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A planning method for 125I implants in cancer therapy

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1990 Phys. Med. Biol. 35 1633 (http://iopscience.iop.org/0031-9155/35/12/004) View the table of contents for this issue, or go to the journal homepage for more

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Phys. Med. Biol., 1990,

Vol. 35, No 12, 1633-1640. Printed in the UK

A planning method for 1251implants in cancer therapy H Meninghert, V Benaryt, S ChaitchickS and S Akselrodt t Tel Aviv University,TheSchool of Physics and Astronomy, PO

Box 39040, Tel Aviv 69978, Israel $ Tel Aviv Sourasky Medical Center, 6 Weizman Street, Tel Aviv 64239, Israel Received 27 September 1989, in final form 25 June 1990 Abstract, A method for planning implants of'"I seeds has been developed. The treatment dose prescribed by the physician is delivered to the tumour, as uniformly as possible, by of seedsandtheirlocationsarederivedby aminimalnumberofseeds.Thenumber requesting that, at any point in the tumour, the dose will be equal to or higher than the prescribed dose. As a result, the total implanted activity is lower for small volumes and higher for large volumes, relative to other implantation protocols which derive their planning from requests on the minimum peripheral dose. Results obtained from computer simulations performed on different tumour shapes and volumes, show a linear dependence between the total implanted activity and the tumour volume. The total activity does not depend on the shape of the tumour. A description of the algorithm of our procedure and a detailed example of its application are presented.

1. Introduction

Permanent interstitial implantswith "'1 seeds are frequently employed in the treatment of different typesof cancer. Thephysical properties of the "'I seeds make them suitable mainlyforlongterm, low energyirradiation of slowlyexpandingtumours.The implantationplanning is usuallyperformedaccordingtothe well knownaverage dimension method (Anderson and Ding 1975). The parameters used to describe the tumour dose (Laughlin et al 1963) are the minimum peripheral dose (MPD), defined as the lowest dose found at the intersection of the periphery of each seed array and a plane halfway the planes carrying the seeds, and the maximum central dose (MCD),defined as the maximum dose foundin a plane halfway between the planes carrying the seeds. The dependenceof MPD as a functionof tumour volume, obtained from theaverage dimension method in a previous study (Rao et a1 1981),showed that: (1) the M P D takes a certain value for every given tumour volume, without relation to the treatment requirements, (2) the MPD decreases steeply from360 Gy (36000 rad) forsmall tumours down to 200 Gy (20000 rad) for larger tumours. A similar reduction occurs in the dose delivered to the entire tumour. Using the average dimension method (Anderson and Ding 1975), we carried out several computer simulations to obtain the dose distributionin various tumour shapes and volumes. The results were to be used as a basis for reference and comparison. We found it difficult to comply with the inter-seed separation resulting from this method (Anderson and Ding 1975, Anderson 1976), since it is specified for seeds in a cubic lattice, not taking into account the tumour geometry. In addition, in some of the cases, our computations showed that doses as low as 60% of the specified M P D occurred inside the tumours. 0031-9155/90/121633+08$03.50 LtdPublishing @ 1990 IOP

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The average dimension method combines a protocol for determining the dose to be delivered to the tumour, with a fast and simple method for calculating the actual implantation parameters. However, the assumption that small tumours tolerate larger radiation doses, which is in agreement with the Memorial Protocol (Anderson and Ding 1975), is no longer generally accepted (Rao et a1 1981). Based on these considerations, it was our aim to develop an implantation planning systemwhichevaluates the total activity and actual seedsitesrequired in order to deliver a tumour dose prescribed by the physician. The dose should be distributed as uniformly as possible over the tumour volume, while taking into account the tumour shape and volume, the activity of the available seeds and the technical limitations imposed by the implantation procedure.

2. Methods 2. l . General principles

Ideally, the implantation planning should result in a uniform dose distribution which is equal to the prescribed dose ( P D ) everywhere inside the tumour, and drops to zero outside the tumour. It is clear, however, that such a result cannot be achieved when using seeds which inevitably create a point of singularity in the absorbed dose curve. Consequently,whentheterm‘uniformity’ is mentionedinthiswork, it should be understood in the followingsense:the tumourdose will beconsidereduniformly distributed and assigned a value which equals PD if doses lower than PD do not occur in the tumour, and the numberof seeds in the tumouris the minimal needed to deliver such a dose distribution. The principles of the planning can be summarized in the following three statements. 1. The tumour dose is determined by the physician, based on a dose prescription protocol of his choice. 2. Doses lower than P D should occur at no point inside the tumour. 3. The number of seeds to be implanted must be the minimum needed to satisfy principles 1 and 2.

