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PubMed1996

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.

Humans↗
PubMed1998

Phantoms for IMRT dose distribution measurement and treatment verification.

BACKGROUND: The verification of intensity-modulated radiation therapy (IMRT) patient treatment dose distributions is currently based on custom-built or modified dose measurement phantoms. The only commercially available IMRT treatment planning and delivery system (Peacock, NOMOS Corp.) is supplied with a film phantom that allows accurate spatial localization of the dose distribution using radiographic film. However, measurements using other dosimeters are necessary for the thorough verification of IMRT. METHODS: We have developed a phantom to enable dose measurements using a cylindrical ionization chamber and the localization of prescription isodose curves using a matrix of thermoluminescent dosimetry (TLD) chips. The external phantom cross-section is identical to that of the commercial phantom, to allow direct comparisons of measurements. A supplementary phantom has been fabricated to verify the IMRT dose distributions for pelvis treatments. RESULTS: To date, this phantom has been used for the verification of IMRT dose distributions for head and neck and prostate cancer treatments. Designs are also presented for a phantom insert to be used with polymerizing gels (e.g., BANG-2) to obtain volumetric dose distribution measurements. CONCLUSION: The phantoms have proven useful in the quantitative evaluation of IMRT treatments.

Head and Neck Neoplasms↗
PubMed1998

A gradient inverse planning algorithm with dose-volume constraints.

An inverse planning algorithm for determining the intensity-modulated beams that will most closely generate a desired dose distribution is presented. The algorithm is three-dimensional and does not explicitly depend on beam energies and modalities. It allows a single prescription dose or a window of acceptable doses to be specified for the target, with additional constraints to account for under- or over-dosing. For the protection of organs at risk, it provides maximum-dose and dose-volume constraints. The latter apply to the entire volume of the organ exposed to the corresponding dose levels. Several levels of each type of constraint, with varying penalty weights, may be specified for each organ. The objective function that serves as the measure of the goodness of the solution is of the least-squares type and is minimized using conjugate gradient methods. Typical clinical cases involving 40,000 points and 4000 rays to be determined require about 10 min of CPU time on a DEC AlphaStation. Results are presented for two clinical sites, prostate and lung. The optimization algorithm yielded plans that featured higher target dose homogeneity, compared with the human planner's plan, while selectively sparing more of the normal organs at the desired dose regions.

Aged↗
PubMed1999

Optimal electron and combined electron and photon therapy in the phase space of complication-free cure.

The possibility of using intensity-modulated high-energy electrons beams alone or in combination with photon beams to treat tumours located at depths from 5 cm to 25 cm has been investigated. A radiobiologically based optimization algorithm using the probability of complication-free tumour control has been used to calculate the optimal dose distributions. Two different target volumes have been used; one advanced cervical cancer with locally involved lymph nodes and one astrocytoma in the upper brain hemisphere. Treatments with only electron beams and also combinations between electron and photon beams have been investigated. The dependence of the expected treatment outcome on the beam energy and directions was investigated, and to some extent on the number of beam portals. It is shown that the beam direction intervals resulting in a high expected treatment outcome increase with increasing electron energy and also with some electron-photon combinations. For an eccentrically placed, not too deeply situated tumour surrounded by sensitive normal tissue it is shown that the expected treatment outcome can be improved by using electron beams in combination with photon beams compared with using two photon beams, and using two electron beams results in almost as high an expected treatment outcome. The possibility of improving the dose conformity from electron beams by adding photon fields parallel or orthogonal to the electron beams is demonstrated.

Algorithms↗
PubMed1998

A proton dose calculation algorithm for conformal therapy simulations based on Molière's theory of lateral deflections.

