446 research outputs found
Local Climatological Data : Urbana, 1889-1970
Urbana has a temperate continental climate with characteristics reflecting its geographical position in Illinois. Urbana's climate is representative of the conditions found in East Central Illinois, which is primarily an area of climatic transition between the northern and southern sectors of the state.published or submitted for publicationis peer reviewedOpenOpe
Mesoscopic and continuum modelling of angiogenesis
Angiogenesis is the formation of new blood vessels from pre-existing ones in
response to chemical signals secreted by, for example, a wound or a tumour. In
this paper, we propose a mesoscopic lattice-based model of angiogenesis, in
which processes that include proliferation and cell movement are considered as
stochastic events. By studying the dependence of the model on the lattice
spacing and the number of cells involved, we are able to derive the
deterministic continuum limit of our equations and compare it to similar
existing models of angiogenesis. We further identify conditions under which the
use of continuum models is justified, and others for which stochastic or
discrete effects dominate. We also compare different stochastic models for the
movement of endothelial tip cells which have the same macroscopic,
deterministic behaviour, but lead to markedly different behaviour in terms of
production of new vessel cells.Comment: 48 pages, 13 figure
Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues.
The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological tissues, and model classification
DNA charge neutralisation by linear polymers I: irreversible binding
We develop a deterministic mathematical model to describe the way
in which polymers bind to DNA by considering the dynamics of the
gap distribution that forms when polymers bind to a DNA plasmid.
In so doing, we generalise existing theory to account for overlaps
and binding cooperativity whereby the polymer binding rate depends
on the size of the overlap The proposed mean-field models are then
solved using a combination of numerical and asymptotic methods. We
find that overlaps lead to higher coverage and hence higher charge
neutralisations, results which are more in line with recent
experimental observations. Our work has applications to gene
therapy where polymers are used to neutralise the negative charges
of the DNA phosphate backbone, allowing condensation prior to
delivery into the nucleus of an abnormal cell
Investigating the influence of growth arrest mechanisms on tumour responses to radiotherapy
Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these
differences impact sensitivity to treatment is an essential step towards
patient-specific treatment design. In this paper, we investigate how two
different mechanisms for growth control may affect tumour cell responses
to fractionated radiotherapy (RT) by extending an existing ordinary differential equation model of tumour growth. In the absence of treatment,
this model distinguishes between growth arrest due to nutrient insufficiency and competition for space and exhibits three growth regimes:
nutrient-limited (NL), space limited (SL) and bistable (BS), where both
mechanisms for growth arrest coexist. We study the effect of RT for
tumours in each regime, finding that tumours in the SL regime typically
respond best to RT, while tumours in the BS regime typically respond
worst to RT. For tumours in each regime, we also identify the biological
processes that may explain positive and negative treatment outcomes and
the dosing regimen which maximises the reduction in tumour burden
DNA charge neutralisation by linear polymers II: reversible binding
We model the way in which polymers bind to DNA and neutralise
its charged backbone by analysing the dynamics of the distribution
of gaps along the DNA.
We generalise existing theory for irreversible binding to construct
new deterministic models which include polymer removal,
movement along the DNA and allow for binding with overlaps.
We show that reversible binding alters the capacity of the DNA
for polymers by allowing the rearrangement of polymer positions
over a longer timescale than when binding is irreversible.
When the polymers do not overlap, allowing reversible binding
increases the number of polymers adhered and hence the charge that
the DNA can accommodate; in contrast, when overlaps occur, reversible
binding reduces the amount of charge neutralised by the polymers
Explicit physics-informed neural networks for non-linear upscaling closure: the case of transport in tissues
In this work, we use a combination of formal upscaling and data-driven
machine learning for explicitly closing a nonlinear transport and reaction
process in a multiscale tissue. The classical effectiveness factor model is
used to formulate the macroscale reaction kinetics. We train a multilayer
perceptron network using training data generated by direct numerical
simulations over microscale examples. Once trained, the network is used for
numerically solving the upscaled (coarse-grained) differential equation
describing mass transport and reaction in two example tissues. The network is
described as being explicit in the sense that the network is trained using
macroscale concentrations and gradients of concentration as components of the
feature space.
Network training and solutions to the macroscale transport equations were
computed for two different tissues. The two tissue types (brain and liver)
exhibit markedly different geometrical complexity and spatial scale (cell size
and sample size). The upscaled solutions for the average concentration are
compared with numerical solutions derived from the microscale concentration
fields by a posteriori averaging. There are two outcomes of this work of
particular note: 1) we find that the trained network exhibits good
generalizability, and it is able to predict the effectiveness factor with high
fidelity for realistically-structured tissues despite the significantly
different scale and geometry of the two example tissue types; and 2) the
approach results in an upscaled PDE with an effectiveness factor that is
predicted (implicitly) via the trained neural network. This latter result
emphasizes our purposeful connection between conventional averaging methods
with the use of machine learning for closure; this contrasts with some machine
learning methods for upscaling where the exact form of the macroscale equation
remains unknown
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