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James L Bedford

Publications and source records attributed to James L Bedford.

17 recordsLinked to original sources
PubMed2006

Comparison of inverse-planned three-dimensional conformal radiotherapy and intensity-modulated radiotherapy for non-small-cell lung cancer.

PURPOSE: Lungs are the major dose-limiting organ during radiotherapy (RT) for non-small-cell lung cancer owing to the development of pneumonitis. This study compared intensity-modulated RT (IMRT) with three-dimensional conformal RT (3D-CRT) in reducing the dose to the lungs. METHODS: Ten patients with localized non-small-cell lung cancer underwent computed tomography (CT). The planning target volume (PTV) was defined and the organs at risk were outlined. An inverse-planning program, AutoPlan, was used to design the beam angle-optimized six-field noncoplanar 3D-CRT plans. Each 3D-CRT plan was compared with a series of five IMRT plans per patient. The IMRT plans were created using a commercial algorithm and consisted of a series of three, five, seven, and nine equidistant coplanar field arrangements and one six-field noncoplanar plan. The planning objectives were to minimize the lung dose while maintaining the dose to the PTV. The percentage of lung volume receiving >20 Gy (V20) and the percentage of the PTV covered by the 90% isodose (PTV90) were the primary endpoints. The PTV90/V20 ratio was used as the parameter accounting for both the reduction in lung volume treated and the PTV coverage. RESULTS: All IMRT plans, except for the three-field coplanar plans, improved the PTV90/V20 ratio significantly compared with the optimized 3D-CRT plan. Nine coplanar IMRT beams were significantly better than five or seven coplanar IMRT beams, with an improved PTV90/V20 ratio. CONCLUSION: The results of our study have shown that IMRT can reduce the dose to the lungs compared with 3D-CRT by improving the conformity of the plan.

Carcinoma, Non-Small-Cell Lung↗
PubMed2006

Intensity-modulated radiotherapy in patients with locally advanced rectal cancer reduces volume of bowel treated to high dose levels.

PURPOSE: To investigate the potential for intensity-modulated radiotherapy (IMRT) to spare the bowel in rectal tumors. METHODS AND MATERIALS: The targets (pelvic nodal and rectal volumes), bowel, and bladder were outlined in 5 patients. All had conventional, three-dimensional conformal RT and forward-planned multisegment three-field IMRT plans compared with inverse-planned simultaneous integrated boost nine-field equally spaced IMRT plans. Equally spaced seven-field and five-field and five-field, customized, segmented IMRT plans were also evaluated. RESULTS: Ninety-five percent of the prescribed dose covered at least 95% of both planning target volumes using all but the conventional plan (mean primary and pelvic planning target volume receiving 95% of the prescribed dose was 32.8 +/- 13.7 Gy and 23.7 +/- 4.87 Gy, respectively), reflecting a significant lack of coverage. The three-field forward planned IMRT plans reduced the volume of bowel irradiated to 45 Gy and 50 Gy by 26% +/- 16% and 42% +/- 27% compared with three-dimensional conformal RT. Additional reductions to 69 +/- 51 cm(3) to 45 Gy and 20 +/- 21 cm(3) to 50 Gy were obtained with the nine-field equally spaced IMRT plans-64% +/- 11% and 64% +/- 20% reductions compared with three-dimensional conformal RT. Reducing the number of beams and customizing the angles for the five-field equally spaced IMRT plan did not significantly reduce bowel sparing. CONCLUSION: The bowel volume irradiated to 45 Gy and 50 Gy was significantly reduced with IMRT, which could potentially lead to less bowel toxicity. Reducing the number of beams did not reduce bowel sparing and the five-field customized segmented IMRT plan is a reasonable technique to be tested in clinical trials.

Humans↗
PubMed2006

Quantifying the effect of respiratory motion on lung tumour dosimetry with the aid of a breathing phantom with deforming lungs.