An algorithm is developed for computing proton dose distributions in the therapeutic energy range (100-250 MeV). The goal is to provide accurate pencil beam dose distributions for two-dimensional or three-dimensional simulations of possible intensity-modulated proton therapy delivery schemes. The algorithm is based on Molière's theory of lateral deflections, which accurately describes the distribution of lateral deflections suffered by incident charged particles. The theory is applied to nonuniform targets through the usual pencil beam approximation which assumes that all protons from a given pencil beam pass through the same material at each depth. Fluence-to-dose conversion is made via Monte Carlo calculated broad-field central-axis depth-dose curves, which accounts for attenuation due to nuclear collisions and range straggling. Calculation speed is enhanced by using a best-fit Gaussian approximation of the radial distribution function at depth. Representative pencil beam and spread-out Bragg-peak computations are presented at 250 MeV and 160 MeV in water. Computed lateral full-widths-at-half-maximum's in water, at the Bragg peak, agree with the expected theoretical lateral values to within 1% at 160 MeV and to within 3% at 250 MeV. This algorithm differs from convolution methods in that the effect of the depth of any inhomogeneities in density or atomic composition are accounted for in a rigorous fashion. The algorithm differs from Fermi-Eyges based methods by accounting in a rigorous way for the effect of nonsmall-angle scattering and screening due to atomic electrons. The computational burden is only slightly greater than that expected using the less-rigorous Fermi-Eyges theory.

Algorithms↗
PubMed1999

Accuracy of numerically produced compensators.

A feasibility study is performed to assess the utility of a computer numerically controlled (CNC) mill to produce compensating filters for conventional clinical use and for the delivery of intensity-modulated beams. A computer aided machining (CAM) software is used to assist in the design and construction of such filters. Geometric measurements of stepped and wedged surfaces are made to examine the accuracy of surface milling. Molds are milled and filled with molten alloy to produce filters, and both the molds and filters are examined for consistency and accuracy. Results show that the deviation of the filter surfaces from design does not exceed 1.5%. The effective attenuation coefficient is measured for CadFree, a cadmium-free alloy, in a 6 MV photon beam. The effective attenuation coefficients at the depth of maximum dose (1.5 cm) and at 10 cm in solid water phantom are found to be 0.546 cm-1 and 0.522 cm-1, respectively. Further attenuation measurements are made with Cerrobend to assess the variations of the effective attenuation coefficient with field size and source-surface distance. The ability of the CNC mill to accurately produce surfaces is verified with dose profile measurements in a 6 MV photon beam. The test phantom is composed of a 10 degrees polystyrene wedge and a 30 degrees polystyrene wedge, presenting both a sharp discontinuity and sloped surfaces. Dose profiles, measured at the depth of compensation (10 cm) beneath the test phantom and beneath a flat phantom, are compared to those produced by a commercial treatment planning system. Agreement between measured and predicted profiles is within 2%, indicating the viability of the system for filter production.

Feasibility Studies↗
PubMed1998

Dosimetric verification of the dynamic intensity-modulated radiation therapy of 92 patients.

PURPOSE: To verify that optimized dose distributions provided by an intensity-modulated radiation therapy (IMRT) system are delivered accurately to human patients. METHODS AND MATERIALS: Anthropomorphic phantoms are used to measure IMRT doses. Four types of verification are developed for: I) system commissioning with beams optimized to irradiate simulated targets in phantoms, II) plans with patient-optimized beams directed to phantoms simulating the patient, III) patient-phantom hybrid plans with patient-optimized beams calculated in phantom without further optimization, and IV) in vivo measurements. Phantoms containing dosimeters are irradiated with patient-optimized beams. Films are scanned and data were analyzed with software. Percent difference between verified and planned maximum target doses is defined as "dose discrepancy" (deltavp). The frequency distribution of type II deltavp from 204 verification films of 92 IMRT patients is fit to a Gaussian. Measurements made in vivo yield discrepancies specified as deltaivp, also fit to a Gaussian. RESULTS AND DISCUSSION: Verification methods revealed three systematic errors in plans that were corrected prior to treatment. Values of [deltavp] for verification type I are <2%. Type II verification discrepancies are characterized by a Gaussian fit with a peak 0.2% from the centroid, and 158 [deltavp] <5%. The 46 values of [deltavp] >5% arise from differences between phantom and patient geometry, and from simulation, calculation, and other errors. Values of [deltavp] for verification III are less than half of the values of [deltavp] for verification II. A Gaussian fit of deltaivp from verification IV shows more discrepancy than the fit of deltavp, attributed to dose gradients in detectors, and exacerbated by immobilization uncertainty. CONCLUSIONS: Dosimetric verification is a critical step in the quality assurance (QA) of IMRT. Hybrid Verification III is suggested as a preliminary quality standard for IMRT.

