Network development in biological gels: Role in lymphatic vessel development.
by
Dr. Tiina Roose
OCIAM and CMB, Mathematical Institute, University of Oxford

Even though the existence of lymphatic vessels has been known since the 17th century, until very recently not very much was known about their functioning and development. This was due to a failure to understand their importance in the proper functioning of tissues. However, in last the 10 years lymphatics have come to the forefront of biomedical research, largely due to findings highlighting their importance to cancer growth and metastasis Stacker et al. (2002). Thus, there are now a large number of experimental studies on the molecular and micromechanical factors that control lymphatic function and development.

We present a model that explains the prepatterning of lymphatic vessel morphology during development. This model is derived using the theory of two phase rubber material due to Flory and co-workers 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 Boardmand&Swartz (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 non-linearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model.

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Date received: May 12, 2008