Reduction of computational dimensionality in inverse radiotherapy planning using sparse matrix operations

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Abstract
For dynamic multileaf collimator-based intensity modulated radiotherapy in which small beam elements are used to generate continuous modulation, the sheer size of the dose calculation matrix could pose serious computational challenges. In order to circumvent this problem, the dose calculation matrix was reduced to a sparse matrix by truncating the weakly contributing entries below a certain cutoff to zero. Subsequently, the sparse matrix was compressed and matrix indexing vectors were generated to facilitate matrix-vector and matrix-matrix operations used in inverse planning. The application of sparsity permitted the reduction of overall memory requirement by an order of magnitude. In addition, the effect of disregarding the small scatter components on the quality of optimization was investigated by repeating the inverse planning using the dense dose calculation matrix. Comparison of dense and sparse matrix-based plans revealed an insignificant difference in optimization outcome, thus demonstrating the feasibility and usefulness of the sparse method in inverse planning. Furthermore, two additional methods of memory minimization are suggested, namely hexagonal dose sampling and limited normal tissue sampling.