The contribution of organ and tumour motion to the degradation of planned dose distributions during radiotherapy to the breathing lung has been experimentally investigated and quantified. An anthropomorphic, tissue-equivalent breathing phantom with deformable lungs has been built, in which the lung tumour can be driven in any arbitrary 3D trajectory. The trajectory is programmed into a motion controller connected to a high-precision moving platform that is connected to the tumour. The motion controller is connected to the accelerator's dose counter and the speed of motion is scaled to the dose rate. This ensures consistent delivery despite variation in either the dose rate or inter-segment timing. For this study, the phantom was made to breathe by a set of periodic equations representing respiratory motion by an asymmetric, trigonometric function. Several motion amplitudes were selected to be applied in the primary axis of motion. Five three-dimensional, geometrically conformal (3DCRT) fractions with different starting phases (spaced uniformly in the breathing cycle) were delivered to the phantom and compared to a delivery where the phantom was static at the end-expiration position. A set of intensity-modulated radiotherapy plans (IMRT) was subsequently delivered in the same manner. Bigger amplitudes of motion resulted in a higher degree of dose blurring. Severe underdosages were observed when deliberately selecting the PTV wrongly, their extent being correlated with the degree of margin error. IMRT motion-averaged dose distributions exhibited areas of high dose in the gross tumour volume (GTV) which were not present in the static irradiations, arising from booster segments that the optimizer was creating to achieve planning target volume (PTV) homogeneity during the inverse-planning process. 3DCRT, on the other hand, did not demonstrate such effects. It has been concluded that care should be taken to control the delivered fluence when delivering IMRT to the breathing lung, even when the PTV margin has been adequately chosen to include the extent of the breathing motion.

Humans↗
PubMed2006

Comparison of forward planning with automated inverse planning for three-dimensional conformal radiotherapy of non-small cell lung cancer without IMRT.

The forward and inverse treatment plans of 10 patients with lung cancer were compared in terms of PTV coverage, sparing of normal lung and time required to generate a plan. The inverse planning produced as good treatment plans as an experienced dosimetrist with considerable reduction in staff time. When translated to other complex sites, inverse non-IMRT planning may have considerable impact on manpower requirements.

Algorithms↗
PubMed2006

Constrained segment shapes in direct-aperture optimization for step-and-shoot IMRT.

Previous studies have shown that, by optimizing segment shapes and weights directly, without explicitly optimizing fluence profiles, effective IMRT plans can be generated with fewer segments. This study proposes a method of direct-aperture optimization with aperture shape constraints, which is designed to provide segmental IMRT plans using a minimum of simple, regular segments. The method uses a cubic function to create smoothly curving multileaf collimator shapes. Constraints on segment dimension and equivalent square are applied, and each segment can be constrained to lie within the previous one, for easy generation of fluence profiles with a single maximum. To simply optimize the segment shapes and reject any shapes which violate the constraints is too inefficient, so an innovative method of feedback optimization is used to ensure in advance that viable aperture shapes are generated. The algorithm is demonstrated using a simple cylindrical phantom consisting of a hemi-annular planning target volume and a central cylindrical organ-at-risk. A simple IMRT rectum case is presented, where segments are used to replace a wedge. More complex cases of prostate and seminal vesicles and prostate and pelvic nodes are also shown. The algorithm produces effective plans in each case with three to five segments per beam. For the simple plans, the constraint that each segment should be contained within the previous one adds additional simplicity to the plan, for a small reduction in plan quality. This study confirms that direct-aperture optimization gives efficient solutions to the segmental IMRT inverse problem and provides a method for generating simple apertures. By using such a method, the workload of IMRT verification may be reduced and simplified, as verification of fluence profiles from individual beams may be eliminated.

Algorithms↗
PubMed2005

The incorporation of SPECT functional lung imaging into inverse radiotherapy planning for non-small cell lung cancer.

BACKGROUND AND PURPOSE: Patients with non-small cell lung cancer (NSCLC) often have inhomogeneous lung perfusion. Radiotherapy planning computed tomography (CT) scans have been accurately co-registered with lung perfusion single photon emission computed tomography (SPECT) scans to design radiotherapy treatments which limit dose to healthy 'perfused' lung. PATIENTS AND METHODS: Patients with localised NSCLC had CT and SPECT scans accurately co-registered in the planning system. The SPECT images were used to define a volume of perfused 'functioning' lung (FL). Inverse planning software was used to create 3D-conformal plans, the planning objective being either to minimise the dose to whole lungs (WL) or to minimise the dose to FL. RESULTS: Four plans were created for each of six patients. The mean difference in volume between WL and FL was 1011.7 cm(3) (range 596.2-1581.1cm(3)). One patient with bilateral upper lobe perfusion deficits had a 16% reduction in FLV(20) (the percentage volume of functioning lung receiving >or=20 Gy). The remaining patients had inhomogeneous perfusion deficits such that inverse planning was not able to sufficiently optimise beam angles to avoid functioning lung. CONCLUSION: SPECT perfusion images can be accurately co-registered with radiotherapy planning CT scans and may be helpful in creating treatment plans for patients with large perfusion deficits.

