In1 J. Radiamn
Oncology
Bd
Phys., Vol. 957-964,
pp
0360-3016/90 $3.00 + .oO Copyright 0 1990 Pergamon Press plc
Pnnted I” the U.S.A. All rights reserved.
??Technical Innovations and Notes
AN INTERACTIVE SYSTEM FOR POINT DOSE OPTIMIZATION GEORGE
STARKSCHALL,
PH.D.,*GREGORYC.HENKELMANN,M.D.+ANDK.KIANANG,M.D.+
The University of Texas M. D. Anderson Cancer Center, 1515 Holcombe Blvd., Houston, TX 77030 An interactive system has been developed to aid in determining optimal photon and electron beams and beam weights for radiotherapy treatment planning. Dose constraints at various points are selected and an algorithm searches for a set of beams and weighting factors that satisfy these constraints. In the event that no combination of beam weights satisfies the choice of treatment modalities and dose constraints, the treatment modalities and dose constraints can be modified interactively. The goal of this procedure is different from that of more conventional optimization schemes in which optimal dose values are specified and the optimization algorithm determines the set of beam weights that yields a dose distribution closest to optimal. Treatment planning, Electrons, Optimization.
an appropriate
minimum radiation dose to adequately control the disease, but, to limit morbidity, the dose to regions outside these volumes must not exceed some maximum. In the case of the photon/electron mixing in the treatment of the parotid tumor, beam weights must be selected to deliver an adequate dose to the target volume, while sparing the contralateral parotid, much of the oral cavity, and often the ipsilateral skin surface. One way to pursue this goal is through a computerized treatment planning system. Several limitations exist, however. The first is that the optimization of treatment plans, at least on most commercially available treatment planning systems, consists primarily of trial and error. The treatment planner selects a “reasonable” set of beam weights; the computer then calculates a dose distribution based on these weights, and the planner evaluates the dose distribution. If the dose distribution satisfies the dose criteria the planner considers it acceptable; otherwise, the planner must change the weights So that the computer can recompute the dose distribution. This procedure is repeated until either an acceptable dose distribution is obtained or the treatment planner runs out of time or patience. The second limitation is procedural. Ideally, treatment planning is an interactive process between the treatment planner and the physician. But the physician may be unwilling to delay treatment while discussions and calculations for acceptable treatment plans proceed, especially if several iterations are required. A recent study (8) has demonstrated that initial judgments of how treatment is to be delivered are often made prior to treatment planning
INTRODUmION
In the planning of radiotherapy for cancers of many sites, frequent use is made of multiple parallel opposed or appositional photon beams of one or more energies, perhaps combined with one or more electron fields with different energies. For example, when a large volume that encompasses the tumor and regional lymph nodes is to be irradiated along with a boost volume that includes only the region of known disease, in this case perhaps a head and neck tumor, the large volume is usually treated by parallel opposed photon fields in the energy range form 6oCo to 6 MV, whereas the boost volume is usually treated via either photon or electron fields, depending on the location of the tumor and involved lymph nodes. Treatment is complicated by the need to reduce the large-volume field to maintain a safe spinal cord dose; treatment to the lymph node regions overlying the spinal cord would then be supplemented with electrons of appropriate energies. In the irradiation of parotid tumors, appositional combinations of photon and electron fields are likely to be used. In planning this treatment the radiotherapist takes advantage of the finite range of the electron beam so as to spare the contralateral parotid. Often, an ipsilateral photon beam is added to the electron field to effect some degree of skin sparing. An important aspect of the treatment plannning involves the careful determination of weights for all the beams. For the case of the combined large volume/boost volume treatment of head and neck tumors, beam weights must be carefully selected so that both volumes receive * Department of Radiation Physics.
This work is supported in part by NC1 grant CA-06294. Accepted for publication 19 July 1989.
+Department of Clinical Radiotherapy.
Reprint requests to: George Starkschall, Ph.D. 957
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I. J. Radiation Oncology 0 Biology 0 Physics
and that changes in the intended treatment plan are relatively infrequent. It is not an uncommon practice for a patient to begin treatment with a provisional plan, subject to change when a final computer-generated treatment plan is approved. If there is considerable delay before the final treatment plan is approved, it may not be possible to implement the plan because of the dose already given the patient. To overcome these difficulties, we describe an approach to beam optimization that facilitates the generation of a set of beams and beam weights that is likely to be acceptable; a computer-generated isodose distribution can then be obtained to confirm the plan. Since neither specialized computer hardware is required, nor is input timeconsuming, these calculations can be done with the radiotherapist present to provide rapid feedback, so treatment delay is rare. METHODS
AND MATERIALS
Previous work in optimization of electron/photon mixing Our early attempts to construct effective optimization systems involved an algorithm for optimizing beam weights for mixing photon and electron radiation beams, developed at our institution by Fields et al. (9, 10). The algorithm, named EMIX, optimizes planning of either appositional beam therapy or boost therapy after parallel opposed treatments. Beam weight optimization is achieved via a least squares approach. The square of the difference between a calculated dose distribution and the clinically desired dose distribution is evaluated. A search is made over the space of all available photon and electron beams, taking two or three beams at a time, and over a finite set of integral relative beam weights. Depending on the choice of machines and number of beam combinations evaluated, the program investigates from 500 to over a quarter million beam weight combinations to select the best distribution. Since its development, this system has been successfully used at our institution as a tool for developing treatment plans, primarily in head and neck radiotherapy. Several shortcomings can be noted with this approach to beam weight optimization. First, the EMIX algorithm uses a “brute force” search technique through all integral combinations of beam weights over a finite set of beam weights, taking into account any additional dose constraints. From the point of view of algorithmic efficiency, a directed search technique should significantly decrease execution time. Moreover, the algorithm completely ignores beam weight combinations that are not in the ratios of small whole numbers. An improved optimization scheme would consider the entire space of possible beam weights. A second shortcoming is that the same type of “brute force” search is used to evaluate beam combinations. A treatment planner would not, for example, consider the
April 1990, Volume 18, Number 4
use of a low energy electron beam to treat a boost volume at a depth beyond the range of the electrons, and yet, the EMIX algorithm evaluates all beam combinations for a specified machine, including clinically undesirable ones. An improvement to EMIX would allow for significantly more input by the planner to restrict the beam search to clinically reasonable modalities and energies. Another shortcoming of the EMIX algorithm is that dose specification is limited to areas of the same diameter. Of course, many treatment plans cover regions with different diameters. The optimization scheme would be improved if it allowed for the calculation of doses to selected points along multiple diameters. The final shortcoming of the EMIX algorithm, the one that has prompted implementation of a different approach, lies in the selection of the objective function used for optimization. The EMIX algorithm calculates the dose to a set of points from each beam and beam weight combination, calculates the square of the difference between the calculated dose and a desired dose, and sums this quality over a planner-defined set of points. The beam and beam weight combination that minimizes this objective function is considered to be the solution of the optimization problem. Unfortunately, this combination may not necessarily be clinically desirable. For example, the clinician may prescribe a uniform dose from the surface to some specified depth in the target volume for a parotid tumor using a set of appositional beams. The plan is to be optimized to deliver 57 Gy at the surface and 65 Gy from 0.5 cm to 4.5 cm depth. Dose is not to exceed 45 Gy at 5.5 cm, the minimum depth of the spinal cord, and 20 Gy at 12.0 cm, the location of the contralateral parotid. A linear accelerator with photon beams of 6 MV and 18 MV and electron beams ranging from 6 MeV to 20 MeV is to be used. The EMIX algorithm indicates that the optimal choice of treatment is a single 15-MeV electron beam with a given dose of 73.1 Gy. The central axis dose distribution for this plan is illustrated in Figure 1. Although the dose distribution meets all the optimization criteria, there may be some concern as to whether the 68.7 Gy delivered at the patient surface is too high and whether the 11% gradient between the dose at 3 cm and the dose at 4.5 cm is too large. The problem is not that the optimization scheme is faulty, but that the optimization criteria lead to a treatment plan that may not necessarily be clinically acceptable. Furthermore, if the physician declines to accept this selection of beam weights, the algorithm gives no indication as to how to modify the treatment plan. One approach to beam weight optimization that attempts to alleviate this problem is to replace the goal of minimizing an objective function with the goal of searching for any set of beam weights that yields a dose distribution within a set of acceptable bounds. Altschuler et al. (2) have argued that the minimization of an objective function is not at all necessary in solving a dose optimi-
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Point dose optimization 0 G. STARKSCHALL efal.
