COLLECTIONS

Documents published in Scipedia

• Non-regularised inverse finite element analysis for 3D traction force microscopy

  J. Muñoz

  Int. J. Numer. Anal. Model. (2016). Vol. 13 (5), pp. 763-781 (Preprint)

  
  

  Abstract

  The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an inverse problem. Here, we resort to the discretisation with finite elements of the associated direct variational formulation, and solve the inverse analysis using a least square approach. This strategy requires the minimisation of an error functional, which is usually regularised in order to obtain a stable system of equations with a unique solution. In this paper we show that for many common three-dimensional geometries, meshes and loading conditions, this regularisation is unnecessary. In these cases, the computational cost of the inverse problem becomes equivalent to a direct finite element problem. For the non-regularised functional, we deduce the necessary and sufficient conditions that the dimensions of the interpolated displacement and traction fields must preserve in order to exactly satisfy or yield a unique solution of the discrete equilibrium equations. We apply the theoretical results to some illustrative examples and to real experimental data. Due to the relevance of the results for biologists and modellers, the article concludes with some practical rules that the finite element discretisation must satisfy.

  Abstract
  The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation [...]

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• Control of cell-cell forces and collective cell dynamics by the intercellular adhesome

  E. Bazellières, V. Conte, A. Elosegui-Artola, X. Serra-Picamal, M. Bintanel-Morcillo, P. Roca-Cusachs, J. Muñoz, M. Sales-Pardo, R. Guimerà, X. Trepat

  Nature Cell Biology (2015). Vol. 17 (4), pp. 409-420

  
  

  Abstract

    Dynamics of epithelial tissues determine key processes in development, tissue healing and cancer invasion. These processes are critically influenced by cell–cell adhesion forces. However, the identity of the proteins that resist and transmit forces at cell–cell junctions remains unclear, and how these proteins control tissue dynamics is largely unknown. Here we provide a systematic study of the interplay between cell–cell adhesion proteins, intercellular forces and epithelial tissue dynamics. We show that collective cellular responses to selective perturbations of the intercellular adhesome conform to three mechanical phenotypes. These phenotypes are controlled by different molecular modules and characterized by distinct relationships between cellular kinematics and intercellular forces. We show that these forces and their rates can be predicted by the concentrations of cadherins and catenins. Unexpectedly, we identified different mechanical roles for P-cadherin and E-cadherin; whereas P-cadherin predicts levels of intercellular force, E-cadherin predicts the rate at which intercellular force builds up.

  Abstract
    Dynamics of epithelial tissues determine key processes in development, tissue healing and cancer invasion. These processes are critically influenced by cell–cell [...]

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• Mapping forces and kinematics during collective cell migration

  X. Serra-Picamal, V. Conte, R. Sunyer, J. Muñoz, X. Trepat

  Methods in Cell Biology (2015). Vol. 125, pp. 309-330

  
  

  Abstract

  Fundamental biological processes including morphogenesis and tissue repair require cells to migrate collectively. In these processes, epithelial or endothelial cells move in a cooperative manner coupled by intercellular junctions. Ultimately, the movement of these multicellular systems occurs through the generation of cellular forces, exerted either on the substrate via focal adhesions (cell–substrate forces) or on neighboring cells through cell–cell junctions (cell–cell forces). Quantitative measurements of multicellular forces and kinematics with cellular or subcellular resolution have become possible only in recent years. In this chapter, we describe some of these techniques, which include particle image velocimetry to map cell velocities, traction force microscopy to map forces exerted by cells on the substrate, and monolayer stress microscopy to map forces within and between cells. We also describe experimental protocols to perform these measurements. The combination of these techniques with high-resolution imaging tools and molecular perturbations will lead to a better understanding of the mechanisms underlying collective cell migration in health and disease.

  Abstract
  Fundamental biological processes including morphogenesis and tissue repair require cells to migrate collectively. In these processes, epithelial or endothelial [...]

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• AAR-based decomposition method for lower-bound limit analysis

  J. Muñoz, R. Syednima

  Proceedings of the ICE-Engineering and Computational Mechanics (2015). Vol. 168 (4), pp. 169-177 (Preprint)

  
  

  Abstract

  Despite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive de-remeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms

  Abstract
  Despite the recent progress in optimisation techniques, finite-element stability analysis of realistic three-dimensional problems is still hampered by the size of the resulting [...]

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• Cell-centred model for the simulation of curved cellular monolayers

  P. Mosaffa, N. Asadipour, D. Millán, A. Rodríguez-Ferran, J. Muñoz

  Computational Particle Mechanics (2015). Vol. 2 (4), pp. 359-370 (Preprint)

  
  

  Abstract

  This paper presents a cell-centred model for the simulation of planar and curved multicellular soft tissues. We propose a computational model that includes stress relaxation due to cell reorganisation (intercellular connectivity changes) and cytoskeleton remodelling (intracellular changes). Cells are represented by their cell centres, and their mechanical interaction is modelled through active non-linear elastic laws with a dynamically changing resting length. Special attention is paid to the handling of connectivity changes between cells, and the relaxation that the tissues exhibit under these topological changes. Cell–cell connectivity is computed by resorting to a Delaunay triangulation, which is combined with a mapping technique in order to obtain triangulations on curved manifolds. Our numerical results show that even a linear elastic cell–cell interaction model may induce a global non-linear response due to the reorganisation of the cell connectivity. This plastic-like behaviour is combined with a non-linear rheological law where the resting length depends on the elastic strain, mimicking the global visco-elastic response of tissues. The model is applied to simulate the elongation of planar and curved monolayers.

  Abstract
  This paper presents a cell-centred model for the simulation of planar and curved multicellular soft tissues. We propose a computational model that includes stress relaxation [...]

