Models of Hydration Dependent Lymphatic Opening, Interstitial Fluid Flows and Ambipolar Diffusion

A theoretical understanding of fluid exchange and the role of initial lymph formation in tissues through mathematical/physical modeling is lacking.

Here, we present three models for tissues rich in negative fixed charges due to glycosaminoglycans interacting with the extracellular matrix.

We first model a lymphatic opening mechanism at relevant hydrations of the interstitium. At each hydration affecting tissue strain, two equations coupled in time are developed and solved with the new lymphatic opening and particle draining mechanism. The lymphatic opening mechanism is then included in a new model of interstitial fluid and macromolecular flow where the influence of different exclusion and available volumes for charged and neutral particles are quantified. For therapeutic interactions with cells, essential differences are found between electrically charged and neutral therapeutic substances. The interstitial fluid hydrostatic pressure gradient and flow are expressed through an extended Darcy equation, derived using similar methods as in kinetic theory of dense gases and fluid flows. Finally, a model for ambipolar diffusion of electrically charged macromolecules in tissue is developed.

Our study will inform transport of charged and neutral macromolecules between the vasculature, interstitium, and the lymphatic system, thus having implications for tissue uptake of therapeutic agents.