Forward Projection Method Research Articles

Radiotherapy delivery error detection with electronic portal imaging device (EPID)-based in vivo dosimetry.

Radiotherapy delivery error detection with electronic portal imaging device (EPID)-based in vivo dosimetry.

Forward projection multilayer refraction model for underwater camera calibration

Unlike imaging in air, underwater imaging is affected by two distinct properties of water: the absorption and scattering effect of water and the refraction effect of water, resulting in the conventional pinhole model no longer being suitable for underwater imaging. Therefore, without prior calibration in air to calculate the camera intrinsic parameters and distortions for subsequent underwater calibration, an underwater multilayer refraction model based on forward projection method is represented. Along the direction of light propagation, the multilayer refraction model presents a unified scale factor instead of focal length during the perspective projection transformation from the camera coordinate system to the image coordinate system. Simulations regarding the analysis of different medium thicknesses, different medium refractive indices, and different point pixels are performed to explore the influence of the above three parameters on the refraction model. Through the underwater parameter identification and verification, the proposed multilayer refraction model has high measurement accuracy, excellent solution efficiency, stable identification results, more identification parameters, and wide application fields, which are suitable for both single-time refraction and double-time refraction.

Approximate projection method for the construction of multi- α -cluster spaces

An approximate but straight forward projection method to molecular many alpha-particle states is proposed and the overlap to the shell model space is determined. The resulting space is in accordance with the shell model, but still contains states which are not completely symmetric under permutations of the alpha-particles, which is one reason to call the construction semi-microscopic. A new contribution is the construction of the 6- and 7-$\alpha$-particle spaces. The errors of the method propagate toward larger number of alpha-particles and larger shell excitations. In order to show the effectiveness of the construction proposed, the so obtained spaces are applied, within an algebraic cluster model, to $^{20}$Ne, $^{24}$Mg and $^{28}$Si, each treated as a many-alpha-particle system. Former results on $^{12}$C and $^{16}$O are resumed.

OA151] Error sensitivity of forward- and back-projection EPID dosimetry for VMAT treatment of the prostate

Introduction Volumetric modulated arc therapy (VMAT) treatments may be verified dosimetrically using an electronic portal imaging device (EPID), either using the forward-projection method to calculate integrated predicted images, which are compared with acquired images, or using the back-projection method to reconstruct delivered dose, for comparison with the planned dose. This study compares the error sensitivity of both methods for prostate treatments. Materials and Methods VMAT treatment plans for prostate and seminal vesicles were created using AutoBeam in-house software, with final dose calculation carried out in Pinnacle3. Patients were treated using the 6 MV beam of a Versa HD accelerator. Portal images were acquired for 46 fractions in 13 patients, and EPID dosimetry was carried out using AutoBeam (forward-projection) and iViewDose (back-projection). Differences between measurements (M) and predictions (P) were evaluated on the central axis of the beam (forward-projection) and at the isocentre (back-projection). The plans were also retrospectively delivered to a Solid Water phantom and errors were deliberately introduced. Errors consisted of a 2–10% increase in monitor units, a 2–10 mm increase in aperture size, a 2–10 mm shift in aperture and introduction of a 10–50 mm air gap into the phantom. Results For the patient images, M-P = 3.1% ± 2.1% (1 SD) for forward-projection and 2.2% ± 2.2% for back-projection, with good correlation between forward-projection and back-projection. For the phantom images, M-P = 0.7% ± 2.0% for forward-projection and 3.0% ± 1.0% for back-projection. Monitor unit and aperture size errors are detected equally by both methods, aperture shift errors are mainly detected in forward-projection due to removal of shifts by the back-projection image processing software, while air gaps have a slightly larger impact on back-projection than forward-projection. Conclusions Each method of EPID dosimetry has its own distinct sensitivity to errors, but overall, both methods can be used reliably for verification of delivered dose. The back-projection method, in clinical use at this centre, enables convenient visualisation of delivered dose to the patient. Other methods, such as cone-beam imaging, are required for verification of patient position, while further work is needed to investigate the potential of time-resolved EPID dosimetry.