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• Forces driving epithelial wound healing

  A. Brugués, E. Anon, V. Conte, J. Veldhuis, M. Gupta, J. Colombelli, J. Muñoz, G. Brodland, B. Ladoux, X. Trepat

  Natura Physics (2014). Vol. 10 (9), pp. 683-690 (Preprint)

  
  

  Abstract

  A fundamental feature of multicellular organisms is their ability to self-repair wounds through the movement of epithelial cells into the damaged area. This collective cellular movement is commonly attributed to a combination of cell crawling and ‘purse-string’ contraction of a supracellular actomyosin ring. Here we show by direct experimental measurement that these two mechanisms are insufficient to explain force patterns observed during wound closure. At early stages of the process, leading actin protrusions generate traction forces that point away from the wound, showing that wound closure is initially driven by cell crawling. At later stages, we observed unanticipated patterns of traction forces pointing towards the wound. Such patterns have strong force components that are both radial and tangential to the wound. We show that these force components arise from tensions transmitted by a heterogeneous actomyosin ring to the underlying substrate through focal adhesions. The structural and mechanical organization reported here provides cells with a mechanism to close the wound by cooperatively compressing the underlying substrate.

  Abstract
  A fundamental feature of multicellular organisms is their ability to self-repair wounds through the movement of epithelial cells into the damaged area. This collective cellular [...]

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• A truss element for modelling reversible softening in living tissues

  J. Muñoz, V. Conte, N. Asadipour, M. Miodownik

  Mechanics Research Communications (2013). Vol. 49, pp. 44-49 (Preprint)

  
  

  Abstract

  We resort to non-linear viscoelasticity to develop a truss element able to model reversible softening in lung epithelial tissues undergoing transient stretch. Such a Maxwell truss element is built by resorting to a three-noded element whose mid-node is kinematically constrained to remain on the line connecting the end-nodes. The whole mechanical system undergoes an additive decomposition of the strains along the truss direction where the total contribution of the mid-node is accounted for by using a null-space projection and static condensation techniques. Assembling of such line-elements in 3D networks allows us to model extended regions of living tissues as well as their anisotropies.

  Abstract
  We resort to non-linear viscoelasticity to develop a truss element able to model reversible softening in lung epithelial tissues undergoing transient stretch. Such a Maxwell [...]

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• Modelling of mixed damage on fibre reinforced composite laminates subjected to low velocity impact

  J. Curiel, S. Phaneendra, J. Muñoz

  International journal of damage mechanics (2013). Vol. 22 (3), pp. 356-374 (Preprint)

  
  

  Abstract

  This article presents a numerical technique for the computation of damage in fibre-reinforced laminated composites which is embedded into an explicit finite element method. The technique is composed of two main components. First, a novel characterisation of the directions in which the various modes of damage propagate, which produces an effective damage localisation. This is conducted taking into consideration the strain-rate dependence. Second, a new mapping between the strain and stress spaces for the computation of the damage surfaces whereby time-stepping convergence is enhanced. Additionally, new damage initiation criteria in terms of strain damage surfaces are presented. Details of the in-house code developed are presented as well as the programming features. The capabilities of the technique are shown by means of tests on single fibre-reinforced element and low velocity impact on the laminate. It is shown that delamination is located in the expected regions by gradual progression of internal damage variables.

  Abstract
  This article presents a numerical technique for the computation of damage in fibre-reinforced laminated composites which is embedded into an explicit finite element method. [...]

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• Physiology-based model of cell viscoelasticity

  J. Muñoz, S. Albo

  Physical review E: statistical, nonlinear and soft matter physics (2013). Vol. 88 (1), pp. 1-8 (Preprint)

  
  

  Abstract

  The measured viscoelastic properties of biological tissues is the result of the passive and active response of the cells. We propose an evolution law of the remodeling process in the cytoskeleton which is able to mimic the viscous properties of biological cellular tissues. Our model is based on dynamical changes of the resting length. We show that under the small strain regime, the linear rheology models are recovered, with the relaxation time being replaced by the cell resistance to remodel. We implement the one-dimensional model into network systems of two and three dimensions, and show that the same conclusions may be drawn for those systems.

  Abstract
  The measured viscoelastic properties of biological tissues is the result of the passive and active response of the cells. We propose an evolution law of the remodeling process [...]

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• A biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo

  V. Conte, F. Ulrich, B. Baum, J. Muñoz, J. Veldhuis, W. Brodland, M. Miodownik

  PloS One (2012). Vol. 7 (4), pp. 1-17

  
  

  Abstract

  The article provides a biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo. Ventral furrow formation is the first large-scale morphogenetic movement in the fly embryo. It involves deformation of a uniform cellular monolayer formed following cellularisation, and has therefore long been used as a simple system in which to explore the role of mechanics in force generation. Here we use a quantitative framework to carry out a systematic perturbation analysis to determine the role of each of the active forces observed. The analysis confirms that ventral furrow invagination arises from a combination of apical constriction and apical–basal shortening forces in the mesoderm, together with a combination of ectodermal forces. We show that the mesodermal forces are crucial for invagination: the loss of apical constriction leads to a loss of the furrow, while the mesodermal radial shortening forces are the primary cause of the internalisation of the future mesoderm as the furrow rises. Ectodermal forces play a minor but significant role in furrow formation: without ectodermal forces the furrow is slower to form, does not close properly and has an aberrant morphology. Nevertheless, despite changes in the active mesodermal and ectodermal forces lead to changes in the timing and extent of furrow, invagination is eventually achieved in most cases, implying that the system is robust to perturbation and therefore over-determined.

  Abstract
  The article provides a biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo. Ventral furrow formation is the first large-scale [...]

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