

ORIGINAL ARTICLE 

Year : 2005  Volume
: 1
 Issue : 2  Page : 8491 

Dose uniformity assessment of intraluminal brachytherapy using HDR 192Ir stepping source
Narayan Prasad Patel^{1}, Bishnu Majumdar^{2}, Pradeep K Hota^{1}, Dayanidhi Singh^{3}
^{1} Departments of Medical Physics, Acharya Harihar Regional Cancer Centre, Cuttack 753 007, India ^{2} Departments of Radiation Oncology, Acharya Harihar Regional Cancer Centre, Cuttack 753 007, India ^{3} Department of Physics, Govt College of Science, Raipur  952 010, India
Correspondence Address: Narayan Prasad Patel Departments of Medical Physics, Acharya Harihar Regional Cancer Centre, Cuttack 753 007 India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09731482.16707
PURPOSE: The aim of this study is to achieve dose uniformity for intraluminal implants by assessment of dose distributions for single catheter generated by using various combinations of source stopping spacing and optimization mode. MATERIALS AND METHODS: A dose distribution was generated using HDR ^{192}Ir stepping source on single straight catheter of fixed length used for Intraluminal brachytherapy. The various combinations of source position spacing and optimization mode were used and these dose distributions were evaluated by using three different parameters. The source position spacings were 0.2, 0.5, 1.0, 1.4, 2.0, 2.5, 3.0 and 3.3 cm. Three different optimization modes that compute the source stopping times along the catheter were used. The parameters used for assessment of dose distributions were statistical analysis of doses to dose reference points, area under natural dosevolume histogram and the dose nonuniformity ratio. RESULTS: None of the combinations of source position spacing and optimization mode was able to generate the desired optimum uniform dose distribution. However in a discrete manner, comparatively higher uniform dose distribution was found with short (0.2 cm) and longer (1.5 to 2.0 cm) source spacing. Optimization mode of Iterative correction was found to be suitable for the single catheter used in intraluminal brachytherapy. Conclusion: The applicator dimension and irradiation target volume should be taken in to consideration while selecting either higher or smaller source position spacing for the single catheter intraluminal brachytherapy. The Anisotropy factor of the source has some role in the variation of the dose uniformity over the target volume.
Keywords: Intraluminal brachytherapy, Treatment planning system, Dose uniformity, Optimization
How to cite this article: Patel NP, Majumdar B, Hota PK, Singh D. Dose uniformity assessment of intraluminal brachytherapy using HDR 192Ir stepping source. J Can Res Ther 2005;1:8491 
How to cite this URL: Patel NP, Majumdar B, Hota PK, Singh D. Dose uniformity assessment of intraluminal brachytherapy using HDR 192Ir stepping source. J Can Res Ther [serial online] 2005 [cited 2021 Sep 27];1:8491. Available from: https://www.cancerjournal.net/text.asp?2005/1/2/84/16707 
> Introduction   
The high dose rate ^{ 192} Ir source in stepping motion with remote after loading machine is commonly used for brachytherapy by most of the radiotherapy centers. Intraluminal brachytherapy is a very effective modality of treatment for obstructive bronchogenic carcinoma, esophageal carcinoma and neoplastic jaundice. [1],[2],[3],[4],[5] Generally single catheter is used for treatment in most of the intraluminal brachytherapy. The aim of HDR brachytherapy (BT) is to deliver a best possible uniform target dose by optimization, which is likely to control the tumor, while limiting the dose to surrounding normal tissues. Optimization in HDR brachytherapy aims to optimize the dose distribution of the implants with rigid catheters or needles by adjusting the dwell time of the stepping source in each dwell position.[6] The dose distribution evaluation on reconstructed coronal, sagittal or transverse planes is a valuable tool for the evaluation of threedimensional dose distributions. Qualities of dose distributions obtained with brachytherapy dosimetry systems were assessed with different types of volume dose histogram (VDH).[7]
Many reports have been published on the evaluation of dose distribution of brachytherapy implants. Important changes in reference points, volume and treatment time can be found by altering the source dwell time and its position.[8] Other studies on optimization are formula for interplanar separation to achieve uniformity in interstitial implant,[9], [10] dose uniformity assessment of interstitial implants using different index [11],[12],[13],[14],[15] and a ratio of volumes technique for interstitial implant.[16] A film dosimetric system was used for assessment of dose distributions at offaxis plane.[17] Dose volume assessment was carried out using different parameters for different source spacing for the intraluminal catheter implant.[18]
There has been a great improvement in the technologies of the remote after loading brachytherapy unit in the recent years, which provides a variety of options to the practitioners for clinical application. The reduced applicator size due to small source has enabled the clinicians to perform HDR procedures in most of the anatomical sites. The stepping source with minimum 1 mm spacing gives high spatial resolution and that provides more flexibility and better isodose distribution for the various implants. The vendors supplied treatmentplanning system incorporated with the variety of optimization mode, which enable the users to achieve optimum uniform dose distribution in different clinical situations. The other options for the users are modification or completely deactivation of source stopping time at any source positions and or changing of spacing between the source positions. Furthermore, the planning systems have ability of assessment of dose homogeneity of the threedimensional dose distribution. In case of single catheter implant using stepping source, inter source spacing and sourcestopping times are only two parameters, which can be altered in the optimization process.
