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Estimation of tissue volume irradiated by intracavitary implants
Inr J. Radiation Oncology Rio/. Phps.. Vol. Printed in the U.S.A. All rights reserved.
25. pp.
733-744 Copyright
0360-3016/93 $6.00 + .Xl 0 1993 Pergamon Press Ltd.
0 Technical Innovations and Notes ESTIMATION OF TISSUE VOLUME IRRADIATED BY INTRACAVITARY IMPLANTS AVRAHAM EISBRUCH, M.D., JEFFREY F. WILLIAMSON, PH.D., D. Ross DICKSON, PERRY W. GRIGSBY, M.D. AND CARLOS A. PEREZ, M.D.
M.D.,
Washington University School of Medicine, Mallinckrodt Institute of Radiology, Radiation Oncology Center, St. Louis, MO Purpose: The volume of space enclosed by a specified isodose surface arising from an intracavitary implant may correlate with clinical outcome. Several investigators have proposed using the product of the three maximum orthogonal dimensions of the isodose surface as a measure of this volume. We have examined the accuracy of this proposal and compared it to a simpler model for estimating volume which requires only knowledge of the mgRaEqhrs (total reference air kerma) and the dose level. Methods and Materials: Orthogonal films from 204 intracavitary implants of 128 patients with carcinoma of the cervix were used to reconstruct the “‘Cs-source coordinates. The source location, strength and duration data were used to calculate dose-volume histograms, yielding the volume enclosed by each dose level as well as its orthogonal dimensions: thickness, width, and height. Using bony landmarks to align films for different insertions in the same patient, similar calculations were repeated for composite implant source coordinates. Results: Curve-fitting techniques revealed that the volume encompassed by each isodose level could be predicted by a modified power-law function of the mgRaEq-hr/dose ratio: predicted volume = 1104.8 - 8.103 *(M/D) + 0.437 - (M/D)‘]. (M/D) ’.635where M/D = mgRaEq-hr/cGy. The volume predicted by this simple model is accurate within + 10% in 95% of the implants when mgRaEq-hr/cGy = 0.8. Accuracy increases with increasing mgRaEqhr/cGy. In contrast, the ratio, product of orthogonal dimensions/actual volume, varies widely from implant-toimplant, as well as differing systematically from one implant type to another. Investigation of the individual orthogonal dimensions demonstrated that width and height, but not thickness, were moderately well correlated with corresponding maximum implant dimensions. However, in all cases the dimensions were more sensitive to changes in mgRaEqhr/cGy than to changes in implant geometry. Conclusions: The product of the orthogonal dimensions is an unsatisfactory estimator of the actual irradiated volume encompassed by an isodose surface. Isodose surface volumes can be accurately estimated knowing only mgRaEq-hr. Prescribing intracavitary brachytherapy by mgRaEq-hr, or its derivative, total reference air kerma, is equivalent to requiring that an isodose surface encompass a specified volume which does not depend on the implant geometry. Constraining the mgRaEq-hr delivered therefore serves to limit the volume of tissue irradiated to high doses. Brachytherapy, cancer.
Dose-volume
histograms, Intracavitary irradiation, ICRU report 38, MgRaEq-hr,
INTRODUCTION
Uterine cervix
therapy of gynecologic malignancies including dose to point A, mgRaEq-hr, vaginal surface dose, and treatment time. Major systems for treatment of cervix cancer differ not only in choice of dose specification criteria, but in applicator design and geometry, insertion and packing techniques, and relative importance of the external-beam and intracavitary components of irradiation. Both the lack of a universal system of dose specification and reporting and variation in treatment techniques have hampered the interpretation of data of tumor control and treatment se-
Intracavitary irradiation is characterized by steep dose gradients in the vicinity of the sources and throughout the tumor and target volumes. This physical characteristic, along with underutilization of computed tomography and magnetic resonance imaging techniques, makes specification of target absorbed dose and maximum dose to critical structures very difficult. Many quantities have been used to report, prescribe, and to constrain intracavitary
Acknowledgement-The
Presented at the 33rd Annual Meeting of ASTRO, Washington, DC, 3-8 November, 1991. Reprint requests to: Jeffrey F. Williamson, Ph.D., Washington University School of Medicine, Mallinckrodt Institute of Radiology, Radiation Oncology Center, 5 10 S. Kings Highway, St. Louis, MO 63 110.
authors wish to thank William Harms, BSc., for his help with the computer software and hardware.
Dr. Eisbruch’s work was supported, in part, by a clinical fellowship awarded by the American Cancer Society. Accepted for publication 7 August 1992. 733
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quelae from different centers (2). Recently, the International Commission on Radiation Units and Measurements (ICRU), in its Report No. 38, proposed the concept of “reference volume enclosed by the reference isodose surface” as a technique-neutral method of specifying dose in intracavitary therapy (6). Specifically, ICRU Report 38 proposed that the reference volume be taken as the 60 Gy isodose surface, resulting from the addition of dose contributions from any external-beam whole-pelvis irradiation and all intracavitary insertions. ICRU proposed that this pear-shaped reference volume be described in terms of its three orthogonal dimensions, height (H), width (W) and thickness (T), measured in the oblique coronal and sagittal planes containing the intrauterine sources (see Fig. 1). The ICRU report provided little rationale for the choice of the 60 Gy isodose surface as the reference volume nor any guidance in using height, width, and thickness in evaluating clinical implants. Subsequent research has followed two pathways. In a series of papers, Potish et al. (11, 12) have investigated the relationship between the individual ICRU-proposed dimensions and geometric characteristics of the implants such as colpostat separation, vertical and horizontal displacement of the tandem from
(a)
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the colpostat source centers, applicator loading, and vaginal and uterine mgRaEq-hr. Other investigators ( l-3, 9, 12- 15) have proposed using the product of ICRU dimensions, T X W X H, to estimate the actual volume encompassed by various isodose surfaces assuming that this product is proportional to the actual volume. The relationship between the TWH product and the traditional dose-specification quantities, point A dose, mgRaEq-hr, and bladder and rectal reference-point doses have been investigated, with contradictory results (2, 12). The correlation between the ICRU product and long-term sequelae of treatment has been investigated (1, 3, 13- 15) the rationale being the well-established correlation between the volume of tissue irradiated by external irradiation and clinical outcome (7). None of these authors limit themselves to investigating the characteristics of the 60 Gy reference isodose, but measure the ICRU dimensions as a function of either total dose or intracavitary dose. We have analyzed 204 actual implants performed at our institution using dose-volume histograms and computer-assisted measurements of ICRU Report 38 dimensions to investigate the relationship between T X W X H and the actual volume encompassed by specified isodose levels. We demonstrate that mgRaEq-hr (or its derivative,
lb)
Fig. 1. Orthogonal radiographs illustrating composite total intracavitary 60-Gy &dose, obtained by combining two implants performed in the same patient: (A) sagittal film, (B) frontal film. Films from the second implant were superimposed on films from the first implant by aligning bony landmarks (grey outline). The straight unbroken lines indicate the source positions of the second implant. The broken lines indicate the ICRU tilted coronal plane (A) and the titled sagittal plane (B). The gaps between the thin black arrows, the thick black arrows and the white arrows denote ICRU dimensions T, W and H, respectively, of the composite isodose.
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total reference air kerma) alone is a more accurate predictor of volume than the ICRU dimensions product. In addition, we show that although the individual dimensions W, H, and T are correlated with implant geometry, mgRaEq-hr is the dominant factor determining these dimensions. MATERIALS
AND METHODS
Implant films and dosimetric data derived from 204 intracavitary implants of 128 patients treated with irradiation alone for carcinoma of the uterine cervix at the Radiation Oncology Center, Mallinckrodt Institute of Radiology (MIR), between 1979 and 1986 were examined. Most patients were treated with two intracavitary implants consisting of Fletcher-Suit tandems and colpostats loaded with Cesium-137 sources* as described below. In cases where anatomical constraints prevented insertion of vaginal colpostats, a uterine tandem alone, or in conjunction with protruding vaginal sources in a Delclos vaginal cylinder (tandem + cylinder implants), were used according to the radiation oncologist’s decision made at the time of insertion. Irradiation was prescribed according to established treatment policies ( lo), which specify whole pelvis doses ( 1O-40 Gy to midline), mgRaEq-hr (6000-8000) to be delivered in two implants, and parametrial boost doses (20-45 Gy) as a function of clinical stage and volume of local disease. Most of the central dose is delivered by intracavitary therapy. Total point A dose plays no formal role in the MIR prescription system; however, because the mgRaEq-hr actually administered by an implant vary with tandem length and colpostat diameter according to fixed rules, the MIR system delivers a relatively constant (& 5%) total dose to point A for similar tumor types (6087 Gy depending on the stage) regardless of applicator dimensions. One hundred and sixty one (16 1) implants consisted of a tandem and colpostats. The range of mgRaEq-hr delivered by these implants was 1007-8 190 (mean and standard deviation: 3569 f 1875 mgRaEq-hr). Forty-three (43) implants consisted of a tandem + cylinder; these delivered 1444-7 150 mgRaEq-hr (mean: 3373 f 1263). Orthogonal radiographs were obtained after each implant to facilitate computer-assisted+ treatment planning. For this study, we used these films to identify the coordinates in space of each cesium source relative to a coordinate system defined by the intersection of the central rays of the two radiographs. When available, these source coordinates were obtained from archival magnetic tapes made during treatment planning which were transferred digitally to a large mini-computers for further study. Otherwise, the
* Model 6D6C intracavitary tubes, 3M Medical/Surgical Division, St. Paul, MN. + Modulex Treatment Planning System, Version puterized Medical Systems, St. Louis, MO.
