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

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

Optimization Restrictions.

*<p>Patient-specific.</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

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

Patient-Specific Simulations of Tumor Cell Distribution and Density for both a Relatively Diffuse and a Relatively Nodular Glioblastoma.

<p>T1Gd and T2 MRIs for two newly diagnosed glioblastoma patients, one relatively diffuse with a low ρ/D (a,c) and one more nodular with a high ρ/D (b,d). A simulation of the diffuse glioma extent predicted by the patient-specific simulation for the diffuse (low ρ/D) patient (e) and the more nodular (high ρ/D) patient (f) is overlayed on the T1Gd MRI with red and blue indicating high and low (but nonzero) glioma cell density, respectively. The effect of GTR is shown as a black region with a white outline and highlights the significant diffuse extent of glioma cells remaining post-GTR. In the more nodular (high ρ/D) case, GTR removes 75% of the pre-treatment glioma cells leaving 8.4e8 cells while in the diffusely invasive (low ρ/D) case, GTR removes only 27% of the pre-treatment glioma cells leaving 4.2e9 cells, an order of magnitude higher than the nodular case. The large number of tumor cells remaining after resection of a diffuse tumor drives recurrence.</p

ρ/D Assessment.

<p>This figure presents an overview of how the “relative invasiveness,” or ρ/D, is obtained. Tumor volumes are segmented from T1Gd and T2 MRI. The measured volume is approximated with a sphere in order to obtain a radius. The T1Gd and T2 radii are associated with different levels of detection, with T2 at low tumor cell density and T1Gd abnormality associated with high tumor cell density. The relationship between these two radii describes the steepness of the tumor cell profile, or “relative invasiveness.”</p

Results of iterative Kaplan-Meier Analysis in each invasiveness cohort.

<p>Number of cells remaining was calculated for each patient, based on their ρ/D and measured residual enhancing disease. Each possible threshold was iterated through to separate the patients into large and small residual tumor cell population cohorts. White boxes correspond to thresholds separating patients into groups with significantly different (p<0.05) survival. White stars indicate tests with no p-value, as the threshold did not separate the patients in the given invasiveness cohort into two groups. Black asterisks indicate tests with p<0.05. Black bins with white x's indicate no the threshold did not separate the patients in the given invasiveness cohort into two groups. For example, for the diffuse case (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099057#pone-0099057-g003" target="_blank">Figure 3</a>, top row), the black bins with white x's represent the fact that even GTR was unable to achieve a remaining cell burden less than the cutoff (up to approximately 10⁹). Further, amongst the most diffuse gliomas, no threshold for a residual cells following resection was found to be significant of outcome represented visually as the lack of a white bar in the top row. Although less dramatic, the moderate cohort was unable to equate a GTR with <10^8.5 cells remaining represented by the black bars with white x's to the left on middle row of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099057#pone-0099057-g003" target="_blank">Figure 3</a>. While resection of tumors in the nodular cohort were able to attain residual disease burdens at all levels down to <10⁷ cells.</p

Clinical Data Table.

<p>Median age and range, distribution of males and females, race (unknown, Caucasian, Asian, Hispanic, Black), median KPS and range, median XRT Dose and range, number of patients diagnosed in the 90's, number of patients diagnosed in 2000 or later, number receiving preoperative steroids, and number of patients who received concurrent Temozolomide with XRT are shown. Proportion chi-square tests were performed to compare steroid administration, concurrent TMZ, and proportion of patients who received GTR vs. STR/Bx between the three invasiveness cohorts. No statistical difference at the P = 0.05 significance level was found in any of these variables between cohorts. ANOVA tests were performed to compare KPS scores, age, and XRT doses between invasiveness cohorts. No difference at the P = 0.05 significance level was found in any of these variables between cohorts.</p><p>* - Indicates no significant difference (p≤0.05) between cohorts in this variable, per Proportion Chi-square test.</p><p>** - Indicates no significant difference (p≤0.05) between cohorts in this variable, per ANOVA test.</p><p>Clinical Data Table.</p