Feasibility of energy adaptive angular meshing for perpendicular and parallel magnetic fields in a grid based Boltzmann solver.

PURPOSE: To develop the enabling algorithmic techniques which allow forward-peaked adaptive angular meshing to be compatible with angular advection of magnetic fields within a deterministic Grid Based Boltzmann Solver (GBBS) for MRI-guided radiotherapy, and establish appropriate energy adaptive meshing schemes which minimize total numerical degrees of freedom while preserving high dosimetric accuracy for parallel and perpendicular magnetic fields. METHODS: A framework to independently adapt angular mesh resolution and basis function refinement of forward and backscattering hemispheres is developed, uniquely accommodating angular advection introduced by magnetic fields. Upwind stabilization techniques to accurately transfer fluence between hemispheres having different discretization are established. To facilitate oblique beam and magnetic field orientations, cardinal forward-peaked mesh orientations were devised to balance requirements for acyclic space-angle sweep ordering, while ensuring the beam predominantly overlaps the forward hemisphere. Energy-dependent fluence anisotropy is investigated, leading to adaptive angular meshing schemes for parallel and perpendicular magnetic fields. Calculated dose distributions were validated against GEANT4 Monte Carlo calculations on slab geometry and anthropomorphic phantoms. RESULTS: Forward-peaked and isotropic energy adaptive angular meshing schemes were developed for parallel and perpendicular magnetic fields respectively, which reduce the number of elements solved by 52.8% and 47.7% respectively compared to static discretization using 32 quadratic elements while retaining over 97% of points passing the gamma 1%/1 mm criterion against Monte Carlo. CONCLUSIONS: Techniques to preserve angular upwind-stabilization between hemispheres of a forward-peaked mesh and establish an acyclic directed space-angle sweep graph enabled energy-adaptive meshing schemes to be developed while accurately solving for magnetic fields. This substantially reduced the numerical degrees of freedom while retaining excellent dosimetric agreement with Monte Carlo. These algorithmic underpinnings contribute towards a fast deterministic GBBS for MRI-guided radiotherapy.

A novel transport sweep architecture for efficient deterministic patient dose calculations in MRI-guided radiotherapy.

Accurate and efficient patient dose calculations are essential for treatment planning in magnetic resonance imaging guided radiotherapy (MRIgRT). Achieving reasonable performance for a space-angle discontinuous finite element method (DFEM) grid based Boltzmann solver (GBBS) with magnetic fields for clinical MRIgRT applications largely depends on how the transport sweep is orchestrated. Compared to classical Discrete Ordinates, DFEM in angle introduces increased angular degrees of freedom and eliminates ray-effect artifacts. However, the inclusion of magnetic fields introduces additional serial dependencies such that parallelization of the space-angle transport sweeps becomes more challenging. Novel techniques for the transport sweep and right-hand source assembly are developed, predicated on limiting the number of bulk material densities modeled in the transport sweep scatter calculations. Specifically, k-means clustering is used to assign sub-intervals of mass-density for each spatial element to execute the scatter-dose calculations using batched multiplication by pre-inverted transport sweep matrices. This is shown to be two orders of magnitude more efficient than solving each elemental system individually at runtime. Even with discrete material densities used in the transport sweep scatter calculations, accuracy is maintained by optimizing the material density assignments using k-means clustering, and by performing the primary photon fluence calculations (ray-tracing) using the underlying continuous density of the computed tomography (CT) image. In the presence of 0.5 T parallel and 1.5 T perpendicular magnetic fields, this approach demonstrates high levels of accuracy with gamma 1%/1 mm passing rates exceeding 94% across a range of anatomical sites compared to GEANT4 Monte Carlo dose calculations which used continuous densities. This deterministic GBBS approach maintains unconditional stability, produces no ray-effect artifacts, and has the benefit of no statistical uncertainty. Runtime on a non-parallelized Matlab implementation averaged 10 min per beam averaging 80 000 spatial elements, paving way for future development based on this algorithmically efficient paradigm.

Proton beam behavior in a parallel configured MRI-proton therapy hybrid: Effects of time-varying gradient magnetic fields.

