Calculation and application of point spread functions for treatment planning with high energy photon beams

A dose calculation algorithm for boron neutron capture therapy using convolution/superposition method

The convolution/superposition (C/S) method originally designed for photon dose calculation was first applied for developing a treatment planning system for boron neutron capture therapy. The original concept of TEGMA (total energy generated per unit mass) was proposed to represent distinctive dose components from neutron reactions with the elements in the patient's tissue. First, neutron fluence distributions in a homogeneous brain phantom irradiated with an energy-groupwise pencil beam of 2.5 × 2.5 mm2 were calculated using the MCNP6.2 code. Then, a library of energy-groupwise TEGMA and KERMA were generated and stored in the developed C/S code. As a benchmark, dose distributions in a cuboid phantom and a human head phantom were calculated using the developed C/S and PHITS Monte Carlo codes. A neutron beam having a continuous epithermal spectrum and a square field of 22.5 × 22.5 mm2 or a circle field of 22.5 mm in diameter was assumed to be incident on the phantoms. The human head phantom was created by the pre-processing including the voxelization and transformation of test DICOM CT images. The differences in boron doses between C/S and MC ranged from 2% to 6%. In nitrogen doses, the differences were from 4% to 9%. A large discrepancy observed in hydrogen lateral dose profiles could be explained by the differences in cross-section data and recoil-proton transport algorithms of MCNP6.2 and PHITS. With isodose curves normalized at the center of the tumor in the human head phantom, they were almost identical in the range of 60%-110% for both cases. The C/S have underestimated the backscattering neutron and showed a larger absorbed dose gradient around 40% region. The calculation time of C/S using Intel i7-10700 processor was less than 1 min for both phantoms. The calculation time of PHITS using three Intel Xeon E5-2640 v4 processors was 15.5 min for the cuboid phantom and ∼380 min for the human head phantom. The proposed algorithm has the advantages of high speed while promising fair accuracy in BNCT dose calculations.

Accuracy Evaluation of Collapsed Cone Convolution Superposition Algorithms for the Nasopharynx Interface in the Early Stage of Nasopharyngeal Carcinoma

This study combined the use of radiation dosimeteric measurements and a custom-made anthropomorphic phantom in order to evaluate the accuracy of therapeutic dose calculations at the nasopharyngeal air-tissue interface. The doses at the nasopharyngeal air-tissue interface obtained utilizing the Pinnacle and TomoTherapy TPS, which are based on collapsed cone convolution superposition (CCCS) algorithms, were evaluated and measured under single $10\times 10\text{c}{\text{m}}^2$ , $2\times 2\text{c}{\text{m}}^2$ , two parallel opposed $2\times 2\text{c}{\text{m}}^2$ and clinical fields for early stage of nasopharyngeal carcinoma by using EBT3, GR-200F, and TLD 100. At the air-tissue interface under a $10\times 10\text{c}{\text{m}}^2$ field, the TPS dose calculation values were in good agreement with the dosimeter measurement with all differences within 3.5%. When measured the single field $2\times 2\text{c}{\text{m}}^2$ , the differences between the average dose were measured at the distal interface for EBT3, GR-200F, and TLD-100 and the calculation values were -15.8%, -16.4%, and -4.9%, respectively. When using the clinical techniques such as IMRT, VMAT, and tomotherapy, the measurement results at the interface for all three techniques did not imply under dose. Small-field sizes will lead to dose overestimation at the nasopharyngeal air-tissue interface due to electronic disequilibrium when using CCCS algorithms. However, under clinical applications of multiangle irradiation, the dose errors caused by this effect were not significant.

A novel analytical method for computing dose from kilovoltage beams used in Image-Guided radiation therapy

PURPOSE

A modified convolution/superposition algorithm is proposed to compute dose from the kilovoltage beams used in IGRT. The algorithm uses material-specific energy deposition kernels instead of water-energy deposition kernels.

METHODS

Monte Carlo simulation was used to model the Elekta XVI unit and determine dose deposition characteristics of its kilovoltage beams. The dosimetric results were compared with ion chamber measurements. The dose from the kilovoltage beams was then computed using convolution/superposition along with material-specific energy deposition kernels and compared with Monte Carlo and measurements. The material-specific energy deposition kernels were previously generated using Monte Carlo.

RESULTS

The obtained gamma indices (using 2%/2mm criteria for 95% of points) were lower than 1 in almost all instances which indicates good agreement between simulated and measured depth doses and profiles. The comparisons of the algorithm with measurements in a homogeneous solid water slab phantom, and that with Monte Carlo in a head and neck CT dataset produced acceptable results. The calculated point doses were within 4.2% of measurements in the homogeneous phantom. Gamma analysis of the calculated vs. Monte Carlo simulations in the head and neck phantom resulted in 94% of points passing with a 2%/2mm criteria.

CONCLUSIONS

The proposed method offers sufficient accuracy in kilovoltage beams dose calculations and has the potential to supplement the conventional megavoltage convolution/superposition algorithms for dose calculations in low energy range.

Introducing matrix sparsity with kernel truncation into dose calculations for fluence optimization

Deep learning algorithms for radiation therapy treatment planning automation require large patient datasets and complex architectures that often take hundreds of hours to train. Some of these algorithms require constant dose updating (such as with reinforcement learning) and may take days. When these algorithms rely on commerical treatment planning systems to perform dose calculations, the data pipeline becomes the bottleneck of the entire algorithm's efficiency. Further, uniformly accurate distributions are not always needed for the training and approximations can be introduced to speed up the process without affecting the outcome. These approximations not only speed up the calculation process, but allow for custom algorithms to be written specifically for the purposes of use in AI/ML applications where the dose and fluence must be calculated a multitude of times for a multitude of different situations. Here we present and investigate the effect of introducing matrix sparsity through kernel truncation on the dose calculation for the purposes of fluence optimzation within these AI/ML algorithms. The basis for this algorithm relies on voxel discrimination in which numerous voxels are pruned from the computationally expensive part of the calculation. This results in a significant reduction in computation time and storage. Comparing our dose calculation against calculations in both a water phantom and patient anatomy in Eclipse without heterogenity corrections produced gamma index passing rates around 99% for individual and composite beams with uniform fluence and around 98% for beams with a modulated fluence. The resulting sparsity introduces a reduction in computational time and space proportional to the square of the sparsity tolerance with a potential decrease in cost greater than 10 times that of a dense calculation allowing not only for faster caluclations but for calculations that a dense algorithm could not perform on the same system.

