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4D CT imaging is a cornerstone of 4D radiotherapy treatment. Clinical 4D CT data are, however, often affected by severe artifacts. The artifacts are mainly caused by breathing irregularity and retrospective correlation of breathing phase information and acquired projection data, which leads to insufficient projection data coverage to allow for proper reconstruction of 4D CT phase images. The recently introduced 4D CT approach i4DCT (intelligent 4D CT sequence scanning) aims to overcome this problem by breathing signal-driven tube control. The present motion phantom study describes the first in-depth evaluation of i4DCT in a real-world scenario. Twenty-eight 4D CT breathing curves of lung and liver tumor patients with pronounced breathing irregularity were selected to program the motion phantom. For every motion pattern, 4D CT imaging was performed with i4DCT and a conventional spiral 4D CT mode. For qualitative evaluation, the reconstructed 4D CT images were presented to clinical experts, who scored image quality. Further quantitative evaluation was based on established image intensity-based artifact metrics to measure (dis)similarity of neighboring image slices. In addition, beam-on and scan times of the scan modes were analyzed. The expert rating revealed a significantly higher image quality for the i4DCT data. The quantitative evaluation further supported the qualitative: While 20% of the slices of the conventional spiral 4D CT images were found to be artifact-affected, the corresponding fraction was only 4% for i4DCT. The beam-on time (surrogate of imaging dose) did not significantly differ between i4DCT and spiral 4D CT. Overall i4DCT scan times (time between first beam-on and last beam-on event, including scan breaks to compensate for breathing irregularity) were, on average, 53% longer compared to spiral CT. Thus, the results underline that i4DCT significantly improves 4D CT image quality compared to standard spiral CT scanning in the case of breathing irregularity during scanning., (© 2021 Institute of Physics and Engineering in Medicine.)

Helical CT has been widely used in clinical diagnosis. In this work, we focus on a new prototype of helical CT, equipped with sparsely spaced multidetector and multi-slit collimator (MSC) in the axis direction. This type of system can not only lower radiation dose, and suppress scattering by MSC, but also cuts down the manufacturing cost of the detector. The major problem to overcome with such a system, however, is that of insufficient data for reconstruction. Hence, we propose a deep learning-based function optimization method for this ill-posed inverse problem. By incorporating a Radon inverse operator, and disentangling each slice, we significantly simplify the complexity of our network for 3D reconstruction. The network is composed of three subnetworks. Firstly, a convolutional neural network (CNN) in the projection domain is constructed to estimate missing projection data, and to convert helical projection data to 2D fan-beam projection data. This is follwed by the deployment of an analytical linear operator to transfer the data from the projection domain to the image domain. Finally, an additional CNN in the image domain is added for further image refinement. These three steps work collectively, and can be trained end to end. The overall network is trained on a simulated CT dataset based on eight patients from the American Association of Physicists in Medicine (AAPM) Low Dose CT Grand Challenge. We evaluate the trained network on both simulated datasets and clinical datasets. Extensive experimental studies have yielded very encouraging results, based on both visual examination and quantitative evaluation. These results demonstrate the effectiveness of our method and its potential for clinical usage. The proposed method provides us with a new solution for a fully 3D ill-posed problem.

Dynamic collimation is an important dose reduction mechanism for helical CT scans, especially for modern wide-beam scanner models. Its implementation and efficacy need to be studied to optimize CT scan protocols and to reduce unnecessary patient dose. The purpose of this study is to evaluate dynamic beam collimation for modern wide-beam CT scanners with direct measurements and to estimate the efficacy for dose reduction. By using a linear-array solid state detector, primary x-ray beam coverage was measured for four CT scanner models: GE Revolution CT, Siemens Somatom Force, Philips iQon, and GE LightSpeed VCT. Supported independently from patient table, the detector remained stationary at the isocenter during helical scans. Data lines were recorded every 0.24 ms throughout one entire helical scan, with a spatial resolution of 0.8 mm along the craniocaudal direction. The measurements were repeated for various scan parameters related to dynamic collimation, including beam collimation width, pitch, rotation time, and scan length. The recorded beam coverage area was used as a surrogate to total primary dose, to model different dynamic collimation mechanisms. The directly measured total radiation range was compared to table travel distance and nominal scan length which equals to the ratio between DLP and CTDIvol. Equations to calculate the percentage dose reduction with dynamic collimation were derived for different mechanisms. Three different dynamic collimation mechanisms were revealed and related linear model parameters were reported for different helical scan parameters. The nominal scan length used to calculate DLP was shown to vary for different dynamic collimation mechanisms. For typical head and abdomen scans with nominal scan lengths of 17.5 cm and 25 cm, percentage dose reduction from dynamic collimation ranged from 2% to 32%. In conclusion, with direct measurements of primary x-ray beam coverage, dynamic collimation mechanisms and related dose reduction effects were characterized for four modern wide-beam CT scanners.

