The effect of applicator geometry on dose specification in cervical cancer

Inr J. Radumon 0ncolog.v BIO/ Phys.. Vol. Printed in the U.S.A. All nghts reserved.

18. pp. 1513-1520

Copyright

0360-3016/90 $3.00 t .I0 0 1990 Pergamon Press plc

??Technical Innovations and Notes

THE EFFECT OF APPLICATOR GEOMETRY ON DOSE SPECIFICATION IN CERVICAL CANCER ROGER A. POTISH, M.D. Departments

of Therapeutic Radiology and of Obstetrics and Gynecology, University of Minnesota Hospital and Clinic, Harvard Street at East River Road, Box 494 UMHC, Minneapolis, MN 55455

The effect of variation of applicator geometry on classic parameters of dose specification was studied in 90 FletcherSuit radium applications in women with cervical cancer. Five statistically significant factors were identified by multiple linear regression analysis and quantified: mg of radium in the colpostats, mg of radium in the tandem, lateral displacement of the colpostats in the frontal plane, vertical separation between the colpostat and tandem sources, and anterior-posterior displacement of the colpostats relative to the tandem. These factors were used to predict “traditional” (i.e., bladder, rectum, and point A) and ICRU dose specification parameters as a function of applicator geometry. Applicator geometry had little effect on the product of ICRU volume specification components, but it greatly affected the individual ICRU components and “traditional” calculation points. Linear regression equations were generated to predict the magnitude of such changes so that the effects of variations in applicator geometry at various prescription points could be predicted radiographically, with subsequent confirmation by computerized dosimetry. Although such regression equations do not replace 3-dimensional computerized dosimetry, they aid applicator placement and treatment planning. Brachytherapy,

Cervical cancer, ICRU, Point A, Dose specification,

INTRODUCTION

Computerized dosimetry.

METHODS

AND MATERIALS

In 1978 and 1979, at the University of Minnesota Hospitals, 90 intracavitary Fletcher-Suit afterloading radium applications* with standard loadings were performed in patients with cervical cancer. All tandems had the same curvature. Radium sources had l-mm platinum filtration, 1S-cm active length, and 2.2-cm physical length. Isodose plots were generated by computer+ with dose calculation based on evaluation of Sievert integrals with the reduced coordinate system of Young and Batho to account for the effects of oblique filtration of individual sources (20). Orthogonal simulator films were used with dummy sources to determine source coordinates. Oblique frontal and sagittal calculation planes were defined by ICRU Report 38 (10). Reproducibility of dosimetry for an individual case has been estimated to be within 5% for repeated dose calculation. Previously studied radium implants were used so that certain measurements did not have to be repeated (12- 14). Cesium measurements would have been quite similar.

Brachytherapy for women with cervical cancer has remained more of an art than a science. Based on mg-h, the early Paris system and its modern descendents, represented most notably by the Fletcher system, provide loading rules for a given application but do not quantitatively specify corrections to be made for various deviations from ideal geometry (4, 6, 7, 19). Similarly, the

Manchester system assumes ideal geometry and a relatively constant dose rate to Point A (17, 18). More recently, the ICRU has presented a number of suggestions for dose specification (10). Although the choice of dose prescription and specification points should not be determined by applicator geometry, relative dose rates at these points and the shapes of isodose surfaces depend on applicator geometry. Despite its importance, the effect of applicator geometry on the values of dose specification parameters has not previously been studied in detail. Thus, the current study analyzes the relationship between applicator geometry and dose specification.

Acknowledgements-I would like to acknowledge the support of Seymour H. Levitt, M.D. and the technical assistance of Mary E. Hartzell, R.T.T., Jane M. Johnson, R.T.T., and Kathy A. Stoeckigt, R.T.T.

Accepted for publication 20 December 1989. * Radium Chemical Co., NY. + Artronix PC-12, St. Louis, MO.

