MCPI: a sub-minute Monte Carlo dose calculation engine for prostate implants

An accelerated Monte Carlo code [Monte Carlo dose calculation for prostate implant (MCPI)] is developed for dose calculation in prostate brachytherapy. MCPI physically simulates a set of radioactive seeds with arbitrary positions and orientations, merged in a three-dimensional (3D) heterogeneous phantom representing the prostate and surrounding tissue. MCPI uses a phase space data source-model to account for seed self-absorption and seed anisotropy. A "hybrid geometry" model (full 3D seed geometry merged in 3D mesh of voxels) is used for rigorous treatment of the interseed attenuation and tissue heterogeneity effects. MCPI is benchmarked against the MCNP5 code for idealized and real implants, for 103Pd and 125I seeds. MCPI calculates the dose distribution (2-mm voxel mesh) of a 103Pd implant (83 seeds) with 2% average statistical uncertainty in 59 s using a single Pentium 4 PC (2.4 GHz). MCPI is more than 10(3) and 10(4) times faster than MCNP5 for prostate dose calculations using 2- and 1-mm voxels, respectively. To illustrate its usefulness, MCPI is used to quantify the dosimetric effects of interseed attenuation, tissue composition, and tissue calcifications. Ignoring the interseed attenuation effect or slightly varying the prostate tissue composition may lead to 6% decreases of D100, the dose delivered to 100% of the prostate. The presence of calcifications, covering 1%-5% of the prostate volume, decreases D80, D90, and D100 by up to 32%, 37%, and 58%, respectively. In conclusion, sub-minute dose calculations, taking into account all dosimetric effects, are now possible for more accurate dose planning and dose assessment in prostate brachytherapy.     

The effect of seed anisotrophy on brachytherapy dose distributions using 125I and 103Pd

We have evaluated the effect of the anisotropy of individual seeds on dose distributions for permanent prostate implants using 125I and 103Pd. The dose distributions were calculated for various implants using both the line source and point source calculational formalisms, for two different models of 125I and 103Pd seeds. The dose distributions were compared using cumulative dose volume histograms (DVH) and cumulative difference dose volume histograms (deltaDVH) for the prostate target volume and for the rectum surface. The DVHs could not distinguish between the dose distributions from isotropic and non-isotropic seeds. However, the deltaDVHs were useful in determining the fraction of the target volume for which the difference between the dose distribution for line sources and for point sources exceeded a threshold value. The dose distributions were calculated (1) for all the seeds oriented co-linearly, along either the x-, y-, or z-axis, and (2) for the seeds at randomized orientations, more closely resembling the clinical situation. For all cases, there was a significant difference in the effect of seed anisotropy from the different seed types. For the geometrically simpler test cases with a small number of seeds, the effect of anisotropy on the dose distribution was too large to ignore for any of the seed types investigated. For the idealized pre-plan case, the effect was much smaller. For clinical prostate implants, the calculations done with seeds oriented co-linearly along the z-axis (needle implant axis) were a reasonable approximation for those from simulations of seeds with randomized orientations. Again, the effect of anisotropy varied drastically between different seed models, and also between different clinical cases. However, the effect of anisotropy must be considered in the context of all the other uncertainties in clinical brachytherapy treatments.     

A Monte Carlo study on the effect of seed design on the interseed attenuation in permanent prostate implants

Standard algorithms for postimplant analysis of transperineal interstitial permanent prostate brachytherapy (TIPPB) are based on AAPM Task Group 43 formalism (TG-43), which makes use of a world entirely made of water. This entails an assignment of the prostate, surrounding organs at risk, as well as all brachytherapy seeds present in a permanent prostate implant to water. Brachytherapy seeds are generally made from high atomic number materials. Because of the simultaneous presence of many brachytherapy seeds in a TIPPB, there is a shielding effect causing an attenuation of energy of the emitted photons generally called the "interseed attenuation" (ISA). This study investigates the impact of seed designs and compositions on the interseed attenuation. For this purpose, six brachytherapy seeds covering a wide variety of seed design and composition were modeled with the GEANT4 Monte Carlo (MC) toolkit. MC has allowed calculation of the contribution of each major component (encapsulation and internal components) of a given seed model to ISA separately. The impact of ISA on real clinical implant configurations was also explored. Two clinical postimplant geometries with different brachytherapy seeds were studied with MC simulations. The change in the clinical parameter D90 was observed. This study shows that Nucletron SelectSeed (similar to the Oncura model 6711), ProstaSeed, and Best Medical model 2335 are the most attenuating designs with 4.8%, 3.9%, and 4.6% of D90 reduction, respectively. The least attenuating seed is a 103Pd seed encapsulated in a polymer shell, the IBt OptiSeed with 1.5%. Finally, based on this systematic study, a new seed design is proposed that is predicted to be the most waterlike brachytherapy seed and thus TG-43 compatible.     