2.75, Com-
source coordinates were re-digitized on the treatment planning computer+ and then transferred to the minicomputer. A computer program, written in FORTRAN, was used to combine multiple implants performed in the same patient (composite implant plans), to calculate dose-volume histograms, to display planar isodose distributions, and to compute W, H, and T. Combining isodoses of two implants is illustrated by Fig. 1. The 3-dimensional linear displacement of the second implant origin relative to that of the first, as well as its angular displacements in the anatomic coronal and sag&al planes, were measured from the films by superposing the source positions of the second onto the orthogonal radiographs of the first. The two sets of films were correlated by aligning bony landmarks such as acetabular rims, lumbar spinous processes, pubic symphysis, and sacrum. The measured angular and linear displacements were used by the computer program to transform the coordinates of subsequent implants into the coordinate system of the first. In addition, the angular and linear displacements of the tilted coronal and sagittal planes, as defined by ICRU Report 38, from the Cartesian coordinate system of the first implant were measured. The computer program used these data to derive a transformation matrix that rotated the coordinates of all implants into the dose calculation coordinate system. Its Y (cephalic-caudad) axis was located at the intersection of the tilted coronal and sagittal planes, its X (transverse axis) lay in the tilted coronal plane, the Z (anterio-posterior) axis lay in the tilted sagittal plane and its origin was positioned near the tip of the inferior-most intrauterine source. In this coordinate system, the ICRU coronal and sag&al planes are the planes Z = 0 and X = 0, respectively. Different implants sometimes demonstrated large linear or angular displacements (as much as 2 cm or 25 degrees) from one another relative to common bony anatomy. In these cases, the average of the individual-insertion ICRU planes was used for calculating composite implant dose distributions. In addition to the coordinate transformation data, the computer program was given source loading and implant duration data. Three-dimensional dose calculations were obtained throughout a 16 X 16 X 14 cm3 rectangular volume centered on and parallel to the ICRU composite-implant coordinate system defined above. A 1.5 mm grid spacing was used. The generalized Sievert integral method described by Williamson ( 16) was used to calculate the single-source dose matrix for the steel-encapsulated Cs- 137 sources. Total dose at each point in the 3-D grid was calculated by summing the dose contributions of individual sources. This method ignores applicator attenuation and
* VAX 8650 Minicomputer, Maynard, MA.
Digital Equipment
Corporation,
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colpostat shielding effects ( 17) following conventional practice in this regard. The volume encompassed by each isodose level between 10 and 200 Gy in 2 Gy increments was calculated by counting the relative number of dose points equal to or exceeding each dose level. When properly normalized and plotted as a function of dose, a cumulative dose-volume histogram (DVH) results. These data represent the volume whose dose equals or exceeds the specified dose. No corrections for volume of tissue displaced by the applicators or packing were made. The computer program, described above, also calculated the maximum orthogonal dimensions for each dose level between 10 and 200 Gy. As recommended by ICRU Report 38, height (H) of an isodose volume is its maximum dimension along the tandem, measured in the oblique frontal plane containing the tandem; width (W) is the maximum dimension perpendicular to the tandem within the same oblique frontal plane and thickness (T) is the maximum dimension perpendicular to the tandem, measured in the oblique sagittal plane containing the tandem (Fig. 1). The computer program calculated H and T by scanning each row of the planar dose matrices, Z = 0 and X = 0, starting from the matrix edges and working towards its center. Linear interpolation was used to define the maximum isodose width in any one row. Thus, for high doses characterized by multiple closed surfaces, the maximum distance between the lateral-most intersections of such isodose surfaces and the X-Y plane was recorded as W. In addition to tabulating T, W, H and T - W * H as a function of intracavitary dose, the program calculated the maximum projected geometric dimensions of the implant, x,,,,~, ymax, and zmaxwhere x,,, = Maxi=l,N [xi] Mini,l,N [xi] and xi denotes the tip or end X-coordinate of the i-th cesium source in the ICRU coordinate system. The dosimetric analysis, described above, was performed for each of the 204 individual implants using the composite-implant ICRU co-ordinate system. In addition, calculations were performed for composite intracavitary implants in the same patient for 37 patients for whom both implants consisted of tandem and colpostats and for 14 patients for whom both implants consisted of a tandem f cylinder. Calculations for both individual and composite implants took into account the mgRaEq-hr actually administered to the patient. A number of hypotheses were tested using the above data. The relationship between the individual orthogonal isodose surface dimensions T, W, H, and the physical dimensions of the implants xmax , ymax, and zmaxwere explored by plotting each isodose dimension against the corresponding geometric dimension. One-dimensional linear regressions were obtained to assess the correlation between these parameters. We discovered that the cor-
9:KaleidaGraph: Data analysis/Graphics Macintosh Application Version 2.0, Synergy Software (PCS Inc), Reading, PA 19606.
Volume 25, Number 4, 1993
relation between T and implant maximum dimensions was greatly improved by exploiting a simple physical model. If the implant sources lying in the X-Y plane are assumed to form a disk-shaped planar source of effective radius R, the isodose dimension, H, perpendicular to this plane along its axis, is given by (5)
(Fq. 1)
where Do = M - H - f and ?r - R* = x,,, - y,,,/2. The symbols D, M, T, and f denote absorbed dose, mgRaEq-hr, the exposure rate constant for Ra-226 (8.25 R cm2 mg-’ h-l), and Roentgen-to-cGy conversion factor (0.96 cGy/ R), respectively. This model approximates the implant by a uniform distribution of radioactivity over a disc of area (x,,, * y,,,&2. Solving (Eq. 1) for H yields
H =a.
xnl,, * YInax exp(b * x max * Yin,x) - 1
0%. 2)
where a = G and b = l/I’ * f* (D/M). In practice, the variables a and b were treated as parameters of best fit and (Eq. 2) fitted to the clinical implant data using a personalcomputer data-analysis package5 equipped with a nonlinear, least-squares parameter-estimation technique (8). To conveniently develop hypotheses concerning the relationship of volume to mgRaEq-hr, idealized intracavitary implant geometries were studied. To develop an idealized implant model based on “average” source coordinates, orthogonal films of 87 intracavitary implants performed in 1987 were reviewed. Colpostat source separations, and the mean x, y, and z displacements of the caudal-most tandem source location from the transverse plane bisecting the vaginal sources were measured and stratified by colpostat diameter. Average source coordinates for each applicator loading used in our system were defined including medium tandem ( 1O-20 mgRaEq loading) and regular tandem ( lo- 1O-20 loading) combined with Delclos mini-colpostats (10 mg loading) and 2,2.5 and 3 cm diameter Fletcher colpostats loaded with 20, 25, and 30 mgRaEq sources, respectively. Three-dimensional dose calculations and DVH’s were evaluated as described above for each loading. The nonlinear, least-squares parameter estimation technique, described above, was used to fit the following power-law model to these DVH data:
V(D, M) = [a + /3(F) + *(;)l]$)’
(Eq.3)
Tissue volume estimation 0
where (Y,p, 6, and t are parameters of best fit, D denotes absorbed dose in cGy, M denotes mgRaEq-hr and V denotes volume (cm3) encompassed by isodose-curve surface, D. This model was tested against the DVH’s derived from the clinical implants. RESULTS The DVH data of the idealized implants, illustrated by Figure 2, shows that volumes encompassed by any specified isodose level is very similar for implants delivering the same ratio, M/D, in units of mgRaEq-hr/cGy, despite significant differences in source loading and relative source positions. Using M/D rather than M or D alone as the independent parameter, suppresses much of the implantto-implant variation in isodose surface location, relative to the radioactive sources, due to differences in mgRaEqhr delivered by different implants. Using nonlinear leastsquares analysis to fit the model, (Eq. 3), to this data, yielded best-fit values for the parameters (Y,& 6 and E of MIR
idealized
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A. EISBRUCHet a/.
104.8, -8.103, 0.437 and 1.635 with a regression coefficient of 0.999997. This model reproduces the DVH’s with an accuracy of 5% for M/D ratios as small as 0.7-l .O depending on loading. For total mgRaEq-hr characteristic of the MIR treatment system, this corresponds to doses between 120- 140% of the point A dose and includes all doses of clinical interest, including doses to bladder and rectal reference points. Physically, the excellent agreement between power-law model and DVH calculations demonstrates that intracavitary implants volumetrically behave like single central point sources, regardless of underlying geometry. Using the notation of the previous section, the DVH of a point source is given by 30
.
Equations (3) and (4) are very similar: the power-law model has an exponent of 1.635 compared to a value of 1.5 for an implant consisting of a single isotropic point lntracavitary
Applications
1000
600
400
60
A toomg m-30
0.4
1 .o
0%. 4)
2.0
10-10-20
4.0
6.0
mgRaEq-hrs/cGy Fig. 2. Dose-volume histograms for idealized MIR implants with different loadings, plotted as a function of mghr/ cGy. The symbols designate actual volumes determined by DVH’s; the solid line indicates the volume predicted by the power-law model (Eq. 3).
I. J. Radiation Oncology ??Biology 0 Physics
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source. The values of V predicted by the power-law model, (Eq. 3), using only total mgRaEq-hr and dose as independent variables, will be referred to as the predicted volume in subsequent discussions. Both predicted volume and the ICRU product, TWH, were compared to the actual volume determined by DVH’s derived from the actual patient implants. A scatterogram of the ratios of predicted volume (according to our power-law model)/actual volume as well as the ratios of TWH product/actual volume are plotted for various dose levels in Figure 3 for the 16 1 individual tandem and colpostat implants. The TWH/actual volume ratios for different implants at any isodose level vary widely with a range as large as 0.2-6.2 at high dose levels. At lower dose levels, which give rise to isodose surfaces further away from the implant, the ratios TWH/actual volume exhibit less implant-to-implant variability. In contrast, the ratios of predicted volume/actual volume for the same implants (Fig. 3B) show significantly less implant-to-implant variability at every isodose level. The means and percent standard deviations of the ratios of predicted/actual volume for individual tandem and colpostats implants (Fig. 4A) are 1.002 f 1.6%, I .016 + 6.4% and 1.099 f 11.7% for the 20, 40, and 60 Gy isodoses, respectively. At higher isodose levels the means show a larger deviation from unity and larger % standard deviations (1.187 + 13.3% and 1.272 f 13% for the 80 Gy and 100 Gy, respectively). No significant difference between the implant types (tandem and colpostats vs tandem + cylinder) was noted. In contrast, the ratio TWH/ actual volume shows large variability at all isodose levels examined, except the 20 Gy level (tandem and colpostat
A.
