Imaging fluid injections into soft biological tissue to extract permeability model parameters

• Published in: Physics of fluids (1994) 2020-01, Vol.32 (1)
• Main Authors: Shrestha, Pranav, Stoeber, Boris
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Constitutive equations; Constitutive relationships; Deformation effects; Flow velocity; Fluid dynamics; Fluid flow; Fluid injection; Fluids; Formability; Mathematical models; Medical devices; Medical electronics; Needles; Optical Coherence Tomography; Parameters; Permeability; Physics; Porous media; Skin; Tissues; Vaccines; Volumetric strain
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5131488

One of the most common health care procedures is injecting fluids, in the form of drugs and vaccines, into our bodies, and hollow microneedles are emerging medical devices that deliver such fluids into the skin. Fluid injection into the skin through microneedles is advantageous because of improved patient compliance and the dose sparing effect for vaccines. Since skin tissue is a deformable porous medium, injecting fluid into the skin involves a coupled interaction between the injected fluid flow and the deformation of the soft porous matrix of skin tissue. Here, we introduce a semiempirical model that describes the fluid transport through skin tissue based on experimental data and constitutive equations of flow through biological tissue. Our model assumes that fluid flows radially outward and tissue deformation varies spherically from the microneedle tip. The permeability of tissue, assumed to be initially homogeneous, varies as a function of volumetric strain in the tissue based on a two-parameter exponential relationship. The model is optimized to extract two macroscopic parameters, k0 and m, for each of the seven experiments on excised porcine skin, using a radial form of Darcy’s law, the two-parameter exponential dependence of permeability on strain, and the experimental data on fluid flow recorded by a flow sensor and tissue deformation captured in real time using optical coherence tomography. The fluid flow estimated by the permeability model with optimized macroscopic parameters matches closely with the recorded flow rate, thus validating our semiempirical model.