Critser JK (1995) Prevention of osmotic
injury to human spermatozoa during addition
and removal of glycerol. Hum Reprod
10:1109–1122
109. Gao DY, Ashworth E, Watson PF, Kleinhans
FW, Mazur P, Critser JK (1993) Hyperosmotic
tolerance of human spermatozoa: separate
effects of glycerol, sodium chloride, and sucrose
on spermolysis. Biol Reprod 49:112–123
110. Fahy G, Wowk B, Wu J, Paynter S (2004)
Improved vitrification solutions based on the
predictability of vitrification solution toxicity.
Cryobiology 48:22–35
111. Elmoazzen HY, Poovadan A, Law GK, Elliott
JAW, McGann LE, Jomha NM (2007)
Dimethyl sulfoxide toxicity kinetics in intact
articular cartilage. Cell Tissue Bank 8:125–133
112. Wang L, Liu J, Zhou GB, Hou YP, Li JJ, Zhu
SE (2011) Quantitative investigations on the
effects of exposure durations to the combined
cryoprotective agents on mouse oocyte vitrification procedures. Biol Reprod 85:884–894
113. Benson JD (2009) Mathematical problems
from cryobiology. Ph.D. thesis, University of
Missouri
114. Karlsson JO, Younis AI, Chan AW, Gould
KG, Eroglu A (2009) Permeability of the
rhesus monkey oocyte membrane to water
and common cryoprotectants. Mol Reprod
Dev 76:321–333
115. Lee E, Markus L (1968) Foundations of optimal control theory. The SIAM series in
applied mathematics. Wiley, New York.
116. Royden HL (1988) Real analysis, 3rd edn.
Prentice-Hall, Englewood Cliffs
117. Sch attler H, Ledzewicz U (2012) Geometric
optimal control: theory, methods and examples. Springer, Berlin
118. Benson JD (2013) Cost functional dependence of optimal CPA equilibration trajectories. Cryobiology 67:404
119. Mazur P (1977) The role of intracellular
freezing in the death of cells cooled at
supraoptimal
rates.
Cryobiology
14:251–272
120. Muldrew K, Acker JP, Elliott JA, McGann LE
(2004) The water to ice transition: implications for living cells. In: Fuller BJ, Lane N,
Benson EE (eds) Life in the Frozen State.
CRC Press, London, pp 93–134
121. Mazur P, Miller R (1976) Permeability of the
human erythrocyte to glycerol in 1 and 2 M
solutions at 0 or 20
∘
C. Cryobiology
13:507–522
122. Morris G, Acton E, Avery S (1999) A novel
approach to sperm cryopreservation. Hum
Reprod 14:1013–1021
123. Karlsson JOM, Eroglu A, Toth TL, Cravalho
EG, Toner M (1996) Fertilization and development of mouse oocytes cryopreserved
using a theoretically optimized protocol.
Hum Reprod 11:1296–1305
124. Wowk B (2010) Thermodynamic aspects of
vitrification. Cryobiology 60:11–22
125. Seki S, Mazur P (2009) The dominance of
warming rate over cooling rate in the survival of mouse oocytes subjected to a vitrification procedure. Cryobiology 59:75–82
126. Barry PH, Diamond JM (1984) Effects of
unstirred layers on membrane phenomena.
Physiol Rev 64:763–872
127. Prickett RC (2010) The application of the
multisolute osmotic virial equation to cryobiology. Ph.D. thesis, University of Alberta,
Edmonton, Alberta
172
James D. Benson
injury to human spermatozoa during addition
and removal of glycerol. Hum Reprod
10:1109–1122
109. Gao DY, Ashworth E, Watson PF, Kleinhans
FW, Mazur P, Critser JK (1993) Hyperosmotic
tolerance of human spermatozoa: separate
effects of glycerol, sodium chloride, and sucrose
on spermolysis. Biol Reprod 49:112–123
110. Fahy G, Wowk B, Wu J, Paynter S (2004)
Improved vitrification solutions based on the
predictability of vitrification solution toxicity.
Cryobiology 48:22–35
111. Elmoazzen HY, Poovadan A, Law GK, Elliott
JAW, McGann LE, Jomha NM (2007)
Dimethyl sulfoxide toxicity kinetics in intact
articular cartilage. Cell Tissue Bank 8:125–133
112. Wang L, Liu J, Zhou GB, Hou YP, Li JJ, Zhu
SE (2011) Quantitative investigations on the
effects of exposure durations to the combined
cryoprotective agents on mouse oocyte vitrification procedures. Biol Reprod 85:884–894
113. Benson JD (2009) Mathematical problems
from cryobiology. Ph.D. thesis, University of
Missouri
114. Karlsson JO, Younis AI, Chan AW, Gould
KG, Eroglu A (2009) Permeability of the
rhesus monkey oocyte membrane to water
and common cryoprotectants. Mol Reprod
Dev 76:321–333
115. Lee E, Markus L (1968) Foundations of optimal control theory. The SIAM series in
applied mathematics. Wiley, New York.
116. Royden HL (1988) Real analysis, 3rd edn.
Prentice-Hall, Englewood Cliffs
117. Sch attler H, Ledzewicz U (2012) Geometric
optimal control: theory, methods and examples. Springer, Berlin
118. Benson JD (2013) Cost functional dependence of optimal CPA equilibration trajectories. Cryobiology 67:404
119. Mazur P (1977) The role of intracellular
freezing in the death of cells cooled at
supraoptimal
rates.
Cryobiology
14:251–272
120. Muldrew K, Acker JP, Elliott JA, McGann LE
(2004) The water to ice transition: implications for living cells. In: Fuller BJ, Lane N,
Benson EE (eds) Life in the Frozen State.
CRC Press, London, pp 93–134
121. Mazur P, Miller R (1976) Permeability of the
human erythrocyte to glycerol in 1 and 2 M
solutions at 0 or 20
∘
C. Cryobiology
13:507–522
122. Morris G, Acton E, Avery S (1999) A novel
approach to sperm cryopreservation. Hum
Reprod 14:1013–1021
123. Karlsson JOM, Eroglu A, Toth TL, Cravalho
EG, Toner M (1996) Fertilization and development of mouse oocytes cryopreserved
using a theoretically optimized protocol.
Hum Reprod 11:1296–1305
124. Wowk B (2010) Thermodynamic aspects of
vitrification. Cryobiology 60:11–22
125. Seki S, Mazur P (2009) The dominance of
warming rate over cooling rate in the survival of mouse oocytes subjected to a vitrification procedure. Cryobiology 59:75–82
126. Barry PH, Diamond JM (1984) Effects of
unstirred layers on membrane phenomena.
Physiol Rev 64:763–872
127. Prickett RC (2010) The application of the
multisolute osmotic virial equation to cryobiology. Ph.D. thesis, University of Alberta,
Edmonton, Alberta
172
James D. Benson