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.