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Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression

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Abstract

Subcutaneous tissue mechanics are important for drug delivery. Yet, even though this material is poroelastic, its mechanical characterization has focused on its hyperelastic response. Moreover, advancement in subcutaneous drug delivery requires effective tissue mimics such as hydrogels for which similar gaps of poroelastic data exist. Porcine subcutaneous samples and gelatin hydrogels were tested under confined compression at physiological conditions and strain rates of 0.01%/s in 5% strain steps with 2600 s of stress relaxation between loading steps. Force-time data were used in an inverse finite element approach to obtain material parameters. Tissues and gels were modeled as porous neo-Hookean materials with properties specified via shear modulus, effective solid volume fraction, initial hydraulic permeability, permeability exponent, and normalized viscous relaxation moduli. The constitutive model was implemented into an isogeometric analysis (IGA) framework to study subcutaneous injection. Subcutaneous tissue exhibited an initial spike in stress due to compression of the solid and fluid pressure buildup, with rapid relaxation explained by fluid drainage, and longer time-scale relaxation explained by viscous dissipation. The inferred parameters aligned with the ranges reported in the literature. Hydraulic permeability, the most important parameter for drug delivery, was in the range \(k_0\in [0.142,0.203]\) mm\(^{4}\)/(N s). With these parameters, IGA simulations showed peak stresses due to a 1-mL injection to reach 48.8 kPa at the site of injection, decaying after drug volume disperses into the tissue. The poro-hyper-viscoelastic neo-Hookean model captures the confined compression response of subcutaneous tissue and gelatin hydrogels. IGA implementation enables predictive simulations of drug delivery.

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Acknowledgements

This work was supported by Eli Lilly and Company.

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Authors and Affiliations

  1. School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

    Jacques Barsimantov, Mario de Lucio, Hector Gomez & Adrian B. Tepole

  2. Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA

    Jordanna Payne, Mazin Hakim, Luis Solorio & Adrian B. Tepole

  3. Indiana University School of Medicine, Indianapolis, IN, USA

    Jordanna Payne

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Contributions

Conceptualization: JBM and ABT; Methodology: JBM, JP, HM, ML, HG, LS, and ABT; Formal analysis and investigation: JBM, JP, HM, and ML; Writing—original draft preparation: JBM and ABT; Writing—review and editing: JBM, JP, HM, ML, HG, LS, and ABT; Funding acquisition: HG, LS, and ABT; Resources: HG, LS, and ABT; Supervision: ABT.

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Correspondence to Adrian B. Tepole.

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The authors declare that there are no conflicts of interest that affected this work. The work described herein was conducted during Mazin Hakim's graduate studies at Purdue University. Mazin Hakim is currently an employee and common stock owner of Eli Lilly and Company.

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Barsimantov, J., Payne, J., de Lucio, M. et al. Poroelastic Characterization and Modeling of Subcutaneous Tissue Under Confined Compression. Ann Biomed Eng (2024). https://doi.org/10.1007/s10439-024-03477-1

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