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insertions: means +- S.D. of 1.903 + 7.2%, 2.09 1 + 17.6%, 2.396 & 27%, 2.590 + 32%, 2.812 + 39% for the 20,40, 60,80 and 100 Gy isodoses, respectively). Comparison of the mean TWH/actual volume ratios of the tandem and colpostats insertions to that of the tandem + cylinder group, reveals mean differences between the two implant types ranging from 10% to 50% over the 20-60 Gy dose range. For the individual insertions, the 120 Gy isodose did not form a single surface in many cases, but formed multiple closed surfaces around individual sources and therefore calculations were not plotted for this dose level. For the composite implant dose calculations, the 120 Gy isodose surface was located further away from the sources, forming a single closed surface in all cases, and was therefore included in the analysis. Volume ratios for the composite insertion plans (Fig. 4B) show less variability compared to individual implants. Since the total mgRaEq-hr delivered by a combined plan is approximately twice that of each single implant, each isodose surface of interest is located farther away from the sources, which now behave more like point sources. The mean of the ratios of predicted volume/actual volume for combined tandem and colpostats insertions is practically unity with S.D. + 1.2%, 1.7%, 2.3%, 3.3%, 6.4%, 9.8% for the 20, 40, 60, 80, 100, and 120 Gy isodose surfaces, respectively. Similar values are observed for tandem f. cylinder applications. The ratios of TWH/actual volume for cumulative implants have less variability (S.D. + 2.8%, 5.9%, 8.7%, 12.2%, 14.7%. and 15.7% for the 20,40,60,80, 100 and 120 cGy isodose surfaces, respectively) than the ratios for individual implants, but significantly more than the predicted volume ratios. Systematic differences between the different im-
TWH Product/Actual Volume
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Volume 25, Number 4, 1993
.
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volume/actual
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O
Tissue volume estimation 0 A. EISBRUCH
INDIVIDUAL INTRACAVITARY INSERTtONS Ratios of TWHlactual volume and radlctad/actual volume at various mghr /c cpy values
INDIVIDUAL INTRACAVITARY INSERTIONS Ratios of TWHhctual volume and predicted/actual volume at various dose levels
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CUMULATIVE INTRACAVlTARY INSERTlONS Ratios of TWHhctual volume and redlctad/actual volume at varlous mghr k 8 y values
CUYULATlVE INTRACAVlTARY INSERTIONS Ratlor ot TWH/actual volume and radtcted/actual volume
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Fig. 4. Volume ratios of (A) individual and (B) composite implants at various isodose levels. Circles denote means of the ratios for tandem and colpostats insertions and triangles denote means for tandem + cylinder insertions. Open symbols are means of the TWH product/actual volume ratios and solid symbols denote means of the predicted volume/actual volume ratios. The vertical bars show the standard deviations.
plant geometries (tandem and colpostats compared to tandem + cylinder) still exist at dose levels above 40 Gy. Figure 5 presents the ratios of predicted/actual volume and of TWH roduct/actual volume as a function of various M/D levepls in units of mgRaEq-hr/cGy (the variable of the power-law volume model). The ratios of predicted/ actual volume exhibit small standard deviations (< 5%) when M/D is greater than 0.8. For M/D = 0.5 the variability is larger: SD = 10.5% for tandem + colpostat and 7.2% for tandem f cylinder implants. There is no difference in the means and deviations of predicted/actual volume ratios of individual implants compared to composite implants. The composite-plan TWH/actual volume ratios and standard deviations vary somewhat from their individual-insertion plan counterparts, especially for small values of M/D. However, none of these variations is significant. Clearly the ratio M/D is a useful parameter in
6.5
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dose-volume analysis: specifying isodose curves in terms of M/D eliminates the variability in mgRaEq-hr characteristic of using dose as an independent parameter and therefore reduces the variability in average distance of any specified isodose curve from the radioactive sources. Figure 6 shows the relationship between the individual ICRU isodose dimensions W, H, and T and the corresponding maximum implant geometric dimension, xmax, y,,,,or z,,, for M/D ratios of 0.5 to 2.0. These data are plotted for 77 individual implants consisting of tandems and colpostats. Applying simple linear regression models of the form I-I = a(M/D) * ymax + WWD)
(Eq. 5)
yields moderately high linear regression coefficients (r values) for the correlation of W and H with xmaxand y,,, respectively: r values of 0.61 to 0.82 for M/D ratios between 1.0 and 2.0. These correlations are qualitatively similar to those found by Potish (1 l), who used much
I. J. Radiation Oncology 0 Biology0 Physics Individual
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Volume 25, Number 4. 1993
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Fig. 6. ICRU isodose dimensions T, W, and H, as a function of the corresponding maximum implant dimensions x,,,~, ymaxand z,,, at various values of M/D (mghr/cGy). The symbols denote the actual ICRU dimensions determined by 3D computer calculations. For each value of M/D, the lines represent best-fit linear regression.
7.0
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Tissue
volume estimation 0
more sophisticated multiple-variable linear models to study the relationship between T, W, and H and implant dimensions for 90 Fletcher intracavitary insertions. In contrast (Fig. 6C), isodose thickness T is poorly correlated wi:h the single variable z,,, with r values ranging from 0.015 to 0.23. In contrast, when the data are fit to our nonlinear model (equation 2), an excellent correlation between T and the area product xmax- ymaxis achieved (Fig. 7): Correlation coefficients vary from 0.77 to 0.84 for M/D values of 0.8 to 2.0. These simple models suggest that, on average, the isodose surface dimensions are much more sensitive to the variable M/D than to small changes in the geometric dimensions of implant. For example, at the average values of xmax- ymax= 25 cm* and M/D = 1.O mgRaEq-hr/cGy, 5% changes in M/D and x,,, - ymaxproduce changes in T of 4.2% and 1.8%, respectively. On average, the parameters T, W, and H are three times more sensitive to M/D changes than to similar relative changes in the corresponding implant dimensions. Figures 6 a,b & 7 indicate that the slopes of W, H, and T with respect to xmax, y,,, , and x,,, - ymax are nearly independent of the M/D ratio. This finding is somewhat surprising since one would expect that the dimensions of low-M/D isodoses, which correspond to high-dose isosurfaces close to the implanted sources, might be more sensitive to changes in implant geometry. This suggests that the 60 Gy total dose level, chosen by the ICRU to Individual Il.0
0.0
Tandem
and
Colpostat
Insertions
,
+
MI”
= “3
A
MI”
Y
x
HI”
= 1.”
.
MI”
= 1.1
.
HI”
I
“A
2.”
i.“‘,‘.‘.,...‘,‘..‘,...‘,...‘,.‘..,.”r IO
15
7.0
1.5
30
3s
Producl of maximum coronal x
I..
*I
I.,
JO
JS
50
implant dimensions
(cm*)
Fig. 7. ICRU isodose surface thickness (T) plotted as a function of the product of the maximum implant coronal dimensions at various values of M/D. The symbols denote the actual dimensions and the lines represent isodose thickness as predicted by the planar source model (Eq. 2) using values of a, b that were estimated by non-linear least-square curve fitting.
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A. EISBRUCHet al.
define the reference volume, yields as good a correlation between isodose dimensions and corresponding implant dimensions as any other choice of reference dose level. In the MIR treatment system, for which the most frequent prescription is 20 Gy whole pelvis irradiation and 8000 mgRaEq-hr of intracavitary therapy, the choice of 60 Gy corresponds to an M/D ratio of 2.0 = (6000 cGy - 2000 cGy contributed to that isodose by the implant)/8000 mgRaEq-hr. Revising this value to M/D of 1.2, the value corresponding approximately to the point A isodose, would not improve the sensitivity the reference volume orthogonal dimensions to what seems to be the most significant implant geometry parameters. DISCUSSION The utility of the ICRU product, TWH, for predicting treatment sequelae, has been examined by several authors (1-3, 12-l 5). This strategy is based on the assumption that TWH is proportional to volume encompassed by the corresponding dose level, that is, that TWH/actual volume is approximately constant over the range of doses and implant geometries under investigation. Contradictory results have been reported: Crook et al. (l), found that Grade 3 rectal complications were correlated with high TWH product, and the zone of risk for severe bladder complications could be described in terms of high bladder doses and large TWH on a 2-dimensional scatterogram. In patients treated by high dose-rate irradiation for cancer of the cervix, Van Lancker et al. (15) found the TWH product to be significantly higher in patients who had late treatment complications compared to patients who did not have late complications. In contrast, Pourquier et al. did not find any correlation between the TWH product and late rectal ( 13) or bladder ( 14) complications. Our study has demonstrated that there is a large insertion-to-insertion variation in the ratio TWH/actual volume at the 60 Gy reference dose level as well as at other dose levels. This finding may help explain the contradictory findings, described above, when volume-dependent treatment sequelae are investigated. If such clinical endpoints truly are volume dependent, a good correlation will be found only if the study parameter used is closely proportional to the actual volume encompassed by the corresponding isodose surface. The TWH product is not a suitable volumetric parameter because of the large variations in its relationship to the actual volume and because of its dependence on the geometry of the implant. An implant consisting of a tandem and colpostats produces pear-shaped isodose surfaces, which (when far away from the implant) approximate a spherical surface the volume of which is approximately V = n/6 (D3) where the diameter D corresponds to the mean value of T, W and H. The relationship between TWH (approximated by D3) and the volume of the sphere is D3/a/6 (D3) z 1.9 1. A tandem -t-cylinder produces isodose volumes that are approximately cylindrical in shape whose volume can be
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approximated by 7r/4 - L* - H where L is the width or thickness of the isodose surface and H its height. The product of ICRU dimensions is L* * H in this case, giving a ratio of TWH/actual volume of L* - H/?r/4 L*H = 1.27. For tandem and colpostats insertions, higher mgRaEq-hr in the colpostats (relative to the mg-hr in the tandem sources) and (less important) wider separations of the colpostats make the resultant isodose surfaces more spherical while lower mg-hr in the colpostats and narrower separation will result in more cylinder-like isodose surfaces. Consequently, the ratio TWH/actual volume of an isodose surface varies between different implants. The correlation between mgRaEq-hr and the isodose surface dimensions T, W, and H was investigated by Potish ( 12) who found a little effect of application geometry on TWH product, but a large effect on the individual ICRU dimensions. The TWH product was found to be in good correlation with mgRaEq-hr, in a linear regression analysis looking separately at each isodose level. A linear relationship between mgRaEq-hr and TWH product for any fixed external irradiation dose was also found by Esche et al. (2). In contrast, we have found a non-linear relationship between volume encompassed by an isodose surface and mgRaEq-hr: Va (mgRaEq-hr)‘.635. Extending this approach, we have developed a modified power-law model, the product of a quadratic term in (M/D) and a power-function term (M/D)’ which, far more accurately than TWH, predicts the actual volume encompassed by any isodose surface over a wide range of doses, D, and mgRaEq-hr, M. This modified power-law model permits prediction of isodose volume, knowing only the mgRaEq-hrs, before computerized isodoses are plotted. The relationship can be used to incorporate volumetric limitations into the initial prescription. The excellent agreement of this simple model with 3-D dose calculations about 204 clinical implants is consistent with the hypothesis that intracavitary implants volumetrically behave like central point sources of radiation over the range of doses of clinical interest. Our formula predicts the volume encompassed by an isodose volume within 5% in 67% of the implants and within f 10% in 95% of the implants when the value of mgRaEq-hr/cGy is 0.8 with accuracy improving with increasing values of mgRaEq-hr/cGy. This correlation holds despite significant variations in implant geometry and loading arising from a variety of tandem lengths and colpostat diameters, variable colpostat separations and tandem-to-colpostat offsets, and different applicators (colpostats vs. vaginal cylinders) which are introduced to customize the treatment to individual patient anatomy. The predictive accuracy of the model is unchanged when applied to composite multiple-insertion implants performed in the same patient, indicating that the additional geometric variation caused by angular and linear displacements of the successive implants relative to the first does not influence the relationship between isodose volume and mgRaEq-hr.
