Mathematical Modeling of Interactions Between Adipogenesis, Fibrosis and Interstitial Fluid Exchange may be Useful for Lymphedema Study

The development of the excess subcutaneous fat and fibrosis is usual for the late stages of lymphedema. Some experimental investigations confirm this by morphological findings on the mouse-model lymph-fluid stasis. On the other hand, the obesity poses deleterious consequences on every organ system, particularly on the lymphatic network. Interactions between adipogenesis, fibrosis and fluid exchange are very interesting for mathematical modelling of the lymphatic flow disturbance. The mathematical modeling of the interaction between adipogenesis and fibrosis is based on the idea of using the Kahn-Hilliard equation, since experimental results show that adipogenesis is a mechanism generated predominantly by diffusion. Application of the Kahn-Hilliard equations to the phenomenological model of adipogenesis allows us to calculate the fractions of lipid droplets and their amounts.