265 research outputs found
Recommended from our members
"High end" research datasets: an exploration of issues, together with results of a survey of the ABLD/EBSLG/APBSLG members
Turing pattern or system heterogeneity? A numerical continuation approach to assessing the role of Turing instabilities in heterogeneous reaction-diffusion systems
Turing patterns in reaction-diffusion (RD) systems have classically been
studied only in RD systems which do not explicitly depend on independent
variables such as space. In practise, many systems for which Turing patterning
is important are not homogeneous with ideal boundary conditions. In
heterogeneous systems with stable steady states, the steady states are also
necessarily heterogeneous which is problematic for applying the classical
analysis. Whilst there has been some work done to extend Turing analysis to
some heterogeneous systems, for many systems it is still difficult to determine
if a stable patterned state is driven purely by system heterogeneity or if a
Turing instability is playing a role. In this work, we try to define a
framework which uses numerical continuation to map heterogeneous RD systems
onto a sensible nearby homogeneous system. This framework may be used for
discussing the role of Turing instabilities in establishing patterns in
heterogeneous RD systems. We study the Schnakenberg and Gierer-Meinhardt models
with spatially heterogeneous production as test problems. It is shown that for
sufficiently large system heterogeneity (large amplitude spatial variations in
morphogen production) it is possible that Turing-patterned and base states
become coincident and therefore impossible to distinguish. Other exotic
behaviour is also shown to be possible. We also study a novel scenario in which
morphogen is produced locally at levels that could support Turing patterning
but on intervals/patches which are on the scale of classical critical domain
lengths. Without classical domain boundaries, Turing patterns are allowed to
bleed through; an effect noted by other authors. In this case, this phenomena
effectively changes the critical domain length. Indeed, we even note that this
phenomena may also effectively couple local patches together and drive
instability in this way.Comment: 10 figure
Modeling the growth of multicellular cancer spheroids in a\ud bioengineered 3D microenvironment and their treatment with an\ud anti-cancer drug
A critical step in the dissemination of ovarian cancer cells is the formation of multicellular spheroids from cells shed from the primary tumor. The objectives of this study were to establish and validate bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer cells in vitro and simultaneously to develop computational models describing the growth of multicellular spheroids in these bioengineered matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and cultured for up to 4 weeks. Immunohistochemistry was used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel.\ud
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Two computational models were developed. In the first model, each spheroid was treated as an incompressible porous medium, whereas in the second model the concept of morphoelasticity was used to incorporate details about internal stresses and strains. Each model was formulated as a free boundary problem. Functional forms for cell proliferation and apoptosis motivated by the experimental work were applied and the predictions of both models compared with the output from the experiments. Both models simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture time and treatment with paclitaxel. Our mathematical models provide new perspectives on previous experimental results and have informed the design of new 3D studies of multicellular cancer spheroids
Growth of confined cancer spheroids: a combined experimental and mathematical modelling approach
We have integrated a bioengineered three-dimensional platform by generating multicellular cancer spheroids in a controlled microenvironment with a mathematical model to investigate\ud
confined tumour growth and to model its impact on cellular processes
Crystalline Order on a Sphere and the Generalized Thomson Problem
We attack generalized Thomson problems with a continuum formalism which
exploits a universal long range interaction between defects depending on the
Young modulus of the underlying lattice. Our predictions for the ground state
energy agree with simulations of long range power law interactions of the form
1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain
boundaries is studied in the context of tilted crystalline order and the
generality of our approach is illustrated with new results for square tilings
on the sphere.Comment: 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference
typo fixe
Spatio-temporal Models of Lymphangiogenesis in Wound Healing
Several studies suggest that one possible cause of impaired wound healing is
failed or insufficient lymphangiogenesis, that is the formation of new
lymphatic capillaries. Although many mathematical models have been developed to
describe the formation of blood capillaries (angiogenesis), very few have been
proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a
markedly different process from angiogenesis, occurring at different times and
in response to different chemical stimuli. Two main hypotheses have been
proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the
edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic
endothelial cells first pool in the wound region following the lymph flow and
then, once sufficiently populated, start to form a network. Here we present two
PDE models describing lymphangiogenesis according to these two different
hypotheses. Further, we include the effect of advection due to interstitial
flow and lymph flow coming from open capillaries. The variables represent
different cell densities and growth factor concentrations, and where possible
the parameters are estimated from biological data. The models are then solved
numerically and the results are compared with the available biological
literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total
Computational modelling of wound healing insights to develop new treatments
About 1% of the population will suffer a severe wound during their life. Thus, it is really important to develop new techniques in order to properly treat these injuries due to the high socioeconomically impact they suppose. Skin substitutes and pressure based therapies are currently the most promising techniques to heal these injuries. Nevertheless, we are still far from finding a definitive skin substitute for the treatment of all chronic wounds. As a first step in developing new tissue engineering tools and treatment techniques for wound healing, in silico models could help in understanding the mechanisms and factors implicated in wound healing. Here, we review mathematical models of wound healing. These models include different tissue and cell types involved in healing, as well as biochemical and mechanical factors which determine this process. Special attention is paid to the contraction mechanism of cells as an answer to the tissue mechanical state. Other cell processes such as differentiation and proliferation are also included in the models together with extracellular matrix production. The results obtained show the dependency of the success of wound healing on tissue composition and the importance of the different biomechanical and biochemical factors. This could help to individuate the adequate concentration of growth factors to accelerate healing and also the best mechanical properties of the new skin substitute depending on the wound location in the body and its size and shape. Thus, the feedback loop of computational models, experimental works and tissue engineering could help to identify the key features in the design of new treatments to heal severe wounds
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