Relative dose uniformity assessment in interstitial implants

Int. J. Radiation Oncology Biol. Phys., Vol. 44, No. 5, pp. 1179 –1184, 1999 Copyright © 1999 Elsevier Science Inc. Printed in the USA. All rights reserved 0360-3016/99/$–see front matter

PII S0360-3016(99)00129-7

PHYSICS CONTRIBUTION

RELATIVE DOSE UNIFORMITY ASSESSMENT IN INTERSTITIAL IMPLANTS VICTY Y. W. WONG, M.SC.,* TO-WAI LEUNG, F.R.C.R.,*

AND

CHOW-MING WONG, F.R.C.S.†

Departments of *Clinical Oncology and †Surgery, Tuen Mun Hospital, Hong Kong Purpose: Two new indices, the peak index (PI) and the new geometry index (NGI), that quantify implant dose uniformity and quality are presented. Their advantages include independence to absolute treatment dose and high sensitivity compared with other adopted dose-uniformity measures. The applicability of these indices were evaluated through computer simulations and several clinically executed implant cases. Target coverage is assumed to be properly observed and will not be discussed herein. Methods and Materials: The natural volume– dose histogram serves as the basis of our investigation. The PI and NGI definitions are based on parameters derived from the histogram. Two computer-simulated implants and 12 clinically executed implants, using high-dose rate remote afterloading techniques, are studied. Various indices that quantify the dose uniformity of the implant, namely the quality index (QI), geometry index, as well as the PI and NGI, are computed, and the results are compared. Results: The PI demonstrated significantly increased sensitivity (up to 5 times) to dose-uniformity evaluation, compared with the QI. The deduced parameter NGI may thus offer a better measure of implant qualities, allowing a more meaningful assessment and correlation between implant qualities to the treatment results. The PI system also offers a guideline to the design of optimal implant geometry. Conclusion: The PI overcomes some of the shortcomings of the QI in that it provides more information about the peaking of the natural dose–volume histogram of a particular implant. The PI and NGI may offer better, more sensitive means to assess implant dose uniformity, independent of prescription dose, than other measures. © 1999 Elsevier Science Inc. Brachytherapy, Interstitial implant, Dose uniformity, Peak index, New geometry index.

INTRODUCTION

METHODS AND MATERIALS

The Paris, Quimby, and Manchester systems are commonly used for the best dose uniformity in brachytherapy planning of interstitial implants. With computerized planning methods and modern stepping-source remote afterloading equipment, we can seek alternatives or variations to these systems to achieve enhanced target dose uniformity (1– 4). The volume-dose histogram (VDH) and the information derived from it, namely, the uniformity index (UI) (5), dose nonuniformity ratio (6), and dose homogeneity index (7), have been proposed to measure dose uniformity. However, these indices depend on the absolute prescription dose and lack the generality for study comparisons. The quality index (QI) (8) proposed by Thomadsen et al. overcomes the above limitations, and, based on that, a new index called the geometry index (GI) (9) was proposed. The GI enables grading the implant quality against an idealized implant. However, our studies showed that the QI is relatively insensitive to implant quality, even though it provides a good measure of the dose uniformity. In this article, we redefine the measure, thus improving its sensitivity while maintaining the benefits it offers.

Cumulative and differential VDH do not offer a clear indication of the implant dose uniformity because of the ubiquitous inverse square law effect from the implant sources. The natural volume– dose histogram (NVDH) proposed by Anderson overcomes this by redefining the plot variables of dV/d␮ versus ␮, where V is the volume enclosed by the isodose level at D, and ␮ ⫽ D ⫺3/.2 (Fig. 1). Thus, the NVDH plot of an idealized point source becomes a horizontal line. Deviations of dosimetric behavior from the inverse square law are highlighted. The NVDH was the basis of our analysis. Several parameters may be derived from the NVDH:

Reprint requests to: Victy Y. W. Wong, M.Sc., Medical Physics Unit, Department of Clinical Oncology, Tuen Mun Hospital, Tsing Chung Koon Road, Hong Kong. Acknowledgments—The authors wish to acknowledge Dr. Frank

Yeung for important technical discussions and his assistance in manuscript preparation. Accepted for publication 2 February 1999.

