1,721,269 research outputs found
The role of anisotropy and fiber dispersion in the mechanics and remodeling of biological tissues
Full text linkIn many soft biological tissues mechanical strength and anisotropy are determined primarily by the presence of fibers, in particular collagen. When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is always negative. However, in fiber reinforced materials the transverse principal strain can change its sign as the load increases, passing through the zero-points, known as perversions. We investigate how the number of perversions in a material reinforced by two symmetrically aligned families of distributed fibers depends both on the degree of fiber dispersion and the model used for fiber dispersion. Angular integration and three variants of the generalized structure tensor approach are considered and discussed. The study of perversions clearly demonstrates the qualitative difference between these approaches in the case of high dispersion of fibers. The results suggest that this difference is primarily due to the way compressive fibers are modeled. Fiber alignment in biological tissues is created and maintained by the cells, which respond to mechanical stimuli arising from properties of the surrounding material. This coupling between mechanical anisotropy and tissue remodeling can be modeled in nonlinear elasticity by a fiber-reinforced hyperelastic material where remodeling is represented as the change in fiber orientation. We study analytically a simple model of fiber reorientation in a rectangular elastic tissue reinforced by two symmetrically arranged families of fibers subject to constant external loads. In this model, the fiber direction tends to align with the maximum principal stretch or strain. We characterize the global behaviour of the system for all material parameters and applied loads, and show that provided the fibers are tensile initially, the system converges to a stable equilibrium, which corresponds to either complete or intermediate fiber alignment. Finally, we consider a model for the coupled growth and fiber reorientation in an elastic incompressible disk. The dynamics of our model is extremely sensitive to the initial condition and characterized by an infinite number of equilibrium states of fiber arrangement. We observed that the stress-induced fiber reorientation and growth laws used in our model produce specific fiber orientation pattern, which suggest a possible mechanism for self-organisation
Theory for Durotactic Axon Guidance.
Full text linkDuring the development of the nervous system, neurons extend bundles of axons that grow and meet other neurons to form the neuronal network. Robust guidance mechanisms are needed for these bundles to migrate and reach their functional target. Directional information depends on external cues such as chemical or mechanical gradients. Unlike chemotaxis that has been extensively studied, the role and mechanism of durotaxis, the directed response to variations in substrate rigidity, remain unclear. We model bundle migration and guidance by rigidity gradients by using the theory of morphoelastic rods. We show that, at a rigidity interface, the motion of axon bundles follows a simple behavior analogous to optic ray theory and obeys Snell's law for refraction and reflection. We use this powerful analogy to demonstrate that axons can be guided by the equivalent of optical lenses and fibers created by regions of different stiffnesses
Cooperative melting in double-stranded peptide chains through local mechanical interactions
Full text linkThe separation of double-stranded peptide chains can occur in two ways: cooperatively or non-cooperatively. These two regimes can be driven either by chemical or thermal effects, or through non-local mechanical interactions. Here, we show explicitly that local mechanical interactions in biological systems may regulate the stability, the reversibility, and the cooperative/non-cooperative character of the debonding transition. We show that this transition is characterized by a single parameter depending on an internal length scale. Our theory describes a wide range of melting transitions found in biological systems such as protein secondary structures, microtubules and tau proteins, and DNA molecules. In these cases, the theory gives the critical force as a function of the chain length and its elastic properties. Our theoretical results provide quantitative predictions for known experimental effects that appear in different biological and biomedical fields
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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Perversions and whips: Static and dynamic problems of elastic filaments
No full textTwo problems of elastic filaments are considered, one a problem of determining the static shape of a filament with intrinsic curvature tinder constant force, and one a problem of determining the dynamical behavior of a planar rod. In the first problem, examining the phenomenon of perversion, methods of dynamical systems are used to examine the static equations of elastic filaments, in which the arc-length of the filament plays the role of time. The phenomenon of perversion, in which two oppositely handed helices are connected by an inversion of chirality, is represented by a heteroclinic orbit of the dynamical system. The second problem is an examination of a whip wave, the propagation of a loop in a whip as it travels the length of the whip to create a sharp crack as the loop reaches the end of the rod and accelerates to supersonic speeds. This study is undertaken in two stages: first we examine the propagation of the loop as it travels down the rod far from the end of the rod, and then we examine the behavior of the rod as the loop reaches the end of the rod and unfolds, accelerating the tip. In the first stage we use techniques of asymptotic analysis and perturbation methods to determine the relationship of the speed of the loop to the radius of the rod. In the second stage we employ a numerical technique to compute the behavior of the loop as it unfolds to determine the relationship of the maximal speed of the tip of the rod to the characteristics of the rod and the forces applied to the handle
Tauopathy staging dynamics of neurodegenerative disease on network-organised reaction-diffusion
Full text linkNeurodegenerative diseases are a group of incurable disorders that are
identified by the progressive loss of cognitive function and degeneration
of the nervous system. Disorders such as Alzheimer’s disease show a systematical progression of the disease’s biological markers. A key finding