weight distribution can then be used for the initial treatment of the patient and as a starting point for generating a complete plan using a more sophisticated treatment planning system. Feasibility constraints. The feasibility search problem as applied to dose optimization can be summarized in the following manner (4, 11): Given a set {j l Of Nj beams with weights Wj and a set {i} of Mi dose calculation points, find that set of beam weights such that
oI 0
5 Aij Wj I bi
for all
Wj 2 0.
j=l
2
4
6
depth
0
10
12
(cm)
Fig. I. Central axis dose distribution for single 15 MeV electron field. The beam weight was selected to minimize the difference in dose btiween that delivered by the field and a prescribed dose of 65 Gy for depths between 0.5 cm and 4.5 cm, while keeping the dose less than 45 Gy at 5.5 cm and 20 Gy at 12.0 cm depths.
zation problem. The clinically important quantities are not the ideal doses to points, but rather the upper and lower bounds to the acceptable values for doses to these points. For example, in the previous case, the clinical objective may not necessarily be to make the dose in the region from 0.5 cm to 4.5 cm as close as possible to 65 Gy. Rather, the important criterion governing the acceptability of the dose distribution is that the dose in that region lie between certain specified bounds, for example, 63 Gy and 67 Gy. But the approach to optimization must be altered to incorporate these optimization criteria. The next section describes how the dose optimization problem may be restated to search for any feasible solution, that is, any solution that satisfies the dose constraints.
Feasibility search algorithms General characteristics. The feasibility
search method presented in this study uses as input a set of maximum and minimum acceptable doses at several points designated by the clinician as well as an indication of the relative importance of the dose constraints at these points. If some set of beam weights can satisfy these specifications, the program will calculate them. If not, the system will indicate this failure to the clinician and suggest dose specifications that may achieve a feasible solution. Determination of the solution beam weight distribution or identification of its absence is extremely rapid; thus, the physician can vary the dose constraints and the radiation modalities interactively until a beam weight distribution that satisfies the dose constraints is found. This beam
* MicroVAX II computer, Maynard, MA.
Digital Equipment
Corporation,
In the above inequality following meanings:
the quantities
Aij and bi have the
1. For all specified points for which Df”““‘, an upper limit to the dose, is given, A, = dij, the dose per unit beam weight from beam j to point i, and bi = Dimax). This insures that the dose to point i does not exceed Dimax). 2. For all specified points for which Dimi”), a lower limit to the dose, is given, Aij = -dij and bi = -Dimin). This insures that the dose to point i is always greater than Dim’“‘. The quantities Dima”’ and Djm’“) are specified by the clinician based upon clinical experience, while the quantity dij is calculated according to an appropriate beam model. In this work, dij is taken to be the central axis depth dose, evaluated at the appropriate physical depth of the calculation point, multiplied by an appropriate factor to account for distance from the source. In the event the point is not included in the radiation field, then dij is set to zero. Several algorithms that search for a solution to the constraint inequalities have appeared in the literature; the one selected for this optimization problem is the one of Cimmino (5,6,7). The Cimmino algorithm is an iterative algorithm that takes a trial solution, tests the feasibility of each of the constraint equations, and modifies the trial solution based on the feasibility of each constraint equation. Unlike the “row-action” algorithms (3) that have also been used as feasibility searches to solve problems in dose optimization (1, 1 l), the Cimmino algorithm evaluates the feasibility of al1 the row inequalities before making any iteration steps. As a result, if the dose constraints yield no feasible solution, the final solution calculated by the algorithm is independent of the order of row action. Although the Cimmino algorithm converges more slowly than some of the other algorithms ( 12), the size of the dose constraint matrices used in this problem are sufficiently small that results are obtained in less than a few seconds of CPU time.$
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for carotid
April 1990, Volume 18, Number 4
e”T
test case
(Gy)
Depth (cm)
Lower
UDDer
0.0 0.5 2.0 3.5 4.5 5.5 12.0
54.0 63.0 63.0 63.0 63.0 -
60.0 67.0 67.0 67.0 67.0 45.0 20.0
1.0 1.0 1.0 1.0 1.0 10.0 1.0
The Cimmino algorithm also has an advantage over several other feasibility search algorithms in that one may incorporate importance weighting into the dose specifications. It is possible to designate certain points as being more important to the optimization than other points and have the algorithm take this into account when searching for a feasible solution. For example, one can specify an upper bound to the dose to the spinal cord and designate it with an importance greater than that given to the doses to other regions. The algorithm will then proceed to search for a feasible solution to the dose constraint problem with a greater emphasis placed on satisfying the dose constraint at the spinal cord. Finally, the feasibility search algorithm has been incorporated into an interactive driving program. The philosophy behind the driving program, which is a key element of this point dose optimization system, is that this system is to be viewed as a “treatment planning tool” designed to assist the treatment planner find an acceptable set of beam weights, rather than as an automatic method of solving the inverse radiotherapy problem. For many treatment planning cases, a specified set of dose constraints may not lead to any feasible soluton. The driving program has been designed so that if no feasible solution to the dose constraints exists, the program offers the clinician the opportunity to modify any of the dose constraints, any of the beams, or any of the dose specification depths, and repeat the feasibility search. Unlike the more conventional trial and error approaches, in which the planner modifies the beam weights and evaluates the resultant dose distributions, this approach provides the planner the opportunity to modify the range of acceptable outcomes, and then attempts to find a set of beams weights that provides a dose distribution that falls within the acceptable
Table lb. Beam weights after 500 iterations bounds in Table 1a
using the dose
Modality
Beam weight (Gy)
6 MV photons 18 MV photons 12 MeV electrons 15 MeV electrons 20 MeV electrons
6.2 6.6 13.7 21.6 19.2
I[
60
Relative imuortance
ii
It1 X
t
+z
s
X
40 -
8 % 20 -
0
0
-I
,,,,‘,,,,‘,,,-‘,,,,‘,,ll’,,,‘_ 2 4
6 depth
a
10
12
(cm)
Fig. 2. Central axis dose distribution for first parotid test case. Dose bounds are summarized in Table la and denoted by the dark vertical line. Beam weights are summarized in Table lb, yielding doses denoted by the symbol X.