Brain Neoplasms↗
PubMed1998

On compensator design for photon beam intensity-modulated conformal therapy.

Recently the compensator has been shown to be an in expensive and reliable dose delivery device for photon beam intensity-modulated radiation therapy (IMRT). The goal of IMRT compensator design is to produce an optimized primary fluence profile at the patient's surface obtained from the optimization procedure. In this paper some of the problems associated with IMRT compensator design, specifically the beam perturbations caused by the compensator, are discussed. A simple formula is derived to calculate the optimal compensator thickness profile from an optimized primary fluence profile. The change of characteristics of a 6 MV beam caused by the introduction of cerrobend compensators in the beam is investigated using OMEGA Monte Carlo codes. It is found that the compensator significantly changes the energy spectrum and the mean energy of the primary photons at the patient's surface. However, beam hardening does not have as significant an effect on the percent depth dose as it does on the energy spectrum. We conclude that in most situations the beam hardening effect can be ignored during compensator design and dose calculation. The influence of the compensator on the contaminant electron buildup dose is found to be small and independent of the compensator thickness of interest. Therefore, it can be ignored in the compensator design and included as a correction into the final dose distribution. The scattered photons from the compensator are found to have no effect on the surface dose. These photons produce a uniform low fluence distribution at the patient's surface, which is independent of compensator shape. This is also true for very large fields and extremely asymmetric and nonuniform compensator thickness profiles. Compared to the primary photons, the scattered photons have much larger angular spread and similar energy spectrum at the patient's surface. These characteristics allow the compensator thickness profile and the dose distribution to be calculated from the optimized fluence profile of primary photons, without considering the scattered photons.

Calibration↗
PubMed1998

Quality assurance of serial tomotherapy for head and neck patient treatments.

PURPOSE: A commercial serial tomotherapy intensity-modulated radiation therapy (IMRT) treatment planning (Peacock, NOMOS Corp., Sewickley, PA) and delivery system is in clinical use. The dose distributions are highly conformal, with large dose gradients often surrounding critical structures, and require accurate localization and dose delivery. Accelerator and patient-specific quality assurance (QA) procedures have been developed that address the localization, normalization, and delivery of the IMRT dose distributions. METHODS AND MATERIALS: The dose distribution delivered by serial tomotherapy is highly sensitive to the accuracy of the longitudinal couch motion. There is also an unknown sensitivity of the dose distribution on the dynamic mutlileaf collimator alignment. QA procedures were implemented that assess these geometric parameters. Evaluations of patient positioning accuracy and stability were conducted by exposing portal films before (single exposure) and after (single or double exposure) treatments. The films were acquired with sequential exposures using the largest available fixed multileaf portal (3.36 x 20 cm2). Comparison was made against digitally reconstructed radiographs generated using independent software and appropriate beam geometries. The delivered dose was verified using homogeneous cubic phantoms. Radiographic film was used to determine the localization accuracy of the delivered isodose distributions, and ionization chambers and thermoluminescent dosimetry (TLD) chips were used to verify absolute dose at selected points. Ionization chamber measurements were confined to the target dose regions and TLD measurements were obtained throughout the irradiated volumes. Because many more TLD measurements were made, a statistical evaluation of the measured-to-calculated dose ratio was possible. RESULTS: The accelerator QA techniques provided adequate monitoring of the geometric patient movement and dynamic multileaf collimator alignment and positional stability. The absolute delivered dose as measured with the ionization chamber varied from 0.94 to 0.98. Based on these measurements, the delivered monitor units for both subsequent QA measurements and patient treatments were adjusted by the ratio of measured to calculated dose. TLD measurements showed agreement, on average, with the ionization chamber measurements. The distribution of TLD measurements in the high-dose regions indicated that measured doses agreed within 4.2% standard deviation of the calculated doses. In the low-dose regions, the measured doses were on average 5% greater than the calculated doses, due to a lack of leakage dose in the dose calculation algorithm. CONCLUSIONS: The QA system provided adequate determination of the geometric and dosimetric quantities involved in the use of IMRT for the head and neck. Ionization chamber and TLD measurements provided accurate determination of the absolute delivered dose throughout target volumes and critical structures, and radiographic film yielded precise dose distribution localization verification. Portal film acquisition and subsequent portal film analysis using 3.36 x 20 cm2 portals proved useful in the evaluation of patient immobilization quality. Adequate bony landmarks were imaged when carefully selected portals were used.

