1,720,968 research outputs found
Cell orientation under stretch: Stability of a linear viscoelastic model
Full text linkThe sensitivity of cells to alterations in the microenvironment and in particular to external mechanical stimuli is significant in many biological and physiological circumstances. In this regard, experimental assays demonstrated that, when a monolayer of cells cultured on an elastic substrate is subject to an external cyclic stretch with a sufficiently high frequency, a reorganization of actin stress fibres and focal adhesions happens in order to reach a stable equilibrium orientation, characterized by a precise angle between the cell major axis and the largest strain direction. To examine the frequency effect on the orientation dynamics, we propose a linear viscoelastic model that describes the coupled evolution of the cellular stress and the orientation angle. We find that cell orientation oscillates tending to an angle that is predicted by the minimization of a very general orthotropic elastic energy, as confirmed by a bifurcation analysis. Moreover, simulations show that the speed of convergence towards the predicted equilibrium orientation presents a changeover related to the viscous–elastic transition for viscoelastic materials. In particular, when the imposed oscillation period is lower than the characteristic turnover rate of the cytoskeleton and of adhesion molecules such as integrins, reorientation is significantly faster
Foreword to the Special Issue in honour of Prof. Luigi Preziosi “Nonlinear mechanics: The driving force of modern applied and industrial mathematics”
Full text linkMathematical modelling is a discipline pledged to identify problems, which may arise from virtually any branch of the human knowledge, and formalise them in the language of mathematics by developing suitable methodologies of investigation. To pursue its goals, modelling must build connections with other mathematical sciences and, in particular, with numerics. Three major examples of the efficiency of such combination are industrial mathematics, mathematical biology and biomechanics. At first sight, industrial mathematics is a branch of applied mathematics focusing on problems that come from industry and it aims at determining solutions relevant to manufacturing. Some relevant examples are petroleum engineering, hydrogeology, and the description of sand dynamics in the neighbourhood of railways in desert zones. On the other hand, the adoption of mathematics to formalise problems of biological relevance has attracted scientists working on population dynamics, epidemiology and related fields. Moreover, a strong impact has been given by the combination of modelling with the mechanics of biological tissues, thereby giving rise to biomechanics. Few examples in this respect are the mechanics of cell motion and migration, which relate to kinetic theories, the mechanics of the interactions between cells and the extracellular matrix, the conversion of mechanical signals into chemical stimuli, and "mathematical oncology". Since it is not possible to present a theoretical corpus of all that, the aim of the present special issue is to put together a list of outstanding scientific papers giving clear connections among nonlinear mechanics, industrial mathematics, biomathematics, biomechanics and kinetic theories, in different fields of interest. This special issue of IJNLM is the Festschrift celebrating the 60th birthday of Luigi Preziosi, whose research is a recognised example of how mechanics may be the fuel for interesting applied mathematics
Mechanics-Based Models to Predict the Alignment of Cells on a Cyclically Stretched Substrate
Full text linkAs pointed out by numerous experiments, the cell cytoskeleton appears to be responsive to external mechanical stimuli. In particular, experimental evidence demonstrates that a population of cells adhering to a substrate which is deformed periodically, for instance to mimic the heartbeat, responds to the strain by reorienting their stress fibres and focal adhesions. At the end of such a process, the cell achieves a specific orientation with respect to the strain direction, and such orientation depends on the characteristics of the external strain. The increasing interest in understanding mechanotransduction phenomena led to a growing attention to the cell realignment behaviour, both from the experimental and from the modelling point of view. Indeed, the contribution of mathematical models turns out to be very important to elucidate some relevant mechanisms and to suggest possible improvements in experimental assays. In this Chapter, we present an overview of mechanics-based mathematical models that have been proposed to describe cell reorientation and we highlight connections among the different research contributions within this field
Effective interface conditions for continuum mechanical models describing the invasion of multiple cell populations through thin membranes
Full text linkWe consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the membranes, is then reduced to a limiting transmission problem whereby each thin membrane is replaced by an effective interface. In order to close the limiting problem, a set of biophysically-consistent transmission conditions is derived through a formal asymptotic method. Models based on such a limiting transmission problem may find fruitful application in a variety of research areas in the biological and medical sciences, including developmental biology, immunology and cancer growth and invasion
An Imaging-Informed Mechanical Framework to Provide a Quantitative Description of Brain Tumour Growth and the Subsequent Deformation of White Matter Tracts
Full text linkCoupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model
Full text linkBrain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth
A computational framework for the personalized clinical treatment of glioblastoma multiforme
No full textIn this work, we develop a computational tool to predict the patient-specific evolution of a highly malignant brain tumour, the glioblastoma multiforme (GBM), and its response to therapy. A diffuse-interface mathematical model based on mixture theory is fed by clinical neuroimaging data that provide the anatomical and microstructural characteristics of the patient brain. The model is numerically solved using the finite element method, on the basis of suitable numerical techniques to deal with the resulting Cahn-Hilliard type equation with degenerate mobility and single-well potential. The results of simulations performed on the real geometry of a patient brain quantitatively show how the tumour expansion dependens on the local tissue structure. We also report the results of a sensitivity analysis concerning the effects of the different therapeutic strategies employed in the clinical Stupp protocol. The simulated results are in qualitative agreement with the observed evolution of GBM during growth, recurrence and response to treatment. Taken as a proof-of-concept, these results open the way to a novel personalized approach of mathematical tools in clinical oncology
An optimization based 3D-1D coupling strategy for tissue perfusion and chemical transport during tumor-induced angiogenesis
Full text linkThe application of an optimization based 3D-1D coupling strategy is proposed, for the first time, for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. A well posed mathematical model is worked out, based on the coupling between a three-dimensional and a one-dimensional equation (3D-1D coupled problem). The problems are then solved in a PDE-constrained optimization framework, under which no mesh conformity is required.
This makes the method particularly suitable for this kind of application, since no remeshing is required as the capillary network grows. In order to handle both the evolution of the quantities of interest and the changes in the geometry, a discrete-hybrid strategy is adopted, combining a continuous modeling of the tissue and of the chemicals with a discrete tip-tracking model to account for the vascular network growth. The tip-tracking strategy, together with some proper rules for branching and anastomosis, is able to provide a realistic representation of the capillary networ
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