PII S0360-3016(00)00552-6

PHYSICS CONTRIBUTION

A NEW POWER LAW FOR DETERMINATION OF TOTAL 125I SEEDACTIVITY FOR ULTRASOUND-GUIDED PROSTATE IMPLANTS:

CLINICAL EVALUATIONS

ANDREW WU, PH.D.,* CHEN-CHIAO LEE, B.S.,* MARK JOHNSON, M.S.,* DOUGLAS BROWN, M.D.,*RONALD BENOIT, M.D.,† RALPH MILER, M.D.,† JEFFERY COHEN, M.D.,† PAUL GEIS, PH.D.,*

ALEX S. J. CHEN, M.D.,* AND SHALOM KALNICKI , M.D.*

Departments of *Radiation Oncology and†Surgery, Division of Urological Surgery, Allegheny General Hospital,West Penn Allegheny Health Systems, Pittsburgh, PA

Purpose: The intraoperative planning with peripheral loading approach is an important technique for ultra-sound-guided transperineal prostate implant. In this paper a sphero-cylindrical dose model is described togenerate a new power law or a look-up table for determination of the total125I activity required to deliver aprescription dose to a given prostate volume.Methods and Materials: Dose calculations were based on the new standards for125I seeds (model 6711)implemented by the National Institute of Standards and Technology (NIST) in 1999. Using the sphero-cylindricaldose model with peripheral loading approach, a new power law for calculating total activity of radioactive iodinerequired to deliver a prescribed dose for the target volume was developed. Accounting for random variation ofthe seed positioning in the prostate and the current air-kerma strength standard of125I seeds, this new power lawis formulated as follows:A (mCi) 5 2.15d (cm)2.00whereA is apparent activity in mCi, or A (U) 5 1.69d (cm)2.00

where A is air-kerma strength in U, required to deliver a cumulative dose of 145 Gy to a prostate gland with anaverage dimension,d, in centimeters.Results: Theefficacy of using the new power law in prostate implants was demonstrated. For clinical evaluations ofthis new power law, 40 patients were chosen in 1998. The average D90 of these 40 patients was 172.0 Gy (SD6 29 Gy).This means that on the average, 90% of the target volume received was 172.0 Gy. The average coverage index (CI)in this study was 94.7 (SD6 4.7). As a result, 94.7% of the target volume received the prescription dose. The dosehomogeneity index (HI) which measured the degree of the dose inhomogeneity was 0.38 (SD6 0.21).Conclusion: This new and simple power law or a new mCi-volume look-up table for125I seed prostateimplantation has been developed and formulated for clinical use. Clinical evaluations expressed in quantitativeparameters such as D90, CI, and HI in prostate implants have been thoroughly analyzed and clearly demon-strated the efficacy of this approach. © 2000 Elsevier Science Inc.

Prostate, Brachytherapy, Iodine-125, Implant.

INTRODUCTION

For ultrasound-guided transperineal prostate implants with125I seeds, a pretreatment plan based on ultrasound imagesis commonly completed before the implant procedure. Nee-dles are preloaded with125I seeds and placed into a prostategland according to the preplan (1–3). However, because ofthe possible pubic arch limitation, the lack of reproducibil-ity of patient position, and uncertainty of volume change ofthe prostate during the procedure, the implant cannot becarried out as planned. As a result, an alternative approach(4, 5) adopted by many centers in this country is to performa plan intraoperatively based on the position of the patientand the size of the gland as well as possible obstruction ofthe pubic arch at the time of the implant procedure. In this

volume-based intraoperative planning, total activity of theradioactive seeds required to deliver a prescribed dose for atarget volume (4) was determined from a look-up tablewhich was originally derived from Anderson’s nomogram(6) and then went through multiple revisions based onclinical observations and experiences (4, 5). The currentmCi-volume look-up table is reasonably good for this in-traoperative planning. However, it was never analyticallyderived or proven. One of the results of this paper is toestablish a dosimetry model to generate a new look-up tableor a new power law.

In the early 1980s, the implants were performed by su-prapubic laparotomy. The average dimension was deter-mined by the dimensions of three major axes measuredmanually with a caliper during laparotomy. Anderson (6)

Reprint requests to: Andrew Wu, Ph.D., Department of Radia-tion Oncology, Allegheny General Hospital, 320 E. North Ave.Pittsburgh, PA 15212.