Algorithms↗
PubMed1995

Optimization of intensity-modulated 3D conformal treatment plans based on biological indices.

To overcome the limitations of the intensity modulation optimization techniques based on dose criteria, we introduce a method for optimizing intensity distributions in which we employ an objective function based on biological indices. The objective function also includes constraints on dose and dose-volume combinations to ensure that the results are consistent with the physician's judgement. We apply a variant of the steepest-descent method to optimize the objective function. The method is three-dimensional and incorporates scattered radiation in the optimization process using an iterative scheme employing the pencil beam convolution method. Previously we had shown that the inverse technique of obtaining optimum intensity distributions, for which the objectives are defined in terms of a desired uniform dose to the target volume and desired upper limits of dose to normal organs, produces satisfactory approximations of the desired dose distributions for prostate plans. However, for lung, the performance of this technique was considerably inferior. Our conclusion was that, in general, it is not sufficient to specify the objectives of optimization purely in terms of a desired pattern of dose and that the objectives should also incorporate biology, perhaps in the form of biological indices. We demonstrate that the biology-based approach produces lung plans that are superior to those produced when only dose-based objectives are used. For the treatment of prostate, the two methods produce comparable dose distributions.

Adenocarcinoma↗
PubMed1997

Modulated beam conformal therapy for head and neck tumors.

PURPOSE: The goal of modulated-beam conformal therapy is to reduce the dose to healthy tissue and sensitive structures around a uniformly irradiated target volume. Multiple intensity-modulated fields offer improved tissue-sparing dose distributions. New computer-based systems for planning and delivering such treatments may soon be available from different commercial sources that will make the formulation of an intensity-modulated treatment plan and its execution widely available at any treatment facility that has the resources to acquire the necessary equipment. This work reports on a study of the integration of two such systems. METHODS AND MATERIALS: Treatment planning was done using a commercially available inverse planning algorithm based on simulated annealing. The plans arbitrarily assumed nine coplanar x-ray beams at nonopposed gantry angles. Intensity modulation was computed for each beam. The modulated field at each gantry angle was broken down into a series of uniform (nonmodulated) subfields, which could be delivered as a sequence to produce the desired dose distribution. Because a large number of subfields was delivered, a multileaf collimator (MLC) was used for field shaping. This allowed rapid and accurate field shaping for treatments made up of several hundred subfields. Computer control of the MLC and linear accelerator allowed delivery of doses less than .01 Gy per subfield. Treatment was delivered on a prototype, computer-controlled accelerator and MLC system. Resulting dose distributions were analyzed using film and an anatomically specific, homogeneous phantom. RESULTS: The treatment plans were evaluated using dose-volume histogram analysis. The plans provided acceptably uniform irradiation of the target volume without exceeding dose tolerances for nearby critical structures. The plans were successfully delivered by a prototype dynamic MLC. The time needed to deliver a sequence of subfields at one gantry angle ranged from 0.7 to 2.0 min. Isodoses from film agreed reasonably well with planned isodose distributions. CONCLUSIONS: It is feasible to plan and deliver fixed gantry, modulated-beam conformal therapy for head and neck tumors with systems being developed commercially. The planned dose distributions exhibit significant potential for sparing closely spaced normal tissue structures in the head and neck.

