A spherical dose model for radiosurgery plan optimization

Corrections of photon beam profiles of small fields measured with ionization chambers using a three-layer neural network

The purpose of this work is to study the feasibility of photon beam profile deconvolution using a feedforward neural network (NN) in very small fields (down to 0.56 × 0.56 cm²). The method's independence of the delivery and scanning system is also investigated. Lateral beam profiles of photon fields between 0.56 × 0.56 cm² and 4.03 × 4.03 cm² were collected on a Siemens Artiste linear accelerator. Three scanning ionization chambers (SNC 125c, PTW 31021, and PTW 31022) of sensitive volumes ranging from 0.016 cm³ to 0.108 cm³ were used with a PTW MP3 water phantom. A reference dataset was also collected with a PTW 60019 microDiamond detector to train and test individual NNs for each ionization chamber. Further testing of the trained NNs was performed with additional test data collected on an Elekta Synergy linear accelerator using a Sun Nuclear 3D Scanner. The results were evaluated with a 1D gamma analysis (0.5 mm/0.5%). After the deconvolution, the gamma passing rates increased from 54.79% to 99.58% for the SNC 125c, from 57.09% to 99.83% for the PTW 31021, and from 91.03% to 96.36% for the PTW 31022. The delivery system, the scanning system, the scanning mode (continuous vs. step‐by‐step), and the electrometer had no significant influence on the results. This study successfully demonstrated the feasibility of using NN to correct the beam profiles of very small photon fields collected with ionization chambers of various sizes. Its independence of the delivery and scanning system was also shown.

Evaluation of a neural network‐based photon beam profile deconvolution method

Purpose

The authors have previously shown the feasibility of using an artificial neural network (ANN) to eliminate the volume average effect (VAE) of scanning ionization chambers (ICs). The purpose of this work was to evaluate the method when applied to beams of different energies (6 and 10 MV) and modalities [flattened (FF) vs unflattened (FFF)], measured with ICs of various sizes.

Methods

The three‐layer ANN extracted data from transverse photon beam profiles using a sliding window, and output deconvolved value corresponding to the location at the center of the window. Beam profiles of seven fields ranging from 2 × 2 to 10 × 10 cm² at four depths (1.5, 5, 10 and 20 cm) were measured with three ICs (CC04, CC13, and FC65‐P) and an EDGE diode detector for 6 MV FF and FFF. Similar data for the 10 MV FF beam was also collected with CC13 and EDGE. The EDGE‐measured profiles were used as reference data to train and test the ANNs. Separate ANNs were trained by using the data of each beam energy and modality. Combined ANNs were also trained by combining data of different beam energies and/or modalities. The ANN's performance was quantified and compared by evaluating the penumbra width difference (PWD) between the deconvolved and reference profiles.

Results

Excellent agreement between the deconvolved and reference profiles was achieved with both separate and combined ANNs for all studied ICs, beam energies, beam modalities, and geometries. After deconvolution, the average PWD decreased from 1–3 mm to under 0.15 mm with separate ANNs and to under 0.20 mm with combined ANN.

Conclusions

The ANN‐based deconvolution method can be effectively applied to beams of different energies and modalities measured with ICs of various sizes. Separate ANNs yielded marginally better results than combined ANNs. An IC‐specific, combined ANN can provide clinically acceptable results as long as the training data includes data of each beam energy and modality.

Assessment of the setup dependence of detector response functions for mega-voltage linear accelerators

PURPOSE

Accurate modeling of beam profiles is important for precise treatment planning dosimetry. Calculated beam profiles need to precisely replicate profiles measured during machine commissioning. Finite detector size introduces perturbations into the measured profiles, which, in turn, impact the resulting modeled profiles. The authors investigate a method for extracting the unperturbed beam profiles from those measured during linear accelerator commissioning.