To determine if the parameters relating lung tissue displacement to a breathing surrogate signal in a previously published respiratory motion model vary with the rate of breathing during image acquisition. An anesthetized pig was imaged using multiple fast helical scans to sample the breathing cycle with simultaneous surrogate monitoring. Three datasets were collected while the animal was mechanically ventilated with different respiratory rates: 12 bpm (breaths per minute), 17 bpm, and 24 bpm. Three sets of motion model parameters describing the correspondences between surrogate signals and tissue displacements were determined. The model error was calculated individually for each dataset, as well asfor pairs of parameters and surrogate signals from different experiments. The values of one model parameter, a vector field denoted [Formula: see text] which related tissue displacement to surrogate amplitude, determined for each experiment were compared. The mean model error of the three datasets was 1.00  ±  0.36 mm with a 95th percentile value of 1.69 mm. The mean error computed from all combinations of parameters and surrogate signals from different datasets was 1.14  ±  0.42 mm with a 95th percentile of 1.95 mm. The mean difference in [Formula: see text] over all pairs of experiments was 4.7%  ±  5.4%, and the 95th percentile was 16.8%. The mean angle between pairs of [Formula: see text] was 5.0  ±  4.0 degrees, with a 95th percentile of 13.2 mm. The motion model parameters were largely unaffected by changes in the breathing rate during image acquisition. The mean error associated with mismatched sets of parameters and surrogate signals was 0.14 mm greater than the error achieved when using parameters and surrogate signals acquired with the same breathing rate, while maximum respiratory motion was 23.23 mm on average.

Breathing motion modeling requires observation of tissues at sufficiently distinct respiratory states for proper 4D characterization. This work proposes a method to improve sampling of the breathing cycle with limited imaging dose. We designed and tested a prospective free-breathing acquisition protocol with a simulation using datasets from five patients imaged with a model-based 4DCT technique. Each dataset contained 25 free-breathing fast helical CT scans with simultaneous breathing surrogate measurements. Tissue displacements were measured using deformable image registration. A correspondence model related tissue displacement to the surrogate. Model residual was computed by comparing predicted displacements to image registration results. To determine a stopping criteria for the prospective protocol, i.e. when the breathing cycle had been sufficiently sampled, subsets of N scans where 5  ⩽  N  ⩽  9 were used to fit reduced models for each patient. A previously published metric was employed to describe the phase coverage, or 'spread', of the respiratory trajectories of each subset. Minimum phase coverage necessary to achieve mean model residual within 0.5 mm of the full 25-scan model was determined and used as the stopping criteria. Using the patient breathing traces, a prospective acquisition protocol was simulated. In all patients, phase coverage greater than the threshold necessary for model accuracy within 0.5 mm of the 25 scan model was achieved in six or fewer scans. The prospectively selected respiratory trajectories ranked in the (97.5  ±  4.2)th percentile among subsets of the originally sampled scans on average. Simulation results suggest that the proposed prospective method provides an effective means to sample the breathing cycle with limited free-breathing scans. One application of the method is to reduce the imaging dose of a previously published model-based 4DCT protocol to 25% of its original value while achieving mean model residual within 0.5 mm.

