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Research Papers

Dynamics of Interstitial Fluid Pressure in Extracellular Matrix Hydrogels in Microfluidic Devices

[+] Author and Article Information
Joe Tien

Department of Biomedical Engineering,
Boston University,
Boston, MA 02215;
Division of Materials Science and Engineering,
Boston University,
Boston, MA 02215
e-mail: jtien@bu.edu

Le Li, Ozgur Ozsun

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215;
Photonics Center,
Boston University,
Boston, MA 02215

Kamil L. Ekinci

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215;
Division of Materials Science and Engineering,
Boston University,
Boston, MA 02215;
Photonics Center,
Boston University,
Boston, MA 02215
e-mail: ekinci@bu.edu

1Corresponding author.

Manuscript received April 7, 2015; final manuscript received July 6, 2015; published online July 22, 2015. Assoc. Editor: Jeffrey Ruberti.

J Biomech Eng 137(9), 091009 (Jul 22, 2015) Paper No: BIO-15-1152; doi: 10.1115/1.4031020 History: Received April 07, 2015

In order to understand how interstitial fluid pressure and flow affect cell behavior, many studies use microfluidic approaches to apply externally controlled pressures to the boundary of a cell-containing gel. It is generally assumed that the resulting interstitial pressure distribution quickly reaches a steady-state, but this assumption has not been rigorously tested. Here, we demonstrate experimentally and computationally that the interstitial fluid pressure within an extracellular matrix gel in a microfluidic device can, in some cases, react with a long time delay to external loading. Remarkably, the source of this delay is the slight (∼100 nm in the cases examined here) distension of the walls of the device under pressure. Finite-element models show that the dynamics of interstitial pressure can be described as an instantaneous jump, followed by axial and transverse diffusion, until the steady pressure distribution is reached. The dynamics follow scaling laws that enable estimation of a gel's poroelastic constants from time-resolved measurements of interstitial fluid pressure.

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References

Figures

Grahic Jump Location
Fig. 1

(a) Experimental setup. Gels were formed in PDMS channels (top wall thickness d) with linear dimensions L × w × h that lay on top of a rigid glass slide. A pressure step P0 was applied to both ends of the gel via tubing, and the distension ξ(t) of the upper PDMS wall structure was measured at the center location denoted by an asterisk. (b) Computational geometries. Models of rectangular channels consisted of the experimental setup without tubing or wells; gel displacements were set to zero along the bottom plane. Models of cylindrical channels (radius R) were allowed to deform equally in all radial directions; gel displacements were not constrained to be zero along the cylindrical axis.

Grahic Jump Location
Fig. 2

Representative distension–time plots from experiments and computational models. Data were obtained from the boldfaced experimental and modeling cases in Table 1 and Supplemental Table S1, available under the “Supplemental Data” tab for this paper on the ASME Digital Collection; the modeling cases were chosen to give qualitatively similar time-dependences to those observed experimentally. (a) and (b) Experimental data. (c) and (d) Computational results. Dotted lines denote the times at which external pressure was applied; solid (red) curves indicate best fits to Eq. (7).

Grahic Jump Location
Fig. 3

Plots of time constant τ versus proposed scaling expressions. (a) Scaling law that incorporates gel poroelastic constants and assumes axial pressure diffusion is rate-limiting. (b) Scaling law that incorporates PDMS distension and assumes axial fluid transport is rate-limiting. (c) Scaling law that assumes axial and transverse pressure diffusion contribute to τ. Open circles: rectangular channels and solid (green) circles: cylindrical channels.

Grahic Jump Location
Fig. 5

Stages in the reaction of an encapsulated gel to externally applied pressure. A gel that is initially at zero pressure deforms instantaneously, thereby establishing an initial interstitial pressure distribution. Axial and transverse pressure diffusion then take place, until the pressure reaches its steady-state distribution. The color maps show the ratio of interstitial to applied pressures, at various times.

Grahic Jump Location
Fig. 4

Scaling behavior of the initial and equilibrium PDMS distensions ξ0 and ξ, respectively, and application to the prediction of a gel's hydraulic permeability kgel. (a) ξ0 versus τ||. (b) Scaling law for ξ that assumes linear response to interstitial fluid pressure, for rectangular channels. The solid (red) line plots the empirical fit of Eq. (14). (c) Plot of measured kgel for collagen gels versus the values predicted from the computed scaling laws. The solid (red) line plots equality.

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