2. Table 1 summarizes the required experimental quantities with
the variables that denote them and their corresponding units
for use in the governing equations in the next steps. Table 2
summarizes the required solution properties, and Table 3
shows an example of how density changes as a function of
temperature for water and some common CPAs.
Table 1
Summary of experimental quantities with corresponding units
Quantity
Description
Units
π s
Osmolality of the surrounding solution
mOsm/kg
π PBS
Baseline osmolality of the PBS solution
mOsm/kg
V PBS
Volume of the PBS solution
mL
W 1
Weight of the tissue before CPA permeation
g
W 2
Weight of the tissue after CPA permeation
g
Table 2
Summary of required CPA and water properties with corresponding units
Parameter Description
Units
M CPA
Molar mass of the CPA
g/mol
ρ CPA (T )
Density of the CPA at each permeation temperature T
g/mL
ρ water (T )
Density of water at each permeation temperature T
g/mL
ρ
∗
water
Density of water at the temperature at which osmolality was measured
(e.g., 0.9978 g/mL at 22
C [11])
g/mL
Table 3
Densities of water and common CPAs at several temperatures [11]
Temperature (
C)
ρ water
(g/mL)
ρ DMSO
(g/mL)
ρ glycerol
(g/mL)
ρ PG
(g/mL)
ρ EG
(g/mL)
4
0.9999
1.102
∗
1.263
∗
1.048
1.124
22
0.9978
1.099
1.260
1.035
1.112
37
0.9933
1.083
1.250
1.024
1.101
Asterisks indicate that the listed density is at the freezing temperature (T f ) of the CPA (T f,DMSO ¼ 19
C; T f,
glycerol ¼ 18
C), because the temperature of interest is below T f
Osmometric Measurements of Cryoprotective Agent Permeation
311