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Large scale optimization under dose-volume restrictions
142
Radiation
Oncology,
Biology,
Physics
October
1989, Volume
after the onset of symptoms ala not arrect tne ultimate increase the median time to response (9 days vs. 14 days, in only one responding nerve (at 14 months).
response p=O.O4).
17, Supplement
1
rate, but did slightly Relapse has been noted
Radiation therapy is a highly effective means of reversing cranial nerve dysfunction in leukemia and lymphoma. Leukemic patients may benefit from a higher dose than previously used in order to improve the level of response.
53 LARGE SCALE OPTIMIZATION UNDER DOSE-VOLUME RESTRICTIONS M. Langer,M.D., R. Brown, M.S., M. Urie, Ph.D., J. Leong,Ph.D., M. Stracher, B.S, J. Shapiro, Ph.D. Harvard Joint Center for Radiation Therapy, Boston, MA 02115; Dept. of Radiation Medicine, Massachusetts General Hospital, Boston, MA 02114; Resource Management Systems, Newton, MA; Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA 02139 Tolerance demands that the doses delivered to fractional volumes of different normal tissue structures not exceed critical limits. An optimal beam weighting may be identified as one which maximizes target dose subject to such tolerance restrictions and to restrictionson tumor dose inhomogeneity. The construction of plans satisfying dose restrictions on fractional organ volumes has not previously been described, but advances in imaging and treatment delivery have made urgent the need for formal optimization under these conditions. We show how an optimal weighting may be found with mathematical programming techniques and introduce dose-volume histograms to verify that the solutions obtained satisfy the posed constraints. Structures are modelled as collections of discrete points as large as 500 within a class, and the doses delivered to these points expressed as linear combinations of the beam weights. It may be shown that the weighting problem is then described by a combinatorial linear program (LP). We formulate the combinatorial LP as a mixed O/l integer linear program, for which optimal and near optimal solutions may be rapidly found. The method is illustrated by the assignment of weights to a set of 10 beams incident on a pelvic target surrounded by bowel, bladder, and rectum. Using a 3-dimensionalplanning system structures of interest were identified on a series of transverse CT slices and coordinates defining the beams established. Different tolerance restrictions were examined so that the sensitivity of the target dose to changes in the normal tissue constraints could be explored. The results of four trials are presented. In each trial, the inhomogeneity of dose across the target was restricted to +3% and the objective taken was maximization of target dose. Dose-volume restrictionswere placed on the normal tissues. No more than 50% of the rectum could receive >56 Gy, and no more than 66% of bladder could receive >60 Gy. The volume of the most sensitive surrounding organ - small bowel - permitted to exceed 40 Gy was varied from 15% to 30% in 5% increments. In addition, limits of 60 Gy, 62 Gy, and 68 Gy were placed on the doses given to any part of bowel, rectum, and bladder respectively. Results were obtained within 10 minutes using the XMP code to solve a sequence of linear programs in which successive fractions of free dichotomous variables with the largest values at the optimum were fixed at one until the full complement of integer variables was exhausted. Smaller problems were solved with either this method or to completion with the branch and bound algorithm of Land and Powell; similar objective values were obtained. Dose-volume histograms verified that that the discovered solutions satisfied the normal tissue constraints; in particular the volume constraints over dose-limiting bowel were satisfied at their upper margin. Tumor inhomogeneitywas kept to within 1% of the desired limit. It was found that changing the volume of small bowel allowed >40 Gy from 15% to 20% yielded a target dose increase of 12%; further expansions of the 40 Gy volume in 5% increments permitted 4% and 7% increases in the target dose. A recurrent problem in treatment planning may be solved rigorously and efficiently with the optimization method described. Dose restrictions on volumes defined in three dimensions may be specified, and the relation between the restricted volumes and the target dose determined.
54 THREE DIMENSIONAL DOSIMETRIC COMPARISON OF RADIATION THERAPY TREATMENT TECHNIQUES FOR CARCINOMA Chu, J., Solin, I>., Hwang, C., Kessler, Fox Chase Cancer
Center/University
H., Hanks,
OF PANCREAS
G.
of Pennsylvania
Conventional Radiation Therapy for carcinoma of the pancreas requires high doses for local control. treatment techniques include four field box (opposed AP-PA and lateral fields) and wedged three field (AP and opposed lateral fields with wedges) beams. The delivery of effective dose to the target volume using the conventional field arrangements is often difficult due to the close proximity of the target volume to several critical organs. The use of opposed anterior inferior and posterior superior oblique fields has the potential of reducing doses to the kidneys which are among the most sensitive critical organs adjacent to the target volume. To analyze the potential benefit of the unconventional fields, we have evaluated 3D treatment plans (1) four field box, (2) three field, (3) four generated for 3 patients for four different beam arrangements: field oblique, consisting of parallel opposed oblique and lateral fields, and (4) six field, consisting of a CT scans at multiple levels were obtained for combination of four field oblique and opposed AP-PA fields. each patient and field shaping blocks for each field were designed using the beam's eye view capability of a
Radiation
Oncology,
Biology,
Physics
October
1989, Volume
after the onset of symptoms ala not arrect tne ultimate increase the median time to response (9 days vs. 14 days, in only one responding nerve (at 14 months).
response p=O.O4).
