GammaPlan-Leksell Gamma Knife radiosurgery treatment planning verification method

This work provides a method for an independent check of Gamma Knife GammaPlan radiosurgery calculations, named the spherical approximation method or SAM. Based on skull dimension measurements, the treated volume of the head is modeled as a sphere of radius R. With this approximation, an analytical solution for fast ray tracing of the path length, for each of the 201 beamlets, of the Gamma Knife helmet collimator was possible. The dose rate at the focus of a single shot is the sum of the contributions of all active beamlets adjusted for both the collimator factor and attenuation. For an arbitrary point, the dose rate is derived at the beamlet level from the focus values adjusted for the new path length attenuation and the appropriate collimators' off-axis profiles. The sum over all beamlets' contributions gives the dose rate at that particular point. At the single shot level, SAM independent check results agree with the GammaPlan for patient calculations to better than +/-6% and, as expected, in spherical phantoms the agreements improve to better than +/-1.0%. For an arbitrary point, multi-shot procedure, the agreement is better than +/-3% and +/-1.5, respectively.     

An empirical model for independent dose verification of the Gamma Knife treatment planning

A formalism for an independent dose verification of the Gamma Knife treatment planning is developed. It is based on the approximation that isodose distribution for a single shot is in the shape of an ellipsoid in three-dimensional space. The dose profiles for a phantom along each of the three major axes are fitted to a function which contains the terms that represent the contributions from a point source, an extrafocal scattering, and a flat background. The fitting parameters are extracted for all four helmet collimators, at various shot locations, and with different skull shapes. The 33 parameters of a patient's skull shape obtained from the Skull Scaling Instrument measurements are modeled for individual patients. The relative doses for a treatment volume in the form of 31 x 31 x 31 matrix of points are extracted from the treatment planning system, the Leksell Gamma-Plan (LGP). Our model evaluates the relative doses using the same input parameters as in the LGP, which are skull measurement data, shot location, weight, gamma-angle of the head frame, and helmet collimator size. For 29 single-shot cases, the discrepancy of dose at the focus point between the calculation and the LGP is found to be within -1% to 2%. For multi-shot cases, the value and the coordinate of the maximum dose point from the calculation agree within +/-7% and +/-3 mm with the LGP results. In general, the calculated doses agree with the LGP calculations within +/-10% for the off-center locations. Results of calculation with this method for the dimension and location of the 50% isodose line are in good agreement with results from Leksell GammaPlan. Therefore, this method can be served as a useful tool for secondary quality assurance of Gamma Knife treatment plans.     

The use of a Leksell-BRW adapter for linac radiosurgery as an adjunct to Gamma Knife treatment

We have investigated the use of an adapter that permits the use of a Leksell coordinate frame with a linear accelerator stereotactic radiosurgery system based on the Brown-Robert-Wells (BRW) design. This device is useful when lesions that are planned for treatment on a Leksell Gamma Knife system are found to be inaccessible to the Gamma Knife. We have found that with this device objects within a head phantom can be targeted by the linear accelerator within an accuracy of approximately 1 mm.     

An algorithm for independent verification of Gamma Knife treatment plans

A formalism for independent treatment verification has been developed for Gamma Knife radiosurgery in analogy to the second checks being performed routinely in the field of external beam radiotherapy. A verification algorithm is presented, and evaluated based on its agreement with treatment planning calculations for the first 40 Canadian Gamma Knife patients. The algorithm is used to calculate the irradiation time for each shot, and the value of the dose at the maximum dose point in each calculation matrix. Data entry consists of information included on the plan printout, and can be streamlined by using an optional plan import feature. Calculated shot times differed from those generated by the treatment planning software by an average of 0.3%, with a standard deviation of 1.4%. The agreement of dose maxima was comparable with an average of -0.2% and a standard deviation of 1.3%. Consistently accurate comparisons were observed for centrally located lesions treated with a small number of shots. Large discrepancies were almost all associated with dose plans utilizing a large number of collimator plugs, for which the simplifying approximations used by the program are known to break down.     

