Establishing implantation uncertainties for focal brachytherapy with I-125 seeds for the treatment of localized prostate cancer.

BACKGROUND: The efficacy of focal continuous low dose-rate brachytherapy (CLDR-BT) for prostate cancer requires that appropriate margins are applied to ensure robust target coverage. In this study we propose a method to establish such margins by emulating a focal treatment in patients treated with CLDR-BT to the entire gland. MATERIAL AND METHODS: In 15 patients with localized prostate cancer, prostate volumes and dominant intra-prostatic lesions were delineated on pre-treatment magnetic resonance imaging (MRI). Delineations and MRI were registered to trans-rectal ultrasound images in the operating theater. The patients received CLDR-BT treatment to the total prostate volume. The implantation consisted of two parts: an experimental focal plan covering the dominant intra-prostatic lesion (F-GTV), followed by a plan containing additional seeds to achieve entire prostate coverage. Isodose surfaces were reconstructed using follow-up computed tomography (CT). The focal dose was emulated by reconstructing seeds from the focal plan only. The distance to agreement between planned and delivered isodose surfaces and F-GTV coverage was determined to calculate the margin required for robust treatment. RESULTS: If patients had been treated only focally, the target volume would have been reduced from an average of 40.9 cm3 for the entire prostate to 5.8 cm3 for the focal plan. The D90 for the F-GTV in the focal plan was 195±60 Gy, the V100 was 94% [range 71-100%]. The maximum distance (cd95) between the planned and delivered isodose contours was 0.48 cm. CONCLUSIONS: This study provides an estimate of 0.5 cm for the margin required for robust coverage of a focal target volume prior to actually implementing a focal treatment protocol.

Flow-induced agitations create a granular fluid: effective viscosity and fluctuations.

We fluidize a granular medium with localized stirring in a split-bottom shear cell. We probe the mechanical response of quiescent regions far from the main flow by observing the vertical motion of cylindrical probes rising, sinking, and floating in the grains. First, we find that the probe motion suggests that the granular material behaves in a liquid-like manner: high-density probes sink and low-density probes float at the depth given by Archimedes' law. Second, we observe that the drag force on moving probes scales linearly with their velocity, which allows us to define an effective viscosity for the system. This effective viscosity is inversely proportional to the rotation rate of the disk which drives the split bottom flow. Moreover, the apparent viscosity depends on radius and mass of the probe: despite the linear dependence of the drag forces on sinking speed of the probe, the granular medium is not simply Newtonian, but exhibits a more complex rheology. The decrease of viscosity with filling height of the cell, combined with the poor correlation between local strain rate and viscosity, suggests that the fluid-like character of the material is set by agitations generated in the stirred region: the relation between applied stress and observed strain rate in one location depends on the strain rate in another location. We probe the nature of the granular fluctuations that we believe mediates these nonlocal interactions by characterizing the small and random up and down motion that the probe experiences. These Gaussian fluctuations exhibit a mix of diffusive and subdiffusive behavior at short times and saturate at a value of roughly 1/10th of a grain diameter longer times, consistent with the picture of a random walker in a potential well. The product of crossover time and effective viscosity is constant, evidencing a direct link between fluctuations and viscosity.

Equipartition of rotational and translational energy in a dense granular gas.

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's law with a van der Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to nonequilibrium systems.

Flow-induced agitations create a granular fluid.

We fluidize a granular medium through localized stirring and probe the mechanical response of quiescent regions far away from the main flow. In these regions the material behaves like a liquid: high-density probes sink, low-density probes float at the depth given by Archimedes' law, and drag forces on moving probes scale linearly with the velocity. The fluidlike character of the material is set by agitations generated in the stirred region, suggesting a nonlocal rheology: the relation between applied stress and observed strain rate in one location depends on the strain rate in another location.