Hannu Helminen

Testing of the analytical anisotropic algorithm for photon dose calculation

The analytical anisotropic algorithm (AAA) was implemented in the Eclipse (Varian Medical Systems) treatment planning system to replace the single pencil beam (SPB) algorithm for the calculation of dose distributions for photon beams. AAA was developed to improve the dose calculation accuracy, especially in heterogeneous media. The total dose deposition is calculated as the superposition of the dose deposited by two photon sources (primary and secondary) and by an electron contamination source. The photon dose is calculated as a three-dimensional convolution of Monte-Carlo precalculated scatter kernels, scaled according to the electron density matrix. For the configuration of AAA, an optimization algorithm determines the parameters characterizing the multiple source model by optimizing the agreement between the calculated and measured depth dose curves and profiles for the basic beam data. We have combined the acceptance tests obtained in three different departments for 6, 15, and 18MV photon beams. The accuracy of AAA was tested for different field sizes (symmetric and asymmetric) for open fields, wedged fields, and static and dynamic multileaf collimation fields. Depth dose behavior at different source-to-phantom distances was investigated. Measurements were performed on homogeneous, water equivalent phantoms, on simple phantoms containing cork inhomogeneities, and on the thorax of an anthropomorphic phantom. Comparisons were made among measurements, AAA, and SPB calculations. The optimization procedure for the configuration of the algorithm was successful in reproducing the basic beam data with an overall accuracy of 3%, 1mm in the build-up region, and 1%, 1mm elsewhere. Testing of the algorithm in more clinical setups showed comparable results for depth dose curves, profiles, and monitor units of symmetric open and wedged beams below dmax. The electron contamination model was found to be suboptimal to model the dose around dmax, especially for physical wedges at smaller source to phantom distances. For the asymmetric field verification, absolute dose difference of up to 4% were observed for the most extreme asymmetries. Compared to the SPB, the penumbra modeling is considerably improved (1%, 1mm). At the interface between solid water and cork, profiles show a better agreement with AAA. Depth dose curves in the cork are substantially better with AAA than with SPB. Improvements are more pronounced for 18MV than for 6MV. Point dose measurements in the thoracic phantom are mostly within 5%. In general, we can conclude that, compared to SPB, AAA improves the accuracy of dose calculations. Particular progress was made with respect to the penumbra and low dose regions. In heterogeneous materials, improvements are substantial and more pronounced for high (18MV) than for low (6MV) energies.

Determination of parameters for a multiple-source model of megavoltage photon beams using optimization methods

Accurate modelling of the radiation output of a medical linear accelerator is important for radiotherapy treatment planning. The major challenge is the adjustment of the model to a specific treatment unit. One approach is to use a multiple-source model containing a set of physical parameters. In this work, the parameters were derived from standard beam data measurements using optimization methods. The source model used includes sub-sources for bremsstrahlung radiation from the target, extra-focal photon radiation and electron contamination. The cost function includes a gamma error measure between measurements and current dose calculations. The procedure was applied to six beam data sets (6 MV to 23 MV) measured with accelerators from three vendors, but the results focus primarily on Varian accelerators. The obtained average gamma error (1%, 1 mm) between dose calculations and measurements used in optimization was smaller than 0.7 for each studied treatment beam and field size, and a minimum of 83% of measurement points passed the gamma < 1 criterion. For experiments made at different SSDs and for asymmetric fields, the average gamma errors were smaller than 1.1. For irregularly shaped MLC apertures, the differences in point doses were smaller than 1.0%. This work demonstrates that the source model parameters can be automatically derived from simple measurements using optimization methods. The developed procedure is applicable to a wide range of accelerators, and has an acceptable accuracy and processing time.

Comparison of Local External Force Functions for Non-rigid Registration of 3D Medical Images

Non-rigid volumetric registration has many applications, including inter-patient image fusion, motion quantification, and automatic atlas-based segmentation. Computation time is often a limiting factor in using current methods in clinical environments. Minimizing computation time requires both the internal and the external force updates to be as efficient as possible. In this article, we concentrate on the choice of the external force function. We compare different methods based on optical flow and propose a new correlation-based external force function. In addition, we propose an acceleration technique and study its effect on image quality and the speed of convergence. The results indicate that the acceleration technique improves both the speed and quality, and increases the stability of all the external force methods considered.

TU-FF-A1-04: Determining Parameters for a Multiple-Source Model of a Linear Accelerator Using Optimization Techniques