Dose Calculation Algorithms for External Radiation Therapy: An Overview for Practitioners

Radiation therapy (RT) is a constantly evolving therapeutic technique; improvements are continuously being introduced for both methodological and practical aspects. Among the features that have undergone a huge evolution in recent decades, dose calculation algorithms are still rapidly changing. This process is propelled by the awareness that the agreement between the delivered and calculated doses is of paramount relevance in RT, since it could largely affect clinical outcomes. The aim of this work is to provide an overall picture of the main dose calculation algorithms currently used in RT, summarizing their underlying physical models and mathematical bases, and highlighting their strengths and weaknesses, referring to the most recent studies on algorithm comparisons. This handy guide is meant to provide a clear and concise overview of the topic, which will prove useful in helping clinical medical physicists to perform their responsibilities more effectively and efficiently, increasing patient benefits and improving the overall quality of the management of radiation treatment.

Generation of material-specific energy deposition kernels for kilovoltage x-ray dose calculations

PURPOSE

Dose calculation of kilovoltage x rays used in Image-Guided Radiotherapy has been investigated in recent years using various methods. Among these methods are model-based ones that suffer from inaccuracies in high-density materials and at interfaces when used in the kilovoltage energy range. The main reason for this is the use of water energy deposition kernels and simplifications employed such as density scaling in heterogeneous media. The purpose of this study was to produce and characterize material-specific energy deposition kernels, which could be used for dose calculations in this energy range. These kernels will also have utility in dose calculations in superficial radiation therapy and orthovoltage beams utilized in small animal irradiators.

METHODS

Water energy deposition kernels with various resolutions; and high-resolution, material-specific energy deposition kernels were generated in the energy range of 10-150 kVp, using the EGSnrc Monte Carlo toolkit. The generated energy deposition kernels were further characterized by calculating the effective depth of penetration, the effective radial distance, and the effective lateral distance. A simple benchmarking of the kernels against Monte Caro calculations has also been performed.

RESULTS

There was good agreement with previously reported water kernels, as well as between kernels with different resolution. The evaluation of effective depth of penetration, and radial and laterals distances, defines the relationship between energy, material density, and the shape of the material-specific kernels. The shape of these kernels becomes more forwardly scattered as the energy and material density are increased. The comparison of the dose calculated using the kernels with Monte Carlo provides acceptable results.

CONCLUSIONS

Water and material-specific energy deposition kernels in the kilovoltage energy range have been generated, characterized, and compared to previous work. These kernels will have utility in dose calculations in this energy range once algorithms capable of employing them are fully developed.

Evaluating small field dosimetry with the Acuros XB (AXB) and analytical anisotropic algorithm (AAA) dose calculation algorithms in the eclipse treatment planning system

Background:

An increasing number of external beam treatment modalities including intensity modulated radiation therapy, volumetric modulated arc therapy (VMAT) and stereotactic radiosurgery uses very small fields for treatment planning and delivery. However, there are major challenges in small photon field dosimetry, due to the partial occlusion of the direct photon beam source’s view from the measurement point, lack of lateral charged particle equilibrium, steep dose-rate gradient and volume averaging effect of the detector response and variation of the energy fluence in the lateral direction of the beam. Therefore, experimental measurements of dosimetric parameters such as percent depth doses (PDDs), beam profiles and relative output factors (ROFs) for small fields continue to be a challenge.

Materials and Methods:

In this study, we used a homogeneous water phantom and the heterogeneous anthropomorphic stereotactic end-to-end verification (STEEV) head phantom for all dose measurements and calculations. PDDs, lateral dose profiles and ROFs were calculated in the Eclipse Treatment Planning System version 13·6 using the Acuros XB (AXB) and the analytical anisotropic algorithms (AAAs) in a homogenous water phantom. Monte Carlo (MC) simulations and measurements using the Exradin W1 Scintillator were also accomplished for four photon energies: 6 MV, 6FFF, 10 MV and 10FFF. Two VMAT treatment plans were generated for two different targets: one located in the brain and the other in the neck (close to the trachea) in the head phantom (CIRS, Norfolk, VA, USA). A Varian Truebeam linear accelerator (Varian, Palo Alto, CA, USA) was used for all treatment deliveries. Calculated results with AXB and AAA were compared with MC simulations and measurements.

Results:

The average difference of PDDs between W1 Exradin Scintillator measurements and MC simulations, AAA and AXB algorithm calculations were 1·2, 2·4 and 3·2%, respectively, for all field sizes and energies. AXB and AAA showed differences in ROF of about 0·3 and 2·9%, respectively, compared with W1 Exradin Scintillator measured values. For the target located in the brain in the head phantom, the average dose difference between W1 Exradin Scintillator and the MC simulations, AAA and AXB were 0·2, 3·2 and 2·7%, respectively, for all field sizes. Similarly, for the target located in the neck, the respective dose differences were 3·8, 5·7 and 3·5%.

Conclusion:

In this study, we compared dosimetric parameters such as PDD, beam profile and ROFs in water phantom and isocenter point dose measurements in an anthropomorphic head phantom representing a patient. We observed that measurements using the W1 Exradin scintillator agreed well with MC simulations and can be used efficiently for dosimetric parameters such as PDDs and dose profiles and patient-specific quality assurance measurements for small fields. In both homogenous and heterogeneous media, the AXB algorithm dose prediction agrees well with MC and measurements and was found to be superior to the AAA algorithm.

Integral dose based inverse optimization objective function promises lower toxicity in head-and-neck

PURPOSE

The voxels in a CT data sets contain density information. Besides its use in dose calculation density has no other application in modern radiotherapy treatment planning. This work introduces the use of density information by integral dose minimization in radiotherapy treatment planning for head-and-neck squamous cell carcinoma (HNSCC).

MATERIALS AND METHODS

Eighteen HNSCC cases were studied. For each case two intensity modulated radiotherapy (IMRT) plans were created: one based on dose-volume (DV) optimization, and one based on integral dose minimization (Energy hereafter) inverse optimization. The target objective functions in both optimization schemes were specified in terms of minimum, maximum, and uniform doses, while the organs at risk (OAR) objectives were specified in terms of DV- and Energy-objectives respectively. Commonly used dosimetric measures were applied to assess the performance of Energy-based optimization. In addition, generalized equivalent uniform doses (gEUDs) were evaluated. Statistical analyses were performed to estimate the performance of this novel inverse optimization paradigm.

RESULTS

Energy-based inverse optimization resulted in lower OAR doses for equivalent target doses and isodose coverage. The statistical tests showed dose reduction to the OARs with Energy-based optimization ranging from ∼2% to ∼15%.

CONCLUSIONS

Integral dose minimization based inverse optimization for HNSCC promises lower doses to nearby OARs. For comparable therapeutic effect the incorporation of density information into the optimization cost function allows reduction in the normal tissue doses and possibly in the risk and the severity of treatment related toxicities.

