Impact of Using Linear Optimization Models in Dose Planning for HDR Brachytherapy

• Purpose: Dose plans generated with optimization models hitherto used in HDR brachytherapy have shown a tendency to yield longer dwell times than manually optimized plans. Concern has been raised for the corresponding undesired hot spots and various methods to mitigate these have been developed. The hypotheses of this work are a) that one cause for the long dwell times is the use of objective functions comprising simple linear penalties and b) that alternative penalties, being piecewise linear, would lead to reduced length of individual dwell times.Methods: The characteristics of the linear penalties and the piecewise linear penalties are analysed mathematically. Experimental comparisons between the two types of penalties are carried out retrospectively for a set of prostate cancer patients.Results: While most dose-volume parameters do not differ significantly between the two types of penalties significant changes can be seen in the dwell times. On the average, total dwell times were reduced by 4.2%, with a reduction of maximum dwell times by 30%, using the alternative penalties.Conclusion: The use of linear penalties in optimization models for HDR brachytherapy is one cause for undesired longer dwell times appearing in mathematically optimized plans. By introducing alternative penalties significant reduction in dwell times can be achieved for HDR brachytherapy dose plans. Although various constraints as to reduce the long dwell times have been developed our finding is of fundamental interest in showing the shape of the objective function to be one reason for their appearance.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Brachytherapy

Optimization

Treatment planning

Linear programming

Piecewise linear functions

MATHEMATICS

MATEMATIK

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