The article aims to determine if a prospective acquisition algorithm can be used to find the ideal set of free-breathing phases for fast-helical model-based 4D-CT. A retrospective five-patient dataset that consisted of 25 repeated free breathing CT scans per patient was used. The sum of the square root amplitude difference between all the breathing phases was defined as an objective function to determine the optimality of sets of breathing phases. The objective function was intended to determine if a specific set of breathing phases would yield a motion model that could accurately predict the motion in all 25 CT scans. Voxel specific motion models were calculated using all combinations of N scans from 25 breathing trajectories, (3  ⩽  N  ⩽  25), and the minimum number of scans required to absolutely characterize the motion model was analyzed. This analysis suggests that the number of scans could potentially be reduced to as few as five scans. When the objective function was large, the resulting motion model provided an excellent approximation to the motion model created using all 25 scans.

Correction for rigid object motion in helical CT can be achieved by reconstructing from a modified source-detector orbit, determined by the object motion during the scan. This ensures that all projections are consistent, but it does not guarantee that the projections are complete in the sense of being sufficient for exact reconstruction. We have previously shown with phantom measurements that motion-corrected helical CT scans can suffer from data-insufficiency, in particular for severe motions and at high pitch. To study whether such data-insufficiency artefacts could also affect the motion-corrected CT images of patients undergoing head CT scans, we used an optical motion tracking system to record the head movements of 10 healthy volunteers while they executed each of the 4 different types of motion ('no', slight, moderate and severe) for 60 s. From these data we simulated 354 motion-affected CT scans of a voxelized human head phantom and reconstructed them with and without motion correction. For each simulation, motion-corrected (MC) images were compared with the motion-free reference, by visual inspection and with quantitative similarity metrics. Motion correction improved similarity metrics in all simulations. Of the 270 simulations performed with moderate or less motion, only 2 resulted in visible residual artefacts in the MC images. The maximum range of motion in these simulations would encompass that encountered in the vast majority of clinical scans. With severe motion, residual artefacts were observed in about 60% of the simulations. We also evaluated a new method of mapping local data sufficiency based on the degree to which Tuy's condition is locally satisfied, and observed that areas with high Tuy values corresponded to the locations of residual artefacts in the MC images. We conclude that our method can provide accurate and artefact-free MC images with most types of head motion likely to be encountered in CT imaging, provided that the motion can be accurately determined.

Novel x-ray medical imaging sensors, such as photon counting detectors (PCDs) and large area CCD and CMOS cameras can involve irregular and/or sparse sampling of the detector plane. Application of such detectors to CT involves undersampling that is markedly different from the commonly considered case of sparse angular sampling. This work investigates volumetric sampling in CT systems incorporating sparsely sampled detectors with axial and helical scan orbits and evaluates performance of model-based image reconstruction (MBIR) with spatially varying regularization in mitigating artifacts due to sparse detector sampling. Volumetric metrics of sampling density and uniformity were introduced. Penalized-likelihood MBIR with a spatially varying penalty that homogenized resolution by accounting for variations in local sampling density (i.e. detector gaps) was evaluated. The proposed methodology was tested in simulations and on an imaging bench based on a Si-strip PCD (total area 5 cm  ×  25 cm) consisting of an arrangement of line sensors separated by gaps of up to 2.5 mm. The bench was equipped with translation/rotation stages allowing a variety of scanning trajectories, ranging from a simple axial acquisition to helical scans with variable pitch. Statistical (spherical clutter) and anthropomorphic (hand) phantoms were considered. Image quality was compared to that obtained with a conventional uniform penalty in terms of structural similarity index (SSIM), image uniformity, spatial resolution, contrast, and noise. Scan trajectories with intermediate helical width (~10 mm longitudinal distance per 360° rotation) demonstrated optimal tradeoff between the average sampling density and the homogeneity of sampling throughout the volume. For a scan trajectory with 10.8 mm helical width, the spatially varying penalty resulted in significant visual reduction of sampling artifacts, confirmed by a 10% reduction in minimum SSIM (from 0.88 to 0.8) and a 40% reduction in the dispersion of SSIM in the volume compared to the constant penalty (both penalties applied at optimal regularization strength). Images of the spherical clutter and wrist phantoms confirmed the advantages of the spatially varying penalty, showing a 25% improvement in image uniformity and 1.8  ×  higher CNR (at matched spatial resolution) compared to the constant penalty. The studies elucidate the relationship between sampling in the detector plane, acquisition orbit, sampling of the reconstructed volume, and the resulting image quality. They also demonstrate the benefit of spatially varying regularization in MBIR for scenarios with irregular sampling patterns. Such findings are important and integral to the incorporation of a sparsely sampled Si-strip PCD in CT imaging.

