Abstract

Cryopreservation via vitrification (glass formation) is a promising approach for long-term preservation of large-size tissues and organs. Unfortunately, thermomechanical stress, which is driven by the tendency of materials to change size with temperature, may lead to structural failure. This study focuses on analysis of thermomechanical stress in a realistic, pillow-like shape cryobag as it is cooled to cryogenic storage, subject to sufficiently high cooling rates to facilitate vitrification. Contrary to common perception, it is demonstrated in this study that the maximum stress in the specimen does not necessarily increase with increasing size of the specimen. In fact, the maximum stress is affected by the combination of two competing effects, associated with the extent of the temperature gradients within the specimen and its overall volume. On one hand, the increase in specimen size gives rise to more prominent temperature gradients, which can intensify the thermomechanical stress. On the other hand, the temperature distribution at the core of larger specimens is more uniform, which leads to a larger portion of the specimen transitioning from fluid to a glassy material almost instantaneously, which carries a moderating effect on the overall mechanical stress at the glassy state (i.e., lower residual stress). In conclusion, this study demonstrates the role of container shape optimization in reducing the thermomechanical stress during cooling.

References

References
1.
Jones
,
B.
, and
Bes
,
M.
,
2012
, “
Keeping Kidneys
,”
Bull. W. H. O.
,
90
(
10
), pp.
718
719
. 10.2471/BLT.12.021012
2.
Rana
,
A.
,
Gruessner
,
A.
,
Agopian
,
V. G.
,
Khalpey
,
Z.
,
Riaz
,
I. B.
,
Kaplan
,
B.
,
Halazun
,
K. J.
,
Busuttil
,
R. W.
, and
Gruessner
,
R. W. G.
,
2015
, “
Survival Benefit of Solid-Organ Transplant in the United States
,”
JAMA Surg.
,
150
(
3
), p.
252
. 10.1001/jamasurg.2014.2038
3.
Giwa
,
S.
,
Lewis
,
J. K.
,
Alvarez
,
L.
,
Langer
,
R.
,
Roth
,
A. E.
,
Church
,
G. M.
,
Markmann
,
J. F.
,
Sachs
,
D. H.
,
Chandraker
,
A.
,
Wertheim
,
J. A.
,
Rothblatt
,
M.
,
Boyden
,
E. S.
,
Eidbo
,
E.
,
Lee
,
W. P. A.
,
Pomahac
,
B.
,
Brandacher
,
G.
,
Weinstock
,
D. M.
,
Elliott
,
G.
,
Nelson
,
D.
,
Acker
,
J. P.
,
Uygun
,
K.
,
Schmalz
,
B.
,
Weegman
,
B. P.
,
Tocchio
,
A.
,
Fahy
,
G. M.
,
Storey
,
K. B.
,
Rubinsky
,
B.
,
Bischof
,
J.
,
Elliott
,
J. A. W.
,
Woodruff
,
T. K.
,
Morris
,
G. J.
,
Demirci
,
U.
,
Brockbank
,
K. G. M.
,
Woods
,
E. J.
,
Ben
,
R. N.
,
Baust
,
J. G.
,
Gao
,
D.
,
Fuller
,
B.
,
Rabin
,
Y.
,
Kravitz
,
D. C.
,
Taylor
,
M. J.
, and
Toner
,
M.
,
2017
, “
The Promise of Organ and Tissue Preservation to Transform Medicine
,”
Nat. Biotechnol.
,
35
(
6
), pp.
530
542
. 10.1038/nbt.3889
4.
Lewis
,
J. K.
,
Bischof
,
J. C.
,
Braslavsky
,
I.
,
Brockbank
,
K. G. M.
,
Fahy
,
G. M.
,
Fuller
,
B. J.
,
Rabin
,
Y.
,
Tocchio
,
A.
,
Woods
,
E. J.
,
Wowk
,
B. G.
,
Acker
,
J. P.
, and
Giwa
,
S.
,
2016
, “
The Grand Challenges of Organ Banking: Proceedings From the First Global Summit on Complex Tissue Cryopreservation
,”
Cryobiology
,
72
(
2
), pp.
169
182
. 10.1016/j.cryobiol.2015.12.001
5.
