'A finite size pencil beam for IMRT dose optimization' - A simpler analytical function for the finite size pencil beam kernel

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 2x₀ can be obtained as the difference between two semi-infinite fields shifted by 2x₀. If the profile is centred about x = 0, it can derive from P(x + x₀) - P(x - x₀). The penumbra influence can be taken by the penumbra tuning factor f. The parameters A₁, A₂, A₃, 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, y₀, A₁, A₂, A₃, A ₄, f₁, f₂) of a pencil beam of width (2x ₀, 2y₀) is defined by multiplication of two independent one-dimensional profiles.