We propose a method to compensate for six degree-of-freedom rigid motion in helical CT of the head. The method is demonstrated in simulations and in helical scans performed on a 16-slice CT scanner. Scans of a Hoffman brain phantom were acquired while an optical motion tracking system recorded the motion of the bed and the phantom. Motion correction was performed by restoring projection consistency using data from the motion tracking system, and reconstructing with an iterative fully 3D algorithm. Motion correction accuracy was evaluated by comparing reconstructed images with a stationary reference scan. We also investigated the effects on accuracy of tracker sampling rate, measurement jitter, interpolation of tracker measurements, and the synchronization of motion data and CT projections. After optimization of these aspects, motion corrected images corresponded remarkably closely to images of the stationary phantom with correlation and similarity coefficients both above 0.9. We performed a simulation study using volunteer head motion and found similarly that our method is capable of compensating effectively for realistic human head movements. To the best of our knowledge, this is the first practical demonstration of generalized rigid motion correction in helical CT. Its clinical value, which we have yet to explore, may be significant. For example it could reduce the necessity for repeat scans and resource-intensive anesthetic and sedation procedures in patient groups prone to motion, such as young children. It is not only applicable to dedicated CT imaging, but also to hybrid PET/CT and SPECT/CT, where it could also ensure an accurate CT image for lesion localization and attenuation correction of the functional image data.

Currently, the BEAMnrc/EGSnrc Monte Carlo (MC) system does not provide a spiral CT source model for the simulation of spiral CT scanning. We developed and validated a spiral CT phase-space source model in the BEAMnrc/EGSnrc system. The spiral phase-space source model was implemented in the DOSXYZnrc user code of the BEAMnrc/EGSnrc system by analyzing the geometry of spiral CT scan-scan range, initial angle, rotational direction, pitch, slice thickness, etc. Table movement was simulated by changing the coordinates of the isocenter as a function of beam angles. Some parameters such as pitch, slice thickness and translation per rotation were also incorporated into the model to make the new phase-space source model, designed specifically for spiral CT scan simulations. The source model was hard-coded by modifying the 'ISource = 8: Phase-Space Source Incident from Multiple Directions' in the srcxyznrc.mortran and dosxyznrc.mortran files in the DOSXYZnrc user code. In order to verify the implementation, spiral CT scans were simulated in a CT dose index phantom using the validated x-ray tube model of a commercial CT simulator for both the original multi-direction source (ISOURCE = 8) and the new phase-space source model in the DOSXYZnrc system. Then the acquired 2D and 3D dose distributions were analyzed with respect to the input parameters for various pitch values. In addition, surface-dose profiles were also measured for a patient CT scan protocol using radiochromic film and were compared with the MC simulations. The new phase-space source model was found to simulate the spiral CT scanning in a single simulation run accurately. It also produced the equivalent dose distribution of the ISOURCE = 8 model for the same CT scan parameters. The MC-simulated surface profiles were well matched to the film measurement overall within 10%. The new spiral CT phase-space source model was implemented in the BEAMnrc/EGSnrc system. This work will be beneficial in estimating the spiral CT scan dose in the BEAMnrc/EGSnrc system.