1513

1514

I. J. Radiation Oncology 0 Biology 0 Physics

As defined by ICRU Report 38, width d, and height dt, of the ICRU reference volume were maximal sizes of the 60-Gy reference volume perpendicular and parallel to the tandem, respectively, in the oblique frontal plane containing the most distal intrauterine source, whereas thickness d, was the maximal size perpendicular to the tandem in the oblique sagittal plane ( 10). In order to study other reference volumes of potential interest, the distances DRw,,, DRn,i and DRr,, at the same ICRU locations but at various dose rates were defined and measured (W = width, H = height, T = thickness, I = isodose rate in cGy/hr) (Figs. I, 2). The product, VR,, of these parameters, was used as a measure of volume ( 1. 3, 15). Because the ICRU implicitly assumed continuity of isodose surfaces, one application with a discontinuous 80 cGy/hr isodose line had to be omitted from further analysis ( 14). All lower isodose rates were continuous. In accordance with the original Manchester definition, point Av was 2 cm lateral to the middle of the tandem and 2 cm superior to the top of the lateral vaginal fornix, identified radiographically in the oblique frontal and sagittal planes (17). Corresponding to the “revised” Manchester definition, point A0 was 2 cm lateral and 2 cm superior to the external cervical OS,identified radiographically as the top of the cervical marker (18). Arithmetic means were calculated if right and left point A dose rates differed. To provide a gradient of normal tissue tolerance points, bladder (Bs, BM, B,) and rectal (Rs, RM, R,) dosage points were measured 5 mm perpendicular to the colpostats (S = superior, M = middle, I = inferior) in the oblique sagittal plane, as shown in Figure 3. Five mm was chosen to represent the minimum thickness of the vesicovaginal and rectovaginal septa ( 11).

Fig. 1. The oblique frontal calculation plane is depicted for a standard Fletcher loading (tandem 15-lo- 10 mg, colpostats 15 mg each). DRw.4D and DRnM are measured as shown at the widest and highest distances of the 40 cGy/hr isodose. CD is the distance between the colpostat sources as they pierce the calculation plane.

June 1990, Volume 18, Number 6

-3

“s

Fig. 2. The oblique sagittal calculation plane of the same application of Figure 1 is used to measure DRT,40, Vs, and Zn. Vs is the vertical distance between the tip of the distal tandem source and the intersection of its vertical projection upon the colpostat sources. Zn is the distance between the middle of the colpostats and the intersection of the projection of the distal tandem source upon the colpostats.

The following application factors were used to predict the above dose specification parameters. Co was the distance between colpostat sources in the oblique frontal plane (Fig. 1). Because the tandem was not always equidistant between the colpostats, Xo was operationally defined as the horizontal distance between the midpoint of Co and the most distal tandem source (7). Vs was the distance between the most distal end of the cervical source and the intersection of its projection onto the colpostat sources in the oblique sagittal plane (Figs. 2, 3). As the middle of the tandem should bisect the height of the colpostats in the oblique sagittal plane, Zb quantitated an-

Fig. 3. Bladder (B) and rectal (R) dose rate measurements are 5 mm perpendicular to the colpostat surfaces in the oblique sagittal plane. Vs is positive if the distal tandem source is superior to the intersection of its projection with the colpostat sources.

1515

Applicator geometry 0 R. A. POTISH Table 1. Abbreviations

RESULTS

and definitions

Width of ICRU 60-Gy reference volume Height of ICRU 60-Gy reference volume Thickness of ICRU 60-Gy reference volume Width of “I” cGy/hr volume Height of “I” cCiy/hr volume DRH,I Thickness of “I” cGy/hr volume D&J Volume of “I” cGy/hr isodose surface VR, Point A 2 cm lateral to tandem, 2 cm above AV vaginal fomix Point A 2 cm lateral to tandem, 2 cm above Ao cervical 0s Superior bladder dose 5 mm from colpostats BS Middle bladder dose 5 mm from colpostats BIVI Inferior bladder dose 5 mm from colpostats BI Superior rectal dose 5 mm from colpostats RS Middle rectal dose 5 mm from colpostats RM Inferior rectal dose 5 mm from colpostats RI Horizontal distance between colpostats in the CD oblique frontal plane Vertical distance between distal cervical source and VS its projection onto colpostat source Anterior-posterior distance between distal cervical ZD source and colpostat midpoint MGAN Milligrams of radium in the tandem Milligrams of radium in the colpostats MGCOL MGToTAL Milligrams of radium in the tandem and colpostats

d, 4, 4 DRw.1

deviations from this ideal (Fig. 2). Angles between the colpostats and tandem were measured in the oblique frontal (CTAoF) and sagittal (CTAos) planes. The final predictors were tandem (MC,N), colpostat (MGco& and total (MGT~T,& mg of radium. Table 1 summarizes all abbreviations and definitions. Linear correlation and multiple regression techniques were used to measure relationships between variables of interest ( 16). Regression variables were selected with forward selection, by which variables were sequentially added until further inclusion of variables added no statistical significance. As no statistical significance was demonstrable for XD, CTAoF, or CTAos, they were omitted from further analysis. Multiple correlation coefficient squared (multiple r2) quantified total predictive power of the regression models by measuring proportionate reduction in total sum of squared deviations, ranging from zero to unity as predictive power maximized (16). Analysis of residuals was performed on selected regressions to test the adequacy of the regression models. The conventional 0.05 level was chosen as the cutoff for statistical significance.

