Fast Superposition Algorithms Research Articles

Elastic Stress Field beneath a Sticking Circular Contact under Tangential Load

Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic half-space which is subject to normal and uniaxial tangential surface tractions that—in the case of elastic decoupling—correspond to rigid normal and tangential translations of a circular surface domain. The stress fields are obtained explicitly and in closed form as the imaginary parts of compact complex-valued expressions. The stress state in the surface and on the central axis are considered in detail. As, within specific approximations that have been discussed at length in the literature, any tangential contact problem with friction can be understood as a certain incremental series of such rigid translations, the solutions presented here can serve as the basis of very fast superposition algorithms for the analysis of subsurface stress fields in general tangential contact problems with friction. This idea is demonstrated by means of the frictional tangential contact between an elastic half-space and a rigid cylindrical flat punch with rounded corners.

Dosimetric Comparison of Different Dose Calculation Algorithms in Postmastectomy Breast Cancer Patients Using Conformal Planning Techniques.

The aim of the current study was to compare three different dose-calculating algorithms, i.e., superposition (SP), fast SP (FSP), and convolution (CV), for breast cancer patients treated with intensity-modulated radiotherapy (IMRT) and field-in-Field forward plan IMRT (FiF-FP-IMRT). The current retrospective study involved 100 postmastectomy breast cancer patients who were given radiotherapy using IMRT and FiF-FP-IMRT planning techniques. All the initially SP-calculated plans were recalculated with the same monitor units for FSP and CV algorithm without change in any of the other planning parameters. The isodose distribution and various plan evaluating parameters, for example, conformity index (CI), homogeneity index, and uniformity index target volume and normal structure doses were compared and analyzed for all the different algorithm calculated plans. In the IMRT plans, all the target and normal structure dose-volume parameters showed a significant difference between all the three different algorithms with P < 0.05. In the FiF-FP-IMRT plans, CV algorithm showed a significant difference in most of the target and normal structure dose-volume parameters. Among quality indexes, only CI showed a significant difference between all the algorithms in both the planning techniques. R50 showed a significant difference with the CV algorithm in both the planning techniques. The change in the dose calculation algorithm resulted in dosimetric changes which must be evaluated by the medical physicists and oncologists while evaluating treatment plans. In the current study with breast patients, the results obtained for target and normal structure doses using the CV algorithm are overestimated as compared to SP and FSP algorithms, producing variable results in air and bony normal structures. However, the ipsilateral lung V5 parameter and the ipsilateral humeral head mean dose were found to be underestimated by the CV algorithm as compared to the SP and FSP algorithm in both the planning techniques.

Comparative Study of Fast Superposition, Superposition Algorithm in Intensity Modulated Radiotherapy Techniques for Prostate Cancer

This study aims to compare the dosimetric coverage of the Planning Target Volume (PTV) and the dose to main organs at risk (OARs) between two different algorithms fast superposition (FSUP), superposition (SUP) using intensity-modulated radiotherapy (IMRT) techniques for prostate cancer. Ten patients with prostate cancer were selected for this study. For each patient, IMRT plans were created with 6 MV photon beam quality using CMS XiO treatment planning system. The delivery of IMRT was carried out using the step and shoot techniques. The dose coverage for each patient was designated to an ICRU report 62 reference point in the PTV, medium coverage of the planned target volume to be 95% of the prescribed dose while the maximum dose in the target volume to be not greater than 107% of the prescribed dose. A hypofractionated prescription dose of 70 Gy/28# at 2.5 Gy per fraction was used. Besides we compared the number of MUs and OARs dose to D15%, D25%, D35%, D50% on both algorithm planning sets. For target, this evaluation was made with comparing the conformity index (CI) and homogeneity index (HI). In our study, the results show the OARs got less dose from the SUP algorithm compared to FSUP algorithms. Statistically not significant difference was observed in V107% of PTV, MU/CC, conformity Index (p = 0.057, p = 0.215, p = 0.370) and 95% PTV Volume received prescription dose from both Plans. But Homogeneity Index for both algorithms was statistically significant (p = 0.000, p = 0.001). For prostate cancer, the superposition algorithm showed better results in the IMRT plan compared to the fast superposition algorithm.

