Convective transport and absorption of drug solute in soft skin tissue*

The subcutaneous (SC) injection is widely used for drug delivery of biotherapeutics, especially for self-administration. Interstitial fluid pressure (IFP) plays a key role in regulating the fluid flow and mass transport in the SC tissue. In this paper, an approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during a SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the IFP. The advantage of this method lies in its time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solutions of poroelastic tissue model. The pressure build-up in the proposed poroelastic medium is investigated for a wide range of elasticity and permeability during and after the injection. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the increasing hydraulic permeability. The increasing porosity and permeability due to deformation alleviates the high pressure and reduces the deformation during the injection. By implementing the Darcy-Brinkman-Forchheimer equation, the non-Darcy flow effect is investigated on the pressure build-up.  At last, the convective transport and lymphatic uptake of drug solute are investigated in a multi-layered poroelastic tissue embedded with a hybrid discrete-continuum vessel network. Our model provides an efficient way to estimate the pressure build-up in the soft tissue. Coupled with the hybrid vessel network, this computational model can be used to study and predict drug clearance at the injection site.