Volume 25. Number 4, 1993
Calculations of an isodose volume for combined intracavitary and external irradiation, in our model, take into account the difference between the isodose whose volume is searched for, and the dose delivered at the same location by external beam therapy. For example, a typical Mallinckrodt treatment prescription consisting of 20 Gy whole pelvis external dose and 8000 mg-hr in two intracavitary implants can be translated into a statement of volume occupied by the 60 Gy reference volume: the intracavitary dose will be 40 Gy and under this condition, the overall treatment is equivalent to treating with intracavitary implants until 40 Gy isodose surface achieves according to our model a volume of [109.8 - 8.1 X 8000/4000 + (8000/4000)*] (8000/4000)1.635 = 296 cm3. For the same mgRaEq-hr prescription, increasing the whole pelvic irradiation to 30, 40, and 50 Gy will result in calculated volumes of 454, 8 14, and 2186 cm3, respectively. The actual measured volumes for 204 implants correlate well with these predicted volumes (Ratio predicted/actual value = 1, standard deviation within 3%). The dependence of ICRU reference dimensions product on the dose of external radiation was investigated by Esche et al. (2) and Nath et al. (9) who found that the TWH product initially rises slowly with increasing external dose but the rate of increase accelerates dramatically above 30 Gy. This is readily explained by the power-law dependence of volume on M/D in our model, and can be easily calculated using it. Our investigation has utilized the quantities equivalent mass of radium (unit: mgRaEq-hr) and mgRaEq-hr to describe source strength and integrated source strength (product of strength and duration), respectively. The ICRU has proposed adopting the quantity total reference air kerma (TRAK) as a measure of integrated source strength, or total output, in place of mgRaEq-hr. Both quantities are measures of the output in free space accumulated at a distance of 1 m from the implant in the absence of patient and applicator attenuation: TRAK is simply the air-kerma in free space that would be measured at 1 m from a hypothetical implant consisting of a point source that administered the same mgRaEq-hr as the implant in the patient. In symbols,
(Eq. 6)
where (Pa)Ra,o.sis the exposure-rate constant for Ra-226 filtered by 0.5 mm of platinum (8.25 R - cm* - mg-’ - h-l), and (W/e) is the mean energy required to produce an ion pair in air (0.876 cGy/R), and TRAK has units pGy * m*. Thus 1 unit of TRAK = 1 pGy- m* = 1 cGy 0 cm* = 0.138 mgRaEq-hr. This relationship, which can be used to transform the M/D ratios in equations (2)-(4) into TRAK/D ratios, shows that our conclusions are equally valid when total reference air kerma is used. Our conclusions regarding dependence of individual
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reference isodose dimensions, the product of ICRU dimensions, and the relationship between volume and mgRaEq-hr are empirical findings and are strictly valid only within the range of implant geometries characteristic of our treatment system. However, generalization of the concept to all intracavitary implants seems reasonable. If so, we have shown that not only is TWH a poor predictor of volume enclosed by isodose surfaces, but that isodose surface volume can be accurately inferred from total intracavitary dose and mgRaEq-hrs (or equivalently TRAK) and therefore conveys no more information than a statement of these two quantities. This has two important consequences. First, isodose-surface volume is no more useful as a prognostic variable than mgRaEq-hr: the correlation between clinical outcome, in terms of tumor control and complications, and volume of ICRU reference isodose surface should be no better nor any worse than the correlation between clinical outcome and mgRaEqhr for a fixed external pelvis dose. Secondly, our findings suggest an additional basic physical interpretation of mgRaEq-hr and total reference air kerma: termination of an intracavitary treatment so as to administer a specified mgRaEq-hr dose is equivalent to treating the patient until any specified reference isodose occupies a fixed volume. From a clinical point of view, use of mgRaEq-hr as a prescription or treatment-constraining parameter is a means of limiting the volume of tissue irradiated to a high dose. In contrast, the individual dimensions T, W, and H, although dominated by the mgRaEq-hr delivered, are moderately well correlated with the coronal area covered by the implanted sources, the colpostat separation, and maximum geometric cephalic-caudad length of the implant, respectively. These parameters, considered individually, convey additional information about the isodose distribution, can not be inferred from a statement of mgRaEq-hr, and may be useful as prognostic factors. Our dosimetric analysis has neglected a number of factors that can potentially influence the tissue volume contained within isodose surface contours. These factors include applicator attenuation and shielding corrections, which are known ( 16) to spare localized regions by 1O25%, as well as the volume occupied by vaginal packing and the applicators themselves. Following classical (and current clinical) practice in this regard seems justifiable since isodose volume and ICRU dimensions are empirical dose specification parameters much like the classical quantities, mgRaEq-hr and point A dose. These quantities seeks to describe the treatment delivered without the aid of quantitative geometric descriptions of the shape and location of the target volume and organs at risk relative to the implanted sources. With respect to tumor control, isodose surface volume is an imprecise prognostic variable, since the specified isodose surface may not encompass all of the gross tumor. With respect to normal tissue tolerance, the fraction of bladder, rectum and small bowel versus more radioresistant connective tissue enclosed within the isodose surface most likely varies significantly
from patient-to-patient as well as with packing and insertion technique. As suggested by other authors (4, 12) the volume of tumor present and magnitude of focal highdose regions in the rectum or bladder may be at least as important as overall volume of tissue treated to a specified dose. Achievement of improved correlation between physical dose specification parameters and clinical outcome probably requires use of 3-D image-based treatment planning to better define patient anatomy in relation to the implant.
CONCLUSIONS We have shown that the growing practice of using the product of ICRU orthogonal dimensions, TWH, in clinical studies to estimate volume enclosed by intracavitary implant isodose surfaces appears to be without physical foundation. The ratio of TWH to true volume given by dose-volume histogram analysis, varies widely from patient-to-patient and from implant type-to-implant type. More importantly, we have shown that over the dose range of therapeutic interest, the actual volume enclosed by isodose surfaces can be accurately estimated from a modified power-law model requiring knowledge only of the intracavitary dose and mgRaEq-hr (or equivalently, total reference air kerma). Consequences of this finding include: (a) volumetrically an intracavitary implant behaves like a central point source: (b) describing an implant in terms of volume contained within its isodose curves has no more information content than a statement of mgRaEq-hr or total reference air kerma; and (c) the volume of tissue irradiated to a specified dose is closely related to total exposure given by the implant in terms of mgRaEq-hr or TRAK. Consequence (b) suggests that the correlation between clinical outcome, in terms of tumor control and complications, and isodose surface volume should be no better nor any worse than the correlation between clinical outcome and mgRaEq-hr for a fixed external pelvis dose. Consequence (c) suggests a new and fundamental physical interpretation of mgRaEq-hr or its derivative, total reference air kerma: Prescribing intracavitary brachytherapy by mgRaFq-hr is equivalent to treating until each specified isodose surface achieves a fixed volume which is independent of the underlying implant geometry. Use of mgRaEq-hr to constrain intracavitary treatment therefore limits the volume of tissue irradiated to high doses. This observation may help explain the clinical utility of mgRaEq-hr as a dose-specification parameter. Finally, the individual reference isodose dimensions, which are more strongly influenced by implant geometry than their product, clearly convey additional information about the spatial extension of the reference isodose surface in their respective planes, can not be reduced to a statement of total exposure from the implant, and may have prognostic significance.
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REFERENCES
1. Crook, J. M.; Esche, B. A.; Chaplain, G.; Isturiz, J.; Sentenac, I.; Horiot, J.-C. Dose-volume analysis and the prevention of radiation sequelae in cervical cancer. Radiother. Oncol. 8:321-332;1987. 2. Esche, B. A.; Crook, J. M.; Isturiz, J.; Horiot, J.-C. Dosi-
3.
4.
5. 6.
7.
8.
9.
metric methods in the optimization of radiotherapy for carcinoma of the uterine cervix. Int. J. Radiat. Oncol. Biol. Phys. 13:1183-1192;1987. Esche, B. A.; Crook, J. M.; Isturiz, J.; Horiot, J.-C. Reference volume, milligram-hours and external irradiation for the Fletcher applicator. Radiother. Oncol. 9:255-2611;1987. Gillin, M. T.; Kline, R. W.; Komaki, R.; Greenberg, M. Correlation of treatment volume with milligram-hours for intracavitary applications for carcinoma of the cervix. Int. J. Radiat. Oncol. Biol. Phys. 11:1407-1412;1985. Hines, G. J.; Brownell, G. R. Radiation dosimetry. New York, NY: Academic Press; 1986:763-765. ICRU Report #38: Dose and volume specification for reporting intracavitary therapy in oncology. Bethesda, Maryland: International Commission on Radiation Units and Measurements: March 1, 1985. Letschet, J. G. J.; Lebesque, J. V.; de Boer, R. W.; Hart, A. A. M.; Bartelink, H. Dose-volume correlation in radiation-related late small-bowel complications: A clinical study. Radiother. Oncol. 18:307-320; 1990. Marquardt, D. W. An algorithm for least-squares estimation of non-linear parameters. J. Sot. Ind. Appl. Math. 11:43 l441;1963. Nath, R.; Urdaneta, N.; Bolanis, N.; Peschel, R. A dosimetric analysis of Morris, Fletcher, and Henschke systems for treatment of uterine cervix carcinoma. Int. J. Radiat. Oncol. Biol. Phys. 2 1:995- 1003; 199 1.
