hematopoietic progenitor cells I: osmotic
characteristics and volume distribution. Cryobiology
36:40–48.
https://doi.org/10.
1006/cryo.1997.2060
34. Woods EJ, Zieger MA, Lakey JR, Liu J, Critser JK (1997) Osmotic characteristics of
isolated human and canine pancreatic islets.
Cryobiology 35:106–113. https://doi.org/
10.1006/cryo.1997.2029
35. Willoughby CE, Mazur P, Peter AT, Critser
JK (1996) Osmotic tolerance limits and properties of murine spermatozoa. Biol Reprod
55:715–727
36. Du J, Tao J, Kleinhans FW, Peter AT, Critser
JK (1994) Determination of boar spermatozoa water volume and osmotic response.
Theriogenology 42:1183–1191
37. Du J, Tao J, Kleinhans FW, Mazur P, Critser
JK (1994) Water volume and osmotic behaviour of mouse spermatozoa determined by
electron paramagnetic resonance. J Reprod
Fertil 101:37–42
38. Benson C, Liu C, Gao D, Critser E, Critser J
(1993) Determination of the osmotic characteristics of hamster pancreatic islets and
isolated pancreatic islet cells. Cell Transplant
2:461–465
39. Mazur P, Schneider U (1986) Osmotic
responses of preimplantation mouse and
bovine embryos and their cryobiological
implications. Cell Biophys 8:259–285
40. Shapiro H (1948) The change in osmotically
inactive fraction produced by cell activation. J
Gen Physiol 32:34–51
41. Prickett RC, Elliott JAW, Hakda S, McGann
LE (2008) A non-ideal replacement for the
Boyle van’t Hoff equation. Cryobiology
57:130–136
42. Ponder E (1940) The red cell as an osmometer. In: Cold Spring Harbor Symposia on
Quantitative Biology, vol 8. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp
133–143
43. Katkov II (2011) On proper linearization,
construction and analysis of the Boyle–van’t
Hoff plots and correct calculation of the
osmotically inactive volume. Cryobiology
62:232–241
44. Katkov II (2008) Challenge from the simple:
some caveats in linearization of the Boylevan’t Hoff and Arrhenius plots. Cryobiology
57:142–149
45. Benson JD (2012) Some comments on recent
discussion of the Boyle van’t Hoff relationship. Cryobiology 64:118–120
46. Casula E, Traversari G, Fadda S, Klymenko
OV, Kontoravdi C, Cincotti A (2019)
Modelling the osmotic behaviour of human
mesenchymal stem cells. Biochem Eng J
151:107296
47. Sun M, Northup N, Marga F, Huber T,
Byfield FJ, Levitan I, Forgacs G (2007) The
effect of cellular cholesterol on membranecytoskeleton adhesion. J Cell Sci. https://
doi.org/10.1242/jcs.001370
48. Benson JD, Chicone CC, Critser JK (2011) A
general model for the dynamics of cell volume, global stability and optimal control. J
Math Biol 63:339–359
49. Moore WJ (1972) Physical chemistry, 4th
edn. Prentice-Hall, Englewood Cliffs
50. Prickett RC, Elliott JAW, McGann LE (2011)
Application of the multisolute osmotic virial
equation to solutions containing electrolytes.
J Phys Chem B 115:14531–14543
51. Benson JD, Bagchi A, Han X, Critser JK,
Woods EJ (2010) Melting point equations
for the ternary system water/sodium chloride/ethylene glycol revisited. Cryobiology
61:352–356
52. Elliott JAW, Prickett RC, Elmoazzen HY,
Porter KR, McGann LE (2007) A multisolute
osmotic virial equation for solutions of interest in biology. J Phys Chem B
111:1775–1785
53. Landau LD, Lifshitz EM (1980) Statistical
physics, vol 5. Course of theoretical physics,
3rd edn. Pergamon Press, Oxford
54. Kleinhans FW, Mazur P (2007) Comparison
of actual vs. synthesized ternary phase diagrams for solutes of cryobiological interest.
Cryobiology 54:212–222
55. Benson JD (2011) Stability analysis of several
non-dilute multiple solute transport equations. J Math Chem 49:859–869
56. Bird RB, Stewart WE, Lightfoot EN (2002)
Transport phenomena, 2nd edn. Wiley,
New York
57. Elliott JAW, Elmoazzen HY, McGann LE
(2000) A method whereby Onsager coefficients may be evaluated. J Chem Phys
113:6573–6578
58. Kedem O, Katchalsky A (1958) Thermodynamic analysis of the permeability of
biological membranes to non-electrolytes.
Biochim Biophys Acta 27:229–246
59. Kleinhans FW (1998) Membrane permeability modeling: Kedem-Katchalsky vs. a
two-parameter
formalism.
Cryobiology
37:271–289
60. Finkelstein A (1987) Water movement
through lipid bilayers, pores, and plasma
membranes: theory and reality. Wiley,
New York
Mathematical Modeling and Optimization of Cryopreservation in Single Cells
169
characteristics and volume distribution. Cryobiology
36:40–48.
https://doi.org/10.
