Parameter generation for the patient-specific biomathematical model.

<p><b>1.</b> Determine radial measurements from serial T1Gd and T2/FLAIR magnetic resonance imaging. <b>2.</b> Compute the invisibility index (D/<i>ρ</i>) from intra-study T1Gd and T2/FLAIR radial measurements. <b>3.</b> Compute the radial velocity () from serial T1Gd or T2/FLAIR radial measurements.</p

Optimization Restrictions.

*<p>Patient-specific.</p

Spatial distribution of optimized plans versus the invisibility index.

<p>The radial distance between the 50% isodose radius and the 50% tumor cell isodensity radius versus the invisibility index (<i>D/ρ)</i> 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.</p

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.

<p>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.</p

Patient Data.

*<p>Extent of Resection.</p>†<p>Still alive.</p>‡<p>Biopsy only.</p>¶<p>Temozolomide.</p>#<p>Subtotal resection.</p>||<p>Carmustine.</p>§<p>Not included in Rockne 2010.</p

Simulated tumor and normal cell densities with clinical and optimized total dose.

<p>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 (<i>D/ρ</i>), as patients with more nodular tumors (low <i>D/ρ</i>, e.g. Patient 12) receive more peaked optimized doses while those for patients with more diffuse tumors (high <i>D/ρ</i>, 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.</p