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A Linear, Biphasic Model Incorporating a Brinkman Term to Describe the Mechanics of Cell-Seeded Collagen Hydrogels

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Abstract

Protein-based hydrogels are commonly used as in vitro models of native tissues because they can mimic specific aspects of the three-dimensional extracellular matrix present in vivo. Bulk mechanical stimulation is often applied to these gels to determine the response of embedded cells to biomechanical factors such as stress and strain. This study develops and applies a linear, biphasic formulation of hydrogel mechanics that includes a Brinkman term to account for viscous effects. The model is used to predict fluid pressure, relative velocity, and estimated shear stress exerted on cells seeded within a cyclically strained collagen hydrogel with and without imposed cross flow. The model was validated using a confined compression creep test of a cardiac fibroblast-seeded collagen type I hydrogel, and the effect of the added Brinkman term was assessed. The model indicated that the effects of strain and interstitial fluid flow are strongly interdependent in the collagen hydrogel. Our results suggest that the contribution of the Brinkman term is greater in protein hydrogels than in native tissues, and that studies that apply cyclic strain to cell-seeded hydrogels should account for the induced interstitial fluid flow. This study, therefore, has relevance to the increasing number of studies that examine cellular responses to mechanical stresses using in vitro hydrogel models.

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Acknowledgments

This study was supported in part by the Microfluidics in Biomedical Sciences Training Program at the University of Michigan, sponsored by the National Institute of Biomedical Imaging and Bioengineering.

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Authors and Affiliations

  1. Department of Biomedical Engineering, University of Michigan, 1101 Beal Ave., Ann Arbor, MI, 48109, USA

    Peter A. Galie & Jan P. Stegemann

  2. Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    Robert L. Spilker

Authors
  1. Peter A. Galie
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  2. Robert L. Spilker
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  3. Jan P. Stegemann
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Corresponding author

Correspondence to Jan P. Stegemann.

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Associate Editor Konstantinos Konstantopoulos oversaw the review of this article.

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Galie, P.A., Spilker, R.L. & Stegemann, J.P. A Linear, Biphasic Model Incorporating a Brinkman Term to Describe the Mechanics of Cell-Seeded Collagen Hydrogels. Ann Biomed Eng 39, 2767–2779 (2011). https://doi.org/10.1007/s10439-011-0371-9

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  • DOI: https://doi.org/10.1007/s10439-011-0371-9

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