Point Dose Measurement for Verification of Treatment Planning System using an Indigenous Heterogeneous Pelvis Phantom for Clarkson, Convolution, Superposition, and Fast Superposition Algorithms

Background: Nowadays, advanced radiotherapy equipment includes algorithms to calculate dose. The verification of the calculated doses is important to achieve accurate results. Mostly homogeneous dosimetric phantoms are available commercially which do not mimic the actual patient anatomy; therefore, an indigenous heterogeneous pelvic phantom mimicking actual human pelvic region has been used to verify the doses calculated by different algorithms. Objective: This study aims to compare the planed dose using different algorithms with measured dose using an indigenous heterogeneous pelvic phantom.Material and Methods: In this experimental study, various three dimensional conformal radiotherapy (3D-CRT) plans were made using different doses calculated by algorithms. The plans were delivered by medical linear accelerator and doses were measured by ion chamber placed in the indigenous pelvic phantom. Planned and measured doses were compared with together and analyzed. Results: The relative electron densities of different parts in the pelvic phantom were found to be in good agreement with that of actual pelvic parts, including bladder, rectum, fats and bones. The highest percentage deviations between planned and measured dose were calculated in the single field for Superposition algorithm (3.09%) and single field with 45˚wedge for Superposition (3.04%). The least percentage deviation was calculated in the opposite field for Convolution which was - 0.08%. The results were within the range of ±5% as recommended by International Commission on Radiation Units and Measurement. Conclusion: The cost-effective indigenous heterogeneous pelvic phantom has the density pattern similar to the actual pelvic region; thus, it can be used for routine patient-specific quality assurance.

The comparison of two calculation algorithms to evaluate the dosimetric effects of thermoplastic masks used in radiotherapy

Abstract In radiation therapy, the accuracy of dose calculation is extremely important for planning quality and treatment implementation. This is achieved through Treatment Planning Systems (TPS) that use different algorithms to calculate the specific dose. Radiation therapy for brain and head & neck (H&N) tumors requires the same high positioning precision of the patient throughout the treatment course. Thus, during fractionated radiotherapy, to immobilize the patient’s head and neck, and to avoid patient movement errors, an immobilization device is used, that is, a thermoplastic mask. However, many studies have shown that TPS overestimate the delivered dose to the skin during the treatment. The aim of this study is to quantify the dosimetric thermoplastic mask effects using two different algorithms that are the superposition and the fast superposition algorithms.

Half Beam Block Technique in Breast Cancer and It’s Dosimetric Analysis using different Algorithms

Introduction: Single isocentre half-beam block (HBB) technique permits the avoidance of hot and cold spots. This technique is very useful in sparing the underlying ipsilateral lung and heart, if the left breast is treated. The major advantage of this technique is that it facilitates the complete sparing of both contralateral breast and lung. Regarding this, the present study aimed to analyse the dosimetric results obtained from the HBB technique in the treatment of breast cancer using three different algorithms. Materials and Methods: For the purpose of the study, a total dose of 5000 cGy was prescribed to the planning target volume (PTV) in 25 fractions per fraction daily, five days a week. The PTV was derived by using 4-7 mm isotropic expansion of the clinical target volume (CTV) clipping 1-3 mm from the patient’s surface in the breast-conserving cases. Three plans were created for each patient using three different algorithms, including convolution, fast superposition, and superposition with the same parameters. Results: The mean doses of PTV-breast and CTV-supraclavicular fossa (SCF) were tabulated and analysed. In the PTV-breast, the maximum and minimum mean doses were 5428.8 and 4930.2 cGy, which were observed in the fast superposition and convolution algorithms, respectively. In the CTV-SCF, the maximum and minimum mean doses were 5428.8 and 5126.8 cGy, respectively, detected in only fast superposition algorithm. Conclusion: As the findings of the present study indicated, the convolution algorithm gives slightly better dosimetric results in breast cancer treatment, compared to the fast superposition and superposition algorithms. Therefore, it is prudent to apply the HBB technique with convolution algorithm using the Elekta XiO planning system in the treatment of breast cancer including supraclavicular lymph node metastasis.

Development of pelvis phantom for verification of treatment planning system using convolution, fast superposition, and superposition algorithms