Hybrid dose calculation: a dose calculation algorithm for microbeam radiation therapy

Microbeam radiation therapy (MRT) is still a preclinical approach in radiation oncology that uses planar micrometre wide beamlets with extremely high peak doses, separated by a few hundred micrometre wide low dose regions. Abundant preclinical evidence demonstrates that MRT spares normal tissue more effectively than conventional radiation therapy, at equivalent tumour control. In order to launch first clinical trials, accurate and efficient dose calculation methods are an inevitable prerequisite. In this work a hybrid dose calculation approach is presented that is based on a combination of Monte Carlo and kernel based dose calculation. In various examples the performance of the algorithm is compared to purely Monte Carlo and purely kernel based dose calculations. The accuracy of the developed algorithm is comparable to conventional pure Monte Carlo calculations. In particular for inhomogeneous materials the hybrid dose calculation algorithm out-performs purely convolution based dose calculation approaches. It is demonstrated that the hybrid algorithm can efficiently calculate even complicated pencil beam and cross firing beam geometries. The required calculation times are substantially lower than for pure Monte Carlo calculations.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

A point kernel algorithm for microbeam radiation therapy

Microbeam radiation therapy (MRT) is a treatment approach in radiation therapy where the treatment field is spatially fractionated into arrays of a few tens of micrometre wide planar beams of unusually high peak doses separated by low dose regions of several hundred micrometre width. In preclinical studies, this treatment approach has proven to spare normal tissue more effectively than conventional radiation therapy, while being equally efficient in tumour control. So far dose calculations in MRT, a prerequisite for future clinical applications are based on Monte Carlo simulations. However, they are computationally expensive, since scoring volumes have to be small. In this article a kernel based dose calculation algorithm is presented that splits the calculation into photon and electron mediated energy transport, and performs the calculation of peak and valley doses in typical MRT treatment fields within a few minutes. Kernels are analytically calculated depending on the energy spectrum and material composition. In various homogeneous materials peak, valley doses and microbeam profiles are calculated and compared to Monte Carlo simulations. For a microbeam exposure of an anthropomorphic head phantom calculated dose values are compared to measurements and Monte Carlo calculations. Except for regions close to material interfaces calculated peak dose values match Monte Carlo results within 4% and valley dose values within 8% deviation. No significant differences are observed between profiles calculated by the kernel algorithm and Monte Carlo simulations. Measurements in the head phantom agree within 4% in the peak and within 10% in the valley region. The presented algorithm is attached to the treatment planning platform VIRTUOS. It was and is used for dose calculations in preclinical and pet-clinical trials at the biomedical beamline ID17 of the European synchrotron radiation facility in Grenoble, France.

Validation of the relative insensitivity of volumetric-modulated arc therapy (VMAT) plan quality to gantry space resolution

Volumetric-modulated arc therapy (VMAT) is an efficient form of radiotherapy used to deliver intensity-modulated radiotherapy beams. The aim of this study was to investigate the relative insensitivity of VMAT plan quality to gantry angle spacing (GS). Most previous VMAT planning and dosimetric work for GS resolution has been conducted for single arc VMAT. In this work, a quantitative comparison of dose-volume indices (DIs) was made for partial-, single- and double-arc VMAT plans optimized at 2°, 3° and 4° GS, representing a large variation in deliverable multileaf collimator segments. VMAT plans of six prostate cancer and six head-and-neck cancer patients were simulated for an Elekta SynergyS® Linac (Elekta Ltd, Crawley, UK), using the SmartArc™ module of Pinnacle³ TPS, (version 9.2, Philips Healthcare). All optimization techniques generated clinically acceptable VMAT plans, except for the single-arc for the head-and-neck cancer patients. Plan quality was assessed by comparing the DIs for the planning target volume, organs at risk and normal tissue. A GS of 2°, with finest resolution and consequently highest intensity modulation, was considered to be the reference, and this was compared with GS 3° and 4°. The differences between the majority of reference DIs and compared DIs were <2%. The metrics, such as treatment plan optimization time and pretreatment (phantom) dosimetric calculation time, supported the use of a GS of 4°. The ArcCHECK™ phantom-measured dosimetric agreement verifications resulted in a >95.0% passing rate, using the criteria for γ (3%, 3 mm). In conclusion, a GS of 4° is an optimal choice for minimal usage of planning resources without compromise of plan quality.

Dosimetric evaluation of synthetic CT for magnetic resonance-only based radiotherapy planning of lung cancer

Background

Interest in MR-only treatment planning for radiation therapy is growing rapidly with the emergence of integrated MRI/linear accelerator technology. The purpose of this study was to evaluate the feasibility of using synthetic CT images generated from conventional Dixon-based MRI scans for radiation treatment planning of lung cancer.

Methods

Eleven patients who underwent whole-body PET/MR imaging following a PET/CT exam were randomly selected from an ongoing prospective IRB-approved study. Attenuation maps derived from the Dixon MR Images and atlas-based method was used to create CT data (synCT). Treatment planning for radiation treatment of lung cancer was optimized on the synCT and subsequently copied to the registered CT (planCT) for dose calculation. Planning target volumes (PTVs) with three sizes and four different locations in the lung were planned for irradiation. The dose-volume metrics comparison and 3D gamma analysis were performed to assess agreement between the synCT and CT calculated dose distributions.

Results

Mean differences between PTV doses on synCT and CT across all the plans were −0.1% ± 0.4%, 0.1% ± 0.5%, and 0.4% ± 0.5% for D95, D98 and D100, respectively. Difference in dose between the two datasets for organs at risk (OARs) had average differences of −0.14 ± 0.07 Gy, 0.0% ± 0.1%, and −0.1% ± 0.2% for maximum spinal cord, lung V20, and heart V40 respectively. In patient groups based on tumor size and location, no significant differences were observed in the PTV and OARs dose-volume metrics (p > 0.05), except for the maximum spinal-cord dose when the target volumes were located at the lung apex (p = 0.001). Gamma analysis revealed a pass rate of 99.3% ± 1.1% for 2%/2 mm (dose difference/distance to agreement) acceptance criteria in every plan.

Conclusions

The synCT generated from Dixon-based MRI allows for dose calculation of comparable accuracy to the standard CT for lung cancer treatment planning. The dosimetric agreement between synCT and CT calculated doses warrants further development of a MR-only workflow for radiotherapy of lung cancer.

A review of uncertainties in radiotherapy dose reconstruction and their impacts on dose-response relationships

Proper understanding of the risk of radiation-induced late effects for patients receiving external photon beam radiotherapy requires the determination of reliable dose-response relationships. Although significant efforts have been devoted to improving dose estimates for the study of late effects, the most often questioned explanatory variable is still the dose. In this work, based on a literature review, we provide an in-depth description of the radiotherapy dose reconstruction process for the study of late effects. In particular, we focus on the identification of the main sources of dose uncertainty involved in this process and summarise their impacts on the dose-response relationship for radiotherapy late effects. We provide a number of recommendations for making progress in estimating the uncertainties in current studies of radiotherapy late effects and reducing these uncertainties in future studies.

