# US 7,466,797 B2 · Error control in algorithmic approach to step-and-shoot intensity modulated radiation therapy > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 7,466,797 B2 - Document ID: US7466797B2 - Status: Granted - Kind: B2 - Application number: 11/085,529 - Filed: 2005-03-22 - Published: 2008-03-13 - Granted: 2008-12-16 - Earliest claimed: 2004-03-22 - Assignees: University of Notre Dame du Lac - Inventors: Shuang Luan; Danny Z. Chen; Xiaobo S. Hu; Chao Wang; Xiaodong Wu; Cedric X. Yu - Web page: https://patentgrep.com/patent/US7466797B2 ## CPC - A61N 5/1042: {with spatial modulation of the radiation beam within the treatment head} - A61N 5/1036: {Leaf sequencing algorithms} - A61N 5/1048: {Monitoring, verifying, controlling systems and methods} - A61N: ELECTROTHERAPY; MAGNETOTHERAPY; RADIATION THERAPY; ULTRASOUND THERAPY (measurement of bioelectric currents A61B; surgical instruments, devices or methods for transferring non-mechanical forms of energy to or from the body A61B18/00; anaesthetic apparatus in general A61M; incandescent lamps H01K; infrared radiators for heating H05B) ## Abstract The present invention provides a method comprising the following steps: (a) partitioning an intensity modulated beam into a set of sub-IMBs; and (b) partitioning the sub-IMBs into segments, wherein steps (a) and (b) introduce no machine delivery error. The present invention also provides a method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; and (b) partitioning the plateaus into segments, wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b). ## Claims ### Claim 1 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; and (b) partitioning the plateaus into segments; and (c) storing in a storage medium a treatment plan based on the segments of step (b), wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b). ### Claim 2 (depends on 1) The method of claim 1, where step (a) further comprises: partitioning the intensity modulated beam (IMB) into a sub-IMB, and wherein the method further comprises the following step: (d) determining the tradeoff curve between the number of segments and error for the sub-IMB. ### Claim 3 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments; and (c) storing in a storage medium a treatment plan based on the segments of step (b), wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b) and wherein step (b) comprises the following the steps: (d) constructing a directed graph based on the plateaus; (e) determining a series of minimum cost flows in the directed graph; (f) determining a tradeoff between the number of segments and machine delivery errors based on the determined minimum cost flows, and (g) extracting the segments from the directed graph based on the tradeoff determined in step (f) to thereby partition the plateaus. ### Claim 4 (depends on 3) The method of claim 3, wherein step (d) comprises the following steps: (h) constructing a directed graph based on intensity modulated beam grids of the plateaus of an intensity modulated beam, wherein vertices of the directed graph include all intersection points of the intensity modulated beam grids of the plateaus that are either part of a peak or an interior of a polygon corresponding to the intensity modulated beam, and wherein the edges of the directed graph include those edges of the plateaus whose end points are graph vertices in the directed graph; (i) for all graph vertices corresponding to the same peak direction, adding either a source vertex or sink vertex to the directed graph; (j) adding edges to the directed graph from the source vertex or sink vertex to respective peak vertices; (k) assigning a unit flow capacity to each graph vertex and edge of the directed graph; and (l) to each edge that is vertical assigning a cost that is equal to the geometric length of the vertical edge, and to each edge that is horizontal a cost of zero. ### Claim 5 (depends on 4) The method of claim 4, wherein step (h) comprises the following steps: (m) extracting connections between a left peak and a right peak of the polygon based on the minimum cost flow; (n) eliminating any remaining unconnected peaks using only horizontal edges; and (o) extracting resulting segments from the directed graph to thereby partition the plateaus. ### Claim 6 (depends on 5) The method of claim 5, wherein for an edge involving a left peak vertex, the direction of the edge is away from the left peak. ### Claim 7 (depends on 5) The method of claim 5, wherein for an edge involving a right peak vertex, the direction of the edge is toward the right peak. ### Claim 8 (depends on 5) The method of claim 5, wherein the direction of a horizontal edge that does not involve any peak vertex is from left to right. ### Claim 9 (depends on 5) The method of claim 5, wherein the direction of a vertical edge that does not involve a peak vertex is bidirectional. ### Claim 10 (depends on 5) The method of claim 5, wherein, for all left peak vertices, a source vertex is added to the directed graph. ### Claim 11 (depends on 5) The method of claim 5, wherein, for all right peak vertices, a sink vertex is added to the directed graph. ### Claim 12 (depends on 5) The method of claim 5, wherein the minimum cost flow in the directed graph yields a maximum set of mutually disjoint paths. ### Claim 13 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments; and (c) storing in a storage medium a treatment plan based on the segments of step (b), wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b), wherein the intensity modulated beam comprises a