Automated Gamma Knife dose planning using polygon clipping and adaptive simulated annealing

The Gamma Knife (Elekta Instruments, Inc., Norcross, GA), a neurosurgical, highly focused radiation delivery device, is used to eradicate deep-seated anomalous tissue within the human brain by delivering a lethal dose of radiation to target tissue. This dose is the accumulated result of delivering sequential "shots" of radiation to the target, where each shot is approximately three-dimensional (3-D) Gaussian in shape. The size and intensity of each shot can be adjusted by varying the time of radiation exposure and by using one of four collimator sizes ranging from 4-18 mm. Current dose planning requires that the dose plan be developed manually to cover the target, and only the target, with a desired minimum radiation intensity using a minimum number of shots. This is a laborious and subjective process that typically leads to suboptimal conformal target coverage by the dose. We have previously presented a forward-direct-method, which, using adaptive simulated annealing and Nelder-Mead simplex optimizers, automates the selection and placement of generic Gaussian-based kernels or "shots" to form a simulated dose plan. In order to make the computation of the problem tractable, the algorithm exploits 2-D contouring and polygon clipping and takes a 2 1/2-D approach to defining the problem. In the current paper we present the results of four experiments on two historical clinical datasets, where the generic kernels have been replaced by patient specific kernels calculated by Elekta's Leksell Gamma Plan software. For these experiments the user only selects the maximum number of shots to use and the optimizers are then given the freedom to vary the number of shots as well as the weight, collimator size, and 3-D location of each shot. Highly conformal and competitive dose plans were generated for these two difficult cases.     

Sensitivity study for CT image use in Monte Carlo treatment planning

An important step in Monte Carlo treatment planning (MCTP), which is commonly performed uncritically, is segmentation of the patient CT data into a voxel phantom for dose calculation. In addition to assigning mass densities to voxels, as is done in conventional TP, this entails assigning media. Mis-assignment of media can potentially lead to significant dose errors in MCTP. In this work, a test phantom with exact-known composition was used to study CT segmentation errors and to quantify subsequent MCTP inaccuracies. For our test cases, we observed dose errors in some regions of up to 10% for 6 and 15 MV photons, more than 30% for an 18 MeV electron beam and more than 40% for 250 kVp photons. It is concluded that a careful CT calibration with a suitable phantom is essential. Generic calibrations and the use of commercial CT phantoms have to be critically assessed.     

Electron bolus design for radiotherapy treatment planning: bolus design algorithms.

Computer algorithms to design bolus for electron beam radiotherapy treatment planning were investigated. Because of the significant electron multiple scatter, there is no unique solution to the problem of bolus design. However, using a sequence of operators, a bolus can be designed that attempts to meet three important criteria: adequate dose delivery to the target volume, avoidance of critical structures, and dose homogeneity within the target volume. Initial calculation of bolus shape was based upon creation operators forcing either the physical or the effective depths of the distal surface of the target volume to a specified value. Modification operators were then applied to the bolus to alter the shape to better meet the design criteria. Because the operators each address a single dosimetric issue, they can often adversely affect some other attribute of the dose distribution. In addition, an extension operator is used to design the bolus thickness outside the target volume. Application of these operators is therefore carried out in certain sequences and each may be used more than once in the design of a particular bolus. The effects of these operators on both the bolus and the resulting dose distribution are investigated for test geometries and patient geometries in the nose, parotid, and paraspinal region.     

Comparison of dose calculation algorithms for treatment planning in external photon beam therapy for clinical situations

A study of the performance of five commercial radiotherapy treatment planning systems (TPSs) for common treatment sites regarding their ability to model heterogeneities and scattered photons has been performed. The comparison was based on CT information for prostate, head and neck, breast and lung cancer cases. The TPSs were installed locally at different institutions and commissioned for clinical use based on local procedures. For the evaluation, beam qualities as identical as possible were used: low energy (6 MV) and high energy (15 or 18 MV) x-rays. All relevant anatomical structures were outlined and simple treatment plans were set up. Images, structures and plans were exported, anonymized and distributed to the participating institutions using the DICOM protocol. The plans were then re-calculated locally and exported back for evaluation. The TPSs cover dose calculation techniques from correction-based equivalent path length algorithms to model-based algorithms. These were divided into two groups based on how changes in electron transport are accounted for ((a) not considered and (b) considered). Increasing the complexity from the relatively homogeneous pelvic region to the very inhomogeneous lung region resulted in less accurate dose distributions. Improvements in the calculated dose have been shown when models consider volume scatter and changes in electron transport, especially when the extension of the irradiated volume was limited and when low densities were present in or adjacent to the fields. A Monte Carlo calculated algorithm input data set and a benchmark set for a virtual linear accelerator have been produced which have facilitated the analysis and interpretation of the results. The more sophisticated models in the type b group exhibit changes in both absorbed dose and its distribution which are congruent with the simulations performed by Monte Carlo-based virtual accelerator.     

