A Monte Carlo approach to patient-specific dosimetry

In internal emitter therapy, an accurate description of the absorbed dose distribution is necessary to establish an administered dose-response relationship, as well as to avoid critical organ toxicity. Given a spatial distribution of cumulated activity, an absorbed dose distribution that accounts for the effects of attenuation and scatter can be obtained using a Monte Carlo method that simulates particle transport across the various densities and atomic numbers encountered in the human body. Patient-specific information can be obtained from CT and SPECT or PET imaging. Since the data from these imaging modalities is discrete, it is necessary to develop a technique to efficiently transport particles across discrete media. The Monte Carlo-based algorithm presented in this article produces accurate absorbed dose distributions due to patient-specific density and radionuclide activity distributions. The method was verified by creating CT and SPECT arrays for the Medical Internal Radionuclide Dose (MIRD) Committee's Standard Man phantom, and reproducing the spatially averaged specific absorbed fractions reported in MIRD Pamphlet 5. The algorithm was used to investigate the implications of replacing a mean absorbed dose with a distribution, and of neglecting atomic number and density variations for various patient geometries and energies. For example, the I-131 specific absorbed fraction for spleen to liver is the same as for liver to spleen, yet the distributions were different. Furthermore, neglecting atomic number variations across the vertebral bone led to an overestimation of I-125 absorbed dose by an order of magnitude, while no error was observed for I-131.

Conformal radiation treatment of prostate cancer using inversely-planned intensity-modulated photon beams produced with dynamic multileaf collimation

PURPOSE

To implement radiotherapy with intensity-modulated beams, based on the inverse method of treatment design and using a multileaf collimation system operating in the dynamic mode.

METHODS AND MATERIALS

An algorithm, based on the inverse technique, has been integrated into the radiotherapy treatment-planning computer system in our Center. This method of computer-assisted treatment design was used to derive intensity-modulated beams to optimize the boost portion of the treatment plan for a patient with a T1c cancer of the prostate. A dose of 72 Gy (in 40 fractions) was given with a six-field plan, and an additional 9 Gy (in five fractions) with six intensity-modulated beams. The intensity-modulated fields were delivered using dynamic multileaf collimation, that is, individual leaves were in motion during radiation delivery, with the treatment machine operating in the clinical mode. Exhaustive quality assurance measurement and monitoring were carried out to ensure safe and accurate implementation.

RESULTS

Dose distribution and dose-volume histogram of the "inverse method" boost plan and of the composite (72 Gy primary + 9 Gy boost) plan were judged clinically acceptable. Compared to a manually designed boost plan, the inverse treatment design gave improved conformality and increased dose homogeneity in the planning target volume. Film and ion chamber dosimetry, performed prior to the first treatment, indicated that each of the six intensity-modulated fields was accurately produced. Thermoluminescent dosimeter (TLD) measurements performed on the patient confirmed that the intended dose was delivered in the treatment. In addition, computer-aided treatment-monitoring programs assured that the multileaf collimator (MLC) position file was executed to the specified precision. In terms of the overall radiation treatment process, there will likely be labor savings in the planning and the treatment phases.

CONCLUSIONS

We have placed into clinical use an integrated system of conformal radiation treatment that incorporated the inverse method of treatment design and the use of dynamic multileaf collimation to deliver intensity-modulated beams. The system can provide better treatment design, which can be implemented reliably and safely. We are hopeful that improved treatment efficacy will result.

Radionuclide photon dose kernels for internal emitter dosimetry

Photon point dose kernels and absorbed fractions were generated in water for the full photon emission spectrum of each radionuclide of interest in nuclear medicine, by simulating the transport of particles using Monte Carlo. The kernels were then fitted to a mathematical expression. Absorbed fractions for point sources were obtained by integrating the kernels over spheres. Photon dose kernels and absorbed fractions were generated for the following radionuclides: I-123, I-124, I-125, I-131, In-111, Cu-64, Cu-67, Ga-67, Ga-68, Re-186, Re-188, Sm-153, Sn-117m, Tc-99m. The Monte Carlo simulation was verified by comparing the dose kernels to published monoenergetic photon kernels. Further validation was obtained by generating an I-125 brachytherapy seed kernel and comparing it with published data. Since Monte Carlo simulation was initialized by sampling from the complete photon spectra of these radionuclides, interpolation between monoenergetic kernels and absorbed fractions was not required. The absorbed-fraction due to uniform spherical distributions can be directly applied for use in internal dosimetry. In addition, the kernels can be used as input for three-dimensional internal dosimetry calculations.

