Table 1 Model parameters and variables
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 |