dose ranges. The clinician is also offered the opportunity to accept any plan that has been determined by the feasibility search algorithm, even if the plan does not satisfy all the dose constraints. The final evaluation of the treatment plan remains the responsibility of the clinician. Clinical examples Parotid bed. Several examples of the use of the feasibility search algorithm in an interactive optimization program are presented. The first example is the one presented in an earlier section of this paper as one in which the traditional optimization methods may not necessarily yield an acceptable solution. In this application, rather than specifying optimal doses, one specifies upper and/or lower bounds to the doses at selected depths as well as a set of beams to be considered in the search for a feasible solution. In this example, the patient has a squamous cell carcinoma of the skin metastatic to the superficial parotid lymph nodes. The primary is completely resected and a superficial parotidectomy performed. The parotidectomy pathology specimen has a negative deep margin but tumor extends through the nodal capsule into the superficial parotid tissue. Postoperative radiotherapy is to be directed to the parotid tumor bed and the ipsilateral upper neck region. The dose constraints for the parotid tumor bed are specified as follows: Surface dose is constrained to between 54 Gy and 60 Gy. The dose to the superficial
Table 2. Beam weights after 500 iterations using the 6 MV ohoton and 15 MeV electron beams onlv Modality
Beam weight (Gy)
6 MV photons 15 MeV electrons
12.0 56.8
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Table 4a. Beam weights after 500 iterations using the dose bounds in Table 3a with both on-cord and off-cord fields Beam weight (Gy) Modality
Incl. cord
Off cord
strip
6 MV photons 18 MV photons 9 MeV electrons 12 MeV electrons 15 MeV electrons 20 MeV electrons
11.1 8.6 2.1 16.1 12.0
4.4 3.3 0.0 4.5 8.7
0.0 9.8 10.5 -
Table 4b. Dose distribution
for beam weights in Table 4a Dose (Gy)
depth
(cm)
Fig. 3. Central axis dose distribution
for two beam plan for first parotid test case. Beam weights are summarized in Table 2. Dose bounds are denoted by the dark vertical line and doses are denoted by the symbol X.
parotid tumor bed at a depth of 0.5 cm to 4.5 cm is constrained to between 63 Gy and 67 Gy delivered at 2 Gy per fraction. The dose to the spinal cord at a minimum
Table 3a. Initial dose bounds for second parotid case Dose bound (Gy) Depth (cm)
Lower
Upper
63.0 63.0 63.0 63.0 -
67.0 67.0 67.0 67.0 45.0 20.0
0.0
Relative importance 1.0 1.0 1.0 1.0 1.0 10.0 1.0
50.0
0.5 2.0 3.5 5.0 5.5 12.0
Table 3b. Beam weights after 500 iterations using the dose bounds in Table 3a Modality
Beam weight (Gy)
6 MV photons 18 MV photons 12 MeV electrons 15 MeV electrons 20 MeV electrons
14.9 1.8 3.9 46.5 0.0
Depth (cm)
Primary diam
Cord diam
0.0 0.5 2.0 3.5 4.5 5.0 5.5 12.0
46.2 61.2 69.9 69.0 60.7 19.9
51.1 61.9 69.5 67.1 58.4 45.2 14.4
depth of 5.5 cm is not to exceed 45 Gy. Finally, the dose to the contralateral parotid at a depth of 12 cm is not to exceed 20 Gy. All points are given a relative weighting of 1 except for the spinal cord, which is given a weighting of 10. We have found that selecting this weighting scheme insures that the dose constraint on the cord is rigidly adhered to. A feasible solution was sought involving 6 MV and 18 MV photons and 12 MeV, 15 MeV, and 20 MeV electrons. After 500 iterations, requiring less than 30 sec-
Table 5a. Final beam weights for second parotid case Beam weight (Gy) Modality
Incl cord
Off cord
strip
6 MV photons 15 MeV electrons 20 MeV electrons
19.4 4.2
9.6 35.2
44.7 -
Table 5b. Dose distribution
for beam weights in Table 5a Dose (Gy)
Table 3c. Dose distribution Depth (cm) 0.0
0.5 2.0 3.5 5.0 5.5 12.0
for beam weights in Table 3b Depth (cm)
Primary diam
Cord diam
0.0 0.5 2.0 3.5 4.5 5.0 5.5 12.0
44.5 62.5 68.0 65.6 61.6 20.0
50.5 62.9 68.1 65.3 58.2 45.0 13.1
Do= (GY) 50.2 60.8 66.4 65.2 51.9 43.2 11.4
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Table 6a. Initial dose bounds for tonsillar fossa test case Dose bound (Gy) Region
Depth (cm)
Lower
Upper
Primary (excluding boost)
1.0 2.0 7.5 (midline) 13.0 14.0 1.0
52.0 52.0 52.0 52.0 52.0 52.0
56.0 56.0 56.0 56.0 56.0 56.0
1.0 1.0 1.0 1.0 1.0 1.0
6.0 (midline) 11.0 2.0 4.0 6.0 7.5 (midline) 8.0 10.0 14.0
0.0 52.0 68.0 68.0 68.0 52.0 52.0 52.0 52.0
45.0 56.0 72.0 72.0 72.0 64.0 64.0 62.0 58.0
10.0 1.0
Post cervical area at pt of max cord dose
Boost
onds of clock time on a multi-user system,* no feasible solution is found, but the resulting set of given doses gives a dose distribution that the clinician has determined to be acceptable. The lower dose at 4.5 cm is acceptable since the tumor only involved the superficial parotid lobe. The dose constraints and beam weight distribution are displayed in Tables la and lb, and resulting dose distribution in Figure 2. To simplify the treatment plan, an additional run is performed using only 6 MV photons and 15 MeV electrons. The beam weights resulting from this run are displayed in Table 2 with the dose distribution in Figure 3. In this case the two dose distributions appear similar, with the exception that the dose to the parotid at 0.5 cm has been reduced from 66.6 Gy to 63.7 Gy, whereas the dose at 4.5 cm has been raised from 58.7 Gy to 61.2 Gy. In this case the two-beam treatment appears to be superior, both because of the dose distribution and because of the decrease in complexity. In a second example, an adenoid cystic carcinoma of the parotid is situated at the junction of the superficial and the deep lobes. The facial nerve sparing resection removes all the gross tumor; however, microscopic tumor is left on the facial nerve. Postoperative radiotherapy is to be directed to the paortid tumor bed and to the facial nerve all the way to its exit from the stylomastoid foramen. The dose constraints are specified as follows: Surface dose is not to exceed 50 Gy. Dose to the parotid, lying at depths between 0.5 cm and 5.0 cm, is constrained to lie between 63 Gy and 67 Gy given at 2 Gy per fraction. Dose to the spinal cord at a minimum depth of 5.5 cm is not to exceed 45 Gy. Finally, dose to the contralateral parotid at a depth of 12.0 cm from the beam entry surface is not to exceed 20 Gy. As in the previous example, all points except the spinal cord are considered to be of equal importance and given a relative value of 1, whereas the cord is given an importance of 10. These dose bounds are summarized in
Relative importance
1.0 1.0 1.0
1.0 1.0 1.0 1.0
Table 3a. A feasible solution is to be achieved by 6 MV and 18 MV photon beams and 12 MeV, 15 MeV, and 20 MeV electron beams. The Cimmino algorithm is used to find a feasible solution, allowing no more than 500 iterations. After 500 iterations, no solution satisfying the dose constraints is Table 6b. Beam weights after 100 iterations using the dose bounds in Table 6a Beam no
Description
Modality
Beam weight (Gy)
1 2 3 4 5 6 7 8 9
Total volume-rt Total volume-h Off cord-rt Off cord-h Post e strip-rt Post e strip-h Boost volume-rt Boost volume-h Boost volume-rt
Cobalt 60 Cobalt 60 Cobalt 60 Cobalt 60 10 MeV electrons 10 MeV electrons 18 MV x-rays 18 MV x-rays 18 MeV electrons
28.5 27.9 10.4 9.7 11.1 11.4 6.1 3.7 9.4
Table 6c. Dose distribution Region Wide field treatment
Post cervical area at pt of max cord dose Total treatment including boost
for beam weights in Table 6b Depth (cm)
Dose (Gy)
1.0 2.0 7.5 (midline) 13.0 14.0 1.0 6.0 (midline) 11.0 2.0 4.0 6.0 7.5 (midline) 8.0 10.0 14.0
55.0 54.4 52.2 53.8 54.3 52.0 41.2 52.0 72.2 71.0 67.7 64.2 63.1 61.4 61.5
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963
et al.
