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Research Papers

# Spatiotemporal Measurement of Freezing-Induced Deformation of Engineered Tissues

[+] Author and Article Information
Ka Yaw Teo

Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019

J. Craig Dutton

Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Bumsoo Han1

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907bumsoo@purdue.edu

1

Corresponding author.

J Biomech Eng 132(3), 031003 (Feb 04, 2010) (8 pages) doi:10.1115/1.4000875 History: Received August 12, 2009; Revised October 02, 2009; Posted December 22, 2009; Published February 04, 2010; Online February 04, 2010

## Abstract

In order to cryopreserve functional engineered tissues (ETs), the microstructure of the extracellular matrix (ECM) should be maintained, as well as the cellular viability since the functionality is closely related to the ECM microstructure. Since the post-thaw ECM microstructure is determined by the deformation of ETs during cryopreservation, freezing-induced deformation of ETs was measured with a newly developed quantum dot (QD)-mediated cell image deformetry system using dermal equivalents as a model tissue. The dermal equivalents were constructed by seeding QD-labeled fibroblasts in type I collagen matrices. After 24 h incubation, the ETs were directionally frozen by exposing them to a spatial temperature gradient (from $4°C$ to $−20°C$ over a distance of 6 mm). While being frozen, the ETs were consecutively imaged, and consecutive pairs of these images were two-dimensionally cross-correlated to determine the local deformation during freezing. The results showed that freezing induced the deformation of ET, and its magnitude varied with both time and location. The maximum local dilatation was $0.006 s−1$ and was always observed at the phase change interface. Due to this local expansion, the unfrozen region in front of the freezing interface experienced compression. This expansion-compression pattern was observed throughout the freezing process. In the unfrozen region, the deformation rate gradually decreased away from the freezing interface. After freezing/thawing, the ET experienced an approximately 28% decrease in thickness and 8% loss in weight. These results indicate that freezing-induced deformation caused the transport of interstitial fluid, and the interstitial fluid was extruded. In summary, the results suggest that complex cell-fluid-matrix interactions occur within ETs during freezing, and these interactions determine the post-thaw ECM microstructure and eventual post-thaw tissue functionality.

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## Figures

Figure 1

Bright field and fluorescence micrographs of engineered tissue, and schematic of QD-mediated cell image deformetry experimental setup. (a) Fibroblasts, embedded in collagen matrix, have a dendritic morphology and are labeled with quantum dots. (b) The overlays of brightfield and TRITC images confirm that quantum dots specifically accumulate in the cytoplasm of fibroblasts. (c) QD-mediated cell image deformetry experimental setup. When engineered tissue is frozen on the directional solidification stage, it is continuously imaged while being illuminated with an excitation light, causing the quantum dots within the embedded fibroblasts to fluoresce.

Figure 2

Cell image deformetry analysis flowchart. (a) Two fluorescence micrographs taken 10 s apart are divided into a grid of 32×32 pixels interrogation windows. The interrogation windows in the initial and delayed images are cross-correlated to produce a map of correlation peaks. The location of the maximum correlation peak provides the two-dimensional displacement vector for the interrogation area. In order to improve the quality of cross-correlation, the delayed interrogation window is shifted toward the estimated deformation direction. (b) A deformation rate vector field is determined for the pair of fluorescence images shown in part (a) by using multipass processing with decreasing interrogation window size (1 iteration of 64×64 pixels followed by 2 iterations of 32×32 pixels) and 50% overlap. Overlaying the fluorescence image with the deformation rate vector field shows that the location of the freezing interface coincides with the location of maximum deformation rates.

Figure 3

Phase change interface location during freezing and curve fit using analytic Neumann’s solution. Interface location is determined from displacement field using ∂u/∂x=0 or u=umax(n=3). Interface location is subsequently curve-fitted to the Neumann solution X(t)=2λαSt with αS=1×106 μm2/s (thermal diffusivity of ice), yielding λ=0.114. Inset shows X(t) plotted against 2αSt, along with a Neumann solution fitting curve (R2=0.978).

Figure 4

Fluorescence micrographs of engineered tissue when (a) X(t)≈1000 μm, (b) X(t)≈2000 μm, and (c) X(t)≈4000 μm. The phase change interface, denoted by arrows, propagates from left to right while the tissue freezes one-dimensionally.

Figure 5

Deformation rate vector fields when (a) X(t)≈1000 μm, (b) X(t)≈2000 μm, and (c) X(t)≈4000 μm. Engineered tissue experiences highly spatiotemporal deformation during freezing. The maximum local deformation rate is observed at the freezing interface. The deformation rate progressively decreases away from the interface in the unfrozen region. A slight to no deformation rate is observed in the frozen region.

Figure 6

Dilatation contours when (a) X(t)≈1000 μm, (b) X(t)≈2000 μm, and (c) X(t)≈4000 μm. Engineered tissue is dilated and compressed in a highly spatiotemporal fashion during freezing. Engineered tissue experiences local expansion immediately following phase change, and a corresponding local compression is observed concurrently in the unfrozen region. Dilatation is approximately zero at the freezing interface.

Figure 7

Averaged deformation rates and dilatation profiles. (a) y-averaged x-deformation rate, (b) y-averaged y-deformation rate, and (c) y-averaged dilatation when X(t)≈1000 μm, 2000 μm, and 4000 μm. One-dimensional freezing induces deformation of engineered tissue primarily in the x direction with an average magnitude ranging from 0 to 1.8 μm/s. Average deformation rates in the y direction are much smaller than those in the x direction.

Figure 8

Post-thaw profile of engineered tissue sample. Engineered tissue becomes significantly thinner after freezing and thawing. In addition, engineered tissue experiences a significant loss in mass after freezing and thawing. These changes in thickness and mass are thought to be caused by the efflux of interstitial fluid during freezing and thawing.

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