Dosimetric validation of intensity-modulated bolus electron conformal therapy planning and delivery using an anthropomorphic cylindrical head phantom

PURPOSE

This work investigated the dosimetric accuracy of the intensity-modulated bolus electron conformal therapy (IM-BECT) planning and delivery process using the decimal ElectronRT (eRT) treatment planning system.

METHODS

An IM-BECT treatment plan was designed using eRT for a cylindrical, anthropomorphic retromolar trigone phantom. Treatment planning involved specification of beam parameters and design of a variable thickness wax bolus and Passive Radiotherapy Intensity Modulator for Electrons (PRIME) device, which was comprised of 33 tungsten island blocks of discrete diameters from 0.158 to 0.223 cm (Intensity Reduction Factors from 0.937 to 0.875, respectively) inside a 10.1 × 6.7 cm2 copper cutout. For comparison of calculation accuracy, a BECT plan was generated by copying the IM-BECT plan and removing the intensity modulation. For both plans, a 16 MeV electron beam was used with 104.7 cm source-to-surface distance to bolus. In-phantom TLD-100 measurements (N = 47) were compared with both eRT planned dose distributions, which used the pencil beam redefinition algorithm with modifications for passive electron intensity modulation (IM-PBRA). Dose difference and distance to agreement (DTA) metrics were computed for each measurement point.

RESULTS

Comparison of measured dose distributions with planned dose distributions yielded dose differences (calculated minus measured) characterized by a mean and standard deviation of -0.36% ± 1.64% for the IM-BECT plan, which was similar to -0.36% ± 1.90% for the BECT plan. All dose measurements were within 5% of the planned dose distribution, with both the BECT and IM-BECT measurement sets having 46/47 (97.8%) points within 3% or within 3 mm of the respective treatment plans.

CONCLUSIONS

It was found that the IM-BECT treatment plan generated using eRT was sufficiently accurate for clinical use when compared to TLD measurements in a cylindrical, anthropomorphic phantom, and was similarly accurate to the BECT treatment plan in the same phantom.

Technical note: Commissioning of a low-cost system for directly 3D printed flexible bolus

PURPOSE

To present the commissioning process of a low-cost solution for directly 3D printed flexible patient specific bolus.

METHODS

The 3D printing solution used in this study consisted of a resin stereolithography 3D printer and a flexible curing resin. To test the dimensional accuracy of the 3D printer, rectangular cuboids with varying dimensions were 3D printed and their measured dimensions were compared to the designed dimensions. Percent Depth Dose (PDD) profiles were measured by irradiating film embedded in a 3D printed phantom made of the flexible material. A CT of the phantom was acquired and used to replicate the irradiation setup in the treatment planning system. PDDs were calculated for both the native HU of the phantom, and with the phantom HU overridden to 300 HU to match its physical density. Dosimetric agreement was characterized by comparing calculated to measured depths of R90, R80, and R50. Upon completion of the commissioning process, a bolus was 3D printed for a clinical case study for treatment of the nose.

RESULTS

Dimensional accuracy of the printer and material combination was found to be good, with all measured dimensions of test cuboids within 0.5 mm of designed. PDD measurements demonstrated the best dosimetric agreement when the material was overridden to 300 HU, corresponding to the measured physical density of the material of 1.18 g/cc. Calculated and measured depths of R90, R80, and R50 all agreed within 1 mm. The bolus printed for the clinical case was free from defects, highly conformal, and led to a clinically acceptable plan.

CONCLUSION

The results of the commissioning measurements performed indicate that the 3D printer and material solution are suitable for clinical use. The 3D printer and material combination can provide a low-cost solution a clinic can implement in-house to directly 3D print flexible bolus.