Carcinoma, Non-Small-Cell Lung↗
PubMed2005

Treatment of extensive scalp lesions with segmental intensity-modulated photon therapy.

PURPOSE: To compare static electron therapy, electron arc therapy, and photon intensity-modulated radiation therapy (IMRT) for treatment of extensive scalp lesions and to examine the dosimetric accuracy of the techniques. METHODS AND MATERIALS: A retrospective treatment-planning study was performed to evaluate the relative merits of static electron fields, arcing electron fields, and five-field photon IMRT. Thermoluminescent dosimeters (TLD) were used to verify the accuracy of the techniques. The required thickness of bolus was investigated, and an anthropomorphic phantom was also used to examine the effects of air gaps between the wax bolus used for the IMRT technique and the patient's scalp. RESULTS: Neither static nor arcing electron techniques were able to provide a reliable coverage of the planning target volume (PTV), owing to obliquity of the fields in relation to the scalp. The IMRT technique considerably improved PTV dose uniformity, though it irradiated a larger volume of brain. Either 0.5 cm or 1.0 cm of wax bolus was found to be suitable. Air gaps of up to 1 cm between the bolus and the patient's scalp were correctly handled by the treatment-planning system and had negligible influence on the dose to the scalp. CONCLUSIONS: Photon IMRT provides a feasible alternative to electron techniques for treatment of large scalp lesions, resulting in improved homogeneity of dose to the PTV but with a moderate increase in dose to the brain.

Aged↗
PubMed2005

Prediction of radiation-induced normal tissue complications in radiotherapy using functional image data.

The aim of this study has been to explicitly include the functional heterogeneity of an organ as a factor that contributes to the probability of complication of normal tissues following radiotherapy. Situations for which the inclusion of this information can be advantageous to the design of treatment plans are then investigated. A Java program has been implemented for this purpose. This makes use of a voxelated model of a patient, which is based on registered anatomical and functional data in order to enable functional voxel weighting. Using this model, the functional dose-volume histogram (fDVH) and the functional normal tissue complication probability (fNTCP) are then introduced as extensions to the conventional dose-volume histogram (DVH) and normal tissue complication probability (NTCP). In the presence of functional heterogeneity, these tools are physically more meaningful for plan evaluation than the traditional indices, as they incorporate additional information and are anticipated to show a better correlation with outcome. New parameters m(f), n(f) and TD(50f) are required to replace the m, n and TD(50) parameters. A range of plausible values was investigated, awaiting fitting of these new parameters to patient outcomes where functional data have been measured. As an example, the model is applied to two lung datasets utilizing accurately registered computed tomography (CT) and single photon emission computed tomography (SPECT) perfusion scans. Assuming a linear perfusion-function relationship, the biological index mean perfusion weighted lung dose (MPWLD) has been extracted from integration over outlined regions of interest. In agreement with the MPWLD ranking, the fNTCP predictions reveal that incorporation of functional imaging in radiotherapy treatment planning is most beneficial for organs with a large volume effect and large focal areas of dysfunction. There is, however, no additional advantage in cases presenting with homogeneous function. Although presented for lung radiotherapy, this model is general. It can also be applied to positron emission tomography (PET)-CT or functional magnetic resonance imaging (fMRI)-CT registered data and extended to the functional description of tumour control probability.

Algorithms↗
PubMed2005

Treatment planning evaluation of non-coplanar techniques for conformal radiotherapy of the prostate.