10. Perez, C. A.; Fox, S.; Lockett, M. A.; Grigsby, P. W.; Camel, H. M.; Galakatos, A.; Kao, M.-S.; Williamson, J. F. Impact of dose in outcome of irradiation alone in carcinoma of the uterine cervix: Analysis of two different methods. Int. J. Radiat. Oncol. Biol. Phys. 2 1:885-898; 199 1. 11. Potish, R. A.; Gerbi, B. J. Cervical cancer: Intracavitary dose specification and prescription. Radiology 165:555560; 1987. 12. Potish, R. A. The effect of applicator geometry on dose specification in cervical cancer. Int. J. Radiat. Oncol. Biol. Phys. 18:1513-1520;1990. 13. Pourquier, H.; Delard, R.; Achille, E.; Daly, N. J.; Horiot, J. C.; Keiling, R.; Pigneux, J.; Rozan, R.; Schraub, S.; VrouSOS,C. A Quantified approach to the analysis and prevention of urinary complications in radiotherapeutic treatment of cancer of the cervix. Int. J. Radiat. Oncol. Biol. Phys. 13: 1025-1033;1987. 14. Pourquier, H.; Dubois, J. B.; Delard, R. Cancer ofthe 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. 15. Van Lancker, M.; Storme, G. Prediction of severe late complications in fractionated, high dose-rate brachytherapy in gynecological applications. Int. J. Radiat. Oncol. Biol. Phys. 20:1125-l 129;1991. 16. Williamson. J. F. Dose calculations about shielded gynecological colpostats. Int. J. Radiat. Oncol. Biol. Phys. 19: 167-178;1990. 17. Williamson, J. F. Monte Carlo and analytic calculation of absorbed dose near ‘.“Cs intracavitary sources. Int. J. Radiat. Oncol. Biol. Phys. 15:227-237; 1988.
25. pp.
733-744 Copyright
0360-3016/93 $6.00 + .Xl 0 1993 Pergamon Press Ltd.
0 Technical Innovations and Notes ESTIMATION OF TISSUE VOLUME IRRADIATED BY INTRACAVITARY IMPLANTS AVRAHAM EISBRUCH, M.D., JEFFREY F. WILLIAMSON, PH.D., D. Ross DICKSON, PERRY W. GRIGSBY, M.D. AND CARLOS A. PEREZ, M.D.
M.D.,
Washington University School of Medicine, Mallinckrodt Institute of Radiology, Radiation Oncology Center, St. Louis, MO Purpose: The volume of space enclosed by a specified isodose surface arising from an intracavitary implant may correlate with clinical outcome. Several investigators have proposed using the product of the three maximum orthogonal dimensions of the isodose surface as a measure of this volume. We have examined the accuracy of this proposal and compared it to a simpler model for estimating volume which requires only knowledge of the mgRaEqhrs (total reference air kerma) and the dose level. Methods and Materials: Orthogonal films from 204 intracavitary implants of 128 patients with carcinoma of the cervix were used to reconstruct the “‘Cs-source coordinates. The source location, strength and duration data were used to calculate dose-volume histograms, yielding the volume enclosed by each dose level as well as its orthogonal dimensions: thickness, width, and height. Using bony landmarks to align films for different insertions in the same patient, similar calculations were repeated for composite implant source coordinates. Results: Curve-fitting techniques revealed that the volume encompassed by each isodose level could be predicted by a modified power-law function of the mgRaEq-hr/dose ratio: predicted volume = 1104.8 - 8.103 *(M/D) + 0.437 - (M/D)‘]. (M/D) ’.635where M/D = mgRaEq-hr/cGy. The volume predicted by this simple model is accurate within + 10% in 95% of the implants when mgRaEq-hr/cGy = 0.8. Accuracy increases with increasing mgRaEqhr/cGy. In contrast, the ratio, product of orthogonal dimensions/actual volume, varies widely from implant-toimplant, as well as differing systematically from one implant type to another. Investigation of the individual orthogonal dimensions demonstrated that width and height, but not thickness, were moderately well correlated with corresponding maximum implant dimensions. However, in all cases the dimensions were more sensitive to changes in mgRaEqhr/cGy than to changes in implant geometry. Conclusions: The product of the orthogonal dimensions is an unsatisfactory estimator of the actual irradiated volume encompassed by an isodose surface. Isodose surface volumes can be accurately estimated knowing only mgRaEq-hr. Prescribing intracavitary brachytherapy by mgRaEq-hr, or its derivative, total reference air kerma, is equivalent to requiring that an isodose surface encompass a specified volume which does not depend on the implant geometry. Constraining the mgRaEq-hr delivered therefore serves to limit the volume of tissue irradiated to high doses. Brachytherapy, cancer.
Dose-volume
histograms, Intracavitary irradiation, ICRU report 38, MgRaEq-hr,
INTRODUCTION
Uterine cervix
therapy of gynecologic malignancies including dose to point A, mgRaEq-hr, vaginal surface dose, and treatment time. Major systems for treatment of cervix cancer differ not only in choice of dose specification criteria, but in applicator design and geometry, insertion and packing techniques, and relative importance of the external-beam and intracavitary components of irradiation. Both the lack of a universal system of dose specification and reporting and variation in treatment techniques have hampered the interpretation of data of tumor control and treatment se-
Intracavitary irradiation is characterized by steep dose gradients in the vicinity of the sources and throughout the tumor and target volumes. This physical characteristic, along with underutilization of computed tomography and magnetic resonance imaging techniques, makes specification of target absorbed dose and maximum dose to critical structures very difficult. Many quantities have been used to report, prescribe, and to constrain intracavitary
Acknowledgement-The
Presented at the 33rd Annual Meeting of ASTRO, Washington, DC, 3-8 November, 1991. Reprint requests to: Jeffrey F. Williamson, Ph.D., Washington University School of Medicine, Mallinckrodt Institute of Radiology, Radiation Oncology Center, 5 10 S. Kings Highway, St. Louis, MO 63 110.
authors wish to thank William Harms, BSc., for his help with the computer software and hardware.
Dr. Eisbruch’s work was supported, in part, by a clinical fellowship awarded by the American Cancer Society. Accepted for publication 7 August 1992. 733
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quelae from different centers (2). Recently, the International Commission on Radiation Units and Measurements (ICRU), in its Report No. 38, proposed the concept of “reference volume enclosed by the reference isodose surface” as a technique-neutral method of specifying dose in intracavitary therapy (6). Specifically, ICRU Report 38 proposed that the reference volume be taken as the 60 Gy isodose surface, resulting from the addition of dose contributions from any external-beam whole-pelvis irradiation and all intracavitary insertions. ICRU proposed that this pear-shaped reference volume be described in terms of its three orthogonal dimensions, height (H), width (W) and thickness (T), measured in the oblique coronal and sagittal planes containing the intrauterine sources (see Fig. 1). The ICRU report provided little rationale for the choice of the 60 Gy isodose surface as the reference volume nor any guidance in using height, width, and thickness in evaluating clinical implants. Subsequent research has followed two pathways. In a series of papers, Potish et al. (11, 12) have investigated the relationship between the individual ICRU-proposed dimensions and geometric characteristics of the implants such as colpostat separation, vertical and horizontal displacement of the tandem from
(a)
Volume 25, Number 4. 1993
the colpostat source centers, applicator loading, and vaginal and uterine mgRaEq-hr. Other investigators ( l-3, 9, 12- 15) have proposed using the product of ICRU dimensions, T X W X H, to estimate the actual volume encompassed by various isodose surfaces assuming that this product is proportional to the actual volume. The relationship between the TWH product and the traditional dose-specification quantities, point A dose, mgRaEq-hr, and bladder and rectal reference-point doses have been investigated, with contradictory results (2, 12). The correlation between the ICRU product and long-term sequelae of treatment has been investigated (1, 3, 13- 15) the rationale being the well-established correlation between the volume of tissue irradiated by external irradiation and clinical outcome (7). None of these authors limit themselves to investigating the characteristics of the 60 Gy reference isodose, but measure the ICRU dimensions as a function of either total dose or intracavitary dose. We have analyzed 204 actual implants performed at our institution using dose-volume histograms and computer-assisted measurements of ICRU Report 38 dimensions to investigate the relationship between T X W X H and the actual volume encompassed by specified isodose levels. We demonstrate that mgRaEq-hr (or its derivative,
lb)
Fig. 1. Orthogonal radiographs illustrating composite total intracavitary 60-Gy &dose, obtained by combining two implants performed in the same patient: (A) sagittal film, (B) frontal film. Films from the second implant were superimposed on films from the first implant by aligning bony landmarks (grey outline). The straight unbroken lines indicate the source positions of the second implant. The broken lines indicate the ICRU tilted coronal plane (A) and the titled sagittal plane (B). The gaps between the thin black arrows, the thick black arrows and the white arrows denote ICRU dimensions T, W and H, respectively, of the composite isodose.
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Tissue volume estimation 0 A. EISBRUCH etal
total reference air kerma) alone is a more accurate predictor of volume than the ICRU dimensions product. In addition, we show that although the individual dimensions W, H, and T are correlated with implant geometry, mgRaEq-hr is the dominant factor determining these dimensions. MATERIALS
AND METHODS
Implant films and dosimetric data derived from 204 intracavitary implants of 128 patients treated with irradiation alone for carcinoma of the uterine cervix at the Radiation Oncology Center, Mallinckrodt Institute of Radiology (MIR), between 1979 and 1986 were examined. Most patients were treated with two intracavitary implants consisting of Fletcher-Suit tandems and colpostats loaded with Cesium-137 sources* as described below. In cases where anatomical constraints prevented insertion of vaginal colpostats, a uterine tandem alone, or in conjunction with protruding vaginal sources in a Delclos vaginal cylinder (tandem + cylinder implants), were used according to the radiation oncologist’s decision made at the time of insertion. Irradiation was prescribed according to established treatment policies ( lo), which specify whole pelvis doses ( 1O-40 Gy to midline), mgRaEq-hr (6000-8000) to be delivered in two implants, and parametrial boost doses (20-45 Gy) as a function of clinical stage and volume of local disease. Most of the central dose is delivered by intracavitary therapy. Total point A dose plays no formal role in the MIR prescription system; however, because the mgRaEq-hr actually administered by an implant vary with tandem length and colpostat diameter according to fixed rules, the MIR system delivers a relatively constant (& 5%) total dose to point A for similar tumor types (6087 Gy depending on the stage) regardless of applicator dimensions. One hundred and sixty one (16 1) implants consisted of a tandem and colpostats. The range of mgRaEq-hr delivered by these implants was 1007-8 190 (mean and standard deviation: 3569 f 1875 mgRaEq-hr). Forty-three (43) implants consisted of a tandem + cylinder; these delivered 1444-7 150 mgRaEq-hr (mean: 3373 f 1263). Orthogonal radiographs were obtained after each implant to facilitate computer-assisted+ treatment planning. For this study, we used these films to identify the coordinates in space of each cesium source relative to a coordinate system defined by the intersection of the central rays of the two radiographs. When available, these source coordinates were obtained from archival magnetic tapes made during treatment planning which were transferred digitally to a large mini-computers for further study. Otherwise, the
* Model 6D6C intracavitary tubes, 3M Medical/Surgical Division, St. Paul, MN. + Modulex Treatment Planning System, Version puterized Medical Systems, St. Louis, MO.
