Bumsoo Han

J Craig Dutton

Soham Ghosh

CiteSeerX

Copyright © 2013 by ASME 1 
 
INTRODUCTION    
 Freezing of biomaterials is emerging as one of the key 
biotechnologies in cell/tissue engineering, medicine and biology.  Its 
applications include – 1) preservation of cell/tissue engineering 
products, 2) quality control of biospecimens cryopreserved in tissue 
banks and repositories, and 3) synthesis procedures of biomaterials 
such as decellularization of native tissues to create acellular (i.e., cell-
free) complex three-dimensional extracellular matrices (ECMs).  
Traditionally, research efforts have focused on determining optimal 
freeze/thaw (F/T) protocols with chemical additives, so called 
cryoprotective agents, for a given cell/tissue-type by comparing the 
outcomes of F/T protocols, which are mainly gauged by cell viability.  
Although cell viability is the major constituent, it has recently been 
recognized that other features beyond viability are also critical to the 
functionality of biomaterials, including the microstructure of the ECM, 
the status of cell-matrix adhesion, and the cytoskeletal structure and 
organization [1, 2, 3].   
 Many biological tissues and biomaterials can be approximated as 
hierarchical porous structures saturated with fluids.  The ECM has a 
fibrous collagen porous structure filled with interstitial fluid, and the 
cytoplasm has a fibrous cytoskeleton porous structure filled with 
cytosol [4, 5]. The ECM is connected to the cytoplasm through a 
complex of proteins on the cell membrane, which is called the "cell-
matrix adhesion complex" (CMAC).  Thus, in order to successfully 
freeze/thaw complex biomaterials, we hypothesize that the biphasic 
(i.e., porous solid and fluid) cytoplasm plays a critical role in freezing-
induced biophysical processes.  This hypothesis is postulated based on 
a nanoscale fluid-structure interaction mechanism in the cytoplasm, 
and hierarchical fluid-structure interactions in the intra-/extra-cellular 
spaces, which are connected via the CMACs.  
 In the present study, we developed an experimental technique to 
measure the spatiotemporal intracellular deformation of cells during 
freezing-induced cell-fluid-matrix interactions.  The measurement 
results are discussed to establish the mechanistic understanding of 
freezing-induced biophysical processes around cells within the ECM. 
  
MATERIALS AND METHODS 
Cell Culture and Fluorescent Bead Internalization in Cells 
 Human dermal fibroblasts were cultured and harvested as 
described previously [3]. The harvested cells were labeled by 
internalizing 520 nm fluorescent beads (Thermo Scientific) according 
to the protocol developed previously [6]. 
Engineered Tissues    
 Engineered tissues (ETs) were prepared after modification of the 
method described in Ref. [3]. Briefly, collagen gel was polymerized 
inside custom-made containers. After polymerization, fibroblasts were 
seeded on or within the collagen gel. After cells were attached, the 
ETs were cultured in medium for approximately 24 hours.  
Freezing and Imaging     
 ETs were directionally frozen on a cryostage (Linkam, MDS 
600). The cryostage was cooled in a way to mimic the temperature 
history in ETs as obtained during macroscopic freezing [3]. While 
freezing, the ETs were imaged using a fluorescence microscope 
(Olympus BX51) with a high-speed CMOS camera (Hispec I, Fastec 
imaging) at 40X magnification and in 10 msec interval (Figure 1(a)). 
Image Postprocessing and Data Analysis   
 The captured images were postprocessed using ImageJ, and the 
locations of beads (i.e. X (t) and Y (t) positions for each bead) were 
tracked by Metamorph. Subsequently, the 2D tracking data were 
smoothed using a Robust Locally Weighted Scatter Plot Smoothing 
method [7]. Using this smoothed data, cells were discretized into 
 
SPATIOTEMPORAL INTRACELLULAR DEFORMATION OF CELLS DURING FREEZING-
INDUCED CELL-FLUID-MATRIX INTERACTIONS 
Soham Ghosh
1
, J. Craig Dutton
2
, Bumsoo Han
1, 3
 
1
School of Mechanical Engineering 
Purdue University 
West Lafayette, IN, U.S.A. 
2
Department of Aerospace Engineering 
University of Illinois at Urbana-Champaign 
Urbana, IL, U.S.A. 
3
Weldon School of Biomedical Engineering 
Purdue University 
West Lafayette, IN, U.S.A. 
Proceedings of the ASME 2013 Summer Bioengineering Conference 
SBC2013 
June 26-29, 2013, Sunriver, Oregon, USA 
SBC2013-14673
Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/28/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Copyright © 2013 by ASME 2 
triangular elements (Figure 1(b)) using the Delaunay algorithm [8]. 
The spatiotemporal deformation of each triangular element was 
quantified using the large deformation analysis method [9]. Through 
the analysis the substrate rotation and translation were nullified, and 
only the local intracellular deformation was captured. From the initial 
and deformed configurations of the triangles, the deformation gradient 
tensor and Left Cauchy Green tensor were evaluated. The eigenvalues 
of the Left Cauchy Green tensor gave the 2D stretch ratios λ1 and λ2. 
The local area-based first invariant given by 2 2
1 1 2I    was 
computed to characterize element deformation. I1 is a measurement of 
the combined expansion and compression of an element. In Figure 1(c) 
the procedure is explained. 
 