BACKGROUND AND PURPOSE: To evaluate the benefit of using non-coplanar treatment plans for irradiation of two different clinical treatment volumes: prostate only (PO) and the prostate plus seminal vesicles (PSV). MATERIAL AND METHODS: An inverse planning algorithm was used to produce three-field, four-field, five-field and six-field non-coplanar treatment plans without intensity-modulation in ten patients. These were compared against a three-field coplanar plan. A dose of 74 Gy was prescribed to the isocentre. Plans were compared using the minimum dose to the planning target volume (PTV), maximum dose to the small bowel, and irradiated volumes of rectum, bladder and femoral head. Biological indices were also evaluated. RESULTS: For the PO group, volume of rectum irradiated to 60 Gy (V(60)) was 22.5+/-3.7% for the coplanar plan, and 21.5+/-5.3% for the five-field non-coplanar plan, which was the most beneficial (p=0.3). For the PSV group, the five-field non-coplanar plan was again the most beneficial. Rectal V(60) was in this case reduced from 41.5+/-10.4% for the coplanar plan to 35.2+/-9.3% for the non-coplanar plan (p=0.02). CONCLUSIONS: The use of non-coplanar beams in conformal prostate radiotherapy provides a small increase in rectal sparing, more significantly with PSV volumes than for PO volumes.

Aged↗
PubMed2004

Verification of inverse planning and treatment delivery for segmental IMRT.

With intensity-modulated radiotherapy (IMRT), it is important that the inverse planning process yields the most appropriate dose distribution for the patient and that the delivered dose then corresponds to the planned dose. This paper presents methods by which the inverse planning and delivery of segmental (step-and-shoot) IMRT can be verified, and gives results for a typical treatment planning system (Pinnacle3 v6.2b, Philips Radiation Oncology Systems, Milpitas, CA). Inverse planning was assessed by observing the reduction in objective function as fields were successively added to three-field prostate, esophagus, and thyroid plans. The ability of the treatment planning system to calculate dose for a segmented field was examined by creating a stepped field with five successively narrowing segments. The complete planning process was then investigated by using two orthogonal IMRT fields to create a homogeneous dose distribution in a cubic water phantom. Finally, a clinical situation was simulated by creating a five-field segmental IMRT plan for a lung target in an anthropomorphic phantom. A conformal plan was also compared for context. Addition of fields to inverse plans generally resulted in a reduction of objective function, indicating consistency of inverse planning solutions. Planned dose for fields with stepped intensity agreed with ionization chamber measurements to within 5%. For orthogonal fields, planned dose distributions agreed well with dose measured using film and agreed with ionization chamber measurements to within 3%. For the anthropomorphic phantom, the standard deviation of difference between planned and measured dose was 4%. Although no consensus has yet been reached on what constitutes an acceptable IMRT plan, these results indicate that step-and-shoot IMRT can be planned and delivered using the system described with comparable accuracy to a standard conformal treatment.

Algorithms↗
PubMed2004

Segmentation of IMRT plans for radical lung radiotherapy delivery with the step-and-shoot technique.

The purpose of this work was to determine a segmentation protocol for the treatment of localized non-small-cell lung cancer (NSCLC) with intensity-modulated radiotherapy (IMRT) that is as effective as possible while practically simple and hence robust to known practical inaccuracies. This study focused on the stratification of continuous profiles into a discrete number of intensity levels. The selection of the segmentation parameters for the delivery of the fluence profiles using multiple static fields has been considered. Five-field equispaced IMRT treatment plans of five patients with NSCLC were selected. The study comprised nine treatment plans for each patient, starting from a conformal plan, optimizing it for IMRT and then segmenting it utilizing different numbers of segments in each case and optimizing for segment weights separately. A conformal plan, optimized for beam directions, collimator and wedge angles, was also used for comparison with the IMRT plans, so as to consider the best coplanar conformal case. A dose objective for the PTV and the organs-at-risk plus a constraint for the spinal cord were set for all inverse plans. All stages were compared with the aid of dose-volume histograms, dose distributions at the plane of the isocenter, intensity maps for key beams and plots of PTV homogeneity and overall conformality versus complexity. The unsegmented IMRT plans gave the best results but cannot be realized in practice with an MLC. They were best approximated by plans that needed 106-167 segments to deliver, but did not deteriorate significantly when approximated by plans which required 26-40 segments in total. All segmented IMRT plans gave a better lung sparing than the conformal plans, indicating that the deterioration of IMRT plans following segmentation is not equivalent to that of unmodulated, conformal plans. However, optimized conformal plans have the potential to approach the lung sparing achieved by segmented IMRT plans. Among the IMRT situations examined, five-field treatment plans for the lung, utilizing a maximum of 40 segments in total, have proven to give a good approximation of the IMRT plans with continuous modulation.

Algorithms↗
PubMed2003

Patient-specific planning for prevention of mechanical collisions during radiotherapy.

