Figure 1.
Parameter generation for the patient-specific biomathematical model.
1. Determine radial measurements from serial T1Gd and T2/FLAIR magnetic resonance imaging. 2. Compute the invisibility index (D/ρ) from intra-study T1Gd and T2/FLAIR radial measurements. 3. Compute the radial velocity () from serial T1Gd or T2/FLAIR radial measurements.
Table 1.
Optimization Restrictions.
Table 2.
Patient Data.
Figure 2.
Computation of the Days Gained metric.
The Days Gained score is the number of days between the post-radiation observation time-point and the time-point on the model-predicted, untreated growth trajectory where the tumor size is equal to the post-treat tumor size. The observations may be actual MRI observations or a chosen simulated time-point.
Figure 3.
Simulated tumor and normal cell densities with clinical and optimized total dose.
Patients are ordered according to tumor diffusivity, from least to greatest and the cell densities are taken at the pre-treatment timepoint. Dose in units Gray is on the left axis while cell density relative to the tumor cell carrying capacity is on the right side. The spatial distribution of the optimized plans is determined primarily by the patient-specific invisibility index (D/ρ), as patients with more nodular tumors (low D/ρ, e.g. Patient 12) receive more peaked optimized doses while those for patients with more diffuse tumors (high D/ρ, e.g. Patient 3) are more spread out along the invasive gradient of the outer edge of the tumor. Patients 2 and 5 show a cell density of zero in the center of the tumor due to subtotal resections.
Figure 4.
Spatial distribution of optimized plans versus the invisibility index.
The radial distance between the 50% isodose radius and the 50% tumor cell isodensity radius versus the invisibility index (D/ρ) for the optimized plans. The horizontal error bars illustrate the range of patient-specific D/p values possible given the observed uncertainty in radial tumor measurements. The vertical error bars represent the minimum and maximum distance from simulations using the expected, minimum and maximum D/p values. The marker is plotted in the center of the range and the center values are positively correlated with Pearson’s correlation r = .98 with p-value = 9e-8, demonstrating that tumors with higher invisibility indices receive optimized doses with shallower gradients and larger high-dose volumes relative to tumor cell density.
Figure 5.
Metrics of treatment and response versus the diffusion coefficient, D, for both the standard-of-care (black) and optimized plans (grey) for all patients with corresponding linear regression lines and Pearson’s correlation coefficients and p-values where appropriate.
A. Equivalent Uniform Dose (EUD) to tumor. 9 of 11 patients received lower tumor EUD, but there is no correlation with the PIRT model parameters. B. Equivalent Uniform Dose (EUD) to normal brain tissue outside of the T1Gd enhancing region. Although smaller in the optimized plans, the normal tissue EUD for both plans is positively correlated with the diffusion coefficient D with Pearson’s correlations r = 0.742 and 0.765; p = 0.009 and 0.005, for the standard-of-care and optimized plans respectively. C. Therapeutic ratio: the ratio of the tumor EUD to that of normal tissue. Therapeutic ratio for both plans is negatively correlated with the diffusion coefficient D with Pearson’s correlations r = −0.78 and −0.84; p = 0.004 and 0.001, for the standard-of-care and optimized plans respectively. D. Days Gained, the model-predicted, untreated growth time between first post-radiation tumor size and that predicted by the model prior to treatment, for both the standard-of-care and optimized plans for all patients.
Figure 6.
Dose-volume histogram showing the total dose delivered to normal brain tissue outside of the T1Gd abnormality for optimized and standard-of-care plans for patient 10.
The lines intersect at 62% of the normal tissue volume, demonstrating that only 2% of the normal tissue receives a higher dose from the optimized plan.