12. Songsasen N, Leibo SP (1997) Cryopreservation of mouse spermatozoa. II. Relationship
between survival after cryopreservation and
osmotic tolerance of spermatozoa from three
strains of mice. Cryobiology 35:255–269
13. Mullen SF, Li M, Li Y, Chen ZJ, Critser JK
(2008) Human oocyte vitrification: the permeability of metaphase II oocytes to water
and ethylene glycol and the appliance toward
vitrification. Fertil Steril 89:1812–1825
14. Karlsson JO, Szurek EA, Higgins AZ, Lee SR,
Eroglu A (2014) Optimization of cryoprotectant loading into murine and human oocytes.
Cryobiology 68:18–28. http://dx.doi.org/
10.1016/j.cryobiol.2013.11.002
15. Seki S, Jin B, Mazur P (2014) Extreme rapid
warming yields high functional survivals of
vitrified 8-cell mouse embryos even when suspended in a half-strength vitrification solution
and cooled at moderate rates to -196
o C. Cryobiology 68:71–78
16. Anderson DM, Benson JD, Kearsley AJ
(2014) Foundations of modeling in cryobiology—I: concentration, Gibbs energy, and
chemical potential relationships. Cryobiology
69:349–360
17. Anderson DM, Benson JD, Kearsley AJ
(2019) Foundations of modeling in cryobiology—II: heat and mass transport in bulk and
at cell membrane and ice-liquid interfaces.
Cryobiology. 91:3–17 https://doi.org/10.
1016/j.cryobiol.2019.09.014
18. Anderson DM, Benson JD, Kearsley AJ
(2019) Foundations of modeling in cryobiology—III: heat and mass transport in a ternary
system. Cryobiology 92:34–46
19. Anderson DM, Benson JD, Kearsley AJ
(2019) Numerical solution of inward solidification of a dilute ternary solution towards a
semi-permeable spherical cell. Math Biosci
316:108240
20. Karlsson JOM, Cravalho EG, Rinkes IHMB,
Tompkins RG, Yarmush ML, Toner M
(1993) Nucleation and growth of ice crystals
inside cultured-hepatocytes during freezing in
the presence of dimethyl-sulfoxide. Biophys J
65:2524–2536
21. Yang G, Zhang A, Xu LX, He X (2009) Modeling the cell-type dependence of diffusionlimited intracellular ice nucleation and growth
during both vitrification and slow freezing. J
Appl Phys 105:114701
22. Chang A, Dantzig JA, Darr BT, Hubel A
(2007) Modeling the interaction of biological
cells with a solidifying interface. J Comput
Phys 226:1808–1829
23. Liu Z, Wan R, Muldrew K, Sawchuk S,
Rewcastle J (2004) A level set variational
formulation for coupled phase change/mass
transfer problems: application to freezing of
biological systems. Finite Elem Anal Des
40:1641–1663
24. Zeng C, He L, Peng W, Ding L, Tang K,
Fang D, Zhang Y (2014) Selection of optimal
reference genes for quantitative RT-PCR
studies of boar spermatozoa cryopreservation.
Cryobiology 68:113–121. http://dx.doi.
org/10.1016/j.cryobiol.2014.01.004
25. Kashuba Benson CM, Benson JD, Critser JK
(2008) An improved cryopreservation
method for a mouse embryonic stem cell
line. Cryobiology 56:120–130
26. Kashuba CM, Benson JD, Critser JK (2014)
Rationally optimized cryopreservation of
multiple mouse embryonic stem cell lines:
II—Mathematical prediction and experimental validation of optimal cryopreservation protocols. Cryobiology 68:176–184. http://dx.
doi.org/10.1016/j.cryobiol.2013.12.003
27. Kashuba CM, Benson JD, Critser JK (2014)
Rationally optimized cryopreservation of
multiple mouse embryonic stem cell lines:
I—comparative fundamental cryobiology of
multiple mouse embryonic stem cell lines
and the implications for embryonic stem cell
cryopreservation protocols. Cryobiology
68:166–175. http://dx.doi.org/10.1016/j.
cryobiol.2013.12.007
28. Agca Y, Liu J, Critser E, Critser J (2000)
Fundamental cryobiology of rat immature
and mature oocytes: hydraulic conductivity
in the presence of Me(2)SO, Me(2)SO permeability, and their activation energies. J Exp
Zool 286:523–533
29. Ridgway
D,
Broderick
G,
LopezCampistrous A, Ru’aini M, Winter P,
Hamilton M, Boulanger P, Kovalenko A, Ellison MJ (2008) Coarse-grained molecular
simulation of diffusion and reaction kinetics
in a crowded virtual cytoplasm. Biophys J
94:3748–3759
30. Lacelle PL, Rothstein A (1966) The passive
permeability of the red blood cell to cations. J
Gen Physiol 50:171–188
31. Agca Y, Liu J, Mullen S, Johnson-Ward J,
Gould K, Chan A, Critser J (2005) Chimpanzee (Pan troglodytes) spermatozoa osmotic
tolerance and cryoprotectant permeability
characteristics. J Androl 26:470–477
32. Newton H, Pegg DE, Barrass R, Gosden RG
(1999) Osmotically inactive volume, hydraulic conductivity, and permeability to dimethyl
sulphoxide of human mature oocytes. J
Reprod Fertil 117:27–33
33. Gao DY, Chang Q, Liu C, Farris K, Harvey K,
McGann LE, English D, Jansen J, Critser JK
(1998) Fundamental cryobiology of human
168
James D. Benson
between survival after cryopreservation and
osmotic tolerance of spermatozoa from three
strains of mice. Cryobiology 35:255–269
13. Mullen SF, Li M, Li Y, Chen ZJ, Critser JK
(2008) Human oocyte vitrification: the permeability of metaphase II oocytes to water
and ethylene glycol and the appliance toward
vitrification. Fertil Steril 89:1812–1825
14. Karlsson JO, Szurek EA, Higgins AZ, Lee SR,
Eroglu A (2014) Optimization of cryoprotectant loading into murine and human oocytes.
