Network Development in Biological Gels: Role in Lymphatic Vessel Development

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.

A Model for Interstitial Drainage Through a Sliding Lymphatic Valve

“…An understanding the mechanics of the lymphatic system and its role in interstitial drainage is therefore of significant physiological importance. In contrast to earlier studies [11,18,38,42,43,44,45], in which lymphatic valves are presumed to open in response to fluid pressure differences between the interstitium and lymphatic lumen, this work outlines a hypothesis for lymphatic drainage of interstitial fluid which is based upon the Rossi conjecture [46]. This presumes that endothelial gap junctions on the lymphatic capillary walls are pulled open in response to swelling of the surrounding tissue (which would occur, for example, when fluid enters the interstitium from the blood capillaries).…”

Multiscale Modelling of Lymphatic Drainage

“…This is an undoubtedly an exciting area, but suffers from a scarcity of systematic experimental knowledge to build truly encompassing models. Thus, only two, very specialised models have been published [10,39]. Roose and Fowler [39] developed a model to describe the fluid flow channelisation within collagen gels.…”

“…Thus, only two, very specialised models have been published [10,39]. Roose and Fowler [39] developed a model to describe the fluid flow channelisation within collagen gels. This channelisation is thought to precede and guide the development of mature lymph vessels in mouse tail.…”

“…There are two preliminary models [10,39], but many more detailed modelling studies performed as part of experimental investigations are still needed. In the secondary lymphatic system, advanced microscopy techniques [1,60] should be more widely used to probe the structure of the secondary lymphatic vessel walls.…”

Designing biomimetic reactive polymer gels

“…2d) and a higher amplitude motion to the left (marked as dx 2 ). The gel's motion is due to the inter-diffusion of the solvent and polymer [27,29,32,33]; the motion of solvent in one direction causes movement of the polymer in the opposite direction. As the light is moved from left to right, the solvent is effectively 'pushed' to the right and thus, the polymer moves to the left [3].…”