plurality of z-posts, and wherein step (a) comprises the following steps: (d) choosing an intensity level d wherein, 1≦d≦I max, wherein Imax is the maximum intensity level of the intensity modulated beam; (e) selecting all z-posts having a height of at least d to form a set of selected z-posts; (f) cutting each selected z-post whose height is ≧d at level d to form a plateau of z-posts of height d; (g) removing the plateau of z-posts from the intensity modulated beam; and (h) recursively partitioning any remaining portion of the intensity modulated beam until there is no remaining portion of the intensity modulated beam. ### Claim 14 (depends on 13) The method of claim 13, wherein step (h) comprises repeating steps (d), (e), (f) and (g) on any remaining portion of the intensity modulated beam until there is no remaining portion of the intensity modulated beam. ### Claim 15 (depends on 13) The method of claim 13, wherein d is a function of the maximum intensity level Imax. ### Claim 16 (depends on 13) The method of claim 13, wherein d = ⌈ I max 2 ⌉ . ### Claim 17 (depends on 13) The method of claim 13, wherein d is based on the volume of the plateau of z-posts. ### Claim 18 (depends on 13) The method of claim 13 wherein d=2i, where i=Int(log2(Imax))−1). ### Claim 19 (depends on 13) The method of claim 13, wherein d has a value such that the volume of the plateau of z-posts is maximized. ### Claim 20 (depends on 13) The method of claim 13, wherein d is determined by the slice method. ### Claim 21 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments; and (c) storing in a storage medium a treatment plan based on the segments of step (b), wherein step (a) comprises partitioning the intensity modulated beam into a sub-IMB and wherein step (a) comprises determining the tradeoff curve between the number of segments and error for the sub-IMB by the following steps: (d) generating a canonical delivery option for each set of field opening endpoints for a plurality of intensity modulated beam columns of the sub-IMB; (e) for every two consecutive intensity modulated beam columns, determining a series of minimum cost g-matchings between the canonical delivery options of the intensity modulated beam columns; (f) determining the tradeoff curves based on the g-matchings; and (g) extracting the segments for the sub-IMB based on the matched field openings of the canonical delivery options from the determined g-matchings in an increasing order of consecutive intensity modulated beam columns to thereby partition the sub-IMB. ### Claim 22 (depends on 21) The method of claim 21, wherein in step (d) only one set of left and right field opening endpoints is generated for each intensity beam column. ### Claim 23 (depends on 21) The method of claim 21, wherein in step (d) more than one set of left and right field opening endpoints is generated for each intensity beam column. ### Claim 24 (depends on 21) The method of claim 21, wherein the matched field openings have no interdigitation and minimum leaf separation. ### Claim 25 (depends on 21) The method of claim 21, wherein the matched field openings have no minimum leaf separation and no interdigitation. ### Claim 26 (depends on 21) The method of claim 21, wherein the matched field openings have interdigitation. ### Claim 27 (depends on 21) The method of claim 21, wherein the method further comprises choosing a number m of Steiner points for forming the sets of field opening endpoints, and wherein each unique canonical delivery option contains at most m Steiner points for each set of field opening endpoints. ### Claim 28 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments, wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b); (c) linking the segments to thereby reduce the number of segments; and (d) storing in a storage medium a treatment plan based on the linked segments of step (c). ### Claim 29 (depends on 28) The method of claim 28, wherein step (a) further comprises: partitioning the intensity modulated beam (IMB) into a sub-IMB, and wherein the method further comprises the following step: (e) determining the tradeoff curve between the number of segments and error for the sub-IMB. ### Claim 30 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments, wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b); (c) linking the segments to thereby reduce the number of segments; and (d) storing in a storage medium a treatment plan based on the linked segments of step (c), wherein step (c) further comprises the following steps: (e) constructing a directed graph H based on the segments extracted; (f) determining a minimum cost g-path cover on the directed graph H; (g) extracting the final segments based on the g-path cover on H therefore segmenting the entire intensity modulated beam. ### Claim 31 (depends on 30) The method of claim 30, wherein step (e) further comprises the following steps: (h) introducing a vertex for each segment; (i) introducing an edge between any two segments that can be delivered together; and (j) assigning a cost to each edge that is the equal to the amount of machine delivery error introduced when delivering the two segments together. ### Claim 32 (depends on 31) The method of claim 31, wherein in step (i), the two segments have no minimum leaf separation and no interdigitation when for a multileaf collimator. ### Claim 33 (depends on 31) The method of claim 31, wherein in step (i), the two segments have interdigitation. ### Claim 34 A method comprises the following steps: (a) generating a canonical delivery option for each