Multi-slice computed tomography (MSCT) scanners have become popular volumetric imaging tools. Deterministic and random properties of the resulting CT scans have been studied in the literature. Due to the large number of voxels in the three-dimensional (3D) volumetric dataset, full characterization of the noise covariance in MSCT scans is difficult to tackle. However, as usage of such datasets for quantitative disease diagnosis grows, so does the importance of understanding the noise properties because of their effect on the accuracy of the clinical outcome. The goal of this work is to study noise covariance in the helical MSCT volumetric dataset. We explore possible approximations to the noise covariance matrix with reduced degrees of freedom, including voxel-based variance, one-dimensional (1D) correlation, two-dimensional (2D) in-plane correlation and the noise power spectrum (NPS). We further examine the effect of various noise covariance models on the accuracy of a prewhitening matched filter nodule size estimation strategy. Our simulation results suggest that the 1D longitudinal, 2D in-plane and NPS prewhitening approaches can improve the performance of nodule size estimation algorithms. When taking into account computational costs in determining noise characterizations, the NPS model may be the most efficient approximation to the MSCT noise covariance matrix.

To reduce positron emission tomography (PET) and computed tomography (CT) misalignments and standardized uptake value (SUV) errors, cine average CT (CACT) has been proposed to replace helical CT (HCT) for attenuation correction (AC). A new method using interpolated average CT (IACT) for AC is introduced to further reduce radiation dose with similar image quality. Six patients were recruited in this study. The end-inspiration and -expiration phases from cine CT were used as the two original phases. Deformable image registration was used to generate the interpolated phases. The IACT was calculated by averaging the original and interpolated phases. The PET images were then reconstructed with AC using CACT, HCT and IACT, respectively. Their misalignments were compared by visual assessment, mutual information, correlation coefficient and SUV. The doses from different CT maps were analyzed. The misalignments were reduced for CACT and IACT as compared to HCT. The maximum SUV difference between the use of IACT and CACT was ∼3%, and it was ∼20% between the use of HCT and CACT. The estimated dose for IACT was 0.38 mSv. The radiation dose using IACT could be reduced by 85% compared to the use of CACT. IACT is a good low-dose approximation of CACT for AC.

The derivative at constant direction is frequently used in inversion of cone-beam data. Several algorithms for computing the derivative have been proposed in the literature. The best algorithm to date has been proposed recently by Noo et al (2007 Phys. Med. Biol. 52 5393-414). In this note we propose a new, simple and efficient formula for computing the derivative. Numerical experiments with helical CT show that our formula and the one of Noo et al provide fairly similar spatial resolution and noise stability, even though the new formula is more efficient and easier to implement.

In this paper, we present a Bayesian maximum a posteriori method for multi-slice helical CT reconstruction based on an L0-norm prior. It makes use of a very low number of projections. A set of surrogate potential functions is used to successively approximate the L0-norm function while generating the prior and to accelerate the convergence speed. Simulation results show that the proposed method provides high quality reconstructions with highly sparse sampled noise-free projections. In the presence of noise, the reconstruction quality is still significantly better than the reconstructions obtained with L1-norm or L2-norm priors.

The temporal pattern of radiation delivery has been shown to influence the tumor cell survival fractions for the same radiation dose. To study the effect more specifically for state of the art rotational radiation delivery modalities, 2 Gy of radiation dose was delivered to H460 lung carcinoma, PC3 prostate cancer cells and MCF-7 breast tumor cells by helical tomotherapy (HT), seven-field LINAC (7F), and continuous dose delivery (CDD) over 2 min that simulates volumetric rotational arc therapy. Cell survival was measured by the clonogenic assay. The number of viable H460 cell colonies was 23.2 +/- 14.4% and 27.7 +/- 15.6% lower when irradiated by CDD compared with HT and 7F, respectively, and the corresponding values were 36.8 +/- 18.9% and 35.3 +/- 18.9% lower for MCF7 cells (p < 0.01). The survival of PC3 was also lower when irradiated by CDD than by HT or 7F but the difference was not as significant (p = 0.06 and 0.04, respectively). The higher survival fraction from HT delivery was unexpected because 90% of the 2 Gy was delivered in less than 1 min at a significantly higher dose rate than the other two delivery techniques. The results suggest that continuous dose delivery at a constant dose rate results in superior in vitro tumor cell killing compared with prolonged, segmented or variable dose rate delivery.