Risk factors for recurrence after keloid surgery with electron radiotherapy

The aim of this study was to investigate the effect of postoperative electron radiotherapy (RT) on local control for keloids and to identify risk factors for recurrence. The clinical data of 82 patients treated at our institution from January 2015 to October 2019 were collected. The data included the general condition of the patients, clinical characteristics of the keloids, treatment plan, local control, and treatment side effects. A total of 82 patients (129 keloids) were included. The study included 23 men (28%) and 59 females (72%). The median patient age was 32 years (range, 18-67 years). Twenty-six recurrences were observed, and the 1-, 3-, and 5-year local control rates were 93%, 81%, and 73%, respectively. Univariate analysis revealed that age (P = .03), hypertension (P = .04), scar shape (P < .001), primary site (P = .02), maximum lesion diameter (P < .001), pain and itching (P = .005), local tension (P = .005), and infection (P < .001) were risk factors for local recurrence. Multivariable analysis revealed that maximum lesion diameter (P < .001), infection (P < .001), interval between surgery and RT (P = .02), and previous treatment (P = .02) were independent risk factors. Complete excision of keloids combined with electron RT is safe and seemingly effective. For keloids with a high risk of recurrence, more aggressive treatment should be chosen, and further prospective studies are needed to explore the optimal treatment.

Effects of surface curvature on electron Monte Carlo (eMC) calculation results

Some clinical situations in radiotherapy require electron beams to be incident on curved patient surfaces. This study presents central-axis dose output (cGy/MU) and percent dose versus depth (PDD) data that show the effects of curvature on results computed by the Varian eMC v15.6 algorithm using 6, 9, 12, 16, and 20 MeV electron beams incident on virtual phantoms with curved surfaces. The phantoms were designed to simulate common treatment sites. The dose outputs at the depth of maximum dose (dmax) on the central axis were observed to decrease 0%-14%, and several features of the PDDs for the A10 applicator changed, including up to 12% increased entrance dose. These dosimetric changes have the greatest effect on treatment sites with a radius of curvature of 10 cm or less, such as the scalp, nose, neck, and extremities. The concept of applying a curvature correction factor based on relative output data is presented to help clinical users mitigate discrepancies between calculations performed by simple monitor unit verification systems and accurate treatment planning dose algorithms.

Auto-commissioning of a Monte Carlo electron beam model with application to photon MLC shaped electron fields

Objective.Presently electron beam treatments are delivered using dedicated applicators. An alternative is the usage of the already installed photon multileaf collimator (pMLC) enabling efficient electron treatments. Currently, the commissioning of beam models is a manual and time-consuming process. In this work an auto-commissioning procedure for the Monte Carlo (MC) beam model part representing the beam above the pMLC is developed for TrueBeam systems with electron energies from 6 to 22 MeV.Approach.The analytical part of the electron beam model includes a main source representing the primary beam and a jaw source representing the head scatter contribution each consisting of an electron and a photon component, while MC radiation transport is performed for the pMLC. The auto-commissioning of this analytical part relies on information pre-determined from MC simulations, in-air dose profiles and absolute dose measurements in water for different field sizes and source to surface distances (SSDs). For validation calculated and measured dose distributions in water were compared for different field sizes, SSDs and beam energies for eight TrueBeam systems. Furthermore, a sternum case in an anthropomorphic phantom was considered and calculated and measured dose distributions were compared at different SSDs.Main results.Instead of the manual commissioning taking up to several days of calculation time and several hours of user time, the auto-commissioning is carried out in a few minutes. Measured and calculated dose distributions agree generally within 3% of maximum dose or 2 mm. The gamma passing rates for the sternum case ranged from 96% to 99% (3% (global)/2 mm criteria, 10% threshold).Significance.The auto-commissioning procedure was successfully implemented and applied to eight TrueBeam systems. The newly developed user-friendly auto-commissioning procedure allows an efficient commissioning of an MC electron beam model and eases the usage of advanced electron radiotherapy utilizing the pMLC for beam shaping.

Flexible real-time skin dosimeter based on a thin-film copper indium gallium selenide solar cell for electron radiation therapy

PURPOSE

Various dosimeters have been proposed for skin dosimetry in electron radiotherapy. However, one main drawback of these skin dosimeters is their lack of flexibility, which could make accurate dose measurements challenging due to air gaps between a curved patient surface and dosimeter. Therefore, the purpose of this study is to suggest a novel flexible skin dosimeter based on a thin-film copper indium gallium selenide (CIGS) solar cell, and to evaluate its dosimetric characteristics.