Hunt
,
C. J.
,
2011
, “
Cryopreservation of Human Stem Cells for Clinical Application: A Review
,”
Transfus. Med. Hemother.
,
38
(
2
), pp.
107
123
. 10.1159/000326623
6.
Berz
,
D.
,
McCormack
,
E. M.
,
Winer
,
E. S.
,
Colvin
,
G. A.
, and
Quesenberry
,
P. J.
,
2007
, “
Cryopreservation of Hematopoietic Stem Cells
,”
Am. J. Hematol.
,
82
(
6
), pp.
463
472
. 10.1002/ajh.20707
7.
Armitage
,
W. J.
,
2009
, “Cryopreservation for Corneal Storage,”
Eye Banking, Developments in Ophthalmology
,
T.
Bredehorn-Mayr
,
G. I. W.
Dunker
, and
W. J.
Armitage
, eds.,
Karger
,
Basel
, pp.
63
69
.
8.
Basu
,
P. K.
,
1995
, “
A Review of Methods for Storage of Corneas for Keratoplasty
,”
Indian J. Ophthalmol.
,
43
(
2
), pp.
55
58
.
9.
Taylor
,
M. J.
, and
Baicu
,
S.
,
2009
, “
Review of Vitreous Islet Cryopreservation: Some Practical Issues and Their Resolution
,”
Organogenesis
,
5
(
3
), pp.
155
166
. 10.4161/org.5.3.9812
10.
Kojayan
,
G. G.
,
Alexander
,
M.
,
Imagawa
,
D. K.
, and
Lakey
,
J. R. T.
,
2018
, “
Systematic Review of Islet Cryopreservation
,”
Islets
,
10
(
1
), pp.
40
49
. 10.1080/19382014.2017.1405202
11.
Taylor
,
M. J.
,
Weegman
,
B. P.
,
Baicu
,
S. C.
, and
Giwa
,
S. E.
,
2019
, “
New Approaches to Cryopreservation of Cells, Tissues, and Organs
,”
Transfus. Med. Hemoth.
,
46
(
3
), pp.
197
215
. 10.1159/000499453
12.
Fahy
,
G. M.
,
MacFarlane
,
D. R.
,
Angell
,
C. A.
, and
Meryman
,
H. T.
,
1984
, “
Vitrification as an Approach to Cryopreservation
,”
Cryobiology
,
21
(
4
), pp.
407
426
. 10.1016/0011-2240(84)90079-8
13.
Wowk
,
B.
,
2010
, “
Thermodynamic Aspects of Vitrification
,”
Cryobiology
,
60
(
1
), pp.
11
22
. 10.1016/j.cryobiol.2009.05.007
14.
Steif
,
P. S.
,
Palastro
,
M. C.
, and
Rabin
,
Y.
,
2007
, “
The Effect of Temperature Gradients on Stress Development During Cryopreservation via Vitrification
,”
Cell Preserv. Technol.
,
5
(
2
), pp.
104
115
. 10.1089/cpt.2007.9994
15.
Eisenberg
,
D. P.
,
Steif
,
P. S.
, and
Rabin
,
Y.
,
2014
, “
On the Effects of Thermal History on the Development and Relaxation of Thermo-Mechanical Stress in Cryopreservation
,”
Cryogenics
,
64
, pp.
86
94
. 10.1016/j.cryogenics.2014.09.005
16.
Rabin
,
Y.
,
Steif
,
P. S.
,
Hess
,
K. C.
,
Jimenez-Rios
,
J. L.
, and
Palastro
,
M. C.
,
2006
, “
Fracture Formation in Vitrified Thin Films of Cryoprotectants
,”
Cryobiology
,
53
(
1
), pp.
75
95
. 10.1016/j.cryobiol.2006.03.013
17.
Rabin
,
Y.
,
Taylor
,
M. J.
,
Walsh
,
J. R.
,
Baicu
,
S.
, and
Steif
,
P. S.
,
2005
, “
Cryomacroscopy of Vitrification I: A Prototype and Experimental Observations on the Cocktails VS55 and DP6
,”
Cell Preserv. Technol.
,
3
(
3
), pp.
169
183
. 10.1089/cpt.2005.3.169
18.
