Annals of Biomedical Engineering

, Volume 45, Issue 4, pp 1027–1038 | Cite as

Computational and Experimental Analysis of Fluid Transport Through Three-Dimensional Collagen–Matrigel Hydrogels

  • Lauren E. Marshall
  • Roy Koomullil
  • Andra R. Frost
  • Joel L. BerryEmail author


A preclinical testing model for cancer therapeutics that replicates in vivo physiology is needed to accurately describe drug delivery and efficacy prior to clinical trials. To develop an in vitro model of breast cancer that mimics in vivo drug/nutrient delivery as well as physiological size and bio-composition, it is essential to describe the mass transport quantitatively. The objective of the present study was to develop in vitro and computational models to measure mass transport from a perfusion system into a 3D extracellular matrix (ECM). A perfusion-flow bioreactor system was used to control and quantify the mass transport of a macromolecule within an ECM hydrogel with embedded through-channels. The material properties, fluid mechanics, and structure of the construct quantified in the in vitro model were input into, and served as validation of, the computational fluid dynamics (CFD) simulation. Results showed that advection and diffusion played a complementary role in mass transport. As the CFD simulation becomes more complex with embedded blood vessels and cancer cells, it will become more recapitulative of in vivo breast cancers. This study is a step toward development of a preclinical testing platform that will be more predictive of patient response to therapeutics than two-dimensional cell culture.


Bioreactor 3D in vitro model Fluid dynamics Mass transport Acellular 



Mass fraction of the species


Unit normal to control volume


Initial maximum FITC-dextran concentration at the channel wall (mg ml−1)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {V}\)

Velocity vector

Into the board vector symbol

\(\Delta P\)

Hydrostatic pressure head (Pa)


Pressure gradient (Pa cm−1)






FITC-dextran concentration at a specific distance and time (mg ml−1)


Cancer associated fibroblasts


Computational fluid dynamics


Maximum concentration (mg ml−1)


Minimum concentration (mg ml−1)


Effective diffusion coefficient (cm2 s−1)


Surface area (cm2)


Fiber diameter (nm)


Elemental volume (cm3)


Extracellular matrix


Complimentary error function


Inviscid flux vector


Fluorescein isothiocyanate




Viscous flux vector


Growth factor reduced


Gray-value intensity


Source term


Hemotoxylin and eosin


Interstitial fluid pressure


Diffusion mass flux of the species (kg s−1 m−2)


Breast cancer epithelial cells


Phosphate-buffered saline




Viscous porous resistance


Conserved variable vector


Flow rate (m3 s−1)


Laminar Schmidt number


Turbulent Schmidt number


Standard error


Scanning electron microscopy


Time (s)


Volume of hydrated ECM sample (ml)


Weight of dehydrated ECM sample (g)


Weight of hydrated ECM sample (g)


Wall shear stress (dyne cm−2)


Distance from channel wall (cm)


In vitro constant


Effective porosity


Contact angle (°)


Turbulent viscosity (Pa s)


Density (g ml−1)


Cross-sectional area of hydrogel


Effective permeability


Thickness of hydrogel


Viscosity (Pa s)



The authors would like to acknowledge T. Wick, J. Murphy Ullrich, J. Richter, and K. Goliwas for their guidance, Heather Forrester, Lindsay Miller, and Michelle Thomas for their technical assistance, Southern Research for use of their core facilities including histological specimen preparation, and the University of Alabama at Birmingham (UAB) Scanning Electron Microscopy and Oxygen Plasma core facilities. Funding for the experimental study was provided by the Department of Defense (DoD) Congressionally Directed Medical Research Programmes (CDMRP; Grant No. BC121367).

Conflict of Interest

The authors have declared that no conflict of interest exists.