Purpose: To determine the parameters of a multiple‐source model for an arbitrary linear accelerator using optimization methods.Method and Materials: A multiple‐source model describing the energy fluence output of a linear accelerator was developed in this study. A point source modeled radiation from the target, a finite‐size source all extra‐focal radiation, and an electron sourcecontaminant particles. The parameters determined were the mean energy curve (for off‐axis softening), intensity profile curve (for non‐uniform photon energy fluence), electron source values, extra‐focal source size, energy, and intensity. The parameters were optimized by minimizing the gamma error between the dose calculation results and the beam data measurements by applying a non‐linear optimization technique not requiring gradient information. The dose was calculated by an algorithm based on superposition/convolution of Monte Carlo determined scatter kernels. The beam data measurements required were depth dose curves, lateral profiles, and diagonal profiles for multiple field sizes. The model requires minimal data about the internal dimensions and construction of the accelerator head. Results: The method was applied to 231 realistic data sets of varying quality and consistency for Elekta, Siemens and Varian accelerators. The gamma error (1%, 3 mm) for an average optimized model was lower than 1.0 for 98% of the measurement points. Typical duration of the optimization to derive the model parameters was 5–15 minutes. In cases where the measurements contained inconsistencies, the resulting gamma errors were significant, which indicates that the method could be useful in quality assurance of measurement data. Conclusion: This study demonstrated that the parameters for a multiple‐source model can be determined in an efficient and stable manner using optimization methods. The model is applicable to an arbitrary accelerator and has clinically acceptable accuracy and execution time. Conflict of Interest: This work was supported by Varian Medical Systems.

SU‐FF‐T‐270: Implementing a Monte Carlo Algorithm for Fields with Dynamic Beam Modifiers

Purpose:Monte Carlo methods for photons are slowly becoming available for normal clinical use. Especially for dynamic or otherwise complex fields Monte Carlo methods can be superior to traditional methods. The time to compute a Monte Carlo dose distribution up to a given accuracy is nearly independent of the complexity of the whole plan. Instead, traditional methods usually require computation time directly proportional to the complexity of the treatment. In this work, VMC++ (Voxel Monte Carlo, National Research Council, Canada) algorithm for fields with dynamic beam modifiers has been implemented. Method and Materials: A Monte Carlo implementation of an accelerator head model for dynamic fields is presented. Cases studied include dynamic wedges, sliding window IMRT fields, and complex arc fields. Except for dynamic wedges, the transport through the relevant components is modeled using VMC++. Tongue‐and‐groove, air cavities, divergent leafs, and rounded leaf tips in a multi‐leaf collimator are taken into account. In the case of dynamic wedges the jaws are modeled as impenetratable blocks. The final patient dose calculation is also done using VMC++ algorithm. Results: Results are presented for each of the dynamic components by comparing the Monte Carlo calculated data to measurements. The agreement is excellent in all cases. The calculation time varies from a few minutes to a few hours, depending on the required accuracy and target volume. Conclusion:Monte Carlo is shown to be a very competitive alternative for traditional methods in modeling accessories, especially for dynamic treatments. The results of the corresponding dose calculation match very well with measured beam data. In addition, the obtained execution times are suitable for routine clinical use. Conflict of Interest: This work has been funded by Varian Medical Systems Inc.

SU‐FF‐T‐83: Algorithm for Optimizing Beam Angles in IMRT Treatment Planning

Purpose: The goal of beam angle optimization in external radiation therapytreatment planning is to find field directions which shall result in an optimal treatment plan. In this work, a beam angle optimization algorithm to be used in Intensity Modulated Radiation Therapy(IMRT)treatment planning has been developed. Method and Materials: The plan optimality is defined by constraints set on the Dose‐Volume Histogram (DVH) of the target(s) and of the critical organs. The same constraints may be applied both in beam angle and in beam profile (beamlet) optimization. In beam angle optimization, either a co‐planar or a non‐coplanar initial search space may be used. The search space is covered with a preset number of uniformly distributed fields. Thereafter, a few beamlet optimization iterations are calculated in order to produce optimal beam profiles. Each field is then removed from the plan, and the corresponding value of the objective function is calculated. The fields with a low importance value are thereafter removed. The process is continued until the desired number of fields in the plan has been reached. Results: The optimized plans have been compared with equispaced beams, class solution —based plans and manually made plans. Beam angle optimization has been found to decrease the OF value typically to 20–80 % of the original value calculated with reference plans. The improvement has been clearly visible also in the shape of the DVH curves. The algorithm has been designed to execute fast (less than 30 minutes) in order to be applicable in routine use for patient‐specific planning. Conclusion: The new beam angle optimization algorithm has been able to produce IMRT plans with superior quality to class solution or manually made plans. Conflict of Interest: This work has been funded by Varian Medical Systems Inc.

Volumetric visualization algorithm development for an FPGA based custom computing machine

Rendering volumetric medical images is a burdensome computational task for contemporary computers due to the large size of the data sets. Custom designed reconfigurable hardware could considerably speed up volume visualization if an algorithm suitable for the platform is used. We present an algorithm and speedup techniques for visualizing volumetric medical CT and MR images with a custom-computing machine based on a Field Programmable Gate Array (FPGA). We also present simulated performance results of the proposed algorithm calculated with a software implementation running on a desktop PC. Our algorithm is capable of generating perspective projection renderings of single and multiple isosurfaces with transparency, simulated X-ray images, and Maximum Intensity Projections (MIP). Although more speedup techniques exist for parallel projection than for perspective projection, we have constrained ourselves to perspective viewing, because of its importance in the field of radiotherapy. The algorithm we have developed is based on ray casting, and the rendering is sped up by three different methods: shading speedup by gradient precalculation, a new generalized version of Ray-Acceleration by Distance Coding (RADC), and background ray elimination by speculative ray selection.