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Table 1 Model simulation for 1, 2, 3, 6, 9, 12, 15 and 18 months

From: Mathematical modelling of spatio-temporal glioma evolution

Model simulation results

t

D (mm^2/day)

0.005

0.3

0.005

0.3

0.04

( days )

ρ (/ day )

0.0025

0.0025

0.04

0.04

0.015

 

P r

3.05

12

3.2

13.5

6.2

30

H r

0

0

2.7

0

0

 

Q r

0

0

0

0

0

 

N r

0

0

0

0

0

 

P r

3.75

16

4.9

19

8.2

60

H r

0

0

5.1

0

0

 

Q r

0

0

0.5

0

0

 

N r

0

0

0.3

0

0

 

P r

4.3

18

6.7

25

9.8

90

H r

0

0

6.7

0

0

 

Q r

0

0

2.6

0

0

 

N r

0

0

1.9

0

0

 

P r

5.6

22

11

45

14

180

H r

0

0

10

42.5

0

 

Q r

0

0

6.5

21.5

0

 

N r

0

0

5.5

18

0

 

P r

6.5

25

14.5

74.5

18.5

270

H r

0

0

13.5

69

14

 

Q r

0

0

9.5

46

0

 

N r

0

0

9

42.5

0

 

P r

7.35

28

18

103

24

360

H r

0

0

17

95

21

 

Q r

0

0

13.3

71

10

 

N r

0

0

12.5

69

9

 

P r

8.15

33

22

131

30

450

H r

0

0

21

123

26.5

 

Q r

0

0

17

100

16

 

N r

0

0

16.5

96

14

 

P r

8.8

40

25.5

157

36

540

H r

0

0

24

149

32

 

Q r

0

0

21

127

21.5

 

N r

0

0

20

125

20

  1. Radius (mm) of each cell population (Proliferative: P r , Hypoxic: H r , Hypoglycemic: Q r , Necrotic: N r ) with respect to each diffusion-proliferation combination.