Background: The cost of commercial pelvis phantom is a burden to the quality assurance in radiotherapy of small and/or low-income radiotherapy centers. That an algorithm is accurate with short treatment time is a prized asset in treatment planning. Objectives: The purpose of this study was to develop a hybrid algorithm that has balance between accuracy and treatment time and design a pelvis phantom for evaluating the accuracy of a linear accelerator monitor unit. Materials and Methods: A pelvis phantom was designed using Plaster of Paris, styrofoam and water with six hollows for inserting materials mimicking different biological tissues, and the ionization chamber. Computed tomography images of the phantom were transferred to the CMS XiO treatment planning system with three different algorithms. Monitor units were obtained with clinical linear accelerator with isocentric setup. The phantom was tested using convolution (C), fast superposition (FSS), and superposition (S) algorithms with respect to an established reference dose of 1 Gy from a large water phantom. Data analysis value was done using GraphPad Prism 5.0. Results: FSS algorithm showed better accuracy than C and S with bone, lung, and solid water inhomogeneous insert. C algorithm was better in terms of treatment time than S. There was no statistically significant difference between the mean doses for all the three algorithms against the reference dose. The maximum percentage deviation was ±4%, which was below ±5% International Commission on Radiation Units and Measurement minimal limit. Conclusion: This algorithm can be employed in the calculation of dose in advance techniques such as intensity-modulated radiation therapy and RapidArc by radiotherapy centers with multiple algorithm system because it is easy to implement. The materials used for the construction of the phantom are very affordable and simple for low-budget radiotherapy centers.

SU-E-T-450: An Evaluation Study of Dose Calculation Algorithms for Stereotactic Body Radiation Therapy in Heterogeneous Phantom.

In Stereotactic body radiation therapy (SBRT) higher dose per fraction is delivered to patients and thus the need for an accurate dose computation is further elevated. However under such conditions of small field geometries, the electronic equilibrium can be lost, making it challenging for the dose-calculation algorithm to accurately predict the dose, especially in the presence of tissue heterogeneities. Thus the aim of this study is to evaluate the performance of the algorithms implemented in our treatment planning system. In this study different phantoms were designed to model the lung with a small tumor volume of sizes that are usually encountered in SBRT. Solid water and cork slabs were used in constructing the phantom body. Perspex pieces of different diameters were created to be inserted in precut holes in the cork to simulate the tumor. The various dose calculation algorithms that are implemented in our CMS XIO planning system were then used for dose calculation inside the target. A significant discrepancies between maximum, minimum and mean dose for PTV was found between Clarkson, FFT Convolution, Fast superposition and superposition algorithms in dose calculation for the lung tumor. The FFT Convolution and Clarkson algorithms have higher calculated minimum dose than that predicted by the superposition and the fast superposition algorithm. A percentage difference as high as 62.5% was obtained between Clarkson and the superposition algorithm in the estimated minimum dose. A percentage difference up to 13.4% was obtained between the FFT Convolution and the superposition algorithm for the estimated maximum dose. Superposition and fast superposition showed little discrepancies for maximum, minimum and mean dose for the PTV. It is very critical to address the accuracy of dose computation for SBRT as a significant dose overestimation can occur inside the target due to the heterogeneous geometries.

Dose perturbations by two carbon fiber treatment couches and the ability of a commercial treatment planning system to predict these effects

To measure the effect of the treatment couch on dose distributions and to investigate the ability of a modern planning system to accurately model these effects. This work measured the dose perturbation at depth and in the dose buildup region when one of two treatment couches, CIVCO (formerly MED-TEC) or Medical Intelligence, was placed between a photon beam source (6, 10, and 18 MV) and the phantom. Beam attenuation was measured in the center of a cylindrical acrylic phantom with a Farmer type ion chamber at multiple gantry angles. Dose buildup was measured in Solid Water with plane parallel ion chambers (NACP-02 and PTW Markus) with the beam normal to both the phantom and couch surfaces. The effective point of measurement method as described [M. R. McEwen et al. "The effective point of measurement of ionization chambers and the build-up anomaly in MV x-ray beams," Med. Phys. 35(3), 950-958 (2008)] was employed to calculate dose in the buildup region. Both experiments were modeled in XiO. Images of the treatment couches were merged with images of the phantoms such that they were included as part of the "patient" image. Dose distributions calculated with superposition and fast superposition algorithms were compared to measurement. The two treatment couches have different radiological signatures and dissimilar water equivalent thicknesses (4.2 vs 6.3 mm.) Maximum attenuation was 7%. Both couches caused significant loss of skin sparing, the worst case showing an increase in surface dose from 17% (no couch) to 88% (with couch). The TPS accurately predicted the surface dose (+/-3%) and the attenuation at depth when the phantom was in contact with the couch. For the open beam the TPS was less successful in the buildup region. The treatment couch is not radio-transparent. Its presence between the patient and beam source significantly alters dose in the patient. For the most part, a modern treatment planning system can adequately predict the altered dose distribution.

