Dose kernel decomposition for spot-based radiotherapy treatment planning

Abstract

Purpose: Pre-calculation of accurate dose deposition kernels for treatment planning of spot-based radiotherapies, such as Gamma Knife (GK) and Gamma Pod (GP), can be very time-consuming and may require large data storage with an enormous number of possible spots. We proposed a novel kernel decomposition (KD) model to address accurate and fast (real-time) dose calculation with reduced data storage requirements for spot-based treatment planning. The application of the KD model was demonstrated for clinical GK and GP radiotherapy platforms.

Methods: The dose deposition kernel at each spot (shot position) is modeled as the product of a shift-invariant kernel based on a reference kernel and spatially variant scale factor. The reference kernel, one for each collimator, is defined at the center of the commissioning phantom for GK and at the center of the treatment target for GP and calculated using the Monte Carlo (MC) method. The spatially variant scale factor is defined as the ratio of the mean tissue maximum ratio (TMR) at the candidate shot position to that at the reference kernel position, and the mean TMR map is calculated within the entire volume through parallel beam ray tracing on the density image followed by averaging over all source directions. The proposed KD dose calculations were compared with the MC method and with the GK and GP treatment planning system (TPS) computations for various shot positions and collimator sizes utilizing a phantom and 14 and 12 clinical plans for GK and GP, respectively.

Results: For the phantom study, the KD Gamma index (3%/1 mm) passing rates were greater than 99% (median 100%) relative to the MC doses, except for the shots close to the boundary. The passing rates dropped below 90% for 8 mm (16 mm) shots positioned within ∼1 cm (∼2 cm) of the boundary. For the clinical GK plans, the KD Gamma passing rates were greater than 99% (median 100%) compared to the MC and greater than 92% (median 99%) compared to the TPS. For the clinical GP plans, the KD Gamma passing rates were greater than 95% (median 98%) compared to the MC and greater than 91% (median 97%) compared to the TPS. The scale factors were calculated in sub-seconds with GPU implementation and only need to be calculated once before treatment plan optimization. The calculation of the dose kernel was also within sub-seconds without requiring beam-by-beam calculation commonly done in the TPS.

Conclusion: The proposed model can provide an accurate dose and enables real-time dose and derivative calculations by kernel shifting and scaling without pre-calculating or requiring large data storage for GK and GP dose deposition kernels during treatment planning. This model could be useful for spot-based radiotherapy treatment planning by allowing an efficient global fine search for optimal spots.

Keywords: Gamma Knife; Gamma Pod; kernel decomposition.

FIGURE 1

The steps of dose kernel decomposition. Left: GK. Right: GP

FIGURE 2

Particle positions in the GK phase space used for the MC dose calculation. The smallest (blue) spots indicate particle positions for the 4-mm collimator. The medium (green) spots are for the 8-mm collimator. The largest (red) spots are for the 16-mm collimator. Note that the hemisphere only shows the surface of phase space recording, not the real GK Perfexion/Icon source distribution, which is on a conical surface^-

FIGURE 3

Particle positions in the GP phase space used for the MC dose calculation for the 25-mm collimator (left) and the 15-mm collimator (right)

FIGURE 4

The MC calculated TMR curves for ⁶⁰Co beams for various collimator diameters (left) and the corresponding zoom-in region (right)

FIGURE 5

The x-profiles (left) and the z-profiles (right) of the GK dose kernels for each cone. The numbers in the legend indicate the cone size in mm. The term cone indicates that all eight constituent sectors have the same collimator size. Solid: TPS profiles. Dashed: MC calculated profiles

FIGURE 6

GK’s sector kernel images on the transverse plane, z = 0, for the 8-mm collimator. The top row (middle row; bottom row), from left to right, corresponds to sector 8, 1, 2 (sector 7, cone, sector 3; sector 6, 5, 4). The center image is the cone kernel, which is the composite of its eight constituent sector kernels. The sector kernels’ intensities are scaled up 8×, so that the intensity display ranges are the same as that for the cone kernel

FIGURE 7

The x-profiles (left) and the y-profiles (right) of the GP dose kernels for both cones. The numbers in the legend indicate the cone size in mm. Solid: TPS profiles. Dashed: MC calculated profiles

FIGURE 8

The TMR ratio maps of the commissioning phantom for GK (left) and GP (right) in the transverse (T), coronal (C), and sagittal (S) views of the central slices

FIGURE 9

The TMR ratio maps of the sample patients for GK (left) and GP (right) in the transverse (T), coronal (C), and sagittal (S) views of the central slices. Here, patient’s head images were cropped slightly to fit in the same physical size as the images of the commissioning phantom for comparison

FIGURE 10

The MC and KD dose comparison for GK (a–c) and GP (d–f). (a,d): The isodose curves of 90%, 50%, and 20% maximum dose of MC (solid) and KD (dashed). The dotted crosshair lines indicate the profile positions. (b,e): the MC and KD x-profiles. (c,f): the MC and KD y-profiles. Legend in the profiles: KD-c0, scale factor not applied; KD-c#, scale factor calculated by the #-mm cone TMR

FIGURE 11

The MC, TPS, and KD isodose curve and dose profile comparisons for the GK case #1 in Table 1. Left: the MC, TPS, and KD isodose curves overlaid on a transverse slice of the patient head image through the target center. The dotted crosshair lines indicate the x- and y-profile positions. Middle: the MC, TPS, and KD x-profiles. Right: the MC, TPS, and KD y-profiles

FIGURE 12

The MC, TPS, and KD isodose curve and dose profile comparisons for the GP Case #1 in Table 2. Left: the MC, TPS, and KD isodose curves overlaid on a transverse slice of the patient image through the target center. The dotted crosshair lines indicate the x- and y-profile positions. Middle: the MC, TPS, and KD x-profiles. Right: the MC, TPS, and KD y-profiles

FIGURE 13

The Gamma index passing rates comparing the reference kernel to the dose kernel in GK. The horizontal axis is the shot position with 0 mm (80 mm) indicating the center (boundary) of the spherical phantom. Left: shots on the x-axis (y = 0, z = 0). Right: shots on the z-axis (x = 0, y = 0)