Steif
,
P. S.
,
Palastro
,
M.
,
Wan
,
C.
,
Baicu
,
S.
,
Taylor
,
M. J.
, and
Rabin
,
Y.
,
2005
, “
Cryomacroscopy of Vitrification, Part II: Experimental Observations and Analysis of Fracture Formation in Vitrified VS55 and DP6
,”
Cell Preserv. Technol.
,
3
(
3
), pp.
184
200
. 10.1089/cpt.2005.3.184
19.
Rabin
,
Y.
, and
Steif
,
P.
,
2006
, “Solid Mechanics Aspects of Cryobiology,”
Advances in Biopreservation
,
J. G.
Baust
, and
J. M.
Baust
, eds.,
CRC Press
,
Boca Raton, FL
, pp.
359
381
.
20.
Solanki
,
P. K.
,
Bischof
,
J. C.
, and
Rabin
,
Y.
,
2017
, “
Thermo-Mechanical Stress Analysis of Cryopreservation in Cryobags and the Potential Benefit of Nanowarming
,”
Cryobiology
,
76
, pp.
129
139
. 10.1016/j.cryobiol.2017.02.001
21.
Rubinsky
,
B.
,
Cravalho
,
E. G.
, and
Mikic
,
B.
,
1980
, “
Thermal Stresses in Frozen Organs
,”
Cryobiology
,
17
(
1
), pp.
66
73
. 10.1016/0011-2240(80)90009-7
22.
Steif
,
P. S.
,
Palastro
,
M. C.
, and
Rabin
,
Y.
,
2007
, “
Analysis of the Effect of Partial Vitrification on Stress Development in Cryopreserved Blood Vessels
,”
Med. Eng. Phys.
,
29
(
6
), pp.
661
670
. 10.1016/j.medengphy.2006.07.010
23.
Eisenberg
,
D. P.
,
Taylor
,
M. J.
, and
Rabin
,
Y.
,
2012
, “
Thermal Expansion of the Cryoprotectant Cocktail DP6 Combined with Synthetic Ice Modulators in Presence and Absence of Biological Tissues
,”
Cryobiology
,
65
(
2
), pp.
117
125
. 10.1016/j.cryobiol.2012.04.011
24.
Steif
,
P. S.
,
Noday
,
D. A.
, and
Rabin
,
Y.
,
2009
, “
Can Thermal Expansion Differences Between Cryopreserved Tissue and Cryoprotective Agents Alone Cause Cracking?
,”
Cryo-Letters
,
30
(
6
), pp.
414
421
.
25.
Rabin
,
Y.
, and
Steif
,
P. S.
,
1998
, “
Thermal Stresses in a Freezing Sphere and Its Application to Cryobiology
,”
ASME J. Appl. Mech.
,
65
(
2
), pp.
328
333
. 10.1115/1.2789058
26.
Rabin
,
Y.
, and
Steif
,
P. S.
,
2000
, “
Thermal Stress Modeling in Cryosurgery
,”
Int. J. Solids Struct.
,
37
(
17
), pp.
2363
2375
. 10.1016/S0020-7683(98)00345-X
27.
Rabin
,
Y.
, and
Steif
,
P. S.
,
2005
, “
Letter to the Editor: Analysis of Thermo-Mechanical Stress in Cryopreservation
,”
Cryo-Letters
,
26
(
6
), pp.
409
412
.
28.
Pegg
,
D. E.
,
Wusteman
,
M. C.
, and
Boylan
,
S.
,
1997
, “
Fractures in Cryopreserved Elastic Arteries
,”
Cryobiology
,
34
(
2
), pp.
183
192
. 10.1006/cryo.1996.1997
29.
Kasai
,
M.
,
Zhu
,
S. E.
,
Pedro
,
P. B.
,
Nakamura
,
K.
,
Sakurai
,
T.
, and
Edashige
,
K.
,
1996
, “
Fracture Damage of Embryos and Its Prevention During Vitrification and Warming
,”
Cryobiology
,
33
(
4
), pp.
459
464
. 10.1006/cryo.1996.0046
30.
Eisenberg
,
D. P.
,
Bischof
,
J. C.
, and
Rabin
,
Y.