Investigation of various energy deposition kernel refinements for the convolution∕superposition method

PURPOSE

Several simplifications used in clinical implementations of the convolution∕superposition (C∕S) method, specifically, density scaling of water kernels for heterogeneous media and use of a single polyenergetic kernel, lead to dose calculation inaccuracies. Although these weaknesses of the C∕S method are known, it is not well known which of these simplifications has the largest effect on dose calculation accuracy in clinical situations. The purpose of this study was to generate and characterize high-resolution, polyenergetic, and material-specific energy deposition kernels (EDKs), as well as to investigate the dosimetric impact of implementing spatially variant polyenergetic and material-specific kernels in a collapsed cone C∕S algorithm.

METHODS

High-resolution, monoenergetic water EDKs and various material-specific EDKs were simulated using the EGSnrc Monte Carlo code. Polyenergetic kernels, reflecting the primary spectrum of a clinical 6 MV photon beam at different locations in a water phantom, were calculated for different depths, field sizes, and off-axis distances. To investigate the dosimetric impact of implementing spatially variant polyenergetic kernels, depth dose curves in water were calculated using two different implementations of the collapsed cone C∕S method. The first method uses a single polyenergetic kernel, while the second method fully takes into account spectral changes in the convolution calculation. To investigate the dosimetric impact of implementing material-specific kernels, depth dose curves were calculated for a simplified titanium implant geometry using both a traditional C∕S implementation that performs density scaling of water kernels and a novel implementation using material-specific kernels.

RESULTS

For our high-resolution kernels, we found good agreement with the Mackie et al. kernels, with some differences near the interaction site for low photon energies (<500 keV). For our spatially variant polyenergetic kernels, we found that depth was the most dominant factor affecting the pattern of energy deposition; however, the effects of field size and off-axis distance were not negligible. For the material-specific kernels, we found that as the density of the material increased, more energy was deposited laterally by charged particles, as opposed to in the forward direction. Thus, density scaling of water kernels becomes a worse approximation as the density and the effective atomic number of the material differ more from water. Implementation of spatially variant, polyenergetic kernels increased the percent depth dose value at 25 cm depth by 2.1%-5.8% depending on the field size, while implementation of titanium kernels gave 4.9% higher dose upstream of the metal cavity (i.e., higher backscatter dose) and 8.2% lower dose downstream of the cavity.

CONCLUSIONS

Of the various kernel refinements investigated, inclusion of depth-dependent and metal-specific kernels into the C∕S method has the greatest potential to improve dose calculation accuracy. Implementation of spatially variant polyenergetic kernels resulted in a harder depth dose curve and thus has the potential to affect beam modeling parameters obtained in the commissioning process. For metal implants, the C∕S algorithms generally underestimate the dose upstream and overestimate the dose downstream of the implant. Implementation of a metal-specific kernel mitigated both of these errors.

A new approach for dose calculation in targeted radionuclide therapy (TRT) based on collapsed cone superposition: validation with (90)Y

To speed-up the absorbed dose (AD) computation while accounting for tissue heterogeneities, a Collapsed Cone (CC) superposition algorithm was developed and validated for (90)Y. The superposition was implemented with an Energy Deposition Kernel scaled with the radiological distance, along with CC acceleration. The validation relative to Monte Carlo simulations was performed on 6 phantoms involving soft tissue, lung and bone, a radioembolisation treatment and a simulated bone metastasis treatment. As a figure of merit, the relative AD difference (ΔAD) in low gradient regions (LGR), distance to agreement (DTA) in high gradient regions and the γ(1%,1 mm) criterion were used for the phantoms. Mean organ doses and γ(3%,3 mm) were used for the patient data. For the semi-infinite sources, ΔAD in LGR was below 1%. DTA was below 0.6 mm. All profiles verified the γ(1%,1 mm) criterion. For both clinical cases, mean doses differed by less than 1% for the considered organs and all profiles verified the γ(3%,3 mm). The calculation time was below 4 min on a single processor for CC superposition and 40 h on a 40 nodes cluster for MCNP (10(8) histories). Our results show that the CC superposition is a very promising alternative to MC for (90)Y dosimetry, while significantly reducing computation time.

Forcing lateral electron disequilibrium to spare lung tissue: a novel technique for stereotactic body radiation therapy of lung cancer

Stereotactic body radiation therapy (SBRT) has quickly become a preferred treatment option for early-stage lung cancer patients who are ineligible for surgery. This technique uses tightly conformed megavoltage (MV) x-ray beams to irradiate a tumour with ablative doses in only a few treatment fractions. Small high energy x-ray fields can cause lateral electron disequilibrium (LED) to occur within low density media, which can reduce tumour dose. These dose effects may be challenging to predict using analytic dose calculation algorithms, especially at higher beam energies. As a result, previous authors have suggested using low energy photons (<10 MV) and larger fields (>5 × 5 cm(2)) for lung cancer patients to avoid the negative dosimetric effects of LED. In this work, we propose a new form of SBRT, described as LED-optimized SBRT (LED-SBRT), which utilizes radiotherapy (RT) parameters designed to cause LED to advantage. It will be shown that LED-SBRT creates enhanced dose gradients at the tumour/lung interface, which can be used to manipulate tumour dose, and/or normal lung dose. To demonstrate the potential benefits of LED-SBRT, the DOSXYZnrc (National Research Council of Canada, Ottawa, ON) Monte Carlo (MC) software was used to calculate dose within a cylindrical phantom and a typical lung patient. 6 MV or 18 MV x-ray fields were focused onto a small tumour volume (diameter ∼1 cm). For the phantom, square fields of 1 × 1 cm(2), 3 × 3 cm(2), or 5 × 5 cm(2) were applied. However, in the patient, 3 × 1 cm(2), 3 × 2 cm(2), 3 × 2.5 cm(2), or 3 × 3 cm(2) field sizes were used in simulations to assure target coverage in the superior-inferior direction. To mimic a 180° SBRT arc in the (symmetric) phantom, a single beam profile was calculated, rotated, and beams were summed at 1° segments to accumulate an arc dose distribution. For the patient, a 360° arc was modelled with 36 equally weighted (and spaced) fields focused on the tumour centre. A planning target volume (PTV) was generated by considering the extent of tumour motion over the patient's breathing cycle and set-up uncertainties. All patient dose results were normalized such that at least 95% of the PTV received at least 54 Gy (i.e. D95 = 54 Gy). Further, we introduce 'LED maps' as a novel clinical tool to compare the magnitude of LED resulting from the various SBRT arc plans. Results from the phantom simulation suggest that the best lung sparing occurred for RT parameters that cause severe LED. For equal tumour dose coverage, normal lung dose (2 cm outside the target region) was reduced from 92% to 23%, comparing results between the 18 MV (5 × 5 cm(2)) and 18 MV (1 × 1 cm(2)) arc simulations. In addition to reduced lung dose for the 18 MV (1 × 1 cm(2)) arc, maximal tumour dose increased beyond 125%. Thus, LED can create steep dose gradients to spare normal lung, while increasing tumour dose levels (if desired). In the patient simulation, a LED-optimized arc plan was designed using either 18 MV (3 × 1 cm(2)) or 6 MV (3 × 3cm(2)) beams. Both plans met the D95 dose coverage requirement for the target. However, the LED-optimized plan increased the maximum, mean, and minimum dose within the PTV by as much as 80 Gy, 11 Gy, and 3 Gy, respectively. Despite increased tumour dose levels, the 18 MV (3 × 1 cm(2)) arc plan improved or maintained the V20, V5, and mean lung dose metrics compared to the 6 MV (3 × 3 cm(2)) simulation. We conclude that LED-SBRT has the potential to increase dose gradients, and dose levels within a small lung tumour. The magnitude of tumour dose increase or lung sparing can be optimized through manipulation of RT parameters (e.g. beam energy and field size).