Comparative study of convolution, superposition, and fast superposition algorithms in conventional radiotherapy, three-dimensional conformal radiotherapy, and intensity modulated radiotherapy techniques for various sites, done on CMS XIO planning system

The aim of this study is to compare the dosimetry results that are obtained by using Convolution, Superposition and Fast Superposition algorithms in Conventional Radiotherapy, Three-Dimensional Conformal Radiotherapy (3D-CRT), and Intensity Modulated Radiotherapy (IMRT) for different sites, and to study the suitability of algorithms with respect to site and technique. For each of the Conventional, 3D-CRT, and IMRT techniques, four different sites, namely, Lung, Esophagus, Prostate, and Hypopharynx were analyzed. Treatment plans were created using 6MV Photon beam quality using the CMS XiO (Computerized Medical System, St.Louis, MO) treatment planning system. The maximum percentage of variation recorded between algorithms was 3.7% in case of Ca.Lung, for the IMRT Technique. Statistical analysis was performed by comparing the mean relative difference, Conformity Index, and Homogeneity Index for target structures. The fast superposition algorithm showed excellent results for lung and esophagus cases for all techniques. For the prostate, the superposition algorithm showed better results in all techniques. In the conventional case of the hypopharynx, the convolution algorithm was good. In case of Ca. Lung, Ca Prostate, Ca Esophagus, and Ca Hypopharynx, OARs got more doses with the superposition algorithm; this progressively decreased for fast superposition and convolution algorithms, respectively. According to this study the dosimetric results using different algorithms led to significant variation and therefore care had to be taken while evaluating treatment plans. The choice of a dose calculation algorithm may in certain cases even influence clinical results.

Dosimetric verification in inhomogeneous phantom geometries for the XiO radiotherapy treatment planning system with 6-MV photon beams

We have developed a practical dose verification method for radiotherapy treatment planning systems by using only a Farmer ionization chamber in inhomogeneous phantoms. In particular, we compared experimental dose verifications of multi-layer phantom geometries and laterally inhomogeneous phantom geometries for homogeneous and inhomogenous dose calculations by using the fast-Fourier-transform convolution, fast-superposition, and superposition in the XiO radiotherapy treatment-planning system. We applied the dose verification method to three kernel-based algorithms in various phantom geometries with water-, lung- and bone-equivalent media of different field sizes. These calculations were then compared with experimental measurements by use of the Farmer ionization chamber. The fast-Fourier-transform convolution algorithm overestimated the dose by about 8% in the lung phantom geometry. The superposition algorithm and the fast-superposition algorithm were both accurate to better than 2% when compared to the measurements even for complex geometries. Our dose verification method was able to clarify the differences and equivalences of the three kernel-based algorithms and measurements with use only of commonly available apparatus. This will be generally useful in commissioning of inhomogeneity-correction algorithms in the clinical practice of treatment planning.

SU‐GG‐T‐540: Impact of Biological Optimization On Plan Quality: An Evaluation of a Commercial Treatment Planning System

Purpose: To evaluate the impact of biological optimization implemented in the new commercial IMRT treatment planning system (TPS) Monaco (CMS, St. Louis, MO) on plan quality as compared to a traditional TPS employing dose‐based optimization (XiO, CMS, St. Louis, MO). Method and Materials: Clinically used IMRT treatment plans for selected head and neck, prostate, and brain cases generated using XiO (version 4.3.3) were compared with corresponding plans generated using Monaco (version 1.0.0). The same CT data, contours, isocenter, number of beams (7–9), beam angles, and calculation grid spacing (2 mm) as in the original XiO plans were used for the Monaco treatment planning. Biological cost functions were used with parameter values suggested in a Monaco training manual as initial guesses. Iterative adjustment of isoconstraint values followed by re‐optimization was continued until approximately 95% coverage of each target volume by a prescription dose was achieved. A Monte Carlo algorithm with 3% variance was used for final dose calculation in Monaco. Dose calculations in XiO were performed using a fast superposition algorithm. Results: Monaco plans tend to result in smaller values of the mean dose and generalized equivalent uniform dose (gEUD) for OARs (15 out of 17 OARs in all plans combined) and greater mean doses and gEUD for targets (4/5). Maximum doses to normal structures are sometimes greater in Monaco compared to XiO (6/17) as a consequence of larger hot spots in target volumes. Dose heterogeneity was increased for all but one target in Monaco plans. Conclusion: The biologically based Monaco TPS has the potential to generate superior IMRT treatment plans compared to the dose‐based XiO TPS, as judged by better or equivalent target coverage accompanied by reduction in normal tissue exposure. However, greater dose inhomogeneity in the target must be accepted in most cases.

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 (~3 mm in each direction) is calculated in about 30 min on a Pentium 4 (1.9 GHz) applying the superposition algorithm described here.