Accepted for publication 10 February 2000.

Int. J. Radiation Oncology Biol. Phys., Vol. 47, No. 5, pp. 1397–1403, 2000Copyright © 2000 Elsevier Science Inc.Printed in the USA. All rights reserved

0360-3016/00/$–see front matter

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developed a nomogram for the matched peripheral dose(MPD) which later related the total activity of125I seeds toa power law of the average dimension of a prostate gland(7). The dose to the prostate is determined by the isodosevolume which is equal to the prostate volume, withoutconsidering the coverage of the gland. In 1993, Anderson(8) again developed another power law relationship for anaverage dimension that is equal to or greater than 3 cm.Unfortunately, the concept of MPD is to define the dose thathas an equal volume of the prostate gland and has nobearing on the coverage of the target volume (9). Today, theadvancement of digital imaging technology enables us toplace seeds in a three-dimensional view and to quantify thedose coverage of the target volume with dose–volume his-tograms.

In 1986, Wuet al. (10) introduced the minimum periph-eral dose (mPD) concept for dose specification of125I seedsimplanted with a cubical lattice geometry in a sphere. Con-sequently, Yuet al. (11) developed a power law for theminimum peripheral dose (mPD) which is defined as theminimum dose at the periphery in the defined target volume.The dose calculation was performed based on Task GroupReport 43 published by the American Association of Phys-icists in Medicine (AAPM) (12), resulting in the change ofthe total dose prescription from 160 Gy to 145 Gy. How-ever, the power law relationship of total activity and averagediameter is based on seeds placed 1 cm apart and distributeduniformly across the target volume. Uniform distribution ofsources in the prostate may contribute a higher dose to theurethra. A higher urethral dose may increase morbidity. Todecrease possible urinary complications, the seeds may bedistributed preferentially at the periphery of the prostategland based on Paterson–Parker rules (13). We describe thedevelopment of a novel power law relationship for periph-eral loading of 125I seeds and report the results of ourevaluations of this new approach in a clinical setting usingdose–volume histograms calculated from the postimplantCT images.

METHODS AND MATERIALS

Dose modelThe prostate is typically wider at the base and narrower at

the apex, lying anterior to the rectum and posterior andcaudal to the bladder. We assume an ideal prostate gland islike a sphero-cylinder. To build an ideal model for dosecalculations, we distribute seeds in a sphero-cylindrical-likeprostate with preferential loading at peripheral needlesshown in Fig. 1. Based on this particular geometry, the totalactivity of the 125I radioactive seeds required for givingcomplete dose coverage and dose distribution to the prostatevolume is calculated.

For isodose curves completely covering the ideal sphero-cylindrical geometry, needles are placed around the periph-ery 3–5 mm inside the capsule at the level of the largestcross-section, usually at the base of the prostate gland. Thefirst seed at the tip of each needle may be implanted rightinside the capsule at the base of a prostate which conformsto a nearly “spherical” shape. Then the seeds are loadedalong all the needles up to the level of the apex like a“cylinder.” At the level of apex, the needles and seeds maybe outside the prostate. Therefore, the entire seed distribu-tion will be like a cylinder that is spherical at one end andflat on the other end.

We divide all inserted needles into two groups: one groupof needles is placed at the periphery approximately 3–5 mminside the capsule and the others are in the core of theprostate. The tips of the core needles will be placed at thecapsule of the base. All needles are loaded with seeds fromthe tip all the way to cover the apex. Because of thepearl-like shape of a prostate, the tips of the peripheralneedles also placed at the capsule of the base are slightlyrecessed from those at the core. However, the seeds in theperipheral needles will be loaded to the level of the apex.Therefore, the shape of the seed distribution seems to besphero-cylindrical. Furthermore, to compensate possibledose deficiencies at both ends of the implant we follow thebasic Paterson–Parker rule (13), for example, double load-ing of the seeds, i.e., two seeds in the first and last centi-

Fig. 1. Schematic diagrams of the side and front views of the spherical cylindrical model of a prostate gland (shadedarea) which is implanted with125I seeds (dots in the side view) through appropriately placed needles (see the front view).

1398 I. J. Radiation Oncology● Biology ● Physics Volume 47, Number 5, 2000

meters at both ends of the needle. The middle space betweenthe needle tips are then loaded evenly. The number of seedsper needle in peripheral or core needles is based on thepercentage of the total activity distributed between the pe-riphery and the core, then divided by the number of theneedles as long as the ratio is 80% at the periphery to 20%at the core. This is illustrated in Fig. 1.