Dose perturbation effects in prostate seed implant brachytherapy with I-125

EGSnrc Monte Carlo simulation was used to investigate dose perturbation effects in prostate seed implant brachytherapy using 125I radioactive seeds used in implant brachytherapy. Dose perturbation effects resulting from the seed mutual attenuation in a prostate seed implant consisting of 27 seeds were investigated. The results showed that for 125I seeds implanted into the prostate at 1.00 cm, 0.75 cm and 0.50 cm apart (uniform spacing), the dose perturbation effects are up to 10%. The volume of the target occupied by the 10% dose difference between the full Monte Carlo simulation and the single seed superposition model decreases with increasing seed spacing. Despite the differences between the Monte Carlo simulation and the simple superposition, there was no significant change in the dose volume histogram for 1 cm and 0.75 cm seed spacing. However, there was a significant change in the dose volume histogram when the seed spacing was 0.5 cm. An analysis of the external volume index (EI), coverage index (CI) and homogeneity index (HI) also showed that there is no difference in these indexes for the 1.00 cm and 0.75 cm seed spacing between the simple superposition model and the full Monte Carlo simulation. Compared to the full Monte Carlo simulations, the simple superposition model overestimated EI, CI and HI by 7%, 5% and 4% respectively for the 0.50 cm seed spacing.     

ALGEBRA: ALgorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy

Task group 43 (TG43)-based dosimetry algorithms are efficient for brachytherapy dose calculation in water. However, human tissues have chemical compositions and densities different than water. Moreover, the mutual shielding effect of seeds on each other (interseed attenuation) is neglected in the TG43-based dosimetry platforms. The scientific community has expressed the need for an accurate dosimetry platform in brachytherapy. The purpose of this paper is to present ALGEBRA, a Monte Carlo platform for dosimetry in brachytherapy which is sufficiently fast and accurate for clinical and research purposes. ALGEBRA is based on the GEANT4 Monte Carlo code and is capable of handling the DICOM RT standard to recreate a virtual model of the treated site. Here, the performance of ALGEBRA is presented for the special case of LDR brachytherapy in permanent prostate and breast seed implants. However, the algorithm is also capable of handling other treatments such as HDR brachytherapy.     

Interseed effects on dose for 125I brachytherapy implants.

Dose calculations in multiseed brachytherapy implants are done by adding the contribution of each individual seed and by assuming that radiation from each seed is unaffected by the presence of the other seeds. To test the validity of this assumption, dose measurements with various configurations of multiseed implants of 125I model 6702 and 125I model 6711 sources were performed. For a linear configuration of three 125I model 6702 seeds at 1-cm separation, with their transverse axes coincident, doses at distances of 3.05 and 5.09 cm from the center along the transverse axis were found to be about 8% lower than the sum of doses from the three individual seeds. However, for three seeds at 1-cm intervals with their longitudinal axes coincident, doses at 3.05 and 5.09 cm distances from the center along the longitudinal axis were found to be about equal to the dose sums from individual seeds. These initial experiments indicated that the magnitude of the interseed effect depends upon the orientation of the seed relative to each other in an implant. To evaluate the importance of this interseed effect for multiseed configurations of 125I model 6702 and 125I model 6711 seeds, dose rates at various distances from a two-plane implant (each plane containing a 3 x 3 array of sources in a 1-cm spacing square grid) were measured in a Solid Water phantom with LiF TLDs. These measurements were carried out in two different planes at different orientations relative to the implant. The average values of the interseed effect at distances ranging from 1 to 7 cm outside the implant were observed to be about the same for 125I model 6702 and model 6711 sources. The mean value of the interseed effect was 6% and the maximum was 12%. On the whole, the interseed effect reduces the dose at the periphery of the iodine implant by 6%.     