Comparison of two different EPID-based solutions performing pretreatment quality assurance: 2D portal dosimetry versus 3D forward projection method

PurposeThe aim of this paper is to characterize two different EPID-based solutions for pre-treatment VMAT quality assurance, the 2D portal dosimetry and the 3D projection technique. Their ability to catch the main critical delivery errors was studied. MethodsMeasurements were performed with a linac accelerator equipped with EPID aSi1000, Portal Dose Image Prediction (PDIP), and PerFRACTION softwares. Their performances were studied simulating perturbations of a reference plan through systematic variations in dose values and micromultileaf collimator position. The performance of PDIP, based on 2D forward method, was evaluated calculating gamma passing rate (%GP) between no-error and error-simulated measurements. The impact of errors with PerFRACTION, based on 3D projection technique, was analyzed by calculating the difference between reference and perturbed DVH (%ΔD). Subsequently pre-treatment verification with PerFRACTION was done for 27 patients of different pathologies. ResultsThe sensitivity of PerFRACTION was slightly higher than sensitivity of PDIP, reaching a maximum of 0.9. Specificity was 1 for PerFRACTION and 0.6 for PDIP. The analysis of patients’ DVHs indicated that the mean %ΔD was (1.2 ± 1.9)% for D2%, (0.6 ± 1.7)% for D95% and (−0.0 ± 1.2)% for Dmean of PTV. Regarding OARs, we observed important discrepancies on DVH but that the higher dose variations were in low dose area (<10 Gy). ConclusionsThis study supports the introduction of the new 3D forward projection method for pretreatment QA raising the claim that the visualization of the delivered dose distribution on patient anatomy has major advantages over traditional portal dosimetry QA systems.

Comparison of forward- and back-projection in vivo EPID dosimetry for VMAT treatment of the prostate

In the forward-projection method of portal dosimetry for volumetric modulated arc therapy (VMAT), the integrated signal at the electronic portal imaging device (EPID) is predicted at the time of treatment planning, against which the measured integrated image is compared. In the back-projection method, the measured signal at each gantry angle is back-projected through the patient CT scan to give a measure of total dose to the patient. This study aims to investigate the practical agreement between the two types of EPID dosimetry for prostate radiotherapy. The AutoBeam treatment planning system produced VMAT plans together with corresponding predicted portal images, and a total of 46 sets of gantry-resolved portal images were acquired in 13 patients using an iViewGT portal imager. For the forward-projection method, each acquisition of gantry-resolved images was combined into a single integrated image and compared with the predicted image. For the back-projection method, iViewDose was used to calculate the dose distribution in the patient for comparison with the planned dose. A gamma index for 3% and 3 mm was used for both methods. The results were investigated by delivering the same plans to a phantom and repeating some of the deliveries with deliberately introduced errors. The strongest agreement between forward- and back-projection methods is seen in the isocentric intensity/dose difference, with moderate agreement in the mean gamma. The strongest correlation is observed within a given patient, with less correlation between patients, the latter representing the accuracy of prediction of the two methods. The error study shows that each of the two methods has its own distinct sensitivity to errors, but that overall the response is similar. The forward- and back-projection EPID dosimetry methods show moderate agreement in this series of prostate VMAT patients, indicating that both methods can contribute to the verification of dose delivered to the patient.

The role of off-focus radiation in scatter correction for dedicated cone beam breast CT.