terior-posterior

Table 2 presents mean values and standard deviations for applicator geometry as a function of application type. The ranges are -6 to +14 mm for Vs, 28 to 53 mm for CD, and -10 to +6 mm for Z,,. There are 16 55-mg applications (tandem 15- 10 mg, colpostats 15 mg each without caps), 38 65-mg applications (tandem 15-10-10 mg, colpostats 15 mg each without caps), 18 75 mg applications (tandem 15-IO- 10 mg, colpostats 20 mg each with 2.5 cm caps), and 12 85 mg applications (tandem 15- lo- 10 mg, colpostats 25 mg each with 3.0 cm caps). The remaining five applications have other standard Fletcher loadings ( 12). Note that MGTANserves as a step function concerning the number of sources in tandem. Linear correlation coefficients between various parameters of applicator geometry are small (Table 3). Only three correlations exceed 0.50. Because loading rules specify more milligrams to be used with larger colpostats, which in turn implies greater lateral separation of the colpostats, a 0.59 correlation exists between Co (the distance between the colpostats) and MGcoL. The 0.69 and 0.89 correlation coefficients, respectively, between MGTANand MGcoL and MGToTALare consequences of loading rules which ensure that the ratio of tandem to total milligrams remains from 0.33 to 0.60 (12). The low correlations between the remaining parameters provide some indication of their independence as predictive factors. Mean values of the dose prescription parameters are shown in Table 4 as a function of application type. The small standard deviations of the ICRU parameters for a given loading are noteworthy because individual patient anatomy might have been expected to cause greater variability, particularly in isodose widths (DRw). Bladder (B), rectal (R), and Point A dose rates show greater relative deviations. Only statistically significant terms are included in the multiple linear regression equations for prediction of dose specification parameters as a function of applicator geometry in Tables 5 and 6. Specific values for various prescription factors can be calculated by substitution of data from Table 2 into these regression equations. Analysis of residuals confirms the adequacy of the high r* linear regression Table 5 models but is unable to determine whether the low r2 present in Table 6 models is a function of the choice of variables or of the assumptions of the models. Table 7 shows the effects upon prescription pa-

Table 2. Mean values of applicator geometry parameters All applications VS CD

ZD

6.3 (4.4) 37.6 (5.2) -4.2 (3.4)

Note: See Table 1 for abbreviations.

55-mg applications 6.2 (4.0) 34.7 (4.2) -4.0 (3.4)

65-mg applications 6.6 (3.9) 35.6 (4.8) -4.4 (3.6)

75-mg applications 5.2 (6.1) 40.7 (3.9) -3.9 (3.6)

Units of Vs, CD, ZD in mm. Standard deviations in parentheses.

85-mg applications 7.2 (3.9) 43.0 (3.5) -4.8 (3.0)

1. J. Radiation Oncology 0 Biology 0 Physics

1516

Table 3. Linear correlation coefficients between applicator geometry parameters

VS VS

vD

ZD

1.OO -0.06

-0.06 -0.20

1.00

MGCOL MGTAN MGTOTAL -0.01 0.59 -0.04

CD

-

ZD

-

-

1 .oo

MGcoL

-

-

-

I .oo

MGTAN

-

-

-

-

-0.07 0.23 -0.1 1 0.30

-0.04 0.55 -0.08 0.89 0.69

1.oo

Note: See Table 1 for abbreviations

rameters caused by varying CD, Vs, and ZD through their ranges.

DISCUSSION In a “classic” Fletcher application, the tandem axis bisects the height of and is equidistant from the colpostats, and the most distal end of the cervical source minimally overlaps the cephalad rim of the colpostats to optimize dose distribution to the cervix, vagina, and parametria (4). This classic position may be intentionally altered for specific clinical situations such as posterior displacement of the colpostats for a posterior cervical lesion (6). More commonly, however, patient anatomy or physician in-

June 1990. Volume

VR80 VR60 VR40 VR2o

132 207 379 1000

(32) (52) (93) (232)

DR W.80 DRw.60 DRw.40 DRw.zo

63 68 79 103

DRH.RO

72 (10) 79 (IO) 91 (10) ll4(11)

DRH.~o DRHAO DRH.ZO

DRT.XO

DRT.~o DRT.IO DRTN

BS

29 38 52 84

(7) (8) (8) (9)