PURPOSE: Real-time magnetic resonance (MR) guidance is of interest to various groups globally because the superior soft tissue contrast MR images offer over other x-ray-based imaging modalities. Because of the precision required in proton therapy, proton therapy treatments rely heavily on image guidance. Integrating a magnetic resonance imaging (MRI) into a proton therapy treatment is a challenge. The charged particles (protons) used in proton therapy experience magnetic forces when travelling through the MRI magnetic fields. Given that it is desired that proton beams can be delivered with submillimeter accuracy, it is important that all potential sources of beam displacement are well modeled and understood. This study investigated the behavior of monoenergetic proton beams in the presence of a simulated set of realistic three-dimensional (3D) vector magnetic gradient fields required for spatial localization during imaging. This deflecting source has not been previously investigated. METHODS: Three-dimensional magnetic vector fields from a superconducting 0.5 T open bore MRI magnet model (previously developed in-house) and 3D magnetic fields from an in-house gradient coil model were applied to two types of computer simulations. In all simulations, monoenergetic proton pencil beams (from 80 to 250 MeV) were used. The initial directions of proton beams were varied. In all simulations, the orientation of the B0 field coincided with the positive z-axis in the simulation geometry. The first type of simulation is based on an analytic magnetic force equation (analytic simulations) while the second type is a full Monte Carlo (MC) simulation. The analytic simulations were limited to propagating the proton beams in vacuum but could be rapidly calculated in a desktop computer while the MC simulations were calculated in a cluster computer. The proton beam locations and dose profiles at the central plane (z = 0 cm) with or without magnetic fields were extracted and used to quantify the effect of the presence of the different magnetic fields on the proton beam. RESULTS: The analytic simulations agree with MC results within 0.025 mm, thus acting as the verification of MC calculations. The presence of the B0 field caused the beam to follow a helical trajectory which resulted in angular offsets of 4.9o , 3.6o , and 2.8o for the 80, 150, and 250 MeV, respectively. Magnetic field deflections caused by a rapid MRI sequence (bSSFP, with maximum gradient strength of 40 mT/m) show a pattern of distortion which remained spatially invariant in the MR's field of view. For the 80 MeV beam, this pattern shows a maximum ranged in the y direction of 1.5 mm. The presence of the B0 field during the bSSFP simulations adds the same beam rotation to the observed during the B0 only simulations. CONCLUSION: This investigation reveals that time-varying gradient magnetic fields required for image generation can cause a small spread in the proton beams used in the study which are independent of the effects arising from the B0 field. Further, studies where clinical beam kernels were convolved with this spread show that these magnetic fields are expected to have an insignificant impact on the beam's entrance dose.

On the direct acquisition of beam's-eye-view images in MRI for integration with external beam radiotherapy.

The recent interest in the integration of external beam radiotherapy with a magnetic resonance (MR) imaging unit offers the potential for real-time adaptive tumour tracking during radiation treatment. The tracking of large tumours which follow a rapid trajectory may best be served by the generation of a projection image from the perspective of the beam source, or 'beam's eye view' (BEV). This type of image projection represents the path of the radiation beam, thus enabling rapid compensations for target translations, rotations and deformations, as well time-dependent critical structure avoidance. MR units have been traditionally incapable of this type of imaging except through lengthy 3D acquisitions and ray tracing procedures. This work investigates some changes to the traditional MR scanner architecture that would permit the direct acquisition of a BEV image suitable for integration with external beam radiotherapy. Based on the theory presented in this work, a phantom was imaged with nonlinear encoding-gradient field patterns to demonstrate the technique. The phantom was constructed with agarose gel tubes spaced two cm apart at their base and oriented to converge towards an imaginary beam source 100 cm away. A corresponding virtual phantom was also created and subjected to the same encoding technique as in the physical demonstration, allowing the method to be tested without hardware limitations. The experimentally acquired and simulated images indicate the feasibility of the technique, showing a substantial amount of blur reduction in a diverging phantom compared to the conventional imaging geometry, particularly with the nonlinear gradients ideally implemented. The theory is developed to demonstrate that the method can be adapted in a number of different configurations to accommodate all proposed integration schemes for MR units and radiotherapy sources. Depending on the configuration, the implementation of this technique will require between two and four additional nonlinear encoding coils.

A novel upwind stabilized discontinuous finite element angular framework for deterministic dose calculations in magnetic fields.