In present study, threedimensional dose distribution of the intraluminal catheter was generated for the dose homogeneity assessment. The catheter was planned for different combinations of source stopping spacing and different optimization process for the dose distribution. The parameters used for the dose distribution analysis are statistical analysis, area under natural dose volume histogram and dose nonuniformity ratio.
> Materials and methods   
The catheter implant generally used for esophageal and bronchogenic carcinoma was taken in the present study. The implant was considered as an ideal, which was single catheter in straight line of 10 cm length. The ^{ 192} Ir HDR brachytherapy source with air kerma strength of 4.033 x 10^{ 4}mGym^{ 2} /h or nominal activity of 10 Ci was used for the treatment time calculation. The treatment planning system,[1] which has different optimization modes, was used for dose distribution. The dosimetric data used in calculation algorithm were Meisberger's polynomial and vendor provided anisotropy factor. Although the system can generates the source positioning points and the dose reference points automatically, but in place of that we have used coordinate methods through keyboard in defining the set of source stopping positions and dose reference points. [Figure  1] shows the catheter implant of 10 cm length. In the figure " Circle" represents the source positions with each spaced by 1 cm from others and " plus" represents the dose reference points each spaced by 0.5 cm and at 1 cm distance from the axis of the catheter. The data of coordinates of the source positioning points and dose reference points was entered through keyboard. Source position spacing of 0.2, 0.5, 1.0, 1.4, 2.0, 2.5 and 3.3 cm were used in this study. The number of source positioning points varies according to the source spacing, but the number of dose reference points was twentyone and unchanged for all plans. These DRPs were at one cm from distance from the central axis of catheter and with a inter spacing of 0.5 cm uniformly over the full length. Dose of 10 Gy was prescribed to all dose reference points.
After the defining of source stopping positions and dose reference points, system uses the full optimization algorithm to compute the appropriate source stopping times. A list of source stopping positions (j = 1…n), dose reference points (i = 1…. m) and prescribed dose to points (i = 1…m) is defined by system. The three dimensional matrix in linear compensating problem which consists of dose rate d (i, j), source stopping times t (j) and prescribed dose at reference point D (j) was solved by means of orthogonal transformations. System uses a special formula to control the span of treatment time. In all calculation, standard optimization constraints Dc=D (where Dc is optimize dose and D is prescribed dose) were used. In our study, sourcestopping times for each and all implant of different source stopping spacing were calculated with three different fast optimization modes provided in the system. These three optimization modes were:
(a) Equal Time (ET): System uses equal stopping times ( + one second) for all defined source positions.
(b) Geometric Distribution (GD): Source stopping positions at the outside of the implant receive a higher stopping times then the inside source stopping positions.
(c) Iterative Correction (IC): Starting with the stopping times from the geometric distribution mode an iterative process begins in order to minimize the violation to the prescribed dosage.
The each combination of source stopping spacing and optimization mode was defined as a "plan". Therefore the number of plans in present study was twentyone. Planning system generates a three dimensional dose distribution on the basis of computed source stopping times. These stopping times calculated are best possible to satisfy the defined dose constraint. This planning system has provision only to generate a 3D cumulative dosevolume histogram for overall treatment volume of implant; it cannot generate separately for target volume and normal tissue. 3D dose volume histograms were generated with a dose for calculation gradient size of 60 x 60. Cumulative volumes vs. dose curves were determined with cumulative dose in increment of 0.25 Gy. In our study we considered different parameters for analysis and comparison of homogeneity of dose distributions. These parameters were:
(a) Statistical analysis of doses at reference points: Optimized dose received by twentyone dose reference points for all dose distributions were tabulated. Mean, standard deviation and skewness of these point doses were calculated. This set of twentyone dose reference points represents the surface of the target volume as a cylinder of diameter of two centimeter. The computed dose at these reference points were the dose received by the outer surface of the target volume.
