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.

References

References
1.
Swartz
,
M. A.
, and
Fleury
,
M. E.
,
2007
, “
Interstitial Flow and Its Effects in Soft Tissues
,”
Annu. Rev. Biomed. Eng.
,
9
, pp.
229
256
.
2.
Helm
,
C.-L. E.
,
Fleury
,
M. E.
,
Zisch
,
A. H.
,
Boschetti
,
F.
, and
Swartz
,
M. A.
,
2005
, “
Synergy Between Interstitial Flow and VEGF Directs Capillary Morphogenesis In Vitro Through a Gradient Amplification Mechanism
,”
Proc. Natl. Acad. Sci. U. S. A.
,
102
(
44
), pp.
15779
15784
.
3.
Tien
,
J.
,
Truslow
,
J. G.
, and
Nelson
,
C. M.
,
2012
, “
Modulation of Invasive Phenotype by Interstitial Pressure-Driven Convection in Aggregates of Human Breast Cancer Cells
,”
PLoS One
,
7
(
9
), p.
e45191
.
4.
Detournay
,
E.
, and
Cheng
,
A. H.-D.
,
1993
, “
Fundamentals of Poroelasticity
,”
Comprehensive Rock Engineering: Principles, Practice and Projects
(Analysis and Design Method, Vol.
II
),
C.
Fairhurst
, ed.,
Pergamon
,
New York
, pp.
113
171
.
5.
Quinn
,
T. M.
,
2013
, “
Flow-Induced Deformation of Poroelastic Tissues and Gels: A New Perspective on Equilibrium Pressure-Flow-Thickness Relations
,”
ASME J. Biomech. Eng.
,
135
(
1
), p.
011009
.
6.
Bowen
,
R. M.
,
1980
, “
Incompressible Porous Media Models by Use of the Theory of Mixtures
,”
Int. J. Eng. Sci.
,
18
(
9
), pp.
1129
1148
.
7.
Wang
,
H. F.
,
2000
,
Theory of Linear Poroelasticity With Applications to Geomechanics and Hydrogeology
,
Princeton University
,
Princeton, NJ
.
8.
Mow
,
V. C.
,
Kuei
,
S. C.
,
Lai
,
W. M.
, and
Armstrong
,
C. G.
,
1980
, “
Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments
,”
ASME J. Biomech. Eng.
,
102
(
1
), pp.
73
84
.
9.
Mow
,
V. C.
,
Holmes
,
M. H.
, and
Lai
,
W. M.
,
1984
, “
Fluid Transport and Mechanical Properties of Articular Cartilage: A Review
,”
J. Biomech.
,
17
(
5
), pp.
377
394
.
10.
Hsu
,
Y.-H.
,
Moya
,
M. L.
,
Hughes
,
C. C. W.
,
George
,
S. C.
, and
Lee
,
A. P.
,
2013
, “
A Microfluidic Platform for Generating Large-Scale Nearly Identical Human Microphysiological Vascularized Tissue Arrays
,”
Lab Chip
,
13
(
15
), pp.
2990
2998
.
11.
Polacheck
,
W. J.
,
Charest
,
J. L.
, and
Kamm
,
R. D.
,
2011
, “
Interstitial Flow Influences Direction of Tumor Cell Migration Through Competing Mechanisms
,”
Proc. Natl. Acad. Sci. U. S. A.
,
108
(
27
), pp.
11115
11120
.
12.
Ozsun
,
O.
,
Thompson
,
R. L.
,
Ekinci
,
K. L.
, and
Tien
,
J.
,
2014
, “
Non-Invasive Mapping of Interstitial Fluid Pressure in Microscale Tissues
,”
Integr. Biol.
,
6
(
10
), pp.
979
987
.
13.
Ozsun
,
O.
,
Yakhot
,
V.
, and
Ekinci
,
K. L.
,
2013
, “
Non-Invasive Measurement of the Pressure Distribution in a Deformable Micro-Channel
,”
J. Fluid Mech.
,
734
, p.
R1
.
14.
Deck
,
L.
, and
de Groot
,
P.
,
1994
, “
High-Speed Noncontact Profiler Based on Scanning White-Light Interferometry
,”
Appl. Opt.
,
33
(
31
), pp.
7334
7338
.
15.
Norris
,
A.
,
1992
, “
On the Correspondence Between Poroelasticity and Thermoelasticity
,”
J. Appl. Phys.
,
71
(
3
), pp.
1138
1141
.
16.
Wong
,
K. H. K.
,
Truslow
,
J. G.
,
Khankhel
,
A. H.
,
Chan
,
K. L. S.
, and
Tien
,
J.
,
2013
, “
Artificial Lymphatic Drainage Systems for Vascularized Microfluidic Scaffolds
,”
J. Biomed. Mater. Res. A
,
101
(
8
), pp.
2181
2190
.
17.
McCarty
,
W. J.
, and
Johnson
,
M.