set of field opening endpoints for an intensity modulated beam; (b) for every two consecutive intensity modulated beam columns of the intensity modulated beam, determining a series of minimum cost g-matchings between the canonical delivery options of the intensity modulated beam columns; (c) determining the tradeoff curves based on the g-matchings; (d) extracting the segments for the intensity modulated beam based on the matched field openings of the canonical delivery options from the determined g-matchings in an increasing order of consecutive intensity modulated beam columns to thereby partition the intensity modulate beam; and (e) storing in a storage medium a treatment plan based on the extracted segments of step (d). ### Claim 35 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; and (b) partitioning the plateaus into segments; and (c) implementing a treatment plan based on the segments of step (b), wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b). ### Claim 36 (depends on 35) The method of claim 35, wherein step (a) further comprises: partitioning the intensity modulated beam (IMB) into a sub-IMB, and wherein the method further comprises the following step: (d) determining the tradeoff curve between the number of segments and error for the sub-IMB. ### Claim 37 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments; and (c) implementing a treatment plan based on the segments of step (b), wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b) and wherein step (b) comprises the following the steps: (d) constructing a directed graph based on the plateaus; (e) determining a series of minimum cost flows in the directed graph; (f) determining a tradeoff between the number of segments and machine delivery errors based on the determined minimum cost flows, and (g) extracting the segments from the directed graph based on the tradeoff determined in step (f) to thereby partition the plateaus. ### Claim 38 (depends on 37) The method of claim 37, wherein step (d) comprises the following steps: (h) constructing a directed graph based on intensity modulated beam grids of the plateaus of an intensity modulated beam, wherein vertices of the directed graph include all intersection points of the intensity modulated beam grids of the plateaus that are either part of a peak or an interior of a polygon corresponding to the intensity modulated beam, and wherein the edges of the directed graph include those edges of the plateaus whose end points are graph vertices in the directed graph; (i) for all graph vertices corresponding to the same peak direction, adding either a source vertex or sink vertex to the directed graph; (j) adding edges to the directed graph from the source vertex or sink vertex to respective peak vertices; (k) assigning a unit flow capacity to each graph vertex and edge of the directed graph; and (l) to each edge that is vertical assigning a cost that is equal to the geometric length of the vertical edge, and to each edge that is horizontal a cost of zero. ### Claim 39 (depends on 38) The method of claim 38, wherein step (h) comprises the following steps: (m) extracting connections between a left peak and a right peak of the polygon based on the minimum cost flow; (n) eliminating any remaining unconnected peaks using only horizontal edges; and (o) extracting resulting segments from the directed graph to thereby partition the plateaus. ### Claim 40 (depends on 39) The method of claim 39, wherein for an edge involving a left peak vertex, the direction of the edge is away from the left peak. ### Claim 41 (depends on 39) The method of claim 39, wherein for an edge involving a right peak vertex, the direction of the edge is toward the right peak. ### Claim 42 (depends on 39) The method of claim 39, wherein the direction of a horizontal edge that does not involve any peak vertex is from left to right. ### Claim 43 (depends on 39) The method of claim 39, wherein the direction of a vertical edge that does not involve a peak vertex is bidirectional. ### Claim 44 (depends on 39) The method of claim 39, wherein, for all left peak vertices, a source vertex is added to the directed graph. ### Claim 45 (depends on 39) The method of claim 39, wherein, for all right peak vertices, a sink vertex is added to the directed graph. ### Claim 46 (depends on 39) The method of claim 39, wherein the minimum cost flow in the directed graph yields a maximum set of mutually disjoint paths. ### Claim 47 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments; and (c) implementing a treatment plan based on the segments of step (b), wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b), wherein the intensity modulated beam comprises a plurality of z-posts, and wherein step (a) comprises the following steps: (d) choosing an intensity level d wherein, 1≦d≦Imax, wherein Imax is the maximum intensity level of the intensity modulated beam; (e) selecting all z-posts having a height of at least d to form a set of selected z-posts; (f) cutting each selected z-post whose height is ≧d at level d to form a plateau of z-posts of height d; (g) removing the plateau of z-posts from the intensity modulated beam; and (h) recursively partitioning any remaining portion of the intensity modulated beam until there is no remaining portion of the intensity modulated beam. ### Claim 48 (depends on 47) The method of claim 47, wherein step (h) comprises repeating steps (d), (e), (f) and (g) on any remaining portion of the intensity modulated beam until there is no remaining portion of the intensity modulated beam. ### Claim 