  1. 1.
    Baluk, P., H. Hashizume, and D. M. McDonald. Cellular abnormalities of blood vessels as targets in cancer. Curr. Opin. Genet. Dev. 15(1):102–111, 2005.CrossRefPubMedGoogle Scholar
  2. 2.
    Barnes, C., L. Speroni, K. P. Quinn, M. Montevil, K. Saetzler, G. Bode-Animashaun, G. McKerr, I. Georgakoudi, C. S. Downes, C. Sonnenschein, C. V. Howard, and A. M. Soto. From single cells to tissues: interactions between the matrix and human breast cells in real time. PLOS One 9(4):1–12, 2014.CrossRefGoogle Scholar
  3. 3.
    Buchanan, C. F., E. E. Voigt, C. S. Szot, J. W. Freeman, P. P. Vlachos, and M. N. Rylander. Three-dimensional microfluidic collagen hydrogels for investigating flow-mediated tumor-endothelial signaling and vascular organization. Tissue Eng. Part C Methods 20(1):64–75, 2014.CrossRefPubMedGoogle Scholar
  4. 4.
    CD-Adapco. Star-ccm+® documentation, 2016.Google Scholar
  5. 5.
    Chen, J. H., G. Agrawal, B. Feig, H. M. Baek, P. M. Carpenter, R. S. Mehta, O. Nalcioglu, and M. Y. Su. Triple-negative breast cancer: MRI features in 29 patients. Ann. Oncol. 18(12):2042–2043, 2007.CrossRefPubMedGoogle Scholar
  6. 6.
    Coopman, P. J., M. E. Bracke, J. C. Lissitzky, G. K. De Bruyne, F. M. Van Roy, J. M. Foidart, and M. M. Mareel. Influence of basement membrane molecules on directional migration of human breast cell lines in vitro. J. Cell Sci. 98(Pt 3):396–401, 1991.Google Scholar
  7. 7.
    Egeblad, M., M. G. Rasch, and V. M. Weaver. Dynamic interplay between the collagen scaffold and tumor evolution. Curr. Opin. Cell Biol. 22(5):697–706, 2010.CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Elden, H. R. Rate of swelling of collagen. Science 128(3339):1624–1625, 1958.CrossRefPubMedGoogle Scholar
  9. 9.
    Evans, S. M., A. L. Litzenberger, A. E. Ellenberger, J. E. Maneval, E. L. Jablonski, and B. M. Vogel. A microfluidic method to measure small molecule diffusion in hydrogels. Mater. Sci. Eng. C 35:322–334, 2014.CrossRefGoogle Scholar
  10. 10.
    Goel, S., D. G. Duda, L. Xu, L. L. Munn, Y. Boucher, D. Fukumura, and R. K. Jain. Normalization of the vasculature for treatment of cancer and other diseases. Physiol. Rev. 91(3):1071–1121, 2011.CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Hamngren Blomqvist, C., C. Abrahamsson, T. Gebäck, A. Altskär, A.-M. Hermansson, M. Nydén, S. Gustafsson, N. Lorén, and E. Olsson. Pore size effects on convective flow and diffusion through nanoporous silica gels. Colloids Surf. A Physicochem. Eng. Asp. 484:288–296, 2015.CrossRefGoogle Scholar
  12. 12.
    Hashizume, H., P. Baluk, S. Morikawa, J. W. McLean, G. Thurston, S. Roberge, R. K. Jain, and D. M. McDonald. Openings between defective endothelial cells explain tumor vessel leakiness. Am. J. Pathol. 156(4):1363–1380, 2000.CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Huang, C. P., J. Lu, H. Seon, A. P. Lee, L. A. Flanagan, H. Y. Kim, A. J. Putnam, and N. L. Jeon. Engineering microscale cellular niches for three-dimensional multicellular co-cultures. Lab Chip 9(12):1740–1748, 2009.CrossRefPubMedPubMedCentralGoogle Scholar
  14. 14.
    Jain, R. K. Determinants of tumor blood flow: a review. Cancer Res. 48:2641–2658, 1988.PubMedGoogle Scholar
  15. 15.
    Jain, R. K., J. D. Martin, and T. Stylianopoulos. The role of mechanical forces in tumor growth and therapy. Ann. Rev. Biomed. Eng. 16:321–346, 2014.CrossRefGoogle Scholar
  16. 16.
    Kalluri, R. Basement membranes: structure, assembly and role in tumour angiogenesis. Nat. Rev. Cancer 3(6):422–433, 2003.CrossRefPubMedGoogle Scholar
  17. 17.
    Kestin, J., M. Sokolov, and W. A. Wakeham. Viscosity of liquid water in the range −8 °C to 150 °C. J. Phys. Chem. Ref. Data 7(3):941–948, 1978.CrossRefGoogle Scholar
  18. 18.
    Kleinman, H. K., and G. R. Martin. Matrigel: basement membrane matrix with biological activity. Semin. Cancer Biol. 15(5):378–386, 2005.CrossRefPubMedGoogle Scholar
  19. 19.