Comparative analyses of linac and Gamma Knife radiosurgery for trigeminal neuralgia treatments

Dedicated linac-based radiosurgery has been reported for trigeminal neuralgia treatments. In this study, we investigated the dose fall-off characteristics and setup error tolerance of linac-based radiosurgery as compared with standard Gamma Knife radiosurgery. In order to minimize the errors from different treatment planning calculations, consistent imaging registration, dose calculation and dose volume analysis methods were developed and implemented for both Gamma Knife and linac-based treatments. Intra-arc setup errors were incorporated into the treatment planning process of linac-based deliveries. The effects of intra-arc setup errors with increasing number of arcs were studied and benchmarked against Gamma Knife deliveries with and without plugging patterns. Our studies found equivalent dose fall-off properties between Gamma Knife and linac-based radiosurgery given a sufficient number of arcs (>7) and small intra-arc errors (<0.5 mm) were satisfied for linac-based deliveries. Increasing the number of arcs significantly decreased the variations in the dose fall-off curve at the low isodose region (e.g. from 40% to 10%) and also improved dose uniformity at the high isodose region (e.g. from 70% to 90%). As the number of arcs increased, the effects of intra-arc setup errors on the dose fall-off curves decreased. Increasing the number of arcs also reduced the integral dose to the distal normal brain tissues. In conclusion, linac-based radiosurgery produces equivalent dose fall-off characteristics to Gamma Knife radiosurgery with a high number of arcs. However, one must note the increased treatment time for a large number of arcs and isocentre accuracies.     

Monte Carlo calculations and GafChromic film measurements for plugged collimator helmets of Leksell Gamma Knife unit.

The Monte Carlo technique and GafChromic films were employed to verify the accuracy of the dose planning system (Leksell GammaPlan) used in Gamma Knife (type B) radiosurgery when plugged collimator helmets were used. The EGS4 Monte Carlo code was used to calculate the dose distribution along the x, y, and z axes when a single shot was delivered at the center point (unit center point: x = 100, y = 100, z = 100) of a spherical polystyrene phantom, with gamma angle of 90 degrees. Two different sizes of the plugged collimator helmets, 4 and 18 mm, were studied. Two typical plugged patterns, 51 plugs and 99 plugs along the y direction, were examined. The results of our Monte Carlo trials showed good consistency with GammaPlan calculations and GafChromic film measurements. Furthermore, the Monte Carlo results showed that radiation leakage from the plugs was too small to affect the overall isodose curve distribution even when the heavily plugged pattern of up to 99 plugs was employed. The results of this project provide confidence to all Gamma Knife centers using the Leksell GammaPlan treatment planning system.     

Implementation of pencil kernel and depth penetration algorithms for treatment planning of proton beams

The implementation of two algorithms for calculating dose distributions for radiation therapy treatment planning of intermediate energy proton beams is described. A pencil kernel algorithm and a depth penetration algorithm have been incorporated into a commercial three dimensional treatment planning system (Helax-TMS, Helax AB, Sweden) to allow conformal planning techniques using irregularly shaped fields, proton range modulation, range modification and dose calculation for non-coplanar beams. The pencil kernel algorithm is developed from the Fermi Eyges formalism and Molière multiple-scattering theory with range straggling corrections applied. The depth penetration algorithm is based on the energy loss in the continuous slowing down approximation with simple correction factors applied to the beam penumbra region and has been implemented for fast, interactive treatment planning. Modelling of the effects of air gaps and range modifying device thickness and position are implicit to both algorithms. Measured and calculated dose values are compared for a therapeutic proton beam in both homogeneous and heterogeneous phantoms of varying complexity. Both algorithms model the beam penumbra as a function of depth in a homogeneous phantom with acceptable accuracy. Results show that the pencil kernel algorithm is required for modelling the dose perturbation effects from scattering in heterogeneous media.     