(b) Natural dose volume histogram (NDVH): Differential volume vs. dose curve was generated from cumulative volume vs. dose curve. The reference dose increases systematically from 4 to 40 Gy in steps of 0.25 Gy.The differential volume vs. dose curve was converted into the natural dose volume histogram (NDVH) as proposed by the Anderson.[19] The NDVH is a plot variable dV/du vs. u (D), where V is the volume enclosed by isodose level at D, and u (D) = D^{3}/^{2} [Figure  2]. The established parameters like uniformity index, quality index and peak index were appeared to be indecisive for comparison of different dose distribution of single catheter implant. We proposed a simple parameter of cumulative area under the implant histogram between the dose D_{1} and D_{2}. Lower limit of dose range D_{1} was kept constant at 5 Gy where as upper limit of dose D_{2} were taken at 10, 15, 20, 25 and 30 Gy.
(c) Dose nonuniformity ratio: The cumulative volume vs. dose curve was used in computing the DNR. The dose nonuniformity ratio is the ratio of volume receiving doses greater then the 1.5 times of reference dose, to the volume that receives equal or greater then the reference dose. The reference dose varies from 4 to 40 Gy in increment of 0.25 Gy.
> Results   
In the present study, the algorithm in planning system consider only the source of nominal activity of 10 Ci to compute the source stopping time to deliver the prescribed dose. [Figure  3](a) shows the distribution of source stopping times vs. source positions along the catheter in case of source position spacing of 0.5 cm from three optimization modes. The distribution of stopping times with the stopping position was uniform and similar for ET and GD optimization modes. A large variation in distribution of stopping times was observed in the IC mode. [Figure  3](b) shows the total activity (Ci x second) required to deliver prescribed dose of 10 Gy to dose reference points for all source spacing with optimization mode of ET, GD and IC. It was observed that total activity increases with increase in source position spacing. A significant variation about 13% in activity was observed in case of ET and GD modes of optimization whereas it was only 3% in IC.
Statistical analysis of optimized dose received by dose reference points for plans are shown in [Figure  4]a, b and c. Mean, standard deviation and skewness of doses from twentyone dose reference points were plotted vs. source stopping spacing for three different optimization modes in [Figure  4](a), 4(b) and 4(c) respectively. It was observed that ET and GD optimization modes always deliver an under prescribed dose with large variation and asymmetric. In case of IC optimization mode, the delivered doses to reference points were found to be uniform, symmetric and very close to the prescribed dose of 10 Gy. However the mean delivered dose in IC mode decreases with increase in the source stopping spacing. For the source stopping spacing of 2 cm, the statistical properties of three optimization modes were found to be analogous. It was observed that for higher source spacing, the statistical properties of dose distributions do not distinguish between the optimization modes.
The NDVH of dose distributions with source spacing of 0.2, 1.0 and 2.0 cm in IC optimization mode using ^{ 192} Ir HDR source along 10 cm straight catheter are shown in [Figure  5]. Similar NDVH were plotted for all other plans. A multiple peaks were observed in the NDVH curve. These peaks were discrete and its position vs. dose changes from one plan to another. The peaks indicate the higher homogeneity at corresponding reference dose then the other dose. The two peaks of same height in any DVH do not mean equal homogeneity or the equal volume covered by the corresponding dose. For the comparison of dose homogeneity between different plans, the areas under the NDVH for different dose ranges were calculated.
