10 research outputs found
Modelling pulsatile blood flow through surgically coupled microvascular anastomoses
The significant rates of post-operative arterial thrombus formation following
the sutured anastomosis (surgical connection) of vessels in microvascular
reconstruction has kindled the development of engineered solutions such as the
UNILINK coupler. These devices reduce thrombosis rates, which recent numerical
studies suggest to be due to decreases in shear strain rate across the
anastomosis site when compared to sutured vessels. In this work we develop and
analytically solve the first mathematical model for the problem of
microvascular anastomosis, leading to the discovery that the rates of
thrombosis using these surgical coupling devices could be further reduced by
decreasing the gradient of the wall deformation at the join.Comment: 8 pages, 3 figure
Sharp quadrature error bounds for the nearest-neighbor discretization of the regularized stokeslet boundary integral equation
The method of regularized stokeslets is a powerful numerical method to solve
the Stokes flow equations for problems in biological fluid mechanics. A recent
variation of this method incorporates a nearest-neighbor discretization to
improve accuracy and efficiency while maintaining the ease-of-implementation of
the original meshless method. This method contains three sources of numerical
error, the regularization error associated from using the regularized form of
the boundary integral equations (with parameter ), and two sources
of discretization error associated with the force and quadrature
discretizations (with lengthscales and ). A key issue to address is
the quadrature error: initial work has not fully explained observed numerical
convergence phenomena. In the present manuscript we construct sharp quadrature
error bounds for the nearest-neighbor discretisation, noting that the error for
a single evaluation of the kernel depends on the smallest distance ()
between these discretization sets. The quadrature error bounds are described
for two cases: with disjoint sets () being close to linear in
and insensitive to , and contained sets () being
quadratic in with inverse dependence on . The practical
implications of these error bounds are discussed with reference to the
condition number of the matrix system for the nearest-neighbor method, with the
analysis revealing that the condition number is insensitive to
for disjoint sets, and grows linearly with for contained sets.
Error bounds for the general case () are revealed to be
proportional to the sum of the errors for each case.Comment: 12 pages, 6 figure
Passively parallel regularized stokeslets
Stokes flow, discussed by G.G. Stokes in 1851, describes many microscopic
biological flow phenomena, including cilia-driven transport and flagellar
motility; the need to quantify and understand these flows has motivated decades
of mathematical and computational research. Regularized stokeslet methods,
which have been used and refined over the past twenty years, offer significant
advantages in simplicity of implementation, with a recent modification based on
nearest-neighbour interpolation providing significant improvements in
efficiency and accuracy. Moreover this method can be implemented with the
majority of the computation taking place through built-in linear algebra,
entailing that state-of-the-art hardware and software developments in the
latter, in particular multicore and GPU computing, can be exploited through
minimal modifications ('passive parallelism') to existing MATLAB computer code.
Hence, and with widely-available GPU hardware, significant improvements in the
efficiency of the regularized stokeslet method can be obtained. The approach is
demonstrated through computational experiments on three model biological flows:
undulatory propulsion of multiple C. Elegans, simulation of progression and
transport by multiple sperm in a geometrically confined region, and left-right
symmetry breaking particle transport in the ventral node of the mouse embryo.
In general an order-of-magnitude improvement in efficiency is observed. This
development further widens the complexity of biological flow systems that are
accessible without the need for extensive code development or specialist
facilities.Comment: 21 pages, 7 figures, submitte
Beta cell lipotoxicity in the development of type 2 diabetes:the need for species-specific understanding
The propensity to develop type 2 diabetes (T2D) is known to have both environmental and hereditary components. In those with a genetic predisposition to T2D, it is widely believed that elevated concentrations of circulatory long-chain fatty acids (LC-FFA) significantly contribute towards the demise of insulin-producing pancreatic β-cells - the fundamental feature of the development of T2D. Over 25 years of research support that LC-FFA are deleterious to β-cells, through a process termed lipotoxicity. However, the work underpinning the theory of β-cell lipotoxicity is mostly based on rodent studies. Doubts have been raised as to whether lipotoxicity also occurs in humans. In this review, we examine the evidence, both in vivo and in vitro, for the pathogenic effects of LC-FFA on β-cell viability and function in humans, highlighting key species differences. In this way, we aim to uncover the role of lipotoxicity in the human pathogenesis of T2D and motivate the need for species-specific understanding.</p
Efficient Implementation of Elastohydrodynamics via Integral Operators
The dynamics of geometrically non-linear flexible filaments play an important
role in a host of biological processes, from flagella-driven cell transport to
the polymeric structure of complex fluids. Such problems have historically been
computationally expensive due to numerical stiffness associated with the
inextensibility constraint, as well as the often non-trivial boundary
conditions on the governing high-order PDEs. Formulating the problem for the
evolving shape of a filament via an integral equation in the tangent angle has
recently been found to greatly alleviate this numerical stiffness. The
contribution of the present manuscript is to enable the simulation of non-local
interactions of multiple filaments in a computationally efficient manner using
the method of regularized stokeslets within this framework. The proposed method
is benchmarked against a non-local bead and link model, and recent code
utilizing a local drag velocity law. Systems of multiple filaments (1) in a
background fluid flow, (2) under a constant body force, and (3) undergoing
active self-motility are modeled efficiently. Buckling instabilities are
analyzed by examining the evolving filament curvature, as well as by
coarse-graining the body frame tangent angles using a Chebyshev approximation
for various choices of the relevant non-dimensional parameters. From these
experiments, insight is gained into how filament-filament interactions can
promote buckling, and further reveal the complex fluid dynamics resulting from
arrays of these interacting fibers. By examining active moment-driven
filaments, we investigate the speed of worm- and sperm-like swimmers for
different governing parameters. The MATLAB(R) implementation is made available
as an open-source library, enabling flexible extension for alternate
discretizations and different surrounding flows.Comment: 37 pages, 17 figure
Doing more with less: the flagellar end piece enhances the propulsive effectiveness of human spermatozoa
Spermatozoa self-propel by propagating bending waves along a predominantly
active elastic flagellum. The organized structure of the "9 + 2" axoneme is
lost in the most-distal few microns of the flagellum, and therefore this region
is unlikely to have the ability to generate active bending; as such it has been
largely neglected in biophysical studies. Through elastohydrodynamic modeling
of human-like sperm we show that an inactive distal region confers significant
advantages, both in propulsive thrust and swimming efficiency, when compared
with a fully active flagellum of the same total length. The beneficial effect
of the inactive end piece on these statistics can be as small as a few percent
but can be above 430%. The optimal inactive length, between 2-18% of the total
length, depends on both wavenumber and viscous-elastic ratio, and therefore is
likely to vary in different species. Potential implications in evolutionary
biology and clinical assessment are discussed.Comment: To Appear, Physical Review Fluids. 25 pages, 14 figure