3D dose reconstruction for narrow beams using ion chamber array measurements

3D dose reconstruction is a verification of the delivered absorbed dose. Our aim was to describe and evaluate a 3D dose reconstruction method applied to phantoms in the context of narrow beams. A solid water phantom and a phantom containing a bone-equivalent material were irradiated on a 6 MV linac. The transmitted dose was measured by using one array of a 2D ion chamber detector. The dose reconstruction was obtained by an iterative algorithm. A phantom set-up error and organ interfraction motion were simulated to test the algorithm sensitivity. In all configurations convergence was obtained within three iterations. A local reconstructed dose agreement of at least 3% / 3mm with respect to the planned dose was obtained, except in a few points of the penumbra. The reconstructed primary fluences were consistent with the planned ones, which validates the whole reconstruction process. The results validate our method in a simple geometry and for narrow beams. The method is sensitive to a set-up error of a heterogeneous phantom and interfraction heterogeneous organ motion.

The effect of gantry spacing resolution on plan quality in a single modulated arc optimization

Volumetric‐modulated arc technique (VMAT) is an efficient form of IMRT delivery. It is advantageous over conventional IMRT in terms of treatment delivery time. This study investigates the relation between the number of segments and plan quality in VMAT optimization for a single modulated arc. Five prostate, five lung, and five head‐and‐neck (HN) patient plans were studied retrospectively. For each case, four VMAT plans were generated. The plans differed only in the number of control points used in the optimization process. The control points were spaced 2°, 3°, 4°, and 6° apart, respectively. All of the optimization parameters were the same among the four schemes. The 2° spacing plan was used as a reference to which the other three plans were compared. The plan quality was assessed by comparison of dose indices (DIs) and generalized equivalent uniform doses (gEUDs) for targets and critical structures. All optimization schemes generated clinically acceptable plans. The differences between the majority of reference and compared DIs and gEUDs were within 3%. DIs and gEUDs which differed in excess of 3% corresponded to dose levels well below the organ tolerances. The DI and the gEUD differences increased with an increase in plan complexity from prostates to HNs. Optimization with gantry spacing resolution of 4° seems to be a very balanced alternative between plan quality and plan complexity.

PACS number: 87.55.de

Biological optimization in volumetric modulated arc radiotherapy for prostate carcinoma

PURPOSE

To investigate the potential benefits achievable with biological optimization for modulated volumetric arc (VMAT) treatments of prostate carcinoma.

METHODS AND MATERIALS

Fifteen prostate patient plans were studied retrospectively. For each case, planning target volume, rectum, and bladder were considered. Three optimization schemes were used: dose-volume histogram (DVH) based, generalized equivalent uniform dose (gEUD) based, and mixed DVH/gEUD based. For each scheme, a single or dual 6-MV, 356° VMAT arc was used. The plans were optimized with Pinnacle(3) (v. 9.0 beta) treatment planning system. For each patient, the optimized dose distributions were normalized to deliver the same prescription dose. The quality of the plans was evaluated by dose indices (DIs) and gEUDs for rectum and bladder. The tallied DIs were D(1%), D(15%), D(25%), and D(40%), and the tallied gEUDs were for a values of 1 and 6. Statistical tests were used to quantify the magnitude and the significance of the observed differences. Monitor units and treatment times for each optimization scheme were also assessed.

RESULTS

All optimization schemes generated clinically acceptable plans. The statistical tests indicated that biological optimization yielded increased organs-at-risk sparing, ranging from ~1% to more than ~27% depending on the tallied DI, gEUD, and anatomical structure. The increased sparing was at the expense of longer treatment times and increased number of monitor units.

CONCLUSIONS

Biological optimization can significantly increase the organs-at-risk sparing in VMAT optimization for prostate carcinoma. In some particular cases, however, the DVH-based optimization resulted in superior treatment plans.

Dosimetric accuracy of tomotherapy dose calculation in thorax lesions

BACKGROUND

To analyse limits and capabilities in dose calculation of collapsed-cone-convolution (CCC) algorithm implemented in helical tomotherapy (HT) treatment planning system for thorax lesions.

METHODS

The agreement between measured and calculated dose was verified both in homogeneous (Cheese Phantom) and in a custom-made inhomogeneous phantom. The inhomogeneous phantom was employed to mimic a patient's thorax region with lung density encountered in extreme cases and acrylic inserts of various dimensions and positions inside the lung cavity. For both phantoms, different lung treatment plans (single or multiple metastases and targets in the mediastinum) using HT technique were simulated and verified. Point and planar dose measurements, both with radiographic extended-dose-range (EDR2) and radiochromic external-beam-therapy (EBT2) films, were performed. Absolute point dose measurements, dose profile comparisons and quantitative analysis of gamma function distributions were analyzed.

RESULTS

An excellent agreement between measured and calculated dose distributions was found in homogeneous media, both for point and planar dose measurements. Absolute dose deviations <3% were found for all considered measurement points, both inside the PTV and in critical structures. Very good results were also found for planar dose distribution comparisons, where at least 96% of all points satisfied the gamma acceptance criteria (3%-3 mm), both for EDR2 and for EBT2 films. Acceptable results were also reported for the inhomogeneous phantom. Similar point dose deviations were found with slightly worse agreement for the planar dose distribution comparison: 96% of all points passed the gamma analysis test with acceptable levels of 4%-4 mm and 5%-4 mm, for EDR2 and EBT2 films respectively. Lower accuracy was observed in high dose/low density regions, where CCC seems to overestimate the measured dose around 4-5%.

CONCLUSIONS

Very acceptable accuracy was found for complex lung treatment plans calculated with CCC algorithm implemented in the tomotherapy TPS even in the heterogeneous phantom with very low lung-density.

