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

Abstract

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.

Multicenter Evaluation of Frequency and Impact of Activity Infiltration in PET Imaging, Including Microscale Modeling of Skin-Absorbed Dose

“…6B), and concentration ratios of hypodermis to the dermis were measured to be 10:1 or greater. A similar pattern is shown in Figure 6C (14), where an injection drug was also dyed red and showed the telltale fracturing between fat cells to accommodate and drain excess fluid.…”

“…Skin is a large and complex organ, but for our purposes it is critical to at least appreciate the structure, function, and dimensions of the major layers. The behavior of fluids when purposely or accidentally injected into the subcutaneous space has been abundantly reported in the literature (12)(13)(14), as tumescent fluid injections into the subcutaneous tissue for purposes of local anesthesia are common for several dermatologic procedures, including liposuction, cutaneous surgery, and drug administration. On injection, the fluid, under pressure, is trapped within the intracellular matrix of the subcutaneous tissue, as the fatty tissue expands severalfold.…”

Solute Transport across the Lymphatic Vasculature in a Soft Skin Tissue

“…For a constant permeability case, k = 1 × 10 −13 m 2 . During the injection process, permeability changes with pressure, following Equation ( 21), and the hydraulic permeability k of the porous medium varies following Equation (22). As shown in Figure 6a,b, the magnitude of the maximum pressure for variable permeability with k 0 = 1 × 10 −13 m 2 is less than half that of constant permeability.…”

“…One approach is reducing the dimension of the numerical simulation. The mathematical equations for the interstitial fluid flow and soft tissue strain are solved in two-dimensional models using a finite element method to study the effect of strain relaxation on fluid drainage and solute transport [21,22], while one-dimensional mathematical models are also used to analyze the fluid flow and solute transport [23]. Another approach is simplifying the stress-strain relation to make the computations more efficient.…”

MPET 2 : a multi-network poroelastic and transport theory for predicting absorption of monoclonal antibodies delivered by subcutaneous injection

“…However, these models focus on the material response and fluid pressure change in interstitial tissue, and do not model the changes of fluid pressures in blood vessels and lymphatic vessels or the drug transport induced by the material responses. Drug transport coupled with tissue deformation is also considered in some studies (Han et al., 2021 ; Hou et al., 2021 ; Zheng et al., 2021a ; Leng et al., 2022 ; Rahimi et al., 2022 ). Nevertheless, these studies apply a linear model to describe the lymphatic uptake assuming that the lymphatic fluid pressure is constant, and ignore changes in lymphatic pressure due to tissue deformation and fluid flow.…”