2.2. Basic approach to the planning procedure

In order to fulfil the above requirements, we defined rl12as the distance from a single seed where the dose, D, drops to 0.5 PD, i.e. D ( r l , * )= 0.5 PD. The location of two neighbouring seeds at a distance of 2 r I l 2 will force the isodose which equals PD to passthroughthemiddlepoint betweenthoseseeds(figure 1). Thisbasicdistance between two seeds should be adjusted for an arrayconsisting of more than two seeds, because the other, more distant seeds, will increase the dose above PD. In addition to the rl12requirement, the outermostseed shell is located so that the PD isodose encloses the tumour volume. Thus, the occurrence of cold spots in the tumour is prevented. If the distance between neighbouring seedsis further increased, the dose at a point midwaybetweentwoseeds will drop below PD, resulting in coldspotsinsidethe tumour, On the other hand, decreasing the distance between neighbouring seeds will cause an unnecessary increase in the total number of seeds inside the tumour. Thus, this arrangement ensures that the number of seeds in the tumour is indeed optimal with respect to dose uniformity.

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Y

2.r1,z Figure 1. Two neighbouring seeds (small crosses) are placed at a distance passes through the middle point between them.

of 2 r , , 2 , and the

PD

isodose

2.3. Planning algorithm The shape and dimensions of the tumour are obtained from CT scan or radiographs. As the next step, the tumour must be divided into slices of equal height. The seeds will be distributed on the central plane of each slice, shell by shell,followingthe symmetry of the tumour. The outermost shell of seeds is first distributed on all the seed planes, so that the isodose equal to PD encloses the tumour. If the dose at any point in the tumour is lower than PD, an inner shellmustbe added. The distance between neighbouring shells is calculated so as to constrain the isodose which equals PD to the curve midway between the shells. Also, the dose on theplaneshalfway between the seed planes should not dropbelow PD. If this occurs, the dose is increased by iteratively decreasing the distance between neighbouring seeds in the seed planes. The algorithmof the proposed planningsystem can be summarized in the following steps. 1. Input: (a) Tumour shape and volume. (b) Dose to be delivered to the tumour. (c) Activity of the available seeds. 2. Define the planes that will carry the seeds. 3. Distribute the seeds in all the seed planes, shell by shell, starting with the outermost shell,whilefollowing the symmetryof thetumour.Computethetumourdose distribution after each shell addition. Keep the minimum dose on the seed planes equal to PD. 4. If the dose on the planes halfway between the seed planes is lower than PD, go back to step 3 and increase the dose in the seed planes by decreasing the distance between neighbouring seeds. 5 . output: (a) The number of seeds and the total activity to be implanted. (b) The precise location (coordinates)of every seed in the calculated configuration. 2.4. Software

The analysis of the results of existing planning systems and the development of a new planning system for ''1 implants required dosimetric calculations for various seed configurations. We therefore developed an interactive computer program, to assist the

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user in the planning process, and to calculate the resulting dose distributions. The dose distribution of the individual seeds is based on thematrix fit approximation (Ling et al 1985), which takes into account the angular dependence of the dose distribution around the 1-125 seed. The program has been written in the PASCAL programming language and developed on an Olivetti M24 personal computer, with 8086 mathematic coprocessor. The computing time is 6 S per seed. This flexible dosimetry program has been used as a research tool throughout our entire study, to assess the performance of the seed implantation algorithm. In fact, it represents an integral part of our implantation method, supporting the user at each step of the planning procedure.

