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Table 1 Parameters and values used in the mathematical models

From: Towards an integrated systems-based modelling framework for drug transport and its effect on tumour cells

Parameter Symbol Value Reference
Tumour blood flow    
Tumour capillary radius RC 100 (μm) [33]
Tumour interstitium radius RT 1200 (μm) Estimated
Tumour length L 1 (cm) [33]
Blood density ρ 1000 (kg/m3) [32]
Blood viscosity μ 0.004 (Pa∙s) [35]
Vascular hydraulic conductivity L p 0.36-2.8 × 10-6 (cm/mmHg∙s) [36]
Tissue hydraulic conductivity K 0.4-2.0 × 10-7 (cm2/mmHg∙s) [36]
Vascular inlet pressure P A 15 (mmHg) [37]
Vascular outlet pressure P V 0 [36]
Ambient pressure P 0 0 [36]
Drug transport (Doxorubicin) D E 1.5778 × 10-6 (cm2/s) [17]
DOX diffusion coefficient    
Rate of transmembrane transport V 1 , V 2 0.28 (ng/(105cells)/min) [14]
(V1 = V2)
Diffusive permeability for DOX P E 2.778 × 10-4 (cm/s) [17]
Michaelis constant for transmembrane transport k 1 0.219 (μg/ml) [14]
Michaelis constant for transmembrane transport k 2 1.37 (ng/(105cells)) [14]
Tumour cell density    
Initial tumour cell density c t,0 106 (cells/mm3) [17]
Tumour cell growth rate a 1 0.5 (day-1) Estimated
Saturation constant in logistic equation b 0.02592 (mm3/(105cells)/day) Estimated
Tumour cell natural decay rate a 2 0.24 (day-1) Estimated
Intracellular signalling:    
Bistable switch    
Michaelis Menten constants V f 27 (hr-1) [38]
Michaelis Menten constants V r 0.459 (hr-1) [38]
Michaelis Menten constants K m1 100 [38]
Michaelis Menten constants K m2 0.01 [38]
Kinetic parameter mediating feedback strength k fb 2.927 (hr-1) [38]
Basal level in the bistable switch p 0.7 Estimated
Parameter mediating input regulation in the bistable switch q 0.3(ng/(105cells))-1 Estimated
Monostable switch    
Kinetic parameter reflecting the time scale of the response k 0.432 (hr-1) Estimated
Associated constant k h 1 (ng/(105cells)) Estimated
Hill coefficient n 10 Estimated
R1 protein activation rate k f 3.6 (hr-1) Estimated
R1 protein degradation rate k r 0.144 (hr-1) Estimated
R1 Threshold for apoptosis switch R 1 , th 0.9 Estimated