Network development in biological gels: role in lymphatic vessel development
Network development in biological gels: role in lymphatic vessel development
In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model.
biomedical modeling, mathematical biology, mathematical modeling
1772-1789
Roose, Tiina
3581ab5b-71e1-4897-8d88-59f13f3bccfe
Fowler, Andrew C.
99a9f72e-c393-439b-892e-b98271776b01
12 July 2008
Roose, Tiina
3581ab5b-71e1-4897-8d88-59f13f3bccfe
Fowler, Andrew C.
99a9f72e-c393-439b-892e-b98271776b01
Roose, Tiina and Fowler, Andrew C.
(2008)
Network development in biological gels: role in lymphatic vessel development.
Bulletin of Mathematical Biology, 70 (6), .
(doi:10.1007/s11538-008-9324-3).
(PMID:18622650)
Abstract
In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model.
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Published date: 12 July 2008
Keywords:
biomedical modeling, mathematical biology, mathematical modeling
Organisations:
Bioengineering Sciences
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Local EPrints ID: 145137
URI: http://eprints.soton.ac.uk/id/eprint/145137
ISSN: 0092-8240
PURE UUID: 0bf50345-614b-4f86-8e32-cf8e2eb3e8d7
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Date deposited: 22 Apr 2010 15:32
Last modified: 14 Mar 2024 02:54
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Author:
Andrew C. Fowler
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