Algorithms↗
PubMed1997

Field margin reduction using intensity-modulated x-ray beams formed with a multileaf collimator.

PURPOSE: In axial, coplanar treatments with multiple fields, the superior and inferior ends of a planning target volume (PTV) are at risk to get underdosed due to the overlapping penumbras of all treatment fields. We have investigated a technique using intensity modulated x-ray beams that allows the use of small margins for definition of the superior and inferior field borders while still reaching a minimum PTV-dose of 95% of the isocenter dose. METHODS AND MATERIALS: The applied intensity modulated beams, generated with a multileaf collimator, include narrow (1.1-1.6 cm) boost fields to increase the dose in the superior and inferior ends of the PTV. The benefits of this technique have been assessed using 3D treatment plans for 10 prostate cancer patients. Treatment planning was performed with the Cadplan 3D planning system (Varian-Dosetek). Dose calculations for the narrow boost fields have been compared with measurements. The application of the boost fields has been tested on the MM50 Racetrack Microtron (Scanditronix Medical AB), which allows fully computer-controlled setup of all involved treatment fields. RESULTS: Compared to our standard technique, the superior-inferior field length can be reduced by 1.6 cm, generally yielding smaller volumes of rectum and bladder in the high dose region. For the narrow boost fields, calculated relative dose distributions agree within 2% or 0.2 cm with measured dose distributions. For accurate monitor unit calculations, the phantom scatter table used in the Cadplan system had to be modified using measured data for square fields smaller than 4 x 4 cm2. The extra time needed at the MM50 for the setup and delivery of the boost fields is usually about 1 min. CONCLUSION: The proposed use of intensity modulated beams yields improved conformal dose distributions for treatment of prostate cancer patients with a superior-inferior field size reduction of 1.6 cm. Treatments of other tumor sites can also benefit from the application of the boost fields.

Humans↗
PubMed1999

Beam intensity modulation to reduce the field sizes for conformal irradiation of lung tumors: a dosimetric study.

PURPOSE: In conformal radiotherapy of lung tumors, penumbra broadening in lung tissue necessitates the use of larger field sizes to achieve the same target coverage as in a homogeneous environment. In an idealized model configuration, some fundamental aspects of field size reduction were investigated, both for the static situation and for a moving tumor, while maintaining the dose homogeneity in the target volume by employing a simple beam-intensity modulation technique. METHODS AND MATERIALS: An inhomogeneous phantom, consisting of polystyrene, cork, and polystyrene layers, with a 6 x 6 x 6 cm3 polystyrene cube inside the cork representing the tumor, was used to simulate a lung cancer treatment. Film dosimetry experiments were performed for an AP-PA irradiation technique with 8-MV or 18-MV beams. Dose distributions were compared for large square fields, small square fields, and intensity-modulated fields in which additional segments increase the dose at the edge of the field. The effect of target motion was studied by measuring the dose distribution for the solid cube, displaced with respect to the beams. RESULTS: For the 18-MV beam, the field sizes required to establish a sufficient target coverage are larger than for the 8-MV beam. For each beam energy, the mean dose in cork can significantly be reduced (at least a factor of 1.6) by decreasing the field size with 2 cm, while keeping the mean target dose constant. Target dose inhomogeneity for these smaller fields is limited if the additional edge segments are applied for 8% of the number of monitor units given with the open fields. The target dose distribution averaged over a motion cycle is hardly affected if the target edge does not approach the field edge to within 3 mm. CONCLUSIONS: For lung cancer treatment, a beam energy of 8 MV is more suitable than 18 MV. The mean lung dose can be significantly reduced by decreasing the field sizes of conformal fields. The smaller fields result in the same biological effect to the tumor if the mean target dose is kept constant. Intensity modulation can be employed to maintain the same target dose homogeneity for these smaller fields. As long as the target (with a 3 mm margin) stays within the field portal, application of a margin for target motion is not necessary.