Dedicated cone beam breast CT (CBBCT) suffers from x-ray scatter contamination. We aim to identify the source of the significant difference between the scatter distributions estimated by two recent methods proposed by our group and to investigate its effect on CBBCT image quality. We recently proposed two novel methods of scatter correction for CBBCT, using a library based (LB) technique and a forward projection (FP) model. Despite similar enhancement on CBBCT image qualities, these two methods obtain very different scatter distributions. We hypothesize that the off-focus radiation (OFR) is the contributor and results in nontrivial signals in x-ray projections, which is ignored in the scatter estimation via the LB method. Experiments using a thin wire test tool are designed to study the effect of OFR on CBBCT spatial resolution by measuring the point spread function (PSF) and the modulation transfer function (MTF). A narrow collimator setting is used to suppress the OFR-induced signals. In addition, "PSFs" and "MTFs" are measured on clinical CBBCT images obtained by the LB and FP methods using small calcifications as point sources. The improvement of spatial resolution achieved by suppressing OFR in the wire experiment as well as in the clinical study is quantified by the improvement ratios of PSFs and spatial frequencies at different MTF values. Our hypothesis that OFR causes the imaging difference between the FP and LB methods is verified if these ratios obtained from experimental and clinical data are consistent. In the wire experiment, the results show that suppression of OFR increases the maximum signal of the PSF by about 14% and reduces the full-width-at-half-maximum (FWHM) by about 12.0%. Similar improvement on spatial resolution is achieved by the FP method compared with the LB method in the patient study. The improvement ratios of spatial frequencies at different MTF values without OFR match very well in both studies at a level of around 16%, with an average root-mean-square difference of 0.47%. The results of the wire experiment and the clinical study indicate that the main difference between the LB and FP methods is whether the OFR-induced signals are included after scatter correction. Our study further shows that OFR significantly affects the image spatial resolution of CBBCT, indicating that the visualization of micro-calcifications is susceptible to OFR contamination. Our finding is therefore important in further improvement of diagnostic performance of CBBCT.

Technical Note: Insertion of digital lesions in the projection domain for dual‐source, dual‐energy CT

To compare algorithms performing material decomposition and classification in dual-energy CT, it is desirable to know the ground truth of the lesion to be analyzed in real patient data. In this work, we developed and validated a framework to insert digital lesions of arbitrary chemical composition into patient projection data acquired on a dual-source, dual-energy CT system. A model that takes into account beam-hardening effects was developed to predict the CT number of objects with known chemical composition. The model utilizes information about the x-ray energy spectra, the patient/phantom attenuation, and the x-ray detector energy response. The beam-hardening model was validated on samples of iodine (I) and calcium (Ca) for a second-generation dual-source, dual-energy CT scanner for all tube potentials available and a wide range of patient sizes. The seven most prevalent mineral components of renal stones were modeled and digital stones were created with CT numbers computed for each patient/phantom size and x-ray energy spectra using the developed beam-hardening model. Each digital stone was inserted in the dual-energy projection data of a water phantom scanned on a dual-source scanner and reconstructed with the routine algorithms in use in our practice. The geometry of the forward projection for dual-energy data was validated by comparing CT number accuracy and high-contrast resolution of simulated dual-energy CT data of the ACR phantom with experimentally acquired data. The beam-hardening model and forward projection method accurately predicted the CT number of I and Ca over a wide range of tube potentials and phantom sizes. The images reconstructed after the insertion of digital kidney stones were consistent with the images reconstructed from the scanner, and the CT number ratios for different kidney stone types were consistent with data in the literature. A sample application of the proposed tool was also demonstrated. A framework was developed and validated for the creation of digital objects of known mineral composition, and for inserting the digital objects into projection data from a commercial dual-source, dual-energy CT scanner. Among other applications, it will allow a systematic investigation of the impact of scan and reconstruction parameters on kidney stone dual-energy properties under rigorously controlled conditions.

Estimating the motion of plant root cells from in vivo confocal laser scanning microscopy images

Images of cellular structures in growing plant roots acquired using confocal laser scanning microscopy have some unusual properties that make motion estimation challenging. These include multiple motions, non-Gaussian noise and large regions with little spatial structure. In this paper, a method for motion estimation is described that uses a robust multi-frame likelihood model and a technique for estimating uncertainty. An efficient region-based matching approach was used followed by a forward projection method. Over small timescales the dynamics are simple (approximately locally constant) and the change in appearance small. Therefore, a constant local velocity model is used and the MAP estimate of the joint probability over a set of frames is recovered. Occurrences of multiple modes in the posterior are detected, and in the case of a single dominant mode, motion is inferred using Laplace’e method. The method was applied to several Arabidopsis thaliana root growth sequences with varying levels of success. In addition, comparative results are given for three alternative motion estimation approaches, the Kanade–Lucas–Tomasi tracker, Black and Anandan’s robust smoothing method, and Markov random field based methods.

