Biomedical Engineering Reference
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(a)
(b)
4x10
16
1.0
4x10
16
1.0
η
ice
η
water
0.8
0.8
3x10
16
3x10
16
0.6
0.6
m
ext
CPA,0
= 0 osmol m
-3
water
m
ext
CPA,0
= 500 osmol m
-3
water
2x10
16
2x10
16
0.4
0.4
1x10
16
1x10
16
0.2
0.2
0
0.0
0
0.0
5.0x10
-15
1.0x10
-14
1.5x10
-14
5.0x10
-15
1.0x10
-14
1.5x10
-14
0.0
0.0
(c)
Cell volume, V [m
-3
]
(d)
Cell volume, V [m
-3
]
1.0
4x10
16
1.0
4x10
16
0.8
0.8
3x10
16
3x10
16
0.6
0.6
m
ext
CPA,0
=5000 osmol m
-3
water
m
ext
CPA,0
= 1000 osmol m
-3
water
2x10
16
2x10
16
0.4
0.4
1x10
16
1x10
16
0.2
0.2
0
0
0.0
0.0
5.0x10
-15
1.0x10
-14
1.5x10
-14
0.0
0.0
5.0x10
-15
1.0x10
-14
1.5x10
-14
Cell volume, V [m
3
]
(e)
Cell volume, V [m
-3
]
(f)
4x10
16
1.0
4x10
16
1.0
0.8
0.8
3x10
16
3x10
16
m
ext
CPA,0
= 11000 osmol m
-3
water
m
ext
CPA,0
= 12000 osmol m
-3
water
0.6
0.6
2x10
16
2x10
16
0.4
0
.4
1x10
16
1x10
16
0.2
0.2
0
0.0
0
0.0
0.0
5.0x10
-15
1.0x10
-14
1.5x10
-14
5.0x10
-15
1.0x10
-14
1.5x10
-14
0.0
Cell volume, V [m
3
]
Cell volume, V [m
3
]
Fig. 16 Model results of cooling stage of a cell suspension carried out at -50C/min with
increasing CPA content in terms of the initial cell-size, internal ice volume percentage g
ice
, and total
water content g
water
profiles at -60C as a function of initial cell volume (adapted from [
10
]):
m
ext
CPA
;
0
= 0 osmol
=
m
water
(a), 500 osmol
=
m
water
(b), 1000 osmol
=
m
water
(c), 5000 osmol
=
m
water
(d),
11000 osmol
=
m
water
(e) 12000 osmol
=
m
water
(f) are considered
range excursions during equilibration stage may not be avoided as mechanisms of
cell mortality, even if all the classes of the size-distributed cell population will be
unfrozen at -60C and eventually vitrified. However, it is worth noting that, the
behaviour of IIF described above, i.e. the occurrence of a maximum value of PIIF,
is actually observed at all cooling rates considered in this work. More specifically,
to reach a completely unfrozen size-distributed cell population at -60C, a lower
CPA content is needed when increasing the cooling rate. Thus, a specific com-
bination of operative conditions (i.e. cooling rate and CPA content) may be found
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