Testing of dynamic multileaf collimation

It has been shown that intensity-modulated fields have the potential to deliver optimum dose distributions, i.e., high dose uniformity in the target and lower doses in the surrounding critical organs. One way to deliver such fields is by using dynamic multileaf collimation (DMLC). This capability is already available in research mode on some treatment machines. While much effort has been devoted to developing algorithms for DMLC, the mechanical reliability of this new treatment delivery mode has not been fully studied. In this work, we report a series of tests designed to investigate the mechanical aspects of DMLC and their implications on dosimetry. Specifically, these tests were designed to examine (1) the stability of leaf speed, (2) the effect of lateral disequilibrium on dose profiles between adjacent leaves, (3) the significance of acceleration and deceleration of leaf motion, (4) the effect of positional accuracy and rounded-end of the leaves, and (5) create a simple test pattern that may serve as a basis for routine quality assurance checks. Results of these tests are presented. The implications on dosimetry and consideration for the design of leaf motion are discussed.

Dosimetric verification of intensity-modulated fields

The optimization of intensity distributions and the delivery of intensity-modulated treatments with dynamic multi-leaf collimators (MLC) offer important improvements to three-dimensional conformal radiotherapy. In this study, a nine-beam intensity-modulated prostate plan was generated using the inverse radiotherapy technique. The resulting fluence profiles were converted into dynamic MLC leaf motions as functions of monitor units. The leaf motion pattern data were then transferred to the MLC control computer and were used to guide the motions of the leaves during irradiation. To verify that the dose distribution predicted by the optimization and planning systems was actually delivered, a homogeneous polystyrene phantom was irradiated with each of the nine intensity-modulated beams incident normally on the phantom. For each exposure, a radiographic film was placed normal to the beam in the phantom to record the deposited dose. The films were calibrated and scanned to generate 2-D isodose distributions. The dose was also calculated by convolving the incident fluence pattern with pencil beams. The measured and calculated dose distributions were compared and found to have discrepancies in excess of 5% of the central axis dose. The source of discrepancies was suspected to be the rounded edges of the leaves and the scattered radiation from the various components of the collimation system. After approximate corrections were made for these effects, the agreement between the two dose distributions was within 2%. We also studied the impact of the "tongue-and-groove" effect on dynamic MLC treatments and showed that it is possible to render this effect inconsequential by appropriately synchronizing leaf motions. This study also demonstrated that accurate and rapid delivery of realistic intensity-modulated plans is feasible using a dynamic multi-leaf collimator.

Generation of arbitrary intensity profiles by combining the scanning beam with dynamic multileaf collimation

An algorithm, which combines the scanning beam with dynamic collimation to generate any arbitrary intensity profile, is presented. The desired intensity profile is assumed to be piecewise linear. The dynamic collimation method used is the "sliding window." The algorithm can be used either for a given scanning beam profile or to simultaneously determine the scanning beam profile and the leaf motions required to generate the desired intensity profile, which minimize the total treatment time. The limitations imposed by the physics of an elementary beam are taken into account. The algorithm is an iterative one, with typical calculation times being of the order of a few milliseconds.

A Monte Carlo model of photon beams used in radiation therapy

A generic Monte Carlo model of a photon therapy machine is described. The model, known as McRad, is based on EGS4 and has been in use since 1991. Its primary function has been the characterization of the incident photon fluence for use by dose calculation algorithms. The accuracy of McRad is examined by comparing the dose distributions in a water phantom generated using only the Monte Carlo data with measured dose distributions for two machines in our clinic; a 6 MV Varian Clinac 600C and the 15 MV beam from a Clinac 2100C. The Monte Carlo generated dose distributions are computed using a dose calculation algorithm based on the use of differential pencil beam kernels. It was found that the match to measured data could be improved if the model is tuned by adjusting the energy of the electron beam incident on the target. The beam profiles were found to be more sensitive indicators of the electron beam energy than the depth dose curves. Beyond the depths reached by contaminant electrons, the computed and measured depth dose curves agree to better than 1%. The comparison of beam profiles indicate that in regions up to within 1 cm of the field edge, the measured and computed doses generally agree to within 2%-3%.

