Pencil Beam Calculations Research Articles

Radiotherapy dose calculations in the presence of hip prostheses

The high density and atomic number of hip prostheses for patients undergoing pelvic radiotherapy challenge our ability to accurately calculate dose. A new clinical dose calculation algorithm, Monte Carlo, will allow accurate calculation of the radiation transport both within and beyond hip prostheses. The aim of this research was to investigate, for both phantom and patient geometries, the capability of various dose calculation algorithms to yield accurate treatment plans. Dose distributions in phantom and patient geometries with high atomic number prostheses were calculated using Monte Carlo, superposition, pencil beam, and no-heterogeneity correction algorithms. The phantom dose distributions were analyzed by depth dose and dose profile curves. The patient dose distributions were analyzed by isodose curves, dose-volume histograms (DVHs) and tumor control probability/normal tissue complication probability (TCP/NTCP) calculations. Monte Carlo calculations predicted the dose enhancement and reduction at the proximal and distal prosthesis interfaces respectively, whereas superposition and pencil beam calculations did not. However, further from the prosthesis, the differences between the dose calculation algorithms diminished. Treatment plans calculated with superposition showed similar isodose curves, DVHs, and TCP/NTCP as the Monte Carlo plans, except in the bladder, where Monte Carlo predicted a slightly lower dose. Treatment plans calculated with either the pencil beam method or with no heterogeneity correction differed significantly from the Monte Carlo plans.

Accuracy of treatment planning calculations for conformal radiotherapy (in English)

This thesis presents methods to define and improve the accuracy of treatment planningdose and volume calculations for conformal radiotherapy, especially in regions with the highest expected benefits—the edges and shielded parts of the beams. The context of this thesis is a verification program of a treatment planning system. It is shown that an appropriately designed “combinatorial verification” makes such a program feasible. Results of this thesis apply to megavoltage photon beams in homogeneous and heterogeneous geometries, to proton beams, and to dose–volume representations. A “field accuracy” concept is shown to facilitate simultaneous checks of dose and distance criteria. This concept is applied to pencil beam calculations in partially blocked photon beams. In a lungtumor phantom large dose discrepancies were found between photon pencil beam calculations and film measurements. This is due to improper scatter handling, as is shown by comparison to results of a point spread kernel algorithm. Methods have been developed for high-resolution measurements of photon beam edges with ionization chambers, thus in particular suited for a program of routine verification measurements. Improvements in accuracy of up to 2 mm in the penumbra have been achieved. Dose distributions and penumbras in small proton beams have been investigated with Monte Carlo calculations and a 2D scintillating screen detector. Accuracy of grid-based volume sampling has been studied, yielding the required grid sizes for specific uncertainties in the volume representation of dose–volume histograms. Finally, bringing the concepts of combinatorial verification and field accuracy together, the feasibility of a comprehensive presentation of calculation accuracy in a conformal prostate treatment plan has been demonstrated.

Monte Carlo evaluation of tissue inhomogeneity effects in the treatment of the head and neck

Purpose: To use Monte Carlo dose calculation to assess the degree to which tissue inhomogeneities in the head and neck affect static field conformal, computed tomography (CT)-based 6-MV photon treatment plans. Methods and Materials: We retrospectively studied the three-dimensional treatment plans that had been used for the treatment of 5 patients with tumors in the nasopharyngeal or paranasal sinus regions. Two patients had large surgical cavities. The plans were designed with a clinical treatment planning system that uses a measurement-based pencil-beam dose-calculation algorithm with an equivalent path-length inhomogeneity correction. Each plan employs conformally-shaped 6-MV photon beams. Patient anatomy and electron densities were obtained from the treatment planning CT images. For each plan, the dose distribution was recalculated with the Monte Carlo method, utilizing the same beam geometry and CT images. The Monte Carlo method accurately accounts for the perturbation effects of local tissue heterogeneities. The Monte Carlo calculated dose distributions were compared with those from the clinical treatment planning system. Results: The degree to which tissue inhomogeneity affects the dose distributions of individual fields varies with the specific anatomic geometry, especially the size and location of air cavities in relation to the beam orientation and field size. Most of the beam apertures completely enclose the air cavities within or adjacent to the gross tumor volume (GTV). Equivalent squares (including blocking) ranged from approximately 5 to 9.5 cm. A common feature observed for individual fields is that the Monte Carlo calculated doses to tissue directly behind and within an air cavity are lower. However, after combining the fields employed in each treatment plan, the overall dose distribution shows only small differences between the two methods. For all 5 patients, the Monte Carlo calculated treatment plans showed a slightly lower dose received by the 95% of target volume (D 95) than the plans calculated with the pencil-beam algorithm. The average difference in the target volume encompassed by the prescription isodose line was less than 2.2%. The difference between the dose-volume histograms (DVHs) of the GTV was generally small. For the brainstem and chiasm, the DVHs of the two plans were similar. For the spinal cord, differences in the details of the DHV and the dose to 1 cc (D 1cc) of the structure were observed, with Monte Carlo calculation generally predicting increased dose indices to the spinal cord. However, these changes are not expected to be clinically significant. Conclusion: For 6-MV photons, the effects of both normal tissue inhomogeneities and surgical air cavities on the target coverage were adequately accounted for by conventional pencil beam methods for all of the cases studied. Although differences in details of the DVHs of the normal structures were observed, depending on whether Monte Carlo or pencil-beam algorithm was used for calculation, these differences are not expected to be clinically significant. In general, the pencil-beam calculation corrected for primary attenuation by the equivalent pathlength is a sufficiently accurate method for head-and-neck treatment planning using 6-MV photons.