Film Dosimetry↗
PubMed1995

Dynamic beam modulation by using a single computer-controlled absorber.

The authors have developed an apparatus able to generate ID intensity-modulated beams, using only one moving absorber within the irradiation field. A procedure for deriving optimized absorber-speed profiles in order to produce the desired fluence/dose profiles has been suggested. Experimental tests show that the system should be sufficiently reliable in reproducing modulated beam profiles of different shape: expected relative doses against measured relative doses have been found to be in agreement in a number of situations within 3% using a nonfocused device. A better agreement should be expected using a focused apparatus (which is currently being developed). Beam modulation by single absorber cannot modulate the beam fluence in any was one wishes, due to physical constraints, which depend on the absorber and field widths and on the shape of the desired fluence profile. However, the authors show that this simple and low-cost tool could offer, with a sufficient degree of accuracy, the possibility of modulating the beam fluence with a high degree of versatility. In particular, a procedure or performing tissue-missing compensation by single-absorber dynamic beam modulation is suggested. Moreover, 'strongly' modulated beam profiles can be created, showing that this simple technique could also have some interesting applications in the field of conformal radiotherapy by non-uniform dose delivery.

Algorithms↗
PubMed1996

A method to study the characteristics of 3D dose distributions created by superposition of many intensity-modulated beams delivered via a slit aperture with multiple absorbing vanes.

Highly conformal dose distributions can be created by the superposition of many radiation fields from different directions, each with its intensity spatially modulated by the method known as tomotherapy. At the planning stage, the intensity of radiation of each beam element (or bixel) is determined by working out the effect of superposing the radiation through all bixels with the elemental dose distribution specified as that from a single bixel with all its neighbours closed (the 'independent-vane' (IV) model). However, at treatment-delivery stage, neighbouring bixels may not be closed. Instead the slit beam is delivered with parts of the beam closed for different periods of time to create the intensity modulation. As a result, the 3D dose distribution actually delivered will differ from that determined at the planning stage if the elemental beams do not obey the superposition principle. The purpose of this paper is to present a method to investigate and quantify the relation between planned and delivered 3D dose distributions. Two modes of inverse planning have been performed: (i) with a fit to the measured elemental dose distribution and (ii) with a 'stretched fit' obeying the superposition principle as in the PEACOCK 3D planning system. The actual delivery has been modelled as a series of component deliveries (CDs). The algorithm for determining the component intensities and the appropriate collimation conditions is specified. The elemental beam from the NOMOS MIMiC collimator is too narrow to obey the superposition principle although it can be 'stretched' and fitted to a superposition function. Hence there are differences between the IV plans made using modes (i) and (ii) and the raw and the stretched elemental beam, and also differences with CD delivery. This study shows that the differences between IV and CD dose distributions are smaller for mode (ii) inverse planning than for mode (i), somewhat justifying the way planning is done within PEACOCK. Using a stretched elemental beam is a useful adjustment to improve the accuracy of inverse planning but the 3D dose distribution actually delivered will display characteristics of the collimation.

Humans↗
PubMed1998

The effects of intra-fraction organ motion on the delivery of dynamic intensity modulation.