1006/cryo.1997.2060
34. Woods EJ, Zieger MA, Lakey JR, Liu J, Critser JK (1997) Osmotic characteristics of
isolated human and canine pancreatic islets.
Cryobiology 35:106–113. https://doi.org/
10.1006/cryo.1997.2029
35. Willoughby CE, Mazur P, Peter AT, Critser
JK (1996) Osmotic tolerance limits and properties of murine spermatozoa. Biol Reprod
55:715–727
36. Du J, Tao J, Kleinhans FW, Peter AT, Critser
JK (1994) Determination of boar spermatozoa water volume and osmotic response.
Theriogenology 42:1183–1191
37. Du J, Tao J, Kleinhans FW, Mazur P, Critser
JK (1994) Water volume and osmotic behaviour of mouse spermatozoa determined by
electron paramagnetic resonance. J Reprod
Fertil 101:37–42
38. Benson C, Liu C, Gao D, Critser E, Critser J
(1993) Determination of the osmotic characteristics of hamster pancreatic islets and
isolated pancreatic islet cells. Cell Transplant
2:461–465
39. Mazur P, Schneider U (1986) Osmotic
responses of preimplantation mouse and
bovine embryos and their cryobiological
implications. Cell Biophys 8:259–285
40. Shapiro H (1948) The change in osmotically
inactive fraction produced by cell activation. J
Gen Physiol 32:34–51
41. Prickett RC, Elliott JAW, Hakda S, McGann
LE (2008) A non-ideal replacement for the
Boyle van’t Hoff equation. Cryobiology
57:130–136
42. Ponder E (1940) The red cell as an osmometer. In: Cold Spring Harbor Symposia on
Quantitative Biology, vol 8. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp
133–143
43. Katkov II (2011) On proper linearization,
construction and analysis of the Boyle–van’t
Hoff plots and correct calculation of the
osmotically inactive volume. Cryobiology
62:232–241
44. Katkov II (2008) Challenge from the simple:
some caveats in linearization of the Boylevan’t Hoff and Arrhenius plots. Cryobiology
57:142–149
45. Benson JD (2012) Some comments on recent
discussion of the Boyle van’t Hoff relationship. Cryobiology 64:118–120
46. Casula E, Traversari G, Fadda S, Klymenko
OV, Kontoravdi C, Cincotti A (2019)
Modelling the osmotic behaviour of human
mesenchymal stem cells. Biochem Eng J
151:107296
47. Sun M, Northup N, Marga F, Huber T,
Byfield FJ, Levitan I, Forgacs G (2007) The
effect of cellular cholesterol on membranecytoskeleton adhesion. J Cell Sci. https://
doi.org/10.1242/jcs.001370
48. Benson JD, Chicone CC, Critser JK (2011) A
general model for the dynamics of cell volume, global stability and optimal control. J
Math Biol 63:339–359
49. Moore WJ (1972) Physical chemistry, 4th
edn. Prentice-Hall, Englewood Cliffs
50. Prickett RC, Elliott JAW, McGann LE (2011)
Application of the multisolute osmotic virial
equation to solutions containing electrolytes.
J Phys Chem B 115:14531–14543
51. Benson JD, Bagchi A, Han X, Critser JK,
Woods EJ (2010) Melting point equations
for the ternary system water/sodium chloride/ethylene glycol revisited. Cryobiology
61:352–356
52. Elliott JAW, Prickett RC, Elmoazzen HY,
Porter KR, McGann LE (2007) A multisolute
osmotic virial equation for solutions of interest in biology. J Phys Chem B
111:1775–1785
53. Landau LD, Lifshitz EM (1980) Statistical
physics, vol 5. Course of theoretical physics,
3rd edn. Pergamon Press, Oxford
54. Kleinhans FW, Mazur P (2007) Comparison
of actual vs. synthesized ternary phase diagrams for solutes of cryobiological interest.
Cryobiology 54:212–222
55. Benson JD (2011) Stability analysis of several
non-dilute multiple solute transport equations. J Math Chem 49:859–869
56. Bird RB, Stewart WE, Lightfoot EN (2002)
Transport phenomena, 2nd edn. Wiley,
New York
57. Elliott JAW, Elmoazzen HY, McGann LE
(2000) A method whereby Onsager coefficients may be evaluated. J Chem Phys
113:6573–6578
58. Kedem O, Katchalsky A (1958) Thermodynamic analysis of the permeability of
biological membranes to non-electrolytes.
Biochim Biophys Acta 27:229–246
59. Kleinhans FW (1998) Membrane permeability modeling: Kedem-Katchalsky vs. a
two-parameter
formalism.
Cryobiology
37:271–289
60. Finkelstein A (1987) Water movement
through lipid bilayers, pores, and plasma
membranes: theory and reality. Wiley,
New York
Mathematical Modeling and Optimization of Cryopreservation in Single Cells
169