METHODS

The CIGS solar cell dosimeter consisted of (a) a customized thin-film CIGS solar cell and (b) a data acquisition (DAQ) system. The CIGS solar cell with a thickness of 0.33 mm was customized to a size of 10 × 10 mm² . This customized solar cell plays a role in converting therapeutic electron radiation into electrical signals. The DAQ system was composed of a voltage amplifier with a gain of 1000, a voltage input module, a DAQ chassis, and an in-house software. This system converted the electrical analog signals (from solar cell) to digital signals with a sampling rate of ≤50 kHz and then quantified/visualized the digital signals in real time. We quantified the linearity/ sampling rate effect/dose rate dependence/energy dependence/field size output factor/reproducibility/curvature/bending recoverability/angular dependence of the CIGS solar cell dosimeter in therapeutic electron beams. To evaluate clinical feasibility, we measured the skin point doses by attaching the CIGS solar cell to an anthropomorphic phantom surface (for forehead, mouth, and thorax). The CIGS-measured doses were compared with calculated doses (by treatment planning system) and measured doses (by optically stimulated luminescent dosimeter).

RESULTS

The normalized signals of the solar cell dosimeter increased linearly as the delivered dose increased. The gradient of the linearly fitted line was 1.00 with an R-square of 0.9999. The sampling rates (2, 10, and 50 kHz) of the solar cell dosimeter showed good performance even at low doses (<50 cGy). The solar cell dosimeter exhibited dose rate independence within 1% and energy independence within 3% error margins. The signals of the solar cell dosimeter were similar (<1%) when penetrating the same side of the CIGS cell regardless of the rotation angle of the solar cell. The field size output factor measured by the solar cell dosimeter was comparable to that measured by the ion chamber. The solar cell signals were similar between the baseline (week 1) and the last time point (week 4). Our detector showed curvature independence within 1.8% (curvatures of <0.10 mm^- ) and bending recovery (curvature of 0.10 mm^-1 ). The differences between measured doses (CIGS solar cell dosimeter vs. optically stimulated luminescent dosimeter) were 7.1%, 9.6%, and 1.0% for forehead, mouth, and thorax, respectively.

CONCLUSION

We present the construction of a flexible skin dosimeter based on a CIGS solar cell. Our findings demonstrate that the CIGS solar cell has a potential to be a novel flexible skin dosimeter for electron radiotherapy. Moreover, this dosimeter is manufactured with low cost and can be easily customized to various size/shape, which represents advantages over other dosimeters.

Delivery of intensity-modulated electron therapy by mechanical scanning: An algorithm study

Purpose

In principle, intensity-modulated electron therapy (IMET) can be delivered through mechanical scanning, with a robotic arm mounting a linac.

Materials and methods

Here is a scanning algorithm to identify the back-and-forth, top-to-bottom (zigzag) pattern scan sequence. The algorithm includes generating beam positions with a uniform resolution according to the applicator size; adopting discrete energies to achieve the depth of 90% dose by compositing energies; selecting energy by locating the target's distal edge; and employing the energy-by-energy scan strategy for step-and-shoot discrete scanning. After a zigzag scan sequence is obtained, the delivery order of the scan spots is optimized by fast simulated annealing (FSA) to minimize the path length. For algorithm evaluation, scan sequences were generated using the computed tomography data of 10 patients with pancreatic cancer undergoing intraoperative radiotherapy, and the results were compared between the zigzag path and an optimized path. A simple calculation of the treatment delivery time, which comprises the irradiation time, the total robotic arm moving time, the time for energy switch, and the time to stop and restart the beam, was also made.

Results

In these clinical cases, FSA optimization shortened the path lengths by 12%-43%. Assuming the prescribed dose was 15 Gy, machine dose rate was 15 Gy/s, energy switch time was 2 s, stop and restart beam time was 20 ms, and robotic arm move speed was 50 mm/s, the average delivery time was 124±38 s. The largest reduction in path length yielded an approximately 10% reduction in the delivery time, which can be further reduced by increasing the machine dose rate and the robotic arm speed, decreasing the time for energy switch, and/or developing more efficient algorithms.

Conclusion

Mechanically scanning IMET is potentially feasible and worthy of further exploration.

[Effect of Differences in Insert Materials of Cutout Block on Dose Distribution in Electron Radiotherapy: Comparison between Measurements and Monte Carlo Simulation]

INTRODUCTION

In electron beam radiotherapy, an irradiation field is created with a cutout block using a low melting point lead alloy. The block can be replaced with a lead plate as a shield. Dose distribution is expected to be affected by differences in the material and thickness of the shield. Thus, this study aimed to investigate the cause of differences in dose distribution by reproducing the electron beam irradiation condition via Monte Carlo simulation, comparing dose distribution when each shield is used and analyzing energy fluence distribution.