Cumulative areas under the NDVH vs. source spacing at different dose ranges of catheter implant of 10 cm are shown in [Figure  6] [a, b and c]. Dose ranges used for this calculation were 510, 515, 520, 525 and 530 Gy. It was observed that at lower dose range 510 Gy, the area remains constant with the source spacing in IC mode whereas steady increase was found for two other modes. For the dose range of 515 Gy, the area under histogram increases rapidly and reaches to maximum value at source spacing of 2.0 cm. This means that source spacing of 2.0 cm gives highest homogeneity in dose range of 10 to 15 Gy. In the present study, the dose 10 Gy is prescribed dose to reference points at 1 cm away from the catheters. Further for the dose range of 520 Gy, large recovery of area under histogram by short source spacing was observed. In this dose range a significant differences between the IC and two other optimization modes was observed. A highest uniformity with shortest source spacing of 0.2 cm in IC mode was observed in the dose rage of 15 to 20 Gy. Similarly source spacing of 1.4 cm shows higher uniformity in the dose between 20 to 25 Gy consequently the cumulative area under histogram turn into maximum for the dose range of 525 Gy. Finally for the dose range of 530 Gy, combinations of IC mode with 0.2, 1.4 and 2.0 cm, GD mode with 1.4 and 2.0 cm and ET with 1.4 and 2.0 cm source spacing shows better dose uniformity. Overall assessment shows that the IC mode was superior to the other optimization modes. The dose uniformity changes with the source spacing and dose level, however the source spacing with higher dose uniformity at lower dose preferably prescribed is more significant.
[Figure  7] shows the plot of DNR vs. reference dose for a source spacing of 0.2, 1 and 2.0 cm using HDR ^{ 192} Ir source of single catheter implant. Similar DNR curves were generated for all plans. From curves, it was observed that behavior of DNR value is varying with the reference dose. The DNRs value moves up and down frequently with the increase in reference dose. However at an arbitrary dose range, the decrease in DNR value is comparatively higher and reaches to a minimum value at a particular dose, and thereafter increases slowly with increase in the reference dose. This turning point where the value of DNR is minimum called as a DNR_{ min} and corresponding particular reference dose called as an RD_{ min} . It has a specific importance as it represents best dose homogeneity. This can be explained as, the volume at higher dose of 1.5 times of reference dose RD_{ min} is compressed in comparison to reference dose volume representing relatively higher spread of volume in this particular dose range. There is an inverse relationship between DNR value and dose homogeneity as an implant having lowest DNR value gives better dose homogeneity. If the volume comprises between the reference dose and higher dose of 1.5 times then the reference dose covers the irradiation target volume then the reference dose RD_{ min} is selected as delivered dose for implant, the dose homogeneity within the volume enclosed by RD_{ min} is optimum.
[Table  1] displays the DNR values for all the plans of HDR implants of single catheter. The value of RD_{ min} , DNR_{ min} , DNR_{10} and volume covered by 10 Gy isodose line for all plans is presented. It was observed that RD_{ min} remains constant at about 16 Gy for source position spacing from 0.2 to 1.4 cm, and then increases with increase in the source position spacing in all optimization modes. The value of DNR_{ min} is observed to be lowest for source separation of 0.2 cm and then increases with the increase in source separation. This value again decreases for source separation of 1.4 cm and then increases with increase in source separation. The value of DNR_{10} decreases with the increase in source separation and reaches to minimum for particular source separation and then increases. The DNR_{10} value was minimum for the source separation of 2.5 cm for ET and GD mode, whereas 2.0 cm only for IC optimization mode. The only major difference between the results of present study and by Saw et al is the relationship between changes of RD_{ min} with source stopping spacing. In previous study, the value of RD_{ min} decreases at constant rate with increase in source position spacing whereas in present study it increases with the source position spacing. However the increase in RD_{ min} was very small for source spacing between 0.2 cm to 1.4 cm then after rapid increase in was observed for higher source spacing.
> Discussion   
Optimization in the HDR brachytherapy aims to optimize the dose distribution of implants with rigid catheters by adjusting the stopping time of the stepping source in each stopping position. In this study, we have considered single straight catheter to achieve a best homogenous dose distribution that confirm to the target volume by choosing a variety of combination of inter source spacing and stopping times. In optimization process, the algorithm calculate the stopping times for the each stopping position depending on the dose constraints points and the set of dose constraints equations. Therefore the number as well as position of dose constraints points may vary the stopping times which results in a deviation in threedimensional dose distribution. To avoid this, the number of dose reference points and its position from axis of the catheter were similar in all plans. The optimum numbers of dose reference points were taken to avoid any variation in dose distribution due to change in source stopping spacing.