(2) (3) (4) (6)

55-mg applications 90 I41 262 699

Number 6

experience lead to suboptimal applications. Regardless of the reason for the departure from ideal, it is important to quantitate the magnitude of these effects on prescription parameters. For a given tumor volume, prescription for cervical cancer generally combines a specific amount of whole pelvis external beam with brachytherapy expressed either in mg-h or in Gy at Point A (4-8, 17-19). More recently, ICRU Report 38 defined d,, d,,, and d, to measure the maximum dimensions of the 60-Gy isodose surface, including brachytherapy and external beam contributions ( 10). While ICRU specifications do not transform these dimensions into a volume, other investigators have defined hwt as the product of these dimensions for the brachytherapy component alone and HWT as this product for the combined 60-Gy of external beam and brachytherapy ( 1, 3. 15). The pear-shaped isodose surfaces lead to actual volumes which are slightly less than half of these products (3). The dimensions of Tables 4, 5. and 7 are analogous to the ICRU 60-Gy reference volume but are expressed in dose rates so that additional isodose surfaces can be studied. If, for example, 100 hr of brachytherapy are given with no external beam, the 60-Gy dimensions are the same as DRW.60,DRH.60, and DRT,OO(i.e. 60 Gy/ 100 hr = 60 cGy/hr). If 20 Gy of external beam is administered, then 40-Gy remain for the ICRU volume,

Table 4. Mean values of dose specification All applications

18,

parameters

65-mg applications

75-mg applications

85-mg applications

(5) (8) (9) (14)

123 190 344 919

(12) (18) (29) (67)

145 231 428 I 129

(13) (17) (24) (60)

(4) (4) (4) (3)

58 64 74 98

(4) (4) (4) (4)

68 74 84 108

(4) (4) (4) (4)

74 81 92 II9

(2) (2) (2) (2)

57 (5)

74 81 92 114

(5) (5) (5) (5)

74 82 95 119

(4) (4) (4) (4)

78 86 99 124

(5) (5) (5) (6)

29 37 51 82

(2) (3) (3) (3)

29 38 54 87

(2) (3) (3) (3)

32 42 59 94

(2) (2) (2) (2)

58 63 72 95

63 (5) 74 (4) 95 (4) 28 36 49 77

(2) (2) (2) (2)

I81 290 535 1300

(IO) (12) (15) (53)

BI

48 (7) 46 (7) 35 (3)

46 (6) 42 (4) 33 (3)

47 (7) 44 (6) 34 (3)

48 (6) 46 (6) 35 (3)

53 (8) 53 (7) 39 (2)

RS Rhl RI

69 (16) 54 (8) 40 (4)

67 (17) 51 (7) 38 (3)

65 (13) 53 (8) 40 (4)

72 (16) 56 (IO) 41 (5)

75 (21) 58 (8) 42 (4)

Av Ao

53 (3) 61 (II)

50 (2) 57 (8)

52 (2) 58 (6)

54 (2) 66 (17)

56 (2) 69 (7)

BM

Note: See Table 1 for abbreviations.

Units of VR in cm3; DR in mm; B, R, A in cGy/hr.

Standard

deviations

in parentheses.

Applicator geometry 0 R. A. Table 5. ICRU regression Multiple VRBo V&, V%, VRzO

= = = =

regression

1517

POTISH

equations (Multiple

equations

(.96/.62) (.96/.64) (.97/.69) (.95/.77)

DRvv.80 = DRW,60 = II? = w,zo =

0.5 1 MGcoL 0.55 MGcoL 0.63 MG co,. 0.78 MGcoL

+ + + +

0.8 1 Cb - 0.10 0.82 CD - 0.13 0.09 MGrAN + 0.23 MGTAN +

Vs + 0.24 Vs + 0.16 0.78 C,, 0.63 Cb -

Z,, + 15.92 Zr, + 19.62 0.16 Vs + 25.15 0.18 Vs + 45.2 1

DRu.80 = DRu.60 = DRu.40 = DR H,ZO=

0.32 0.32 0.43 0.59

MGcoL MGco,. MGco,. MGcoL

+ + + +

1.84 1.90 1.89 1.96

MGr,,N MGTAN MGrAN MGTAN

0.46 0.30 0.29 0.24

0.40 0.50 0.53 0.51

f$r,w, = T,60= ;p = T.ZO=

0.21 0.36 0.46 0.60

MGcor. MGcoL MGco,. MGcoL

+ +

0.16 0.24 0.14 0.41

Cb - 0.27 Vs - 0.17 Z,, + 28.63 CD - 0.33 Vs - 0.27 Zb + 35.09 MGTAN - 0.18 Co - 0.30 Vs - 0.24 Z,, + 38.97 MGTAN -0.26Vs-0.21Z,,+50.11