A common unwanted difficulty in treatment planning, especially in non-coplanar radiotherapy set-ups, is the potential collision of the rotating gantry with the couch and/or the patient's body. A technique and computer program that detects these and signals avoidance of such beam directions is presented. The problem was approached using analytical geometry. The separate components within the treatment room have either been measured and modelled for an Elekta linear accelerator, or read out from a Pinnacle3 treatment planning system and are represented as an integer grid of points in three-dimensional (3D) space. The module is attached to the treatment planning system and can provide rejection or acceptance of unwanted beam directions in a plan. In contrast to previous work that has only used patient models, each individual patient's outlines are considered here in their actual treatment position inclusive of any immobilization device. The extremities of the patient superiorly and inferiorly to the scanned region are simulated by an expanded version of the RANDO phantom. In this way, 'potential' collisions can be detected in addition to the certain ones. Patient position is not a limiting factor for the accuracy of the collision detection anymore, as each set-up is always created around the isocentre. Maps of allowed and forbidden zones within the treatment suite have been created by running the code for all possible gantry and couch angles for three commonly arising cases: a head and neck plan utilizing a small stereotactic collimator, a prostate plan with multileaf collimators and an abdominal plan with the lead tray attached. In the last case, the 3D map permitted significantly fewer set-up combinations. Good agreement between prediction and experiment confirmed the capability of the program and introduces a promising add-on for treatment planning.

Humans↗
PubMed2003

Class solutions for conformal external beam prostate radiotherapy.

PURPOSE: To determine a class solution coplanar plan from comparisons of three-field (3F), four-field (4F), and six-field (6F) plans in conformal non-intensity-modulated prostate radiotherapy. METHODS AND MATERIALS: Doses to two clinical target volumes, prostate only (PO) and prostate plus seminal vesicles (PSV) were evaluated in each of 10 patients using a variety of 3F, 4F, and 6F plans with a planning target volume margin of 10 mm. All plans were prescribed to 64 and 74 Gy. The class solution plan for each of 3F, 4F, and 6F was chosen from a variety of symmetrical and asymmetrical field arrangements that had been previously assessed. The class solution plans, 3F (0, 90, 270 degrees ), 4F (35, 90, 270, 325 degrees ), and 6F (50/lat/25) were compared with reference plans: 3F (0, 120, 240 degrees ), 4F (0, 90, 180, 270 degrees ), and 6F (55, 90, 125, 235, 270, 305 degrees ). Rectal volumes irradiated to greater than 50% (V(50)), 80% (V(80)), and 90% (V(90)) of the prescribed dose, normal tissue complication probabilities (NTCP) for rectum, bladder, and femoral heads (FH), and tumor control probabilities (TCP) were assessed. FH tolerance was set at 52 Gy to 10% volume. RESULTS: The field arrangement that gave the lowest irradiated rectal volume with acceptable bladder and FH doses was a 3F (0, 90, 270 degrees ) class solution plan. This plan gave a reduction in rectal V(80) of 1.2-12.4% for the PO group and 2.3-23.8% for the PSV group compared with the other plans. The reduction in rectal V(90) was 0.2-11.9% for the PO group and 1.5-23.3% for the PSV group using the 3F (0, 90, 270 degrees ) plan. This plan provided one of the lowest rectal NTCPs, but the difference was not significant when compared with the 4F class solution plan. When target volumes with 10-mm margins remain unchanged to 74 Gy, the irradiated rectal volumes for all plans were higher and rectal NTCPs can be trebled. CONCLUSION: The use of appropriate beam arrangements can provide a class solution plan using only 3 fields compared with 4 or 6 fields for the parameters considered. Both 3F (0, 90, 270 degrees ) and 4F (35, 90, 270, 325 degrees ) plans can be used as a class solution plan. Other practical issues that may influence the choice of class solution include delivery time with smaller number of fields, ease of verification, the use of 10-mm multileaf collimation vs. conformal blocks, and field shape fitting limitations when using dynamic wedges.

Adenocarcinoma↗
PubMed2003

A systematic study of techniques for elective cervical nodal irradiation with anterior or opposed anterior and posterior beams.