49 (depends on 47) The method of claim 47, wherein d is a function of the maximum intensity level Imax. ### Claim 50 (depends on 47) The method of claim 47, wherein d = ⌈ I max 2 ⌉ . ### Claim 51 (depends on 47) The method of claim 47, wherein d is based on the volume of the plateau of z-posts. ### Claim 52 (depends on 47) The method of claim 47 wherein d=2i, where i=Int(log2(Imax))−1). ### Claim 53 (depends on 47) The method of claim 47, wherein d has a value such that the volume of the plateau of z-posts is maximized. ### Claim 54 (depends on 47) The method of claim 47, wherein d is determined by the slice method. ### Claim 55 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments; and (c) implementing a treatment plan based on the segments of step (b), wherein step (a) comprises partitioning the intensity modulated beam into a sub-IMB and wherein step (a) comprises determining the tradeoff curve between the number of segments and error for the sub-IMB by the following steps: (d) generating a canonical delivery option for each set of field opening endpoints for a plurality of intensity modulated beam columns of the sub-IMB; (e) for every two consecutive intensity modulated beam columns, determining a series of minimum cost g-matchings between the canonical delivery options of the intensity modulated beam columns; (f) determining the tradeoff curves based on the g-matchings; and (g) extracting the segments for the sub-IMB based on the matched field openings of the canonical delivery options from the determined g-matchings in an increasing order of consecutive intensity modulated beam columns to thereby partition the sub-IMB. ### Claim 56 (depends on 55) The method of claim 55, wherein in step (d) only one set of left and right field opening endpoints is generated for each intensity beam column. ### Claim 57 (depends on 55) The method of claim 55, wherein in step (d) more than one set of left and right field opening endpoints is generated for each intensity beam column. ### Claim 58 (depends on 55) The method of claim 55, wherein the matched field openings have no interdigitation and minimum leaf separation. ### Claim 59 (depends on 55) The method of claim 55, wherein the matched field openings have no minimum leaf separation and no interdigitation. ### Claim 60 (depends on 55) The method of claim 55, wherein the matched field openings have interdigitation. ### Claim 61 (depends on 55) The method of claim 55, wherein the method further comprises choosing a number m of Steiner points for forming the sets of field opening endpoints, and wherein each unique canonical delivery option contains at most m Steiner points for each set of field opening endpoints. ### Claim 62 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments, wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b); (c) linking the segments to thereby reduce the number of segments; and (d) implementing a treatment plan based on the linked segments of step (c). ### Claim 63 (depends on 62) The method of claim 62, wherein step (a) further comprises: partitioning the intensity modulated beam (IMB) into a sub-IMB, and wherein the method further comprises the following step: (f) determining the tradeoff curve between the number of segments and error for the sub-IMB. ### Claim 64 A method comprising the following steps: (a) recursively partitioning an intensity modulated beam into plateaus; (b) partitioning the plateaus into segments, wherein step (a) comprises determining a tradeoff between machine delivery error and the number of segments into which the plateaus will be partitioned in step (b); (c) linking the segments to thereby reduce the number of segments; and (d) implementing a treatment plan based on the linked segments of step (c), wherein step (c) further comprises the following steps: (e) constructing a directed graph H based on the segments extracted; (f) determining a minimum cost g-path cover on the directed graph H; (g) extracting the final segments based on the g-path cover on H therefore segmenting the entire intensity modulated beam. ### Claim 65 (depends on 64) The method of claim 64, wherein step (e) further comprises the following steps: (h) introducing a vertex for each segment; (i) introducing an edge between any two segments that can be delivered together; and (j) assigning a cost to each edge that is the equal to the amount of machine delivery error introduced when delivering the two segments together. ### Claim 66 (depends on 65) The method of claim 65, wherein in step (i), the two segments have no minimum leaf separation and no interdigitation when for a multileaf collimator. ### Claim 67 (depends on 65) The method of claim 65, wherein in step (i), the two segments have interdigitation. ### Claim 68 A method comprises the following steps: (a) generating a canonical delivery option for each set of field opening endpoints for an intensity modulated beam; (b) for every two consecutive intensity modulated beam columns of the intensity modulated beam, determining a series of minimum cost g-matchings between the canonical delivery options of the intensity modulated beam columns; (c) determining the tradeoff curves based on the g-matchings; (d) extracting the segments for the intensity modulated beam based on the matched field openings of the canonical delivery options from the determined g-matchings in an increasing order of consecutive intensity modulated beam columns to thereby partition the intensity modulate beam; and (e) implementing a treatment plan based on the extracted segments of step (d).