Both total activity and the distribution of that activitywithin the implanted prostate are important factors in de-termining implant quality. The seed distribution influencesisodose coverage and dose inhomogeneity of the gland. Thismay affect both cure rates and the complications rate. Withthis unique sphero-cylindrical geometry, the total activitiesof the125I seeds, which ensures that the 145 Gy isodose lineencompasses every axial plane of the volume, are calculatedfor the diameters of the sphero-cylinder of 3.54 cm, 3.64cm, 3.86 cm, 4.80 cm, and 5.2 cm respectively. The rules ofseed distribution or loading may be based on the size of theprostate volume. In general, the seeds may be placed 75–100% in the peripheral needles and 0–25% in those needlesat the core. The results are listed in Table 1. To illustratethis, the isodose distributions of the middle cross-section ofthe sphero-cylindrical geometry with 5.2 cm of diameter areshown in Fig. 2. In this cross-section, there are 13 needlesat the periphery and three needles at the core. We placed75% of the activity or seeds at the periphery and 25% at thecore. The 145 Gy isodose line well covers the 5.2 cm of thediameter of the gland. Figure 3 shows a postimplant trans-verse CT image of the base of the prostate showing thepositions of the125I seeds after implantation.

From Table 1 the total activities for delivering 145 Gy areplotted against the diameters of the gland in a log–log scalefor sphero-cylindrical model in Fig. 4. A least-squares fit forthese five points appears to be linear. The slope of the linearline in the log–log scale is the index of the new power law.

In the clinical performance of a real implant procedure,however, it may be inevitable to have random variations ofthe seed positions during and after the implant procedure.Thus, it was recommended that approximately 15% of thetotal activity should be added to the total activity for thetarget volume to receive the minimum peripheral dose (11,14). Furthermore, the National Institute of Standards and

Technology (NIST) has implemented a new primary cali-bration standard for the125I source since January 1, 1999.NIST revised the air-kerma strength (Sk) standard for the125I seeds. Relative to prior seed calibration values, currentcalibration values are numerically decreased by approxi-mately 10% (15, 16). Incorporating this result, the netincrease of mCi in the new power law due to the deviation

Table 1. Total activities calculated for sphero-cylindrical modelfor prostate implants using I125 seeds for 145 Gy*

d (cm)Volume

(cc) A (mCi)Peripheralloading

3.54 23.07 25.96 90–65%3.64 25.00 27.05 90–65%3.86 30.00 30.60 90–75%4.80 57.50 45.90 89–80%5.20 73.10 56.75 87–80%

*Total activities in mCi required to give 145 Gy to the givenaverage diameters, 3.54 cm, 3.64 cm, 3.86 cm, 4.80 cm, and 5.20cm of prostate glands calculated from the sphero-cylindrical dosemodel.

Fig. 2. The isodose distribution of the axial view of the middlecross-section of a sphero-cylindrical geometry of diameter of 5.2cm. The isodose line of 145 cm certainly covers the entire diameter.

Fig. 3. A real CT image of transverse cross-section of the base ofthe prostate showing the placement of the125I seeds after implan-tation.

1399Power law for total I125 seed activity ● A. WU et al.

of the seed positions and new primary calibration standardfrom the values generated from the dose model is approx-imately 5%. Consequently, a new power law has beenformulated. The plots of the new power law of the sphero-cylindrical model corrected with NIST 1999 and the powerequations developed by Anderson (9) and Yu (11) areshown in the same graph (Fig. 4) for comparison.

Implant proceduresThe details of the implant procedure are as follows:

1) A volume study is performed using an ultrasound scanon the patient’s prostate gland a few weeks before theimplant procedure. The total seed activity required todeliver the prescribed dose is estimated using the newlook-up table.

2) The number of seeds is ordered based on the total seedactivity required and is usually in the range between 80and 120 seeds (17) depending on the size of the pa-tient’s prostate and the availability of the seed strengthfrom the manufacturer.

3) Before the implant procedure, the patient is placed inthe lithotomy position. Another volume study is done

to verify the volume previously measured. Should thetwo volumes be different as the result of either thenatural progress of the disease or the hormone manip-ulations, the new activity required for the new volumeis recalculated from the look-up table (Table 2) or thenew power law (eq. 1). The correct total number ofseeds for the implant is determined on the basis of theseed activity available for this procedure.