Intensity modulated irradiation of a thorax phantom: comparisonsbetween measurements, Monte Carlo calculations and pencil beamcalculations

The present study investigates the application of compensators forthe intensity modulated irradiation of a thorax phantom. Measurements arecompared with Monte Carlo and standard pencil beam algorithm dosecalculations. Compensators were manufactured to produce the intensity profilesthat were generated from the scientific version of the KonRad IMRTtreatment-planning system for a given treatment plan. The comparison of dosedistributions calculated with a pencil beam algorithm, with the Monte Carlocode EGS4 and with measurements is presented. By measurements in a waterphantom it is demonstrated that the method used to manufacture thecompensators reproduces the intensity profiles in a suitable manner.Monte Carlo simulations in a water phantom show that theaccelerator head model used for simulations is sufficient. No significantoverestimations of dose values inside the target volume by the pencil beamalgorithm are found in the thorax phantom. An overestimation of dose values inlung by the pencil beam algorithm is also not found. Expected dose calculationerrors of the pencil beam algorithm are suppressed, because the dose to thelow density region lung is reduced by the use of a non-coplanar beamarrangement and by intensity modulation.

Monte Carlo dose calculations for dynamic IMRT treatments

Dose calculations for intensity modulated radiation therapy (IMRT) face newchallenges due to the complex leaf geometry and time dependent nature of thedelivery. A fast method of particle transport through a dynamic multileafcollimator (MLC) geometry that accounts for photon attenuation and first-scatteredCompton photon production has been incorporated into an existing Monte Carlocode used for patient dose calculations. Dosimetric agreement betweencalculation and measurement for two photon energies and MLC types is withinexperimental error for the sliding window tests. For a patient IMRT field, theMonte Carlo calculations are closer to measured dose than similarsuperposition or pencil beam calculations.

Evaluation of a pencil-beam dose calculation technique for charged particle radiotherapy

Purpose : The purpose of this article is to evaluate a pencil-beam dose calculation algorithm for protons and heavier charged particles in complex patient geometries defined by computed tomography (CT) data and to compare isodose distributions calculated with the new technique to those calculated with conventional algorithms in selected patients with skull-base tumors. Methods and Materials : Monte Carlo calculations were performed to evaluate the pencil-beam algorithm in patient geometries for a modulated 150-MeV proton beam. A modified version of a Mont Carlo code described in a previous publication (18) was used for these comparisons. Tissue densities were inferred from patient CT data on a voxel-by-voxel basis, and calculations were peformed with an without tissue compensators. A dose calculation module using the new algorithm was written, and treatment plans using the new algorithm were compared to plans using standard ay-tracing techniques for 10 patients with clival chordoma and three patients with nasopharyngeal carcinoma who were treated with helium ions at Lawrence Berkeley National Laboratory (LBL). Results : Pencil beam calculations agreed well with Monte Carlo calculations in the patient geometries. The pencil-beam algorithm predicted several multiple-scattering effects that are not modeled by conventional ray-tracing calculations. These includes (a) the widening of the penumbra as a function of beam penetration, (b) the degradation in the sharpness of the dose gradient at the end of the particle range in hgihly heterogeneous regions, and (c) the appearance of hot and cold dose regions in the shadow of cmplex heterogeneities. In particular, pencil-beam calculations indicated that the dose distribution within the target was not a homogeneous as expected on the basis of ray-tracing calculations. on average, for the 13 patients considered, only about 72% of the cone down target volume received at least 99% of the prescribed dose, whereas, 93% of the conedwn volume was contained within the 95% isodose surface. This may e significant because in standard charged particle dose calculations, the dose across the spread-Bragg peak is assumed to be uniform and equal to the maximum or prescribed dose. Conclusions : Dose distributions computed with the pencil-beam model are more accurate than ray-tracing calculations, providing additional information to clinicians, which may influence the doses they prescribe. In particular, these calculations indicate that for some patients with skull-base tumors, it may be advantageous to prescribe proton doses to a lower isodose level than is commonly done.