METHODS

In-plane and cross-plane data were collected for an Elekta Synergy linac at 6 MV using ionization chambers of volume 0.01, 0.04, 0.13, and 0.65 cm3 and a diode of surface area 0.64 mm2. The detectors were orientated with the stem perpendicular to the beam and pointing away from the gantry. Profiles were measured for a 10 x 10 cm2 field at depths ranging from 0.8 to 25.0 cm and SSDs from 90 to 110 cm. Shaping parameters of a Gaussian response function were obtained relative to the Edge detector. The Gaussian function was deconvolved from the measured ionization chamber data. The Edge detector profile was taken as an approximation to the true profile, to which deconvolved data were compared. Data were also collected with CC13 and Edge detectors for additional fields and energies on an Elekta Synergy, Varian Trilogy, and Siemens Oncor linear accelerator and response functions obtained. Response functions were compared as a function of depth, SSD, and detector scan direction. Variations in the shaping parameter were introduced and the effect on the resulting deconvolution profiles assessed.

RESULTS

Up to 10% setup dependence in the Gaussian shaping parameter occurred, for each detector for a particular plane. This translated to less than a +/- 0.7 mm variation in the 80%-20% penumbral width. For large volume ionization chambers such as the FC65 Farmer type, where the cavity length to diameter ratio is far from 1, the scan direction produced up to a 40% difference in the shaping parameter between in-plane and cross-plane measurements. This is primarily due to the directional difference in penumbral width measured by the FC65 chamber, which can more than double in profiles obtained with the detector stem parallel compared to perpendicular to the scan direction. For the more symmetric CC13 chamber the variation was only 3% between in-plane and cross-plane measurements.

CONCLUSIONS

The authors have shown that the detector response varies with detector type, depth, SSD, and detector scan direction. In-plane vs. cross-plane scanning can require calculation of a direction dependent response function. The effect of a 10% overall variation in the response function, for an ionization chamber, translates to a small deviation in the penumbra from that of the Edge detector measured profile when deconvolved. Due to the uncertainties introduced by deconvolution the Edge detector would be preferable in obtaining an approximation of the true profile, particularly for field sizes where the energy dependence of the diode can be neglected. However, an averaged response function could be utilized to provide a good approximation of the true profile for large ionization chambers and for larger fields for which diode detectors are not recommended.

Analytical description of dose profile behaviour in Gamma Knife radiosurgery

Stereotactic Gamma Knife radiosurgery utilizes ionizing beams from (60)Co sources and relies on a combination of collimator sizes, weighting, etc to generate a high-dose region that is conformal with a designated target volume. Dose computation is typically performed by computer, but in this paper, single collimator dose profile behaviour is modelled analytically and then extended to accommodate multiple collimators of different weights with co-located isocentres. The dose profile from a single helmet is derived from a top-hat beam profile approximation and an idealized symmetric distribution of sources is used to represent the 201 sources within a collimating helmet. The results from the analysis are validated by an independent numerical model and also compared with those obtained by other groups using numerical and experimental methods. With respect to multiple collimators, the relationship between the size (full width half maximum) of the irradiated volume and relative collimator weighting is also examined using the simple analytical model. The simplicity of the mathematics clarifies the relationship between beam profile, dose profile and multiple collimator behaviour, and provides data that compare favourably with published literature.

Automated gamma knife radiosurgery treatment planning with image registration, data-mining, and Nelder-Mead simplex optimization

Gamma knife treatments are usually planned manually, requiring much expertise and time. We describe a new, fully automatic method of treatment planning. The treatment volume to be planned is first compared with a database of past treatments to find volumes closely matching in size and shape. The treatment parameters of the closest matches are used as starting points for the new treatment plan. Further optimization is performed with the Nelder-Mead simplex method: the coordinates and weight of the isocenters are allowed to vary until a maximally conformal plan specific to the new treatment volume is found. The method was tested on a randomly selected set of 10 acoustic neuromas and 10 meningiomas. Typically, matching a new volume took under 30 seconds. The time for simplex optimization, on a 3 GHz Xeon processor, ranged from under a minute for small volumes (<1000 cubic mm, 2-3 isocenters), to several tens of hours for large volumes (>30,000 cubic mm, >20 isocenters). In 8/10 acoustic neuromas and 8/10 meningiomas, the automatic method found plans with conformation number equal or better than that of the manual plan. In 4/10 acoustic neuromas and 5/10 meningiomas, both overtreatment and undertreatment ratios were equal or better in automated plans. In conclusion, data-mining of past treatments can be used to derive starting parameters for treatment planning. These parameters can then be computer optimized to give good plans automatically.