Isotope choice and the effect of edema on prostate brachytherapy dosimetry

In prostate brachytherapy, post implant dosimetry quality parameters may be strongly affected by edema brought on by the trauma of the implant procedure since the amount of edema and the time course of its resolution are highly variable from patient to patient. Edema was simulated from preplans on three prostates which had ultrasound prostate volumes of 18.7, 40.7 and 60.2 cm3 expanded to planning volumes of 32.9, 60.0 and 87.8 cm3, respectively. The preplans were designed so that identical seed distributions for a given prostate gave virtually identical target dose coverage of 99.7+/-0.3% of the planning volume when using either 125I or 103Pd. Simulated CT edema volume expansions of 0%, 10%, 20% and 30% were imposed anisotropically in accordance with clinical observations so that the expansion in the superior-inferior direction was twice that of the transverse dimensions. Dose-volume histograms (DVHs) were analyzed for each prostate as a function of isotope and degree of edema. The 103Pd implants were more greatly affected by fixed amounts of edema than 125I implants, and the slopes of the DVH curves indicate less homogeneity from 103Pd implants. The DVHs were then weighted according to the portion of the isotope decay curve occupied by each edema step for half-lives of edema resolution of 5, 10 and 20 days which are within the range of clinically observed resolution times. The weighted DVHs were summed to give a net DVH corresponding to the overall dynamic effect of edema. A greater fraction of the defined prostate volume received doses in the range of likely therapeutic significance, from 75% to 125% of the prescribed minimal peripheral dose (mPD), from 125I implants than from 103Pd implants. These differences in dosimetric quality arise from two differences in the physical properties of the isotopes: more rapid attenuation of 103Pd photons with distance creates cool spots in an edematous prostate, and the shorter half-life of 103Pd causes a greater fraction of the isotope decay to consist of the prostate in an edematous state. An increase in 103Pd seed strength by about 10% beyond that required to achieve equal coverage with an identical seed distribution using 125I should minimize the differences brought on by edema.     

The effect of seed orientation deviations on the quality of 125I prostate implants.

We quantified the effect of seed orientation deviations on five prostate seed implant cases at our institution. While keeping their positions fixed, the iodine-125 seeds were assigned orientations sampled from a realistic probability distribution derived from the post-implant radiographs of ten patients. Dose distributions were calculated with both a model that explicitly includes anisotropy (TG43 anisotropy function) and a point source model (TG43 anisotropy factor). Orientation deviations had only a small influence on prostate dose-volume histograms: the 95% confidence intervals on the volumes receiving 100%, 150% and 200% dose were at most +/-0.8%, +/-1.1% and +/-0.6% of the prostate volume, respectively. The dose-volume histograms of anisotropic seed distributions were marginally better than those with isotropic point-source seeds. Anisotropy caused a displacement of cold spots (regions receiving <100% of the prescribed dose) in <1% of the prostate volume. Our results indicate no net benefit to prostate dosimetry in using more isotropic seeds. Furthermore, we propose a new 'weighted anisotropy function' to better account for the effects of anisotropy when seed orientation is unknown. Conceptually, the TG43 anisotropy factor described in AAPM TG43 averages the effect of anisotropy over all solid angles, with the implicit assumption that all seed orientations are equally probable. In prostate implants, however, seeds are preferentially oriented parallel to the needle axis. The proposed weighted anisotropy function incorporates this non-uniform probability.     

Potential impact of prostate edema on the dosimetry of permanent seed implants using the new 131Cs (model CS-1) seeds