Angular discretization impacts nearly every aspect of a deterministic solution to the linear Boltzmann transport equation, especially in the presence of magnetic fields, as modeled by a streaming operator in angle. In this work a novel stabilization treatment of the magnetic field term is developed for an angular finite element discretization on the unit sphere, specifically involving piecewise partitioning of path integrals along curved element edges into uninterrupted segments of incoming and outgoing flux, with outgoing components updated iteratively. Correct order-of-accuracy for this angular framework is verified using the method of manufactured solutions for linear, quadratic, and cubic basis functions in angle. Higher order basis functions were found to reduce the error especially in strong magnetic fields and low density media. We combine an angular finite element mesh respecting octant boundaries on the unit sphere to spatial Cartesian voxel elements to guarantee an unambiguous transport sweep ordering in space. Accuracy for a dosimetrically challenging scenario involving bone and air in the presence of a 1.5 T parallel magnetic field is validated against the Monte Carlo package GEANT4. Accuracy and relative computational efficiency were investigated for various angular discretization parameters. 32 angular elements with quadratic basis functions yielded a reasonable compromise, with gamma passing rates of 99.96% (96.22%) for a 2%/2 mm (1%/1 mm) criterion. A rotational transformation of the spatial calculation geometry is performed to orient an arbitrary magnetic field vector to be along the z-axis, a requirement for a constant azimuthal angular sweep ordering. Working on the unit sphere, we apply the same rotational transformation to the angular domain to align its octants with the rotated Cartesian mesh. Simulating an oblique 1.5 T magnetic field against GEANT4 yielded gamma passing rates of 99.42% (95.45%) for a 2%/2 mm (1%/1 mm) criterion.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy.

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Sliding window prior data assisted compressed sensing for MRI tracking of lung tumors.

PURPOSE: Hybrid magnetic resonance imaging and radiation therapy devices are capable of imaging in real-time to track intrafractional lung tumor motion during radiotherapy. Highly accelerated magnetic resonance (MR) imaging methods can potentially reduce system delay time and/or improves imaging spatial resolution, and provide flexibility in imaging parameters. Prior Data Assisted Compressed Sensing (PDACS) has previously been proposed as an acceleration method that combines the advantages of 2D compressed sensing and the KEYHOLE view-sharing technique. However, as PDACS relies on prior data acquired at the beginning of a dynamic imaging sequence, decline in image quality occurs for longer duration scans due to drifts in MR signal. Novel sliding window-based techniques for refreshing prior data are proposed as a solution to this problem. METHODS: MR acceleration is performed by retrospective removal of data from the fully sampled sets. Six patients with lung tumors are scanned with a clinical 3 T MRI using a balanced steady-state free precession (bSSFP) sequence for 3 min at approximately 4 frames per second, for a total of 650 dynamics. A series of distinct pseudo-random patterns of partial k-space acquisition is generated such that, when combined with other dynamics within a sliding window of 100 dynamics, covers the entire k-space. The prior data in the sliding window are continuously refreshed to reduce the impact of MR signal drifts. We intended to demonstrate two different ways to utilize the sliding window data: a simple averaging method and a navigator-based method. These two sliding window methods are quantitatively compared against the original PDACS method using three metrics: artifact power, centroid displacement error, and Dice's coefficient. The study is repeated with pseudo 0.5 T images by adding complex, normally distributed noise with a standard deviation that reduces image SNR, relative to original 3 T images, by a factor of 6. RESULTS: Without sliding window implemented, PDACS-reconstructed dynamic datasets showed progressive increases in image artifact power as the 3 min scan progresses. With sliding windows implemented, this increase in artifact power is eliminated. Near the end of a 3 min scan at 3 T SNR and 5× acceleration, implementation of an averaging (navigator) sliding window method improves our metrics by the following ways: artifact power decreases from 0.065 without sliding window to 0.030 (0.031), centroid error decreases from 2.64 to 1.41 mm (1.28 mm), and Dice coefficient agreement increases from 0.860 to 0.912 (0.915). At pseudo 0.5 T SNR, the improvements in metrics are as follows: artifact power decreases from 0.110 without sliding window to 0.0897 (0.0985), centroid error decreases from 2.92 mm to 1.36 mm (1.32 mm), and Dice coefficient agreements increases from 0.851 to 0.894 (0.896). CONCLUSIONS: In this work we demonstrated the negative impact of slow changes in MR signal for longer duration PDACS dynamic scans, namely increases in image artifact power and reductions of tumor tracking accuracy. We have also demonstrated sliding window implementations (i.e., refreshing of prior data) of PDACS are effective solutions to this problem at both 3 T and simulated 0.5 T bSSFP images.

Influence of standard RF coil materials on surface and buildup dose from a 6 MV photon beam in magnetic field.