Selective source blocking for Gamma Knife radiosurgery of trigeminal neuralgia based on analytical dose modelling

We have developed an automatic critical region shielding (ACRS) algorithm for Gamma Knife radiosurgery of trigeminal neuralgia. The algorithm selectively blocks 201 Gamma Knife sources to minimize the dose to the brainstem while irradiating the root entry area of the trigeminal nerve with 70-90 Gy. An independent dose model was developed to implement the algorithm. The accuracy of the dose model was tested and validated via comparison with the Leksell GammaPlan (LGP) calculations. Agreements of 3% or 3 mm in isodose distributions were found for both single-shot and multiple-shot treatment plans. After the optimized blocking patterns are obtained via the independent dose model, they are imported into the LGP for final dose calculations and treatment planning analyses. We found that the use of a moderate number of source plugs (30-50 plugs) significantly lowered (approximately 40%) the dose to the brainstem for trigeminal neuralgia treatments. Considering the small effort involved in using these plugs, we recommend source blocking for all trigeminal neuralgia treatments with Gamma Knife radiosurgery.

Real-time inverse planning for Gamma Knife radiosurgery

The challenges of real-time Gamma Knife inverse planning are the large number of variables involved and the unknown search space a priori. With limited collimator sizes, shots have to be heavily overlapped to form a smooth prescription isodose line that conforms to the irregular target shape. Such overlaps greatly influence the total number of shots per plan, making pre-determination of the total number of shots impractical. However, this total number of shots usually defines the search space, a pre-requisite for most of the optimization methods. Since each shot only covers part of the target, a collection of shots in different locations and various collimator sizes selected makes up the global dose distribution that conforms to the target. Hence, planning or placing these shots is a combinatorial optimization process that is computationally expensive by nature. We have previously developed a theory of shot placement and optimization based on skeletonization. The real-time inverse planning process, reported in this paper, is an expansion and the clinical implementation of this theory. The complete planning process consists of two steps. The first step is to determine an optimal number of shots including locations and sizes and to assign initial collimator size to each of the shots. The second step is to fine-tune the weights using a linear-programming technique. The objective function is to minimize the total dose to the target boundary (i.e., maximize the dose conformity). Results of an ellipsoid test target and ten clinical cases are presented. The clinical cases are also compared with physician's manual plans. The target coverage is more than 99% for manual plans and 97% for all the inverse plans. The RTOG PITV conformity indices for the manual plans are between 1.16 and 3.46, compared to 1.36 to 2.4 for the inverse plans. All the inverse plans are generated in less than 2 min, making real-time inverse planning a reality.

Development of a rapid planning technique based on heuristic target shaping for stereotactic radiosurgery

Stereotactic radiosurgery (SRS) is a technique to delivering a high dose to a target region and a low dose to a critical organ by using only one or a few irradiations. Traditionally, SRS is performed using a Gamma knife with using 201 cobalt 60 sources or a linear accelerator with equally spaced noncoplanar arcs. Finding a specific condition that includes the target in the prescription dose while sparing the critical organ is tedious, because there are many combinations of positions and collimator sizes for each isocenter. Many methods of identifying suitable planning condition automatically have been proposed. However, there are some limitations using these methods. These include a long calculation time to obtain the final plan, and difficulties finding a unique solution due to different tumor shapes. This study uses three steps to solve these problems. (1) The dose distribution of one isocenter is modeled as a sphere. This makes it possible to reduce the time needed to obtain the result due to the absence of a dose calculation. (2) The target was constructed by piling up cylinders along a virtual axis, which was the longest line in a given target. (3) Spheres were then packed in each cylinder according to the position and diameter of each cylinder in order to cover each target divided by the height of the cylinder. The results of applying three imaginary targets were found to be satisfactory in terms of: target coverage-more than 50%, the reproducibility of the result and the calculation time-several tens of seconds. The PITV ratio was less than 2.0. However, the dose applied to normal tissue around the target must be reduced slightly. Planner or conventional optimization algorithms might easily solve this limitation.

Clinical implementation of an automated planning system for gamma knife radiosurgery

PURPOSE

To evaluate an automated treatment planning system for gamma knife radiosurgery. This planning system was developed in our clinic and is now in routine clinical use. The system simultaneously optimizes the shot sizes, locations, and weights. It also guides the user in selecting the total number of radiation shots.