Effect of ocular implants of different materials on the dosimetry of external beam radiation therapy

PURPOSE

To study the attenuation and scattering effects of ocular implants, made from different materials, on the dose distributions of a 6 MV photon beam, and 6, 9, and 12 MeV electron beams used in orbital radiotherapy.

METHODS AND MATERIALS

Central axis depth-dose measurements were performed in a polystyrene phantom with embedded spherical ocular implants using film dosimetry of a 6 MV photon beam and electron beams of 6, 9, and 12 MeV energy. The isodose distributions were also calculated by a computerized treatment planning system using computerized tomography (CT) scans of a polystyrene phantom that had silicone, acrylic, and hydroxyapatite ocular implants placed into it.

RESULTS

Electron beam dose distributions display distortions both on the measured and calculated data. This effect is most accentuated for the hydroxyapatite implants, for which the transmissions through ocular implants are on the order of 93% for the 6 MV photon beam, and range from 60% for 6 MeV electrons to 90% for 12 MeV electrons.

CONCLUSION

We studied the effect of ocular implants of various materials, embedded in a polystyrene phantom, on the dose distributions of a 6 MV photon beam, and 6, 9, and 12 MeV electron beams. Our investigations show that while 6 MV photons experience only a few percent attenuation, lower energy electron beam with 60% transmission is not a suitable choice of treating tumors behind the ocular implants.

Beam characteristics of a new generation 50 MeV racetrack microtron

The first of a new generation of microtron accelerators has been installed and tested. It is currently in use for multisegment conformal radiotherapy at our institution. The unit produces x rays and electrons from 10 to 50 MeV in 5 MeV increments. It incorporates a 64 leaf, doubly focused multileaf collimator (MLC), which can be used to shape x-ray and electron beams. Both x-ray and electron beams are produced by magnetically scanning the electron beams from the accelerator. The new generation unit incorporates a purging magnet to sweep away any primary or secondary electrons that pass through the target(s). In this paper, the beam characteristics of the accelerator that were studied during acceptance testing are described. Representative examples of depth doses, beam profiles, output factors, and elementary beam distributions are presented and discussed, in comparison with the earlier generation of microtron accelerators and with other radiotherapy machines.

Mean mass energy absorption coefficient ratios for megavoltage x-ray beams

Mean mass energy absorption coefficient ratios of acrylic, polystyrene, and water to air, were calculated using Monte Carlo generated energy spectra. The energy spectra were calculated for 4- to 50-MV x-ray beams, from machines using flattening filters and scanning beams. The validity of these spectra was verified by comparing the measured ionization ratios with the calculated values. The agreement was found to be within 1.9%. For beams of energy below 6 MV, our estimates of the mean mass energy absorption coefficient ratios agree well with those recommended by the TG-21 protocol. For higher energy beams, the discrepancy increases to about 3%. It was found that the discrepancy is attributable to the different spectra used in these calculations.

Analysis of the photon beam treatment planning data for a scanning beam machine

The characteristics of photon beams from the Scanditronix MM50 radiation therapy machine that are necessary for treatment planning are described. The MM50 uses a scanning beam instead of a conventional flattening filter to achieve flat dose distributions. At each beam energy, a scan pattern is chosen, depending on the field size; the small scan pattern (S) is used for field sizes up to 10 x 10 cm, the medium scan pattern (M) is used for field sizes up to 20 x 20 cm, and the large scan pattern (L) is used for the larger field sizes. The dose distributions of the beams associated with the 10 MV S, M, and L scan patterns, the 25 MV S, M, and L patterns, and the 50 MV S and M patterns are described. The data reported includes central axis data, beam profiles, and output factors. In addition to the measured data, our dose calculation model requires a pencil beam kernel for each beam. The kernel is constructed using the average photon energy spectrum, which is generated using a Monte Carlo simulation of the MM50. The simulation, based on EGS4, is also used to generate the radial variation of fluence and energy fluence, which is required by a new dose calculation model that does not require the measurement of beam profiles. The Monte Carlo generated data; the photon energy spectrum, the fluence, and the energy fluence are presented.