4) From the transrectal ultrasound images, the posteriorborder of the gland is aligned at 3–5 mm below thebottom or second row of the template holes.

5) By scanning the transaxial images, the image of thelargest cross-section is chosen as the base for implant.

6) Two localizing needles are inserted approximately8–10 mm away from the urethra at 4 and 8 o’clockdirections, preventing gland rotation or the seeds beingplaced too close to the urethra.

7) Needles are placed at the 12 o’clock position andapproximately 3–5 mm inside from the periphery of thegland, working from the top down along the circum-ference of the capsule at approximately 8–12 mm apart.

8) At the core of the gland, place an additional 1–2 moreneedles other than the two localized if there is still space.

Fig. 4. A total activity in mCi required to be implanted in a prostate is plotted against its average dimension in centimeterfor a prescription dose of 145 Gy in log–log scale. The triangles and the squares show the power laws developed byAnderson and Yu respectively. The circles show the power law derived from our sphero-cylindrical model of prostateimplants only. Most importantly, the diamonds are the new power law calculated from the sphero-cylindrical model withthe consideration of both the random placement of the seeds and new correction of the air kerma strength standard fromNIST.

1400 I. J. Radiation Oncology● Biology ● Physics Volume 47, Number 5, 2000

9) In general, based on the size of the gland, 80% of thetotal seeds will be loaded and evenly distributed to allperipheral needles. The remaining 20% will be loadedin the core needles. Besides the double-loading at theends of all needle, the rest of the seeds are evenlydistributed from the base to the apex.

10) The Mick applicator is used for seed placement in eachneedle with appropriate spacings calculated to simulatethe sphero-cylindrical model.

11) Dosimetry evaluation is performed based on the CTscan (Fig. 3).

Implant evaluationsSince 1997, we at Allegheny General Hospital have per-

formed prostate implants on more than 400 patients. Amongthem we have chosen 40 patients who have been implantedwith 125I seeds as the primary treatment of their prostatecancer in a 4-month period for evaluation. The implant

qualities of all 40 implants were evaluated using the volumecoverage index (CI) (11, 14) , i.e., the percentage of thevolumes enclosed by the dose that is equal to or larger thanthe prescription dose, and the dose homogeneity index (HI)(18, 19) which is equal to the unity minus the ratio of thevolumes enclosed by 150% and 100% of the prescribeddose. In the AAPM Task Group 64 Report (14), it isrecommended that D90, the dose level that covers 90% ofthe target volume, be used as an indicator of the quality ofthe implant. In real practice, the good implants will becharacterized with D90 that are equal to or greater than theprescription doses.

RESULTS

A new power lawBased on the proposed sphero-cylindrical model, the total

activities were calculated as a function of average dimen-sions or volume, listed in Table 1 and plotted on a log–logscale in Fig. 4. The data points are best fitted with a straightline. From its slope, we have obtained a new power law forthe sphero-cylindrical model loaded preferentially at theperiphery as follows:A 5 2.05d2.00 whered is the averagedimension of the gland in centimeters andA is the totalactivity of 125I seeds in mCi required to deliver 145 Gy tothe implant.

In practice, the seeds implanted in the gland are, ingeneral, not perfectly placed according to the plan. Toaccount for the random variation of the seed positions in theprostate, an increase of 15% of the total activity in mCi wasrecommended (9). In fact, this power law is 15% over-planned, and is very close to the one used at the early stageof the development of this technique (20). Since the imple-mentation of the new NIST calibration standards in 1999,approximately a 10% decrease in the air-kerma strengthstandard has been detected (15,16). As a result, a net of 5%of the total activity should be added to the power lawdeveloped from the sphero-cylindrical model shown in eq.1. The final power law or nomogram is modified and shownas follows:

A 5 2.15d2.00 (1)

Equation 1 is illustrated at the upper corner and plotted onthe log–log scale for 145 Gy shown in Fig. 4. At the sametime, the other power law such as the sphero-cylindricalmodel with NIST, Anderson’s MPD (7) as well as Yu’smPD (8) power laws are also shown and plotted for 145 Gyon the same log–log scale for comparison.

