On the relationships between electron spot size, focal spot size, and virtual source position in Monte Carlo simulations.

PURPOSE: Every year, new radiotherapy techniques including stereotactic radiosurgery using linear accelerators give rise to new applications of Monte Carlo (MC) modeling. Accurate modeling requires knowing the size of the electron spot, one of the few parameters to tune in MC models. The resolution of integrated megavoltage imaging systems, such as the tomotherapy system, strongly depends on the photon spot size which is closely related to the electron spot. The aim of this article is to clarify the relationship between the electron spot size and the photon spot size (i.e., the focal spot size) for typical incident electron beam energies and target thicknesses. METHODS: Three electron energies (3, 5.5, and 18 MeV), four electron spot sizes (FWHM = 0, 0.5, 1, and 1.5 mm), and two tungsten target thicknesses (0.15 and 1 cm) were considered. The formation of the photon beam within the target was analyzed through electron energy deposition with depth, as well as photon production at several phase-space planes placed perpendicular to the beam axis, where only photons recorded for the first time were accounted for. Photon production was considered for "newborn" photons intersecting a 45 x 45 cm2 plane at the isocenter (85 cm from source). Finally, virtual source position and "effective" focal spot size were computed by back-projecting all the photons from the bottom of the target intersecting a 45 x 45 cm2 plane. The virtual source position and focal spot size were estimated at the plane position where the latter is minimal. RESULTS: In the relevant case of considering only photons intersecting the 45 x 45 cm2 plane, the results unambiguously showed that the effective photon spot is created within the first 0.25 mm of the target and that electron and focal spots may be assumed to be equal within 3-4%. CONCLUSIONS: In a good approximation photon spot size equals electron spot size for high energy X-ray treatments delivered by linear accelerators.

Monte Carlo simulation of helical tomotherapy with PENELOPE.

Helical tomotherapy (HT) delivers intensity-modulated radiation therapy (IMRT) using the simultaneous movement of the couch, the gantry and the binary multileaf collimator (MLC), a procedure that differs from conventional dynamic or step-and-shoot IMRT. A Monte Carlo (MC) simulation of HT in the helical mode therefore requires a new approach. Using validated phase-space files (PSFs) obtained through the MC simulation of the static mode with PENELOPE, an analytical model of the binary MLC, called the 'transfer function' (TF), was first devised to perform the transport of particles through the MLC much faster than time-consuming MC simulation and with no significant loss of accuracy. Second, a new tool, called TomoPen, was designed to simulate the helical mode by rotating and translating the initial coordinates and directions of the particles in the PSF according to the instantaneous position of the machine, transporting the particles through the MLC (in the instantaneous configuration defined by the sinogram), and computing the dose distribution in the CT structure using PENELOPE. Good agreement with measurements and with the treatment planning system of tomotherapy was obtained, with deviations generally well within 2%/1 mm, for the simulation of the helical mode for two commissioning procedures and a clinical plan calculated and measured in homogeneous conditions.

The impact of linac output variations on dose distributions in helical tomotherapy.

It has been suggested for quality assurance purposes that linac output variations for helical tomotherapy (HT) be within +/-2% of the long-term average. Due to cancellation of systematic uncertainty and averaging of random uncertainty over multiple beam directions, relative uncertainties in the dose distribution can be significantly lower than those in linac output. The sensitivity of four HT cases with respect to linac output uncertainties was assessed by scaling both modeled and measured systematic and random linac output uncertainties until a dose uncertainty acceptance criterion failed. The dose uncertainty acceptance criterion required the delivered dose to have at least a 95% chance of being within 2% of the planned dose in all of the voxels in the treatment volume. For a random linac output uncertainty of 5% of the long-term mean, the maximum acceptable amplitude of the modeled, sinusoidal, systematic component of the linac output uncertainty for the four cases was 1.8%. Although the measured linac output variations represented values that were outside of the +/-2% tolerance, the acceptance criterion did not fail for any of the four cases until the measured linac output variations were scaled by a factor of almost three. Thus, the +/-2% tolerance in linac output variations for HT is a more conservative tolerance than necessary.

Evaluation of a diode array for QA measurements on a helical tomotherapy unit.

