Identification of Crucial Parameters in a Mathematical Multiscale Model of Glioblastoma Growth

Table 3

The parameter scalings whose combinations result in a decrease of the tumour expansion velocity and the tumour volume. The first and second column list the parameters (𝑘_𝑙1) and factors (𝑏_𝑛1) whose corresponding variations (𝑘_𝑙1⋅𝑏_𝑛1) combined with the second parameter scalings (𝑘_𝑙2⋅𝑏_𝑛2) (given for different initial glucose concentrations in the third (1.125 gL⁻¹), fourth (2.25 gL⁻¹), and fifth (4.5 gL⁻¹) column) resulted in 𝛿𝑀^time>0.01 and 𝛿𝑀^total<−0.01.

𝑘𝑙1	𝑏𝑛1	𝑘𝑙2∗𝑏𝑛2
		1.125 g L^−1	2.25 g L^−1	4.5 g L^−1
𝑘1	0.01	—	—	𝑘7⋅100
	10	—	𝑘^𝑐211⋅5	—
	50	𝑘10⋅0.01	𝑘9⋅100; 𝑘^𝑐211⋅10	𝑘^𝑖1⋅0.01; 𝑘9⋅{50,100}; 𝑘10⋅0.01
𝑘^𝑖1	0.01	—	𝑘8⋅50	𝑘8⋅50
𝑘2	0.01	—	—	𝑘4⋅0.01; 𝑘7⋅0.01
	50	𝑘^𝑖1⋅0.01; 𝑘9⋅100; 𝑘10⋅0.01	𝑘^𝑖1⋅0.01; 𝑘9⋅100; 𝑘10⋅0.01	𝑘9⋅100; 𝑘10⋅0.01; 𝑘^𝑐211⋅10
𝑘4	50	𝑘2⋅100; 𝑘3⋅0.01; 𝑘10⋅100	𝑘9⋅0.01	𝑘8⋅100
𝑘7	50	—	—	𝑘8⋅100; 𝑘9⋅0.01
𝑘^𝑐211	5	𝑘8⋅10; 𝑘9⋅0.1;	𝑘3⋅0.01; 𝑘4⋅0.1;	𝑘8⋅10; 𝑘9⋅0.1
		𝑘10⋅10; 𝑘12⋅5	𝑘7⋅0.1; 𝑘10⋅50
	10	𝑘12⋅10	—	—
	50	𝑘8⋅100; 𝑘9⋅0.01	𝑘8⋅100; 𝑘12⋅50	𝑘8⋅100; 𝑘9⋅0.01; 𝑘10⋅100; 𝑘12⋅50
	100	—	𝑘12⋅100	—