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Table 1 Model parameters and variables

From: Forecasting tumor and vasculature response dynamics to radiation therapy via image based mathematical modeling

Parameter or variable Interpretation Source
\( {\phi}_T\left(\overline{x},t\right) \) Tumor cell volume fraction Measured from DW-MRI
\( {\phi}_V\left(\overline{x},t\right) \) Blood volume fraction Measured from DCE-MRI
kp,T Tumor cell proliferation rate Calibrated
\( {\theta}_{T,V}\left(\overline{x},t\right) \) Combined \( {\phi}_T \) and \( {\phi}_V \) carrying capacity Calculated
\( {\theta}_T\left(\overline{x},t\right) \) Tumor cell carrying capacity Calculated Eq. [4]
DT,0,DV,0 \( {\phi}_T \) and \( {\phi}_V \) diffusion coefficients in absence of mechanically coupling Calibrated
G Shear modulus Literature [34]
v Poisson’s Ratio Literature [34]
λ1 Coupling Constants Calibrated
λ2 Coupling Constants Set to 1
\( {\phi}_{V,\mathrm{thresh}} \) Threshold on \( {\phi}_V \) for carrying capacity to decrease Calibrated
θmax Max carrying capacity Calibrated
θmin Minimum value for carrying capacity Assigned from DW-MRI
kp,V Vasculature proliferation rate Calibrated
kd,V Vasculature death rate Calibrated
d Distance top the periphery of the tumor Calculated
θV Maximum blood volume Assigned from DCE-MRI
αI Treatment efficacy (immediate effect) Calibrated
αLT Treatment efficacy (long term effect) Calibrated
Dose Treatment dose (in Gy) Assigned
α Radiosensitivity Parameters Calibrated
β Radiosensitivity Parameter Assigned
\( \overline{\phi_{V, pre- treatment}} \) Average pre-treatment\( {\phi}_V\left(\overline{x},t\right) \) Calculated