Table 7a. Initial dose bounds for buccal mucosa test case Dose bound (Gy) Region Wide field treatment
Post cervical area at pt of max cord dose
Total treatment including boost
Depth (cm)
Lower
Upper
1.0 3.0 6.0 (midline) 9.0 11.0 1.0 7.0 (midline) 13.0 1.0 3.0 6.0 (midline) 9.0 11.0
48.0 48.0 48.0 48.0 48.0 48.0 0.0 48.0 66.0 66.0 66.0 48.0 48.0
52.0 52.0 52.0 52.0 52.0 52.0 45.0 52.0 70.0 70.0 70.0 56.0 52.0
found. The given doses and calculated doses provided as output after the iterations are shown in Tables 3b and 3c. As seen from Table 3c, the large dose gradient required between the target volume depth of 5 cm and the minimum spinal cord depth of 5.5 cm is not likely to be achievable. Due to these constraints, substitutions of a reduced dose off the spinal cord and lower energy electrons to supplement treatment to the region overlying the spinal cord are specified. The beam weights and dose distribution for this revised plan are shown in Tables 4a and 4b. As can be seen, by making the necessary off-cord reduction, a higher electron energy can be used to increase the target volume at a depth of 5 cm. To minimize complexity the plan is reoptimized eliminating beams with relatively low given dose weightings. The new plan uses only the 6 MV photons combined with 20 MeV electrons for the region not overlying the cord and 15 MeV electrons for the region overlying the cord. The beam weights and depth dose distribution are shown in Tables 5a and 5b. Tonsillar fossa. Perhaps the most frequent cases in which optimization of photon and electron beam combinations occur are those in which the primary and upper neck are treated with parallel opposed low-energy photons to, control subclinical disease, followed by a boost to the gross tumor. An illustrative case is the treatment planning for a flat 5 cm squamous cell carcinoma of the right tonsillar fossa in which no nodes are clinically positive. It is desired to treat subclinical disease to between 52 Gy and 56 Gy at 1.8 Gy per fraction, using parallel opposed lateral cobalt fields. At a maximum spinal cord dose of 45 Gy, the lateral photon fields are to be reduced off the spinal cord and the posterior cervical lymph node areas supplemented with 10 MeV electron strips. The tonsillar primary is 4 cm below the right skin surface. The boost is planned to give a dose of 68 to 72 Gy at a depth from 2 cm to 6 cm. Optimization for the boost was done using parallel opposed 18 MV photon beams, as well as an ipsilateral 18 MeV electron beam. After 500 iterations, no feasible
Relative importance 1.0 1.0 1.0 1.0 1.0 1.0 10.0 1.0 1.0 1.0 1.0 1.0 1.0
solution that satisfies all constraints was found; however, the dose distribution resulting from these beam weights was considered acceptable by the clinician. The dose constraints, optimal beam weights, and resulting dose distributions are displayed in Tables 6a, 6b, and 6c. Buccal mucosa. Another example of combining photon and electron fields is illustrated by the case of a 5 cm squamous cell carcinoma of the right buccal mucosa with extension through the retromolar area to the ipsilateral
Table 7b. Beam weights after 500 iterations using the dose bounds in Table 7a Beam no.
Description
Modality
Beam weight (Gy)
1 2 3 4 5 6 7
Total volume-t? Total volume-lt Off cord-t? Off cord-lt Post e strip-rt Post e strip-h Boost volume-rt
Cobalt 60 Cobalt 60 Cobalt 60 Cobalt 60 9 MeV electrons 9 MeV electrons 20 MeV electrons
24.6 26.5 6.4 8.7 11.1 10.6 20.6
Table 7c. Dose distribution Region Wide field treatment
Post cervical area at pt of max cord dose Total treatment including boost
for beam weights in Table 7b Depth (cm)
Dose (Gy)
1.0 3.0 6.0 (midline) 9.0 11.0 1.0 7.0 (midline) 13.0 1.0 3.0 6.0 (midline) 9.0 11.0
49.7 49.5 49.6 50.6 51.5 48.0 37.9 48.5 70.1 70.0 65.9 54.0 52.0
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soft palate. The neck nodes are clinically negative. The initial treatment volume includes the primary and bilateral upper neck lymph node regions. Parallel opposed lateral 6oCo fields are to be used. These fields are to be reduced to maintain spinal cord tolerance, and 9 MeV electron fields are to be used to supplement treatment to the area overlying the spinal cord. The final boost volume to the primary tumor was accomplished with an ipsilateral 20 MeV electron field. The optimization criteria are summarized in Table 7a. The dose of 48 Gy to 52 Gy at 2 Gy per fraction is selected for subclinical disease and 66 Gy to 70 Gy for areas of gross disease. The target volume around the primary tumor extends from 1 cm to 6 cm below the right skin surface. Although convergence is not achieved in 500 iterations, the dose distribution resulting from the optimization lies within 0.1 Gy of the specified dose bounds and is thus accepted. The beam weights and resulting doses are also illustrated in Tables 7a and 7b.
April 1990, Volume 18, Number 4
SUMMARY An interactive system for optimizing point doses has been developed that offers the following features: Dose optimization
points may lie at any point within the patient volume. Optimization is achieved by specifying dose bounds to optimization points and beams to be considered. The system will search for any combination of weights of the specified beams such that the dose lies within these bounds. The relative importance of optimization points can be specified. Although dose constraints frequently lead to infeasible solutions, the system allows the user the opportunity to change either dose constraints or beams, and reoptimize. At any point in the process the user may accept a solution and record it.
REFERENCES Altschuler, M. D.; Censor, Y.; Powlis, W. D.; Smith, A. R.; Wallace, R. E. Selecting beams and beam weights for 3-d treatment planning. Med. Phys. 13:590; 1986. 2. Altschuler, M. D.; Powlis, W. D.; Censor, Y. Teletherapy treatment planning with physician requirements included in the calculation: I. Concepts and methodology. In: Paliwal, B. R., Herbert, D. E., Orton, C. G., eds. Optimization of cancer radiotherapy, AAPM Symposium Proceedings #5. New York, NY: American Institute of Physics; 1985:443452. 3. Censor. Y. Row-action methods for huge and sparse systems and their applications. SIAM Rev. 23:444-466; 1981. Censor, Y.; Altschuler, M. D.; Powlis, W. D. A computational solution of the inverse problem in radiation therapy treatment planning. Appl. Math. Comput. 25:57-87; 1988. Censor, Y.; Altschuler, M. D.; Powlis, W. D. On the use of Cimmino’s simultaneous projections method for computing a solution of the inverse problem in radiation therapy treatment planning. Inverse Prob. 4:607-623; 1988. Censor, Y.; Elfving, T. New methods for linear inequalities. Linear Algebra Appl. 42: 199-2 11; 1982.
7. Cimmino, G. Calculo approssimato per le soluzioni dei sistemi di equazioni lineari. Ricerca Sci. Roma 1938-XVI, ser II, anno IX, 1:326-333; 1938. 8. Doppke, K. P., Goitein, M. A survey of the information gained from planning treatment with a computer. Med. Phys. 15:258-262; 1988. 9. Fields, R. S.; Hogstrom, K. R. Computer model for combining electron and photon beams. In: Paliwal, B. R., ed. Proceedings of the Symposium on Electron Dosimetry and Arc Therapy, AAPM Symposium Proceedings #2. New York, NY: American Institute of Physics; 1982: 16 l- 180. 10. Fields, R. S.; Spanos, W. J.; Tapley, N. duV.; Cundiff, J. H.; Sampiere, V. A. Computer optimization for combining electron and photon beams (Abstr.). Int. J. Radiat. Oncol. Biol. Phys. 6: 1444; 1980. 11. Powlis, W. D.; Altschuler, M. D.; Censor, Y.; Buhle, Jr., E. L. Semi-automated radiotherapy treatment planning with a mathematical model to satisfy treatment goals. Int. J. Radiat. Oncol. Biol. Phys. 16:27 l-276; 1989. 12. Starkschall, G. Considerations for optimization of dose distributions for conformal radiation therapy (Abstr.). Radiology 165(P):185; 1987.
