A finite viscoelastic–plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress–strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress–strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.     

A polyconvex anisotropic strain–energy function for soft collagenous tissues

Polyconvexity of a strain–energy function is a very important mathematical condition, especially in the context of a boundary-value problem. In the present paper, we propose an exponential polyconvex anisotropic strain–energy function. It is given by a series with an arbitrary number of terms and associated material constants. Each term of this series a priori satisfies the condition of the energy- and stress-free natural state so that no additional restrictions have to be imposed. Due to the exponential form, the proposed hyperelastic model is suitable for soft biological tissues. Thus, a good agreement with experimental data on different types of tissues is achieved.     

How to test very soft biological tissues in extension?

Mechanical properties of very soft tissues, such as brain, liver and kidney, until recently have largely escaped the attention of researchers because these tissues do not bear mechanical loads. However, developments in Computer-Integrated and Robot-Aided Surgery - in particular, the emergence of automatic surgical tools and robots - as well as advances in Virtual Reality techniques, require closer examination of the mechanical properties of very soft tissues and, ultimately, the construction of corresponding, realistic mathematical models. A body of knowledge about mechanical properties of very soft tissues, assembled in recent years, has been almost exclusively based on the results of compression, indentation and impact tests. There are no results of tensile tests available. This state of affairs, in the author's opinion, is caused by the lack of analytical solution relating a measured quantity - machine head displacement - to strain in simple extension experiments of cylindrical samples with low aspect ratio. In the paper this important solution is presented. The theoretical solution obtained is valid for isotropic, incompressible materials for moderate deformations (<30%) when it can be assumed that planes initially perpendicular to the direction of applied extension remain plane. Two astonishing results are obtained: (i) deformed shape of a cylindrical sample subjected to uniaxial extension is independent on the form of constitutive law, (ii) vertical extension in the plane of symmetry lambda(z) is proportional to the total change of height for strains as large as 30%. The importance and relevance of these results to testing procedures in Biomechanics is highlighted.     

Biomaterials approaches to modeling macrophage–extracellular matrix interactions in the tumor microenvironment

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A new method for choosing the computational cell in stochastic reaction–diffusion systems

How to choose the computational compartment or cell size for the stochastic simulation of a reaction–diffusion system is still an open problem, and a number of criteria have been suggested. A generalized measure of the noise for finite-dimensional systems based on the largest eigenvalue of the covariance matrix of the number of molecules of all species has been suggested as a measure of the overall fluctuations in a multivariate system, and we apply it here to a discretized reaction–diffusion system. We show that for a broad class of first-order reaction networks this measure converges to the square root of the reciprocal of the smallest mean species number in a compartment at the steady state. We show that a suitably re-normalized measure stabilizes as the volume of a cell approaches zero, which leads to a criterion for the maximum volume of the compartments in a computational grid. We then derive a new criterion based on the sensitivity of the entire network, not just of the fastest step, that predicts a grid size that assures that the concentrations of all species converge to a spatially-uniform solution. This criterion applies for all orders of reactions and for reaction rate functions derived from singular perturbation or other reduction methods, and encompasses both diffusing and non-diffusing species. We show that this predicts the maximal allowable volume found in a linear problem, and we illustrate our results with an example motivated by anterior-posterior pattern formation in Drosophila, and with several other examples.     

The micromechanics of fluid–solid interactions during growth in porous soft biological tissue

In this paper, we address some modelling issues related to biological growth. Our treatment is based on a formulation for growth that was proposed within the context of mixture theory (J Mech Phys Solids 52:1595–1625, 2004). We aim to make this treatment more appropriate for the physics of porous soft tissues, paying particular attention to the nature of fluid transport, and mechanics of fluid and solid phases. The interactions between transport and mechanics have significant implications for growth and swelling. We also reformulate the governing differential equations for reaction-transport of solutes to represent the incompressibility constraint on the fluid phase of the tissue. This revision enables a straightforward implementation of numerical stabilisation for the advection-dominated limit of these equations. A finite element implementation with operator splitting is used to solve the coupled, non-linear partial differential equations that arise from the theory. We carry out a numerical and analytic study of the convergence of the operator splitting scheme subject to strain- and stress-homogenisation of the mechanics of fluid–solid interactions. A few computations are presented to demonstrate aspects of the physical mechanisms, and the numerical performance of the formulation.     

