Influence of Initial Residual Stress on Growth and Pattern Creation for a Layered Aorta

Mechanical models and measurement methods of solid stress in tumors

In addition to genetic mutations, biomechanical factors also affect the structures and functions of the tumors during tumor growth, including solid stress, interstitial fluid pressure, stiffness, and microarchitecture. Solid stress affects tumors by compressing cancer and stromal cells and deforming blood and lymphatic vessels which reduce supply of oxygen, nutrients and drug delivery, making resistant to treatment. Researchers simulate the stress by creating mechanical models both in vitro and in vivo. Cell models in vitro are divided into two dimensions (2D) and three dimensions (3D). 2D models are simple to operate but exert pressure on apical surface of the cells. 3D models, the multicellular tumor spheres, are more consistent with the actual pathological state in human body. However, the models are more difficult to establish compared with the 2D models. Besides, the procedure of the animal models in vivo is even more complex and tougher to operate. Then, researchers challenged to quantify the solid stress through some measurement methods. We compared the advantages and limitations of these models and methods, which may help to explore new therapeutic targets for normalizing the tumor's physical microenvironment. KEY POINTS: •This is the first review to conclude the mechanical models and measurement methods in tumors. •The merit and demerit of these models and methods are compared. •Insights into further models are discussed.

Modelling of longitudinally cut carrot curling induced by the vascular cylinder-cortex interference pressure

Cut carrot pieces are popular convenience foods, which enable the use of misshapen or physiologically imperfect produce. Cut carrots curl due to residual stress, which limits their shelf life and causes unnecessary food waste. The aim of this study is to identify the geometrical and environmental factors which have the most influence on their longevity. An analytical equation was developed using compound cylinder solutions, and this was used to define carrot-specific finite element (FE) models. Over 100 longitudinally cut Lancashire Nantes carrot halves were characterized, each was modelled analytically and verified using FE models. This model was evaluated by comparing predicted curvatures to ones experimentally measured over a week. The average radius of curvature decreased from 1.61 to 1.1 m a week after. A 1.32× reduction in the elastic modulus after 7 days was observed. The moisture content reduction relates to 22% weight loss, correlating to the decreasing radius of curvature. Subsequently, carrots are recommended to be stored in humidity-controlled environments. The experimental results from this study match the predictions made using mechanical principles. The research provides a methodology to predict the deformation of cut root vegetables, and the procedure is likely to be applicable to other plant structures.

Mechanobiological tissue instability induced by stress-modulated growth

The growth of biological tissues, which is regulated by a variety of factors, can induce stresses that may, in turn, destabilize the tissues into diverse patterns. In most previous studies, however, tissue growth was usually assumed as a prescribed parameter independent of stresses, limiting our understanding of the mechanobiological morphogenesis of real tissues. In this paper, we propose a theoretical model to investigate the mechanobiological response of soft tissues undergoing stress-modulated growth. Linear stability analysis is first performed to elucidate the surface instability mechanism induced by stress-modulated volumetric growth. We further conduct finite element simulations to validate the theoretical prediction and, particularly, to capture the post-buckling pattern evolution. Our results show that the non-uniform stresses, which evolve with the tissue growth and morphogenesis, exert mechanical feedback on the growth itself, producing up-down asymmetric surface morphologies as observed in, for example, the gyrification of human brains and brain organoids. It is also revealed that large residual stresses are unnecessary to cause mechanobiological instability and subsequent asymmetric patterning, which has long been believed to be driven by sufficiently high stresses. The present work could help us to understand the morphological changes of biological tissues under physiological and pathological conditions.

Representing the stress and strain energy of elastic solids with initial stress and transverse texture anisotropy

Real-world solids, such as rocks, soft tissues and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the ‘texture anisotropy’. This anisotropy can stem from preferential grain alignment in polycrystalline materials, aligned micro-cracks or structural reinforcement, such as collagen bundles in biological tissues, steel rods in pre-stressed concrete and reinforcing fibres in composites. Here, we establish a framework for initially stressed solids with transverse texture anisotropy. We consider that the strain energy per unit mass of the reference is an explicit function of the elastic deformation gradient, the initial stress tensor and the texture anisotropy. We determine the corresponding constitutive relations and develop examples of nonlinear strain energies that depend explicitly on the initial stress and direction of texture anisotropy. As an application, we then employ these models to analyse the stress distribution of an inflated initially stressed cylinder with texture anisotropy and the tension of a welded metal plate. We also deduce the elastic moduli needed to describe linear elasticity from stress reference with transverse texture anisotropy. As an example, we show how to measure the stress with small-amplitude shear waves.

Prestressing Strategy for Strengthening Biocomposites: A Numerical Study

Natural materials developed in complex architectures that comprise hard and soft phases often display extraordinary mechanical properties, such as the combination of high strength and toughness. Besides the structural arrangements, residual stress is ubiquitous in those materials. Although evidence shows its significant role in the functionalities and properties of the composites, good or bad, residual stress is not fully understood and utilized. In this study, we show through extensive numerical simulations the role of the prestress in strengthening typical brick-and-mortar biocomposites. We investigate the influence of the prestressing modes, as well as the geometrical and material parameters. The results promise a deep understanding of the relation between the prestress and the material strength and may inspire a new dimension of material design.

Active elasticity drives the formation of periodic beading in damaged axons

In several pathological conditions, such as coronavirus infections, multiple sclerosis, Alzheimer's and Parkinson's diseases, the physiological shape of axons is altered and a periodic sequence of bulges appears. Experimental evidences suggest that such morphological changes are caused by the disruption of the microtubules composing the cytoskeleton of the axon. In this paper, we develop a mathematical model of damaged axons based on the theory of continuum mechanics and nonlinear elasticity. The axon is described as a cylinder composed of an inner passive part, called axoplasm, and an outer active cortex, composed mainly of F-actin and able to contract thanks to myosin-II motors. Through a linear stability analysis we show that, as the shear modulus of the axoplasm diminishes due to the disruption of the cytoskeleton, the active contraction of the cortex makes the cylindrical configuration unstable to axisymmetric perturbations, leading to a beading pattern. Finally, the nonlinear evolution of the bifurcated branches is investigated through finite element simulations.

Prescribing patterns in growing tubular soft matter by initial residual stress

Initial residual stress is omnipresent in biological tissues and soft matter, and can affect growth-induced pattern selection significantly. Here we demonstrate this effect experimentally by letting soft tubes grow in the presence or absence of initial residual stress and by observing different growth pattern evolutions. These experiments motivate us to model the mechanisms at play when a growing bilayer tubular organ spontaneously displays buckling patterns on its inner surface. We demonstrate that not only differential growth, geometry and elasticity, but also initial residual stress distribution, exert a notable influence on these pattern phenomena. Prescribing an initial residual stress distribution offers an alternative or a more effective way to implement pattern selection for growable bio-tissues or soft matter. The results also show promise for the design of 4D bio-mimic printing protocols or for controlling hydrogel actuators.