MATERIALS AND METHODS

Radiation interaction in the treatment device manufactured by Varian was assessed using the general-purpose simulation code, and the dose distribution in the water was calculated. Electron energy fluence and incident angle of the electron fluence incident on the water surface were analyzed, and the effect of the difference in the shield was investigated in the irradiation field limited to 3 cm or less.

RESULTS

Regarding dose distribution, the deviation in the buildup area became larger when the lead plate was made thinner. A difference of 1.6-6.8% was observed on an average when comparing the buildup region of depth dose distributions except for 1×1 cm² field. In electron energy fluence, the lower the lead thickness, the higher the low energy component, which affected the buildup region. The effect was greater as the electron beam energy increased.

CONCLUSION

It was possible to evaluate the difference in scattered radiation between the low melting point lead alloy and the lead plate by MC simulation. Based on the study findings, the effect of scattered electrons generated from the block was strong as a factor.

A novel real-time shapeable soft rubber bolus for clinical use in electron radiotherapy

We have developed soft rubber (SR) bolus that can be shaped in real-time by heating flexibly and repeatedly. This study investigated whether the SR bolus could be used as an ideal bolus, such as not changing of the beam characteristics and homogeneity through the bolus and high plasticity to adhere a patient in addition to real-time shapeable and reusability, in electron radiotherapy. Percentage depth doses (PDDs) and lateral dose profiles (LDPs) were obtained for 4, 6, and 9 MeV electron beams and were compared between the SR and conventional gel boluses. For the LDP at depth of 90% dose, the penumbra as lateral distance between the 80% and 20% isodose lines (P_80-20) and the width of 90% dose level (r₉₀) were compared. To evaluate adhesion, the air gap volume between the boluses and nose of a head phantom was evaluated on CT image. The dose profiles along the center axis for the 6 MeV electron beam with SR, gel, and virtual boluses (thickness = 5 mm) on the head phantom were also calculated for the irradiation of 200 monitor unit with a treatment planning system and the depth of the maximum dose (d_max) and maximum dose (D_max) were compared. The PDDs,P_80-20, andr₉₀between the SR and gel boluses corresponded well (within 2%, 0.4 mm, and 0.7 mm, respectively). The air gap volumes of the SR and gel boluses were 3.14 and 50.35 cm³, respectively. Thed_maxwith SR, gel and virtual boluses were 8.0, 6.0, and 7.0 mm (no bolus: 12.0 mm), and theD_maxvalues were 186.4, 170.6, and 186.8 cGy, respectively. The SR bolus had the equivalent electron beam characteristics and homogeneity to the gel bolus and achieved excellent adhesion to a body surface, which can be used in electron radiotherapy as an ideal bolus.

Dosimetric evaluation of skin collimation with tungsten rubber for electron radiotherapy: A Monte Carlo study

PURPOSE

Skin collimation provides a sharp penumbra for electron beams, while the effect of bremsstrahlung from shielding materials is a concern. This phantom study was conducted to evaluate the safety and efficacy of a real-time variable shape rubber containing-tungsten (STR) that can be placed on a patient's skin.

METHODS

Electron beam profiles were acquired with the STR placed on a water-equivalent phantom and low melting-point alloy (LMA) placed at the applicator according to commonly used procedures (field sizes: 20- and 40-mm diameters). Depth and lateral dose profiles for 6- and 12-MeV electron beams were obtained by Monte Carlo (MC) simulations and were benchmarked against film measurements. The width of the off-axis distance between 80% and 20% doses (P80-20 ) and the maximum dose were obtained from the lateral dose profiles. Bremsstrahlung emission was analyzed by MC simulations at the depth of maximum dose (R100 ).

RESULTS

The depth dose profiles calculated by the MC simulations were consistently within 2% of the measurements. The P80-20 at R100 for 20- and 40-mm diameters were 4.0 mm vs. 7.6 mm (STR vs. LMA) and 4.5 mm vs. 9.2 mm, respectively, for the 6-MeV electron beam with 7.0-mm-thick STR, and 2.7 mm vs. 5.6 mm and 4.5 mm vs. 7.1 mm, respectively, for the 12-MeV electron beam with 12.0-mm-thick STR. A hotspot was not observed on the lateral dose profiles obtained with the STR at R100 . The bremsstrahlung emission under the region shielded by the STR was comparable to that obtained with the LMA, even though the STR was placed on the surface of the phantom.

