130 research outputs found
A tangential regularization method for backflow stabilization in hemodynamics
In computational simulations of fluid flows, instabilities at the Neumann boundaries may appear during backflow regime. It is widely accepted that this is due to the incoming energy at the boundary, coming from the convection term, which cannot be controlled when the velocity field is unknown. We propose a stabilized formulation based on a local regularization of the fluid velocity along the tangential directions on the Neumann boundaries. The stabilization term is proportional to the amount of backflow, and does not require any further assumption on the velocity profile. The perfomance of the method is assessed on a two- and three-dimensional Womersley flows, as well as considering a hemodynamic physiological regime in a patient-specific aortic geometry
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Multiscale modeling of weakly compressible elastic materials in harmonic regime and applications to microscale structure estimation
This article is devoted to the modeling of elastic materials composed
by an incompressible elastic matrix and small compressible gaseous
inclusions, under a time harmonic excitation. In a biomedical context, this
model describes the dynamics of a biological tissue (e.g. lung or liver) when
wave analysis methods (such as Magnetic Resonance Elastography) are used to
estimate tissue properties. Due to the multiscale nature of the problem,
direct numerical simulations are prohibitive.We extend the homogenized model
introduced in [Baffico, Grandmont, Maday, Osses, SIAM J. Mult. Mod. Sim.,
7(1), 2008] to a time harmonic regime to describe the solid-gas mixture from
a macroscopic point of view in terms of an effective elasticity tensor.
Furthermore, we derive and validate numerically analytical approximations for
the effective elastic coefficients in terms of macroscopic parameters. This
simplified description is used to to set up an efficient variational approach
for the estimation of the tissue porosity, using the mechanical response to
external harmonic excitations
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A tangential regularization method for backflow stabilization in hemodynamics
In computational simulations of fluid flows, instabilities at the Neumann boundaries may appear during backflow regime. It is widely accepted that this is due to the incoming energy at the boundary, coming from the convection term, which cannot be controlled when the velocity field is unknown. We propose a stabilized formulation based on a local regularization of the fluid velocity along the tangential directions on the Neumann boundaries. The stabilization term is proportional to the amount of backflow, and does not require any further assumption on the velocity profile. The perfomance of the method is assessed on a twoand three-dimensional Womersley flows, as well as considering a hemodynamic physiological regime in a patient-specific aortic geometry
Multiscale modeling of weakly compressible elastic materials in harmonic regime and application to microscale structure estimation
This article is devoted to the modeling of elastic materials composed by an incompressible elastic matrix and small compressible gaseous inclusions, under a time harmonic excitation. In a biomedical context, this model describes the dynamics of a biological tissue (e.g. lung or liver) when wave analysis methods (such as Magnetic Resonance Elastography) are used to estimate tissue properties. Due to the multiscale nature of the problem, direct numerical simulations are prohibitive. We extend the homogenized model introduced in [Baffico, Grandmont, Maday, Osses, SIAM J. Mult. Mod. Sim., 7(1), 2008] to a time harmonic regime to describe the solid-gas mixture from a macroscopic point of view in terms of an effective elasticity tensor. Furthermore, we derive and validate numerically analytical approximations for the effective elastic coefficients in terms of macroscopic parameters. This simplified description is used to to set up an efficient variational approach for the estimation of the tissue porosity, using the mechanical response to external harmonic excitations
A Stokes-consistent backflow stabilization for physiological flows
In computational fluid dynamics incoming flow at open boundaries, or \emph{backflow}, often yields to unphysical instabilities for
high Reynolds numbers. It is widely accepted that this is due to the incoming energy
arising from the convection term, which cannot be \emph{a priori} controlled when the velocity field is unknown at the boundary.
In order to improve the robustness of the numerical simulations, we propose a stabilized formulation
based on a penalization of the residual of a weak Stokes problem on the open boundary, whose viscous part controls the
incoming convective energy, while the inertial term contributes to the kinetic energy. We also present different strategies
for the approximation of the boundary
pressure gradient, which is needed for defining the stabilization term.
The method has the advantage that it does not require neither artificial modifications or extensions of the
computational domain. Moreover, it is consistent with the Womersley solution. We illustrate our approach
on numerical examples ~- both academic and real-life -~ relevant to blood and respiratory flows. The results also
show that the stabilization parameter can be reduced with the mesh size
Multiscale modeling of palisade formation in gliobastoma multiforme
Palisades are characteristic tissue aberrations that arise in glioblastomas. Observation of palisades is considered as a clinical indicator of the transition from a noninvasive to an invasive tumour. In this article we propose a computational model to study the influence of genotypic and phenotypic heterogeneity in palisade formation. For this we produced three dimensional realistic simulations, based on a multiscale hybrid model, coupling the evolution of tumour cells and the oxygen diffusion in tissue, that depict the shape of palisades during its formation. Our results can be summarized as the following: (1) we show that cell heterogeneity is a crucial factor in palisade formation and tumour growth; (2) we present results that can explain the observed fact that recursive tumours are more malignant than primary tumours; and (3) the presented simulations can provide to clinicians and biologists for a better understanding of palisades 3D structure as well as glioblastomas growth dynamic
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Multiscale modeling of palisade formation in gliobastoma multiforme
Palisades are characteristic tissue aberrations that arise in
glioblastomas. Observation of palisades is considered as a clinical indicator
of the transition from a noninvasive to an invasive tumour. In this article
we propose a computational model to study the influence of genotypic and
phenotypic heterogeneity in palisade formation. For this we produced three
dimensional realistic simulations, based on a multiscale hybrid model,
coupling the evolution of tumour cells and the oxygen diffusion in tissue,
that depict the shape of palisades during its formation. Our results can be
summarized as the following: (1) we show that cell heterogeneity is a crucial
factor in palisade formation and tumour growth; (2) we present results that
can explain the observed fact that recursive tumours are more malignant than
primary tumours; and (3) the presented simulations can provide to clinicians
and biologists for a better understanding of palisades 3D structure as well
as glioblastomas growth dynamics
Reconstruction of Quasi-Local Numerical Effective Models from Low-Resolution Measurements
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward models that are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that an identification of the matrix representation related to these effective models is possible. On the one hand, this provides a reasonable surrogate in cases where a direct reconstruction is unfeasible due to a mismatch between the coarse data scale and the microscopic quantities to be reconstructed. On the other hand, the approach allows us to investigate the requirement for a certain non-locality in the context of numerical homogenization. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments
Reduced Lagrange multiplier approach for non-matching coupled problems in multiscale elasticity
This paper presents a numerical method for the simulation of elastic solid
materials coupled to fluid inclusions. The application is motivated by the
modeling of vascularized tissues and by problems in medical imaging which
target the estimation of effective (i.e., macroscale) material properties,
taking into account the influence of microscale dynamics, such as fluid flow in
the microvasculature. The method is based on the recently proposed Reduced
Lagrange Multipliers framework. In particular, the interface between solid and
fluid domains is not resolved within the computational mesh for the elastic
material but discretized independently, imposing the coupling condition via
non-matching Lagrange multipliers. Exploiting the multiscale properties of the
problem, the resulting Lagrange multipliers space is reduced to a
lower-dimensional characteristic set. We present the details of the stability
analysis of the resulting method considering a non-standard boundary condition
that enforces a local deformation on the solid-fluid boundary. The method is
validated with several numerical examples
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