5. Benson JD, Kearsley AJ, Higgins AZ (2012)
Mathematical optimization of procedures for
cryoprotectant equilibration using a toxicity
cost function. Cryobiology 64:144–151
6. Davidson AF, Benson JD, Higgins AZ (2014)
Mathematically optimized cryoprotectant
equilibration procedures for cryopreservation
of human oocytes. Theor Biol Med Model
11:13
7. Davidson AF, Glasscock C, McClanahan DR,
Benson JD, Higgins AZ (2015) Toxicity minimized cryoprotectant addition and removal
procedures for adherent endothelial cells.
PLoS One 10:e0142828
8. Karlsson JO, Szurek EA, Higgins AZ, Lee SR,
Eroglu A (2013) Optimization of cryoprotectant loading into murine and human oocytes.
Cryobiology 68:18–28
9. Mukherjee IN, Li Y, Song YC, Long RC, Sambanis A (2008) Cryoprotectant transport
through articular cartilage for long-term storage: experimental and modeling studies.
Osteoarthr Cartil 16:1379–1386
10. Benson JD, Higgins AZ, Desai K, Eroglu A
(2018) A toxicity cost function approach to
optimal CPA equilibration in tissues. Cryobiology 80:144–155
11. Han X, Ma L, Benson J, Brown A, Critser JK
(2009) Measurement of the apparent diffusivity of ethylene glycol in mouse ovaries through
rapid MRI and theoretical investigation of
cryoprotectant perfusion procedures. Cryobiology 58:298–302
12. He YM, Devireddy RV (2005) An inverse
approach to determine solute and solvent permeability parameters in artificial tissues. Ann
Biomed Eng 33:709–718
13. Devireddy RV (2005) Predicted permeability
parameters of human ovarian tissue cells to
various cryoprotectants and water. Mol Reprod
Dev 70:333–343
14. Hubel A, Bidault N, Hammer B (2002) Transport characteristics of glycerol and propylene
glycol in an engineered dermal replacement.
ASME Conf Proc 2002(36509):121–122
15. Muldrew K, Sykes B, Schachar N, McGann LE
(1996) Permeation kinetics of dimethyl sulfoxide
in
articular
cartilage.
Cryo-Lett
17:331–340
16. Zieger MA, Woods EJ, Lakey JR, Liu J, Critser
JK (1999) Osmotic tolerance limits of canine
pancreatic islets. Cell Transplant 8:277–284
17. Jomha NM, Law GK, Abazari A, Rekieh K,
Elliott JAW, McGann LE (2009) Permeation
of several cryoprotectant agents into porcine
articular cartilage. Cryobiology 58:110–114
18. Papanek TH (1978) The water permeability of
the human erythrocyte in the temperature
range +25
C to À10
C. PhD thesis,
Massachusetts Institute of Technology
19. 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
20. Woods E (1999) Water and cryoprotectant permeability characteristics of isolated human and
canine pancreatic islets. Cell Transplant
8:549–559
21. Liu J, Zieger MA, Lakey JR, Woods EJ, Critser
JK (1997) The determination of membrane
permeability coefficients of canine pancreatic
islet cells and their application to islet cryopreservation. Cryobiology 35:1–13
22. Abazari A, Elliott JA, Law GK, McGann LE,
Jomha NM (2009) A biomechanical triphasic
approach to the transport of nondilute solutions in articular cartilage. Biophys J
97:3054–3064
23. Xu X, Cui Z, Urban JPG (2003) Measurement
of the chondrocyte membrane permeability to
Me 2 SO, glycerol and 1,2-propanediol. Med
Eng Phys 25:573–579
24. Vasquez-Rivera A, Sommer KK, Oldenhof H,
Higgins AZ, Brockbank KGM, Hilfiker A,
Wolkers WF (2018) Simultaneous monitoring
of different vitrification solution components
permeating into tissues. Analyst 143:420–428
25. Comper WD, Laurent TC (1978) Physiological function of connective-tissue polysaccharides. Physiol Rev 58:255–315
26. Forbes RM, Cooper AR, Mitchell HH (1953)
The composition of the adult human body as
determined by chemical analysis. J Biol Chem
203:359–366
27. Kojima J, Nakamura N, Kanatani M, Omori K
(1975) The glycosaminoglycans in human
hepatic cancer. Cancer Res 35:542–547
28. Aukland K, Nicolaysen G (1981) Interstitial
fluid volume – local regulatory mechanisms.