Oncology
Bd
Phys., Vol. 957-964,
pp
0360-3016/90 $3.00 + .oO Copyright 0 1990 Pergamon Press plc
Pnnted I” the U.S.A. All rights reserved.
??Technical Innovations and Notes
AN INTERACTIVE SYSTEM FOR POINT DOSE OPTIMIZATION GEORGE
STARKSCHALL,
PH.D.,*GREGORYC.HENKELMANN,M.D.+ANDK.KIANANG,M.D.+
The University of Texas M. D. Anderson Cancer Center, 1515 Holcombe Blvd., Houston, TX 77030 An interactive system has been developed to aid in determining optimal photon and electron beams and beam weights for radiotherapy treatment planning. Dose constraints at various points are selected and an algorithm searches for a set of beams and weighting factors that satisfy these constraints. In the event that no combination of beam weights satisfies the choice of treatment modalities and dose constraints, the treatment modalities and dose constraints can be modified interactively. The goal of this procedure is different from that of more conventional optimization schemes in which optimal dose values are specified and the optimization algorithm determines the set of beam weights that yields a dose distribution closest to optimal. Treatment planning, Electrons, Optimization.
an appropriate
minimum radiation dose to adequately control the disease, but, to limit morbidity, the dose to regions outside these volumes must not exceed some maximum. In the case of the photon/electron mixing in the treatment of the parotid tumor, beam weights must be selected to deliver an adequate dose to the target volume, while sparing the contralateral parotid, much of the oral cavity, and often the ipsilateral skin surface. One way to pursue this goal is through a computerized treatment planning system. Several limitations exist, however. The first is that the optimization of treatment plans, at least on most commercially available treatment planning systems, consists primarily of trial and error. The treatment planner selects a “reasonable” set of beam weights; the computer then calculates a dose distribution based on these weights, and the planner evaluates the dose distribution. If the dose distribution satisfies the dose criteria the planner considers it acceptable; otherwise, the planner must change the weights So that the computer can recompute the dose distribution. This procedure is repeated until either an acceptable dose distribution is obtained or the treatment planner runs out of time or patience. The second limitation is procedural. Ideally, treatment planning is an interactive process between the treatment planner and the physician. But the physician may be unwilling to delay treatment while discussions and calculations for acceptable treatment plans proceed, especially if several iterations are required. A recent study (8) has demonstrated that initial judgments of how treatment is to be delivered are often made prior to treatment planning
INTRODUmION
In the planning of radiotherapy for cancers of many sites, frequent use is made of multiple parallel opposed or appositional photon beams of one or more energies, perhaps combined with one or more electron fields with different energies. For example, when a large volume that encompasses the tumor and regional lymph nodes is to be irradiated along with a boost volume that includes only the region of known disease, in this case perhaps a head and neck tumor, the large volume is usually treated by parallel opposed photon fields in the energy range form 6oCo to 6 MV, whereas the boost volume is usually treated via either photon or electron fields, depending on the location of the tumor and involved lymph nodes. Treatment is complicated by the need to reduce the large-volume field to maintain a safe spinal cord dose; treatment to the lymph node regions overlying the spinal cord would then be supplemented with electrons of appropriate energies. In the irradiation of parotid tumors, appositional combinations of photon and electron fields are likely to be used. In planning this treatment the radiotherapist takes advantage of the finite range of the electron beam so as to spare the contralateral parotid. Often, an ipsilateral photon beam is added to the electron field to effect some degree of skin sparing. An important aspect of the treatment plannning involves the careful determination of weights for all the beams. For the case of the combined large volume/boost volume treatment of head and neck tumors, beam weights must be carefully selected so that both volumes receive * Department of Radiation Physics.
This work is supported in part by NC1 grant CA-06294. Accepted for publication 19 July 1989.
+Department of Clinical Radiotherapy.
Reprint requests to: George Starkschall, Ph.D. 957
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and that changes in the intended treatment plan are relatively infrequent. It is not an uncommon practice for a patient to begin treatment with a provisional plan, subject to change when a final computer-generated treatment plan is approved. If there is considerable delay before the final treatment plan is approved, it may not be possible to implement the plan because of the dose already given the patient. To overcome these difficulties, we describe an approach to beam optimization that facilitates the generation of a set of beams and beam weights that is likely to be acceptable; a computer-generated isodose distribution can then be obtained to confirm the plan. Since neither specialized computer hardware is required, nor is input timeconsuming, these calculations can be done with the radiotherapist present to provide rapid feedback, so treatment delay is rare. METHODS
AND MATERIALS
Previous work in optimization of electron/photon mixing Our early attempts to construct effective optimization systems involved an algorithm for optimizing beam weights for mixing photon and electron radiation beams, developed at our institution by Fields et al. (9, 10). The algorithm, named EMIX, optimizes planning of either appositional beam therapy or boost therapy after parallel opposed treatments. Beam weight optimization is achieved via a least squares approach. The square of the difference between a calculated dose distribution and the clinically desired dose distribution is evaluated. A search is made over the space of all available photon and electron beams, taking two or three beams at a time, and over a finite set of integral relative beam weights. Depending on the choice of machines and number of beam combinations evaluated, the program investigates from 500 to over a quarter million beam weight combinations to select the best distribution. Since its development, this system has been successfully used at our institution as a tool for developing treatment plans, primarily in head and neck radiotherapy. Several shortcomings can be noted with this approach to beam weight optimization. First, the EMIX algorithm uses a “brute force” search technique through all integral combinations of beam weights over a finite set of beam weights, taking into account any additional dose constraints. From the point of view of algorithmic efficiency, a directed search technique should significantly decrease execution time. Moreover, the algorithm completely ignores beam weight combinations that are not in the ratios of small whole numbers. An improved optimization scheme would consider the entire space of possible beam weights. A second shortcoming is that the same type of “brute force” search is used to evaluate beam combinations. A treatment planner would not, for example, consider the
April 1990, Volume 18, Number 4
use of a low energy electron beam to treat a boost volume at a depth beyond the range of the electrons, and yet, the EMIX algorithm evaluates all beam combinations for a specified machine, including clinically undesirable ones. An improvement to EMIX would allow for significantly more input by the planner to restrict the beam search to clinically reasonable modalities and energies. Another shortcoming of the EMIX algorithm is that dose specification is limited to areas of the same diameter. Of course, many treatment plans cover regions with different diameters. The optimization scheme would be improved if it allowed for the calculation of doses to selected points along multiple diameters. The final shortcoming of the EMIX algorithm, the one that has prompted implementation of a different approach, lies in the selection of the objective function used for optimization. The EMIX algorithm calculates the dose to a set of points from each beam and beam weight combination, calculates the square of the difference between the calculated dose and a desired dose, and sums this quality over a planner-defined set of points. The beam and beam weight combination that minimizes this objective function is considered to be the solution of the optimization problem. Unfortunately, this combination may not necessarily be clinically desirable. For example, the clinician may prescribe a uniform dose from the surface to some specified depth in the target volume for a parotid tumor using a set of appositional beams. The plan is to be optimized to deliver 57 Gy at the surface and 65 Gy from 0.5 cm to 4.5 cm depth. Dose is not to exceed 45 Gy at 5.5 cm, the minimum depth of the spinal cord, and 20 Gy at 12.0 cm, the location of the contralateral parotid. A linear accelerator with photon beams of 6 MV and 18 MV and electron beams ranging from 6 MeV to 20 MeV is to be used. The EMIX algorithm indicates that the optimal choice of treatment is a single 15-MeV electron beam with a given dose of 73.1 Gy. The central axis dose distribution for this plan is illustrated in Figure 1. Although the dose distribution meets all the optimization criteria, there may be some concern as to whether the 68.7 Gy delivered at the patient surface is too high and whether the 11% gradient between the dose at 3 cm and the dose at 4.5 cm is too large. The problem is not that the optimization scheme is faulty, but that the optimization criteria lead to a treatment plan that may not necessarily be clinically acceptable. Furthermore, if the physician declines to accept this selection of beam weights, the algorithm gives no indication as to how to modify the treatment plan. One approach to beam weight optimization that attempts to alleviate this problem is to replace the goal of minimizing an objective function with the goal of searching for any set of beam weights that yields a dose distribution within a set of acceptable bounds. Altschuler et al. (2) have argued that the minimization of an objective function is not at all necessary in solving a dose optimi-
959
Point dose optimization 0 G. STARKSCHALL efal.