PURPOSE: Magnetic resonance guided teletherapy systems aspire to image the patient concurrently with the radiation delivery. Thus, the radiofrequency (RF) coils used for magnetic resonance imaging, placed on or close to patient skin and in close proximity to the treatment volume, would be irradiated leading to modifications of radiation dose to the skin and in the buildup region. The purpose of this work is to measure and assess these dose modifications due to standard off-the-shelf RF coil materials. METHODS: A typical surface coil was approximated as layered sheets of polycarbonate, copper tape, and Teflon to emulate the base, conductor, and cover, respectively. A separate investigation used additional coil materials, such as copper pipe, plastic coil housing, a typical coil padding material, and a thin copper conductor. The materials were placed in the path of a 6 MV photon beam at various distances from polystyrene phantoms in which the surface and buildup doses were measured. The experiments were performed on a clinical Varian linac with no magnetic field and with a 0.21 T electromagnet producing a magnetic field parallel to the beam central axis. The authors repeated similar experiments in the presence of a 0.22 T magnetic field oriented perpendicular to the beam central axis using an earlier linac-MR prototype, with a biplanar permanent magnet. The radiation detectors used for the measurements were two different parallel plate ion chambers and GAFChromic films. RESULTS: A typical open beam surface dose of 20% (relative to open beam Dmax) was increased to 63% by the coil padding material and to >74% by all other materials when placed in direct contact with the phantom, irrespective of magnetic field presence or orientation. Without a magnetic field, the surface dose decreased as the test materials were moved away from the phantom surface toward the radiation source, reaching between 30% and 40% at 10 cm gap between the phantom and the test materials. In the presence of the transverse magnetic field, the surface dose reduction was more rapid reaching a dose level of 30%-40% with only 3-4 cm gap. In the presence of the parallel magnetic field, as expected, the surface dose did not decrease considerably as the gap between the phantom surface and test materials was increased; the surface dose remained >60% at 10 cm gap for all tested materials except for the thin copper conductor. CONCLUSIONS: As expected, placing coil materials in direct contact with the phantom surface increases the surface dose considerably. The surface dose is reduced by creating a gap between the coil materials and phantom surface. This dose reduction happens more rapidly in the presence of a transverse magnetic field. However, the surface dose stays relatively large irrespective of the gap in the presence of a parallel magnetic field. Thus, the standard, off-the-shelf RF coils should be used with caution in integrated linac-MR systems, especially those using a parallel magnetic field orientation in which case the RF coils will probably need to be reconfigured to create open ports for the radiation beam.

Correlation between k-space sampling pattern and MTF in compressed sensing MRSI.

PURPOSE: To investigate the relationship between the k-space sampling patterns used for compressed sensing MR spectroscopic imaging (CS-MRSI) and the modulation transfer function (MTF) of the metabolite maps. This relationship may allow the desired frequency content of the metabolite maps to be quantitatively tailored when designing an undersampling pattern. METHODS: Simulations of a phantom were used to calculate the MTF of Nyquist sampled (NS) 32 × 32 MRSI, and four-times undersampled CS-MRSI reconstructions. The dependence of the CS-MTF on the k-space sampling pattern was evaluated for three sets of k-space sampling patterns generated using different probability distribution functions (PDFs). CS-MTFs were also evaluated for three more sets of patterns generated using a modified algorithm where the sampling ratios are constrained to adhere to PDFs. RESULTS: Strong visual correlation as well as high R2 was found between the MTF of CS-MRSI and the product of the frequency-dependant sampling ratio and the NS 32 × 32 MTF. Also, PDF-constrained sampling patterns led to higher reproducibility of the CS-MTF, and stronger correlations to the above-mentioned product. CONCLUSIONS: The relationship established in this work provides the user with a theoretical solution for the MTF of CS MRSI that is both predictable and customizable to the user's needs.

CNR considerations for rapid real-time MRI tumor tracking in radiotherapy hybrid devices: Effects of B0 field strength.

