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Research Papers

Biphasic Investigation of Tissue Mechanical Response During Freezing Front Propagation

[+] Author and Article Information
Jamie Wright

Joint Graduate Program in Biomedical Engineering,  University of Texas at Arlington and University of Texas Southwestern Medical Center at Dallas,Bioengineering Department,  University of Texas at Arlington, Arlington, TX 76019

Bumsoo Han

School of Mechanical Engineering,Weldon School of Biomedical Engineering,  Purdue University, West Lafayette, IN 47907

Cheng-Jen Chuong1

Joint Graduate Program in Biomedical Engineering,  University of Texas at Arlington and University of Texas Southwestern Medical Center at Dallas,Bioengineering Department,  University of Texas at Arlington, Arlington, TX 76019chuong@uta.edu

1

Corresponding author.

J Biomech Eng 134(6), 061005 (Jun 13, 2012) (11 pages) doi:10.1115/1.4006682 History: Received August 26, 2011; Revised March 28, 2012; Posted April 30, 2012; Published June 13, 2012; Online June 13, 2012

Cryopreservation of engineered tissue (ET) has achieved limited success due to limited understanding of freezing-induced biophysical phenomena in ETs, especially fluid-matrix interaction within ETs. To further our understanding of the freezing-induced fluid-matrix interaction, we have developed a biphasic model formulation that simulates the transient heat transfer and volumetric expansion during freezing, its resulting fluid movement in the ET, elastic deformation of the solid matrix, and the corresponding pressure redistribution within. Treated as a biphasic material, the ET consists of a porous solid matrix fully saturated with interstitial fluid. Temperature-dependent material properties were employed, and phase change was included by incorporating the latent heat of phase change into an effective specific heat term. Model-predicted temperature distribution, the location of the moving freezing front, and the ET deformation rates through the time course compare reasonably well with experiments reported previously. Results from our theoretical model show that behind the marching freezing front, the ET undergoes expansion due to phase change of its fluid contents. It compresses the region preceding the freezing front leading to its fluid expulsion and reduced regional fluid volume fractions. The expelled fluid is forced forward and upward into the region further ahead of the compression zone causing a secondary expansion zone, which then compresses the region further downstream with much reduced intensity. Overall, it forms an alternating expansion-compression pattern, which moves with the marching freezing front. The present biphasic model helps us to gain insights into some facets of the freezing process and cryopreservation treatment that could not be gleaned experimentally. Its resulting understanding will ultimately be useful to design and improve cryopreservation protocols for ETs.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) A diagram illustrating the experimental setup used by Teo [33] to measure the ET’s response to directional freeze by employing the CID technique. (b) Experimentally measured temperature profiles recorded on either side of the ET across the gap [37].

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Figure 2

Temperature dependent material properties: αT (thermal expansion coefficient), cP (specific heat at constant pressure), cL (effective specific heat accounting for latent heat), ρ (density), E (Young’s modulus), F(T) (mass fraction of frozen tissue in mushy state), Khyd (hydraulic conductivity), and KT (thermal conductivity)

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Figure 3

Model-predicted (in red) and experimentally determined (in blue) [33] locations of the freezing front at different time steps

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Figure 4

(a1) Contours showing model predicted 3D dilatation rate in the ET when the freezing front is at location x = 1 mm, (a2) x = 2 mm, and (a3) x = 4 mm. (b1) 2D Contour of dilatation rate at the upper surface of the ET when the freezing front is at location x = 1 mm, (b2) x = 2 mm, and (b3) x = 4 mm. (c1) Contours showing measurement of 2D dilatation rate derived using CID [33] when the freezing front is at location x = 1 mm, (c2) x = 2 mm, and (c3) at location x = 4 mm. Reference line over (a1), (a2), and (a3) and that across (b1)-(c1), (b2)-(c2), and (b3)-(c3) pairs are to highlight the instantaneous location of the freezing front between modeling predication and measurement.

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Figure 5

Deformation rates calculated from simulation (solid line) and derived using CID (dotted line) [33] taken from the top surface of the ET when the freezing front is located at 1000 (blue), 2000 (red), and 3000 (green) μm, or 1, 2, 3 mm, respectively. The corresponding time steps are 85, 140, and 215 s.

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Figure 6

Fluid velocity vector plots when the freezing front is at location (a) x = 1 mm, (b) x = 2 mm, and (c) x = 4 mm, respectively

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Figure 7

Model-predicted instantaneous fluid volume fractions in the ET when the freezing front location is at (a) x = 1 mm, (b) x = 2 mm, and (c) x = 4 mm, respectively. Note that the initial volume fraction is ϕf (x, y, z, t = 0) = 0.914.

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Figure 8

Volumetric strains in the ET when the freezing front is at location (a) x = 1 mm, (b) x = 2 mm, and (c) x = 4 mm, respectively

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Figure 9

The first principal stress in the ET when the freezing front is at location (a) x = 2 mm and (b) x = 4 mm. The third principal stress when the freezing front is at location (c) x = 2 mm and (d) x = 4 mm.

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Figure 10

2D profiles taken from the upper surface of the ET when the freezing front is at location x = 2 mm (t = 140 s): (a) dilatational rate, (b) x-deformation rate, (c) fluid velocity, and (d) normalized fluid volume fraction with ϕf (t = 0) = 0.914 as the normalization factor. To aid in visualizing the alternating response, vertical broken lines were added to highlight the four successive regions labeled as E1 (primary expansion), C1 (primary compression), E2 (secondary expansion), and C2 (secondary compression).

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