Use of the Cimmino algorithm and continuous approximation for the dose deposition kernel in the inverse problem of radiation treatment planning

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Abstract
An approximate continuous data fitting model for the dose deposition kernel was developed. The model uses a discrete Fourier transform to interpolate dose values in patient space and intensity distribution in treatment space. The continuous kernel was applied to the inverse problem of radiation treatment planning. In the problem a prescribed dose distribution was to be created using intensity modulation of several fields. The Cimmino algorithm suitable for solving large systems of inequalities was adapted. Upper and lower dose constraints for planning target volume (PTV) and organs at risk (OAR) can be implemented into the algorithm. Using continuous and discrete kernels an intensity modulation was computed in a two-dimensional phantom with a PTV and low-dose region, and in the real three-dimensional patient planning. Intensity modulations obtained using continuous and discrete kernels were in good agreement.