PURPOSE: This work examines the subject of contrast-to-noise ratio (CNR), specifically between tumor and tissue background, and its dependence on the MRI field strength, B0. This examination is motivated by the recent interest and developments in MRI/radiotherapy hybrids where real-time imaging can be used to guide treatment beams. The ability to distinguish a tumor from background tissue is of primary importance in this field, and this work seeks to elucidate the complex relationship between the CNR and B0 that is too often assumed to be purely linear. METHODS: Experimentally based models of B0-dependant relaxation for various tumor and normal tissues from the literature were used in conjunction with signal equations for MR sequences suitable for rapid real-time imaging to develop field-dependent predictions for CNR. These CNR models were developed for liver, lung, breast, glioma, and kidney tumors for spoiled gradient-echo, balanced steady-state free precession (bSSFP), and single-shot half-Fourier fast spin echo sequences. RESULTS: Due to the pattern in which the relaxation properties of tissues are found to vary over B0 field (specifically the T1 time), there was always an improved CNR at lower fields compared to linear dependency. Further, in some tumor sites, the CNR at lower fields was found to be comparable to, or sometimes higher than those at higher fields (i.e., bSSFP CNR for glioma, kidney, and liver tumors). CONCLUSIONS: In terms of CNR, lower B0 fields have been shown to perform as well or better than higher fields for some tumor sites due to superior T1 contrast. In other sites this effect was less pronounced, reversing the CNR advantage. This complex relationship between CNR and B0 reveals both low and high magnetic fields as viable options for tumor tracking in MRI/radiotherapy hybrids.

Minimal skin dose increase in longitudinal rotating biplanar linac-MR systems: examination of radiation energy and flattening filter design.

The magnetic fields of linac-MR systems modify the path of contaminant electrons in photon beams, which alters patient entrance skin dose. Also, the increased SSD of linac-MR systems reduces the maximum achievable dose rate. To accurately quantify the changes in entrance skin dose, the authors use EGSnrc Monte Carlo calculations that incorporate 3D magnetic field of the Alberta 0.5 T longitudinal linac-MR system. The Varian 600C linac head geometry assembled on the MRI components is used in the BEAMnrc simulations for 6 MV and 10 MV beam models and skin doses are calculated at an average depth of 70 µm using DOSXYZnrc. 3D modeling shows that magnetic fringe fields decay rapidly and are small at the linac head. SSDs between 100 and 120 cm result in skin-dose increases of between ~6%-19% and ~1%-9% for the 6 and 10 MV beams, respectively. For 6 MV, skin dose increases from ~10.5% to ~1.5% for field-size increases of 5 × 5 cm(2) to 20 × 20 cm(2). For 10 MV, skin dose increases by ~6% for a 5 × 5 cm(2) field, and decreases by ~1.5% for a 20 × 20 cm(2) field. Furthermore, the proposed reshaped flattening filter increases the dose rate from the current 355 MU min(-1) to 529 MU min(-1) (6 MV) or 604 MU min(-1) (10 MV), while the skin-dose increases by only an additional ~2.6% (all percent increases in skin dose are relative to D max). This study suggests that there is minimal increase in the entrance skin dose and minimal/no decrease in the dose rate of the Alberta longitudinal linac-MR system. The even lower skin dose increase at 10 MV offers further advantages in future designs of linac-MR prototypes.

Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: Application to MRI-guided radiotherapy.

PURPOSE: The advent of magnetic resonance imaging (MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann transport equation to accurately account for the effects of magnetic fields on radiotherapy doses. METHODS: The authors present a detailed description of their new formalism and compare its accuracy to geant4 Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors' new formalism was determined using a gamma analysis with a 2%/2 mm criterion. RESULTS: Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiation transport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions. CONCLUSIONS: A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann transport equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against geant4, even in cases of strong magnetic field strengths and low density air.

Technical Note: Response measurement for select radiation detectors in magnetic fields.

PURPOSE: Dose response to applied magnetic fields for ion chambers and solid state detectors has been investigated previously for the anticipated use in linear accelerator-magnetic resonance devices. In this investigation, the authors present the measured response of selected radiation detectors when the magnetic field is applied in the same direction as the radiation beam, i.e., a longitudinal magnetic field, to verify previous simulation only data. METHODS: The dose response of a PR06C ion chamber, PTW60003 diamond detector, and IBA PFD diode detector is measured in a longitudinal magnetic field. The detectors are irradiated with buildup caps and their long axes either parallel or perpendicular to the incident photon beam. In each case, the magnetic field dose response is reported as the ratio of detector signals with to that without an applied longitudinal magnetic field. The magnetic field dose response for each unique orientation as a function of magnetic field strength was then compared to the previous simulation only studies. RESULTS: The measured dose response of each detector in longitudinal magnetic fields shows no discernable response up to near 0.21 T. This result was expected and matches the previously published simulation only results, showing no appreciable dose response with magnetic field. CONCLUSIONS: Low field longitudinal magnetic fields have been shown to have little or no effect on the dose response of the detectors investigated and further lend credibility to previous simulation only studies.

Neural-network based autocontouring algorithm for intrafractional lung-tumor tracking using Linac-MR.