in Alzheimer’s disease is the hierarchical accumulation of toxic proteins
which leads to a disease staging identification called staging. Many studies
have used mathematical and computational models to explore the transport of toxic proteins. In this thesis, we investigate mathematical network
models based on the prion-like hypothesis coupled with a linear transport
principle to understand key features of the dynamics and extract information about toxic tau propagation. We consider three key problems. We
use the Fisher-Kolmogorov-Petrovsky-Piskunov equation as a paradigm
for the dynamics. First, we examine a model selection. We introduce a
novel approach, based on braid diagrams, for studying the structured progression of tau protein evolving on a network. Second, we extract arrival
time estimates for the dynamics. We present and compare three different estimates for the arrival time: (a) the linear arrival time obtained
by linearizing the underlying system, (b) the Lambert time obtained by
considering the interaction of two nodes, and (c) the nonlinear arrival
time obtained by asymptotic techniques. Finally, we examine the role
of brain regional heterogeneity and consider directed networks based on
asymmetric brain connectivities. We study staging and arrival time for
both heterogeneous and directed network systems. Overall, this study on
tau protein propagation on networks with respect to staging and time of
arrival provides new tools to investigate systematically the spatiotemporal
evolution of toxic tau protein in the brain
Self-assembly in mechanical systems
Full text linkInspired by biological membrane shaping in the cell through means of curvature-inducing proteins, we investigate the interplay between membrane curvature and the distribution and movement of shape-inducing objects which are free to move as a consequence of the underlying shape. We initially study the self-assembly of a filament, taken as a proxy for the cross-section of a biomembrane, which is primarily driven by the chemical kinetics of attaching proteins and find that, under certain mechanical stiffness regimes of the attaching proteins, pattern formation occurs. Regions of high and low protein concentration form before spatially uniform filament shapes are obtained by means of protein adhesion and movement governed by diffusion and local curvature-seeking. However, noting that the curvature-mediated protein movement on membranes has been biologically observed to be long-range, we next study the self-assembly of embedded inclusions on a membrane as a result of the underlying geometry. We first derive an interaction law for the shape-mediated interaction of inclusions which break symmetry and find that there is a finite equilibrium distance to which the inclusions will aggregate. We derive corresponding equations of motion which describe this curvature-mediated aggregation mechanism and, using this framework, we investigate some of the properties of these self-assembled configurations, including their energy, stability, and their collective elastic behavior. Lastly, we consider the interaction energies of embedded inclusions on a periodic domain and determine that this mechanism may explain computational results of how proteins form rings to promote tubulation on cylindrical membranes.</p
Mathematical modelling of clearance and proteopathy in neurodegenerative diseases with application to Alzheimer’s disease
No full textFew subjects in the history of biomedicine have captivated the scientific and lay communities alike as profoundly as Alzheimer’s disease (AD), yet there are many open questions concerning its fundamental disease dynamics. Characterised by a systematic progression of biological markers, natural questions arise surrounding the exact mechanisms driving the spatiotemporally distinctive cascade of misfolded proteins in the Alzheimer’s brain. Solutions to these questions can elucidate mechanisms for targeted treatment. Motivated by experimental observations, network models of neurodegeneration provide a powerful tool to uncover mechanistic relationships, deeply explore biophysical hypotheses gripping the clinical community, and conduct in silico experimentation in man. Most urgently, the clinical com- munity increasingly suggest the fundamental importance of the brain’s clearance mechanisms in neurodegeneration. In response, our research addresses the potential driving factors of AD and how they interact, with the overarching theme of mathematically quantifying the role of clearance in neurodegeneration.
Part I of the thesis delivers the first theoretical model of coupled brain clearance and proteopathy. The resulting network reaction-diffusion system yields analytical insights into the connection between proteopathic spreading and clearance. Further, our computational approach on high-resolution brain graphs constructed from the data of 426 patients generates valuable simulations of 40 years of AD progression in less than 14 seconds of computational time, demonstrating numerically the underlying dynamics of neurodegeneration. Striking observations include regional brain clearance not only dictating the equilibrium of a healthy or unhealthy brain, but also shaping the trajectory and timescales of neurodegeneration. Part II subsequently bridges the gap between glymphatic clearance hypotheses and AD progression through multi-modal MRI regression to extract patient-specific heterogeneous clearance distributions across the connectome and the resulting downstream pathology. Finally, in Part III, we advance in vitro chemical kinetic models to account for physiological phenomena at the brain scale, thus capturing varying toxicity, transport and clearance dynamics across the aggregate size spectrum. Crucially, this extension allows the spatiotemporal upscaling of the analysis and simulation of monoclonal antibodies, notably revealing that the success of treatments fundamentally hinges on their nuanced relationship with clearance dynamics.
Alzheimer’s research is changing, and mathematics provides a critical bridge from experimental observations and clinical hypotheses, to analytical relationships and computational simulation, to a deep understanding of the underlying physio- logical mechanisms and implementation of mathematically-informed intervention in humans. In this context, the findings of our work provide a theoretical framework for a growing body of medical research showing the vital role of clearance in the aetiology and progression of neurodegeneration, identifying clearance as a potentially powerful therapeutic target
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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