Peak dose (PD): The dose at the max dV/d␮ within the sampled volume Low dose (LD): The dose value at dV/d␮ half way between the dV/d␮ at PD and the asymptotic value of dV/d␮ as ␮30 High dose (HD): The dose value at dV/d␮ half way between the dV/du␮ at PD and the asymptotic value of dV/d␮ as ␮ 3 infinity

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The PI rationale, and some properties follow.

Fig. 1. Nature volume– dose histogram of a regular double planar implant containing nine catheters with intercatheter and interplanar spacing of 1-cm and 4-cm active length. Prescription dose of 550cGy at 1 cm above the center of the implant.

Peak width: ␮(HD) ⫺ ␮(LD) As a measure of dose uniformity over the sample volume, Anderson defined the uniformity index (UI) as UI ⫽

冒

V共TD兲 ⫺ V共HD兲 ␮ 共TD兲 ⫺ ␮ 共HD兲 V共TD兲 ␮ 共TD兲

(1)

which clearly depends on the absolute treatment dose (TD). Thus, comparing two studies with different treatment doses would not be meaningful. Thomadsen et al. (8) introduced the QI to quantify implant dose uniformity, independent of the treatment dose, viz: QI ⫽

冒

V共LD兲 ⫺ V共HD兲 ␮ 共LD兲 ⫺ ␮ 共HD兲 V共LD兲 ␮ 共LD兲

冋

⫽ 1⫺

V共HD兲 V共LD兲

册冒冋

1⫺

␮ 共HD兲 ␮ 共LD兲

(2)

册

Although this measure rectifies the TD dependency issue, the sensitivity to variation in dose uniformity, especially for relatively “poor” implants, is low. In Eq. 2, V(HD)/V(LD) is small, as are ␮(HD)/␮(LD). Rewriting this equation gives QI ⬇ 1 ⫺

V共HD兲 ␮ 共HD兲 ⫹ V共LD兲 ␮ 共LD兲

Thus, further change to the implant dose distribution yields only marginal variation in the QI value and, hence, a low sensitivity to differences for “poor” implants. Based on the premise that: the higher and narrower the NVDH peak, the higher the dose uniformity, we propose a new measure, the peak index (PI), defined as: dV dV 共PD兲 ⫺ 共LD兲 d␮ d␮ ␮ 共LD兲 ⫺ ␮ 共HD兲 PI ⫽ dV ␮ 共LD兲 共LD兲 d␮

冒

(3)

1) The ratiometric nature of the variables maintains the independence of the units of measurements, i.e., two implants with identical relative geometry but different prescription doses have the same PI value. 2) The use of dV/d␮ in the numerator, as opposed to the volume (V), enhances the sensitivity of the measure because of the variability of this parameter. This is analogous to the improved sensitivity of the differential VDH over that of the cumulative VDH. 3) dV/d␮ is a directly measurable quantity for the NVDH, and its pictorial representation offers a more direct and intuitive interpretation. 4) Since TD is not involved, its independence is maintained. In Eq. 3, the numerator is essentially a normalized measure of the peak amplitude, and the denominator is a normalized measure of the peak width. For good implants, a high PI is attained through a small peak width and a large difference between the dV/d␮ at PD and LD. For relatively “poor” implants, although the peak widths become proportionally larger, the normalized peak amplitude remains proportional to the differential volume between the PD and LD. Therefore, sensitivity in this situation is not lost. As an extension of the PI, we also define a new geometry index (NGI) as:

NGI ⫽

PI nonoptimized executed implant PI nonoptimized idealized implant

as a measure of the implant quality, which depends solely on the insertion quality, regardless of the actual dosimetry of the executed treatment. PI, QI, and NGI are applied to evaluate the dose uniformity and implant geometry quality of two sets of computersimulated planar implants and 12 clinically executed single plane (4 –5 catheters) and double plane (9 catheters) implants. In all cases, catheters were loaded with an Ir-192 radioactive stepping source with a dwell spacing of 0.5 cm. The NDVH was computed over a volume surrounding the implant, with boundaries extending 1 cm from the outermost source positions in all three dimensions. Two million random samples were taken in all cases. Study 1 In the first study, we evaluated the dose uniformity of planar implants, either with or without optimizing a dose. Geometric optimization (10) was applied to optimize the dose. Following are the implant descriptions for this study. Case 1: single plane, 4 parallel catheters at 1-cm separation, 4-cm active length. Case 2: single plane, 5 parallel catheters at 1-cm separation, 4-cm active length. Case 3: double plane, 4 and 5 staggered catheters, 4-cm active length, interplane separation of 1 cm

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Fig. 2. Dose distributions in transverse view of two irregular implants with five coplanar catheters of 4-cm active length. Dose of 550 cGy prescribed at 5 mm above implant center. Implant containing cross needles resulting in hot and cold spots (a). Implant configured in “fan shape” (b).

