Mixed-dimensional multi-scale poroelastic modeling of adipose tissue for subcutaneous injection

Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has gained increasing interest in the pharmaceutical industry. The transport, distribution and absorption of mAbs in the skin after injection are not yet well-understood. Experiments have shown that fibrous septa form preferential channels for fluid flow in the tissue. The majority of mAbs can only be absorbed through lymphatics which follow closely the septa network. Therefore, studying drug transport in the septa network is vital to the understanding of drug absorption. In this work, we present a mixed-dimensional multi-scale (MDMS) poroelastic model of adipose tissue for subcutaneous injection. More specifically, we model the fibrous septa as reduced-dimensional microscale interfaces embedded in the macroscale tissue matrix. The model is first verified by comparing numerical results against the full-dimensional model where fibrous septa are resolved using fine meshes. Then, we apply the MDMS model to study subcutaneous injection. It is found that the permeability ratio between the septa and matrix, volume capacity of the septa network, and concentration-dependent drug viscosity are important factors affecting the amount of drug entering the septa network which are paths to lymphatics. Our results show that septa play a critical role in the transport of mAbs in the subcutaneous tissue, and this role was previously overlooked.