,
2016
, “
Thermomechanical Stress in Cryopreservation Via Vitrification With Nanoparticle Heating as a Stress-Moderating Effect
,”
ASME J. Biomech. Eng.
,
138
(
138
), pp.
1
8
.
31.
Etheridge
,
M. L.
,
Xu
,
Y.
,
Rott
,
L.
,
Choi
,
J.
,
Glasmacher
,
B.
, and
Bischof
,
J. C.
,
2014
, “
RF Heating of Magnetic Nanoparticles Improves the Thawing of Cryopreserved Biomaterials
,”
Technology
,
2
(
3
), pp.
229
242
. 10.1142/S2339547814500204
32.
Liu
,
X.
,
Zhao
,
G.
,
Chen
,
Z.
,
Panhwar
,
F.
, and
He
,
X.
,
2018
, “
Dual Suppression Effect of Magnetic Induction Heating and Microencapsulation on Ice Crystallization Enables Low-Cryoprotectant Vitrification of Stem Cell-Alginate Hydrogel Constructs
,”
ACS Appl. Mater. Interfaces
,
10
(
19
), pp.
16822
16835
. 10.1021/acsami.8b04496
33.
Pan
,
J.
,
Shu
,
Z.
,
Zhao
,
G.
,
Ding
,
W.
,
Ren
,
S.
,
Sekar
,
P. K.
,
Peng
,
J.
,
Chen
,
M.
, and
Gao
,
D.
,
2018
, “
Towards Uniform and Fast Rewarming for Cryopreservation With Electromagnetic Resonance Cavity: Numerical Simulation and Experimental Investigation
,”
Appl. Therm. Eng.
,
140
, pp.
787
798
. 10.1016/j.applthermaleng.2018.05.015
34.
Manuchehrabadi
,
N.
,
Gao
,
Z.
,
Zhang
,
J.
,
Ring
,
H. L.
,
Shao
,
Q.
,
Liu
,
F.
,
McDermott
,
M.
,
Fok
,
A.
,
Rabin
,
Y.
,
Brockbank
,
K. G. M.
,
Garwood
,
M.
,
Haynes
,
C. L.
, and
Bischof
,
J. C.
,
2017
, “
Improved Tissue Cryopreservation Using Inductive Heating of Magnetic Nanoparticles
,”
Sci. Transl. Med.
,
9
(
379
), p.
eaah4586
. 10.1126/scitranslmed.aah4586
35.
Robinson
,
M. P.
, and
Pegg
,
D. E.
,
1999
, “
Rapid Electromagnetic Warming of Cells and Tissues
,”
IEEE Trans. Biomed. Eng.
,
46
(
12
), pp.
1413
1425
. 10.1109/10.804569
36.
Evans
,
S.
,
2000
, “
Electromagnetic Rewarming: The Effect of CPA Concentration and Radio Source Frequency on Uniformity and Efficiency of Heating
,”
Cryobiology
,
40
(
2
), pp.
126
138
. 10.1006/cryo.2000.2232
37.
Solanki
,
P. K.
, and
Rabin
,
Y.
,
2018
, “
Analysis of Polarized-Light Effects in Glass-Promoting Solutions With Applications to Cryopreservation and Organ Banking
,”
PLoS One
,
13
(
6
), p.
e0199155
. 10.1371/journal.pone.0199155
38.
Jimenez Rios
,
J. L.
, and
Rabin
,
Y.
,
2006
, “
Thermal Expansion of Blood Vessels in Low Cryogenic Temperatures, Part II: Vitrification With VS55, DP6, and 7.05M DMSO
,”
Cryobiology
,
52
(
2
), pp.
284
294
. 10.1016/j.cryobiol.2005.12.005
39.
Plitz
,
J.
,
Rabin
,
Y.
, and
Walsh
,
J. R.
,
2004
, “
The Effect of Thermal Expansion of Ingredients on the Cocktails VS55 and DP6
,”
Cell Preserv. Technol.
,
2
(
3
), pp.
215
226
. 10.1089/cpt.2004.2.215
40.
Jimenez Rios
,
J. L.
,
Steif
,
P. S.
, and
Rabin
,
Y.
,
2007
, “
Stress-Strain Measurements and Viscoelastic Response of Blood Vessels Cryopreserved by Vitrification
,”
Ann. Biomed. Eng.