2.5. Practicalconsiderations The planning system musttakeintoaccounttechnicallimitationsimposed by the currently employed implantation technique.First, the distance between the seed planes can be varied in multiples of 0.5 cm only. In addition, the seeds are inserted into the tumour in arrays, each array by a separate needle. In order to minimize the number of needles, each needle should contain a seed for every seed plane. Whenever possible, it is preferable to select the direction of access of the needles along the mainaxis of the tumour (Bauer-Kirpeset a1 1988). The seedswill be oriented of each seed parallel to the direction of implantation. Theoretically, the orientation can be determined by the post implantation seed identification process, due to the high radiopacity of the silver wire. Practically, however, it is not an easy task to find the exact orientation of every seed in an array consisting of a large number of seeds. The original orientation of the seeds at the time of implantation can be taken as a good first approximation in the dosimetric calculation. If many seeds rotate randomly aftertheimplantation,thepointapproximation may beused in thecomputations instead of the matrix fit, without causing significant difference in the resulting dose distribution. 3. Calculations and results

3.1. An example of the use of our algorithm To illustrate the use of our algorithm, we hereby apply it to a cylindrical tumour with radius, r = 1.5 cm, height, h = 3 cm and volume, V = 21.2 cm3. A dose (PD) of 160 Gy (16 000 rad) must be delivered to that tumour and theactivity, A of the available seeds is 18.5 MBq (0.5 mCi). First, we must decide which planeswill carry the seeds. A distance of 1 cm between the seed planes is suitable for 18.5 MBq seeds because it will not cause hot or cold spots on the planes midway between the seed planes. Our choice of the direction of implantation along the cylinder axis (Bauer-Kirpes et a1 1988), makes it possible to select the seed planes at h = 0.5, 1.5 and 2.5 cm, or at 0, 1, 2 and 3 cm. If we choose the first option, the top and bottom planes of the tumour ( h = 0 and 3 cm)will contain cold spots. Therefore, we decide to implant four planes at h = 0, 1, 2 and 3 cm. The seedaxes will beorientedperpendicularlytotheseedplanes.Thebasicdistance between two seeds in a seed plane, defined as 2 r , , 2 r which was computed using the matrix fit (Ling et a1 1985), equals 0.9 cm. The distance of the outermost seed shell from the tumour periphery mustbe 0.1 cm in order to have the 100% PD isodose

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enclosing the whole tumour. Using these values, the number of seeds as well as the coordinates of the seeds in the outermost shell can be found. As a result, ten seeds will be located in the outermost shell at r = 1.4 cm, with a distance of 0.9 cm between neighbouring seeds. An identical shell design is placed on all the other seed planes. As the nextstep,thedosedistribution in theentiretumour is checked.The computation shows that the dose on the tumour axis drops to 75% PD. Therefore, one more seed has to be added in the centre of every seed plane. Computing again the dose distribution in the tumour, we observe already after this first iteration that the minimal tumour dose (MTD) equals 100% PD, while M C D = 136% PD. We thus obtained a distribution which complies with our requirements. Hence, the tumour will be implanted with 4 planes of 11 seeds each, and the total activity will be 814 MBq (21 mCi). Figure2 shows the resulting isodose distribution in several planes, as well asthelocation of theseeds in the implant. It is clearfromthedisplayed isodoses, that in all the planes considered, the dose is equal to or higher than PD. No cold spots occurred at any point in the tumour. The same procedure has been applied to cubic, cylindrical and spherical shaped tumours, ranging in volume from 1 to 125 cm3. Similarly to the example described above in detail, the calculations resulted in dose distributions with MTD? PD, without cold spots occurring.Based on these computations, we plotted thetotal activity required -2

-1

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Figure 2. Isodose distribution on selected planes in a cylindrical tumour with radius, r = 1.5 cm, height, h = 3 cm and volume, V = 21.2 cm3. 44 seeds (small crosses) are implanted in 4 planes, located at z = 0, 1, 2 and 3 cm. The total implanted activity, A =S14 MBq (22 mCi). ( a ) z = 0 , 3 cm, ( b ) z =OS, 2.5 cm, ( c ) z = 1, 2 cm, ( d ) z = 1.5 cm. ..... 75%, - loo%, . . . .125%.

etH Meningher

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to deliver 160 Gy (16000 rad) for the different shapes and volumes that have been checked (figure 3). All the points can be fitted by one curve. The total activity has a linear dependenceon the tumourvolume, and it does not dependon the tumour shape. 4. Discussion andsummary

The new concept behind our procedure is the elimination of the linkbetween the tumour volume and the total activity to be implanted in the tumour. The selection of PD, rather than the tumour volume, or the average dimension of the tumour, as the essential parameter in our planningsystem, resulted in the linear dependence between the totalactivity required to deliver 160 Gy (16000 rad) and the tumour volume, without any dependence on the tumour shape. The total activity required to deliver a certain treatment dose is higher than the activity prescribed by other protocols (Anderson and Ding 1975, Krishnaswamy 1979, Rao et a1 1981, Wu et a1 1985), but the increase in the activity is necessary if cold spots are to be avoided. The 160 Gy value has been selected because it is the dose which is often used in implantation treatments, and it was a convenient value for comparisonof results. It should be stressed that our method is not limited to any specific dose value planning, and if the steps described in our algorithm are followed, a dose distribution with MTD 2 PD can be easily configured. Furthermore, our method is valid for other types of seeds as well (like, for example, samarium-l45 (Fairchild et a1 1987)), provided that their dose distribution is known.