2.75, Com-
source coordinates were re-digitized on the treatment planning computer+ and then transferred to the minicomputer. A computer program, written in FORTRAN, was used to combine multiple implants performed in the same patient (composite implant plans), to calculate dose-volume histograms, to display planar isodose distributions, and to compute W, H, and T. Combining isodoses of two implants is illustrated by Fig. 1. The 3-dimensional linear displacement of the second implant origin relative to that of the first, as well as its angular displacements in the anatomic coronal and sag&al planes, were measured from the films by superposing the source positions of the second onto the orthogonal radiographs of the first. The two sets of films were correlated by aligning bony landmarks such as acetabular rims, lumbar spinous processes, pubic symphysis, and sacrum. The measured angular and linear displacements were used by the computer program to transform the coordinates of subsequent implants into the coordinate system of the first. In addition, the angular and linear displacements of the tilted coronal and sagittal planes, as defined by ICRU Report 38, from the Cartesian coordinate system of the first implant were measured. The computer program used these data to derive a transformation matrix that rotated the coordinates of all implants into the dose calculation coordinate system. Its Y (cephalic-caudad) axis was located at the intersection of the tilted coronal and sagittal planes, its X (transverse axis) lay in the tilted coronal plane, the Z (anterio-posterior) axis lay in the tilted sagittal plane and its origin was positioned near the tip of the inferior-most intrauterine source. In this coordinate system, the ICRU coronal and sag&al planes are the planes Z = 0 and X = 0, respectively. Different implants sometimes demonstrated large linear or angular displacements (as much as 2 cm or 25 degrees) from one another relative to common bony anatomy. In these cases, the average of the individual-insertion ICRU planes was used for calculating composite implant dose distributions. In addition to the coordinate transformation data, the computer program was given source loading and implant duration data. Three-dimensional dose calculations were obtained throughout a 16 X 16 X 14 cm3 rectangular volume centered on and parallel to the ICRU composite-implant coordinate system defined above. A 1.5 mm grid spacing was used. The generalized Sievert integral method described by Williamson ( 16) was used to calculate the single-source dose matrix for the steel-encapsulated Cs- 137 sources. Total dose at each point in the 3-D grid was calculated by summing the dose contributions of individual sources. This method ignores applicator attenuation and
* VAX 8650 Minicomputer, Maynard, MA.
Digital Equipment
Corporation,
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colpostat shielding effects ( 17) following conventional practice in this regard. The volume encompassed by each isodose level between 10 and 200 Gy in 2 Gy increments was calculated by counting the relative number of dose points equal to or exceeding each dose level. When properly normalized and plotted as a function of dose, a cumulative dose-volume histogram (DVH) results. These data represent the volume whose dose equals or exceeds the specified dose. No corrections for volume of tissue displaced by the applicators or packing were made. The computer program, described above, also calculated the maximum orthogonal dimensions for each dose level between 10 and 200 Gy. As recommended by ICRU Report 38, height (H) of an isodose volume is its maximum dimension along the tandem, measured in the oblique frontal plane containing the tandem; width (W) is the maximum dimension perpendicular to the tandem within the same oblique frontal plane and thickness (T) is the maximum dimension perpendicular to the tandem, measured in the oblique sagittal plane containing the tandem (Fig. 1). The computer program calculated H and T by scanning each row of the planar dose matrices, Z = 0 and X = 0, starting from the matrix edges and working towards its center. Linear interpolation was used to define the maximum isodose width in any one row. Thus, for high doses characterized by multiple closed surfaces, the maximum distance between the lateral-most intersections of such isodose surfaces and the X-Y plane was recorded as W. In addition to tabulating T, W, H and T - W * H as a function of intracavitary dose, the program calculated the maximum projected geometric dimensions of the implant, x,,,,~, ymax, and zmaxwhere x,,, = Maxi=l,N [xi] Mini,l,N [xi] and xi denotes the tip or end X-coordinate of the i-th cesium source in the ICRU coordinate system. The dosimetric analysis, described above, was performed for each of the 204 individual implants using the composite-implant ICRU co-ordinate system. In addition, calculations were performed for composite intracavitary implants in the same patient for 37 patients for whom both implants consisted of tandem and colpostats and for 14 patients for whom both implants consisted of a tandem f cylinder. Calculations for both individual and composite implants took into account the mgRaEq-hr actually administered to the patient. A number of hypotheses were tested using the above data. The relationship between the individual orthogonal isodose surface dimensions T, W, H, and the physical dimensions of the implants xmax , ymax, and zmaxwere explored by plotting each isodose dimension against the corresponding geometric dimension. One-dimensional linear regressions were obtained to assess the correlation between these parameters. We discovered that the cor-
9:KaleidaGraph: Data analysis/Graphics Macintosh Application Version 2.0, Synergy Software (PCS Inc), Reading, PA 19606.
Volume 25, Number 4, 1993
relation between T and implant maximum dimensions was greatly improved by exploiting a simple physical model. If the implant sources lying in the X-Y plane are assumed to form a disk-shaped planar source of effective radius R, the isodose dimension, H, perpendicular to this plane along its axis, is given by (5)
(Fq. 1)
where Do = M - H - f and ?r - R* = x,,, - y,,,/2. The symbols D, M, T, and f denote absorbed dose, mgRaEq-hr, the exposure rate constant for Ra-226 (8.25 R cm2 mg-’ h-l), and Roentgen-to-cGy conversion factor (0.96 cGy/ R), respectively. This model approximates the implant by a uniform distribution of radioactivity over a disc of area (x,,, * y,,,&2. Solving (Eq. 1) for H yields
H =a.
xnl,, * YInax exp(b * x max * Yin,x) - 1
0%. 2)
where a = G and b = l/I’ * f* (D/M). In practice, the variables a and b were treated as parameters of best fit and (Eq. 2) fitted to the clinical implant data using a personalcomputer data-analysis package5 equipped with a nonlinear, least-squares parameter-estimation technique (8). To conveniently develop hypotheses concerning the relationship of volume to mgRaEq-hr, idealized intracavitary implant geometries were studied. To develop an idealized implant model based on “average” source coordinates, orthogonal films of 87 intracavitary implants performed in 1987 were reviewed. Colpostat source separations, and the mean x, y, and z displacements of the caudal-most tandem source location from the transverse plane bisecting the vaginal sources were measured and stratified by colpostat diameter. Average source coordinates for each applicator loading used in our system were defined including medium tandem ( 1O-20 mgRaEq loading) and regular tandem ( lo- 1O-20 loading) combined with Delclos mini-colpostats (10 mg loading) and 2,2.5 and 3 cm diameter Fletcher colpostats loaded with 20, 25, and 30 mgRaEq sources, respectively. Three-dimensional dose calculations and DVH’s were evaluated as described above for each loading. The nonlinear, least-squares parameter estimation technique, described above, was used to fit the following power-law model to these DVH data:
V(D, M) = [a + /3(F) + *(;)l]$)’
(Eq.3)
Tissue volume estimation 0
where (Y,p, 6, and t are parameters of best fit, D denotes absorbed dose in cGy, M denotes mgRaEq-hr and V denotes volume (cm3) encompassed by isodose-curve surface, D. This model was tested against the DVH’s derived from the clinical implants. RESULTS The DVH data of the idealized implants, illustrated by Figure 2, shows that volumes encompassed by any specified isodose level is very similar for implants delivering the same ratio, M/D, in units of mgRaEq-hr/cGy, despite significant differences in source loading and relative source positions. Using M/D rather than M or D alone as the independent parameter, suppresses much of the implantto-implant variation in isodose surface location, relative to the radioactive sources, due to differences in mgRaEqhr delivered by different implants. Using nonlinear leastsquares analysis to fit the model, (Eq. 3), to this data, yielded best-fit values for the parameters (Y,& 6 and E of MIR
idealized
737
A. EISBRUCHet a/.
104.8, -8.103, 0.437 and 1.635 with a regression coefficient of 0.999997. This model reproduces the DVH’s with an accuracy of 5% for M/D ratios as small as 0.7-l .O depending on loading. For total mgRaEq-hr characteristic of the MIR treatment system, this corresponds to doses between 120- 140% of the point A dose and includes all doses of clinical interest, including doses to bladder and rectal reference points. Physically, the excellent agreement between power-law model and DVH calculations demonstrates that intracavitary implants volumetrically behave like single central point sources, regardless of underlying geometry. Using the notation of the previous section, the DVH of a point source is given by 30
.
Equations (3) and (4) are very similar: the power-law model has an exponent of 1.635 compared to a value of 1.5 for an implant consisting of a single isotropic point lntracavitary
Applications
1000
600
400
60
A toomg m-30
0.4
1 .o
0%. 4)
2.0
10-10-20
4.0
6.0
mgRaEq-hrs/cGy Fig. 2. Dose-volume histograms for idealized MIR implants with different loadings, plotted as a function of mghr/ cGy. The symbols designate actual volumes determined by DVH’s; the solid line indicates the volume predicted by the power-law model (Eq. 3).
