Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable

Dynamic micro-3D-printed substrates for characterizing cellular responses to topography

textCell cultures provide researchers the opportunity to observe cell behavior in response to specific, well-defined environmental cues, leading to insights that enable better engineering design for tissue culture and other biomedical applications. Chemical and electrical stimuli have been successfully applied to cultured cells to approximate aspects of the dynamic conditions experienced in vivo. However, in vitro topographical cues have mostly been limited to static substrates that do not subject cells to the dynamic conditions they experience in vivo when tissue remodels during development and wound healing. Delivering dynamic topographical cues to cultured cells can answer long-standing questions about mechanisms of cell morphology changes. Such capabilities could also facilitate engineering of wound-healing matrices and nerve guidance conduits by promoting migration of cells and providing directional guidance to cellular processes. This dissertation describes the development of approaches for introducing in situ topographical cues to cell cultures and inducing responses such as neurite guidance and cell alignment. Both strategies undertaken in this work make use of multiphoton-promoted photochemistry to print and manipulate three-dimensional microscopic protein hydrogel structures. In one approach, a technique referred to as micro-3D printing, topographical guidance cues are printed in the proximity of cultured cells to guide the growth of cellular processes. By translating a tightly-focused pulsed laser beam through a printing reagent solution flooding cultured cells, features are printed that provide physical guidance to extending neurites from NG108-15 cells, a neuronal model cell type. In another approach, an innovative technique known as micro-3D imprinting is developed for producing micrometer-scale depressions on the surfaces of photoresponsive protein hydrogels. The impact of various experimental parameters on topographical feature dimensions is characterized. Micro-3D imprinting is used to introduce dynamic topographical changes on a cell culture substrate, demonstrating that NIH-3T3 cells, a fibroblast cell model, alter their morphology and alignment in response to the introduction of a grooved surface topography. This set of approaches introduces new tools to the repertoire of cell biologists for exploring the behavior of cells growing in a spatio-temporally dynamic environment, opening possibilities for studies of cellular behavior in conditions that may better reflect environments cells experience in vivo.Biomedical Engineerin

Contact inhibition of growth described using a multiphase model and an individual cell-based model

In this work the phenomenon of contact inhibition of growth is studied by applying an individual based model and a continuum multiphase model to describe cell colony growth in vitro. The impact of different cell behavior in response to mechanical cues is investigated. The work aims at comparing the results from both models from the qualitative and, whenever possible, also the quantitative point of view

Modeling and simulation of multi-cellular systems using hybrid FEM/Agent-based approaches

