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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
Article

Abstract

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.

Keywords

Bioreactor 3D in vitro model Fluid dynamics Mass transport Acellular 

Abbreviations

φ

Mass fraction of the species

\(\vec{n}\)

Unit normal to control volume

C0

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)

p

Pressure gradient (Pa cm−1)

2D

Two-dimensional

3D

Three-dimensional

C(t,x)

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

CAF

Cancer associated fibroblasts

CFD

Computational fluid dynamics

Cmax

Maximum concentration (mg ml−1)

Cmin

Minimum concentration (mg ml−1)

D

Effective diffusion coefficient (cm2 s−1)

dA

Surface area (cm2)

Dfiber

Fiber diameter (nm)

dv

Elemental volume (cm3)

ECM

Extracellular matrix

erfc

Complimentary error function

F

Inviscid flux vector

FITC

Fluorescein isothiocyanate

FN

Fibronectin

G

Viscous flux vector

GFR

Growth factor reduced

GV

Gray-value intensity

H

Source term

H&E

Hemotoxylin and eosin

IFP

Interstitial fluid pressure

Jj

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

MDA-MB-231s

Breast cancer epithelial cells

PBS

Phosphate-buffered saline

PDMS

Polydimethylsiloxane

Pv

Viscous porous resistance

Q

Conserved variable vector

q

Flow rate (m3 s−1)

Sc

Laminar Schmidt number

Sct

Turbulent Schmidt number

SE

Standard error

SEM

Scanning electron microscopy

t

Time (s)

Vhydrated

Volume of hydrated ECM sample (ml)

wdehydrated

Weight of dehydrated ECM sample (g)

whydrated

Weight of hydrated ECM sample (g)

WSS

Wall shear stress (dyne cm−2)

x

Distance from channel wall (cm)

β

In vitro constant

ε

Effective porosity

Θ

Contact angle (°)

μt

Turbulent viscosity (Pa s)

ρ

Density (g ml−1)

A

Cross-sectional area of hydrogel

k

Effective permeability

l

Thickness of hydrogel

μ

Viscosity (Pa s)

Notes

Acknowledgments

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.

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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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