PURPOSE: To develop a neural-network based autocontouring algorithm for intrafractional lung-tumor tracking using Linac-MR and evaluate its performance with phantom and in-vivo MR images. METHODS: An autocontouring algorithm was developed to determine both the shape and position of a lung tumor from each intrafractional MR image. A pulse-coupled neural network was implemented in the algorithm for contrast improvement of the tumor region. Prior to treatment, to initiate the algorithm, an expert user needs to contour the tumor and its maximum anticipated range of motion in pretreatment MR images. During treatment, however, the algorithm processes each intrafractional MR image and automatically generates a tumor contour without further user input. The algorithm is designed to produce a tumor contour that is the most similar to the expert's manual one. To evaluate the autocontouring algorithm in the author's Linac-MR environment which utilizes a 0.5 T MRI, a motion phantom and four lung cancer patients were imaged with 3 T MRI during normal breathing, and the image noise was degraded to reflect the image noise at 0.5 T. Each of the pseudo-0.5 T images was autocontoured using the author's algorithm. In each test image, the Dice similarity index (DSI) and Hausdorff distance (HD) between the expert's manual contour and the algorithm generated contour were calculated, and their centroid positions were compared (Δd centroid). RESULTS: The algorithm successfully contoured the shape of a moving tumor from dynamic MR images acquired every 275 ms. From the phantom study, mean DSI of 0.95-0.96, mean HD of 2.61-2.82 mm, and mean Δd centroid of 0.68-0.93 mm were achieved. From the in-vivo study, the author's algorithm achieved mean DSI of 0.87-0.92, mean HD of 3.12-4.35 mm, as well as Δd centroid of 1.03-1.35 mm. Autocontouring speed was less than 20 ms for each image. CONCLUSIONS: The authors have developed and evaluated a lung tumor autocontouring algorithm for intrafractional tumor tracking using Linac-MR. The autocontouring performance in the Linac-MR environment was evaluated using phantom and in-vivo MR images. From the in-vivo study, the author's algorithm achieved 87%-92% of contouring agreement and centroid tracking accuracy of 1.03-1.35 mm. These results demonstrate the feasibility of lung tumor autocontouring in the author's laboratory's Linac-MR environment.

FEM design and simulation of a short, 10 MV, S-band Linac with Monte Carlo dose simulations.

PURPOSE: Current commercial 10 MV Linac waveguides are 1.5 m. The authors' current 6 MV linear accelerator-magnetic resonance imager (Linac-MR) system fits in typical radiotherapy vaults. To allow 10 MV treatments with the Linac-MR and still fit within typical vaults, the authors design a 10 MV Linac with an accelerator waveguide of the same length (27.5 cm) as current 6 MV Linacs. METHODS: The first design stage is to design a cavity such that a specific experimental measurement for breakdown is applicable to the cavity. This is accomplished through the use of finite element method (FEM) simulations to match published shunt impedance, Q factor, and ratio of peak to mean-axial electric field strength from an electric breakdown study. A full waveguide is then designed and tuned in FEM simulations based on this cavity design. Electron trajectories are computed through the resulting radio frequency fields, and the waveguide geometry is modified by shifting the first coupling cavity in order to optimize the electron beam properties until the energy spread and mean energy closely match values published for an emulated 10 MV Linac. Finally, Monte Carlo dose simulations are used to compare the resulting photon beam depth dose profile and penumbra with that produced by the emulated 10 MV Linac. RESULTS: The shunt impedance, Q factor, and ratio of peak to mean-axial electric field strength are all matched to within 0.1%. A first coupling cavity shift of 1.45 mm produces an energy spectrum width of 0.347 MeV, very close to the published value for the emulated 10 MV of 0.315 MeV, and a mean energy of 10.53 MeV, nearly identical to the published 10.5 MeV for the emulated 10 MV Linac. The depth dose profile produced by their new Linac is within 1% of that produced by the emulated 10 MV spectrum for all depths greater than 1.5 cm. The penumbra produced is 11% narrower, as measured from 80% to 20% of the central axis dose. CONCLUSIONS: The authors have successfully designed and simulated an S-band waveguide of length of 27.5 cm capable of producing a 10 MV photon beam. This waveguide operates well within the breakdown threshold determined for the cavity geometry used. The designed Linac produces depth dose profiles similar to those of the emulated 10 MV Linac (waveguide-length of 1.5 m) but yields a narrower penumbra.

A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields.