0

50

100 Tumour volume [ c m 3 )

150

200

Figure 3. The total activity required to deliver 160 Cy (16000 rad) as a function of tumour volume.

The maximum central dose was not considered in this work, since the planning method that we developed results in the minimal number of seeds that are required to deliver the prescribed dose to the tumour volume. In order to lower the MCD, the number of seeds or the total activity in the tumour must be decreased, but this would cause MTD to fall below PD, which is not allowed by our method. Therefore, M C D is not a free parameter, but a constraint thatmay not be adjusted without tamperingwith the whole dose distribution. On the other hand, dose distributions with a low PD for adefiniteregion of the tumour (like, for example, whenaradiosensitiveorgan is locatedinclose vicinity to the tumour), can be easilyconfigured, by dividing the tumour into two parts, and by planning for each part separately.

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Another feature thatsingles out our methodis the fact that it is based on numerical, andnotempiricalgrounds. An attempt to developatheoreticalmodelhasbeen originally made, but the singular natureof the seeds dose distribution and the practical constraints imposed by the implantation procedure made the theoretical solutionvery difficult, and the only feasible solution was the numerical one. The '*'I seeds were approximated by the matrix fit (Ling et a1 1985), rather than the less accurate point approximation (Anderson1976), since we requested our method to be very sensitive to variations in MTD. MTD often occurs on the tumour periphery, and it has been shown (Ling et a1 1979) that the use of the point approximation may result in a decrease of up to 25% in the tumour peripheral doses. In addition, the computation time is not affected by the type of approximation employed, so the use of the matrix fit seems to be the natural choice. It is often the case that tumours which are treated by 1-125 seed implants can be approximately looked upon as regular shapes, or as a combination of regular shapes. The case of the tumour outline differing in adjacent seed planes is encountered, for example, in the case of a spherical tumour. We did not detail the treatment planning of a spherical tumour, since it seems too tedious for an introductory paper, and the basic principles of our method are well described by the example of the cylindrical tumour. The planning for a spherical tumour is accomplished by planning the seed distribution on the central plane of the sphere. Each other seed plane consists of the replication of the inner seed shells of the adjacent larger seed plane. For example, in a sphere which must accommodate five seed planes, we can implant three seed shells on the central plane, but only thetwo inner seed shells will be implanted on the planes adjacent to the central plane. The upper and lower planes will be implanted with the inner shell only. If the sphere dimension can accommodate an even number of seed planes, six for example, we will start the planning from the two identical seed planes which are adjacent to the central plane, and the central plane itself will carry no seeds. Theplanningforatumour with highirregularities (a star-shapedtumour,for example) cannot be done automatically. The physicist must determine if he prefers to implant the seeds in arrays and sometimes give a higher dose to the tumour, or to implant the minimal number of seeds but to use a larger number of needles. The accuracy of the placement of a seed in the implant is limited due to the current implantation techniques and needles used. In addition, even if the implantation has been extremely accurate, the seedscan still rotate and even migrate after theirimplantation in the tumour. This is true regardless of the planning system that is being used. For implants with a large number of seeds, the effect on the dose delivered to the tumour is minor,however, the dose uniformitycanbecomepoor. We believe that practical implantation difficulties are not a sufficient reason to neglect accuracy at the planning stage and implant the seeds randomly. Starting a radiation treatment from an optimal planning would have a better chance of creating the required dose distribution in the implanted tumour. Itcertainly would be desirable to compare the computed dose distribution with the dose distribution actually obtained in the tumour under various conditions of implantation according to our planning technique. In conclusion, the presented planningsystem provides a fast and flexible procedure for the design of "'I implants. A user-friendly computer program has been developed as well, to allow fast and accurate dosimetric calculations before and after the implantation. As a result, the physician can easily find the total activity, the number of seeds andtheiractuallocations, which arerequired in ordertoensureanoptimaldose distribution inside the tumour.