Cryobiology 68:18–28. http://dx.doi.org/
10.1016/j.cryobiol.2013.11.002
15. Seki S, Jin B, Mazur P (2014) Extreme rapid
warming yields high functional survivals of
vitrified 8-cell mouse embryos even when suspended in a half-strength vitrification solution
and cooled at moderate rates to -196
o C. Cryobiology 68:71–78
16. Anderson DM, Benson JD, Kearsley AJ
(2014) Foundations of modeling in cryobiology—I: concentration, Gibbs energy, and
chemical potential relationships. Cryobiology
69:349–360
17. Anderson DM, Benson JD, Kearsley AJ
(2019) Foundations of modeling in cryobiology—II: heat and mass transport in bulk and
at cell membrane and ice-liquid interfaces.
Cryobiology. 91:3–17 https://doi.org/10.
1016/j.cryobiol.2019.09.014
18. Anderson DM, Benson JD, Kearsley AJ
(2019) Foundations of modeling in cryobiology—III: heat and mass transport in a ternary
system. Cryobiology 92:34–46
19. Anderson DM, Benson JD, Kearsley AJ
(2019) Numerical solution of inward solidification of a dilute ternary solution towards a
semi-permeable spherical cell. Math Biosci
316:108240
20. Karlsson JOM, Cravalho EG, Rinkes IHMB,
Tompkins RG, Yarmush ML, Toner M
(1993) Nucleation and growth of ice crystals
inside cultured-hepatocytes during freezing in
the presence of dimethyl-sulfoxide. Biophys J
65:2524–2536
21. Yang G, Zhang A, Xu LX, He X (2009) Modeling the cell-type dependence of diffusionlimited intracellular ice nucleation and growth
during both vitrification and slow freezing. J
Appl Phys 105:114701
22. Chang A, Dantzig JA, Darr BT, Hubel A
(2007) Modeling the interaction of biological
cells with a solidifying interface. J Comput
Phys 226:1808–1829
23. Liu Z, Wan R, Muldrew K, Sawchuk S,
Rewcastle J (2004) A level set variational
formulation for coupled phase change/mass
transfer problems: application to freezing of
biological systems. Finite Elem Anal Des
40:1641–1663
24. Zeng C, He L, Peng W, Ding L, Tang K,
Fang D, Zhang Y (2014) Selection of optimal
reference genes for quantitative RT-PCR
studies of boar spermatozoa cryopreservation.
Cryobiology 68:113–121. http://dx.doi.
org/10.1016/j.cryobiol.2014.01.004
25. Kashuba Benson CM, Benson JD, Critser JK
(2008) An improved cryopreservation
method for a mouse embryonic stem cell
line. Cryobiology 56:120–130
26. Kashuba CM, Benson JD, Critser JK (2014)
Rationally optimized cryopreservation of
multiple mouse embryonic stem cell lines:
II—Mathematical prediction and experimental validation of optimal cryopreservation protocols. Cryobiology 68:176–184. http://dx.
doi.org/10.1016/j.cryobiol.2013.12.003
27. Kashuba CM, Benson JD, Critser JK (2014)
Rationally optimized cryopreservation of
multiple mouse embryonic stem cell lines:
I—comparative fundamental cryobiology of
multiple mouse embryonic stem cell lines
and the implications for embryonic stem cell
cryopreservation protocols. Cryobiology
68:166–175. http://dx.doi.org/10.1016/j.
cryobiol.2013.12.007
28. Agca Y, Liu J, Critser E, Critser J (2000)
Fundamental cryobiology of rat immature
and mature oocytes: hydraulic conductivity
in the presence of Me(2)SO, Me(2)SO permeability, and their activation energies. J Exp
Zool 286:523–533
29. Ridgway
D,
Broderick
G,
LopezCampistrous A, Ru’aini M, Winter P,
Hamilton M, Boulanger P, Kovalenko A, Ellison MJ (2008) Coarse-grained molecular
simulation of diffusion and reaction kinetics
in a crowded virtual cytoplasm. Biophys J
94:3748–3759
30. Lacelle PL, Rothstein A (1966) The passive
permeability of the red blood cell to cations. J
Gen Physiol 50:171–188
31. Agca Y, Liu J, Mullen S, Johnson-Ward J,
Gould K, Chan A, Critser J (2005) Chimpanzee (Pan troglodytes) spermatozoa osmotic
tolerance and cryoprotectant permeability
characteristics. J Androl 26:470–477
32. Newton H, Pegg DE, Barrass R, Gosden RG
(1999) Osmotically inactive volume, hydraulic conductivity, and permeability to dimethyl
sulphoxide of human mature oocytes. J
Reprod Fertil 117:27–33
33. Gao DY, Chang Q, Liu C, Farris K, Harvey K,
McGann LE, English D, Jansen J, Critser JK
(1998) Fundamental cryobiology of human
168
James D. Benson