Initial clinical experience with computer-controlled conformal radiotherapy of the prostate using a 50-MeV medical microtron

PURPOSE

We have described previously a model for delivering computer-controlled radiation treatments. We report here on the implementation and first year's clinical experience with such treatments using a 50 MeV medical microtron.

METHODS AND MATERIALS

The microtron is equipped with a multileaf collimator and is capable of setting up and treating a sequence of fixed fields called segments, under computer control. An external computer derives machine parameters for the segments from a three-dimensional treatment planning system, transfers them to the microtron control computer, checks the machine settings before allowing dose delivery to begin, and records the treatment. We describe the patient treatment methodology, portal film acquisition, electronic portal imaging, and quality assurance.

RESULTS

Patient treatments began in July 1992, comprising six-segment conformal treatments of the prostate. Using the recorded treatment data, the system performance has been examined and compared to other treatment machines. The average treatment time is 10 min, of which 4 min is for computer-controlled setup and irradiation; the remaining time is for patient positioning and checking of clearances. Long-term reproducibility of computer-controlled setup of the gantry and multileaf position is better than 0.5 degrees and 1 mm, respectively. Termination due to a machine fault has occurred in 5.5% of treatments, improving to 2.5% in recent months.

CONCLUSION

Our initial experience indicates that computer-controlled segmental therapy can be performed reliably on a routine basis. Treatment times with the microtron are significantly shorter than with conventional linacs, and setup accuracy is consistent with that needed for conformal therapy. We believe that treatment times can be further improved through software upgrades and integration of electronic portal imaging.

Beam profiles along the nonwedged direction for large wedged fields

Beam profiles along the nonwedged direction of a wedged field produced by a linear accelerator exhibit more "sagging" than that of an open field at the same depth. For large fields, the profiles of open and wedged fields can differ by as much as 7%. The extra "sagging" of wedged profiles is mainly due to the difference in penetration between on- and off-axis rays caused by the variation of beam quality across the field. An algorithm was developed to estimate an "effective" depth such that the profile of a wedged field can be approximated by the open-field profile at the effective depth. The algorithm was verified by measured beam profiles for 6- and 15-MV x-ray beams for 15 degree, 30 degree, 45 degree, and 60 degree wedges.

Dose calculation for photon beams with intensity modulation generated by dynamic jaw or multileaf collimations

A dose calculation algorithm has been developed for photon beams with intensity modulation generated by dynamic jaw or multileaf collimations. First, an in-air fluence distribution is constructed based on the dynamic motion of the jaws or leaves, taking into account the variation of output with field size defined by the jaws. The fluence distribution is then convolved with the appropriate pencil beam kernel to give correction factors which are used to calculate the dose distribution for an intensity-modulated photon field. The proposed algorithm is strictly valid in homogeneous media only, patient heterogeneity correction is accounted for in an approximate manner. Dose distributions at several depths and for several field sizes were calculated for 6- and 15-MV x-ray beams for a set of standard wedges produced by dynamic jaws. Measurements were made with film and an ion chamber. Comparisons between calculated and measured data show good agreement (within 2%) for both dose profiles and wedge factors. Similar calculations and measurements were also made for a 25-MV intensity-modulated photon field produced by dynamic motion of a multileaf collimator. Agreement between calculations and measurements is also good (within 3%). The "tongue-and-groove" effect associated with a multileaf collimator design is also examined using a ring-shaped field produced by matching two component fields. The computation time for a dynamic-collimated field is the same as that for an irregular field shaped by conventional blocks. The algorithm is applicable to any pattern of jaw or multileaf motions. The strengths and remaining problems of the algorithm are discussed.

Generation of arbitrary intensity profiles by dynamic jaws or multileaf collimators

An algorithm, which calculates the motions of the collimator jaws required to generate a given arbitrary intensity profile, is presented. The intensity profile is assumed to be piecewise linear, i.e., to consist of segments of straight lines. The jaws move unidirectionally and continuously with variable speed during radiation delivery. During each segment, at least one of the jaws is set to move at the maximum permissible speed. The algorithm is equally applicable for multileaf collimators (MLC), where the transmission through the collimator leaves is taken into account. Examples are presented for different intensity profiles with varying degrees of complexity. Typically, the calculation takes less than 10 ms on a VAX 8550 computer.