Muchas de las propiedades biomecánicas de los organismos multicelulares surgen directamente de las interacciones entre células. Las células de los órganos y tejidos interactúan entre sí y con su entorno de diferentes formas. Debido a este hecho, es fundamental analizar cómo estas interacciones se traducen como propiedades mecánicas a nivel del tejido. Por ejemplo, las adhesiones entre células determinan la rigidez aparente de una capa epitelial. Las interacciones célula-matriz pueden además determinar la formación de muchas estructuras biológicas y su morfología. Estos sistemas multicelulares no se pueden considerar como estructuras estáticas ya que sufren constantes cambios causados por la proliferación, la reorganización o la migración celular. Por lo tanto, es necesario estudiar la dinámica de la célula y las interacciones individuales para comprender plenamente cómo funcionan los fenómenos a escalas superiores, desde el desarrollo de tejidos hasta el crecimiento de tumores.Recientemente, el uso de enfoques basados en agentes se ha vuelto muy popular para modelar sistemas multicelulares. Los modelos basados en agentes representan células como entidades individuales. Estos modelos son especialmente adecuados para estudiar fenómenos biofísicos que ocurren a nivel celular. Aquí las interacciones célula-célula se pueden simular directamente de forma mecanicista. Además, estos modelos capturan realmente bien las heterogeneidades presentes en las estructuras biológicas. Por otra parte, los modelos continuos se utilizan comúnmente en problemas de escalas mayores. A diferencia de los modelos basados en agentes, en estos no representan células como entidades individuales, sino que se definen leyes constitutivas para modelar procesos biológicos, físicos y químicos. Por lo tanto, las propiedades celulares se promedian usando parámetros macroscópicos, y estos modelos a menudo trabajan con la densidad celular en lugar de entidades celulares separadas. En cualquier caso, los modelos continuos presentan una buena escalabilidad y una excelente representación de fenómenos físicos particulares como el transporte masivo y las transmisiones de fuerza en medios continuos.En esta tesis, se exploran las posibilidades que los enfoques híbridos pueden ofrecer para desarrollar nuevos modelos de sistemas multicelulares. Se presentan dos modelos híbridos diferentes que combinan un modelo basado en agentes y un modelo continuo. Ambos enfoques tienen en común que el modelo continuo se resuelve utilizando el método de los elementos finitos. También se muestra, siguiendo este patrón de diseño, cómo resolver varias de las limitaciones intrínsecas de cada tipo individual de modelo.En primer lugar, se presenta un modelo híbrido para simular la mecánica epitelial monocapa. Este modelo se centra en el modelado de las interacciones mecánicas célula-célula y célula-sustrato, pero también en la topología y morfología de los tejidos. Con este enfoque se reproducen tejidos epiteliales proliferativos, movimientos celular colectivo y procesos de migración. El segundo modelo presentado en esta tesis se ha diseñado para simular agregados celulares en entornos tridimensionales. Se estudian las interacciones mecánicas entre células, pero este modelo se centra especialmente en analizar cómo afecta el transporte de oxígeno a las células en un proceso de agrupamiento en 3D.Finalmente, se comparan los resultados de ambos modelos con datos experimentales de otros autores y se discuten los beneficios de combinar diferentes tipos de modelos. Se demuestra que los enfoques híbridos que se proponen en este trabajo son capaces de simular una amplia variedad de sistemas multicelulares. De hecho, son particularmente útiles para estudiar cómo algunos fenómenos emergen de las interacciones celulares individuales a escalas biológicas más grandes.<br /

Simulating tissue mechanics with Agent Based Models: concepts and perspectives

International audienceIn this paper we present an overview of agent based models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings and capabilities of the major agent based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results

Mathematical modeling of avascular tumor growth

Cancer is an extremely complex disease, both in terms of its causes and consequences to the body. Cancer cells acquire the ability to proliferate without control, invade the surrounding tissues and eventually form metastases. It is becoming increasingly clear that a description of tumors that is uniquely based on molecular biology is not enough to understand thoroughly this illness. Quantitative sciences, such as physics, mathematics and engineering, can provide a valuable contribution to this field, suggesting new ways to examine the growth of the tumor and to investigate its interaction with the neighboring environment. In this dissertation, we deal with mathematical models for avascular tumor growth. We evaluate the effects of physiological parameters on tumor development, with a particular focus on the mechanical response of the tissue. We start from tumor spheroids, an effective three-dimensional cell culture, to investigate the first stages of tumor growth. These cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the mechanical stress are formulated on the basis of experimental observations. The growth curves of the model are compared to the experimental data, with good agreement for the different experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is also presented. Then, we perform a parametric analysis to identify the key parameters that drive the system response. We conclude this part by introducing governing equations for transport and uptake of a chemotherapeutic agent, designed to target cell proliferation. In particular, we investigate the combined effect of compressive stresses and drug action. Interestingly, we find that variation in tumor spheroid volume, due to the presence of a drug targeting cell proliferation, depends considerably on the compressive stress level of the cell aggregate. In the second part of the dissertation, we study a constitutive law describing the mechanical response of biological tissues. We introduce this relation in a biphasic model for tumor growth based on the mechanics of fluid-saturated porous media. The internal reorganization of the tissue in response to mechanical and chemical stimuli is described by enforcing the multiplicative decomposition of the deformation gradient tensor associated with the solid phase motion. In this way, we are able to distinguish the contributions of growth, rearrangement of cellular bonds, and elastic distortion, occurring during tumor evolution. Results are presented for a benchmark case and for three biological configurations. We analyze the dependence of tumor development on the mechanical environment, with particular focus on cell reorganization and its role in stress relaxation. Finally, we conclude with a summary of the results and with a discussion of possible future extensions