PURPOSE: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today's treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. METHODS: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf_macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm(2) field as well as a smaller 2 × 2 cm(2) field. RESULTS: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm's high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization. CONCLUSIONS: The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann transport equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.

Development and reliability of a multi-modality scoring system for evaluation of disease progression in pre-clinical models of osteoarthritis: celecoxib may possess disease-modifying properties.

OBJECTIVE: We sought to develop a comprehensive scoring system for evaluation of pre-clinical models of osteoarthritis (OA) progression, and use this to evaluate two different classes of drugs for management of OA. METHODS: Post-traumatic OA (PTOA) was surgically induced in skeletally mature rats. Rats were randomly divided in three groups receiving either glucosamine (high dose of 192 mg/kg) or celecoxib (clinical dose) or no treatment. Disease progression was monitored utilizing micro-magnetic resonance imaging (MRI), micro-computed tomography (CT) and histology. Pertinent features such as osteophytes, subchondral sclerosis, joint effusion, bone marrow lesion (BML), cysts, loose bodies and cartilage abnormalities were included in designing a sensitive multi-modality based scoring system, termed the rat arthritis knee scoring system (RAKSS). RESULTS: Overall, an inter-observer correlation coefficient (ICC) of greater than 0.750 was achieved for each scored feature. None of the treatments prevented cartilage loss, synovitis, joint effusion, or sclerosis. However, celecoxib significantly reduced osteophyte development compared to placebo. Although signs of inflammation such as synovitis and joint effusion were readily identified at 4 weeks post-operation, we did not detect any BML. CONCLUSION: We report the development of a sensitive and reliable multi-modality scoring system, the RAKSS, for evaluation of OA severity in pre-clinical animal models. Using this scoring system, we found that celecoxib prevented enlargement of osteophytes in this animal model of PTOA, and thus it may be useful in preventing OA progression. However, it did not show any chondroprotective effect using the recommended dose. In contrast, high dose glucosamine had no measurable effects.

Dose response of selected solid state detectors in applied homogeneous transverse and longitudinal magnetic fields.

PURPOSE: MR-Linac devices under development worldwide will require standard calibration, commissioning, and quality assurance. Solid state radiation detectors are often used for dose profiles and percent depth dose measurements. The dose response of selected solid state detectors is therefore evaluated in varying transverse and longitudinal magnetic fields for this purpose. METHODS: The Monte Carlo code PENELOPE was used to model irradiation of a PTW 60003 diamond detector and IBA PFD diode detector in the presence of a magnetic field. The field itself was varied in strength, and oriented both transversely and longitudinally with respect to the incident photon beam. The long axis of the detectors was oriented either parallel or perpendicular to the photon beam. The dose to the active volume of each detector in air was scored, and its ratio to dose with zero magnetic field strength was determined as the "dose response" in magnetic field. Measurements at low fields for both detectors in transverse magnetic fields were taken to evaluate the accuracy of the simulations. Additional simulations were performed in a water phantom to obtain few representative points for beam profile and percent depth dose measurements. RESULTS: Simulations show significant dose response as a function of magnetic field in transverse field geometries. This response can be near 20% at 1.5 T, and it is highly dependent on the detectors' relative orientation to the magnetic field, the energy of the photon beam, and detector composition. Measurements at low transverse magnetic fields verify the simulations for both detectors in their relative orientations to radiation beam. Longitudinal magnetic fields, in contrast, show little dose response, rising slowly with magnetic field, and reaching 0.5%-1% at 1.5 T regardless of detector orientation. Water tank and in air simulation results were the same within simulation uncertainty where lateral electronic equilibrium is present and expectedly differed at the beam edge in transverse field orientations only. Due to the difference in design, the two detectors behaved differently. CONCLUSIONS: When transverse magnetic fields are present, great care must be taken when using diamond or diode detectors. Dose response varies with relative detector orientation, magnetic field strength, and between detectors. This response can be considerable (∼20% for both detectors). Both detectors in longitudinal fields exhibit little to no dose response as a function of magnetic field. Water tank simulations seem to suggest that the diode detector is better suited to general beam commissioning, and each detector must be investigated separately.

Longitudinal evaluation of the metabolic response of a tumor xenograft model to single fraction radiation therapy using magnetic resonance spectroscopy.