There are several studies have been published in literatures about the quantitative analysis of the dose distribution by using different parameters. A significant changes in the volume covered by dose line was observed by changing spacing between the dwell positions the source dwell times in case of uterovaginal applicator in treatment of ca cervix.[8] The parameters used for the assessment of different implants were dose uniformity index,[12], [13] dosevolume ratio technique,[9], [16] equivalent uniform dose,[10] peak index and new geometry index,[11] dose nonuniformity ratio[14], [15], [18] and three volumetric irradiation indices.[14], [18] The parameters used for the assessment of threedimensional dose distribution of the single catheter intraluminal implant were dose nonuniformity ratio and three volumetric irradiation indices.[18] Natural volume dose histogram provides graphical indication of the dose rate uniformity and clinically relevant volumedose assessment of interstitial implants.[19]
In the present study, the parameters used for assessment of the dose distribution were statistical analysis, area under NDVH and the dose nonuniformity ratio. The three volumetric irradiation indices could not be employed because the treatment planning system can generate cumulative dosevolume histogram only for the whole implant. Our aim is to achieve uniform prescribed dose inside and able to cover the target volume (as cylindrical shape for Intraluminal implant) with a sharp fall in dose outside. The statistical analysis of the dose at the dose reference points gives a broad picture of the dose distribution over the surface of the cylinder. The others two parameters cumulative area under NDVH and the DNR analyze the homogeneity of the dose distribution over the range of defined dose distribution. The NDVH was generated using the differential dosevolume histogram whereas the DNR was calculated using cumulative dosevolume histogram. Both the parameters explain about the spread ness of dose volume, but difference between these two is that DNR value at reference dose is influence with the volume of 1.5 times higher dose than the reference dose whereas NDVH depends upon the concern dose volume. The NDVH curve shows a several peaks of different heights at different dose, which changes their position and heights with the change in the source stopping spacing. For the comparison between different plans we propose to calculate the cumulative area under NDVH between different dose ranges. The dose range used in this study was clinically significant as it covers within and outside of the target volume situated off axis from the catheter.
The statistical analysis shows that IC mode delivers the uniform prescribed dose over the dose reference points with the source spacing from 0.2 cm to 1.5 cm after that the standard deviation becomes significant (10 % >). From the cumulative area under NDVH it was observed that the dose distribution from the source stopping spacing of 0.2, 1.5 and 2 cm shows almost equal and superior homogeneity. This superior uniformity was observed at different dose levels, which was obviously supported by the DNR. The cumulative area of the plan with source stopping spacing of 0.2 cm and 1.5 cm increases drastically in the dose range of 1520 Gy, which was supported by the DNR study as the DNRmin was obtained at the reference dose of 16 Gy in all optimization modes. The cumulative area for the 2.0 cm spacing shows maximum value in the dose range of 1015 Gy it was reflected by the DNR study. Dose distribution with 2.0 cm source spacing shows the maximum dose uniformity at prescribed reference dose of 10 Gy at 1 cm offaxis from the catheter.
In a report,[18] similar study was performed for single catheter with source spacings of from 0.5 cm to 3 cm; however the details of dosimetric data and optimization mode employed was not described. The above study shows a smooth DNR curve and constant decrease in RDmin (Gy) with increase in the source stopping spacing whereas in the present study the results were contradictory. The RDmin (Gy) increases irregularly with the increase in the source stopping spacing for all optimization modes. This contradiction can be due to the anisotropic nature of the source, which could have played an important role in the variation of the dose distribution. However, the grid size used in present study for generating dose distribution in the planning system could have made some variation in the results. The dose distribution of a single source used in the present study was found to be of anisotropic nature as shown in [Figure  8]. The axis ratio (2a/2b) was higher than the one for all isodose line. The other disclosure in present study is the better dose uniformity of the source stopping spacing of 0.2 cm, however this source separation was not considered by the previous study.[18] The dose assessment using radiochromic film [17] support our results as in their study, the dose uniformity with source spacing of 0.25 cm was higher than the source spacing of 0.5 cm.