weight distribution can then be used for the initial treatment of the patient and as a starting point for generating a complete plan using a more sophisticated treatment planning system. Feasibility constraints. The feasibility search problem as applied to dose optimization can be summarized in the following manner (4, 11): Given a set {j l Of Nj beams with weights Wj and a set {i} of Mi dose calculation points, find that set of beam weights such that
oI 0
5 Aij Wj I bi
for all
Wj 2 0.
j=l
2
4
6
depth
0
10
12
(cm)
Fig. I. Central axis dose distribution for single 15 MeV electron field. The beam weight was selected to minimize the difference in dose btiween that delivered by the field and a prescribed dose of 65 Gy for depths between 0.5 cm and 4.5 cm, while keeping the dose less than 45 Gy at 5.5 cm and 20 Gy at 12.0 cm depths.
zation problem. The clinically important quantities are not the ideal doses to points, but rather the upper and lower bounds to the acceptable values for doses to these points. For example, in the previous case, the clinical objective may not necessarily be to make the dose in the region from 0.5 cm to 4.5 cm as close as possible to 65 Gy. Rather, the important criterion governing the acceptability of the dose distribution is that the dose in that region lie between certain specified bounds, for example, 63 Gy and 67 Gy. But the approach to optimization must be altered to incorporate these optimization criteria. The next section describes how the dose optimization problem may be restated to search for any feasible solution, that is, any solution that satisfies the dose constraints.
Feasibility search algorithms General characteristics. The feasibility
search method presented in this study uses as input a set of maximum and minimum acceptable doses at several points designated by the clinician as well as an indication of the relative importance of the dose constraints at these points. If some set of beam weights can satisfy these specifications, the program will calculate them. If not, the system will indicate this failure to the clinician and suggest dose specifications that may achieve a feasible solution. Determination of the solution beam weight distribution or identification of its absence is extremely rapid; thus, the physician can vary the dose constraints and the radiation modalities interactively until a beam weight distribution that satisfies the dose constraints is found. This beam
* MicroVAX II computer, Maynard, MA.
Digital Equipment
Corporation,
In the above inequality following meanings:
the quantities
Aij and bi have the
1. For all specified points for which Df”““‘, an upper limit to the dose, is given, A, = dij, the dose per unit beam weight from beam j to point i, and bi = Dimax). This insures that the dose to point i does not exceed Dimax). 2. For all specified points for which Dimi”), a lower limit to the dose, is given, Aij = -dij and bi = -Dimin). This insures that the dose to point i is always greater than Dim’“‘. The quantities Dima”’ and Djm’“) are specified by the clinician based upon clinical experience, while the quantity dij is calculated according to an appropriate beam model. In this work, dij is taken to be the central axis depth dose, evaluated at the appropriate physical depth of the calculation point, multiplied by an appropriate factor to account for distance from the source. In the event the point is not included in the radiation field, then dij is set to zero. Several algorithms that search for a solution to the constraint inequalities have appeared in the literature; the one selected for this optimization problem is the one of Cimmino (5,6,7). The Cimmino algorithm is an iterative algorithm that takes a trial solution, tests the feasibility of each of the constraint equations, and modifies the trial solution based on the feasibility of each constraint equation. Unlike the “row-action” algorithms (3) that have also been used as feasibility searches to solve problems in dose optimization (1, 1 l), the Cimmino algorithm evaluates the feasibility of al1 the row inequalities before making any iteration steps. As a result, if the dose constraints yield no feasible solution, the final solution calculated by the algorithm is independent of the order of row action. Although the Cimmino algorithm converges more slowly than some of the other algorithms ( 12), the size of the dose constraint matrices used in this problem are sufficiently small that results are obtained in less than a few seconds of CPU time.$
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I. J. Radiation Oncology 0 Biology 0 Physics Table la. Initial dose bounds Dose bound
for carotid
April 1990, Volume 18, Number 4
e”T
test case
(Gy)
Depth (cm)
Lower
UDDer
0.0 0.5 2.0 3.5 4.5 5.5 12.0
54.0 63.0 63.0 63.0 63.0 -
60.0 67.0 67.0 67.0 67.0 45.0 20.0
1.0 1.0 1.0 1.0 1.0 10.0 1.0
The Cimmino algorithm also has an advantage over several other feasibility search algorithms in that one may incorporate importance weighting into the dose specifications. It is possible to designate certain points as being more important to the optimization than other points and have the algorithm take this into account when searching for a feasible solution. For example, one can specify an upper bound to the dose to the spinal cord and designate it with an importance greater than that given to the doses to other regions. The algorithm will then proceed to search for a feasible solution to the dose constraint problem with a greater emphasis placed on satisfying the dose constraint at the spinal cord. Finally, the feasibility search algorithm has been incorporated into an interactive driving program. The philosophy behind the driving program, which is a key element of this point dose optimization system, is that this system is to be viewed as a “treatment planning tool” designed to assist the treatment planner find an acceptable set of beam weights, rather than as an automatic method of solving the inverse radiotherapy problem. For many treatment planning cases, a specified set of dose constraints may not lead to any feasible soluton. The driving program has been designed so that if no feasible solution to the dose constraints exists, the program offers the clinician the opportunity to modify any of the dose constraints, any of the beams, or any of the dose specification depths, and repeat the feasibility search. Unlike the more conventional trial and error approaches, in which the planner modifies the beam weights and evaluates the resultant dose distributions, this approach provides the planner the opportunity to modify the range of acceptable outcomes, and then attempts to find a set of beams weights that provides a dose distribution that falls within the acceptable
Table lb. Beam weights after 500 iterations bounds in Table 1a
using the dose
Modality
Beam weight (Gy)
6 MV photons 18 MV photons 12 MeV electrons 15 MeV electrons 20 MeV electrons
6.2 6.6 13.7 21.6 19.2
I[
60
Relative imuortance
ii
It1 X
t
+z
s
X
40 -
8 % 20 -
0
0
-I
,,,,‘,,,,‘,,,-‘,,,,‘,,ll’,,,‘_ 2 4
6 depth
a
10
12
(cm)
Fig. 2. Central axis dose distribution for first parotid test case. Dose bounds are summarized in Table la and denoted by the dark vertical line. Beam weights are summarized in Table lb, yielding doses denoted by the symbol X.
