Modeling on monitoring the growth and rupture assessment of saccular aneurysms

The unpredictable rupture of saccular aneurysms especially of the intracerebral aneurysm is a knotty problem that always results in high mortality. Traditional diagnosis of medical images, which gives the aneurysm size and compares with a speculated critical size from clinical statistics, was demonstrated inadequate to forecasting rupture. Here, we propose a new detecting strategy that uses a dielectric elastomer (DE) capacitance sensor to monitor the growth of saccular aneurysms and deliver both the wall stress and geometric parameters. Based on the elastic growth theory together with the finite deformation analyses, the correlation between the real-time output capacitance of the DE sensor and the wall stress and/or geometry of an aneurysm is derived. Compared to clinic statistics and biomechanics simulations, the wall stress and geometric size may be used as combined indicators to assess the rupture risk of a saccular aneurysm. Numerical results show that an output relative capacitance of 30 indicates a high risk of rupture. Finally, the sensitivity and resolution of the DE sensor are proved adequately high for monitoring the growth state and evaluating the rupture risk of a saccular aneurysm

Electro-mechanically guided growth and patterns

Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and capture some growth phenomena found in Nature, we extend volume growth theory to account for an electro-elasticity coupling. Based on the multiplicative decomposition, we present a general analysis of isotropic growth and pattern formation of electro-elastic solids under external mechanical and electrical fields. As an example, we treat the case of a tubular structure to illustrate an electro-mechanically guided growth affected by axial strain and radial voltage. Our numerical results show that a high voltage can enhance the non-uniformity of the residual stress distribution and induce extensional buckling, while a low voltage can delay the onset of wrinkling shapes and can also generate more complex morphologies. Within a controllable range, axial tensile stretching shows the ability to stabilise the tube and help form more complex 3D patterns, while compressive stretching promotes instability. Both the applied voltage and external axial strain have a significant impact on guiding growth and pattern formation. Our modelling provides a basic tool for analysing the growth of electro-elastic materials, which can be useful for designing a pattern prescription strategy or growth self-assembly in Engineering

Canceling the elastic Poynting effect with geometry

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity)

Nonlinear indentation of second-order hyperelastic materials

The classical problem of indentation on an elastic substrate has found new applications in the field of the Atomic Force Microscopy. However, linearly elastic indentation models are not sufficiently accurate to predict the force–displacement relationship at large indentation depths. For hyperelastic materials, such as soft polymers and biomaterials, a nonlinear indentation model is needed. In this paper, we use second-order elasticity theory to capture larger amplitude deformations and material nonlinearity. We provide a general solution for the contact problem for deformations that are second-order in indentation amplitude with arbitrary indenter profiles. Moreover, we derive analytical solutions by using either parabolic or quartic surfaces to mimic a spherical indenter. The analytical prediction for a quartic surface agrees well with finite element simulations using a spherical indenter for indentation depths on the order of the indenter radius. In particular, the relative error between the two approaches is less than 1% for an indentation depth equal to the indenter radius, an order of magnitude less than that observed with models which are either first-order in indentation amplitude or those which are second-order in indentation amplitude but with a parabolic indenter profile

MEI Kodierung der frühesten Notation in linienlosen Neumen

Das Optical Neume Recognition Project (ONRP) hat die digitale Kodierung von musikalischen Notationszeichen aus dem Jahr um 1000 zum Ziel – ein ambitioniertes Vorhaben, das die Projektmitglieder veranlasste, verschiedenste methodische Ansätze zu evaluieren. Die Optical Music Recognition-Software soll eine linienlose Notation aus einem der ältesten erhaltenen Quellen mit Notationszeichen, dem Antiphonar Hartker aus der Benediktinerabtei St. Gallen (Schweiz), welches heute in zwei Bänden in der Stiftsbibliothek in St. Gallen aufbewahrt wird, erfassen. Aufgrund der handgeschriebenen, linienlosen Notation stellt dieser Gregorianische Gesang den Forscher vor viele Herausforderungen. Das Werk umfasst über 300 verschiedene Neumenzeichen und ihre Notation, die mit Hilfe der Music Encoding Initiative (MEI) erfasst und beschrieben werden sollen. Der folgende Artikel beschreibt den Prozess der Adaptierung, um die MEI auf die Notation von Neumen ohne Notenlinien anzuwenden. Beschrieben werden Eigenschaften der Neumennotation, um zu verdeutlichen, wo die Herausforderungen dieser Arbeit liegen sowie die Funktionsweise des Classifiers, einer Art digitalen Neumenwörterbuchs

Modified multiplicative decomposition model for tissue growth: Beyond the initial stress-free state

The multiplicative decomposition model is widely employed for predicting residual stresses and morphologies of biological tissues due to growth. However, it relies on the assumption that the tissue is initially in a stress-free state, which conflicts with the observations that any growth state of a biological tissue is under a significant level of residual stresses that helps to maintain its ideal mechanical conditions. Here, we propose a modified multiplicative decomposition model in which the initial state (or reference configuration) of a biological tissue is endowed with a residual stress instead of being stress-free.Releasing theoretically the initial residual stress, the initially stressed state is first transmitted into a virtual stress-free state, thus resulting in an initial elastic deformation. The initial virtual stress-free state subsequently grows to another counterpart with a growth deformation, and the latter is further integrated into its natural configuration of a real tissue with an excessive elastic deformation that ensures tissue compatibility. With this decomposition, the total deformation arising during growth may be expressed as the product of elastic deformation, growth deformation and initial elastic deformation, while the corresponding free energy density should depend on the initial residual stress and the total deformation. Three key issues including the explicit expression of the free energy density, the predetermination of the initial elastic deformation, and the initial residual stress are addressed.Finally, we consider a tubular organ as a representative example to demonstrate the effects of the proposed initial residual stress on stress distribution and on shape formation through an incremental stability analysis. Our results suggest that the initial residual stress exerts a major influence on the growth stress and the morphology of biological tissues. The model bridges the gap between any two growth states of a biological tissue that is endowed with a certain level of residual stresses. (C) 2018 Elsevier Ltd. All rights reserved.This work was supported by the National Natural Science Foundation of China through grant Nos. 11621062 and 11772295, and was also partly supported by the Fundamental Research Funds for the Central Universities 2016XZZX001-05.peer-reviewed2020-05-1

Influence of initial residual stress on growth and pattern creation for a layered aorta

Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growth-induced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters. This modelling provides promising avenues for designing and directing some appropriate morphology of a given tissue or organ and achieve some targeted biomedical function. In this paper, we rely on a modified, augmented theory to reveal how we can obtain growth-induced residual stress and pattern evolution of a layered artery by starting from an existing, non-zero initial residual stress state. We use experimentally determined residual stress distributions of aged bi-layered human aortas and quantify their influence by a magnitude factor. Our results show that initial residual stress has a more significant impact on residual stress accumulation and the subsequent evolution of patterns than geometry and material parameters. Additionally, we provide an essential explanation for growth-induced patterns driven by differential growth coupled to an initial residual stress. Finally, we show that initial residual stress is a readily available way to control growth-induced pattern creation for tissues and thus may provide a promising inspiration for biomedical engineering.peer-reviewe