Perspectives of multidimensional conformal radiation treatment

We consider the present technological advancement that underlies the implementation of computer-controlled conformal radiotherapy. We also consider the developments in modern biology that may provide input to therapy planning. The concept of multidimensional conformal radiotherapy is advanced, which integrates geometrical precision and biological conformality, to optimize the treatment planning for individual patients, with a view to improve the overall success of radiotherapy.

The use of a multi-leaf collimator for conformal radiotherapy of carcinomas of the prostate and nasopharynx

We investigate the use of a multi-leaf collimator for conformal radiation therapy of carcinomas of the prostate and of the nasopharynx. Following verification of dose calculation algorithms for multi-leaf collimated fields using film dosimetry, we compute dose distributions for multi-field conformal treatment using fields shaped with either the multi-leaf collimator or conventional cerrobend blocks. We compare the two sets of treatment plans using graphical isodose displays, tissue specific dose volume histograms, tumor control probabilities, and normal tissue complication probabilities. We also incorporate setup errors into the calculated dose distributions to assess the effect of treatment uncertainties on the various criteria. Based on these comparisons, we conclude that for multi-field conformal radiotherapy for these two disease sites, the use of multi-leaf collimation is equivalent to that of conventional cerrobend blocks.

Stereotactic treatment of brain tumors with radioactive implants or external photon beams: radiobiophysical aspects

We perform calculations, based on the linear-quadratic model, to assess the biologically effective doses (BED) of tumor and normal tissue in the stereotactic irradiation of brain tumors with either radioactive implants or radiosurgery techniques. Treatment protocols for radiosurgery and radioactive implants, as obtained from the literature, are reviewed and compared. A figure of merit is defined to be the ratio of tumor to normal tissue BED, expressed in units of Gy10/Gy3. These comparisons indicate a clear radiobiological advantage for brachytherapy, unless the radiosurgery is to be delivered in a large number of fractions. The differences in dose uniformity, and in the volume of normal tissue encompassed by the high dose regions, are factors that may also influence clinical results.

Beam characteristics of a new model of 6-MV linear accelerator

This paper describes the beam characteristics and dosimetry measurements performed on the 6-MV photon beam of a new model of linear accelerator, three of which were recently introduced and installed in our institution. Percent depth dose and tissue maximum ratio tables for a variety of field sizes and depths, as well as other parameters used for treatment planning are presented. These accelerators are the first of their kind using both hardware and software tools to control interlocks. Checking procedures for these interlocks are available from the authors upon request. Comparison of characteristic parameters between these three new 6-MV linear accelerators and with the 6-MV beams of two other accelerators is also made.

Diode dosimetry of models 6711 and 6712 125I seeds in a water phantom

Two-dimensional relative dose distributions have been measured around 125I brachytherapy seeds. The two seed models studied, models 6711 and 6712, were manufactured by the 3M Company. Silicon detectors immersed in water phantoms were used to measure the dose. A computerized data acquisition system that controlled the radial position of the diode and the angular rotation of the seed, as well as a manually controlled system were used to collect and store the data. Our results show that the two seed models have relative dose distributions which are quite similar; however, the absolute dose distributions are sufficiently different to warrant separate look-up tables for the two seed models. Additionally, our results are compared with dose distribution data previously obtained for the model 6711 seed.

Interinstitutional experience in verification of external photon dose calculations

Under the auspices of NCI contracts, four institutions have collaborated to assess the accuracy of the pixel-based dose calculation methods they employ for external photon treatment planning. The approach relied on comparing calculations using each group's algorithm with measurements in phantoms of increasing complexity. The first set of measurements consisted of ionization chamber measurements in water phantoms in normally incident square fields, an elongated field, a wedged field, a blocked field, and an obliquely incident beam. The second group of measurements was carried out using thermoluminescent dosimeters in phantoms designed to investigate the effects of surface curvature, high density heterogeneities, and low density heterogeneities. The final study tested the entire treatment planning system, including CT data conversion, in an anthropomorphic phantom. Overall, good agreement between calculation and measurements was found for all algorithms. Regions in which discrepancies were observed are pointed out, areas for algorithm improvement are identified and the clinical import of algorithm accuracy is discussed.