t = 0 sec
(a) (b)
1 1( ), ( )X i Y i
2 2( ), ( )X i Y i 3 3( ), ( )X i Y i
(c)
Measured 
displacement from 
bead tracing
X(t), Y(t) by Robust 
Locally Weighted 
Scatter Plot 
Smoothing
Triangular element 
formation by 
Delaunay algorithm
1 1( ), ( )X t Y t
2 2( ), ( )X t Y t
3 3( ), ( )X t Y t
( ) ( )
( ) ( )
( ) ( )
( ) ( )
X t X t
X i Y i
F
Y t Y t
X i Y i
  
  
 
  
   
Deformation 
gradient 
tensor
Left Cauchy Green Tensor
TB F F 
Eigenvalues of 
2 2
1 2: ,B  
2 2
1 1 2I   First invariant
Initial 
triangle
Triangle at 
time t
X(t) and Y(t) are 
linear functions of 
X(i) and Y(i)
20 μm
 
Figure 1: (a) Fluorescent bead-labeled cell attached on ET, (b) 
Discretized cell with triangular mesh elements, (c) Summary of the 
large deformation analysis method. 
 
RESULTS AND DISCUSSION 
 In Figure 2, a cell is shown undergoing deformation during 
freezing. At t = 2 sec, the freeze-front first touches the left side of the 
cell and propagates towards the right at subsequent times. The 
triangular elements deform as the freeze-front approaches and passes. 
Although the movement of the freeze-front is 1D planar, the cell 
experiences very complex and spatiotemporally varying displacement 
resulted from translation, rotation and local deformation. 
 
Translation, 
rotation and 
deformation
t = 3 sec t = 6 sec
Direction of freeze-
front movement
F
re
e
z
e
-f
ro
n
t
 
Figure 2: A triangular element is shown to deform, translate and 
rotate. The dotted line is the freeze-front location. 
 
 Figure 3 shows the spatiotemporal deformation in the cell. The 
element highlighted in (a) undergoes a local deformation to (b). At 5.6 
sec, just before freeze-front touches the element, I1 = 1.05 (<2, the 
region is compressed) and at 6.05 sec (just after freeze-front passes the 
element) I1 = 3.69 (>2, the region is expanded). At 8.3 sec, further 
element expansion is observed with I1 = 6.01. In (c) and (d) this 
compression and expansion are shown at the same time steps as 
contour plots of I1. These plots quantify the intracellular deformation 
at any spatial location at given time points. Figure 3(e) shows the 
history of I1 in the given element. Such a sudden deformation change 
characterized by an almost 500% increase in the value of I1 in a time 
frame of 2.3 sec may lead to rupture of the CMAC in that region. 
From the previous study [3], ECM deformation is shown to have a 
much lower value (dilatation rate = 0.01 sec-1) for the same freezing 
condition. The present results suggest that the maximum intracellular 
strain rate is 0.43 sec-1 so that the CMAC is under significant 
mechanical loading and possible rupture which implies loss of 
functionality. In addition, sudden jerk movements around cell-matrix 
adhesion points were also noted (data not shown), which are thought 
to be associated with the rupture of the CMAC. Further research is still 
ongoing to investigate the effects of different cytoskeleton structures 
during the process, and also to simultaneously measure the intra- and 
extra-cellular deformation under a hierarchical poroelastic framework.  
 
time (second)
fi
rs
t 
in
v
a
ri
a
n
t
(c) (d)
C
o
n
to
u
r 
o
f 
fi
rs
t 
in
v
a
ri
a
n
t
(a) (b)
t=5.6 sec t=8.3 sec
(e)
t=5.6 sec t=8.3 sec
Freeze front 
touches cell
F
re
e
z
e
 f
o
n
t 
to
u
c
h
e
s
 
e
le
m
e
n
t 
(5
.6
 s
)
t=6.05 s
t=8.3 s
 
Figure 3: One portion of the cell (in yellow dotted square) is under 
compression (a) and under expansion at (b). In (c) and (d) the 
element is shown in black dotted squares as part of the spatial 
invariant contour at the same time points. (e) shows the temporal 
invariant history of the triangular element. 
 
ACKNOWLEDGEMENT 
This research was partially supported by NIH R01 EB008388, and 
NSF CBET-1009465. 
 
REFERENCES       
[1] Gerson et al, 2009, Cryobiology, 59, 171-9 
[2] Venkatasubramanian et al, 2010, Ann Biomed Engg, 38, 694-706 
[3] Teo et al, 2011, Biomaterials, 32, 5380-5390 
[4] Charras et al, 2008, Biophysical Journal, 94, 1836-1853   
[5] Ingber, 2003. Journal of Cell Science, 115, 1157-1173 
[6] Grinnell et al, 1986, Experimental Cell Research, 162, 44-4 
[7] Cleveland et al, 1979, J Amer Stat Assoc, 74, 829-836 
[8] Delaunay et al, 1934, Otd Mate, 7, 793-800 
[9] Cowin et al, Tissue Mechanics, 2007, Springer 
 
Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 06/28/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use


Spatiotemporal Intracellular Deformation of Cells During Freezing-Induced Cell-Fluid-Matrix Interactions

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=5C87CE96B7D6C517918CE5AEED5A2D82?doi=10.1.1.1075.1567&rep=rep1&type=pdf

Spatiotemporal Intracellular Deformation of Cells During Freezing-Induced Cell-Fluid-Matrix Interactions

Abstract

Similar works

Full text

Available Versions

CiteSeerX