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We present a method of directly optimizing on deviations in clinical goalvalues in radiation therapy treatment planning. Using a new mathematicalframework in which metrics derived from the dose-volume histogram are regardedas functionals of an auxiliary random variable, we are able to obtainvolume-at-dose and dose-at-volume as infinitely differentiable functions of thedose distribution with easily evaluable function values and gradients.Motivated by the connection to risk measures in finance, which is formalized inthis framework, we also derive closed-form formulas for mean-tail-dose anddemonstrate its capability of reducing extreme dose values in taildistributions. Numerical experiments performed on a prostate and ahead-and-neck patient case show that the direct optimization of dose-volumehistogram metrics produced marginally better results than or outperformedconventional planning objectives in terms of clinical goal fulfilment, controlof low- and high-dose tails of target distributions and general plan qualitydefined by a pre-specified evaluation measure. The proposed frameworkeliminates the disconnect between optimization functions and evaluation metricsand may thus reduce the need for repetitive user interaction associated withconventional treatment planning. The method also has the potential of enhancingplan optimization in other settings such as multicriteria optimization andautomated treatment planning.

Direct optimization of dose-volume histogram metrics in radiation therapy treatment planning