In this work, a method for direct incorporation of patient motion into tomotherapy dose calculations is developed and validated. This computational method accounts for all treatment dynamics and can incorporate random as well as cyclical motion data. Hence, interplay effects between treatment dynamics and patient motion are taken into account during dose calculation. This allows for a realistic assessment of intra-fraction motion on the dose distribution. The specific approach entails modifying the position and velocity events in the tomotherapy delivery plan to accommodate any known motion. The computational method is verified through phantom and film measurements. Here, measured prostate motion and simulated respiratory motion tracks were incorporated in the dose calculation. The calculated motion-encoded dose profiles showed excellent agreement with the measurements. Gamma analysis using 3 mm and 3% tolerance criteria showed over 97% and 96% average of points passing for the prostate and breathing motion tracks, respectively. The profile and gamma analysis results validate the accuracy of this method for incorporating intra-fraction motion into the dose calculation engine for assessment of dosimetric effects on helical tomotherapy dose deliveries.

Cone-beam spiral backprojection is computationally highly demanding. At first sight, the backprojection requirements are similar to those of cone-beam backprojection from circular scans such as it is performed in the widely used Feldkamp algorithm. However, there is an additional complication: the illumination of each voxel, i.e. the range of angles the voxel is seen by the x-ray cone, is a complex function of the voxel position. In general, one needs to multiply a voxel-specific weight w(x, y, z, alpha) prior to adding a projection from angle alpha to a voxel at position x, y, z. Often, the weight function has no analytically closed form and must be numerically determined. Storage of the weights is prohibitive since the amount of memory required equals the number of voxels per spiral rotation times the number of projections a voxel receives contributions and therefore is in the order of up to 10(12) floating point values for typical spiral scans. We propose a new algorithm that combines the spiral symmetry with the ability of today's 64 bit operating systems to store large amounts of precomputed weights, even above the 4 GB limit. Our trick is to backproject into slices that are rotated in the same manner as the spiral trajectory rotates. Using the spiral symmetry in this way allows one to exploit data-level paralellism and thereby to achieve a very high level of vectorization. An additional postprocessing step rotates these slices back to normal images. Our new backprojection algorithm achieves up to 17 giga voxel updates per second on our systems that are equipped with four standard Intel X7460 hexa core CPUs (Intel Xeon 7300 platform, 2.66 GHz, Intel Corporation). This equals the reconstruction of 344 images per second assuming that each slice consists of 512 x 512 pixels and receives contributions from 512 projections. Thereby, it is an order of magnitude faster than a highly optimized code that does not make use of the spiral symmetry. In its present version, the spiral backprojection algorithm is pixel-driven. A ray-driven version and a corresponding high performance forward projector can be easily designed. Thus, our findings can be used to speed up any type of image reconstruction algorithm (approximate or exact analytical algorithms and iterative algorithms) and therefore yield a versatile and valuable component of future image reconstruction pipelines.

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.

Since the beam width on the helical tomotherapy machine produced by TomoTherapy Inc., is typically a few centimeters in the longitudinal direction (into the bore), the optimizer must choose to have a relatively high intensity local to the inside edge of a tumor or planning treatment volume (PTV) when avoiding an immediately adjacent organ at risk (OAR), either superior or inferior. By using a standalone version of the TomoTherapy dose calculator, a realistic beam is applied to idealized deconvolution schemes including the MATLAB Optimizer Toolbox for a simple one-dimensional PTV with adjacent OARs. The results are compared to a clinical example on the TomoTherapy planning station. It is learned that a Gibbs phenomenon type of oscillation in the dose within the tumor under these special circumstances is not unique to TomoTherapy, but is related to the attempt to form a sharp dose gradient-sharper than the beam profile with typical optimization constraints set to achieve a uniform dose as close as possible to the prescription. The clinical implication is that the Gibbs-induced cold spots force the dose to increase in the PTV if a typical PTV dose-volume constraint is used. It is recommended that the dose prescription be smoothed prior to optimization or the dosimetric goals for an OAR adjacent to the PTV are such that a sharp dose falloff is not demanded, especially if the user reduces the requirements that such an OAR be of both high importance and immediately adjacent to the PTV edge.

