Modeling growth in biological materials

The biomechanical modeling of growing tissues has recently become an area of intense interest. In particular, the interplay between growth patterns and mechanical stress is of great importance, with possible applications to arterial mechanics, embryo morphogenesis, tumor development, and bone remodeling. This review aims to give an overview of the theories that have been used to model these phenomena, categorized according to whether the tissue is considered as a continuum object or a collection of cells. Among the continuum models discussed is the deformation gradient decomposition method, which allows a residual stress field to develop from an incompatible growth field. The cell-based models are further subdivided into cellular automata, center-dynamics, and vertex-dynamics models. Of these the second two are considered in more detail, especially with regard to their treatment of cell-cell interactions and cell division. The review concludes by assessing the prospects for reconciliation between these two fundamentally different approaches to tissue growth, and by identifying possible avenues for further research. © 2012 Society for Industrial and Applied Mathematics

Methods for Structural Pattern Recognition: Complexity and Applications

Katedra kybernetik

Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

International audienc

Hybrid cell-centred/vertex model for multicellular systems

This thesis presents a hybrid vertex/cell-centred approach to mechanically simulate planar cellular monolayers undergoing cell reorganisation. Cell centres are represented by a triangular nodal network, while the cell boundaries are formed by an associated vertex network. The two networks are coupled through a kinematic constraint which we allow to relax progressively. Cell-cell connectivity changes due to cell reorganisation or remodelling events, are accentuated. These situations are handled by using a variable resting length and applying an Equilibrium-Preserving Mapping (EPM) on the new connectivity, which computes a new set of resting lengths that preserve nodal and vertex equilibrium. As a by-product, the proposed technique enables to recover fully vertex or fully cell-centred models in a seamless manner by modifying a numerical parameter of the model. The properties of the model are illustrated by simulating monolayers subjected to imposed extension and during a wound healing process. The evolution of forces and the EPM are analysed during the remodelling events.Esta tesis presenta un modelo híbrido para la simulación mecánica de monocapas celulares. Este modelo combina métodos de vértices y centrados en la célula, y está orientado al análisis de deformaciones con reorganización celular. Los núcleos vienen representados por nodos que forman una malla triangular, mientras que las contornos (membranas y córtex) forman una malla poligonal de vértices. Las dos mallas se acoplan a través de una restricción cinemática que puede ser relajada de forma controlada. El estudio hace especial hincapié en los cambios de conectividad, tanto debidos a la reorganización celular como el remodelado del citoesqueleto. Estas situaciones se abordan a través de una longitud de referencia variable y aplicando un Mapeo con Conservación de Equilibrio (EPM) que minimiza el error en el equilibrio nodal y en los vértices. La técnica resultante puede ser adaptada progresivamente a través de un parámetro, dando lugar a un modelo exclusivamente de vértices o a uno de centros. Sus propiedades se ilustran en simulaciones de monocapas sujetas a una extensión impuesta y durante el proceso de cicatrizado de heridas. La evolución de las fuerzas y los efectos del EPM durante el remodelado se analizan en estos ejemplos

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

Applications of nonlinear dynamics to information processing

The reported results are direct applications of nonlinear dynamics to information processing or are relevant for the applications. In the second chapter we describe a simple method for estimating the embedding dimension that can be used as a first step in constructing nonlinear models. The method for the reduction of measurement noise in chaotic systems that is presented in the third chapter is attractive in the cases where high accuracy is necessary. Next we propose how to overcome some problems encountered in constructing models of complex nonlinear systems. Finally, the behaviour of one-dimensional cellular automata useful for the detection of velocities of patterns is shown and explained in the last chapter. The method of estimating the embedding dimension is based on the idea that when the observed dynamical system is deterministic and smooth and the embedding dimension is correctly chosen, the relationship between the successive reconstructed state vectors should be described as a continuous mapping. To check if the given embedding dimension is a good one we search for pairs of state vectors whose distance is smaller than some number. For each pair we compute the distance between the successors of the elements of pairs and represent this distance graphically. When the embedding dimension is equal or larger than the minimum correct dimension, all distances are small in comparison to distances for incorrect dimensions. The method for noise reduction is developed assuming that the map of the system is known and the noise is bounded. The closer the initial condition is to the true state of the system, the longer the computed trajectory follows the observed trajectory. To reduce the uncertainty in knowing the given state we recursively search for the state for which the computed trajectory follows the observed trajectory as long as possible. The method is demonstrated on several twodimensional invertible and noninvertible chaotic maps. When the map is known exactly an arbitrary level of noise reduction can be achieved. With the increase of the complexity of a nonlinear system it is harder to construct its model. We propose to discover first how to construct a model of a similar but simple system. Discovered heuristics can be useful in modeling more complex systems. We demonstrate the approach by constructing a deterministic feed-forward neural network that can extract velocities of onedimensional patterns. Analysing simpler models we discovered how to estimate the necessary numbers of neurons; what are the useful ranges of the parameters of the network and what are the potential functional dependencies between the parameters. The class of one-dimensional cellular automata whose state is a function of both the previous state and a time-dependant input is described. As inputs we considered the sequences of binary strings that represent black-and-white objects moving in front of a white background. As outputs we considered the trajectory of the automaton. For some rules the automaton will evolve to the zero state for all velocities of the object except for the velocities in specific narrow range. The phenomenon is persistent even when a strong noise is present in input patterns but unreliable units of the automaton or having a more complex input break it down

Physical crowds and psychological crowds: applying self-categorization theory to computer simulation of collective behaviour

Computer models are used to simulate pedestrian behaviour for safety at mass events. Previous research has indicated differences between physical crowds of co-present individuals, and psychological crowds who mobilise collective behaviour through a shared social identity. This thesis aimed to examine the assumptions models use about crowds, conduct two studies of crowd movement to ascertain the behavioural signatures of psychological crowds, and implement these into a theoretically-driven model of crowd behaviour. A systematic review of crowd modelling literature is presented which explores the assumptions about crowd behaviour being used in current models. This review demonstrates that models portray the crowd as either an identical mass with no inter-personal connections, unique individuals with no connections to others, or as small groups within a crowd. Thus, no models have incorporated the role of self-categorisation theory needed to simulate collective behaviour. The empirical research in this thesis aimed to determine the behavioural effects of self-categorisation on pedestrian movement. Findings from a first study illustrate that, in comparison to a physical crowd, perception of shared social identities in the psychological crowd motivated participants to maintain close proximity with ingroup members through regulation of their speed and distance walked. A second study showed that collective self-organisation seemed to be increased by the presence of an outgroup, causing ingroup members to tighten formation to avoid splitting up. Finally, a computer model is presented which implements the quantified behavioural effects of self-categorisation found in the behavioural studies. A self-categorisation parameter is introduced to simulate ingroup members self-organising to remain together. This is compared to a physical crowd simulation with group identities absent. The results demonstrate that the self-categorisation parameter provides more accurate simulation of psychological crowd behaviour. Thus, it is argued that models should implement self-categorisation into simulations of psychological crowds to increase safety at mass events

Microstructure modeling and crystal plasticity parameter identification for predicting the cyclic mechanical behavior of polycrystalline metals

Computational homogenization permits to capture the influence of the microstructure on the cyclic mechanical behavior of polycrystalline metals. In this work we investigate methods to compute Laguerre tessellations as computational cells of polycrystalline microstructures, propose a new method to assign crystallographic orientations to the Laguerre cells and use Bayesian optimization to find suitable parameters for the underlying micromechanical model from macroscopic experiments