Computer-optimized treatment plans, aimed to enhance tumour control and reduce normal tissue complication, generally require non-uniform beam intensities. One of the techniques for delivering intensity-modulated beams is the use of dynamic multileaf collimation, where the beam aperture moves and the field shape changes during irradiation. When intensity-modulated beams are delivered with dynamic collimation, the problem of intra-fraction organ motion can cause distortions to the desired beam intensities. Unlike static field treatments, where intra-fraction organ motion only affects the boundaries creating broad dose penumbra, the interplay of the movement of the beam aperture and the movement of the patient anatomy can create 'hot' and 'cold' spots throughout the field. The mechanism for creating these effects is not well understood. This paper provides a simple analytical model which illustrates the fundamental mechanism for creating the dosimetric variations in the target when both the beam aperture and the target move during irradiation. Numerical analysis was carried out which calculates the cumulative primary photon fluence, or beam intensity, received by each point in the target, for a given pattern of motion. The results show that, for clinically realistic parameters, the magnitude of intensity variations in the target can be greater than 100% of the desired beam intensity. The magnitude of the photon intensity variations is strongly dependent on the speed of the beam aperture relative to the speed of the target motion, and the width of the scanning beam relative to the amplitude of target motion. The effects of fractionation as well as methods of minimizing and eliminating the dosimetric effects of intra-fraction organ motion are discussed.

Biophysical Phenomena↗
PubMed1998

Configuration options for intensity-modulated radiation therapy using multiple static fields shaped by a multileaf collimator.

One-dimensional (1D) intensity-modulated beams (IMBs) can be generated by multiple static fields (MSFs) created by a multileaf collimator (MLC) with the radiation switched off between field re-settings (Bortfeld-Boyer method). Each component irradiation is of equal fluence. This paper presents and analyses the formulae for the number of physically allowed combinations of leaf settings which generate any given IMB. The formulae are general to an IMB with any number of local minima and extend from the well-known N! formula for a single-peaked IMB with N left-leaf (L-leaf) and N right-leaf (R-leaf) positions. A 'combination' is a set of N L-leaf and R-leaf pairings. A 'physically allowed combination' is one in which no L-leaf is paired with an R-leaf to its left. The physically allowed combinations are grouped by specific properties into classes in which the well-known techniques of 'leaf-sweep' and 'close-in' are just two members. Consideration of these properties leads to a new suggestion of the 'forced-baseline' configuration in which the first intensity increment is delivered for the full field width and there remain choices concerning the delivery of the rest of the IMB within which two different possibilities are 'one-out-of-sync leaf-sweep' and 'minimum leaf travel'. The extension to 2D is briefly introduced.

Models, Theoretical↗
PubMed1998

Configuration options for intensity-modulated radiation therapy using multiple static fields shaped by a multileaf collimator. II: constraints and limitations on 2D modulation.

This paper addresses the technique of using multiple static multileaf-collimator-shaped field components to create a two-dimensional intensity-modulated beam (2D IMB). It addresses the physical constraints on the problem of determining the optimum field-component leaf configurations under the circumstances that (i) the static field components are shaped by leaves alone and (ii) the 2D intensity distribution is delivered by exactly N field components when there are N rising-intensity equal-fluence increments in the 1D channel containing the maximum fluence in the 2D IMB. This corresponds to the least inefficient delivery. In general it is noted that an optimum solution (set of field-component leaf configurations) with zero tongue-and-groove underdose may not exist (depending on the distribution) and an exhaustive search for the set of leaf configurations with the minimum tongue-and-groove underdose is impossible for realistically sized problems. Against this background iterative methods to examine a limited search space are shown to yield an optimum solution with zero tongue-and-groove underdose for certain intensity distributions. These searches are not robust and can be defeated. The problem of finding an optimum solution may be generally insoluble for some 2D IMBs under the conditions (i) and (ii). If, however, a larger number of field components is permitted and/or the accelerator jaws may also be used, in addition to the multileaves, then an optimum solution with zero tongue-and-groove underdose can always be found with lower efficiency.

Biophysical Phenomena↗