coefficients are available for various CPAs. However, Fick’s law has
several limitations, including the assumption that tissue volume is
constant and that the solution is ideal and dilute. Fick’s law also
does not account for the effects of cell membrane transport. To
address these limitations a variety of more complicated tissue transport models have been presented in the cryobiology literature.
These models address important features of CPA transport in tissues, including solution nonideality, coupling between interstitial
transport and cell membrane transport, transport-induced tissue
size changes, and fixed electrical charges. However, there is not one
model that captures all of these features. Thus, there is a need for a
general framework for modeling CPA transport in tissue that can be
applied to any tissue type.
Novel approaches are currently being pursued that show promise for establishing a more general tissue transport modeling framework. For instance, agent-based modeling involves the
construction of a tissue by assembly of a group of agents, each of
which represents a cell, and applies rules for how the agents interact
with each other and with their environment. A tissue can be built
based on known anatomical features and can include multiple cell
types with different membrane transport properties. This modeling
approach is currently under investigation for rational design of
cryopreservation methods [41]. Another current area of investigation is the augmentation of the biomechanical model presented by
Abazari and colleagues [22] to account for cell membrane transport
and cell size changes [42]. This would expand the utility of the
model to include tissue types with a higher cell density than cartilage. These promising new approaches have the potential to open
new opportunities for computer-aided design of CPA loading and
removal procedures for tissues.
Acknowledgments
This work was supported by funding from NIH grant R01
EB027203.
References
1. Gao DY, Liu J, Liu C, Mcgann LE, Watson PF,
Kleinhans FW, Mazur P, Critser ES, Critser JK
(1995) Prevention of osmotic injury to human
spermatozoa during addition and removal of
glycerol. Hum Reprod 10:1109–1122
2. Madden PW, Pegg DE (1992) Calculation of
corneal endothelial-cell volume during the
addition and removal of cryoprotective compounds. Cryo-Lett 13:43–50
3. Karlsson JOM, Younis AI, Chan AWS, Gould
KG, Eroglu A (2009) Permeability of the rhesus monkey oocyte membrane to water and
common cryoprotectants. Mol Reprod Dev
76:321–333
4. Benson JD, Chicone CC, Critser JK (2012)
Analytical optimal controls for the state constrained addition and removal of cryoprotective agents. Bull Math Biol 74:1516–1530
186
Ross M. Warner and Adam Z. Higgins
several limitations, including the assumption that tissue volume is
constant and that the solution is ideal and dilute. Fick’s law also
does not account for the effects of cell membrane transport. To
address these limitations a variety of more complicated tissue transport models have been presented in the cryobiology literature.
These models address important features of CPA transport in tissues, including solution nonideality, coupling between interstitial
transport and cell membrane transport, transport-induced tissue
size changes, and fixed electrical charges. However, there is not one
model that captures all of these features. Thus, there is a need for a
general framework for modeling CPA transport in tissue that can be
applied to any tissue type.
Novel approaches are currently being pursued that show promise for establishing a more general tissue transport modeling framework. For instance, agent-based modeling involves the
construction of a tissue by assembly of a group of agents, each of
which represents a cell, and applies rules for how the agents interact
with each other and with their environment. A tissue can be built
based on known anatomical features and can include multiple cell
types with different membrane transport properties. This modeling
approach is currently under investigation for rational design of
cryopreservation methods [41]. Another current area of investigation is the augmentation of the biomechanical model presented by
Abazari and colleagues [22] to account for cell membrane transport
and cell size changes [42]. This would expand the utility of the
model to include tissue types with a higher cell density than cartilage. These promising new approaches have the potential to open
new opportunities for computer-aided design of CPA loading and
removal procedures for tissues.
Acknowledgments
This work was supported by funding from NIH grant R01
EB027203.
References
1. Gao DY, Liu J, Liu C, Mcgann LE, Watson PF,
Kleinhans FW, Mazur P, Critser ES, Critser JK
(1995) Prevention of osmotic injury to human
spermatozoa during addition and removal of
glycerol. Hum Reprod 10:1109–1122
2. Madden PW, Pegg DE (1992) Calculation of
corneal endothelial-cell volume during the
addition and removal of cryoprotective compounds. Cryo-Lett 13:43–50
3. Karlsson JOM, Younis AI, Chan AWS, Gould
KG, Eroglu A (2009) Permeability of the rhesus monkey oocyte membrane to water and
common cryoprotectants. Mol Reprod Dev
76:321–333
4. Benson JD, Chicone CC, Critser JK (2012)
Analytical optimal controls for the state constrained addition and removal of cryoprotective agents. Bull Math Biol 74:1516–1530
186
Ross M. Warner and Adam Z. Higgins