,
35
(
12
), pp.
2077
2086
. 10.1007/s10439-007-9372-0
41.
Ehrlich
,
L. E.
,
Fahy
,
G. M.
,
Wowk
,
B.
,
Malen
,
J. A.
, and
Rabin
,
Y.
,
2017
, “
Thermal Analyses of a Human Kidney and a Rabbit Kidney During Cryopreservation by Vitrification
,”
ASME J. Biomech. Eng.
,
140
(
1
), p.
011005
. 10.1115/1.4037406
42.
Feig
,
J. S. G.
,
Solanki
,
P. K.
,
Eisenberg
,
D. P.
, and
Rabin
,
Y.
,
2016
, “
Polarized Light Scanning Cryomacroscopy, Part II: Thermal Modeling and Analysis of Experimental Observations
,”
Cryobiology
,
73
(
2
), pp.
272
281
. 10.1016/j.cryobiol.2016.06.004
43.
Song
,
Y. C.
,
Khirabadi
,
B. S.
,
Lightfoot
,
F.
,
Brockbank
,
K. G. M.
, and
Taylor
,
M. J.
,
2000
, “
Vitreous Cryopreservation Maintains the Function of Vascular Grafts
,”
Nat. Biotechnol.
,
18
(
3
), pp.
296
299
. 10.1038/73737
44.
Noday
,
D. A.
,
Steif
,
P. S.
, and
Rabin
,
Y.
,
2009
, “
Viscosity of Cryoprotective Agents Near Glass Transition: A New Device, Technique, and Data on DMSO, DP6, and VS55
,”
Exp. Mech.
,
49
(
5
), pp.
663
672
. 10.1007/s11340-008-9191-8
45.
Aminabhavi
,
T. M.
, and
Gopalakrishna
,
B.
,
1995
, “
Density, Viscosity, Refractive Index, and Speed of Sound in Aqueous Mixtures of N,N-Dimethylformamide, Dimethyl Sulfoxide, N,N-Dimethylacetamide, Acetonitrile, Ethylene Glycol, Diethylene Glycol, 1,4-Dioxane, Tetrahydrofuran, 2-Methoxyethanol, and 2-Ethoxyethanol at 298.15K
,”
J. Chem. Eng. Data
,
40
(
4
), pp.
856
861
. 10.1021/je00020a026
46.
Ehrlich
,
L. E.
,
Feig
,
J. S. G.
,
Schiffres
,
S. N.
,
Malen
,
J. A.
, and
Rabin
,
Y.
,
2015
, “
Large Thermal Conductivity Differences Between the Crystalline and Vitrified States of DMSO With Applications to Cryopreservation
,”
PLoS One
,
10
(
5
), p.
e0125862
. 10.1371/journal.pone.0125862
47.
Westh
,
P.
,
1994
, “
Thermal Expansivity, Molar Volume, and Heat Capacity of Liquid Dimethyl Sulfoxide-Water Mixtures at Subzero Temperatures
,”
J. Phys. Chem.
,
98
(
12
), pp.
3222
3225
. 10.1021/j100063a028
48.
Rabin
,
Y.
, and
Plitz
,
J.
,
2005
, “
Thermal Expansion of Blood Vessels and Muscle Specimens Permeated With DMSO, DP6, and VS55 at Cryogenic Temperatures
,”
Ann. Biomed. Eng.
,
33
(
9
), pp.
1213
1228
. 10.1007/s10439-005-5364-0
49.
Jimenez Rios
,
J. L.
, and
Rabin
,
Y.
,
2007
, “
A New Device for Mechanical Testing of Blood Vessels at Cryogenic Temperatures
,”
Exp. Mech.
,
47
(
3
), pp.
337
346
. 10.1007/s11340-007-9038-8
50.
Solanki
,
P. K.
, and
Rabin
,
Y.
,
2019
, “
Counterintuitive Scaling Effects in the Developing Thermomechanical Stress During Cryogenic Cooling of the Kidney With Implications to Electromagnetic Rewarming for Organ Recovery
,”
Summer Biomechanics, Bioengineering and Biotransport Conference
,
Seven Springs, PA
,
June 25–28
.
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