17, Supplement
1
rate, but did slightly Relapse has been noted
Radiation therapy is a highly effective means of reversing cranial nerve dysfunction in leukemia and lymphoma. Leukemic patients may benefit from a higher dose than previously used in order to improve the level of response.
53 LARGE SCALE OPTIMIZATION UNDER DOSE-VOLUME RESTRICTIONS M. Langer,M.D., R. Brown, M.S., M. Urie, Ph.D., J. Leong,Ph.D., M. Stracher, B.S, J. Shapiro, Ph.D. Harvard Joint Center for Radiation Therapy, Boston, MA 02115; Dept. of Radiation Medicine, Massachusetts General Hospital, Boston, MA 02114; Resource Management Systems, Newton, MA; Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA 02139 Tolerance demands that the doses delivered to fractional volumes of different normal tissue structures not exceed critical limits. An optimal beam weighting may be identified as one which maximizes target dose subject to such tolerance restrictions and to restrictionson tumor dose inhomogeneity. The construction of plans satisfying dose restrictions on fractional organ volumes has not previously been described, but advances in imaging and treatment delivery have made urgent the need for formal optimization under these conditions. We show how an optimal weighting may be found with mathematical programming techniques and introduce dose-volume histograms to verify that the solutions obtained satisfy the posed constraints. Structures are modelled as collections of discrete points as large as 500 within a class, and the doses delivered to these points expressed as linear combinations of the beam weights. It may be shown that the weighting problem is then described by a combinatorial linear program (LP). We formulate the combinatorial LP as a mixed O/l integer linear program, for which optimal and near optimal solutions may be rapidly found. The method is illustrated by the assignment of weights to a set of 10 beams incident on a pelvic target surrounded by bowel, bladder, and rectum. Using a 3-dimensionalplanning system structures of interest were identified on a series of transverse CT slices and coordinates defining the beams established. Different tolerance restrictions were examined so that the sensitivity of the target dose to changes in the normal tissue constraints could be explored. The results of four trials are presented. In each trial, the inhomogeneity of dose across the target was restricted to +3% and the objective taken was maximization of target dose. Dose-volume restrictionswere placed on the normal tissues. No more than 50% of the rectum could receive >56 Gy, and no more than 66% of bladder could receive >60 Gy. The volume of the most sensitive surrounding organ - small bowel - permitted to exceed 40 Gy was varied from 15% to 30% in 5% increments. In addition, limits of 60 Gy, 62 Gy, and 68 Gy were placed on the doses given to any part of bowel, rectum, and bladder respectively. Results were obtained within 10 minutes using the XMP code to solve a sequence of linear programs in which successive fractions of free dichotomous variables with the largest values at the optimum were fixed at one until the full complement of integer variables was exhausted. Smaller problems were solved with either this method or to completion with the branch and bound algorithm of Land and Powell; similar objective values were obtained. Dose-volume histograms verified that that the discovered solutions satisfied the normal tissue constraints; in particular the volume constraints over dose-limiting bowel were satisfied at their upper margin. Tumor inhomogeneitywas kept to within 1% of the desired limit. It was found that changing the volume of small bowel allowed >40 Gy from 15% to 20% yielded a target dose increase of 12%; further expansions of the 40 Gy volume in 5% increments permitted 4% and 7% increases in the target dose. A recurrent problem in treatment planning may be solved rigorously and efficiently with the optimization method described. Dose restrictions on volumes defined in three dimensions may be specified, and the relation between the restricted volumes and the target dose determined.
54 THREE DIMENSIONAL DOSIMETRIC COMPARISON OF RADIATION THERAPY TREATMENT TECHNIQUES FOR CARCINOMA Chu, J., Solin, I>., Hwang, C., Kessler, Fox Chase Cancer
Center/University
H., Hanks,
OF PANCREAS
G.
of Pennsylvania
Conventional Radiation Therapy for carcinoma of the pancreas requires high doses for local control. treatment techniques include four field box (opposed AP-PA and lateral fields) and wedged three field (AP and opposed lateral fields with wedges) beams. The delivery of effective dose to the target volume using the conventional field arrangements is often difficult due to the close proximity of the target volume to several critical organs. The use of opposed anterior inferior and posterior superior oblique fields has the potential of reducing doses to the kidneys which are among the most sensitive critical organs adjacent to the target volume. To analyze the potential benefit of the unconventional fields, we have evaluated 3D treatment plans (1) four field box, (2) three field, (3) four generated for 3 patients for four different beam arrangements: field oblique, consisting of parallel opposed oblique and lateral fields, and (4) six field, consisting of a CT scans at multiple levels were obtained for combination of four field oblique and opposed AP-PA fields. each patient and field shaping blocks for each field were designed using the beam's eye view capability of a