Proton magnetic resonance spectroscopy (MRS) was used to evaluate the metabolic profile of human glioblastoma multiform brain tumors grown as xenografts in nude mice before, and at multiple time points after single fraction radiation therapy. Tumors were grown over the thigh in 16 mice in this study, of which 5 served as untreated controls and 11 had their tumors treated to 800 cGy with 200 kVp x-rays. Spectra were acquired within 24 h pre-treatment, and then at 3, 7 and 14 d post-treatment using a 9.4 T animal magnetic resonance (MR) system. For the untreated control tumors, spectra (1-2 per mouse) were acquired at different stages of tumor growth. Spectra were obtained with the PRESS pulse sequence using a 3  ×  3 × 3 mm(3) voxel. Analysis was performed with the LCModel software platform. Six metabolites were profiled for this analysis: alanine (Ala), myo-inositol (Ins), taurine (Tau), creatine and phosphocreatine (Cr + PCr), glutamine and glutamate (Glu + Gln), and total choline (glycerophosphocholine + phosphocholine) (GPC + PCh). For the treated cohort, most metabolite/water concentration ratios were found to decrease in the short term at 3 and 7 d post-treatment, followed by an increase at 14 d post-treatment toward pre-treatment values. The lowest concentrations were observed at 7 d post-treatment, with magnitudes (relative to pre-treatment concentration ratios) of: 0.42  ±  24.6% (Ala), 0.43  ±  15.3% (Ins), 0.68  ±  27.9% (Tau), 0.52  ±  14.6% (GPC+PCh), 0.49  ±  21.0% (Cr + PCr) and 0.78  ±  24.5% (Glu + Gln). Control animals did not demonstrate any significant correlation between tumor volume and metabolite concentration, indicating that the observed kinetics were the result of the therapeutic intervention. We have demonstrated the feasibility of using MRS to follow multiple metabolic markers over time for the purpose of evaluating therapeutic response of tumors to radiation therapy. This study provides supporting evidence that metabolite/water concentration ratios have the potential to be used as biomarkers for the assessment of the response to therapy.

Prior data assisted compressed sensing: a novel MR imaging strategy for real time tracking of lung tumors.

PURPOSE: Hybrid radiotherapy-MRI devices promise real time tracking of moving tumors to focus the radiation portals to the tumor during irradiation. This approach will benefit from the increased temporal resolution of MRI's data acquisition and reconstruction. In this work, the authors propose a novel spatial-temporal compressed sensing (CS) imaging strategy for the real time MRI--prior data assisted compressed sensing (PDACS), which aims to improve the image quality of the conventional CS without significantly increasing reconstruction times. METHODS: Conventional 2D CS requires a random sampling of partial k-space data, as well as an iterative reconstruction that simultaneously enforces the image's sparsity in a transform domain as well as maintains the fidelity to the acquired k-space. PDACS method requires the additional acquisition of the prior data, and for reconstruction, it additionally enforces fidelity to the prior k-space domain similar to viewsharing. In this work, the authors evaluated the proposed PDACS method by comparing its results to those obtained from the 2D CS and viewsharing methods when performed individually. All three methods are used to reconstruct images from lung cancer patients whose tumors move and who are likely to benefit from lung tumor tracking. The patients are scanned, using a 3T MRI, under free breathing using the fully sampled k-space with 2D dynamic bSSFP sequence in a sagittal plane containing lung tumor. These images form a reference set for the evaluation of the partial k-space methods. To create partial k-space, the fully sampled k-space is retrospectively undersampled to obtain a range of acquisition acceleration factors, and reconstructed with 2D-CS, PDACS, and viewshare methods. For evaluation, metrics assessing global image artifacts as well as tumor contour shape fidelity are determined from the reconstructed images. These analyses are performed both for the original 3T images and those at a simulated 0.5T equivalent noise level. RESULTS: In the 3.0T images, the PDACS strategy is shown to give superior results compared to viewshare and conventional 2D CS using all metrics. The 2D-CS tends to perform better than viewshare at the low acceleration factors, while the opposite is true at the high acceleration factors. At simulated 0.5T images, PDACS method performs only marginally better than the viewsharing method, both of which are superior compared to 2D CS. The PDACS image reconstruction time (0.3 s/image) is similar to that of the conventional 2D CS. CONCLUSIONS: The PDACS method can potentially improve the real time tracking of moving tumors by significantly increasing MRI's data acquisition speeds. In 3T images, the PDACS method does provide a benefit over the other two methods in terms of both the overall image quality and the ability to accurately and automatically contour the tumor shape. MRI's data acquisition may be accelerated using the simpler viewsharing strategy at the lower, 0.5T magnetic field, as the marginal benefit of the PDACS method may not justify its additional reconstruction times.