I. J. Radiation Oncology ??Biology 0 Physics
738
source. The values of V predicted by the power-law model, (Eq. 3), using only total mgRaEq-hr and dose as independent variables, will be referred to as the predicted volume in subsequent discussions. Both predicted volume and the ICRU product, TWH, were compared to the actual volume determined by DVH’s derived from the actual patient implants. A scatterogram of the ratios of predicted volume (according to our power-law model)/actual volume as well as the ratios of TWH product/actual volume are plotted for various dose levels in Figure 3 for the 16 1 individual tandem and colpostat implants. The TWH/actual volume ratios for different implants at any isodose level vary widely with a range as large as 0.2-6.2 at high dose levels. At lower dose levels, which give rise to isodose surfaces further away from the implant, the ratios TWH/actual volume exhibit less implant-to-implant variability. In contrast, the ratios of predicted volume/actual volume for the same implants (Fig. 3B) show significantly less implant-to-implant variability at every isodose level. The means and percent standard deviations of the ratios of predicted/actual volume for individual tandem and colpostats implants (Fig. 4A) are 1.002 f 1.6%, I .016 + 6.4% and 1.099 f 11.7% for the 20, 40, and 60 Gy isodoses, respectively. At higher isodose levels the means show a larger deviation from unity and larger % standard deviations (1.187 + 13.3% and 1.272 f 13% for the 80 Gy and 100 Gy, respectively). No significant difference between the implant types (tandem and colpostats vs tandem + cylinder) was noted. In contrast, the ratio TWH/ actual volume shows large variability at all isodose levels examined, except the 20 Gy level (tandem and colpostat
A.
.
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insertions: means +- S.D. of 1.903 + 7.2%, 2.09 1 + 17.6%, 2.396 & 27%, 2.590 + 32%, 2.812 + 39% for the 20,40, 60,80 and 100 Gy isodoses, respectively). Comparison of the mean TWH/actual volume ratios of the tandem and colpostats insertions to that of the tandem + cylinder group, reveals mean differences between the two implant types ranging from 10% to 50% over the 20-60 Gy dose range. For the individual insertions, the 120 Gy isodose did not form a single surface in many cases, but formed multiple closed surfaces around individual sources and therefore calculations were not plotted for this dose level. For the composite implant dose calculations, the 120 Gy isodose surface was located further away from the sources, forming a single closed surface in all cases, and was therefore included in the analysis. Volume ratios for the composite insertion plans (Fig. 4B) show less variability compared to individual implants. Since the total mgRaEq-hr delivered by a combined plan is approximately twice that of each single implant, each isodose surface of interest is located farther away from the sources, which now behave more like point sources. The mean of the ratios of predicted volume/actual volume for combined tandem and colpostats insertions is practically unity with S.D. + 1.2%, 1.7%, 2.3%, 3.3%, 6.4%, 9.8% for the 20, 40, 60, 80, 100, and 120 Gy isodose surfaces, respectively. Similar values are observed for tandem f. cylinder applications. The ratios of TWH/actual volume for cumulative implants have less variability (S.D. + 2.8%, 5.9%, 8.7%, 12.2%, 14.7%. and 15.7% for the 20,40,60,80, 100 and 120 cGy isodose surfaces, respectively) than the ratios for individual implants, but significantly more than the predicted volume ratios. Systematic differences between the different im-
TWH Product/Actual Volume
6.0 L 5.0
Volume 25, Number 4, 1993
.
:
;
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volume/actual
volume
for
O
Tissue volume estimation 0 A. EISBRUCH
INDIVIDUAL INTRACAVITARY INSERTtONS Ratios of TWHlactual volume and radlctad/actual volume at various mghr /c cpy values
INDIVIDUAL INTRACAVITARY INSERTIONS Ratios of TWHhctual volume and predicted/actual volume at various dose levels
L
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739
et al.
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CUMULATIVE INTRACAVlTARY INSERTlONS Ratios of TWHhctual volume and redlctad/actual volume at varlous mghr k 8 y values
CUYULATlVE INTRACAVlTARY INSERTIONS Ratlor ot TWH/actual volume and radtcted/actual volume
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Fig. 4. Volume ratios of (A) individual and (B) composite implants at various isodose levels. Circles denote means of the ratios for tandem and colpostats insertions and triangles denote means for tandem + cylinder insertions. Open symbols are means of the TWH product/actual volume ratios and solid symbols denote means of the predicted volume/actual volume ratios. The vertical bars show the standard deviations.
plant geometries (tandem and colpostats compared to tandem + cylinder) still exist at dose levels above 40 Gy. Figure 5 presents the ratios of predicted/actual volume and of TWH roduct/actual volume as a function of various M/D levepls in units of mgRaEq-hr/cGy (the variable of the power-law volume model). The ratios of predicted/ actual volume exhibit small standard deviations (< 5%) when M/D is greater than 0.8. For M/D = 0.5 the variability is larger: SD = 10.5% for tandem + colpostat and 7.2% for tandem f cylinder implants. There is no difference in the means and deviations of predicted/actual volume ratios of individual implants compared to composite implants. The composite-plan TWH/actual volume ratios and standard deviations vary somewhat from their individual-insertion plan counterparts, especially for small values of M/D. However, none of these variations is significant. Clearly the ratio M/D is a useful parameter in
6.5
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-
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Fig. 5. Volume ratios of (A) individual and (B) composite implants at various values of mghr/cGy. The symbols are same as in Fig. 4.
dose-volume analysis: specifying isodose curves in terms of M/D eliminates the variability in mgRaEq-hr characteristic of using dose as an independent parameter and therefore reduces the variability in average distance of any specified isodose curve from the radioactive sources. Figure 6 shows the relationship between the individual ICRU isodose dimensions W, H, and T and the corresponding maximum implant geometric dimension, xmax, y,,,,or z,,, for M/D ratios of 0.5 to 2.0. These data are plotted for 77 individual implants consisting of tandems and colpostats. Applying simple linear regression models of the form I-I = a(M/D) * ymax + WWD)
(Eq. 5)
yields moderately high linear regression coefficients (r values) for the correlation of W and H with xmaxand y,,, respectively: r values of 0.61 to 0.82 for M/D ratios between 1.0 and 2.0. These correlations are qualitatively similar to those found by Potish (1 l), who used much
I. J. Radiation Oncology 0 Biology0 Physics Individual
Tandem
and
Colpostat
Volume 25, Number 4. 1993
Insertions
Individual
Tandem
and
Colpostat
Insertions
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??
x +
+
-
5.0
*
Fig. 6. ICRU isodose dimensions T, W, and H, as a function of the corresponding maximum implant dimensions x,,,~, ymaxand z,,, at various values of M/D (mghr/cGy). The symbols denote the actual ICRU dimensions determined by 3D computer calculations. For each value of M/D, the lines represent best-fit linear regression.
7.0
8.0
9.0
Cephalic-Caudal Implant Y m.. Nrn)
(b)
10.0
Dimension
--I 11.0
Tissue
volume estimation 0
more sophisticated multiple-variable linear models to study the relationship between T, W, and H and implant dimensions for 90 Fletcher intracavitary insertions. In contrast (Fig. 6C), isodose thickness T is poorly correlated wi:h the single variable z,,, with r values ranging from 0.015 to 0.23. In contrast, when the data are fit to our nonlinear model (equation 2), an excellent correlation between T and the area product xmax- ymaxis achieved (Fig. 7): Correlation coefficients vary from 0.77 to 0.84 for M/D values of 0.8 to 2.0. These simple models suggest that, on average, the isodose surface dimensions are much more sensitive to the variable M/D than to small changes in the geometric dimensions of implant. For example, at the average values of xmax- ymax= 25 cm* and M/D = 1.O mgRaEq-hr/cGy, 5% changes in M/D and x,,, - ymaxproduce changes in T of 4.2% and 1.8%, respectively. On average, the parameters T, W, and H are three times more sensitive to M/D changes than to similar relative changes in the corresponding implant dimensions. Figures 6 a,b & 7 indicate that the slopes of W, H, and T with respect to xmax, y,,, , and x,,, - ymax are nearly independent of the M/D ratio. This finding is somewhat surprising since one would expect that the dimensions of low-M/D isodoses, which correspond to high-dose isosurfaces close to the implanted sources, might be more sensitive to changes in implant geometry. This suggests that the 60 Gy total dose level, chosen by the ICRU to Individual Il.0
0.0
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and
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,
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I..
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JS
50
implant dimensions
(cm*)
Fig. 7. ICRU isodose surface thickness (T) plotted as a function of the product of the maximum implant coronal dimensions at various values of M/D. The symbols denote the actual dimensions and the lines represent isodose thickness as predicted by the planar source model (Eq. 2) using values of a, b that were estimated by non-linear least-square curve fitting.