A hybrid model of intercellular tension and cell–matrix mechanical interactions in a multicellular geometry

Biomechanics and Modeling in Mechanobiology - Epithelial cells form continuous sheets of cells that exist in tensional homeostasis. Homeostasis is maintained through cell-to-cell junctions that...     

A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry,cell deformability,and cell–matrix adhesion

Biomechanics and Modeling in Mechanobiology - Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell...     

Lipid–protein interactions in biological membranes: A dynamic perspective

Though an increasing number of biological functions at the membrane are attributed to direct associations between lipid head groups and protein side chains or lipid protein hydrophobic attractive forces, surprisingly limited information is available about the dynamics of these interactions. The static in vitro representation provided by membrane protein structures, including very insightful lipid–protein binding geometries, still fails to recapitulate the dynamic behavior characteristic of lipid membranes. Experimental measures of the interaction time of lipid–protein association are very rare, and have only provided order-of-magnitude estimates in an extremely limited number of systems. In this review, a brief outline of the experimental approaches taken in this area to date is given. The bulk of the review will focus on two methods that are promising techniques for measuring lipid–protein interactions: time-resolved fluorescence microscopy, and two-dimensional infrared (2D IR) spectroscopy. Time-resolved fluorescence microscopy is the name given to a sophisticated toolbox of measurements taken using pulsed laser excitation and time-correlated single photon counting (TCSPC). With this technique the dynamics of interaction can be measured on the time scale of nanoseconds to milliseconds. 2D IR is a femtosecond nonlinear spectroscopy that can resolve vibrational coupling between lipids and proteins at molecular-scale distances and at time scales from femtoseconds to picoseconds. These two methods are poised to make significant advances in our understanding of the dynamic properties of biological membranes. This article is part of a Special Issue entitled: Membrane protein structure and function.     

A biological framework for understanding farmers’ plant breeding

We present a framework for understanding farmer plant breeding (including both choice of varieties and populations and plant selection) in terms of the basic biological model of scientific plant breeding, focusing on three key components of that model: 1) genetic variation, 2) environmental variation and variation of genotype-by-environment interaction, and 3) plant selection. For each of these concepts we suggest questions for research on farmers’plant breeding (farmers’ knowledge, practice, and crop varieties and growing environments). A sample of recent research shows a range of explicit and implicit answers to these questions which are often contradictory, suggesting that generalizations based on experience with specific varieties, environments or farmers may not be valid. They also suggest that farmers’ practice reflects an understanding of their crop varieties and populations that is in many ways fundamentally similar to that of plant breeders; yet, is also different, in part because the details of their experiences are different. Further research based on this framework should be valuable for participatory or collaborative plant breeding that is currently being proposed to reunite farmer and scientific plant breeding.     

Integrins and chondrocyte–matrix interactions in articular cartilage

The integrin family of cell adhesion receptors plays a major role in mediating interactions between cells and the extracellular matrix. Normal adult articular chondrocytes express α1β1, α3β1, α5β1, α10β1, αVβ1, αVβ3, and αVβ5 integrins, while chondrocytes from osteoarthritic tissue also express α2β1, α4β1, α6β1. These integrins bind a host of cartilage extracellular matrix (ECM) proteins, most notably fibronectin and collagen types II and VI, which provide signals that regulate cell proliferation, survival, differentiation, and matrix remodeling. By initiating signals in response to mechanical forces, chondrocyte integrins also serve as mechanotransducers. When the cartilage matrix is damaged in osteoarthritis, fragments of fibronectin are generated that signal through the α5β1 integrin to activate a pro-inflammatory and pro-catabolic response which, if left unchecked, could contribute to progressive matrix degradation. The cell signaling pathways activated in response to excessive mechanical signals and to fibronectin fragments are being unraveled and may represent useful therapeutic targets for slowing or stopping progressive matrix destruction in arthritis.     

PH-dependent cell–cell interactions in the green alga Chara

Protoplasma - Characean internodal cells develop alternating patterns of acid and alkaline zones along their surface in order to facilitate uptake of carbon required for photosynthesis. In this...     

A phenomenological cohesive model for the macroscopic simulation of cell–matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell–matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell–matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell–matrix adhesions.