‘A finite size pencil beam for IMRT dose optimization’—a simpler analytical function for the finite size pencil beam kernel

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Abstract
A simple and finite-termed analytical function for the finite size pencil beam kernel was constructed. The dose cross-profile of a semi-infinite field with field edge at x = 0 can be well fitted by the Boltzmann function. The pencil beam cross-profile of width 2x(0) can be obtained as the difference between two semi-infinite fields shifted by 2x(0). If the profile is centred about x = 0, it can derive from P(x + x(0)) - P(x - x(0)). The penumbra influence can be taken by the penumbra tuning factor f. The parameters A(1), A(2), A(3), A(4), f can be obtained by fitting depth-dose curves and cross-profiles for a set of square fields. The two-dimensional dose distribution F(x, y, x(0), y(0), A(1), A(2), A(3), A(4), f(1), f(2)) of a pencil beam of width (2x(0), 2y(0)) is defined by multiplication of two independent one-dimensional profiles.

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