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Research Papers

Interaction Between the Interstitial Fluid and the Extracellular Matrix in Confined Indentation

[+] Author and Article Information
Yiling Lu

Medical Engineering Division, School of Engineering and Materials Science, Queen Mary, University of London, London E1 4NS, UK

Wen Wang1

Medical Engineering Division, School of Engineering and Materials Science, Queen Mary, University of London, London E1 4NS, UKwen.wang@qmul.ac.uk

1

Corresponding author.

J Biomech Eng 130(4), 041011 (Jun 11, 2008) (10 pages) doi:10.1115/1.2939310 History: Received January 12, 2007; Revised March 24, 2008; Published June 11, 2008

The Movement of the interstitial fluid in extracellular matrices not only affects the mechanical properties of soft tissues, but also facilitates the transport of nutrients and the removal of waste products. In this study, we aim to quantify interstitial fluid movement and fluid-matrix interaction in a new loading configuration—confined tissue indentation, using a poroelastic theory. The tissue sample sits in a cylindrical chamber and loading is applied on the top central surface of the specimen by a porous indenter that is fixed on the specimen. The interaction between the solid and the fluid is examined using a finite element method under ramp and cyclic loads. Typical compression-relaxation responses of the specimen are observed in a ramp load. Under a cyclic load, the system reaches a dynamic equilibrium after a number of loading cycles. Fluid circulation, with opposite directions in the loading and unloading phases in the extracellular matrix, is observed. The most significant variation in the fluid pressure locates just beneath the indenter. Fluid pressurization arrives at equilibrium much faster than the solid matrix deformation. As the loading frequency increases, the location of the peak pressure oscillation moves closer to the indenter and the magnitude of the pressure oscillation increases. Concomitantly, the axial stress variation of the solid matrix is reduced. It is found that interstitial fluid movement helps to alleviate severe strain of the solid matrix beneath the indenter. This study quantifies the interaction between the interstitial fluid and the extracellular matrix by decomposing the loading response of the specimen into the “transient” and “dynamic equilibrium” phases. Confined indentation in this manuscript gives a better representation of some in vitro and in vivo loading configurations where the indenter covers part of the top surface of the tissue.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Relative fluid velocity and pressure in the specimen under a ramp load t0=500s and ε0=0.1. Results on the axis of the specimen at z=0.1 (dotted line, deep zone), z=0.5 (dashed line, middle zone), and z=0.9 (solid line, superficial zone) are given. (a) The axial relative velocity of the fluid. (b) Fluid pressure.

Grahic Jump Location
Figure 3

Fluid pressure and solid matrix stress under a cyclic load (f=0.1Hz) at different depths in the tissue sample underneath the edge of the loading indenter (r=0.2). z=0.1 (dotted line), 0.5 (dashed line), and 0.9 (solid line). (a) Fluid pressure. (b) Axial stress of the solid matrix.

Grahic Jump Location
Figure 4

Fluid pressure and relative velocity distribution in the specimen under a cyclic load (f=0.1Hz) in dynamic equilibrium. The left half of each panel shows the fluid pressure contours and the right half shows the fluid relative velocity vectors. Velocity scale and pressure legend apply to all panels.

Grahic Jump Location
Figure 5

Time-averaged mean values (left) and their amplitude of variation (right) at three depths in the tissue sample under a cyclic load (f=0.1Hz) after reaching dynamic equilibrium state. z=0.1 (dotted line), 0.5 (dashed line), and 0.9 (solid line). (a) Fluid pressure. (b) Axial stress of the solid matrix.

Grahic Jump Location
Figure 6

Effect of the loading frequency on the time-averaged mean values (left) and their amplitude of variation (right) in dynamic equilibrium states. In the figure, z=0.9. f=0.01Hz (dotted line), 0.1Hz (dashed line), and 1.0Hz (solid line). (a) Fluid pressure. (b) Axial stress of the solid matrix.

Grahic Jump Location
Figure 7

Reaction force on the indenter under different loading frequencies. (a) The first 15 loading cycles. f=0.01Hz (dotted line), 0.1Hz (dashed line), and 1Hz (solid line). (b) After reaching the dynamic equilibrium state. The solid bars represent the mean reaction forces and the open bars represent their amplitude of variation.

Grahic Jump Location
Figure 8

Interstitial fluid pressure under different loading configurations. Results show t=3∕8T in a dynamic equilibrium state with f=0.1Hz. The left panels are given for comparison only (D∕L=1.0 and d∕L=0.4). The right panels show a specimen with the same height, L, but three times the diameter, D∕L=3.0. (a) d∕L=0.4. (b) d∕L=1.2.

Grahic Jump Location
Figure 1

Schematics of the confined indentation configuration. A cylindrical tissue sample is immersed in fluid in a rigid confining chamber. External load is applied via a porous indenter in the central region of the top surface of the specimen.

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