Note: See Table 1 for

Cb CD CD Co

+ + + +

Vs vs Vs Vs

12)

(.88/.87) (.91/.90) (.93/.93) (.94/.94)

2.82 MGco,_ + 3.56 MG-rAN - 0.79 Vs - SO.78 4.88 MGco,_ + 5.22 MGTAN - 0.98 Vs - 132.62 9.34 MGco,_ + 8.84 MGTAN - 244.96 2 1.89 MGco,_ + 22.45 MGTAN + 3.04 C,, - 634.19

-

?/MGrorAL

+ + + +

0.41 0.51 0.41 0.34

Zb Zb Zr, Zb

+ + + +

(.83/.43) (.86/.49) (.88/.57) (.89/.67)

16.73 14.95 2 1.73 34.84

(.50/.24) (.59/.34) (.72/.57) (.87/.82)

abbreviations. Units of VR in cm3; DR in mm.

and 100 hr of brachytherapy leads to the same volume as DRw,40, DRH,40r and DRT.I~ (i.e. (60 Gy-20 Gy)/ 100 hr = 40 cGy/hr). All of these dimensions are strong functions of application type. The virtually identical dose rate widths (DRw) for 55- and 65mg applications are a result of their determination primarily by colpostat milligrams (MGcoL) and spacing (Cn). The extra tandem source in the 65-mg applications does not widen the isodose surface by more than 3 mm (Table 4). As the milligrams and separation of the colpostats increase in the 75- and 85-mg applications, DRw widens accordingly. The design of the applicator and loading rules ensure an almost one-to-one correspondence between DRw and Cn. If, for example, the mean value of DRW.80for each application type (Table 4) is divided by its corresponding CD (Table 2), the ratio varies only from 1.6 to 1.7. Similar divisions for DRW,60, DRW,40, DRw,zo yield respective ratios of 1.8-1.9, 2.1, and 2.6-2.8. Thus, for the Fletcher applicator with standard loadings, DRvv is a simple linear function of horizontal distance between the colpostats. The inclusion of

other variables adds only minimal predictive power (Table 5). Determined chiefly by the number of tandem sources, dose rate heights (DRn) are very similar for 65-, 75-, and 85-mg applications, all of which have three tandem sources (Table 4). The extra milligrams in the colpostats of 75- and 85-mg applications heighten DRn only slightly relative to 65-mg applications. The 55-mg applications have a 17-19 mm shorter DRn compared to 65-mg applications, slightly less than its 22-mm physical length since the tandem tip curves out of the calculation plane. In essence, the extra 10 milligrams of radium in the tandem serve as a step function. Vs adds some predictive power because isodose height elongates with greater vertical separation between the tandem and colpostat sources (Fig. 4, Tables 5, 7). As the colpostats move anteriorly relative to the tandem (i.e. as Zn increases), DRu broadens (Fig. 5, Tables 5,7). As the distance between the colpostats (C,) widens, DRu narrows (Tables 5, 7) because more laterally separated colpostats contribute less to the oblique sagittal plane where DRn is measured.

Table 6. Bladder, rectal, and point A regression equations Multiple

regression

equations

(Multiple

f /MGToTAL f)

Bs = 0.45 MGco,_ - 0.42 CD - 0.62 Vs - 1.21 Zr, + 47.05 Br,, = 0.67 MGcoL - 0.50 C,, - 0.66 V, - 0.62 Z,, + 42.2 I B, = 0.40 MGco,_ - 0.4 1 Cn - 0.28 Vs - 0.18 Zr, + 37.40

(.52/.10) (.55/.26) (.58/.24)

Rs = 0.74 MGco,_ - 0.60 CD - 0.62 Vs + 2.97 Z,, + 8 1.60 Rhl = 0.45 MGcoL - 0.53 CD - 0.67 Vs + 1.24 Zb + 56.46 R, = 0.27 MGcoL + 0.23 MGTAN - 0.49 CD - 0.37 Vs + 0.44 Z,, + 45.53

(.56/.04) (.69/.07) (.66/.07)

Av = 0.22 MGco,_ + 0.12 MGTA~ - 0.14 Vs - 0.34 Zr, + 40.55 Ao = 0.61 MGco,_ - 1.54 Vs + 49.52

(.71/.50) (.55/. 16)

Note: See Table 1 for abbreviations.