,
2007
, “
The Hydraulic Conductivity of Matrigel
,”
Biorheology
,
44
(
5–6
), pp.
303
317
.
18.
Ng
,
C. P.
, and
Pun
,
S. H.
,
2008
, “
A Perfusable 3D Cell-Matrix Tissue Culture Chamber for In Situ Evaluation of Nanoparticle Vehicle Penetration and Transport
,”
Biotechnol. Bioeng.
,
99
(
6
), pp.
1490
1501
.
19.
Chrobak
,
K. M.
,
Potter
,
D. R.
, and
Tien
,
J.
,
2006
, “
Formation of Perfused, Functional Microvascular Tubes In Vitro
,”
Microvasc. Res.
,
71
(
3
), pp.
185
196
.
20.
Yang
,
Y.-L.
,
Leone
,
L. M.
, and
Kaufman
,
L. J.
,
2009
, “
Elastic Moduli of Collagen Gels Can be Predicted From Two-Dimensional Confocal Microscopy
,”
Biophys. J.
,
97
(
7
), pp.
2051
2060
.
21.
Carr
,
M. E.
,
Shen
,
L. L.
, and
Hermans
,
J.
,
1976
, “
A Physical Standard of Fibrinogen: Measurement of the Elastic Modulus of Dilute Fibrin Gels With a New Elastometer
,”
Anal. Biochem.
,
72
(
1–2
), pp.
202
211
.
22.
Leiderman
,
R.
,
Barbone
,
P. E.
,
Oberai
,
A. A.
, and
Bamber
,
J. C.
,
2006
, “
Coupling Between Elastic Strain and Interstitial Fluid Flow: Ramifications for Poroelastic Imaging
,”
Phys. Med. Biol.
,
51
(
24
), pp.
6291
6313
.
23.
Netti
,
P. A.
,
Baxter
,
L. T.
,
Boucher
,
Y.
,
Skalak
,
R.
, and
Jain
,
R. K.
,
1995
, “
Time-Dependent Behavior of Interstitial Fluid Pressure in Solid Tumors: Implications for Drug Delivery
,”
Cancer Res.
,
55
(
22
), pp.
5451
5458
.
24.
Armstrong
,
C. G.
,
Lai
,
W. M.
, and
Mow
,
V. C.
,
1984
, “
An Analysis of the Unconfined Compression of Articular Cartilage
,”
ASME J. Biomech. Eng.
,
106
(
2
), pp.
165
173
.
25.
Kim
,
S.
,
Lee
,
H.
,
Chung
,
M.
, and
Jeon
,
N. L.
,
2013
, “
Engineering of Functional, Perfusable 3D Microvascular Networks on a Chip
,”
Lab Chip
,
13
(
8
), pp.
1489
1500
.
26.
Nguyen
,
Q. T.
,
Hwang
,
Y.
,
Chen
,
A. C.
,
Varghese
,
S.
, and
Sah
,
R. L.
,
2012
, “
Cartilage-Like Mechanical Properties of Poly (Ethylene Glycol)-Diacrylate Hydrogels
,”
Biomaterials
,
33
(
28
), pp.
6682
6690
.
27.
Fung
,
Y. C.
,
1993
,
Biomechanics: Mechanical Properties of Living Tissues
,
Springer-Verlag
,
New York
.
28.
Basser
,
P. J.
,
1992
, “
Interstitial Pressure, Volume, and Flow During Infusion Into Brain Tissue
,”
Microvasc. Res.
,
44
(
2
), pp.
143
165
.
29.
Chandran
,
P. L.
, and
Barocas
,
V. H.
,
2004
, “
Microstructural Mechanics of Collagen Gels in Confined Compression: Poroelasticity, Viscoelasticity, and Collapse
,”
ASME J. Biomech. Eng.
,
126
(
2
), pp.
152
166
.
30.
Chiarelli
,
P.
,
Basser
,
P. J.
,
Derossi
,
D.
, and
Goldstein
,
S.
,
1992
, “
The Dynamics of a Hydrogel Strip
,”
Biorheology
,
29
(
4
), pp.
383
398
.
31.
Ateshian
,
G. A.
, and
Weiss
,
J. A.
,
2010
, “
Anisotropic Hydraulic Permeability Under Finite Deformation
,”
ASME J. Biomech. Eng.
,
132
(
11
), p.
111004
.
32.
Charlaix
,
E.
,
Kushnick
,
A. P.
, and
Stokes
,
J. P.
,
1988
, “
Experimental Study of Dynamic Permeability in Porous Media
,”
Phys. Rev. Lett.
,
61
(
14
), pp.
1595
1598
.
33.
Sheng
,
P.
, and
Zhou
,
M.-Y.
,
1988
, “
Dynamic Permeability in Porous Media
,”
Phys. Rev. Lett.
,
61
(
14
), pp.
1591
1594
.
You do not currently have access to this content.