A comprehensive three-dimensional radiation treatment planning system

A comprehensive software system has been developed to allow 3-dimensional planning of radiation therapy treatments using the extensive anatomical information made available by imaging modalities such as CT and MR. Biological structures of interest and tumor volumes are defined by outlines drawn on a sequence of CT slices. Beam set-ups may then be determined in three dimensions by displaying the structure contours in a beam's eye view, or in two dimensions using a single CT cut. Each beam defined may be shaped by the specification of block aperture contours, and its intensity may be modified with the use of planar compensators. 3D dose calculation algorithms are discussed. To evaluate the calculation results, dose volume histograms are provided, as well as various types of displays in two and three dimensions, including dose on arbitrarily oriented planes, dose on the surface of anatomical objects, and isodose surfaces. Computer generated beam films are also available as an aid in patient set-up verification. These tools, and others, provide the basis for a comprehensive 3D system that can be used throughout the treatment planning process.

Extraction of pencil beam kernels by the deconvolution method

A method has been developed to extract pencil beam kernels from measured broad beam profiles. In theory, the convolution of a symmetric kernel with a step function will yield a function that is symmetric about the inflection point. Conversely, by deconvolution, the kernel may be extracted from a measured distribution. In practice, however, due to the uncertainties and errors associated with the measurements and due to the singularities produced in the fast Fourier transforms employed in the deconvolution process, the kernels thus obtained and the dose distributions calculated therefrom, often exhibit erratic fluctuations. We propose a method that transforms measured profiles to new, modified distributions so that they satisfy the theoretical symmetry condition. The resultant kernel from the deconvolution is then free of fluctuations. We applied this method to compute photon and electron dose distributions at various depths in water and electron fluence distributions in air. The agreement between measured and computed profiles is within 1% in dose or 1 mm in distance in high dose gradient regions.

The effect of angular spread on the intensity distribution of arbitrarily shaped electron beams

Knowledge of the relative intensity distribution at the patient's surface is essential for pencil beam calculations of three-dimensional dose distributions for arbitrarily shaped electron beams. To calculate the relative intensity distribution, the spatial spread resulting from angular spread is convolved with a two-dimensional step function whose shape corresponds to the applicator aperture. Two different approaches to obtain angular spread or the equivalent spatial spread are investigated. In the first method, the pencil beam angular spread is assumed to be Gaussian in shape. The angular spread constants (sigma theta) are then obtained from the slopes of measured intensity profiles. In the second method, the angular spread, in the form of an array of numerical values, is obtained by the deconvolution of measured intensity profiles. After obtaining the angular spread, the calculation for convolution is done in a number of parallel planes normal to the central axis at various distances from the electron collimator. Intensity at any arbitrary point in space is computed by interpolating between intensity distributions in adjacent planes on either side of the point. The effects of variations in angular spread as a function of field size for two treatment machines, one with a scanned electron beam and the other with a scattering foil, have been studied. The consequences of assuming angular spread to be of Gaussian shape are also examined. The electron intensity calculation techniques described in this paper apply primarily to methods of dose calculations that employ pencil beams generated using Monte Carlo simulations.

Dose computations for asymmetric fields defined by independent jaws

Asymmetric fields defined by independent jaws can be used to split a beam or to match adjacent fields. We have extended a method originally developed for symmetric fields to calculate the dose for asymmetric fields. The dose to a point is computed as the product of the tissue maximum ratio (TMR), the off center ratio (OCR), and the inverse square factor. The TMR is computed from the measured central axis depth doses for symmetric fields. The OCR is obtained by multiplying the primary OCR (POCR) and the boundary factors (BF's) for the four jaws. The POCR's and BF's were derived from measured beam profiles, which include the effect of off-axis beam quality variations. Using this method, the beam profiles and isodose distributions for asymmetric fields of a 6-MV accelerator were calculated and compared with the measured data. The agreement is within experimental errors both in the penumbra region and along the central ray of the asymmetric field.