Physiol Rev 61:556–643
29. Lai WM, Hou JS, Mow VC (1991) A triphasic
theory for the swelling and deformation behaviors of articular-cartilage. J Biomech Eng
113:245–258
30. de Freitas RC, Diller KR, Lachenbruch CA,
Merchant FA (2006) Network thermodynamic
model of coupled transport in a multicellular
tissue the islet of Langerhans. Ann N Y Acad Sci
858:191–204
31. Crank J (1975) The mathematics of diffusion,
2nd edn. Oxford University Press, Oxford
Tissue Transport Modeling
187
Mathematical optimization of procedures for
cryoprotectant equilibration using a toxicity
cost function. Cryobiology 64:144–151
6. Davidson AF, Benson JD, Higgins AZ (2014)
Mathematically optimized cryoprotectant
equilibration procedures for cryopreservation
of human oocytes. Theor Biol Med Model
11:13
7. Davidson AF, Glasscock C, McClanahan DR,
Benson JD, Higgins AZ (2015) Toxicity minimized cryoprotectant addition and removal
procedures for adherent endothelial cells.
PLoS One 10:e0142828
8. Karlsson JO, Szurek EA, Higgins AZ, Lee SR,
Eroglu A (2013) Optimization of cryoprotectant loading into murine and human oocytes.
Cryobiology 68:18–28
9. Mukherjee IN, Li Y, Song YC, Long RC, Sambanis A (2008) Cryoprotectant transport
through articular cartilage for long-term storage: experimental and modeling studies.
Osteoarthr Cartil 16:1379–1386
10. Benson JD, Higgins AZ, Desai K, Eroglu A
(2018) A toxicity cost function approach to
optimal CPA equilibration in tissues. Cryobiology 80:144–155
11. Han X, Ma L, Benson J, Brown A, Critser JK
(2009) Measurement of the apparent diffusivity of ethylene glycol in mouse ovaries through
rapid MRI and theoretical investigation of
cryoprotectant perfusion procedures. Cryobiology 58:298–302
12. He YM, Devireddy RV (2005) An inverse
approach to determine solute and solvent permeability parameters in artificial tissues. Ann
Biomed Eng 33:709–718
13. Devireddy RV (2005) Predicted permeability
parameters of human ovarian tissue cells to
various cryoprotectants and water. Mol Reprod
Dev 70:333–343
14. Hubel A, Bidault N, Hammer B (2002) Transport characteristics of glycerol and propylene
glycol in an engineered dermal replacement.
ASME Conf Proc 2002(36509):121–122
15. Muldrew K, Sykes B, Schachar N, McGann LE
(1996) Permeation kinetics of dimethyl sulfoxide
in
articular
cartilage.
Cryo-Lett
17:331–340
16. Zieger MA, Woods EJ, Lakey JR, Liu J, Critser
JK (1999) Osmotic tolerance limits of canine
pancreatic islets. Cell Transplant 8:277–284
17. Jomha NM, Law GK, Abazari A, Rekieh K,
Elliott JAW, McGann LE (2009) Permeation
of several cryoprotectant agents into porcine
articular cartilage. Cryobiology 58:110–114
18. Papanek TH (1978) The water permeability of
the human erythrocyte in the temperature
range +25
C to À10
C. PhD thesis,
Massachusetts Institute of Technology
19. 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
20. Woods E (1999) Water and cryoprotectant permeability characteristics of isolated human and
canine pancreatic islets. Cell Transplant
8:549–559
21. Liu J, Zieger MA, Lakey JR, Woods EJ, Critser
JK (1997) The determination of membrane
permeability coefficients of canine pancreatic
islet cells and their application to islet cryopreservation. Cryobiology 35:1–13
22. Abazari A, Elliott JA, Law GK, McGann LE,
Jomha NM (2009) A biomechanical triphasic
approach to the transport of nondilute solutions in articular cartilage. Biophys J
97:3054–3064
23. Xu X, Cui Z, Urban JPG (2003) Measurement
of the chondrocyte membrane permeability to
Me 2 SO, glycerol and 1,2-propanediol. Med
Eng Phys 25:573–579
24. Vasquez-Rivera A, Sommer KK, Oldenhof H,
Higgins AZ, Brockbank KGM, Hilfiker A,
Wolkers WF (2018) Simultaneous monitoring
of different vitrification solution components
permeating into tissues. Analyst 143:420–428
25. Comper WD, Laurent TC (1978) Physiological function of connective-tissue polysaccharides. Physiol Rev 58:255–315
26. Forbes RM, Cooper AR, Mitchell HH (1953)
The composition of the adult human body as
determined by chemical analysis. J Biol Chem
203:359–366
27. Kojima J, Nakamura N, Kanatani M, Omori K
(1975) The glycosaminoglycans in human
hepatic cancer. Cancer Res 35:542–547
28. Aukland K, Nicolaysen G (1981) Interstitial
fluid volume – local regulatory mechanisms.
Physiol Rev 61:556–643
29. Lai WM, Hou JS, Mow VC (1991) A triphasic
theory for the swelling and deformation behaviors of articular-cartilage. J Biomech Eng
113:245–258
30. de Freitas RC, Diller KR, Lachenbruch CA,
Merchant FA (2006) Network thermodynamic
model of coupled transport in a multicellular
tissue the islet of Langerhans. Ann N Y Acad Sci
858:191–204
31. Crank J (1975) The mathematics of diffusion,
2nd edn. Oxford University Press, Oxford
Tissue Transport Modeling
187