Modeling of fibrous biological tissues with a general invariant that excludes compressed fibers

Dispersed collagen fibers in fibrous soft biological tissues have a significant effect on the overall mechanical behavior of the tissues. Constitutive modeling of the detailed structure obtained by using advanced imaging modalities has been investigated extensively in the last decade. In particular, our group has previously proposed a fiber dispersion model based on a generalized structure tensor. However, the fiber tension–compression switch described in that study is unable to exclude compressed fibers within a dispersion and the model requires modification so as to avoid some unphysical effects. In a recent paper we have proposed a method which avoids such problems, but in this present study we introduce an alternative approach by using a new general invariant that only depends on the fibers under tension so that compressed fibers within a dispersion do not contribute to the strain-energy function. We then provide expressions for the associated Cauchy stress and elasticity tensors in a decoupled form. We have also implemented the proposed model in a finite element analysis program and illustrated the implementation with three representative examples: simple tension and compression, simple shear, and unconfined compression on articular cartilage. We have obtained very good agreement with the analytical solutions that are available for the first two examples. The third example shows the efficacy of the fibrous tissue model in a larger scale simulation. For comparison we also provide results for the three examples with the compressed fibers included, and the results are completely different. If the distribution of collagen fibers is such that it is appropriate to exclude compressed fibers then such a model should be adopted

A novel approach to modelling and simulating the contact behaviour between a human hand model and a deformable object

A deeper understanding of biomechanical behaviour of human hands becomes fundamental for any human hand-operated Q2 activities. The integration of biomechanical knowledge of human hands into product design process starts to play an increasingly important role in developing an ergonomic product-to-user interface for products and systems requiring high level of comfortable and responsive interactions. Generation of such precise and dynamic models can provide scientific evaluation tools to support product and system development through simulation. This type of support is urgently required in many applications such as hand skill training for surgical operations, ergonomic study of a product or system developed and so forth. The aim of this work is to study the contact behaviour between the operators’ hand and a hand-held tool or other similar contacts, by developing a novel and precise nonlinear 3D finite element model of the hand and by investigating the contact behaviour through simulation. The contact behaviour is externalised by solving the problem using the bi-potential method. The human body’s biomechanical characteristics, such as hand deformity and structural behaviour, have been fully modelled by implementing anisotropic hyperelastic laws. A case study is given to illustrate the effectiveness of the approac

A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells

Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation amenable for parallel computations. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, capturing the experimental response. The proposed framework is expected to have impact on the understanding how imperfect mechano-transduction could lead to emergent pathological responses.Comment: 31 pages, 17 figure

Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity

A Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution demonstrates the accuracy of the error estimators. Finally the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The popular elastic law of Fung that describes the non-linear stress- strain behavior of soft biological tissues is extended into a viscoelastic material model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a three-dimensional constitutive model that is suitable for general analysis. The model is derived in a configuration that differs from the current, or spatial, configuration by a rigid-body rotation; it being the polar configuration. Mappings for the fractional-order operators of integration and differentiation between the polar and spatial configurations are presented as a theorem. These mappings are used in the construction of the proposed viscoelastic model

Morphogenesis and proportionate growth: A finite element investigation of surface growth with coupled diffusion

Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic laws that orchestrate their function are accounted for, a minimal theoretical model may exhibit similar growth behaviors. The ubiquity of surface growth, a mechanism by which material is added or removed on the boundaries of the body, has motivated the development of theoretical models, which can capture the diffusion-coupled kinetics that govern it. However, due to their complexity, application of these models has been limited to simplified geometries. In this paper, we tackle these complexities by developing a finite element framework to study the diffusion-coupled growth and morphogenesis of finite bodies formed on uniform and flat substrates. We find that in this simplified growth setting, the evolving body exhibits a sequence of distinct growth stages that are reminiscent of natural systems, and appear spontaneously without any externally imposed regulation or coordination. The computational framework developed in this work can serve as the basis for future models that are able to account for growth in arbitrary geometrical settings, and can shed light on the basic physical laws that orchestrate growth and morphogenesis in the natural world

Simulation of red blood cells in microcapillaries : on the study of a deformable particle in steady and oscillating Poiseuille flow

Red blood cells (RBCs) are the major cellular component of blood (about 98%). Therefore, they are the principal responsible for blood dynamics. At the scale of cells, the inertial forces are negligible and the blood flow is modeled with the Stokes equation. In this thesis, we present a two-dimensional numerical study of RBC behavior under flow using the capsule and the vesicle model. First, in a shear flow, we compare the motion and deformation of the shape in both models. Next, we investigate the behavior of a single, and a pair of vesicles in a steady and oscillating Poiseuille flow. For the steady Poseuille flow the shape of the vesicle depends on the flow strength, the mechanical properties of the membrane, and the width of the channel as reported in the past. The oscillation of the flow is introduced using amplitude modulation of the Poiseuille flow to mimic the pulsatile flow in the human circulatory system. We found that the flow oscillation can accelerate the transition of the vesicle from its initial to its final shape. We also observed shape transition of the Snaking shape (a shape where the vesicle shows an oscillatory motion like a swimmer flagella) to parachute or unconfined slipper shapes. For the pair of vesicles, the flow oscillation also decreases the distance between the vesicles. The influence of the oscillation flow was only observed for low flow rate. While for a higher rate, as the shape transition becomes instantaneous the influence of flow oscillation is then insignificant.Rote Blutzellen (RBCs, engl. Red Blood Cells) sind der zelluläre Hauptbestandteil des Blutes (ca. 98%). Aufgrunddessen sind sie hauptverantwortlich für die dynamischen Eigenschaften des Blutes. Auf zellulärer Ebene sind die Inertialkräfte vernachlässigbar und die Blutströmung wird durch die Stokes-Gleichung modelliert. In der vorliegenden Arbeit präsentieren wir eine zweidimensionale numerische Studie des Verhaltens von RBC in Strömung mithilfe des Kapsel- sowie des Vesikelmodells. Als Erstes wird die Bewegung sowie die Deformation in beiden Modellen im Scherfluss verglichen. Im nächsten Schritt untersuchen wir das Verhalten eines einzelnen sowie eines Vesikelpaars in stationärer sowie oszillierender Poiseuilleströmung. Für stationäre Poiseuilleströmung wurde in der Vergangenheit bereits aufgezeigt, dass die Form des Vesikels von der Flussstärke, den mechanischen Eigenschaften der Membran sowie der Kanalbreite abhängt. Die Oszillation der Strömung wird mittels Amplitudenmodulation des Poiseuilleflusses erreicht und ahmt die pulsierende Strömung im menschlichen Kreislaufsystem nach. Es zeigte sich, dass die Strömungsoszillation den Übergang des Vesikels von seinem Anfangs- zu seinem Endzustand beschleunigen kann. Wir beobachteten auch den Übergang der «Snaking»-Form (ein Zustand, bei dem das Vesikel eine oszillierende Bewegung ähnlich einem Flagellum vollführt) zur «parachute»- oder «unconfined slipper»-Form. Für ein Vesikelpaar führt die Oszillation auch zu einer Verringerug des Abstandes zwischen den Vesikeln. Der Einfluss der oszillierenden Strömung wurde nur für niedrige Flussraten beobachtet. Für höhere Flussraten ist der Einfluss der Oszillation unerheblich, da der Übergang zwischen den Formen instantan erfolgt