Dose rate units in cGy/hr.

1. J. Radiation Oncology 0 Biology 0 Physics

1518

Table 7. Effect of applicator geometry prescription parameters

Parameter

CD

vs

(28 to 53 mm)

(-6 to 14 mm)

DRw.80 DRW,OO DRw.40 DRw.zo DRH.BO DRH.~o DRH.~o DRH,~o

-2 -3 -4 -4

20 20 20 16 -12 -8 -7 -6

BM

BI Rs RM

RI

6s h to 6 mm) 4

RI 8 7 5 -3 -4 -4 -3

-10 -12 -10

-12 -13 -6

-19 -10 -3

-15 -13 -12

-12 -13 -7

48 20

-2 -

-3 -31

-5

Note: See Table 1 for abbreviations. Units of DR in mm: B, R, A in cCy/hr. Ranges in parentheses.

Determined mainly by the tandem source closest to the cervix and by the colpostats, dose rate thickness (DR,) gradually increases with application type (Table 4). It is not as easily predictable as DRw and DRu , demonstrated by its lower r2 (Table 5). Because DRT is measured near

Bs BM

??

ZD

(-10

-5 -7 -6 -5

-

Bs

on

8 10 II 10

-4 -6 -4

June 1990, Volume 18, Number 6

??

I IRI I-l

I vs I Fig. 4. As the colpostats are displaced superiorly relative to the tandem sources, Vs decreases and becomes negative. Therefore, because of increasing overlap between sources, a more negative Vs is associated with higher bladder (B) and rectal (R) isodose rates and with greater isodose widths (DR,) and thicknesses (DRr) (Tables 5-7). This effect is increased by the bladder and rectal dose calculation points being carried more superiorly into regions of greater dose rate. Isodose height (DRn), on the other hand, decreases with decreasing Vs because the overall height is shortened.

-

I vs I Fig. 5. As the colpostats are displaced anteriorly, Zn increases and becomes positive. Bladder (B) and rectal (R) calculation points are carried with the colpostats. This, plus associated degrees of overlap between tandem and colpostat sources, is responsible for the effects of Zn on the prescription parameters of Tables 5, 6, and 7.

the junction of tandem and colpostat sources, the more source overlap, represented vertically by Vs and anteriorlyposteriorly by Zn, the thicker is DRr (Figs. 4, 5, Tables 5, 7). Similarly, wider Co leads to narrower DRr because the colpostats are farther from the midline oblique sagittal calculation plane (Tables 5,7). Increasing amounts of radium in the colpostats (MGcoL) and tandem (MGTAN) also thicken DRr (Table 5). Even though DRw, DRT, and DRn have several significant predictive components in their regression equations, their product (VR) does not (Table 5) (3). The explanation for this phenomenon is presented in Table 7. An increase in Cn expands DRw but contracts DRn and DRT. An increase in Vs or Zn enlarges DRn but constricts DRw and DRT. Thus the individual components of the product VR tend to balance each other. The slightly different shapes of the isodose surfaces (Figs. 1, 2) do result in some minor predictive power of Vs for VRso and VRbO and of Co for VRzO(Table 5). The multiple r* for all the variables is only slightly greater than that obtainable by simply using total mg (MGTo~) for VR but substantially greater for the individual components of DRw , DRu, and DRr . At isodose surfaces progressively more distant from the applicator, the applicator itself becomes a point source of radiation, resulting in a direct proportionality and perfect correlation between mg-h and VR or hwt (3). At both near and distant isodose surfaces, volume increases linearly with total milligrams even though the individual dimensions do not. Certain dose specification parameters can be considered “traditional” in that they have been clinically used for decades although their validity has never been conclusively proven. Many such “traditional” (bladder, rectal, and point A) doses have so many inherent difficulties that their use is proscribed in the Fletcher system. Anatomic dis-

