69 research outputs found
Initial/boundary-value problems of tumor growth within a host tissue
This paper concerns multiphase models of tumor growth in interaction with a
surrounding tissue, taking into account also the interplay with diffusible
nutrients feeding the cells. Models specialize in nonlinear systems of possibly
degenerate parabolic equations, which include phenomenological terms related to
specific cell functions. The paper discusses general modeling guidelines for
such terms, as well as for initial and boundary conditions, aiming at both
biological consistency and mathematical robustness of the resulting problems.
Particularly, it addresses some qualitative properties such as a priori
nonnegativity, boundedness, and uniqueness of the solutions. Existence of the
solutions is studied in the one-dimensional time-independent case.Comment: 30 pages, 5 figure
Resultant pressure distribution pattern along the basilar membrane in the spiral shaped cochlea
Cochlea is an important auditory organ in the inner ear. In most mammals, it
is coiled as a spiral. Whether this specific shape influences hearing is still
an open problem. By employing a three dimensional fluid model of the cochlea
with an idealized geometry, the influence of the spiral geometry of the cochlea
is examined. We obtain solutions of the model through a conformal
transformation in a long-wave approximation. Our results show that the net
pressure acting on the basilar membrane is not uniform along its spanwise
direction. Also, it is shown that the location of the maximum of the spanwise
pressure difference in the axial direction has a mode dependence. In the
simplest pattern, the present result is consistent with the previous theory
based on the WKB-like approximation [D. Manoussaki, Phys. Rev. Lett. 96,
088701(2006)]. In this mode, the pressure difference in the spanwise direction
is a monotonic function of the distance from the apex and the normal velocity
across the channel width is zero. Thus in the lowest order approximation, we
can neglect the existance of the Reissner's membrane in the upper channel.
However, higher responsive modes show different behavior and, thus, the real
maximum is expected to be located not exactly at the apex, but at a position
determined by the spiral geometry of the cochlea and the width of the cochlear
duct. In these modes, the spanwise normal velocities are not zero. Thus, it
indicates that one should take into account of the detailed geometry of the
cochlear duct for a more quantitative result. The present result clearly
demonstrates that not only the spiral geometry, but also the geometry of the
cochlear duct play decisive roles in distributing the wave energy.Comment: 21 pages. (to appear in J. Biol. Phys.
Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth
Blood vessels form either when dispersed endothelial cells (the cells lining
the inner walls of fully-formed blood vessels) organize into a vessel network
(vasculogenesis), or by sprouting or splitting of existing blood vessels
(angiogenesis). Although they are closely related biologically, no current
model explains both phenomena with a single biophysical mechanism. Most
computational models describe sprouting at the level of the blood vessel,
ignoring how cell behavior drives branch splitting during sprouting. We present
a cell-based, Glazier-Graner-Hogeweg-model simulation of the initial patterning
before the vascular cords form lumens, based on plausible behaviors of
endothelial cells. The endothelial cells secrete a chemoattractant, which
attracts other endothelial cells. As in the classic Keller-Segel model,
chemotaxis by itself causes cells to aggregate into isolated clusters. However,
including experimentally-observed adhesion-driven contact inhibition of
chemotaxis in the simulation causes randomly-distributed cells to organize into
networks and cell aggregates to sprout, reproducing aspects of both de novo and
sprouting blood-vessel growth. We discuss two branching instabilities
responsible for our results. Cells at the surfaces of cell clusters attempting
to migrate to the centers of the clusters produce a buckling instability. In a
model variant that eliminates the surface-normal force, a dissipative mechanism
drives sprouting, with the secreted chemical acting both as a chemoattractant
and as an inhibitor of pseudopod extension. The branching instabilities
responsible for our results, which result from contact inhibition of
chemotaxis, are both generic developmental mechanisms and interesting examples
of unusual patterning instabilities.Comment: Thoroughly revised version, now in press in PLoS Computational
Biology. 53 pages, 13 figures, 2 supporting figures, 56 supporting movies,
source code and parameters files for computer simulations provided.
Supporting information: http://www.psb.ugent.be/~romer/ploscompbiol/ Source
code: http://sourceforge.net/projects/tst
Early Embryonic Vascular Patterning by Matrix-Mediated Paracrine Signalling: A Mathematical Model Study
During embryonic vasculogenesis, endothelial precursor cells of mesodermal origin known as angioblasts assemble into a characteristic network pattern. Although a considerable amount of markers and signals involved in this process have been identified, the mechanisms underlying the coalescence of angioblasts into this reticular pattern remain unclear. Various recent studies hypothesize that autocrine regulation of the chemoattractant vascular endothelial growth factor (VEGF) is responsible for the formation of vascular networks in vitro. However, the autocrine regulation hypothesis does not fit well with reported data on in vivo early vascular development. In this study, we propose a mathematical model based on the alternative assumption that endodermal VEGF signalling activity, having a paracrine effect on adjacent angioblasts, is mediated by its binding to the extracellular matrix (ECM). Detailed morphometric analysis of simulated networks and images obtained from in vivo quail embryos reveals the model mimics the vascular patterns with high accuracy. These results show that paracrine signalling can result in the formation of fine-grained cellular networks when mediated by angioblast-produced ECM. This lends additional support to the theory that patterning during early vascular development in the vertebrate embryo is regulated by paracrine signalling
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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