Clinically a single catheter is used for the treatment of esophageal and endobronchial malignancies. Several studies show a significant variation in physical dimension of the applicator and prescription of target volume as well as the dose with the clinical situation. In case of the endobronchial application, the dose prescription depths reported in the literatures varies with in the range of 0.5 cm to 2 cm. The most of the studies prescribe the dose at 1cm from the central axis of catheter. The diameter of the applicator used in endobronchial implant is about 2 mm comparatively very small dimension then the irradiated target volume. In case of esophageal application, the dose is generally prescribed at 1cm from the axis of source catheter whereas the diameter of applicator varies with the clinical situations. In that case, the physical dimension of the applicator becomes vital as applicator with small diameter could results in higher morbidity, mucositis, ulceration and fibrosis. This is due to the large and inhomogeneous dose received by the surface of the tumor or normal mucosa, which comes into contact with the surface of applicator.[20] These two different clinical situation and results of present study suggest for the use of smaller and larger source stopping spacing for the applicator of larger and smaller diameter respectively. A larger source spacing (1.5 to 2.0 cm) should be prefer for the endobronchial treatment as always thin catheter is used for the treatment. Although large inhomogeneous dose distribution is observed just around the source with larger spacing, but the total volume encompass with inhomogeneous dose is insignificant in comparison to uniform dose volume. However the overall length of the catheter should be taken in to account while opting for larger source spacing. The use of large source stopping spacing for the esophageal application may not generate uniform dose distribution over the surface of target volume. When the applicator with large diameter is used for esophageal and intravaginal treatment, the shorter source stopping spacing (0.2 cm) is suggested as large and inhomogeneous dose volume remains inside the applicator.
> Conclusion   
The present study suggests that the clinical target volume and physical parameter of the applicator should be taken into consideration for the selection of the source stopping spacing. In case of the applicator of smaller diameter with target volume of large diameter, the larger source spacing (2 cm) should be preferred. In case of applicator with larger diameter and narrow cylindrical target volume, the small source spacing (2 mm) gives comparatively higher uniform dose distribution. The study shows that the anisotropy factor of the source plays some role in altering the homogeneity of the dose distribution which recommends for the independent evaluation of the uniformity of dose distribution for each type of the system as well as the source used for the treatment.
Abacus Planning System,
IsotopenTechnik, GmBH, (Presently Varian Medical System), Germany
> References   
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3.  Marsiglia H, Baldeyrou P, Lartigau E. Highdoserate brachytherapy as sole modality for earlystage endobronchial carcinoma. Int J Radiat Oncol Biol Phys 2000;47:66572. 
4.  Rosenblatt E, Pisch J, Villamena PC. HDR endobronchial irradiation in malignant airway obstruction. International Brachytherapy. USA: Baltimore / Washington; 1992. p. 46770. 
5.  Montemaggi P, Luzi S, Caspiani O. Intraluminal brachytherapy in treatment of neoplastic jaundice International Brachytherapy. USA: Baltimore/ Washington; 1992. p. 4924. 
6.  Van der Laarse R, Prins, TPE. Introduction to HDR brachytherapy optimization. Textbook of Brachytherapy from Radium to Optimization. Netherlands: Nucletron International B. V.; 1994. p. 33172. 
7.  Hilaris BS, Tenner M, High M. ThreeDimensional brachytherapy treatment planning. International Brachytherapy. USA: Baltimore/ Washington; 1992. p. 1178. 
8.  Cetingoz R, Ataman OU, Tuncel N. Optimization to high dose rate brachytherapy for uterovaginal applications. Int J Radiat Oncol Biol Phys 2001;58:316. 
9.  Zwicker RD, SchmidtUllrich RK. Dose uniformity in a planer interstitial implant system. Int J Radiat Oncol Biol Phys 1995;31:14955. 
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12.  Paul JM, Koch RF, Philip PC. Uniformity of dose distribution in interstitial implants. Endocurie Hypertherm. Oncol 1986;2:10718. 
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17.  Skwarchuk MW, Ochran TG, Komaki R. The use of radiochromic film to measure dose distributions resulting from high dose rate ^{192}subIridium single catheter treatments. Int J Radiat Oncol Biol Phys 1996;34:17381. 
18.  Saw CB, Korb LJ, Pawlicki T. Dose volume assessment of high dose rate ^{192}subIr endobronchial implants. Int J Radiat Oncol Biol Phys 1996;34:91722. 
19.  Anderson LLA. "Natural" volume dose histogram for brachytherapy. Med Phys 1986;13:898903. 
20.  Joslin CA, Flynn A, Hall EJ, Arnold. Principle and practice of brachytherapy using afterloading system. 338 Euston Road, London NW13BH 2001:22556. 
[Figure  1], [Figure  2], [Figure  3], [Figure  4], [Figure  5], [Figure  6], [Figure  7], [Figure  8]
[Table  1]