METHODS AND MATERIALS

We assessed the clinical significance of the automated system by comparing an optimized plan with a manual plan for 10 consecutive patients treated at our gamma knife facility. Each treatment plan was analyzed using dose-volume histograms in conjunction with the conformity index, the minimum target dose, and the integral normal tissue dose.

RESULTS

On average, the treatment plan produced by the inverse planning tool provided an improved conformity index, a higher minimum target dose, and a reduced volume of the 30% isodose line as compared to the corresponding plan developed by an experienced physician. An optimized treatment plan can typically be produced in 10 min or less.

CONCLUSIONS

The automated planning system consistently provides a high-quality treatment plan while reducing the time required for gamma knife treatment planning.

Treatment planning for stereotactic radiosurgery with photon beams

Stereotactic Radiosurgery (SRS) has evolved as a unique discipline that combines aspects of both surgery and radiation oncology. Technological developments in the past few decades have provided a wide array of treatment techniques, including (i) the Gamma Knife; (ii) Linac-based stereotactic techniques using circular collimators or using micro multileaf collimators (mMLCs); (iii) the Cyber Knife, using an x-band linac mounted on a robotic arm; and (iv) serial and spiral tomotherapy. This paper provides a review of the treatment planning methods for stereotactic radiosurgery. Because of the differences in planning strategies used for each SRS technique, this paper will provide both a general review of the pre-requisites and common features of SRS treatment planning and the planning techniques specific to each of the SRS techniques.

Dependence of normal brain integral dose and normal tissue complication probability on the prescription isodose values for gamma-knife radiosurgery

A recent multi-institutional clinical study suggested possible benefits of lowering the prescription isodose lines for stereotactic radiosurgery procedures. In this study, we investigate the dependence of the normal brain integral dose and the normal tissue complication probability (NTCP) on the prescription isodose values for gamma-knife radiosurgery. An analytical dose model was developed for gamma-knife treatment planning. The dose model was commissioned by fitting the measured dose profiles for each helmet size. The dose model was validated by comparing its results with the Leksell gamma plan (LGP, version 5.30) calculations. The normal brain integral dose and the NTCP were computed and analysed for an ensemble of treatment cases. The functional dependence of the normal brain integral dose and the NCTP versus the prescribing isodose values was studied for these cases. We found that the normal brain integral dose and the NTCP increase significantly when lowering the prescription isodose lines from 50% to 35% of the maximum tumour dose. Alternatively, the normal brain integral dose and the NTCP decrease significantly when raising the prescribing isodose lines from 50% to 65% of the maximum tumour dose. The results may be used as a guideline for designing future dose escalation studies for gamma-knife applications.

Inverse treatment planning for Gamma Knife radiosurgery

An inverse treatment planning system for Gamma Knife radiosurgery has been developed using nonlinear programming techniques. The system optimizes the shot sizes, locations, and weights for Gamma Knife treatments. In the patient's prescription, the user can specify both the maximum number of shots of radiation and a minimum isodose line that must surround the entire treatment volume. After satisfying all of the constraints included in the prescription, the system maximizes the conformity of the dose distribution. This automated approach to treatment planning has been applied retrospectively to a series of patient cases, and each optimized plan has been compared to the corresponding manual plan produced by an experienced user. The results demonstrate that this tool can often improve the tumor dose homogeneity while using fewer shots than were included in the original plan. Therefore, inverse treatment planning should improve both the quality and the efficiency of Gamma Knife treatments.

Exact analytical solution of the convolution integral equation for a general profile fitting function and Gaussian detector kernel

One of the most important aspects in the metrology of radiation fields is the problem of the measurement of dose profiles in regions where the dose gradient is large. In such zones, the 'detector size effect' may produce experimental measurements that do not correspond to reality. Mathematically it can be proved, under some general assumptions of spatial linearity, that the disturbance induced in the measurement by the effect of the finite size of the detector is equal to the convolution of the real profile with a representative kernel of the detector. In this work the exact relation between the measured profile and the real profile is shown, through the analytical resolution of the integral equation for a general type of profile fitting function using Gaussian convolution kernels.