936 research outputs found
Multiphysics/multiscale modeling and applications of coupled processes in biological and nanotechnological systems
No full text
On the Benard problem
No full textIn literature there is no mathematical proof of the experimentally trivial stability of the
rest state for a layer of compressible fluid heated from above. In the case of layer heated
from below it is known that the system shows a threshold in the temperature gradient below
which the fluid is not sensible to the imposed difference of temperature. Only semi empirical
justifications are available for this phenomenon, see [6].
Neglecting the thermal conductivity, we are able to prove that for a layer of compressible
fluid between two rigid planes kept at constant temperature, the rest state is linearly stable
for every values of the parameters involved in two cases: a) the layer is heated from above (see
section 3); b) the layer is heated from below and the gradient of temperature imposed is less
then a precise quantity, namely g=cp, where g is the gravity constant, and cp is the specific
heat at constant pressure, known as adiabatic gradient , the same that we find in Jeffreys’
pap
Role of ocular perfusion pressure in glaucoma: the issue of multicollinearity in statistical regression models
No full textA Stabilized Dual Mixed Hybrid Finite Element Method with Lagrange Multipliers for Three-Dimensional Elliptic Problems with Internal Interfaces
No full textThis work studies an elliptic boundary value problem with diffusive, advective and reactive terms, in a three-dimensional domain composed of two media separated by a selective interface. For the numerical approximation of the problem we propose a novel approach that combines, for the first time: (1) a dual mixed hybrid (DMH) finite element method (FEM) based on the lowest order Raviart-Thomas space (RT0); (2) a Three-Field formulation; and (3) a Streamline Upwind/Petrov-Galerkin (SUPG) stabilization method. After proving that the weak formulation of the proposed method and its numerical counterpart are both uniquely solvable and that the finite element scheme enjoys optimal convergence properties with respect to the discretization parameter, we present an efficient implementation based on static condensation, which reduces the method to a nonconforming finite element approach on a grid made by three-dimensional simplices. Extensive computational tests indicate that: (1) the theoretical convergence properties are verified; (2) the DMH-RT0 FEM is accurate and stable even in the presence of marked interface jump discontinuities in the solution and its associated normal flux; and (3) in the case of strongly dominating advective terms, the SUPG stabilization resolves accurately steep boundary and/or interior layers without introducing spurious unphysical oscillations or excessive smearing of the solution front
The role of structural viscoelasticity in deformable porous media with incompressible constituents: Applications in biomechanics
No full textThe main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue sca olds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the uid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer's disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine
Thermodynamic derivation of a non-linear poroelastic model describing hemodynamics-mechanics interplay in the lamina cribrosa
No full textIn this paper we formulate a poroelastic model starting from a model of species di usion in an elastic material. The model is applied to study the mechanics of the lamina cribrosa (LC) in the eye. The LC is a porous tissue at the head of the optic nerve. Deformation of this tissue and impairment of blood flow induced by tissue deformation are considered to be related to the pathogenesis of glaucoma.
The governing equations are derived from general thermomechanical principles. We carefully revise the role of the energy-stress Eshelby tensor, mutuated from the framework of tissue growth, in describing the hemo-mechanical behaviour of the tissue.
The model accounts for non-linear deformations of the solid matrix and deforma- tion-induced changes in porosity and permeability. The model provides a qualitative better undertanding of the phatophysiology and pathogenesis of glaucoma in terms of coupling between tissue deformation and the resulting impaired hemodynamics inside the LC
Numerical simulation and analysis of multiscale interface coupling between a poroelastic medium and a lumped hydraulic circuit: comparison between functional iteration and operator splitting methods
No full textWe consider a multiscale problem modeling the flow of a fluid through a deformable porous medium, described by a system of partial differential equations (PDEs), connected with a lumped hydraulic circuit, described by a system of ordinary differential equations (ODEs). This PDE/ODE coupled problem includes interface conditions enforcing the continuity of mass and the balance of stresses across models at different scales. In the present article, we address questions related to the solution methods of the PDE/ODE coupled problem via staggered algorithms, focusing on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the interface conditions. We provide sufficient conditions for the convergence of functional iterations and prove that the energy-based operator splitting method is unconditionally stable with respect to the size of the time discretization step
Statistical methods in medicine: application to the study of glaucoma progression
No full textStatistical models provide a variety of powerful methods for data analysis in medicine. In this chapter, we aim at illustrating the insights that statistical models can provide regarding the study of disease progression. In particular, we analyze a unique dataset on glaucoma progression by means of mixed-effects statistical models, where the form of the probability distribution for the multiple measurements is assumed to be the same for each individual in the study, but the parameters of that distribution can vary over individuals. Two illustrative case studies are presented in the context of structural and functional progression in glaucoma
Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation
No full textThe scientific community continues to accrue evidence that blood flow alterations and ischemic conditions in the retina play an important role in the pathogenesis of ocular diseases. Many factors influence retinal hemodynamics and tissue oxygenation, including blood pressure, blood rheology, oxygen arterial permeability and tissue metabolic demand. Since the influence of these factors on the retinal circulation is difficult to isolate in vivo, we propose here a novel mathematical and computational model describing the coupling between blood flow mechanics and oxygen ((Formula presented.)) transport in the retina. Albeit in a simplified manner, the model accounts for the three-dimensional anatomical structure of the retina, consisting in a layered tissue nourished by an arteriolar/venular network laying on the surface proximal to the vitreous. Capillary plexi, originating from terminal arterioles and converging into smaller venules, are embedded in two distinct tissue layers. Arteriolar and venular networks are represented by fractal trees, whereas capillary plexi are represented using a simplified lumped description. In the model, (Formula presented.) is transported along the vasculature and delivered to the tissue at a rate that depends on the metabolic demand of the various tissue layers. First, the model is validated against available experimental results to identify baseline conditions. Then, a sensitivity analysis is performed to quantify the influence of blood pressure, blood rheology, oxygen arterial permeability and tissue oxygen demand on the (Formula presented.) distribution within the blood vessels and in the tissue. This analysis shows that: (1) systemic arterial blood pressure has a strong influence on the (Formula presented.) profiles in both blood and tissue; (2) plasma viscosity and metabolic consumption rates have a strong influence on the (Formula presented.) tension at the level of the retinal ganglion cells; and (3) arterial (Formula presented.) permeability has a strong influence on the (Formula presented.) saturation in the retinal arterioles
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