Tissue heterogeneity in IMRT dose calculation for lung cancer

The aim of this study was to evaluate the differences in accuracy of dose calculation between 3 commonly used algorithms, the Pencil Beam algorithm (PB), the Anisotropic Analytical Algorithm (AAA), and the Collapsed Cone Convolution Superposition (CCCS) for intensity-modulated radiation therapy (IMRT). The 2D dose distributions obtained with the 3 algorithms were compared on each CT slice pixel by pixel, using the MATLAB code (The MathWorks, Natick, MA) and the agreement was assessed with the γ function. The effect of the differences on dose-volume histograms (DVHs), tumor control, and normal tissue complication probability (TCP and NTCP) were also evaluated, and its significance was quantified by using a nonparametric test. In general PB generates regions of over-dosage both in the lung and in the tumor area. These differences are not always in DVH of the lung, although the Wilcoxon test indicated significant differences in 2 of 4 patients. Disagreement in the lung region was also found when the Γ analysis was performed. The effect on TCP is less important than for NTCP because of the slope of the curve at the level of the dose of interest. The effect of dose calculation inaccuracy is patient-dependent and strongly related to beam geometry and to the localization of the tumor. When multiple intensity-modulated beams are used, the effect of the presence of the heterogeneity on dose distribution may not always be easily predictable.

Towards real-time radiation therapy: GPU accelerated superposition/convolution

We demonstrate the use of highly parallel graphics processing units (GPUs) to accelerate the superposition/convolution (S/C) algorithm to interactive rates while reducing the number of approximations. S/C first transports the incident fluence to compute the total energy released per unit mass (TERMA) grid. Dose is then calculated by superimposing the dose deposition kernel at each point in the TERMA grid and summing the contributions to the surrounding voxels. The TERMA algorithm was enhanced with physically correct multi-spectral attenuation and a novel inverse formulation for increased performance, accuracy and simplicity. Dose deposition utilized a tilted poly-energetic inverse cumulative-cumulative kernel, with the novel option of using volumetric mip-maps to approximate solid angle ray casting. Exact radiological path ray casting decreased discretization errors. We achieved a speedup of 34x-98x over a highly optimized CPU implementation.

Variations of lung density and geometry on inhomogeneity correction algorithms: a Monte Carlo dosimetric evaluation

This work contributed the following new information to the study of inhomogeneity correction algorithm: (1) Evaluation of lung dose calculation methods as a function of lung relative electron density (rhoe,lung) and treatment geometry and (2) comparison of doses calculated using the collapsed cone convolution (CCC) and adaptive convolution (AC) in lung using the Monte Carlo (MC) simulation with the EGSnrc-based code. The variations of rhoe,lung and geometry such as the position and dimension of the lung were studied with different photon beam energies and field sizes. Three groups of inhomogeneous lung phantoms, namely, "slab," "column," and "cube," with different positions, volumes, and shapes of lung in water as well as clinical computed tomography lung images were used. The rhoe,lung in each group of phantoms vary from 0.05 to 0.7. 6 and 18 MV photon beams with small (4 x 4 cm2) and medium (10 x 10 cm2) field sizes produced by a Varian 21 EX linear accelerator were used. This study reveals that doses in the inhomogeneous lung calculated by the CCC match well with those by AC within +/- 1%, indicating that the AC, with an advantage of shorter computing times (three to four times shorter than CCC), is a good substitute for CCC. Comparing the CCC and AC to MC in general, significant dose deviations are found when the rhoe,lung is < or =0.3. The degree of deviation depends on the photon beam energy and field size and is relatively large when high-energy photon beams with small fields are used. For penumbra widths (20%-80%), the CCC and AC agree well with MC for the slab and cube phantoms with the lung volumes at the central beam axis (CAX). However, deviations (>2 mm) occur in the column phantoms, with two lung volumes separated by a unit density column along the CAX in the middle using the 18 MV beam with 4 x 4 cm2 field for rhoe,lung < or =0.1. This study provides new dosimetric data to evaluate the impact of the variations of rhoe,lung and geometry on dose calculations in inhomogeneous media using CCC and AC.

Evaluation of dose prediction errors and optimization convergence errors of deliverable-based head-and-neck IMRT plans computed with a superposition/convolution dose algorithm

The purpose of this study is to evaluate dose prediction errors (DPEs) and optimization convergence errors (OCEs) resulting from use of a superposition/convolution dose calculation algorithm in deliverable intensity-modulated radiation therapy (IMRT) optimization for head-and-neck (HN) patients. Thirteen HN IMRT patient plans were retrospectively reoptimized. The IMRT optimization was performed in three sequential steps: (1) fast optimization in which an initial nondeliverable IMRT solution was achieved and then converted to multileaf collimator (MLC) leaf sequences; (2) mixed deliverable optimization that used a Monte Carlo (MC) algorithm to account for the incident photon fluence modulation by the MLC, whereas a superposition/convolution (SC) dose calculation algorithm was utilized for the patient dose calculations; and (3) MC deliverable-based optimization in which both fluence and patient dose calculations were performed with a MC algorithm. DPEs of the mixed method were quantified by evaluating the differences between the mixed optimization SC dose result and a MC dose recalculation of the mixed optimization solution. OCEs of the mixed method were quantified by evaluating the differences between the MC recalculation of the mixed optimization solution and the final MC optimization solution. The results were analyzed through dose volume indices derived from the cumulative dose-volume histograms for selected anatomic structures. Statistical equivalence tests were used to determine the significance of the DPEs and the OCEs. Furthermore, a correlation analysis between DPEs and OCEs was performed. The evaluated DPEs were within +/- 2.8% while the OCEs were within 5.5%, indicating that OCEs can be clinically significant even when DPEs are clinically insignificant. The full MC-dose-based optimization reduced normal tissue dose by as much as 8.5% compared with the mixed-method optimization results. The DPEs and the OCEs in the targets had correlation coefficients greater than 0.71, and there was no correlation for the organs at risk. Because full MC-based optimization results in lower normal tissue doses, this method proves advantageous for HN IMRT optimization.

Design of mini phantom and measurement of cobalt-60 beam data parameters

Low cost mini phantoms were fabricated indigenously with different water equivalent material such as polymethyl methacrylate and Bee's wax of different shapes (with dome top surface and flat top surface). The beam parameters of the Co-60 machine, such as head scatter correction factor (S_h), phantom scatter correction factor (S_P), total scatter correction factor (S_C,P), collimator exchange effect were measured. Output ratio measurements were taken for both mini phantom and water phantom for different square and rectangular field sizes. Normalized output ratios were compared with ESTRO published values and (Storchi and Van Gasteren) S and G data. The percentage of variation between the measured and the literature values is about 0.7%. Collimator exchange effect were measured for water and mini phantom for different field size, were compared with ESTRO value. This was found to be 0.5% and 1.0% respectively. Phantom scatter correction factors were calculated for square and rectangular filed sizes; this was compared with ESTRO values, found to be 0.7% for square and 1.0% for rectangular filed size. It was also noted that there were no appreciable variation observed in ion chamber readings of different materials of mini phantoms for dome and flat surfaces. Mini phantom measurements were done for all types of phantoms and the measured values were compared with the existing data and they were in good agreement with the published values.

