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Table 2 Effects of parameter constraints on optimized piecewise constant procedures for equilibration of human oocytes with EG

From: Mathematically optimized cryoprotectant equilibration procedures for cryopreservation of human oocytes

Procedure

Step

Non-permeating solute, M1(Osm/kg)

EG, M2(Osm/kg)

Time, t(min)

Toxicity (Jα)

Constraints:

0 ≤ M 1  ≤ 24

0 ≤ M 2  ≤ 24

t ≥ 0

 

Addition

1

0

1.4

20

130

 

2

0

2.4

16

 

3

0

24

0.094

Removal

1

1.8

0

3.6

22

 

2

0.66

0

15

Constraints:

0 ≤ M 1  ≤ 24

0 ≤ M 2  ≤ 24

t ≥ 1

 

Addition

1

0

1.3

19

240

 

2

0

2.4

16

 

3

0

17

1.0

Removal

1

2.0

0

3.6

25

 

2

0.65

0

15

Constraints:

0 ≤ M 1  ≤ 24

0 ≤ M 2  ≤ 16

t ≥ 1

 

Addition

1

0

1.4

20

250

 

2

0

2.5

16

 

3

1.2

16

1.0

Removal

1

1.8

0

3.5

22

 

2

0.68

0

13

Constraints:

0.05 ≤ M 1  ≤ 24

0 ≤ M 2  ≤ 16

t ≥ 1

 

Addition*

1

0.050

1.4

24

 
 

2

0.050

2.4

20

280

 

3

1.2

16

1.0

 

Removal*

1

1.8

0

3.6

23

 

2

0.66

0

14

 
  1. The goal state for EG addition was sf/wf = 53.7, which is equivalent to an intracellular concentration of 8.5 mol/L, or 16 Osm/kg.
  2. *These procedures are illustrated in Figure 5.