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RBsume Description d'une mtthode de mise au point d'un plan de traitement par implantation d'lode

125,

Les auteurs ont mis au point une mtthode de planification des traitements par implants de grains d'lode 125. La dose prescrite par le mtdecin est dClivrCe B la tumeur avec une distribution aussi uniforme que possible en utilisant un nombre minimal de grains. Le nombre et I'emplacement des grains est dtfini de telle sorte qu'en tout point de la tumeurla dose soit Cgale ou suptrieure zi la dose prescrite. En constquence, I'activitt totale implantbe est plus faible pour les petits volumes et plus tlevte pour les grands volumes, comparativement aux autres protocoles d'implantation dont les mtthodes de prtparation tiennent compte du fait que la dose doit itre minimale en ptriphtrie. Les rtsultats obtenus B partirdesimulationspar ordinateur effectuts sur des tumeurs de formes et de volumes difftrents, montrent qu'il existe une relation lintaire entre l'activitt totale implantbe etle volume tumoral, I'activitt totale ne dependant pas de la forme de la tumeur. Les auteurs prtsentent enfin une description de I'algorithme utilist pour cette mtthode et un exemple dttaillt de son application.

Zusammenfassung Ein Bestrahlungsplanungsmethode fur '2SI-Implantate in der Krebstherapie. Es wurde eine Methode zur Bestrahlungsplanung von implantierten 1251-Seeds entwickelt. Die vom Arzt verschriebene Behandlungsdosis wird dabei dem Tumor so gleichformig wie moglich mit einer minimalen Anzahl von Seeds verabreicht. Die Anzahl der Seeds und ihre Lage wird bestimmt durch die Forderung, da13 in jedem Punkt des Tumors die Dosis gleich oder hoher als die verschriebene Dosis ist. Daraus ergibt sich, daB die implantierte Gesamtaktivitat niedriger ist fur kleine Volumen und hoher fur gro13e Volumen verglichen mit anderenImplantations-Protokollen, die die Daten fur die Planung ableiten von der Forderung einer minimalen peripharen Dosis. Die Ergebnisse von Computersimulationen, die fur verschiedene Tumorformenund-volumendurchgefuhrtwurden,zeigeneinelineareAbhangigkeitzwischendergesamten Form des Tumors implantierten Aktivitat und dem Tumorvolumen. Die Gesamtaktivitat hangt nicht von der ab. Eine Beschreibung des Algorithmus dieses Verfahrens und ein ausfuhrliches Anwendungsbeispiel wird vorgestellt.

References Anderson L L 1976 Spacing nomograph for interstitial implants of '"1 seeds Med. Phys. 3 48-51 AndersonLLandDing I Y 1975 DosimetricConsiderations for lodine-125 Afterloading: 20 Years of Experience, 2955-2975 ed B S Hilaris (New York: Memorial Sloan-Kettering Cancer Center) pp 63-72 Bauer-Kirpes B, Sturm V, Schlegel W and Lorenz W J 1988 Computerized optimization of lZsl implants in brain tumours Int. J. Radiat. Oncol. BioL Phys. 14 1013-23 Fairchild R G, Kalef-Ezra J, Packer S, Wielopolsky L, Laster B H, Robertson J S, Mausner L and Kanellitsas C 1987 Samarium-145: a new brachytherapy source Phys. Med. Biol. 32 847-58 Krishnaswamy V 1979 Dose tables for '"1 seed implants Radiology 132 727-30 Laughlin J S, Silver W M, Holodny E I and Ritter F W 1963 A dose description system for interstitial radiation therapy Am. J. Roentgenol. 89 470-90 Ling C C, Anderson L L and Shipley WU 1979 Dose inhomogeneity in interstitial implants using '"1 seeds Int. J. Radiat. Oncol. Biol. Phys. 5 419-25 Ling C C, Schell M C, Yorke E D, Palos B B and Kubiatowicz D0 1985 Two-dimensional dose distribution of '*'I seeds Med. Phys. 12 652-5 Rao G U V, Kan P T and Howells R 1981 Interstitial volume implants with 1-125 seeds Int. J. Radiat. Oncol. B i d . Phys. 7 431-8 Wu A, Zwicker R D, SternickE S 1985 Tumour dose specification of1-125 seed implants Med. Phys. 12 27-31