PURPOSE: To assess target coverage and dose homogeneity using conventional radiotherapy (RT) and intensity-modulated RT (IMRT) with anterior and posterior beams for elective irradiation of the cervical lymph nodes in patients with head and neck cancer. MATERIALS AND METHODS: A planning study was performed in six patients who had undergone radical RT for head and neck cancer. RT plans to irradiate the cervical lymph nodes using a single anterior field, or opposed anterior and posterior fields, with 6 or 10 MV photons were compared. Plans using IMRT for missing-tissue compensation were also studied. An algorithm was developed to guide clinicians to the most appropriate treatment technique depending on the nodal groups to be irradiated. RESULTS: With 6 MV single field (SF) irradiation significant under-dose (minimum dose <70% of prescription dose) was seen in nodal groups II and V, due to their posterior position. With SF 10 MV the mean dose to level II was higher (p<0.001) and dose homogeneity to levels Ib and II was improved. Using opposed fields (OF), minimum doses to the nodes in levels II and V were improved. OF using 10 MV showed significant advantage over 6 MV with reduction of maximum doses to levels II, III and V. SF 10 MV IMRT improved maximum doses to levels Ib and II compared to SF 6 MV IMRT. OF IMRT gave the best dose distributions with optimal mean dose and dose homogeneity. Beam energy made no difference with OF IMRT. CONCLUSIONS: The optimal technique for elective cervical node irradiation depends on the lymph node levels within the PTV. If irradiation of the level II or V nodes is required, then the OF IMRT technique with either 6 or 10 MV gives the best dose distributions. In the absence of IMRT, then OF conventional techniques are best. If the aim is to irradiate levels III and IV or level IV only, then 6 MV SF non-IMRT is the simplest technique.

Algorithms↗
PubMed2003

Elimination of importance factors for clinically accurate selection of beam orientations, beam weights and wedge angles in conformal radiation therapy.

A method of simultaneously optimizing beam orientations, beam weights, and wedge angles for conformal radiotherapy is presented. This method removes the need for importance factors by optimizing one objective only, subject to a set of rigid constraints. This facilitates the production of inverse solutions which, without trial-and-error modification of importance factors, precisely satisfy the specified constraints. The algorithm minimizes an objective function which is based upon the single objective to be optimized, but which is forced to an artificially high value when the constraints are not met, so that only satisfactory solutions are allowed. Due to the complex nature of the objective function space, including multiple local minima separated by large regions of plateau, a random search technique equivalent to fast simulated annealing is used for producing inverse plans. To illustrate the novel features of the new algorithm, a simulation is first presented, for the case of a cylindrical phantom. The morphology of the objective function space is shown to be significantly different for the new algorithm, compared to that for a conventional quadratic objective function. Clinical cases for prostate and craniopharyngioma are then presented. For the prostate case, the objective is to reduce irradiated rectal volume. Three-field, four-field, and six-field optimizations, with or without orientation optimization, are shown to provide solutions which are consistent with previously reported plans and class solutions. For the craniopharyngioma case, which involves the use of a high-precision stereotactic conformal technique, the objective is to reduce the irradiated volume of normal brain. Practically feasible beam angles are produced which, compared to a standard plan, provide a small but worthwhile sparing of normal brain. The algorithm is thereby shown to be robust and suitable for clinical application.

Algorithms↗
PubMed2002

Speed versus accuracy in a fast convolution photon dose calculation for conformal radiotherapy.

A convolution dose calculation for megavoltage photon beams is described and the compromise between speed and accuracy examined. The algorithm is suitable for treatment planning optimization, where the need is for a fast, flexible method requiring minimal beam data but providing an accurate result. The algorithm uses a simple tabular beam model, together with a discrete scatter kernel. These beam parameters are fitted either to a measured dose distribution, or to a dose distribution calculated using a more accurate dose calculation algorithm. The calculation is then applied to pelvic and thoracic conformal plans, and the results compared with those provided by a commercial radiotherapy treatment planning system (Pinnacle3, Philips Radiation Oncology Systems, Milpitas, CA), which has been verified against measurements. The calculation takes around 4 s to compute a 100 x 100 mm field, and agreement of the dose-volume histograms with the commercial treatment planning system is to within 5% dose or 8% volume. Use of a grid resolution coarser than 5 x 5 x 5 mm is found to be inaccurate, whereas calculating primary dose on a coarse grid and interpolating is found to increase speed without significantly reducing accuracy. Kernel resolution influences the speed and accuracy, but using 12 discrete points provides a fast result with a limited error. Thus, the algorithm is suitable for optimization applications.

Algorithms↗