Our aim in this work was to study the potential dosimetric effect of prostate edema on the accuracy of conventional pre- and post-implant dosimetry for prostate seed implants using the newly introduced 131Cs seed, whose radioactive decay half-life (approximately 9.7 days) is directly comparable to the average edema resolution half-life (approximately 10 days) observed previously by Waterman et al. for 125I implants [Int. J. Radiat. Oncol. Biol. Phys. 41, 1069-1077 (1998)]. A systematic calculation of the relative dosimetry effect of prostate edema on the 131Cs implant was performed by using an analytic solution obtained previously [Int. J. Radiat. Oncol. Biol. Phys. 47, 1405-1419 (2000)]. It was found that conventional preimplant dosimetry always overestimates the true delivered dose as it ignores the temporary increase of the interseed distance caused by edema. The overestimation for 131Cs implants ranged from 1.2% (for a small edema with a magnitude of 10% and a half-life of 2 days) to approximately 45% (for larger degree edema with a magnitude of 100% and a half-life of 25 days). The magnitude of pre- and post-implant dosimetry error for 131Cs implants was found to be similar to that of 103Pd implants for typical edema characteristics (magnitude < 100%, and half-life <25 days); both of which are worse compared to 125I implants. The preimplant dosimetry error for 131Cs implants cannot be compensated effectively without knowing the edema characteristics before the seed implantation. On the other hand, the error resulted from a conventional post-implant dosimetry can be minimized (to within +/-6%) for 131Cs implants if the post-implant dosimetry is performed at 10+/-2 days post seed implantation. This "optimum" post-implant dosimetry time is shorter than those determined previously for the 103Pd and 125I implants at 16+/-4 days and 6+/-1 weeks, respectively.     

Experimental determination of the anisotropy function for the model 200 103Pd "light seed" and derivation of the anisotropy constant based upon the linear quadratic model

Since the publication of the AAPM Task Group 43 report in 1995, Model 200 103Pd seed, which has been widely used in prostate seed implants and other brachytherapy procedures, has undergone some changes in its internal geometry resulting from the manufacturer's transition from lower specific activity reactor-produced 103Pd ("heavy seeds") to higher specific activity accelerator-produced radioactive material ("light seeds"). Based on previously reported theoretical calculations and measurements, the dose rate constants and the radial dose functions of the two types of seeds are nearly the same and have already been reported. In this work, the anisotropy function of the "light seed" was experimentally measured and an averaging method for the determination of the anisotropy constant from distance-dependent values of anisotropy factors is presented based upon the continuous low dose rate irradiation linear quadratic model for cell killing. The anisotropy function of Model 200 103Pd "light seeds" was measured in a Solid Water phantom using 1 X 1 x 1 mm micro LiF TLD chips at radial distances of 1, 2, 3, 4, 5, and 6 cm and at angles from 0 to 90 degrees with respect to the longitudinal axis of the seeds. At a radial distance of 1 cm, the measured anisotropy function of the 103Pd "light seed" is considerably lower than that of the 103Pd "heavy seed" reported in the TG 43 report. Our measured values at all radial distances are in excellent agreement with the results of a Monte Carlo simulation reported by Weaver, except for points along and near the seed longitudinal axis. The anisotropy constant of the 103Pd "light seed" was calculated using the linear quadratic biological model for cell killing in 30 clinical implants. For the model 200 "light seed," it has a value of 0.865. However, our biological model calculations lead us to conclude that if the anisotropy factors of an interstitial brachytherapy seed vary significantly over radial distances anisotropy constant should not be used as an approximation for anisotropy characteristics of a brachytherapy seed.     

The impact of edema on planning 125I and 103Pd prostate implants.

Permanent transperineal interstitial 125I and 103Pd prostate implants are generally planned to deliver a specific dose to a clinically defined target volume; however, the post-implant evaluation usually reveals that the implant delivered a lower or higher dose than planned. This difference is generally attributed to such factors as source placement errors, overestimation of the prostate volume on CT, and post-implant edema. In the present work we investigate the impact of edema alone. In routine prostate implant planning, it is customary to assume that both the prostate and seeds are static throughout the entire treatment time, and post-implant edema is not taken into consideration in the dosimetry calculation. However, prostate becomes edematous after seed implantation, typically by 50% in volume [Int. J. Radiat. Oncol., Biol., Phys. 41, 1069-1077 (1998)]. The edema resolves itself exponentially with a typical half-life of 10 days. In this work, the impact of the edema-induced dynamic change in prostate volume and seed location on the dose coverage of the prostate is investigated. The total dose delivered to the prostate was calculated by use of a dynamic model, which takes edema into account. In the model, the edema resolves exponentially with time, as reported in a separate study based on serial CT scans [Int. J. Radiat. Oncol., Biol., Phys. 41, 1069-1077 (1998)]. The model assumes that the seeds were implanted exactly as planned, thus eliminating the effect of source placement errors. Implants based on the same transrectal ultrasound (TRUS) images were planned using both 125I and 103Pd sources separately. The preimplant volume and planned seed locations were expanded to different degrees of edema to simulate the postimplant edematous prostate on day 0. The model calculated the dose in increments of 24 h, appropriately adjusting the prostate volume, seed locations, and source strength prior to each time interval and compiled dose-volume histograms (DVH) of the total dose delivered. A total of 30 such DVHs were generated for each implant using different combinations of edema half-life and magnitude. In addition, a DVH of the plan was compiled in the conventional manner, assuming that the prostate volume and seeds were static during treatment. A comparison of the DVH of the static model to the 30 edema corrected DVHs revealed that the plan overestimated the total dose by an amount that increased with the magnitude of the edema and the edema half-life. The maximum overestimation was 15% for 125I and 32% for 103Pd. For more typical edema parameters (a 50% increase in volume and a 10 day half-life) the static plan for 125I overestimated the total dose by about 5%, whereas that for 103Pd overestimated it by about 12%.     