Dosimetry evaluationsFor dosimetry evaluations, it is recommended by the

AAPM TG-64 (14) to use D90, in comparison with theprescribed dose as an indicator of the implant quality fordose coverage. An implant with good coverage is charac-terized by D90 equal to or greater than the prescribed dose.

Table 2. A new power law based on peripheral loading andNIST 1999*

V (cm3)A (mCi)145 Gy

A (mCi)110 Gy

7 12.1 9.28 13.3 10.19 14.4 10.9

10 15.4 11.712 17.4 13.214 19.3 14.616 21.1 16.018 22.8 17.320 24.4 18.522 26.0 19.824 27.6 20.926 29.1 22.128 30.6 23.230 32.0 24.332 33.4 25.434 34.8 26.436 36.1 27.438 37.5 28.440 38.8 29.442 40.1 30.444 41.3 31.346 42.6 32.348 43.8 33.250 45.0 34.152 46.2 35.054 47.4 35.956 48.5 36.858 49.7 37.760 50.8 38.562 51.9 39.464 53.0 40.266 54.1 41.168 55.2 41.970 56.3 42.7

*A new look-up table or a new power law based on the sphero-cylindrical dose model accounted for the random placement ofseeds and the 1999 new air-kerma strength standard set by theNational Institute of Standards and Technology (NIST).

1401Power law for total I125 seed activity ● A. WU et al.

In addition, there are two more volumetric parameters,namely coverage index (CI) and homogeneity index (HI),which quantify the coverage of the prescribed dose and theuniformity of dose within the125I implanted target volumerespectively.

The D90 values for all 40 patients implanted with125Iseeds are plotted chronologically in Fig. 5. The averagevalue of the D90 is 172.0 Gy (SD6 29 Gy) which meansthat on the average, 90% of the target volume measured byCT immediately after implants has been covered by 172.0

Fig. 6. The plot of coverage indices (CI) of 40 patients with prostate implants. The average CI of all 40 patients is 94.7%(SD 6 4.7%). CI is the fraction of target volume receiving a dose equal to or greater than the prescription dose.

Fig. 5. The plot of D90 values of 40 patients with prostate implants. The average D90 of all 40 patients is 172 Gy (SD629 Gy) which is larger than 145 Gy. D90 is the dose covering 90% of the prostate volume and is a good indicator if itis equal to or greater than the prescription dose.

1402 I. J. Radiation Oncology● Biology ● Physics Volume 47, Number 5, 2000

Gy. This is larger than the prescription dose 145 cGy. InFig. 5, one may observe that those patients having implantsperformed in the later days seem to show higher D90 values.This trend may simply be due to accumulation of experiencein this procedure. The coverage index (CI) of those patientsis also plotted in Fig. 6, and their average is 94.7% (SD64.7%) which means 94.7% of the target volume measuredby CT immediately after implants is covered by the pre-scription dose. Their average dose homogeneity index (HI)is 0.38 (SD6 0.21) which means that 38% of the targetvolume in fact, has a dose variation between 100% and150% of the prescription dose.

Finally, we tabulated in Table 2 the prostate gland volumesbased on the measurements from the ultrasound scans and thetotal activity of the125I seeds calculated from the new powerlaw, shown in eq. 1, in compliance with NIST 1999 standards.This is the new power law or the new look-up table forperipheral loading approach for prostate implants.

CONCLUSIONS

In this paper, we have adopted a sphero-cylindricalmodel to simulate a typical prostate gland implanted with

125I seeds (model 6711) for preferentially loading at theperiphery. The total activity of these radioactive seeds for145 Gy has been shown as a function of the averagedimension with some exponent shown in eq. 1. A newpower law relationship between total activity and averagedimension of the gland has been analytically derived. It isbased on new NIST 1999 standards and also accounts forthe natural randomness of seed placement. A newlook-up table generated from the power law allows easyand quick determination of the total activity of125I seedsrequired for delivering 145 Gy to the given prostatevolume in an operating room.

In our pool of 40 early-stage prostate cancer patients forwhom we performed only125I implants for 145 Gy with ourtechnique, the average dose level covering 90% of the targetvolume, D90, was greater than or equal to the prescriptiondose. Also, the average target volume covered by the pre-scription dose was greater than 90%. These are very impor-tant indicators for excellent quality of the implants whichgive very good coverage of the diseased gland. In conclu-sion, the efficacy of using this new power law between totalactivity and average dimension in our clinical application isillustrated.

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