultrasound elastography and, in general, in most diagnostic imaging modalities yet. In this paper, we investigate the effect of an underlying IFP contrast on ultrasound axial strain and axial shear strain imaging using finite element analysis. Our results show that an underlying contrast in IFP creates a new contrast mechanism in both the axial strain and axial shear strain elastographic images. This information might be important for a better interpretation of elastographic images of tumors.

Contribution of material properties of cellular components on the viscoelastic, stress-relaxation response of a cell during AFM indentation

ABSTRACT The close relationship between the mechanical properties of biological cells, namely, elasticity, viscosity, and the state of its disease condition has been widely investigated using atomic force microscopy (AFM). In this study, computational simulation of the AFM indentation is carried out using a finite element (FE) model of an adherent cell. A parametric evaluation of the material properties of the cellular components on the viscoelastic, stress-relaxation response during AFM indentation is performed. In addition, the loading rate, the size of the nucleus, and the geometry of the cell are varied. From the present study, it is found that when comparing the material properties derived from experimental force-deflection curves, the influence of loading rates should be accommodated. It also provides a framework that can quantify the variation of the mechanical property with various stages of malignancy of the cancer cell, a potential procedure for cancer diagnosis.

Multiscale Computational Analysis of Biomechanical Systems

The material properties of biological materials, often derived from experiments, are found to vary by orders of magnitude. This disparity in experimentally-derived mechanical properties can be understood only by mathematical models that correlate the structural constituents to its mechanical response. New mechano-biological computational models that consider the effect of microstructural constituents on the response of biological materials are considered in this paper. Various mathematical models are presented to study the macroscopic effects, such as deformation and diffusion in tissues, using multi-scale computational models. The implementation of the computational models for the determination of mechanical behaviour in pathological conditions like cancer progression, cardiovascular diseases, and gynaecological conditions are discussed. The significance of this work lies in the use of a multi-physical modelling of the complex material geometry as well as physical processes representing physiological systems, thereby establishing a suitable and efficient multi-scale computational framework.

MICRO-CONSTITUENT BASED VISCOELASTIC FINITE ELEMENT ANALYSIS OF BIOLOGICAL CELLS

A viscoelastic analysis of the biological cell considering the microcellular material properties is carried out in this work. Three separate regions of the cell: the actin cortex, cytoplasm and nucleus are considered. The outer cortex and cytoplasm are modeled using standard linear viscoelastic model (SLS) and standard neo-Hookean viscoelastic solid, and a linear elastic material model is considered for the nucleus. The effect of the material properties of cytoplasm and actin cortex on the derivable parameters from three major experimental studies of magnetic twisting cytometry (MTC) and atomic force microscopy (AFM) and micropipette aspiration (MPA) are analyzed using the finite element method. The bead center displacement for the MTC, reaction force for AFM, and aspiration length ratio for the MPA are the major quantities derived from the finite element analysis. A number of parametric studies are also conducted and it is observed that SLS and SnHS models predict nearly identical results for the material constants.

Multiscale Homogenization Based Analysis of Polymeric Nanofiber Scaffolds

In this paper a two scale asymptotic expansion homogenization using a spectral/hp finite element approach is used to estimate the mechanical properties of polymeric poly-lactic acid nanofibers. The mechanical properties of the nanofibers are derived hierarchically from the elastic modulus of the crystalline lactic acid monomer and subsequently the mesoscale properties of the shish-kebab fibril is derived by the finite element based homogenization method. The fiber modulus is further refined by the Northolt and van der Houts continuous chain theory. The continuum chain model is modified to include the effect of the finite element spectral degree and the volume fractions of the shish-kebab phases. Finally, the effective property of the scaffold is estimated using the well known micromechanics methods. The significance of this paper lies in the hierarchical transfer of material properties from the lowest atomistic scale to the highest scales without resorting to any experimental data. The theoretical results are found to correlate well with the reported experimental results.