Monte Carlo dosimetry of the selectSeed 125I interstitial brachytherapy seed

This work provides full dosimetric data for the new selectSeed 125I prostate seed source to be distributed by Nucletron B.V. The AAPM TG-43 dosimetric formalism and the new 1999 NIST air kerma strength calibration standard have been followed. Air kerma strength, dose rate constant, radial dose functions, anisotropy functions, and anisotropy factors were calculated using Monte Carlo simulation. Corresponding calculations were also performed for the commercially available 6711 seed source, which is of similar design, for reasons of comparison. The calculated dose rate constant of the selectSeed was 0.954+/-0.005 cGy h(-1) U(-1) compared to 0.953+/-0.005 cGy h(-1) U(-1) for the 6711 source design. The latter value for the 6711 source suggests that the correction factor proposed by NIST for conversion of dose rate constants to the new 1999 NIST calibration standard may be overestimated by 2-3%. Radial dose functions of the two sources were found in good agreement for radial distances up to 4 cm, the selectSeed being less penetrating at greater radial distances (approximately 4% at 10 cm). The selectSeed source presents similar anisotropy characteristics with the 6711 source design. For both source designs, a distance and polar angle dependent discontinuity of anisotropy function values was observed owing to the dose contribution of radioactivity distributed on the ends of the cylindrical source cores. Variation of dosimetric parameters with possible variation in radioactive silver halide coating thickness of the silver source core of the new source was also investigated.     

Experimental determination of the TG-43 dosimetric characteristics of EchoSeed model 6733 I25I brachytherapy source

Recently an improved design of a 125I brachytherapy source has been introduced for interstitial seed implants, particularly for prostate seed implants. This design improves the in situ ultrasound visualization of the source compared to the conventional seed. In this project, the TG-43 recommended dosimetric characteristics of the new brachytherapy source have been experimentally determined in Solid Water phantom material. The measured dosimetric characteristics of the new source have been compared with data reported in the literature for other source designs. The measured dose rate constant, A, in Solid Water was multiplied by 1.05 to extract the dose rate constant in water. The dose rate constant of the new source in water was found to be 0.99 +/- 8% cGy h(-1) U(-1). The radial dose function was measured at distances between 0.5 and 10 cm using LiF TLDs in Solid Water phantom. The anisotropy function, F(r, theta), was measured at distances of 2, 3, 5, and 7 cm.     

Edema-induced increase in tumour cell survival for 125I and 103Pd prostate permanent seed implants--a bio-mathematical model