Applicatorgeometry0 R. A. POTISH tortions said to render point A meaningless include lesions restricted primarily to one cervical lip, massive cervical lesions expanding the cervix or isthmus, vaginal tumor involvement, and parametrial shortening with its associated tandem angulation (6). In addition, point Ao is in a region of such steep dose gradient that its dose varies greatly within millimeters (13). As explained elsewhere, point A0 is such a strong function of Vs that it is useless for prescription (13). Although point Av requires many predictive parameters (Table 6), it gradually and linearly increases as a function of application type (Table 4). Its small standard deviations indicate its achievement of one of the original goals of the Manchester system-a definable point with a constant dose rate relatively independent of applicator geometry (13, 17, 18). Although point Av or various modifications thereof remain in widespread use, their use is not recommended by the ICRU (8, 10). Bladder and rectal dose calculation points are also widely used with varying definitions even though their utility is controversial (5). The ICRU defines the rectal dose calculation point very similarly to RI, and one study was able to establish a dose-response relationship for rectal complications at this point ( 15). The ICRU specifies bladder dose at the catheter bulb, which generally is close to Bs. Computed tomography has shown, however, that the maximum bladder dose may well exceed the ICRU dose by a factor of three or more (9). In any event, if careful attention is paid to treatment volume, mg-h, and applicator geometry, bladder and rectal complications will be minimal (4-7, 19). Attention paid only to global quantities such as mg-h will not necessarily minimize bladder and rectal doses and complications. Since anterior bladder (Bs, BM, B,) and posterior rectal ( Rs, RM, R,) dose rates generally vary between 40 and 80 cGy/hr and are located close to the points at which DRT is measured, the effect of applicator geometry on these parameters is similar (Table 5, Figs. 2, 3). Rectal (R) and bladder (B) dose rates, respectively, wax and wane with Zo as its position reflects progressive overlap of tandem and colpostat sources (Fig. 5, Tables 5, 7). In addition, because bladder and rectal calculation points are defined relative to the colpostats, dose rates vary with Zo as the position of the calculation points relative to the isodoses change (Figs. 3, 5). As demonstrated by the low r2 (correlation coefficients), doses at bladder and rectal points are not at all closely related to mg-h (Table 6). If all other parameters are held constant, then bladder and rectal dose are directly proportional to mg-h. Thus, this apparent lack of association is due to geometric changes which compensate for mg-h changes. The relatively low multiple r2 of Table 6 also show that the inclusion of applicator geometry parameters adds incomplete predictive power. As noted above, analysis of residuals confirmed the adequacy of the high r2 linear regression Table 5 models but was unable to determine whether the low r2 present in Table 6 models was

1519

a function of the choice of variables or of the assumptions of the models. Further work is in process with other statistical models to find better models for prediction of bladder, rectal, and Point A dose rates. The regression equations of Tables 5 and 6 are useful for prediction of the effect of applicator geometry at specified points of interest. Thus, for example, if the colpostats are to be intentionally displaced posteriorly for a posterior cervical lip lesion, the quantitative effects on various prescription parameters can be predicted in the oblique frontal and sagittal planes (6). Similarly, decisions concerning repacking for suboptimal applicator geometry can be performed while the patient is still under anesthesia if operating room radiography is available. Final confirmation can be provided by conventional computerized dosimetry. If applicator geometry is less than ideal for a first implant, then pretreatment planning can optimize a second implant. It is possible to predict, for example, the effect of additional posterior packing in not only reducing rectal dose but increasing bladder dose. Although the regression equations do not replace three-dimensional treatment planning, they are an aid in applicator placement. Finally, data generated from the present study can be incorporated into the design of new applicators. Caveats concerning specific values of the data must be kept in mind. The multiple r2 of the Table 5 and 6 equations quantitatively indicate the linearity and scatter of the data, with an r* of unity denoting perfect prediction. Therefore, greater r2 implies more precise prediction. The present study does not account for shielding within the colpostats, and different applicators or loadings would also yield different data (2). The applications studied in the present manuscript were performed by experienced radiation and gynecologic oncologists, resulting in applicator geometry that was relatively free of deviation. The maximum skewness between tandem and colpostats in the oblique frontal plane (CTAoF), for example, was only 10 degrees. Less ideal applications would be even less predictable, and the linearity of the predictive parameters would diminish. Although various volumes (VR, HWT, hwt) are highly correlated with mg-h despite being close enough to the applicator that they do not behave like point sources, their clinical use remains unproven (3, 14). These correlations serve to translate mg-h into mm3 in three dimensions at a given level of Gy, but do not yet offer any clinically substantiated improvement in the avoidance of recurrence or complication. As ICRU isodoses are not directly related to tumor anatomy, it is unlikely that they reflect target dose or volume. Similarly, bladder or rectal tolerance may well be better described by various other bladder or rectal calculation points or volumes (9, 15). Mg-h, on the other hand, are directly related to small bowel and sigmoid dose, and excessive whole pelvis Gy and mg-h do lead to complications in these organs as well as to the bladder and rectum (6, 7, 19). As shown quantitatively in Tables 6

1520

1. J. Radiation Oncology 0 Biology 0 Physics

and 7, applicator geometry strongly influences bladder and rectal dosage, and any prescription system which relies solely on volume for dose specification must by necessity be incomplete. Neither point A nor mg-h nor ICRU concepts account for clinically meaningful hot and cold spots

June 1990. Volume 18, Number 6

in tumor and normal tissue (6, 14). Satisfactory dose specification and delineation of parameters predictive of normal tissue damage and tumor control remain an unsolved problem in the management of women with cervital cancer.

