Study of the relationships between brachytherapy plan parameters in an attempt to verify total dwell time in vaginal cylinder applications

Abstract Purpose Source strength (Sk), sizes of vaginal cylinder applicators (VCA), number of dwell positions (DPs), and the prescribed dose (D) are basic parameters in brachytherapy (BT) treatment planning contributing to total dwell time (TDT). This study was aimed at assessing the relationships between the specified variables in an attempt to verify the TDT in high‐dose‐rate (HDR) vaginal cylinder applications. Methods One hundred and twenty‐one patients treated with Gynesource‐Co60 (Bebig, Germany) using VCAs of diameters 20, 25, and 30 mm at University College Hospital, Nigeria, were enrolled in this study. Brachytherapy doses ranging from 3 to 7 Gy were always prescribed to points 5 mm away from the cylinder's surface. Treatment planning was undertaken on HDR‐Basic treatment planning system (TPS) which utilizes source step size of 5 mm. Data on the stated parameters related to the first BT fractions of the patients were acquired. With the aid of EViews statistical software, two forms of mathematical models were thereafter developed. The resulting TDTs from the models were compared with the TPS values using Minitab statistical software. Results The relationships obtained for the increasing sizes of the VCA were TDT1(min)=2.22+3.17DSk;TDT1(min)=3.52+3.74DSk;TDT1(min)=−1.96+6.91DSkandTDT2(min)=0.50−0.03Sk+0.02D+0.55DPs;TDT2(min)=7.08−0.06Sk+0.02D+0.67DPs;TDT2(min)=7.02−0.11Sk+0.03D+1.25DPs The model‐based TDTs correlate with the TPS‐calculated values with r1 = 0.80 (P = 0.412) and r2 = 0.97 (P = 0.468). Conclusions The findings of this study could suggest likely variations in the treatment time when certain changes occur in the related parameters. The increasing size of the vaginal cylinder has a positive influence on the brachytherapy treatment time. The latter model has been a useful tool in the verification of the dose delivery time at the first HDR brachytherapy center in Nigeria and West Africa.

(HDR) techniques. 1 High-dose-rate brachytherapy has, however, become the major practice across the world, particularly in the developed nations. 2 Its choice as a substitute for the LDR technique is due to the related advantages. These include shortened treatment time, outpatient-based treatment, and improved patient comfort. In addition, the use of the HDR vaginal cylinders is simple and offers better placement of the applicators in relation to the desired anatomic structures than the tandem-ring and tandem-ovoid combinations. There is also a better dosimetric control for the small and high-intensity source that moves through the cylinder at 5-mm intervals. 3 The HDR technique, however, requires a stricter level of quality assurance (QA) to ensure adequate safety in its operations including the computerized treatment planning. Each step in the integrated process of RT needs quality control and quality assurance to prevent a number of errors and to give high confidence that patients will receive the prescribed treatment correctly. [4][5][6] One vital component of the QA is the independent checks of total dwell times for brachytherapy dose delivery by manual calculations or a second computer program. | 69 use of source step size of 5 mm only. Therefore, treatment lengths at the institution which normally range from 2 to 10 cm correspond to source activation at 4-20 DPs along the catheter.
Mayo and Ulin 8 earlier described a method for checking the treatment time calculation for HDR vaginal cylinder treatments. For dose prescription points located only at 5 mm away from cylinder surface, the authors proposed the determination of a scaling factor K that relates the prescribed dose D, the source strength Sk, and the total treatment time TT, in the form of In this study, we acquired dosimetric data on Cobalt-60 airkerma strength, doses to the prescription points, numbers of dwell positions, and the TDT related to the initial ICBT applications of the subjects considered. The first and the second parameters were reexpressed in cGy.cm 2 /min and cGy, respectively, in order for TDTs to be obtained directly in minutes which is realistic for HDR treatments. EViews (version 9) statistical software (Canada) was used on the three sets of data (based on applicator diameters) to perform a regression analysis in two phases. Firstly, the three quantities highlighted in eq. (1) were modeled to verify their relationship.
Regression analysis of the treatment planning data involving three parameters yielded a relationship given as: This is a resemblance of eq. (1) in literature.
By comparing the resulting eq. (2) with the previous, a mathematical expression (eq. 3) for the treatment time factor was obtained.
While b 0 is the intercept, b 1 being the slope represents the treatment time factor which can be evaluated as: The values of the parameter K were therefore evaluated for the three sizes of the VCA. The other stage involved the inclusion of the number of the DPs as an additional parameter in the statistical analysis.
Further regression analysis incorporating the treatment length factor (number of DPs) resulted in a mathematical relationship as follows: The two models developed were used to generate predicted dose delivery times which were compared with the corresponding TPS values.

| RESULTS
The descriptive of brachytherapy plan parameters and the corresponding P-values as determined by the analysis of variance are presented in Table 2.
The values of the coefficients b 0 and b 1 for the respective diameters of the applicators are given in Table 3. In Table 4, the resulting K values evaluated using eq. (3) are presented.
The intercepts and the coefficients of the variables related to eq. (4) for the three cylinder sizes are therefore presented in Table 5.
Regression analyses in both cases were at a level of significance of 0.01.
In  Results of ANOVA (Table 2) Table 3 presents the combined outputs of the regression analysis involving three variables. We recall that a treatment time factor, K, was earlier identified in the study of Mayo and Ulin. 8 According to the authors, the cylinder radius, prescription radius, and the active lengths prescribed to 5 mm depth and to the surface of the VCA were both given considerations in the determination of K. This study considered the sizes of the VCA separately in the process of evaluating K for dose prescriptions to 5 mm away from the cylinder's surface only. The coefficient b 1 in Table 3 which is representative of K showed a significant dependence on the cylinder radius which normally determines the prescription radius for a given treatment plan.
It is therefore a precursor to the pattern of the evaluated treatment time factors, K, presented in Table 4, showing variability with treatment lengths along the different applicator sizes as illustrated in Fig. 2. In general, it was found to have increased with the number of dwell positions activated for treatment. Moreover, the factor becomes more significant as the applicator becomes bigger in size.
This could be attributed to the fact that the proximity of the dose prescription points to the source positions at the center of the intravaginal applicator (Fig. 1)     The verification program which requires an input of the S k and the related parameters is spreadsheet based and can be executed in less than a minute. Our institutional study has also helped to gain insights on how the total dwell time for cylinder applications would vary with the treatment parameters in order to be properly guided in HDR brachytherapy administration. This knowledge is also needful when certain changes are made to BT parameters from one treatment fraction to another. As most gynecological cancers present late in Nigeria, there is a great strain on the country's radiotherapy facilities. 10 A judicious use of the HDR brachytherapy equipment which is grossly inadequate in Nigeria is therefore of the essence.

| CONCLUSIONS
This study on vaginal cylinder applications is with regards to the use of Cobalt-60 on HDR-Basic TPS operating with a single-source step size of 5 mm. The outcomes could suggest likely variations in the treatment time when certain changes occur in the related parameters.
The study has demonstrated that elongation of the dose delivery time increases with the size of the VCA. It is needful to ensure the choice of applicator size and the treatment length along the cylinder is always appropriate for the individual patients in order to justify the TDT that would result. The latter model developed has been a useful tool for the verification of the dose delivery time at the first HDR brachytherapy center in Nigeria. Similar studies should be undertaken by other institutions to assess the weights of the existing relationships among the specified parameters. Such works could consider predetermining the total dwell time, particularly for HDR 60 Co applications, when the dose is prescribed to points 5 mm away from the VCA's surface only.