Extension, inflation and torsion of a residually-stressed circular cylindrical tube

In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress

Fluctuations and differential contraction during regeneration of Hydra vulgaris tissue toroids

We studied regenerating bilayered tissue toroids dissected from Hydra vulgaris polyps and relate our macroscopic observations to the dynamics of force-generating mesoscopic cytoskeletal structures. Tissue fragments undergo a specific toroid-spheroid folding process leading to complete regeneration towards a new organism. The time scale of folding is too fast for biochemical signalling or morphogenetic gradients which forced us to assume purely mechanical self-organization. The initial pattern selection dynamics was studied by embedding toroids into hydro-gels allowing us to observe the deformation modes over longer periods of time. We found increasing mechanical fluctuations which break the toroidal symmetry and discuss the evolution of their power spectra for various gel stiffnesses. Our observations are related to single cell studies which explain the mechanical feasibility of the folding process. In addition, we observed switching of cells from a tissue bound to a migrating state after folding failure as well as in tissue injury. We found a supra-cellular actin ring assembled along the toroid's inner edge. Its contraction can lead to the observed folding dynamics as we could confirm by finite element simulations. This actin ring in the inner cell layer is assembled by myosin- driven length fluctuations of supra-cellular {\alpha}-actin structures (myonemes) in the outer cell-layer.Comment: 19 pages and 8 figures, submitted to New Journal of Physic

Modeling the growth of multicellular cancer spheroids in a\ud bioengineered 3D microenvironment and their treatment with an\ud anti-cancer drug

A critical step in the dissemination of ovarian cancer cells is the formation of multicellular spheroids from cells shed from the primary tumor. The objectives of this study were to establish and validate bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer cells in vitro and simultaneously to develop computational models describing the growth of multicellular spheroids in these bioengineered matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and cultured for up to 4 weeks. Immunohistochemistry was used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel.\ud \ud Two computational models were developed. In the first model, each spheroid was treated as an incompressible porous medium, whereas in the second model the concept of morphoelasticity was used to incorporate details about internal stresses and strains. Each model was formulated as a free boundary problem. Functional forms for cell proliferation and apoptosis motivated by the experimental work were applied and the predictions of both models compared with the output from the experiments. Both models simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture time and treatment with paclitaxel. Our mathematical models provide new perspectives on previous experimental results and have informed the design of new 3D studies of multicellular cancer spheroids

Capture and Modeling of Non-Linear Heterogeneous Soft Tissue

This paper introduces a data-driven representation and modeling technique for simulating non-linear heterogeneous soft tissue. It simplifies the construction of convincing deformable models by avoiding complex selection and tuning of physical material parameters, yet retaining the richness of non-linear heterogeneous behavior. We acquire a set of example deformations of a real object, and represent each of them as a spatially varying stress-strain relationship in a finite-element model. We then model the material by non-linear interpolation of these stress-strain relationships in strain-space. Our method relies on a simple-to-build capture system and an efficient run-time simulation algorithm based on incremental loading, making it suitable for interactive computer graphics applications. We present the results of our approach for several non-linear materials and biological soft tissue, with accurate agreement of our model to the measured data.Engineering and Applied Science

Análise Biomecânica de Calo Ósseo usando Método Sem Malha

O osso é um tecido fisiologicamente dinâmico e que quando lesionado tem a capacidade de se reparar com o próprio tecido, não envolvendo um tecido cicatrizante, ao contrário de outros tecidos. Esta característica torna-o particularmente interessante para investigar os processos inerentes de fraturas ósseas. A maior parte das fraturas cicatriza através de uma sequência de processos de diferenciação de tecidos, desde os processos iniciais de hematoma, aos tecidos conjuntivos, e através da cartilagem ao osso. No entanto, qualquer falha neste processo pode resultar em uniões tardias, más uniões ou não uniões. A compreensão na totalidade deste processo ainda constitui um desafio. Os mecanismos que envolvem os processos de estimulação mecânica não se encontram bem compreendidos, em consequência da complexidade dos testes experimentais in vivo, que se tornam dependentes de dados in vitro, tornando difícil validar os pressupostos biológicos. Consequentemente, os modelos computacionais têm demonstrado serem bastante úteis e eficazes na investigação sobre a cicatrização óssea. Desta forma, com o presente trabalho foi possível analisar as condições mecânicas de um calo ósseo resultante de uma fratura, assim como compreender as metodologias de análise numérica aplicadas. O modelo teve por base um estudo in vivo de forma a obter uma variação temporal progressiva da forma do calo e das propriedades mecânicas durante a cicatrização óssea. Com este modelo obtiveram-se os campos de tensão e deformação nas diferentes fases do processo de regeneração, obtendo-se resultados que se encontram em conformidade com a literatura. Adicionalmente, foi aplicado um algoritmo de remodelação óssea em combinação com o Radial Point Interpolation Method (RPIM) que foi capaz de reproduzir as condições apresentadas pela respetiva imagem histológica nesta fase. Por último, espera-se que os trabalhos desenvolvidos neste âmbito possibilitem a conceção de estratégias mais precisas e eficazes tanto para o tratamento como para aceleração da cura. De forma complementar, encontram-se em desenvolvimento modelos específicos dos pacientes e que incorporam variabilidade genética.Bone is a physiologically dynamic tissue that, when injured, has the ability to repair itself, not involving scar tissue, unlike other tissues. This characteristic makes it particularly interesting for investigating the inherent processes of bone fractures. Most fractures heal through a sequence of tissue differentiation processes, from the initial hematoma, to connective tissues and through cartilage to bone. However, any failure in this process can result in a delayed union, mal-union or non-union. A complete understanding of this process is still a challenge. The mechanisms surrounding the mechanical stimulation processes are relatively poorly understood as a result of the complexity of in vivo experimental tests, which become dependent on in vitro data, making it difficult to validate the biological assumptions. Consequently, computational models have proven to be very useful and effective in the investigation of bone healing. Therefore, in the present work, it was possible to analyse the mechanical conditions of a bone callus as a consequence of a fracture and to understand the methodologies of numerical analysis applied. The model was based on an in vivo experimental study in order to obtain a progressive temporal variation of the callus shape and mechanical properties during bone healing. With this model, the stress and strain fields in the different phases of the regeneration process were obtained, where the results are in agreement with the literature. Additionally, a bone remodelling algorithm was applied in combination with the Radial Point Interpolation Method (RPIM), which was able to reproduce the conditions presented by the respective histological image at this stage. Finally, it is expected that the work developed in this area will enable the design of more accurate and effective strategies for both treatment and accelerating healing. Complementarily, patient-specific models and the incorporation of genetic variability are being developed

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