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.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Roose T,Fowler ACdoi
10.1007/s11538-008-9324-3subject
Has Abstractpub_date
2008-08-01 00:00:00pages
1772-89issue
6eissn
0092-8240issn
1522-9602journal_volume
70pub_type
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