Case 4: single plane, 5 catheters, 4-cm active length, 2 catheters crossed producing local hot and cold spots (Fig. 2a). Case 5: single plane, 5 catheters, 4-cm active length, arranged in fan shape (Fig. 2b).

dose prescribed was 57.5 Gy (range: 45– 63.7 Gy) in 10 fractions over 6 days. Dose optimization using geometric optimization was applied in all cases to improve overall treatment dose uniformity.

Study 2 In the second study, we attempted to determine the optimal interplane spacing for a double-plane implant with 4/5 staggered catheters. The catheter separation is 1-cm and 4-cm active length. The investigation was conducted for interplane separations ranging from 0.8 to 1.6 cm at 0.2-cm steps. Since the prescribed dose was defined as 1 cm above the implant center, the 100% isodose enclosed a similar dose volume of approximately 30 cm3 for all the cases. No dose optimization was applied in this study. Study 3 Finally, we evaluated the implant quality for 12 patients with carcinoma of the tongue and the correlation to treatment results. The patients were treated between 1994 and 1997 with interstitial brachytherapy using high-dose rate stepping-source remote afterloading techniques. The afterloading catheters were positioned through the submandibule, with the assistance of template set. Nine patients were treated with single plane implants (4 –5 catheters) and the remaining with 4/5 double-plane implants. The medium

RESULTS Study 1 Table 1 shows the computed QI, PI, and (PI)GO (PI value resulting from appling geometric dose optimization) values for the five cases. For the two “irregular” implants (i.e., the fan shape and crossed implants), the QI values differ only slightly, and compared with the regular planar implants, the differences amount to approximately 16%. The PI values for the irregular implant differ from the regular planar implants by more than 60%, indicating the PI is significantly more sensitive to the implant dose uniformity. Figure 3 compares two NVDH of the regular single plane implant (case 2) and the irregular implant (case 5). The difference in dose uni-

Table 1. Comparison between the QI, PI, and (PI)GO values of regular and irregular implants*

Single plane (4 catheters) Single plane (5 catheters) Double plane (4 ⫹ 5 catheters) Crossed implant (5 catheters) Fan shape (5 catheters)

QI

PI

(PI)GO

1.37 1.37 2.04 1.14 1.15

0.54 0.57 1.49 0.13 0.20

0.83 0.97 3.12 0.21 0.25

GO ⫽ geometrical optimization applied for dose calculation. * Irregular implants included the crossed catheters and the fan shape implants.

Fig. 3. Natural volume– dose histograms for (1) regular single planar implant consisting of 5 catheters with 4-cm active length, (2) irregular implant with crossed catheter, as illustrated in Fig. 2a. Symbol (⬘) denotes values obtained from the irregular implant.

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two irregular implants were used as references to compare the geometric quality of the implants.

DISCUSSION Based on Study 1, the computed PI shows that a doubleplane implant generally gives better dose uniformity than the similar implant volume using more catheters. Irregular implants, because of the source divergence or the hot and cold spots, yield poor dose uniformity. All of these findings agree with our general experience and treatment planning practices. Thus, it may be inferred that the NGI offers a sensitive assessment of the implant quality. Comparing cases 2, 4, and 5, the (PI)GO values reached 0.97, 0.21, and 0.25, respectively. Even though dose optimization improved the overall dose uniformity in all three cases, the resulting (PI)GO values for irregular implants remained low. Thus, it is imperative that a good implant should be preceded by a good uniform geometry— dose optimization only lessens the shortcomings of an implant. It cannot eliminate underlying limitations. To cross validate the results in Study 2, we examined the dose uniformity in a qualitative sense. Three dose profiles were taken, one along the prescription point level (PPL), another along the basal dose points level (BDPL), and the last along the central axis level (CAL) (Fig. 5). For the BDPL and CAL, it was clear that an increase in interplane separation improved the dose uniformity seen by the reduced relative variation in the percentage dose level along the distance from the implant center. This is attributed to the increased distance from the sources. However, the reverse is true for the PPL dose profile, due to the reduced distance from the sources. Intuitively, we may infer that the optimal dose uniformity can be reached “half-way” between 8 –16 mm.