A helical tomotherapy system is used in our clinic to deliver intensity-modulated radiation therapy (IMRT) treatments. Since this machine is designed to deliver IMRT treatments, the traditional field flatness requirements are no longer applicable. This allows the unit to operate without a field flatness filter and consequently the 400 mm wide fan beam is highly inhomogeneous in intensity. The shape of this beam profile is mapped during machine commissioning and for quality assurance purposes the shape of the beam profile needs to be monitored. The use of a commercial diode array for quality assurance measurements is investigated. Central axis beam profiles were acquired at different depths using solid water built-up material. These profiles were compared with ion chamber scans taken in a water tank to test the accuracy of the diode array measurements. The sensitivity of the diode array to variations in the beam profile was checked. Over a seven week period, beam profiles were repeatedly measured. The observed variations are compared with those observed with an on-board beam profile monitor. The diode measurements were in agreement with the ion chamber scans. In the high dose, low gradient region the average ratio between the diode and ion chamber readings was 1.000 +/- 0.005 (+/- 1 standard deviation). In the penumbra region the agreement was poorer but all diodes passed the distance to agreement (DTA) requirement of 2 mm. The trend in the beam profile variations that was measured with the diode array device was in agreement with the on-board monitor. While the calculated amount of variation differs between the devices, both were sensitive to subtle variations in the beam profile. The diode array is a valuable tool to quickly and accurately monitor the beam profile on a helical tomotherapy unit.

The use of megavoltage CT (MVCT) images for dose recomputations.

Megavoltage CT (MVCT) images of patients are acquired daily on a helical tomotherapy unit (TomoTherapy, Inc., Madison, WI). While these images are used primarily for patient alignment, they can also be used to recalculate the treatment plan for the patient anatomy of the day. The use of MVCT images for dose computations requires a reliable CT number to electron density calibration curve. In this work, we tested the stability of the MVCT numbers by determining the variation of this calibration with spatial arrangement of the phantom, time and MVCT acquisition parameters. The two calibration curves that represent the largest variations were applied to six clinical MVCT images for recalculations to test for dosimetric uncertainties. Among the six cases tested, the largest difference in any of the dosimetric endpoints was 3.1% but more typically the dosimetric endpoints varied by less than 2%. Using an average CT to electron density calibration and a thorax phantom, a series of end-to-end tests were run. Using a rigid phantom, recalculated dose volume histograms (DVHs) were compared with plan DVHs. Using a deformed phantom, recalculated point dose variations were compared with measurements. The MVCT field of view is limited and the image space outside this field of view can be filled in with information from the planning kVCT. This merging technique was tested for a rigid phantom. Finally, the influence of the MVCT slice thickness on the dose recalculation was investigated. The dosimetric differences observed in all phantom tests were within the range of dosimetric uncertainties observed due to variations in the calibration curve. The use of MVCT images allows the assessment of daily dose distributions with an accuracy that is similar to that of the initial kVCT dose calculation.

Theoretical calculation of electronic stopping power of water vapor by proton impact.

The energy loss of proton beams in water vapor is analyzed with a full quantum-mechanical treatment, the distorted-wave model. This model takes into account distortion effects due to the long-range Coulomb potential. Projectile energies from 10 keV up to 1 MeV are considered. Mean stopping power and equilibrium charge-state fractions are calculated and compared with experimental data. The validity of Bragg's additivity rule is investigated.

A feasible method for clinical delivery verification and dose reconstruction in tomotherapy.

Delivery verification is the process in which the energy fluence delivered during a treatment is verified. This verified energy fluence can be used in conjunction with an image in the treatment position to reconstruct the full three-dimensional dose deposited. A method for delivery verification that utilizes a measured database of detector signal is described in this work. This database is a function of two parameters, radiological path-length and detector-to-phantom distance, both of which are computed from a CT image taken at the time of delivery. Such a database was generated and used to perform delivery verification and dose reconstruction. Two experiments were conducted: a simulated prostate delivery on an inhomogeneous abdominal phantom, and a nasopharyngeal delivery on a dog cadaver. For both cases, it was found that the verified fluence and dose results using the database approach agreed very well with those using previously developed and proven techniques. Delivery verification with a measured database and CT image at the time of treatment is an accurate procedure for tomotherapy. The database eliminates the need for any patient-specific, pre- or post-treatment measurements. Moreover, such an approach creates an opportunity for accurate, real-time delivery verification and dose reconstruction given fast image reconstruction and dose computation tools.

