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Variable depth recursion algorithm for leaf sequencing
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10.1118/1.2431083
/content/aapm/journal/medphys/34/2/10.1118/1.2431083
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/34/2/10.1118/1.2431083

Figures

Image of FIG. 1.
FIG. 1.

This is a flow chart of the variable depth recursion algorithm. The bold “T” and “F” around the decision diamonds stand for “True” and “False,” respectively. The subscript “j” is the number of levels being tested and is also the iteration index for a segment. The inner loop, responsible for testing segments with various levels, is indicated by the dashed rectangle. The process in the thick line rectangle is where the recursion takes place as described in the text.

Image of FIG. 2.
FIG. 2.

Comparison of the number of segments (top) and relative fluence (bottom) resulting from the various IMFAST related algorithms when there is no sequencing constraint. The line is for the fully modified IMFAST algorithm (“modified”), the “x” mark is for the original IMFAST algorithm (“original”), and the square is for the variable depth recursion (“vdr”) algorithm. The values are normalized to those for the algorithm of Bortfeld et al. The square lies on top of the line in the top graph, indicating that VDR is tied with the fully modified IMFAST algorithm. The increases in the relative fluence are minimal, with VDR having a slightly higher result than the minimum in some cases.

Image of FIG. 3.
FIG. 3.

Comparison of the number of segments (top) and relative fluence (bottom) resulting from the various IMFAST related algorithms with the collision constraint. The symbols have the same meaning as those in Fig. 2. Again, the squares lie on top of the line, indicating that VDR and the fully modified IMFAST algorithm perform equally well.

Image of FIG. 4.
FIG. 4.

Comparison of the number of segments (top) and relative fluence (bottom) resulting from the various IMFAST related algorithms with the tongue-and-groove constraint. The symbols have the same meaning as those in Fig. 2. Again, the squares lie on top of the line, indicating that VDR and the fully modified IMFAST algorithm perform equally well.

Image of FIG. 5.
FIG. 5.

Comparison of the number of segments (top) and relative fluence (bottom) resulting from the various IMFAST related algorithms with the tongue-and-groove and collision constraint. The symbols have the same meaning as those in Fig. 2. Again, the squares lie on top of the line, or appear slightly below it as many times as they appear slightly above it, indicating that VDR and the fully modified IMFAST algorithm perform equally well.

Image of FIG. 6.
FIG. 6.

Relative speeds of the various IMFAST related algorithms. The fully modified IMFAST algorithm has a value of 1. VDR is about 10–40 times faster than the fully modified IMFAST algorithm.

Tables

Generic image for table
TABLE I.

(A) The average of the number of segments and the average of the relative fluence for the various algorithms for the 100 random maps with various maximum map levels, for the case where no constraint was applied. ‘B’ is the algorithm of Bortfeld et al. (Ref. 9), ‘G’ is the algorithm of Galvin, Chen, and Smith (Ref. 4), ‘X’ is the algorithm of Xia and Verhey (Ref. 5), ‘Q’ is the algorithm of Que (Ref. 6), and ‘C’ is the algorithm of Crooks et al. (Ref. 8). ‘V0’ and ‘V15’ stand for the variable depth recursion algorithm with and , respectively. The last two columns give the percent decrease in the number of segments for V15 relative to V0 and B. The top three results for each level are in bold.

Generic image for table
TABLE II.

(A) The average of the number of segments and the average of the relative fluence for the various algorithms for the 100 random maps with various maximum map levels, for the case where no interdigitation was allowed. The meanings of the labels are the same as those in table I.

Generic image for table
TABLE III.

The number of segments and relative fluence resulting from the application of various recursion depths to 100 random maps with maximum map levels in the typical clinical range. “D0” stands for no recursion, where as “D1,” “D2,” and “D3” stand for recursion depths of 1, 2, and 3, respectively. The collision and tongue and groove constraints were applied.

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/content/aapm/journal/medphys/34/2/10.1118/1.2431083
2007-01-26
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Variable depth recursion algorithm for leaf sequencing
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/34/2/10.1118/1.2431083
10.1118/1.2431083
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