Fig. 4. (a) Cross-sectional view of a double plane implant of a staggered 4/5 catheter configuration. Doses profiles along (b) prescription point level (PPL), (c) basal dose point level (BDPL), and (d) central axis level (CAL) of implants in differ plane separation ranged from 0.8 to 1.6 cm in 0.2 cm depth.

formity between a good and a poor implant was indicated by a distinctive peak and a flat curve on the NVDH. Study 2 A plot of the PI value for the double plane implant at different interplane separation is shown in Fig. 4. The optimal dose uniformity was reached at 1.2 cm. Study 3 Table 2 shows the QI, PI, and NGI values of the 12 patients with tongue implants and the results of follow-up. The mean (PI)GO values are 0.38 and 1.12 for the single and double plane implants, respectively. The NGI values of the

Table 2. Relationship between clinical results and values of PI, (PI)GO, and NGI for the 12 executed implants* Patient

No. of caths.

Active length (cm)

Tumor stage

Local disease status

Length of follow-up (mo)

PI

(PI)GO

1 6 11 8 7 9 12 2 3 5 10 4 Crossed implant Fan shape

4 4 4 5 5 5 5 5 5 9 9 9 5 5

4.0 2.5 3.0 4.0 4.0 4.0 4.0 4.0 4.0 3.5 4.0 3.5 4.0 4.0

1 1 1 2 2 1 2 1 1 2 2 1 / /

c c c c c c c c c c c c / /

30† 42 17 6† 36 21 16 49 48 45 18 46 / /

0.40 0.31 0.29 0.40 0.38 0.36 0.33 0.32 0.30 0.89 0.81 0.76 / /

0.41 0.40 0.34 0.43 0.44 0.39 0.37 0.34 0.34 1.19 1.17 1.00 / /

c ⫽ control. * The NGI values of the two irregular implants are also included for comparison. † Died of other disease; unmarked are alive and well.

NGI 0.40/0.54 ⫽ 74% 0.31/0.54 ⫽ 57% 0.29/0.54 ⫽ 54% 0.40/0.57 ⫽ 70% 0.38/0.57 ⫽ 67% 0.36/0.57 ⫽ 63% 0.33/0.57 ⫽ 58% 0.32/0.57 ⫽ 56% 0.30/0.57 ⫽ 53% 0.89/1.49 ⫽ 60% 0.81/1.49 ⫽ 54% 0.76/1.49 ⫽ 51% 0.13/0.57 ⫽ 23% 0.2/0.57 ⫽ 35%

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Fig. 5. PI values for double planar implants with varied plane separation ranged from 8 to 16 mm in 2 mm depth increments.

The findings from the PI versus the interplane separation reinforce this belief (see Fig. 4) and indeed provide us with a quantitative conclusion of optimal interplane spacing for this implant. The NGI values for the 12 executed implants ranged from 51% to 74%, which is more than twice that of the irregular implant (see Table 2). This implies that the executed implants exhibit a reasonably acceptable geometry. The proportionally large (PI)GO values indicate implants with good dose uniformity. Study 3 appears to provide a positive correlation between the NGI values and the treatment results. Current follow-up is still insufficient for us to draw conclusions as the precise cause of these treatment results. However, the preliminary results are encouraging, and we await further clinical trials to solidify this correlation. Based on our new findings in Study 2, the 1-cm interplane spacing we have adopted is suboptimal. The new indices we have developed will allow better treatment planning in the future. PI and NGI were designed solely for implant dose uniformity assessment; however, target coverage was not addressed. We think it should be addressed.

CONCLUSION The new dose uniformity measure, PI, overcomes some of the shortcomings of the QI in that it yields more information about the NDVH peaking in a particular implant. PI provides more sensitive evaluation of the implant dose uniformity. PI provides a quantitative assessment in dose uniformity over the implant volume. It allows comparison between different studies, as implants dose uniformity are graded in a relative manner. PI may be used as a geometric guideline in implant configuration before implantation to achieve optimal implant dose uniformity. Since application of dose optimization cannot definitely improve dose homogeneity, the prerequisite for a good implant is uniform implant geometry. The NGI system may offer a sensitive approach to assess implantation quality. Computer simulations reinforce the validity and applicability of the new PI measure, and preliminary clinical results have provided encouraging results, which warrant further investigation.

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