CONCLUSIONS

Skin collimator with STR provided superior dosimetric characteristics and comparable bremsstrahlung emission to LMA collimator at the applicator. STR could be a new tool for the safe and efficient delivery of electron radiotherapy.

First Clinical Experience of Tungsten Rubber Electron Adaptive Therapy With Real-time Variable-shape Tungsten Rubber

BACKGROUND/AIM

We investigated the dosimetric characteristics of electron radiotherapy for auricular keloid using real-time variable-shape tungsten rubber (STR).

PATIENTS AND METHODS

For the first evaluation, STR was shaped into a rectangular irradiation field (3.0×5.0 cm²). In the next step, the STR was reshaped to fit the target (3.5×6.5 cm²) for the second evaluation. Percentage depth doses (PDDs) and lateral dose profiles were obtained with 6-MeV electron beams and compared with those of low-melting-point lead (LML).

RESULTS

Compared to the LML on electron applicator, PDD differences were within 0.4 mm, while the penumbras as width of 20-80% dose levels were smaller (maximum reductions: 75.8% and 82.9% at first and second evaluations, respectively). The treatment process of shaping the STR, decision on output, and irradiation was completed within 45 min.

CONCLUSION

Electron radiotherapy using STR for keloid can be performed with excellent dose distribution in a short time. First clinical experience found the STR is suitable for use in individualized and immediate electron radiotherapy.

Validation of a Monte Carlo model for multi leaf collimator based electron delivery

PURPOSE

To develop and validate a Monte Carlo model of the Varian TrueBeam to study electron collimation using the existing photon multi-leaf collimators (pMLC), instead of conventional electron applicators and apertures.

MATERIALS AND METHODS

A complete Monte Carlo model of the Varian TrueBeam was developed using Tool for particle simulation (TOPAS) (version 3.1.p3). Vendor-supplied information was used to model the treatment head components and the source parameters. A phase space plane was setup above the collimating jaws and captured particles were reused until a statistical uncertainty of 1% was achieved in the central axis. Electron energies 6, 9, 12, 16, and 20 MeV with a jaw-defined field of 20 × 20 cm² at iso-center, pMLC-defined fields of 6.8 × 6.8 cm² and 11.4 × 11.4 cm² at 80 cm source-to-surface distance (SSD) and an applicator-defined field of 10 × 10 cm² at iso-center were evaluated. All the measurements except the applicator-defined fields were measured using an ionization chamber in a water tank using 80 cm SSD. The dose difference, distance-to-agreement and gamma index were used to evaluate the agreement between the Monte Carlo calculations and measurements. Contributions of electron scattering off pMLC leaves and inter-leaf leakage on dose profiles were evaluated and compared with Monte Carlo calculations. Electron transport through a heterogeneous phantom was simulated and the resulting dose distributions were compared with film measurements. The validated Monte Carlo model was used to simulate several clinically motivated cases to demonstrate the benefit of pMLC-based electron delivery compared to applicator-based electron delivery.

RESULTS

Calculated and measured percentage depth-dose (PDD) curves agree within 2% after normalization. The agreement between normalized percentage depth dose curves were evaluated using one-dimensional gamma analysis with a local tolerance of 2%/1 mm and the %points passing gamma criteria was 100% for all energies. For jaw-defined fields, calculated profiles agree with measurements with pass rates of >97% for 2%/2 mm gamma criteria. Calculated FWHM and penumbra width agree with measurements within 0.4 cm. For fields with tertiary collimation using an pMLC or applicator, the average gamma pass rate of compared profiles was 98% with 2%/2 mm gamma criteria. The profiles measured to evaluate the pMLC leaf scattering agreed with Monte Carlo calculations with an average gamma pass rate of 96.5% with 3%/2 mm gamma criteria. Measured dose profiles below the heterogenous phantom agreed well with calculated profiles and matched within 2.5% for most points. The calculated clinically applicable cases using TOPAS MC and Eclipse TPS for single enface electron beam, electron-photon mixed beam and a matched electron-electron beam exhibited a reasonable agreement in PDDs, profiles and dose volume histograms.