This paper shows how to significantly accelerate cone-beam CT reconstruction and 3D deformable image registration using the stream-processing model. We describe data-parallel designs for the Feldkamp, Davis and Kress (FDK) reconstruction algorithm, and the demons deformable registration algorithm, suitable for use on a commodity graphics processing unit. The streaming versions of these algorithms are implemented using the Brook programming environment and executed on an NVidia 8800 GPU. Performance results using CT data of a preserved swine lung indicate that the GPU-based implementations of the FDK and demons algorithms achieve a substantial speedup--up to 80 times for FDK and 70 times for demons when compared to an optimized reference implementation on a 2.8 GHz Intel processor. In addition, the accuracy of the GPU-based implementations was found to be excellent. Compared with CPU-based implementations, the RMS differences were less than 0.1 Hounsfield unit for reconstruction and less than 0.1 mm for deformable registration.

In the last few years, mathematically exact algorithms, including the backprojection-filtration (BPF) algorithm, have been developed for accurate image reconstruction in helical cone-beam CT. The BPF algorithm requires minimum data, and can reconstruct region-of-interest (ROI) images from data containing truncations. However, similar to other existing reconstruction algorithms for helical cone-beam CT, the BPF algorithm involves a backprojection with a spatially varying weighting factor, which is computationally demanding and, more importantly, can lead to undesirable numerical properties in reconstructed images. In this work, we develop a rebinned BPF algorithm in which the backprojection invokes no spatially varying weighting factor for accurate image reconstruction from helical cone-beam projections. This rebinned BPF algorithm is computationally more efficient and numerically more stable than the original BPF algorithm, while it also retains the nice properties of the original BPF algorithm such as minimum data requirement and ROI-image reconstruction from truncated data. We have also performed simulation studies to validate and evaluate the rebinned BPF algorithm.

In computed tomography, analytical fan-beam (FB) and cone-beam (CB) image reconstruction often involves a view-dependent data differentiation. The implementation of this differentiation step is critical in terms of resolution and image quality. In this work, we present a new differentiation scheme that is robust to changes in the data acquisition geometry and to coarse view sampling. Our scheme was compared to two previously suggested methods, which we call the direct scheme and the chain-rule scheme. Image reconstructions were performed from computer-simulated data of the Shepp-Logan phantom, the FORBILD thorax phantom and a modified FORBILD head phantom. For FB reconstruction, we investigated three acquisition geometries: a circular, an ellipse-shaped and a square-shaped trajectory. For CB reconstruction, the circle-plus-line trajectory was considered. Image comparison showed that the new scheme performs consistently well when varying the scenario, in both FB and CB geometry, unlike the other two schemes.

Cone-beam computed tomography (CBCT) enables three-dimensional imaging with isotropic resolution and a shorter acquisition time compared to a helical CT scanner. Because a larger object volume is exposed for each projection, scatter levels are much higher than in collimated fan-beam systems, resulting in cupping artifacts, streaks and quantification inaccuracies. In this paper, a general method to correct for scatter in CBCT, without supplementary on-line acquisition, is presented. This method is based on scatter calibration through off-line acquisition combined with on-line analytical transformation based on physical equations, to adapt calibration to the object observed. The method was tested on a PMMA phantom and on an anthropomorphic thorax phantom. The results were validated by comparison to simulation for the PMMA phantom and by comparison to scans obtained on a commercial multi-slice CT scanner for the thorax phantom. Finally, the improvements achieved with the new method were compared to those obtained using a standard beam-stop method. The new method provided results that closely agreed with the simulation and with the conventional CT scanner, eliminating cupping artifacts and significantly improving quantification. Compared to the beam-stop method, lower x-ray doses and shorter acquisition times were needed, both divided by a factor of 9 for the same scatter estimation accuracy.