Contribution from the inner shell of water vapour to dose profiles under proton and alpha particle irradiation.

Doubly differential cross sections for electron emission calculated using the CDW-EIS model and a simple approximation for the electron transport in the target are used to obtain dose profiles around the ion path for proton and alpha particles in water vapour. The contribution from each initial molecular orbital is determined. At large distances from the track, discrepancies are found with other models and with the well known r-2 dependence.

Multiple ionization in the earlier stages of water radiolysis.

We have studied the fragmentation of water vapour molecules induced by collision with a Xe44+ beam at 6.7 MeV/u. From the measurement of the fragment time of flight, we show that the amount of fragmentation due to multiple ionization is very large. In the case of single ionization, we are able to reproduce accurately the experimental cross sections by calculating for each molecular level the single-ionization cross section in the framework of the CDW-EIS theory and with a diagram of dissociation modified with respect to the diagram obtained in the case of dipolar ionization. By using qualitative arguments based on the ability of the medium to neutralize a charged species, we tentatively extend our result to liquid water. From our analysis, we show that ionizations involving three or more ejected electrons could enhance the oxygen production. For the physicochemical phase we estimate that the rate of oxygen production by multiple ionization represents approximately 18% of the OH rate produced by single ionization.

On the verification of the incident energy fluence in tomotherapy IMRT.

For any radiotherapy verification technique, it is desirable that issues with the accelerator, multileaf collimator and patient position be detected. In previous works, an effective method for this level of verification was presented. This paper identifies second-order issues affecting the part of the process in which the incident energy fluence is verified. These problems will affect any rotational intensity-modulated radiotherapy delivery that divides each rotation or arc into projections: however the solutions offered in this paper are specific to the method previously developed. The issues affecting the energy fluence verification method include leaf bouncing. delivery implementation and leaf latency. All three matters were found to introduce small errors in the verified energy fluence values for a small fraction of leaf states. The overall effect on the deposited dose over the course of a rotational delivery involving thousands of beam pulses per rotation is negligible. Regardless, effective correction strategies are presented; these are utilized in order to characterize both the delivered energy fluence and deposited dose as accurately as possible.

Iterative approaches to dose optimization in tomotherapy.

This paper will present the results of an investigation into three iterative approaches to inverse treatment planning. These techniques have been examined in the hope of developing an optimization algorithm suitable for the large-scale problems that are encountered in tomotherapy. The three iterative techniques are referred to as the ratio method, iterative least-squares minimization and the maximum-likelihood estimator. Our results indicate that each of these techniques can serve as a useful tool in tomotherapy optimization. As compared with other mathematical programming techniques, the iterative approaches can reduce both memory demands and time requirements. In this paper, the results from small- and large-scale optimizations will be analysed. It will also be demonstrated that the flexibility of the iterative techniques can be greatly enhanced through the use of dose-volume histogram based penalty functions and/or through the use of weighting factors assigned to each region of the patient. Finally, results will be presented from an investigation into the stability of the iterative techniques.

Megavoltage CT on a tomotherapy system.

A megavoltage computed tomography (MVCT) system was developed on the University of Wisconsin tomotherapy benchtop. This system can operate either axially or helically, and collect transmission data without any bounds on delivered dose. Scan times as low as 12 s per slice are possible, and scans were run with linac output rates of 100 MU min(-1), although the system can be tuned to deliver arbitrarily low dose rates. Images were reconstructed with clinically reasonable doses ranging from 8 to 12 cGy. These images delineate contrasts below 2% and resolutions of 3.0 mm. Thus, the MVCT image quality of this system should be sufficient for verifying the patient's position and anatomy prior to radiotherapy. Additionally, synthetic data were used to test the potential for improved MVCT contrast using maximum-likelihood (ML) reconstruction. Specifically, the maximum-likelihood expectation-maximization (ML-EM) algorithm and a transmission ML algorithm were compared with filtered backprojection (FBP). It was found that for expected clinical MVCT doses enough imaging photons are used such that little benefit is conferred by the improved noise model of ML algorithms. For significantly lower doses, some quantitative improvement is achieved through ML reconstruction. Nonetheless, the image quality at those lower doses is not satisfactory for radiotherapy verification.

Calibration of a tomotherapeutic MVCT system.