741
A. EISBRUCHet al.
define the reference volume, yields as good a correlation between isodose dimensions and corresponding implant dimensions as any other choice of reference dose level. In the MIR treatment system, for which the most frequent prescription is 20 Gy whole pelvis irradiation and 8000 mgRaEq-hr of intracavitary therapy, the choice of 60 Gy corresponds to an M/D ratio of 2.0 = (6000 cGy - 2000 cGy contributed to that isodose by the implant)/8000 mgRaEq-hr. Revising this value to M/D of 1.2, the value corresponding approximately to the point A isodose, would not improve the sensitivity the reference volume orthogonal dimensions to what seems to be the most significant implant geometry parameters. DISCUSSION The utility of the ICRU product, TWH, for predicting treatment sequelae, has been examined by several authors (1-3, 12-l 5). This strategy is based on the assumption that TWH is proportional to volume encompassed by the corresponding dose level, that is, that TWH/actual volume is approximately constant over the range of doses and implant geometries under investigation. Contradictory results have been reported: Crook et al. (l), found that Grade 3 rectal complications were correlated with high TWH product, and the zone of risk for severe bladder complications could be described in terms of high bladder doses and large TWH on a 2-dimensional scatterogram. In patients treated by high dose-rate irradiation for cancer of the cervix, Van Lancker et al. (15) found the TWH product to be significantly higher in patients who had late treatment complications compared to patients who did not have late complications. In contrast, Pourquier et al. did not find any correlation between the TWH product and late rectal ( 13) or bladder ( 14) complications. Our study has demonstrated that there is a large insertion-to-insertion variation in the ratio TWH/actual volume at the 60 Gy reference dose level as well as at other dose levels. This finding may help explain the contradictory findings, described above, when volume-dependent treatment sequelae are investigated. If such clinical endpoints truly are volume dependent, a good correlation will be found only if the study parameter used is closely proportional to the actual volume encompassed by the corresponding isodose surface. The TWH product is not a suitable volumetric parameter because of the large variations in its relationship to the actual volume and because of its dependence on the geometry of the implant. An implant consisting of a tandem and colpostats produces pear-shaped isodose surfaces, which (when far away from the implant) approximate a spherical surface the volume of which is approximately V = n/6 (D3) where the diameter D corresponds to the mean value of T, W and H. The relationship between TWH (approximated by D3) and the volume of the sphere is D3/a/6 (D3) z 1.9 1. A tandem -t-cylinder produces isodose volumes that are approximately cylindrical in shape whose volume can be
742
I. J. Radiation Oncology 0 Biology 0 Physics
approximated by 7r/4 - L* - H where L is the width or thickness of the isodose surface and H its height. The product of ICRU dimensions is L* * H in this case, giving a ratio of TWH/actual volume of L* - H/?r/4 L*H = 1.27. For tandem and colpostats insertions, higher mgRaEq-hr in the colpostats (relative to the mg-hr in the tandem sources) and (less important) wider separations of the colpostats make the resultant isodose surfaces more spherical while lower mg-hr in the colpostats and narrower separation will result in more cylinder-like isodose surfaces. Consequently, the ratio TWH/actual volume of an isodose surface varies between different implants. The correlation between mgRaEq-hr and the isodose surface dimensions T, W, and H was investigated by Potish ( 12) who found a little effect of application geometry on TWH product, but a large effect on the individual ICRU dimensions. The TWH product was found to be in good correlation with mgRaEq-hr, in a linear regression analysis looking separately at each isodose level. A linear relationship between mgRaEq-hr and TWH product for any fixed external irradiation dose was also found by Esche et al. (2). In contrast, we have found a non-linear relationship between volume encompassed by an isodose surface and mgRaEq-hr: Va (mgRaEq-hr)‘.635. Extending this approach, we have developed a modified power-law model, the product of a quadratic term in (M/D) and a power-function term (M/D)’ which, far more accurately than TWH, predicts the actual volume encompassed by any isodose surface over a wide range of doses, D, and mgRaEq-hr, M. This modified power-law model permits prediction of isodose volume, knowing only the mgRaEq-hrs, before computerized isodoses are plotted. The relationship can be used to incorporate volumetric limitations into the initial prescription. The excellent agreement of this simple model with 3-D dose calculations about 204 clinical implants is consistent with the hypothesis that intracavitary implants volumetrically behave like central point sources of radiation over the range of doses of clinical interest. Our formula predicts the volume encompassed by an isodose volume within 5% in 67% of the implants and within f 10% in 95% of the implants when the value of mgRaEq-hr/cGy is 0.8 with accuracy improving with increasing values of mgRaEq-hr/cGy. This correlation holds despite significant variations in implant geometry and loading arising from a variety of tandem lengths and colpostat diameters, variable colpostat separations and tandem-to-colpostat offsets, and different applicators (colpostats vs. vaginal cylinders) which are introduced to customize the treatment to individual patient anatomy. The predictive accuracy of the model is unchanged when applied to composite multiple-insertion implants performed in the same patient, indicating that the additional geometric variation caused by angular and linear displacements of the successive implants relative to the first does not influence the relationship between isodose volume and mgRaEq-hr.
Volume 25. Number 4, 1993
Calculations of an isodose volume for combined intracavitary and external irradiation, in our model, take into account the difference between the isodose whose volume is searched for, and the dose delivered at the same location by external beam therapy. For example, a typical Mallinckrodt treatment prescription consisting of 20 Gy whole pelvis external dose and 8000 mg-hr in two intracavitary implants can be translated into a statement of volume occupied by the 60 Gy reference volume: the intracavitary dose will be 40 Gy and under this condition, the overall treatment is equivalent to treating with intracavitary implants until 40 Gy isodose surface achieves according to our model a volume of [109.8 - 8.1 X 8000/4000 + (8000/4000)*] (8000/4000)1.635 = 296 cm3. For the same mgRaEq-hr prescription, increasing the whole pelvic irradiation to 30, 40, and 50 Gy will result in calculated volumes of 454, 8 14, and 2186 cm3, respectively. The actual measured volumes for 204 implants correlate well with these predicted volumes (Ratio predicted/actual value = 1, standard deviation within 3%). The dependence of ICRU reference dimensions product on the dose of external radiation was investigated by Esche et al. (2) and Nath et al. (9) who found that the TWH product initially rises slowly with increasing external dose but the rate of increase accelerates dramatically above 30 Gy. This is readily explained by the power-law dependence of volume on M/D in our model, and can be easily calculated using it. Our investigation has utilized the quantities equivalent mass of radium (unit: mgRaEq-hr) and mgRaEq-hr to describe source strength and integrated source strength (product of strength and duration), respectively. The ICRU has proposed adopting the quantity total reference air kerma (TRAK) as a measure of integrated source strength, or total output, in place of mgRaEq-hr. Both quantities are measures of the output in free space accumulated at a distance of 1 m from the implant in the absence of patient and applicator attenuation: TRAK is simply the air-kerma in free space that would be measured at 1 m from a hypothetical implant consisting of a point source that administered the same mgRaEq-hr as the implant in the patient. In symbols,
(Eq. 6)
where (Pa)Ra,o.sis the exposure-rate constant for Ra-226 filtered by 0.5 mm of platinum (8.25 R - cm* - mg-’ - h-l), and (W/e) is the mean energy required to produce an ion pair in air (0.876 cGy/R), and TRAK has units pGy * m*. Thus 1 unit of TRAK = 1 pGy- m* = 1 cGy 0 cm* = 0.138 mgRaEq-hr. This relationship, which can be used to transform the M/D ratios in equations (2)-(4) into TRAK/D ratios, shows that our conclusions are equally valid when total reference air kerma is used. Our conclusions regarding dependence of individual
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Tissue volume estimation 0 A. EISBRUCHef a/
reference isodose dimensions, the product of ICRU dimensions, and the relationship between volume and mgRaEq-hr are empirical findings and are strictly valid only within the range of implant geometries characteristic of our treatment system. However, generalization of the concept to all intracavitary implants seems reasonable. If so, we have shown that not only is TWH a poor predictor of volume enclosed by isodose surfaces, but that isodose surface volume can be accurately inferred from total intracavitary dose and mgRaEq-hrs (or equivalently TRAK) and therefore conveys no more information than a statement of these two quantities. This has two important consequences. First, isodose-surface volume is no more useful as a prognostic variable than mgRaEq-hr: the correlation between clinical outcome, in terms of tumor control and complications, and volume of ICRU reference isodose surface should be no better nor any worse than the correlation between clinical outcome and mgRaEqhr for a fixed external pelvis dose. Secondly, our findings suggest an additional basic physical interpretation of mgRaEq-hr and total reference air kerma: termination of an intracavitary treatment so as to administer a specified mgRaEq-hr dose is equivalent to treating the patient until any specified reference isodose occupies a fixed volume. From a clinical point of view, use of mgRaEq-hr as a prescription or treatment-constraining parameter is a means of limiting the volume of tissue irradiated to a high dose. In contrast, the individual dimensions T, W, and H, although dominated by the mgRaEq-hr delivered, are moderately well correlated with the coronal area covered by the implanted sources, the colpostat separation, and maximum geometric cephalic-caudad length of the implant, respectively. These parameters, considered individually, convey additional information about the isodose distribution, can not be inferred from a statement of mgRaEq-hr, and may be useful as prognostic factors. Our dosimetric analysis has neglected a number of factors that can potentially influence the tissue volume contained within isodose surface contours. These factors include applicator attenuation and shielding corrections, which are known ( 16) to spare localized regions by 1O25%, as well as the volume occupied by vaginal packing and the applicators themselves. Following classical (and current clinical) practice in this regard seems justifiable since isodose volume and ICRU dimensions are empirical dose specification parameters much like the classical quantities, mgRaEq-hr and point A dose. These quantities seeks to describe the treatment delivered without the aid of quantitative geometric descriptions of the shape and location of the target volume and organs at risk relative to the implanted sources. With respect to tumor control, isodose surface volume is an imprecise prognostic variable, since the specified isodose surface may not encompass all of the gross tumor. With respect to normal tissue tolerance, the fraction of bladder, rectum and small bowel versus more radioresistant connective tissue enclosed within the isodose surface most likely varies significantly
from patient-to-patient as well as with packing and insertion technique. As suggested by other authors (4, 12) the volume of tumor present and magnitude of focal highdose regions in the rectum or bladder may be at least as important as overall volume of tissue treated to a specified dose. Achievement of improved correlation between physical dose specification parameters and clinical outcome probably requires use of 3-D image-based treatment planning to better define patient anatomy in relation to the implant.
CONCLUSIONS We have shown that the growing practice of using the product of ICRU orthogonal dimensions, TWH, in clinical studies to estimate volume enclosed by intracavitary implant isodose surfaces appears to be without physical foundation. The ratio of TWH to true volume given by dose-volume histogram analysis, varies widely from patient-to-patient and from implant type-to-implant type. More importantly, we have shown that over the dose range of therapeutic interest, the actual volume enclosed by isodose surfaces can be accurately estimated from a modified power-law model requiring knowledge only of the intracavitary dose and mgRaEq-hr (or equivalently, total reference air kerma). Consequences of this finding include: (a) volumetrically an intracavitary implant behaves like a central point source: (b) describing an implant in terms of volume contained within its isodose curves has no more information content than a statement of mgRaEq-hr or total reference air kerma; and (c) the volume of tissue irradiated to a specified dose is closely related to total exposure given by the implant in terms of mgRaEq-hr or TRAK. Consequence (b) suggests that the correlation between clinical outcome, in terms of tumor control and complications, and isodose surface volume should be no better nor any worse than the correlation between clinical outcome and mgRaEq-hr for a fixed external pelvis dose. Consequence (c) suggests a new and fundamental physical interpretation of mgRaEq-hr or its derivative, total reference air kerma: Prescribing intracavitary brachytherapy by mgRaFq-hr is equivalent to treating until each specified isodose surface achieves a fixed volume which is independent of the underlying implant geometry. Use of mgRaEq-hr to constrain intracavitary treatment therefore limits the volume of tissue irradiated to high doses. This observation may help explain the clinical utility of mgRaEq-hr as a dose-specification parameter. Finally, the individual reference isodose dimensions, which are more strongly influenced by implant geometry than their product, clearly convey additional information about the spatial extension of the reference isodose surface in their respective planes, can not be reduced to a statement of total exposure from the implant, and may have prognostic significance.
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I. J. Radiation Oncology 0 Biology0 Physics
Volume 25, Number 4, 1993
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