20,097 research outputs found
Non-regularised inverse finite element analysis for 3D traction force microscopy
The tractions that cells exert on a gel substrate from the observed
displacements is an increasingly attractive and valuable information in
biomedical experiments. The computation of these tractions requires in
general the solution of an inverse problem. Here, we resort to the discretisation
with finite elements of the associated direct variational formulation,
and solve the inverse analysis using a least square approach.
This strategy requires the minimisation of an error functional, which is
usually regularised in order to obtain a stable system of equations with
a unique solution. In this paper we show that for many common threedimensional
geometries, meshes and loading conditions, this regularisation
is unnecessary. In these cases, the computational cost of the inverse
problem becomes equivalent to a direct finite element problem. For the
non-regularised functional, we deduce the necessary and sufficient conditions
that the dimensions of the interpolated displacement and traction
fields must preserve in order to exactly satisfy or yield a unique solution
of the discrete equilibrium equations. We apply the theoretical results to
some illustrative examples and to real experimental data. Due to the relevance
of the results for biologists and modellers, the article concludes with
some practical rules that the finite element discretisation must satisfy.Peer ReviewedPostprint (author's final draft
Characterization of coorbit spaces with phase-space covers
We show that coorbit spaces can be characterized in terms of arbitrary
phase-space covers, which are families of phase-space multipliers associated
with partitions of unity. This generalizes previously known results for
time-frequency analysis to include time-scale decompositions. As a by-product,
we extend the existing results for time-frequency analysis to an irregular
setting.Comment: 31 pages. Revised version (title slightly changed). Typos fixe
Surgery of spline-type and molecular frames
We prove a result about producing new frames for general spline-type spaces
by piecing together portions of known frames. Using spline-type spaces as
models for the range of certain integral transforms, we obtain results for
time-frequency decompositions and sampling.Comment: 34 pages. Corrected typo
Computational medical imaging for total knee arthroplasty using visualitzation toolkit
This project is presented as a Master Thesis in the field of Civil Engineering, Biomedical specialization. As the
project of an Erasmus exchange student, this thesis has been under supervision both the Universite Livre de
Bruxelles and the Universitat Politecnica de Catalunya. The purpose of this thesis to put in practice all the
knowledges acquired during this Master in Industrial Engineering in UPC and to be a support for medical staff
in total knee arthoplasty procedures.
Prof. Emmanuel Thienpont has been working for years as orthopaedic surgeon at the Hospital Sant Luc,
Brussels. His years of work and research have been mainly focused on Total Knee Arthroplasty or TKA. During
one of the most important steps of this procedure, the orthopaedic surgeon has to cut the head of the femur
following two perpendicular cutting planes. Nevertheless, the orientation of these planes are directly dependant
of the femur constitution.
This Master Thesis has been conceived in order to offer the surgeon a tool to determine the proper direction
planes in a previous step before the surgical procedure. This project pretends to give the surgeon an openfree
computational platform to access to patient geometrical and physiological information before involving the
subject in any invasive procedure
Sliding joints in 3D beams: conserving algorithms using the master-slave approach
This paper proposes two time-integration algorithms for motion of geometrically
exact 3D beams under sliding contact conditions. The algorithms are derived using the socalled
master–slave approach, in which constraint equations and the related time-integration
of a system of differential and algebraic equations are eliminated by design. Specifically, we
study conservation of energy and momenta when the sliding conditions on beams are imposed
and discuss their algorithmic viability. Situations where the contact jumps to adjacent finite
elements are analysed in detail and the results are tested on two representative numerical
examples. It is concluded that an algorithmic preservation of kinematic constraint conditions
is of utmost importance.Peer ReviewedPostprint (author's final draft
Multitaper estimation on arbitrary domains
Multitaper estimators have enjoyed significant success in estimating spectral
densities from finite samples using as tapers Slepian functions defined on the
acquisition domain. Unfortunately, the numerical calculation of these Slepian
tapers is only tractable for certain symmetric domains, such as rectangles or
disks. In addition, no performance bounds are currently available for the mean
squared error of the spectral density estimate. This situation is inadequate
for applications such as cryo-electron microscopy, where noise models must be
estimated from irregular domains with small sample sizes. We show that the
multitaper estimator only depends on the linear space spanned by the tapers. As
a result, Slepian tapers may be replaced by proxy tapers spanning the same
subspace (validating the common practice of using partially converged solutions
to the Slepian eigenproblem as tapers). These proxies may consequently be
calculated using standard numerical algorithms for block diagonalization. We
also prove a set of performance bounds for multitaper estimators on arbitrary
domains. The method is demonstrated on synthetic and experimental datasets from
cryo-electron microscopy, where it reduces mean squared error by a factor of
two or more compared to traditional methods.Comment: 28 pages, 11 figure
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