Megavoltage CT provides the ability to image the patient before, during or after a radiotherapy treatment. This allows one to verify not only the placement of a patient's external boundary, but also the locations of internal anatomy. In addition, the reconstructed MVCT values are potentially useful for treatment planning inhomogeneity corrections and dose reconstruction. To this end, dosimetric calibration of the University of Wisconsin Tomotherapy Benchtop MVCT system was investigated. It was found that MVCT values correlate extremely well with electron density and that unlike kilovoltage CT, this correlation is well maintained for higher atomic number materials. Improvements of the order of 1% in the dosimetric calculations of high atomic number materials should be possible by deriving input images from MVCT as opposed to kVCT, and calibrating in terms of electron density, as opposed to physical density.

Megavoltage CT image reconstruction during tomotherapy treatments.

An integrated tomotherapy system allows for improved radiotherapy verification by enabling the collection of megavoltage computed tomography (MVCT) images before or after treatment delivery. In this investigation, the possibility of collecting MV tomographic data and reconstructing images during a tomotherapy treatment is examined. By overcoming difficulties with the normalization of modulated treatment data and with the incompleteness of treatment data, it is possible to use data collected during tomotherapeutic treatments for MVCT reconstruction. The benefits of these techniques include potential increases in patient throughput, reductions in imaging dose, visualization of the patient in the treatment position and improvements in image contrast.

Maximum likelihood as a common computational framework in tomotherapy.

Tomotherapy is a dose delivery technique using helical or axial intensity modulated beams. One of the strengths of the tomotherapy concept is that it can incorporate a number of processes into a single piece of equipment. These processes include treatment optimization planning, dose reconstruction and kilovoltage/megavoltage image reconstruction. A common computational technique that could be used for all of these processes would be very appealing. The maximum likelihood estimator, originally developed for emission tomography, can serve as a useful tool in imaging and radiotherapy. We believe that this approach can play an important role in the processes of optimization planning, dose reconstruction and kilovoltage and/or megavoltage image reconstruction. These processes involve computations that require comparable physical methods. They are also based on equivalent assumptions, and they have similar mathematical solutions. As a result, the maximum likelihood approach is able to provide a common framework for all three of these computational problems. We will demonstrate how maximum likelihood methods can be applied to optimization planning, dose reconstruction and megavoltage image reconstruction in tomotherapy. Results for planning optimization, dose reconstruction and megavoltage image reconstruction will be presented. Strengths and weaknesses of the methodology are analysed. Future directions for this work are also suggested.

Image/patient registration from (partial) projection data by the Fourier phase matching method.

A technique for 2D or 3D image/patient registration, PFPM (projection based Fourier phase matching method), is proposed. This technique provides image/patient registration directly from sequential tomographic projection data. The method can also deal with image files by generating 2D Radon transforms slice by slice. The registration in projection space is done by calculating a Fourier invariant (FI) descriptor for each one-dimensional projection datum, and then registering the FI descriptor by the Fourier phase matching (FPM) method. The algorithm has been tested on both synthetic and experimental data. When dealing with translated, rotated and uniformly scaled 2D image registration, the performance of the PFPM method is comparable to that of the IFPM (image based Fourier phase matching) method in robustness, efficiency, insensitivity to the offset between images, and registration time. The advantages of the former are that subpixel resolution is feasible, and it is more insensitive to image noise due to the averaging effect of the projection acquisition. Furthermore, the PFPM method offers the ability to generalize to 3D image/patient registration and to register partial projection data. By applying patient registration directly from tomographic projection data, image reconstruction is not needed in the therapy set-up verification, thus reducing computational time and artefacts. In addition, real time registration is feasible. Registration from partial projection data meets the geometry and dose requirements in many application cases and makes dynamic set-up verification possible in tomotherapy.

Delivery verification in sequential and helical tomotherapy.

