Extension of the composite smeared finite element (CSFE) to include lymphatic system in modeling mass transport in capillary systems and biological tissue

Abstract

We have recently introduced a composite smeared finite element (CSFE) to model gradientdriven mass transport in biological tissue. The transport from capillary system is smeared in a way to transform 1D transport to a continuum, while the tissue is considered as a continuum. Coupling between the smeared pressure and concentration field is achieved through 1D connectivity elements assigned at each FE node. Here we extend our smeared model to include the lymphatic system. The lymphatic vessels are treated in a way analogous to the capillaries, by introducing the corresponding Darcy and diffusion tensors. Additional connectivity elements are added. In the numerical examples we demonstrate accuracy of the smeared model and the effects of the lymph on the pressure and concentration within the extracellular space, assuming that there is no transport to the cell space.