A method to evaluate dose errors introduced by dose mapping processes for mass conserving deformations

Purpose: To present a method to evaluate the dose mapping error introduced by the dose mapping process. In addition, apply the method to evaluate the dose mapping error introduced by the 4D dose calculation process implemented in a research version of commercial treatment planning system for a patient case. Methods: The average dose accumulated in a finite volume should be unchanged when the dose delivered to one anatomic instance of that volume is mapped to a different anatomic instance-provided that the tissue deformation between the anatomic instances is mass conserving. The average dose to a finite volume on image S is defined as (d(S)) over bar =e(s)/m(S), where e(S) is the energy deposited in the mass m(S) contained in the volume. Since mass and energy should be conserved, when (d(S)) over bar is mapped to an image R((d(S -> R)) over bar=(d(R)) over bar), the mean dose mapping error is defined as (Delta d(m)) over bar=vertical bar(d(R)) over bar-(d(S)) over bar vertical bar=vertical bar e(R)/m(R)-e(S)/m(S)|, where the e(R) and e(S) are integral doses (energy deposited), and m(R) and m(S) are the masses within the region of interest (ROI) on image R and the corresponding ROI on image S, where R and S are the two anatomic instances from the same patient. Alternatively, application of simple differential propagation yields the differential dose mapping error, Delta(d(d)) over bar=vertical bar partial derivative(d) over bar/partial derivative e*Delta e+partial derivative(d) over bar partial derivative m*Delta m vertical bar=vertical bar(e(S)-e(R))/m(R)-(m(S)-m(R))/m(R)(2)*e(R)vertical bar=alpha vertical bar(d(R)) over bar-(d(S)) over bar vertical bar with alpha=m(S)/m(R). A 4D treatment plan on a ten-phase 4D-CT lung patient is used to demonstrate the dose mapping error evaluations for a patient case, in which the accumulated dose, (D-R) over bar=Sigma(9)(S=0)(d(S -> R)) over bar, and associated error values (Delta(D-m) over bar and Delta(D-d) over bar) are calculated for a uniformly spaced set of ROIs. Results: For the single sample patient dose distribution, the average accumulated differential dose mapping error is 4.3%, the average absolute differential dose mapping error is 10.8%, and the average accumulated mean dose mapping error is 5.0%. Accumulated differential dose mapping errors within the gross tumor volume (GTV) and planning target volume (PTV) are lower, 0.73% and 2.33%, respectively. Conclusions: A method has been presented to evaluate the dose mapping error introduced by the dose mapping process. This method has been applied to evaluate the 4D dose calculation process implemented in a commercial treatment planning system. The method could potentially be developed as a fully-automatic QA method in image guided adaptive radiation therapy (IGART). (C) 2012 American Association of Physicists in Medicine. [DOI:10.1118/1.3684951]