Two-phase Modeling of Fluid Injection Inside Subcutaneous Layer of Skin

TL;DR

This paper presents a two-dimensional mathematical model to analyze the biomechanical and fluid dynamics of subcutaneous tissue during injections, considering tissue anisotropy, viscosity, and pressure effects to assess pain and tissue response.

Contribution

It introduces a novel two-phase modeling approach for subcutaneous tissue that accounts for anisotropic hydraulic conductivity and tissue deformation during injections.

Findings

Stress fields correlate with pain intensity.

Eddy structures form near injection sites due to high pressure.

Tissue response depends on anisotropy and fluid viscosity.

Abstract

Being motivated by the delivery of drugs and vaccines through subcutaneous (SC) injection in human bodies, a theoretical investigation is performed using a two-dimensional mathematical model in the cartesian coordinate. In general, a large variety of biological tissues behave as deformable porous material with anisotropic hydraulic conductivity. Consequently, one can adopt the field equations of mixture theory to describe the behavior of the interstitial fluid and adipose cell present in the subcutaneous layer of skin. During the procedure, a medical person takes a big pinch of the skin of the injection application area between the thumb and index finger and holds. This process pulls the fatty tissue away from the muscle and makes the injection process easier. In this situation, the small aspect ratio (denoted as $\delta$) of the subcutaneous layer (SCL) i.e., $\delta^2\sim0.01$ would simplify the governing equation for tissue dynamics as it becomes a perturbation parameter. This study highlights the issue of the mechanical response of the adipose tissue in terms of the anisotropic hydraulic conductivity variation, the viscosity of the injected drug, the mean depth of subcutaneous tissue, etc. In particular, the computed stress fields can measure the intensity of pain to be experienced by a patient after this procedure. Also, this study discusses the biomechanical impact of the creation of one or more eddy structures (s) near the area of applying injection, which is due to high pressure developed there, increased tissue anisotropy, fluid viscosity, etc.