An accurate kernel model is of vital importance for pencil-beam dose algorithm in charged particle therapy using precise spot-scanning beam delivery,in which an accurate depiction of the low dose envelope is especially crucial.Although the dose level of the low dose envelope is under 3 or 4 orders of magnitude to the dose in the beam axis,the superimposed effect cannot be neglected.In many primary versions of treatment planning system(TPS)for proton or carbon ion therapy,two-dimension single Gaussian model is used to calculate the lateral dose distribution of pencil beam in medium[1????3].However,it was found that the single Gaussian model does not depict adequately the dose contributed from secondary particles especially for low dose envelope.
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