Edema caused by the surgical procedure of prostate seed implantation expands the source-to-point distances within the prostate and hence decreases the dose coverage. The decrease of dose coverage results in an increase in tumour cell survival. To investigate the effects of edema on tumour cell survival, a bio-mathematical model of edema and the corresponding cell killing by continuous low dose rate irradiation (CLDRI) was developed so that tumour cell surviving fractions can be estimated in an edematous prostate for both 125I and 103Pd seed implants. The dynamic nature of edema and its resolution were modelled with an exponential function V(T) = V(p)(1 + M exp(-0.693T/ T(e))) where V(p) is the prostate volume before implantation, M is the edema magnitude and T(e) is edema half-life (EHL). The dose rate of a radioactive seed was calculated according to AAPM TG43, i.e. D = SkAg(r)phi(an)/r2, where r is the distance between a seed and a given point. The distance r is now a function of time because of edema. The g(r) was approximated as 1/r(0,4) and 1/r(0.8) for 125I and 103Pd, respectively. By expanding the mathematical expression of the resultant dose rate in a Taylor series of exponential functions of time, the dose rate was made equivalent to that produced from multiple fictitious radionuclides of different decay constants and strengths. The biologically effective dose (BED) for an edematous prostate implant was then calculated using a generalized Dale equation. The cell surviving fraction was computed as exp(-alphaBED), where alpha is the linear coefficient of the survival curve. The tumour cell survival was calculated for both 125I and 103Pd seed implants and for different tumour potential doubling time (TPDT) (from 5 days to 30 days) and for edemas of different magnitudes (from 0% to 95%) and edema half-lives (from 4 days to 30 days). Tumour cell survival increased with the increase of edema magnitude and EHL. For a typical edema of a half-life of 10 days and a magnitude of 50%. the edema increased tumour cell survival by about 1 and 2 orders of magnitude for 125I and 103Pd seed implants respectively. At the extreme (95% edema magnitude and an edema half-life of 30 days), the increase was more than 3 and 5 orders of magnitude for 125I and I03Pd seed implants respectively. The absolute increases were almost independent of TPDT and the prostate edema did not significantly change the effective treatment time. Tumour cell survival for prostate undergoing CLDRI using 125I or 103Pd seeds may be increased substantially due to the presence of edema caused by surgical trauma. This effect appears to be more pronounced for 103Pd than 125I because of the shorter half-life of 103Pd. If significant edema is observed post implantation, then a boost to the prostate using external beam radiotherapy may be considered as a part of the treatment strategy.     

Mathematical solutions of the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus sources, and applications for quality assurance

Analytic solutions for the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus shapes containing uniform distributions of air-kerma are derived. These geometry functions describe how dose distributions vary strictly due to source geometry and not including attenuation or scatter effects. This work extends the use of geometry functions for individual sources to applicators containing multiple sources. Such geometry functions may be used to verify dose distributions computed using advanced techniques, including QA of model-based dose calculation algorithms. The impact of source curvature on linear and planar implants is considered along with the specific clinical case of brachytherapy eye plaques. For eye plaques, the geometry function for a domed distribution is used with published Monte Carlo dose distributions to determine a radial dose function and anisotropy function which includes all the scatter and attenuation effects due to the phantom, eye plaque and sources. This TG-43 model of brachytherapy eye plaques exactly reproduces azimuthally averaged Monte Carlo calculations, both inside and outside the eye.     

Thermoluminescent dosimetry of the SourceTech Medical model STM1251 125I seed

Many new models of 125I seeds are being introduced, mainly due to the increase in prostate seed implants. We have evaluated the SourceTech Medical (STM), model STM1251, 125I seed using thermoluminescent dosimeters (TLDs) in a solid water phantom. TLD cubes, LiF TLD-100, with dimension 1 mm on each edge, were irradiated at various distances, 1, 2, 3, and 5 cm, at angles ranging from 0 degrees to 90 degrees in 10 degrees increments. Sensitivity calibration of the TLDs was achieved by irradiation to 10 cGy with 6 MV x rays from a clinical linear accelerator, Clinac 600C. Concurrent with the 125I seed exposures, several TLDs were also exposed to 10 cGy with the 600C as a control set. Dose rates per unit air kerma strength were determined based on the 1999 NIST traceable standard for the STM1251 seed. They are presented as a function of distance r and angle theta. The TG-43 parameters, including the dose rate constant, lambda, anisotropy function, F(r,theta), radial dose function, g(r), anisotropy factor, phian(r), and anisotropy constant, phi, were obtained for use in radiation treatment planning software. The value of lambda was determined as 1.07 +/- 5.5% cGy U(-1) h(-1), which is comparable to model 6702 and to the value determined using the point extrapolation method by Kirov and Williamson. We also find agreement between our TLD data and their Monte Carlo results for g(r), F(r,theta), phian(r), and phi. Additionally, agreement is found with the TLD data of Li and Williamson for lambda and g(r).