Concurrent multimodality image segmentation by active contours for radiotherapy treatment planning

Multimodality imaging information is regularly used now in radiotherapy treatment planning for cancer patients. The authors are investigating methods to take advantage of all the imaging information available for joint target registration and segmentation, including multimodality images or multiple image sets from the same modality. In particular, the authors have developed variational methods based on multivalued level set deformable models for simultaneous 2D or 3D segmentation of multimodality images consisting of combinations of coregistered PET, CT, or MR data sets. The combined information is integrated to define the overall biophysical structure volume. The authors demonstrate the methods on three patient data sets, including a nonsmall cell lung cancer case with PET/CT, a cervix cancer case with PET/CT, and a prostate patient case with CT and MRI. CT, PET, and MR phantom data were also used for quantitative validation of the proposed multimodality segmentation approach. The corresponding Dice similarity coefficient (DSC) was 0.90 +/- 0.02 (p < 0.0001) with an estimated target volume error of 1.28 +/- 1.23% volume. Preliminary results indicate that concurrent multimodality segmentation methods can provide a feasible and accurate framework for combining imaging data from different modalities and are potentially useful tools for the delineation of biophysical structure volumes in radiotherapy treatment planning.     

On the implementation of dose-volume objectives in gradient algorithms for inverse treatment planning

A method that allows a straightforward implementation of dose-volume constraints in gradient algorithms for inverse treatment planning is presented. The method is consistent with the penalty function approach, which requires the formulation of an objective function with penalty terms proportional to the magnitudes of constraint violations. Dose constraints with respect to minimum and maximum target dose levels are incorporated in quadratic, dose-penalty terms. Analogously, quadratic volume-penalty terms in the objective function reflect the violation of dose-volume constraints imposing limits on the fractions of healthy organ volumes that can be irradiated above specified dose levels. It has been demonstrated that within the framework of this formulation neither modified objective functions nor finite difference gradient calculations are necessary for the incorporation of gradient minimization algorithms. As an example, a simple steepest descent algorithm is presented along with its application to illustrate prostate and lung cases.     

Selection and determination of beam weights based on genetic algorithms for conformal radiotherapy treatment planning

A genetic algorithm has been used to optimize the selection of beam weights for external beam three-dimensional conformal radiotherapy treatment planning. A fitness function is defined, which includes a difference function to achieve a least-square fit to doses at preselected points in a planning target volume, and a penalty item to constrain the maximum allowable doses delivered to critical organs. Adjustment between the dose uniformity within the target volume and the dose constraint to the critical structures can be achieved by varying the beam weight variables in the fitness function. A floating-point encoding schema and several operators, like uniform crossover, arithmetical crossover, geometrical crossover, Gaussian mutation and uniform mutation, have been used to evolve the population. Three different cases were used to verify the correctness of the algorithm and quality assessment based on dose-volume histograms and three-dimensional dose distributions were given. The results indicate that the genetic algorithm presented here has considerable potential.     

Investigation of MR image distortion for radiotherapy treatment planning of prostate cancer

MR imaging based treatment planning for radiotherapy of prostate cancer is limited due to MR imaging system related geometrical distortions, especially for patients with large body sizes. On our 0.23 T open scanner equipped with the gradient distortion correction (GDC) software, the residual image distortions after the GDC were <5 mm within the central 36 cm x 36 cm area for a standard 48 cm field of view (FOV). In order to use MR imaging alone for treatment planning the effect of residual MR distortions on external patient contour determination, especially for the peripheral regions outside the 36 cm x 36 cm area, must be investigated and corrected. In this work, we performed phantom measurements to quantify MR system related residual geometric distortions after the GDC and the effective FOV. Our results show that for patients with larger lateral dimensions (>36 cm), the differences in patient external contours between distortion-free CT images and GDC-corrected MR images were 1-2 cm because of the combination of greater gradient distortion and loss of field homogeneity away from the isocentre and the uncertainties in patient setup during CT and MRI scans. The measured distortion maps were used to perform point-by-point corrections for patients with large dimensions inside the effective FOV. Using the point-by-point method, the geometrical distortion after the GDC were reduced to <3 mm for external contour determination and the effective FOV was expanded from 36 cm to 42 cm.