REFERENCES 1. Crook, J. M.; Esche, B. A.; Chaplain, Cl.; Isturiz, J.; Sentenac, I.; Horiot, J. C. Dose-volume analysis and the prevention of radiation sequelae in cervical cancer. Radiother. Oncol. 8321-332; 1987. 2. Delclos, L.; Fletcher, G. H.; Sampiere, V.; Grant, W. Can the Fletcher gamma ray colpostat system be extrapolated to other systems? Cancer 41:970-979; 1978. 3. Esche, B. A.; Crook, J. M.; Isturiz, J.; Horiot, J. C. Reference volume, milligram-hours and external irradiation for the Fletcher applicator. Radiother. Oncol. 9:255-26 1; 1987. 1st edition. Phil4. Fletcher, G. H. Textbook of radiotherapy, adelphia, PA: Lea & Febiger; 1966. 5. Fletcher, G. H.; Brown, T. C.; Rutledge, F. N. Clinical significance of rectal and bladder dose measurements in radium therapy of cancer of the uterine cervix. Am. J. Roentgenol. 79:421-449; 1958. 6. Fletcher, G. H.; Hamberger, A. D. Squamous cell carcinoma of the uterine cervix. In: Fletcher, G. H., ed. Textbook of radiotherapy, 3rd edition. Philadelphia, PA: Lea & Febiger: 1980:720-773. D. M.; Fletcher, 7. Hamberger, A. D.; Unal, A.; Gershenson. G. H. Analysis of the severe complications of irradiation of carcinoma of the cervix: whole pelvis irradiation and intracavitary radium. Int. J. Radiat. Oncol. Biol. Phys. 9:367371; 1983. 8. Hanks, G. E.; Herring, D. F.; Kramer, S. Patterns of care outcome studies. Results of the national practice in cancer of the cervix. Cancer 5 1:959-967: 1983. 9. Hunter, R. D.; Wong, F.; Moore, C.: Notley. H. M.; Wilkinson, J. Bladder base dosage in patients undergoing intracavitary therapy. Radiother. Oncol. 7: 189- 197; 1986. 10. ICRU report 38: dose and volume specification for reporting intracavitary therapy in gynecology. Bethesda: ICRU, 1985: l-16.

1 1. Lukka, H. R.; Moore, C. J.; Hunter, R. D. The relationship between the bladder and the cervix in patients undergoing intracavitary therapy. Br. J. Radiol. 60:355-359; 1987. 12. Potish, R. A.; Deibel, F. C.; Khan, F. M. The relationship between milligram-hours and dose to point A in carcinoma of the cervix. Radiology 145:479-483; 1982. 13. Potish, R. A.; Gerbi, B. J. Role of point A in the era of computerized dosimetry. Radiology 158:827-83 I; 1986. 14. Potish. R. A.: Gerbi, B. J. Cervical cancer: intracavitary dose specification and prescription. Radiology 165:555-560: 1987. 15. Pourquier, H.; Dubois, J. B.; Delard, R. Cancer of the uterine cervix: dosimetric guidelines for prevention of late rectal and rectosigmoid complications as a result of radiotherapeutic treatment. Int. J. Radiat. Oncol. Biol. Phys. 8: 18871895: 1982. 16. Snedecor, G. W.; Cochran, W. G. Statistical methods, 7th edition. Ames, IA: The Iowa State University Press; 1980. 17. Tod, M. C.; Meredith, W. J. A dosage system for use in the treatment of cancer of the uterine cervix. Br. J. Radiol. 11: 809-824; 1938. 18. Tod, M. C.; Meredith, W. J. Treatment of cancer of the cervix uteri-a revised “Manchester method.” Br. J. Radiol. 261252-257; 1953. 19. Unal. A.: Hamberger, A. D.; Seski, J. C.; Fletcher, G. H. An analysis of the severe complications of irradiation of carcinoma of the uterine cervix: treatment with intracavitary radium and parametrial irradiation. Int. J. Radiat. Oncol. Biol. Phys. 7:999- 1004; 198 I. 20. Young, M. E.; Batho, H. F. Dose tables for linear radium sources calculated by an electronic computer. Br. J. Radiol. 37:38-44; 1964.