CONCLUSION

We present a validation of a Monte Carlo model of Varian TrueBeam for pMLC-based electron delivery. Monte Carlo calculations agreed with measurements satisfying gamma criterion of 1%/1 mm for depth dose curves and 2%/1 mm for dose profiles. The simulation of clinically applicable cases demonstrated the clinical utility of pMLC-based electrons and the use of MC simulations for development of advanced radiation therapy techniques.

[Dose Distribution Combinations of Different Electron Beam Energy for Treatment Region Expansion in High-energy Electron Beam Radiation Therapy: A Feasibility Study]

INTRODUCTION

External electron beams have excellent distributions in treatment for superficial tumors while suppressing influence deeper normal tissue. However, the skin surface cannot be given a sufficient dose due to the build-up effect. In this study, we have investigated the combination of electron beams to expand the treatment region by keeping the dose gradient beyond d_max.

MATERIALS AND METHODS

The percentage depth doses of different electron beams were superimposed on a spreadsheet to determine the combinations of electron beams so that the treatment range was maximized. Based on the obtained weight for electron beams, dose distributions were calculated using a treatment planning system and examined for potential clinical application.

RESULTS

With the combination of 4 MeV and 9 MeV electron beams, the 90% treatment range in the depth direction increased by 8.0 mm, and with 4 MeV and 12 MeV beams, it increased by 4.0 mm, with the same maximum dose depth and halfdose depth of the absorbed dose. The dose calculations were performed using the treatment planning system yielded similar results with a matching degree of ±1.5%.

CONCLUSIONS

Although the influences of low monitor unit values and daily output differences remain to be considered, the results suggest that the proposed approach can be clinically applied to expand treatment regions easily.

Estimation of Backscatter from Internal Shielding in Electron Beam Radiotherapy Using Monte Carlo Simulations (EGSnrc) and Gafchromic Film Measurements

Purpose:

The purpose of the study was to estimate the backscatter electron dose in internal shielding during electron beam therapy using Monte Carlo (MC) simulations and Gafchromic film measurements.

Materials and Methods:

About 6 and 9 MeV electron beams from a Varian 2100C linac were simulated using BEAMnrc MC code. Various clinical situations of internal shielding were simulated by modeling water phantoms with 2 mm lead sheets placed at different depths. Electron backscatter factors (EBF), a ratio of dose at tissue-shielding interface to the dose at the same point without the shielding, were estimated. The role of 2 mm aluminum in reduction of backscatter was investigated. The measurements were also performed using Gafchromic films and results were compared with MC simulations.

Results:

For particular beam energy, the EBF value initially increased with depth in the buildup region and then decreased rapidly. The highest value of EBF for both the energies is nearly same though at different depths. Decreased EBF was observed for 9 MeV beam in comparison to the 6 MeV beam for the same depth of shielding placement. Two millimeter aluminum reduced the backscatter by nearly 25% at maximum backscatter condition for both the energies, though the effectiveness slightly decreased at higher energy. The range of backscatter electrons was varying from 5 to 12 mm in the upstream direction from the interface. The Gafchromic film-measured EBF and MC-simulated EBF were matching well within the clinically acceptable limits except in close vicinity of tissue-lead interface.

Conclusions:

This study provides an important clinical data to design internal shielding at the local clinical setup and confirms applicability of MC simulations in backscatter dose calculations at interfaces where physical measurements are difficult to perform.

Cutaneous metastasis of prostate carcinoma treated with electron radiotherapy

Introduction

Prostate carcinoma is typically diagnosed and treated, and it rarely manifests as cutaneous metastases. We herein report electron radiotherapy for the treatment of cutaneous metastases causing cellulitis, with a durable clinical response achieved.

Case presentation

A 70-year-old male patient with scrotal cutaneous metastasis of prostate carcinoma was undergoing treatment with docetaxel chemotherapy due to recurring cellulitis originating from the scrotum, and his treatment was interrupted. We administered electron radiotherapy to the scrotal cutaneous metastasis lesions, as irradiation was difficult, and obtained a good clinical effect. Subsequently, he continued chemotherapy, and the scrotal lesions remained clear and dry with no recurring cellulitis for 1 year.

Conclusion

Electron radiotherapy is one of the safe and effective treatment options for controlling cutaneous metastasis of prostate carcinoma.