dose ranges. The clinician is also offered the opportunity to accept any plan that has been determined by the feasibility search algorithm, even if the plan does not satisfy all the dose constraints. The final evaluation of the treatment plan remains the responsibility of the clinician. Clinical examples Parotid bed. Several examples of the use of the feasibility search algorithm in an interactive optimization program are presented. The first example is the one presented in an earlier section of this paper as one in which the traditional optimization methods may not necessarily yield an acceptable solution. In this application, rather than specifying optimal doses, one specifies upper and/or lower bounds to the doses at selected depths as well as a set of beams to be considered in the search for a feasible solution. In this example, the patient has a squamous cell carcinoma of the skin metastatic to the superficial parotid lymph nodes. The primary is completely resected and a superficial parotidectomy performed. The parotidectomy pathology specimen has a negative deep margin but tumor extends through the nodal capsule into the superficial parotid tissue. Postoperative radiotherapy is to be directed to the parotid tumor bed and the ipsilateral upper neck region. The dose constraints for the parotid tumor bed are specified as follows: Surface dose is constrained to between 54 Gy and 60 Gy. The dose to the superficial
Table 2. Beam weights after 500 iterations using the 6 MV ohoton and 15 MeV electron beams onlv Modality
Beam weight (Gy)
6 MV photons 15 MeV electrons
12.0 56.8
Point dose optimization 0 G. STARKSCHALL et al.
961
Table 4a. Beam weights after 500 iterations using the dose bounds in Table 3a with both on-cord and off-cord fields Beam weight (Gy) Modality
Incl. cord
Off cord
strip
6 MV photons 18 MV photons 9 MeV electrons 12 MeV electrons 15 MeV electrons 20 MeV electrons
11.1 8.6 2.1 16.1 12.0
4.4 3.3 0.0 4.5 8.7
0.0 9.8 10.5 -
Table 4b. Dose distribution
for beam weights in Table 4a Dose (Gy)
depth
(cm)
Fig. 3. Central axis dose distribution
for two beam plan for first parotid test case. Beam weights are summarized in Table 2. Dose bounds are denoted by the dark vertical line and doses are denoted by the symbol X.
parotid tumor bed at a depth of 0.5 cm to 4.5 cm is constrained to between 63 Gy and 67 Gy delivered at 2 Gy per fraction. The dose to the spinal cord at a minimum
Table 3a. Initial dose bounds for second parotid case Dose bound (Gy) Depth (cm)
Lower
Upper
63.0 63.0 63.0 63.0 -
67.0 67.0 67.0 67.0 45.0 20.0
0.0
Relative importance 1.0 1.0 1.0 1.0 1.0 10.0 1.0
50.0
0.5 2.0 3.5 5.0 5.5 12.0
Table 3b. Beam weights after 500 iterations using the dose bounds in Table 3a Modality
Beam weight (Gy)
6 MV photons 18 MV photons 12 MeV electrons 15 MeV electrons 20 MeV electrons
14.9 1.8 3.9 46.5 0.0
Depth (cm)
Primary diam
Cord diam
0.0 0.5 2.0 3.5 4.5 5.0 5.5 12.0
46.2 61.2 69.9 69.0 60.7 19.9
51.1 61.9 69.5 67.1 58.4 45.2 14.4
depth of 5.5 cm is not to exceed 45 Gy. Finally, the dose to the contralateral parotid at a depth of 12 cm is not to exceed 20 Gy. All points are given a relative weighting of 1 except for the spinal cord, which is given a weighting of 10. We have found that selecting this weighting scheme insures that the dose constraint on the cord is rigidly adhered to. A feasible solution was sought involving 6 MV and 18 MV photons and 12 MeV, 15 MeV, and 20 MeV electrons. After 500 iterations, requiring less than 30 sec-
Table 5a. Final beam weights for second parotid case Beam weight (Gy) Modality
Incl cord
Off cord
strip
6 MV photons 15 MeV electrons 20 MeV electrons
19.4 4.2
9.6 35.2
44.7 -
Table 5b. Dose distribution
for beam weights in Table 5a Dose (Gy)
Table 3c. Dose distribution Depth (cm) 0.0
0.5 2.0 3.5 5.0 5.5 12.0
for beam weights in Table 3b Depth (cm)
Primary diam
Cord diam
0.0 0.5 2.0 3.5 4.5 5.0 5.5 12.0
44.5 62.5 68.0 65.6 61.6 20.0
50.5 62.9 68.1 65.3 58.2 45.0 13.1
Do= (GY) 50.2 60.8 66.4 65.2 51.9 43.2 11.4
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Table 6a. Initial dose bounds for tonsillar fossa test case Dose bound (Gy) Region
Depth (cm)
Lower
Upper
Primary (excluding boost)
1.0 2.0 7.5 (midline) 13.0 14.0 1.0
52.0 52.0 52.0 52.0 52.0 52.0
56.0 56.0 56.0 56.0 56.0 56.0
1.0 1.0 1.0 1.0 1.0 1.0
6.0 (midline) 11.0 2.0 4.0 6.0 7.5 (midline) 8.0 10.0 14.0
0.0 52.0 68.0 68.0 68.0 52.0 52.0 52.0 52.0
45.0 56.0 72.0 72.0 72.0 64.0 64.0 62.0 58.0
10.0 1.0
Post cervical area at pt of max cord dose
Boost
onds of clock time on a multi-user system,* no feasible solution is found, but the resulting set of given doses gives a dose distribution that the clinician has determined to be acceptable. The lower dose at 4.5 cm is acceptable since the tumor only involved the superficial parotid lobe. The dose constraints and beam weight distribution are displayed in Tables la and lb, and resulting dose distribution in Figure 2. To simplify the treatment plan, an additional run is performed using only 6 MV photons and 15 MeV electrons. The beam weights resulting from this run are displayed in Table 2 with the dose distribution in Figure 3. In this case the two dose distributions appear similar, with the exception that the dose to the parotid at 0.5 cm has been reduced from 66.6 Gy to 63.7 Gy, whereas the dose at 4.5 cm has been raised from 58.7 Gy to 61.2 Gy. In this case the two-beam treatment appears to be superior, both because of the dose distribution and because of the decrease in complexity. In a second example, an adenoid cystic carcinoma of the parotid is situated at the junction of the superficial and the deep lobes. The facial nerve sparing resection removes all the gross tumor; however, microscopic tumor is left on the facial nerve. Postoperative radiotherapy is to be directed to the paortid tumor bed and to the facial nerve all the way to its exit from the stylomastoid foramen. The dose constraints are specified as follows: Surface dose is not to exceed 50 Gy. Dose to the parotid, lying at depths between 0.5 cm and 5.0 cm, is constrained to lie between 63 Gy and 67 Gy given at 2 Gy per fraction. Dose to the spinal cord at a minimum depth of 5.5 cm is not to exceed 45 Gy. Finally, dose to the contralateral parotid at a depth of 12.0 cm from the beam entry surface is not to exceed 20 Gy. As in the previous example, all points except the spinal cord are considered to be of equal importance and given a relative value of 1, whereas the cord is given an importance of 10. These dose bounds are summarized in
Relative importance
1.0 1.0 1.0
1.0 1.0 1.0 1.0
Table 3a. A feasible solution is to be achieved by 6 MV and 18 MV photon beams and 12 MeV, 15 MeV, and 20 MeV electron beams. The Cimmino algorithm is used to find a feasible solution, allowing no more than 500 iterations. After 500 iterations, no solution satisfying the dose constraints is Table 6b. Beam weights after 100 iterations using the dose bounds in Table 6a Beam no
Description
Modality
Beam weight (Gy)
1 2 3 4 5 6 7 8 9
Total volume-rt Total volume-h Off cord-rt Off cord-h Post e strip-rt Post e strip-h Boost volume-rt Boost volume-h Boost volume-rt
Cobalt 60 Cobalt 60 Cobalt 60 Cobalt 60 10 MeV electrons 10 MeV electrons 18 MV x-rays 18 MV x-rays 18 MeV electrons
28.5 27.9 10.4 9.7 11.1 11.4 6.1 3.7 9.4
Table 6c. Dose distribution Region Wide field treatment
Post cervical area at pt of max cord dose Total treatment including boost
for beam weights in Table 6b Depth (cm)
Dose (Gy)
1.0 2.0 7.5 (midline) 13.0 14.0 1.0 6.0 (midline) 11.0 2.0 4.0 6.0 7.5 (midline) 8.0 10.0 14.0
55.0 54.4 52.2 53.8 54.3 52.0 41.2 52.0 72.2 71.0 67.7 64.2 63.1 61.4 61.5
Point dose optimization 0 G.