A method for total skin electron treatment for infants

Diseases such as mycosis fungoides require the treatment of a patient's total skin surface with superficial radiation. In a unique clinical situation, a 14-month-old child presented with a need for total skin treatment. A typical total skin technique requires overlapping electron beams, using 6 body positions, each with the gantry rotated for 2 angulations, or ‘6 positions-12 fields’. Adaptation of this technique for infants is complicated by the small diameter of some body parts, and by the necessity to treat while the patient is anesthetized. Even degraded, low energy electrons can easily penetrate fingers and toes. Therefore, dose from 6 positions becomes additive, and the total dose to small circumferences can be 3 to 4 times more than skin dose on the torso, raising concerns about uneven bone growth in the developing child. Special phantoms were designed for extensive dosimetry needed to determine both dose rate and dose summation from the overlapping beams. Computerized electron pencil beam calculations were compared to TLD measurements. Unique compensating techniques were used to deliver uniform dose. A modification of the 6 position-12 field technique will be described; and accessories used to reduce high dose regions will be illustrated.

Optimization of pencil beam widths for electron‐beam dose calculations

The pencil beam method of calculating dose distributions for electron-beam radiotherapy has been very useful, however, several limitations in the approach have been recognized. One such limitation is the lack of a mechanism to model range straggling of electrons. For stationary electron-beam calculations, range straggling is incorporated incompletely in the planar-fluence-to-dose conversion factor, which uses measured percentage depth dose curves to force the calculated percentage depth dose to reproduce the measurement. When calculating the dose distribution for an arced beam using a pencil beam algorithm, insufficient modeling of the pencil beams leads to larger errors than when using a stationary beam algorithm. The calculated depth of maximum dose is systematically over-estimated by the pencil beam calculations. We will show that the lack of a way to account for range straggling in the arc-electron pencil beam calculation is primarily responsible for this discrepancy. Methods of incorporating range straggling into the electron pencil beam dose calculation have been presented before, but no data have been shown to support their use for heterogeneous phantoms (patients). This paper presents a similar range-straggling modification, as well as data to show that this model can predict pencil beam width to within 20% for heterogeneous slab phantoms. For stationary electron-beam calculations, the calculated isodose lines follows the measured isodose lines to within 1 mm down to the 10% dose level.(ABSTRACT TRUNCATED AT 250 WORDS)

A multiray model for calculating electron pencil beam distribution.

Based on the Fermi-Eyges theory, a set of recursion relations was derived for calculating electron distributions in the layered geometry. The electron distribution at a specific depth was obtained by convolving the upstream electron distribution with a kernel determined by the scattering parameters of the layer. Modifications were made to overcome some inherent limitations of the Fermi-Eyges theory. For each point in the medium, the most probable, or mean, path traversed by the electrons in reaching the point was derived. The skewness of the mean paths and the related energy degradation were included in a multiray model for pencil beam calculations. The resultant electron planar fluence distributions are no longer Gaussian as predicted by the original theory. The effects of edges or localized inhomogeneities are also included. Comparisons between our calculations and Monte Carlo simulations show good agreement.

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.

Electron dose distributions in experimental phantoms: a comparison with 2D pencil beam calculations

Dose distributions were measured and computed within inhomogeneous phantoms irradiated with beams of electrons having initial energies of 10 and 18 MeV. The measurements were made with a small p-type silicon diode and the calculations were performed using the pencil beam algorithm developed originally at the M D Anderson Hospital (MDAH). This algorithm, which is available commercially on many radiotherapy planning computers, is based on the Fermi-Eyges theory of electron transport. The phantoms used in this work were composed of water into which two- and three-dimensional inhomogeneities of aluminium and air (embedded in wax) were introduced. This was done in order to simulate the small bones and the air cavities encountered clinically in radiation therapy of the chest wall or neck. The authors intent was to test the adequacy of the two-dimensional implementation of the pencil beam approach. The agreement between measured and computed doses is very good for inhomogeneities which are essentially two-dimensional but discrepancies as large as 40% were observed for more complex three-dimensional inhomogeneities. The authors can only trace the discrepancies to the complex interplay of numerous approximations in the Fermi-Eyges theory of multiple scattering and its adaptation for practical computer-aided radiotherapy planning.

Clinical evaluation of an algorithm for inhomogeneity corrections of electron beam dosimetry

An algorithm for inhomogeneity correction of electron beam dose distributions has been developed at U.T. M. D. Anderson Hospital and Tumor Institute. The enhanced perturbation of the electron beam requires a more rigorous and exact analysis compared to megavoltage photon beams. The algorithm uses a pencil beam calculation model to correct for air gap, tissue inhomogeneity and field shape. Cross sectional computer tomography data provide surface contour and tissue inhomogeneity information. The accuracy of the calculation model has been verified by TLD measurements in tissue substitute phantoms reconstructed from CT patient scans.