Conformal and conformal avoidance radiation therapy are new therapeutic techniques that are generally characterized by high dose gradients. The success of this kind of treatment relies on quality assurance procedures in order to verify the delivery of the treatment. A delivery verification technique should consider quality assurance procedures for patient positioning and radiation delivery verification. A methodology for radiation delivery verification was developed and tested with our tomotherapy workbench. The procedure was investigated for two cases. The first treatment using a torus-shaped target was optimized for 72 beam directions and sequentially delivered as a single slice to a 33 cm diameter cylinder of homogeneous solid water. For the second treatment, a random pattern of energy fluence was helically delivered for two slices to a 9.0 cm diameter phantom containing inhomogeneities. The presented process provides the energy fluence (or a related quantity) delivered through the multileaf collimator (MLC) using the signal measured at the exit detector during the treatment delivery. As this information is created for every pulse of the accelerator, the energy fluence and state for each MLC leaf were verified on a pulse-by-pulse basis. The pulse-by-pulse results were averaged to obtain projection-by-projection information to allow for a comparison with the planned delivery. The errors between the planned and delivered energy fluences were concentrated between +/-2.0%, with none beyond +/-3.5%. In addition to accurately achieving radiation delivery verification, the process is fast, which could translate to radiation delivery verification in real time. This technique can also be extended to reconstruct the dose actually deposited in the patient or phantom (dose reconstruction).

On the accuracy and effectiveness of dose reconstruction for tomotherapy.

Dose reconstruction is a process that re-creates the treatment-time dose deposited in a patient provided there is knowledge of the delivered energy fluence and the patient's anatomy at the time of treatment. A method for reconstructing dose is presented. The process starts with delivery verification, in which the incident energy fluence from a treatment is computed using the exit detector signal and a transfer matrix to convert the detector signal to energy fluence. With the verified energy fluence and a CT image of the patient in the treatment position, the treatment-time dose distribution is computed using any model-based algorithm such as convolution/superposition or Monte Carlo. The accuracy of dose reconstruction and the ability of the process to reveal delivery errors are presented. Regarding accuracy, a reconstructed dose distribution was compared with a measured film distribution for a simulated breast treatment carried out on a thorax phantom. It was found that the reconstructed dose distribution agreed well with the dose distribution measured using film: the majority of the voxels were within the low and high dose-gradient tolerances of 3% and 3 mm respectively. Concerning delivery errors, it was found that errors associated with the accelerator, the multileaf collimator and patient positioning might be detected in the verified energy fluence and are readily apparent in the reconstructed dose. For the cases in which errors appear in the reconstructed dose, the possibility for adaptive radiotherapy is discussed.

Registration using tomographic projection files.

An algorithm has been developed and experimentally verified for tomographic registration--a patient positioning method using internal anatomy and standard external fiducial marks. This algorithm improves patient set-up and verification to an accuracy sufficient for tomotherapy. By implementation of this technique, the time-consuming reconstruction process is avoided. Instead, offsets in the x, y and z directions are determined directly from sinogram data by an algorithm that utilizes cross-correlations and Fourier transforms. To verify the efficiency and stability of the algorithm, data were collected on the University of Wisconsin's dedicated tomotherapy research workbench. The experiment indicates offset statistical errors of less than +/-0.8 mm for offsets up to 30 mm. With standard clinical techniques, initial patient offsets are expected to be less than 5 mm, so the 30 mm limitation is of no consequence. The angular resolution for the direction of patient translation is within the +/-2 degrees needed for tomotherapy.

Quality assurance of a helical tomotherapy machine.

Helical tomotherapy has been developed at the University of Wisconsin, and 'Hi-Art II' clinical machines are now commercially manufactured. At the core of each machine lies a ring-gantry-mounted short linear accelerator which generates x-rays that are collimated into a fan beam of intensity-modulated radiation by a binary multileaf, the modulation being variable with gantry angle. Patients are treated lying on a couch which is translated continuously through the bore of the machine as the gantry rotates. Highly conformal dose-distributions can be delivered using this technique, which is the therapy equivalent of spiral computed tomography. The approach requires synchrony of gantry rotation, couch translation, accelerator pulsing and the opening and closing of the leaves of the binary multileaf collimator used to modulate the radiation beam. In the course of clinically implementing helical tomotherapy, we have developed a quality assurance (QA) system for our machine. The system is analogous to that recommended for conventional clinical linear accelerator QA by AAPM Task Group 40 but contains some novel components, reflecting differences between the Hi-Art devices and conventional clinical accelerators. Here the design and dosimetric characteristics of Hi-Art machines are summarized and the QA system is set out along with experimental details of its implementation. Connections between this machine-based QA work, pre-treatment patient-specific delivery QA and fraction-by-fraction dose verification are discussed.