Optimal Threshold Selection for Tomogram Segmentation by Projection Distance Minimization

Grey value thresholding is a segmentation technique commonly applied to tomographic image reconstructions. Many procedures have been proposed to optimally select the grey value thresholds based on the tomogram data only (e.g., using the image histogram). In this paper, a projection distance minimization (PDM) method is presented that uses the tomographic projection data to determine optimal thresholds. These thresholds are computed by minimizing the distance between the forward projection of the segmented image and the measured projection data. An important contribution of the current paper is the efficient implementation of the forward projection method, which makes the use of the original projection data as a segmentation criterion feasible. Simulation experiments applied to various phantom images show that our proposed method obtains superior results compared to established histogram-based methods.

Development of TOF-PET using Cherenkov Radiation

We proposed a new concept of TOF-PET (Time-of-Flight Positron Emission Tomography) using Cherenkov radiation. Basic experiments revealed a timing resolution of 170ps, but the detection efficiency was less than those of the conventional BaF2 scintillators. Through simulation studies, we confirmed that the spatial resolution and the S/N ratio of the images reconstructed with TOF information were 1.5 and 3 times better, respectively, than they were without TOF information, when we adopted the FP (Forward Projection) method combined with the ML-EM (Maximum Likelihood Expectation Maximization) algorithm as an image reconstruction algorithm. Consequently, we concluded that TOF-PET using Cherenkov radiation is a promising candidate for next-generation PET. We concluded that PWO (PbWO4) is the best Cherenkov radiator from the viewpoint of detection efficiency. Additionally, we found that the Monte Carlo algorithm was able to generate images having error bars and thus to make quantitative diagnoses possible.

Development of TOF-PET using Cherenkov Radiation

We proposed a new concept of TOF-PET (Time-of-Flight Positron Emission Tomography) using Cherenkov radiation. Basic experiments revealed a timing resolution of 170ps, but the detection efficiency was less than those of the conventional BaF2 scintillators. Through simulation studies, we confirmed that the spatial resolution and the S/N ratio of the images reconstructed with TOF information were 1.5 and 3 times better, respectively, than they were without TOF information, when we adopted the FP (Forward Projection) method combined with the ML-EM (Maximum Likelihood Expectation Maximization) algorithm as an image reconstruction algorithm. Consequently, we concluded that TOF-PET using Cherenkov radiation is a promising candidate for next-generation PET. We concluded that PWO (PbWO4) is the best Cherenkov radiator from the viewpoint of detection efficiency. Additionally, we found that the Monte Carlo algorithm was able to generate images having error bars and thus to make quantitative diagnoses possible.

Sonographic fetal weight estimation in a south-east Asian population.

To determine the optimal sonographic fetal weight estimation formula for a mixed south-east Asian population near term. Seventy-eight uncomplicated pregnancies were monitored between January 1996 and January 1997. Biparietal diameter, head circumference, abdominal circumference and femur length were measured and the following formulae were tested: Campbell, Shepherds and Hadlock. The estimated fetal weight was calculated by 12 different methods. The weight estimate was then projected forward to the time of delivery using the gestation-adjusted forward projection method. The weight estimation error was derived from the difference between the projected fetal weight and birth weight, and expressed as a percentage of birth weight. The mean time interval from the time of ultrasound fetal weight estimation to delivery was 4.4 days. The birth weight ranged between 2,330 to 4,215 g. The best performing formula was Hadlock's formula using the head circumference, abdominal circumference and femur, with the perimeters calculated using the ellipse function. The standard deviation of error for this formula was 8.66%. Even though the Hadlock formula was originally derived from an American population, it was equally useful in south-east Asian population.

Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition

AbstractA finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed. An implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces. A two‐time level implicit method is used, while Taylor's forward projection method is employed for taking account of the nonlinearities. An iterative method is described which predicts unknown surface conditions. An example is illustrated which is typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation.

On the numerical solution of phase change problems in transient non‐linear heat conduction

AbstractA finite difference solution for the transient non‐linear heat conduction with phase change in a finite slab is proposed. A two‐time level implicit method is used while Taylor's forward projection method is employed for taking into account the non‐linearities. The stability due to the boundary conditions at the moving front is verified. The numerical solution is compared with the analytical solutions and found to be in close agreement.