    Li, Q., A. B. Chow, and R. R. Mattingly. Three-dimensional overlay culture models of human breast cancer reveal a critical sensitivity to mitogen-activated protein kinase kinase inhibitors. J. Pharmacol. Exp. Ther. 332(3):821–828, 2010.CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Lochter, A., and M. J. Bissell. Involvement of extracellular matrix constituents in breast cancer. Semin. Cancer Biol. 6(3):165–173, 1995.CrossRefPubMedGoogle Scholar
  21. 21.
    Marshall, L. E., K. F. Goliwas, L. M. Miller, A. D. Penman, A. R. Frost and J. L. Berry. Flow-perfusion bioreactor system for engineered breast cancer surrogates to be used in preclinical testing. J. Tissue Eng. Regen. Med., 2015.Google Scholar
  22. 22.
    Nathanson, S. D., and L. Nelson. Interstitial fluid pressure in breast cancer, benign breast conditions, and breast parenchyma. Ann. Surg. Oncol. 1(4):333–338, 1994.CrossRefPubMedGoogle Scholar
  23. 23.
    Planeix, F., M. A. Siraj, F. C. Bidard, B. Robin, C. Pichon, X. Sastre-Garau, M. Antoine, and N. Ghinea. Endothelial follicle-stimulating hormone receptor expression in invasive breast cancer and vascular remodeling at tumor periphery. J. Exp. Clin. Cancer Res. 34:12, 2015.CrossRefPubMedPubMedCentralGoogle Scholar
  24. 24.
    Price, G. M., K. H. Wong, J. G. Truslow, A. D. Leung, C. Acharya, and J. Tien. Effect of mechanical factors on the function of engineered human blood microvessels in microfluidic collagen gels. Biomaterials 31(24):6182–6189, 2010.CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Rivron, N. C., J. Rouwkema, J. Liu, J. de Boer, and C. A. van Blitterswijk. Engineering vascularized tissues in vitro. Eur. Cell Mater. 15:27–40, 2008.CrossRefPubMedGoogle Scholar
  26. 26.
    Shamloo, A., N. Mohammadaliha, and M. Mohseni. Integrative utilization of microenvironments, biomaterials and computational techniques for advanced tissue engineering. J. Biotechnol. 212:71–89, 2015.CrossRefPubMedGoogle Scholar
  27. 27.
    Sharma, S. V., D. A. Haber, and J. Settleman. Cell line-based platforms to evaluate the therapeutic efficacy of candidate anticancer agents. Nat. Rev. Cancer 10(4):241–253, 2010.CrossRefPubMedGoogle Scholar
  28. 28.
    Sukmana, I. Microvascular guidance: a challenge to support the development of vascularised tissue engineering construct. Sci. World J. 2012:201352, 2012.CrossRefGoogle Scholar
  29. 29.
    Szot, C. S., C. F. Buchanan, J. W. Freeman, and M. N. Rylander. 3D in vitro bioengineered tumors based on collagen I hydrogels. Biomaterials 32(31):7905–7912, 2011.CrossRefPubMedPubMedCentralGoogle Scholar
  30. 30.
    Wang, Q.-M., A. C. Mohan, M. L. Oyen, and X.-H. Zhao. Separating viscoelasticity and poroelasticity of gels with different length and time scales. Acta Mech. Sin. 30(1):20–27, 2014.CrossRefGoogle Scholar
  31. 31.
    Wolf, K., M. Te Lindert, M. Krause, S. Alexander, J. Te Riet, A. L. Willis, R. M. Hoffman, C. G. Figdor, S. J. Weiss, and P. Friedl. Physical limits of cell migration: Control by ecm space and nuclear deformation and tuning by proteolysis and traction force. J Cell Biol. 201(7):1069–1084, 2013.CrossRefPubMedPubMedCentralGoogle Scholar
  32. 32.
    Wong, A. D., and P. C. Searson. Live-cell imaging of invasion and intravasation in an artificial microvessel platform. Cancer Res. 74(17):4937–4945, 2014.CrossRefPubMedPubMedCentralGoogle Scholar
  33. 33.
    Yousif, L. F., J. Di Russo, and L. Sorokin. Laminin isoforms in endothelial and perivascular basement membranes. Cell Adhes. Migr. 7(1):101–110, 2013.CrossRefGoogle Scholar
  34. 34.
    Zhu, Z., G. Wu, H. Wei, H. Yang, Y. He, S. Xie, Q. Zhao, and X. Guo. Investigation of the permeability and optical clearing ability of different analytes in human normal and cancerous breast tissues by spectral domain oct. J. Biophotonics 5(7):536–543, 2012.CrossRefPubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2016

Authors and Affiliations

  • Lauren E. Marshall
    • 1
  • Roy Koomullil
    • 1
  • Andra R. Frost
    • 1
  • Joel L. Berry
    • 1
    Email author
  1. 1.Department of Biomedical EngineeringUniversity of Alabama at Birmingham, Shelby Biomedical Research Bldg. Rm. 802BirminghamUSA

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