Fourier deconvolution reveals the role of the Lorentz function as the convolution kernel of narrow photon beams.

The two-dimensional lateral dose profiles D(x, y) of narrow photon beams, typically used for beamlet-based IMRT, stereotactic radiosurgery and tomotherapy, can be regarded as resulting from the convolution of a two-dimensional rectangular function R(x, y), which represents the photon fluence profile within the field borders, with a rotation-symmetric convolution kernel K(r). This kernel accounts not only for the lateral transport of secondary electrons and small-angle scattered photons in the absorber, but also for the 'geometrical spread' of each pencil beam due to the phase-space distribution of the photon source. The present investigation of the convolution kernel was based on an experimental study of the associated line-spread function K(x). Systematic cross-plane scans of rectangular and quadratic fields of variable side lengths were made by utilizing the linear current versus dose rate relationship and small energy dependence of the unshielded Si diode PTW 60012 as well as its narrow spatial resolution function. By application of the Fourier convolution theorem, it was observed that the values of the Fourier transform of K(x) could be closely fitted by an exponential function exp(-2pilambdanu(x)) of the spatial frequency nu(x). Thereby, the line-spread function K(x) was identified as the Lorentz function K(x) = (lambda/pi)[1/(x(2) + lambda(2))], a single-parameter, bell-shaped but non-Gaussian function with a narrow core, wide curve tail, full half-width 2lambda and convenient convolution properties. The variation of the 'kernel width parameter' lambda with the photon energy, field size and thickness of a water-equivalent absorber was systematically studied. The convolution of a rectangular fluence profile with K(x) in the local space results in a simple equation accurately reproducing the measured lateral dose profiles. The underlying 2D convolution kernel (point-spread function) was identified as K(r) = (lambda/2pi)[1/(r(2) + lambda(2))](3/2), fitting experimental results as well. These results are discussed in terms of their use for narrow-beam treatment planning.

The effect of a carbon-fiber couch on the depth-dose curves and transmission properties for megavoltage photon beams.

PURPOSE: To investigate the attenuation of a carbon-fiber tabletop and a combiboard, alongside with the depth-dose profile in a solid-water phantom. MATERIAL AND METHODS: Depth-dose measurements were performed with a Roos chamber for 6- and 10-MV beams for a typical field size (15 cm x 15 cm, SSD [source-surface distance] 100 cm). A rigid-stem ionization chamber was used to measure transmission factors. RESULTS: Transmission factors varied between 93.6% and 97.3% for the 6-MV beam, and 95.1% and 97.7% for the 10-MV photon beam. The lowest transmission factors were observed for the oblique gantry angle of 150 degrees with the table-combiboard combination. The surface dose normalized to a depth of 5 cm increased from 59.4% (without table, 0 degrees gantry), to 108.6% (tabletop present, 180 degrees gantry), and further to 120% (table-combiboard combination) for 6-MV photon beam. For 10 MV, the increase was from 39.6% (without table), to 88.9% (with table), and to 105.6% (table-combiboard combination). For the 150 degrees angle (tablecombiboard combination), the dose increased from 59.4% to 120% (6 MV) and from 39% to 108.1% (10 MV). CONCLUSION: Transmission factors for tabletops and accessories directly interfering with the treatment beam should be measured and implemented into the treatment-planning process. The increased surface dose to the skin should be considered.