STARKSCHALL
963
et al.
Table 7a. Initial dose bounds for buccal mucosa test case Dose bound (Gy) Region Wide field treatment
Post cervical area at pt of max cord dose
Total treatment including boost
Depth (cm)
Lower
Upper
1.0 3.0 6.0 (midline) 9.0 11.0 1.0 7.0 (midline) 13.0 1.0 3.0 6.0 (midline) 9.0 11.0
48.0 48.0 48.0 48.0 48.0 48.0 0.0 48.0 66.0 66.0 66.0 48.0 48.0
52.0 52.0 52.0 52.0 52.0 52.0 45.0 52.0 70.0 70.0 70.0 56.0 52.0
found. The given doses and calculated doses provided as output after the iterations are shown in Tables 3b and 3c. As seen from Table 3c, the large dose gradient required between the target volume depth of 5 cm and the minimum spinal cord depth of 5.5 cm is not likely to be achievable. Due to these constraints, substitutions of a reduced dose off the spinal cord and lower energy electrons to supplement treatment to the region overlying the spinal cord are specified. The beam weights and dose distribution for this revised plan are shown in Tables 4a and 4b. As can be seen, by making the necessary off-cord reduction, a higher electron energy can be used to increase the target volume at a depth of 5 cm. To minimize complexity the plan is reoptimized eliminating beams with relatively low given dose weightings. The new plan uses only the 6 MV photons combined with 20 MeV electrons for the region not overlying the cord and 15 MeV electrons for the region overlying the cord. The beam weights and depth dose distribution are shown in Tables 5a and 5b. Tonsillar fossa. Perhaps the most frequent cases in which optimization of photon and electron beam combinations occur are those in which the primary and upper neck are treated with parallel opposed low-energy photons to, control subclinical disease, followed by a boost to the gross tumor. An illustrative case is the treatment planning for a flat 5 cm squamous cell carcinoma of the right tonsillar fossa in which no nodes are clinically positive. It is desired to treat subclinical disease to between 52 Gy and 56 Gy at 1.8 Gy per fraction, using parallel opposed lateral cobalt fields. At a maximum spinal cord dose of 45 Gy, the lateral photon fields are to be reduced off the spinal cord and the posterior cervical lymph node areas supplemented with 10 MeV electron strips. The tonsillar primary is 4 cm below the right skin surface. The boost is planned to give a dose of 68 to 72 Gy at a depth from 2 cm to 6 cm. Optimization for the boost was done using parallel opposed 18 MV photon beams, as well as an ipsilateral 18 MeV electron beam. After 500 iterations, no feasible
Relative importance 1.0 1.0 1.0 1.0 1.0 1.0 10.0 1.0 1.0 1.0 1.0 1.0 1.0
solution that satisfies all constraints was found; however, the dose distribution resulting from these beam weights was considered acceptable by the clinician. The dose constraints, optimal beam weights, and resulting dose distributions are displayed in Tables 6a, 6b, and 6c. Buccal mucosa. Another example of combining photon and electron fields is illustrated by the case of a 5 cm squamous cell carcinoma of the right buccal mucosa with extension through the retromolar area to the ipsilateral
Table 7b. Beam weights after 500 iterations using the dose bounds in Table 7a Beam no.
Description
Modality
Beam weight (Gy)
1 2 3 4 5 6 7
Total volume-t? Total volume-lt Off cord-t? Off cord-lt Post e strip-rt Post e strip-h Boost volume-rt
Cobalt 60 Cobalt 60 Cobalt 60 Cobalt 60 9 MeV electrons 9 MeV electrons 20 MeV electrons
24.6 26.5 6.4 8.7 11.1 10.6 20.6
Table 7c. Dose distribution Region Wide field treatment
Post cervical area at pt of max cord dose Total treatment including boost
for beam weights in Table 7b Depth (cm)
Dose (Gy)
1.0 3.0 6.0 (midline) 9.0 11.0 1.0 7.0 (midline) 13.0 1.0 3.0 6.0 (midline) 9.0 11.0
49.7 49.5 49.6 50.6 51.5 48.0 37.9 48.5 70.1 70.0 65.9 54.0 52.0
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I. J. Radiation Oncology 0 Biology0 Physics
soft palate. The neck nodes are clinically negative. The initial treatment volume includes the primary and bilateral upper neck lymph node regions. Parallel opposed lateral 6oCo fields are to be used. These fields are to be reduced to maintain spinal cord tolerance, and 9 MeV electron fields are to be used to supplement treatment to the area overlying the spinal cord. The final boost volume to the primary tumor was accomplished with an ipsilateral 20 MeV electron field. The optimization criteria are summarized in Table 7a. The dose of 48 Gy to 52 Gy at 2 Gy per fraction is selected for subclinical disease and 66 Gy to 70 Gy for areas of gross disease. The target volume around the primary tumor extends from 1 cm to 6 cm below the right skin surface. Although convergence is not achieved in 500 iterations, the dose distribution resulting from the optimization lies within 0.1 Gy of the specified dose bounds and is thus accepted. The beam weights and resulting doses are also illustrated in Tables 7a and 7b.
April 1990, Volume 18, Number 4
SUMMARY An interactive system for optimizing point doses has been developed that offers the following features: Dose optimization
points may lie at any point within the patient volume. Optimization is achieved by specifying dose bounds to optimization points and beams to be considered. The system will search for any combination of weights of the specified beams such that the dose lies within these bounds. The relative importance of optimization points can be specified. Although dose constraints frequently lead to infeasible solutions, the system allows the user the opportunity to change either dose constraints or beams, and reoptimize. At any point in the process the user may accept a solution and record it.
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7. Cimmino, G. Calculo approssimato per le soluzioni dei sistemi di equazioni lineari. Ricerca Sci. Roma 1938-XVI, ser II, anno IX, 1:326-333; 1938. 8. Doppke, K. P., Goitein, M. A survey of the information gained from planning treatment with a computer. Med. Phys. 15:258-262; 1988. 9. Fields, R. S.; Hogstrom, K. R. Computer model for combining electron and photon beams. In: Paliwal, B. R., ed. Proceedings of the Symposium on Electron Dosimetry and Arc Therapy, AAPM Symposium Proceedings #2. New York, NY: American Institute of Physics; 1982: 16 l- 180. 10. Fields, R. S.; Spanos, W. J.; Tapley, N. duV.; Cundiff, J. H.; Sampiere, V. A. Computer optimization for combining electron and photon beams (Abstr.). Int. J. Radiat. Oncol. Biol. Phys. 6: 1444; 1980. 11. Powlis, W. D.; Altschuler, M. D.; Censor, Y.; Buhle, Jr., E. L. Semi-automated radiotherapy treatment planning with a mathematical model to satisfy treatment goals. Int. J. Radiat. Oncol. Biol. Phys. 16:27 l-276; 1989. 12. Starkschall, G. Considerations for optimization of dose distributions for conformal radiation therapy (Abstr.). Radiology 165(P):185; 1987.