Development of dose delivery verification by PET imaging of photonuclear reactions following high energy photon therapy

A method for dose delivery monitoring after high energy photon therapy has been investigated based on positron emission tomography (PET). The technique is based on the activation of body tissues by high energy bremsstrahlung beams, preferably with energies well above 20 MeV, resulting primarily in 11C and 15O but also 13N, all positron-emitting radionuclides produced by photoneutron reactions in the nuclei of 12C, 16O and 14N. A PMMA phantom and animal tissue, a frozen hind leg of a pig, were irradiated to 10 Gy and the induced positron activity distributions were measured off-line in a PET camera a couple of minutes after irradiation. The accelerator used was a Racetrack Microtron at the Karolinska University Hospital using 50 MV scanned photon beams. From photonuclear cross-section data integrated over the 50 MV photon fluence spectrum the predicted PET signal was calculated and compared with experimental measurements. Since measured PET images change with time post irradiation, as a result of the different decay times of the radionuclides, the signals from activated 12C, 16O and 14N within the irradiated volume could be separated from each other. Most information is obtained from the carbon and oxygen radionuclides which are the most abundant elements in soft tissue. The predicted and measured overall positron activities are almost equal (-3%) while the predicted activity originating from nitrogen is overestimated by almost a factor of two, possibly due to experimental noise. Based on the results obtained in this first feasibility study the great value of a combined radiotherapy-PET-CT unit is indicated in order to fully exploit the high activity signal from oxygen immediately after treatment and to avoid patient repositioning. With an RT-PET-CT unit a high signal could be collected even at a dose level of 2 Gy and the acquisition time for the PET could be reduced considerably. Real patient dose delivery verification by means of PET imaging seems to be applicable provided that biological transport processes such as capillary blood flow containing mobile 15O and 11C in the activated tissue volume can be accounted for.

Fifty years of Monte Carlo simulations for medical physics

Monte Carlo techniques have become ubiquitous in medical physics over the last 50 years with a doubling of papers on the subject every 5 years between the first PMB paper in 1967 and 2000 when the numbers levelled off. While recognizing the many other roles that Monte Carlo techniques have played in medical physics, this review emphasizes techniques for electron-photon transport simulations. The broad range of codes available is mentioned but there is special emphasis on the EGS4/EGSnrc code system which the author has helped develop for 25 years. The importance of the 1987 Erice Summer School on Monte Carlo techniques is highlighted. As an illustrative example of the role Monte Carlo techniques have played, the history of the correction for wall attenuation and scatter in an ion chamber is presented as it demonstrates the interplay between a specific problem and the development of tools to solve the problem which in turn leads to applications in other areas.

History of tomotherapy

Tomotherapy is the delivery of intensity modulated radiation therapy using rotational delivery of a fan beam in the manner of a CT scanner. In helical tomotherapy the couch and gantry are in continuous motion akin to a helical CT scanner. Helical tomotherapy is inherently capable of acquiring CT images of the patient in treatment position and using this information for image guidance. This review documents technological advancements of the field concentrating on the conceptual beginnings through to its first clinical implementation. The history of helical tomotherapy is also a story of technology migration from academic research to a university-industrial partnership, and finally to commercialization and widespread clinical use.

Beam modeling and verification of a photon beam multisource model

Dose calculations for treatment planning of photon beam radiotherapy require a model of the beam to drive the dose calculation models. The beam shaping process involves scattering and filtering that yield radiation components which vary with collimator settings. The necessity to model these components has motivated the development of multisource beam models. We describe and evaluate clinical photon beam modeling based on multisource models, including lateral beam quality variations. The evaluation is based on user data for a pencil kernel algorithm and a point kernel algorithm (collapsed cone) used in the clinical treatment planning systems Helax-TMS and Nucletron-Oncentra. The pencil kernel implementations treat the beam spectrum as lateral invariant while the collapsed cone involves off axis softening of the spectrum. Both algorithms include modeling of head scatter components. The parameters of the beam model are derived from measured beam data in a semiautomatic process called RDH (radiation data handling) that, in sequential steps, minimizes the deviations in calculated dose versus the measured data. The RDH procedure is reviewed and the results of processing data from a large number of treatment units are analyzed for the two dose calculation algorithms. The results for both algorithms are similar, with slightly better results for the collapsed cone implementations. For open beams, 87% of the machines have maximum errors less than 2.5%. For wedged beams the errors were found to increase with increasing wedge angle. Internal, motorized wedges did yield slightly larger errors than external wedges. These results reflect the increased complexity, both experimentally and computationally, when wedges are used compared to open beams.

A finite size pencil beam for IMRT dose optimization

Dose optimization for intensity modulated radiotherapy (IMRT) using small field elements (beamlets) requires the computation of a large number of very small, often only virtual fields of typically a few mm to 1 cm in size. The primary requirements for a suitable dose computation algorithm are (1) speed and (2) proper consideration of the penumbra of the fields which are composed of these beamlets. Here, a finite size pencil beam (fsPB) algorithm is proposed which was specifically designed for the purpose of beamlet-based IMRT. The algorithm employs an analytical function for the cross-profiles of the beamlets which is based on the assumption of self-consistency, i.e. the requirement that an arbitrary superposition of abutting beamlets should add up to a homogeneous field. The depth dependence is stored in tables derived from Monte Carlo computed dose distributions. It is demonstrated that the algorithm produces accurately the output factors and cross-profiles of typical multi-leaf-shaped segments. Due to the accurate penumbra model, the dose distribution features physically feasible gradients at any stage of the iterative optimization, which eliminates the problem of large discrepancies in normal tissue dose due to misaligned gradients between optimized and recomputed treatment plans.

Calculation of photon energy deposition kernels and electron dose point kernels in water

Effects of changes in the physics of EGSnrc compared to EGS4/PRESTA on energy deposition kernels for monoenergetic photons and on dose point kernels for beta sources in water are investigated. In the diagnostic energy range, Compton binding corrections were found to increase the primary energy fraction up to 4.5% at 30 keV with a corresponding reduction of the scatter component of the kernels. Rayleigh scattered photons significantly increase the scatter component of the kernels and reduce the primary energy fraction with a maximum 12% reduction also at 30 keV where the Rayleigh cross section in water has its maximum value. Sampling the photo-electron angular distribution produces a redistribution of the energy deposited by primaries around the interaction site causing differences of up to 2.7 times in the backscattered energy fraction at 20 keV. Above the pair production threshold, the dose distribution versus angle of the primary dose component is significantly different from the EGS4 results. This is related to the more accurate angular sampling of the electron-positron pair direction in EGSnrc as opposed to using a fixed angle approximation in default EGS4. Total energy fractions for photon beams obtained with EGSnrc and EGS4 are almost the same within 0.2%. This fact suggests that the estimate of the total dose at a given point inside an infinite homogeneous water phantom irradiated by broad beams of photons will be very similar for kernels calculated with both codes. However, at interfaces or near boundaries results can be very different especially in the diagnostic energy range. EGSnrc calculated kernels for monoenergetic electrons (50 keV, 100 keV, and 1 MeV) and beta spectra (32P and 90Y) are in excellent agreement with reported EGS4 values except at 1 MeV where inclusion of spin effects in EGSnrc produces an increase of the effective range of electrons. Comparison at 1 MeV with an ETRAN calculation of the electron dose point kernel shows excellent agreement.

Using FDG-PET activity as a surrogate for tumor cell density and its effect on equivalent uniform dose calculation

The concept of equivalent uniform dose (EUD) has been suggested as a means to quantitatively consider heterogeneous dose distributions within targets. Tumor cell density/function is typically assumed to be uniform. We herein propose to use 18F-labeled 2-deoxyglucose (FDG) positron emission tomography (PET) tumor imaging activity as a surrogate marker for tumor cell density to allow the EUD concept to include intratumor heterogeneities and to study its effect on EUD calculation. Thirty-one patients with lung cancer who had computerized tomography (CT)-based 3D planning and PET imaging were studied. Treatment beams were designed based on the information from both the CT and PET scans. Doses were calculated in 3D based on CT images to reflect tissue heterogeneity. The EUD was calculated in two different ways: first, assuming a uniform tumor cell density within the tumor target; second, using FDG-PET activity (counts/cm3) as a surrogate for tumor cell density at different parts of tumor to calculate the functional-imaging-weighted EUD (therefore will be labeled fEUD for convenience). The EUD calculation can be easily incorporated into the treatment planning process. For 28/31 patients, their fEUD and EUD differed by less than 6%. Twenty-one of these twenty-eight patients had tumor volumes < 200 cm3. In the three patients with larger tumor volume, the fEUD and EUD differed by 8%-14%. Incorporating information from PET imaging to represent tumor cell density in the EUD calculation is straightforward. This approach provides the opportunity to include heterogeneity in tumor function/metabolism into the EUD calculation. The difference between fEUD and EUD, i.e., whether including or not including the possible tumor cell density heterogeneity within tumor can be significant with large tumor volumes. Further research is needed to assess the usefulness of the fEUD concept in radiation treatment.

Accurate convolution/superposition for multi-resolution dose calculation using cumulative tabulated kernels

Convolution/superposition (C/S) is regarded as the standard dose calculation method in most modern radiotherapy treatment planning systems. Different implementations of C/S could result in significantly different dose distributions. This paper addresses two major implementation issues associated with collapsed cone C/S: one is how to utilize the tabulated kernels instead of analytical parametrizations and the other is how to deal with voxel size effects. Three methods that utilize the tabulated kernels are presented in this paper. These methods differ in the effective kernels used: the differential kernel (DK), the cumulative kernel (CK) or the cumulative-cumulative kernel (CCK). They result in slightly different computation times but significantly different voxel size effects. Both simulated and real multi-resolution dose calculations are presented. For simulation tests, we use arbitrary kernels and various voxel sizes with a homogeneous phantom, and assume forward energy transportation only. Simulations with voxel size up to 1 cm show that the CCK algorithm has errors within 0.1% of the maximum gold standard dose. Real dose calculations use a heterogeneous slab phantom, both the 'broad' (5 x 5 cm2) and the 'narrow' (1.2 x 1.2 cm2) tomotherapy beams. Various voxel sizes (0.5 mm, 1 mm, 2 mm, 4 mm and 8 mm) are used for dose calculations. The results show that all three algorithms have negligible difference (0.1%) for the dose calculation in the fine resolution (0.5 mm voxels). But differences become significant when the voxel size increases. As for the DK or CK algorithm in the broad (narrow) beam dose calculation, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 10% (7%) of the maximum dose. As for the broad (narrow) beam dose calculation using the CCK algorithm, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 1% of the maximum dose. Among all three methods, the CCK algorithm is demonstrated to be the most accurate one for multi-resolution dose calculations.

Enhanced spectral discrimination through the exploitation of interface effects in photon dose data

The convolution/superposition algorithm for computing dose from photon beams in radiation therapy planning requires knowledge of the energy spectrum. The algorithm can compute the dose for a polyenergetic beam as the weighted sum of the individual dose contributions from monoenergetic beams. In this study we exploit interface effects apparent in the dose distributions to discriminate among spectra of high energy photon beams. We have studied the sensitivity of the depth dose distribution to the energy components using a hypothetical beam for various field sizes and depths in water and water-lung-water media. Six theoretical spectra were simulated. We compared depth dose data from these spectra using three quantitative measures which are inherently free of normalization ambiguities: for homogeneous water, the ratio D20/D10 and a logarithmic derivative in the buildup region LD(build-up) and for inhomogeneous lung/water, the lung correction factor (CF). It was found that the ability of both the CF and the LD(build-up) tests to discriminate between the various theoretical spectra were superior to that of the D20/D10 test. This discriminating power of the CF test decreases with increasing field size due to restored electronic equilibrium. The CF test, though, has some advantages over the LD(build-up) test since it is less prone to electron contamination issues and numerical errors. A practical example with a 15 MV photon beam illustrates the process. Consequently, we suggest that as part of a beam-commissioning methodology, designated electronic disequilibrium test cases be implemented in unambiguously determining the correct energy spectrum to be used.

Development and clinical application of a fast superposition algorithm in radiation therapy

BACKGROUND AND PURPOSE

Dose calculation algorithms play a central role for the optimization and verification of treatment plans in radiation therapy. Complex treatment techniques like intensity modulated radiotherapy (IMRT) require accurate and fast dose algorithms especially for clinical cases which involve severe tissue inhomogeneities. For these cases the standard dose engine in current treatment planning systems--the convolution of photon pencil beams--usually fails to predict the dose with the required accuracy. The role of more accurate but time consuming dose calculations like superposition algorithms or Monte Carlo simulations in clinical practice is under investigation at several therapy centers.

PATIENTS AND METHODS

The paper presents the design, implementation and the first application of a superposition algorithm in a clinical setting at the German Cancer Research Center (DKFZ). It first describes in detail how the superposition algorithm is adapted to the dose delivery system at DKFZ in terms of standard dosimetric data. Then details of the implementation of the algorithm are given with a focus on various methods for the reduction of dose computation times. Next, the algorithm is evaluated in various experiments with dosimetric phantoms. These studies are employed for the development of time efficient sampling strategies of the elemental dose kernels. Finally, the algorithm is applied to dose calculations of clinical cases with tumors adjacent to lung tissue.

RESULTS

Severe differences in dose coverage of the tumors and dose burden of the surrounding tissues in comparison to standard pencil beam calculations are observed. A standard 4-7 beam plan in a convenient dose grid (approximately 3 mm in each direction) is calculated in about 30 min on a Pentium 4 (1.9 GHz) applying the superposition algorithm described here.