The rapid implementation of advanced treatment planning and delivery technologies for radiation therapy has brought new challenges in evaluating the most effective treatment modality. Intensity-modulated radiotherapy (IMRT) using multi-leaf collimators (MLC) and helical tomotherapy (HT) are becoming popular modes of treatment delivery and their application and effectiveness continues to be investigated. Presently, there are several treatment planning systems (TPS) that can generate and optimize IMRT plans based on user-defined objective functions for the internal target volume (ITV) and organs at risk (OAR). However, the radiobiological parameters of the different tumours and normal tissues are typically not taken into account during dose prescription and optimization of a treatment plan or during plan evaluation. The suitability of a treatment plan is typically decided based on dosimetric criteria such as dose-volume histograms (DVH), maximum, minimum, mean and standard deviation of the dose distribution. For a more comprehensive treatment plan evaluation, the biologically effective uniform dose (D) is applied together with the complication-free tumour control probability (P(+)). Its utilization is demonstrated using three clinical cases that were planned with two different forms of IMRT. In this study, three different cancer types at different anatomical sites were investigated: head and neck, lung and prostate cancers. For each cancer type, a linac MLC-based step-and-shoot IMRT plan and a HT plan were developed. The MLC-based IMRT treatment plans were developed on the Philips treatment-planning platform, using the Pinnacle 7.6 software release. For the tomotherapy HiArt plans, the dedicated tomotherapy treatment planning station was used, running version 2.1.2. By using D as the common prescription point of the treatment plans and plotting the tissue response probabilities versus D for a range of prescription doses, a number of plan trials can be compared based on radiobiological measures. The applied plan evaluation method shows that in the head and neck cancer case the HT treatment gives better results than MLC-based IMRT in terms of expected clinical outcome P(+) of 62.2% and 46.0%, D to the ITV of 72.3 Gy and 70.7 Gy, respectively). In the lung cancer and prostate cancer cases, the MLC-based IMRT plans are better over the clinically useful dose prescription range. For the lung cancer case, the HT and MLC-based IMRT plans give a P(+) of 66.9% and 72.9%, D to the ITV of 64.0 Gy and 66.9 Gy, respectively. Similarly, for the prostate cancer case, the two radiation modalities give a P(+) of 68.7% and 72.2%, D to the ITV of 86.0 Gy and 85.9 Gy, respectively. If a higher risk of complications (higher than 5%) could be allowed, the complication-free tumour control could increase by over 40%, 2% and 30% compared to the initial dose prescription for the three cancer cases, respectively. Both MLC-based IMRT and HT can encompass the often-large ITV required while they minimize the volume of the organs at risk receiving high doses. Radiobiological evaluation of treatment plans may provide an improved correlation of the delivered treatment with the clinical outcome by taking into account the dose-response characteristics of the irradiated targets and normal tissues. There may exist clinical cases, which may look dosimetrically similar but in radiobiological terms may be quite different. In such situations, traditional dose-based evaluation tools can be complemented by the use of P(+)--D diagrams to effectively evaluate and compare treatment plans.

The previous theoretical work of a delivery transfer function (DTF) in radiotherapy is expanded to include the unique intensity modulation method of helical tomotherapy. In addition to the collimation of each beamlet, and the Gaussian scatter convolution spreading of the dose that other radiotherapy units have, helical tomotherapy uses 51 small arcs of varying lengths to adjust the intensity. The blurring from these arcs is not taken into account during treatment planning. A theoretical DTF is constructed, and a calculation is performed which includes this unique source motion in relation to the other DTF components. Various typical delivery parameters are used to generate resolution maps for a constant intensity projection. Near the isocenter, the transverse (to a given beam direction) blurring is small but at larger radii (>6 cm), the source blurring dominates over leaf size. For most clinical situations, this inherent source motion blurring is expected to be negligible.

With the increased use of cone beam CT (CBCT) for daily patient setup, the accumulated dose from CBCT may be significantly higher than that from simulation CT or portal imaging. The objective of this work is to measure the dose from daily pelvic scans with fixed technical settings and collimations. CBCT scans were acquired in half-fan mode using a half bowtie and x-rays were delivered in pulsed-fluoro mode. The skin doses for seven prostate patients were measured on an IRB-approved protocol. TLD capsules were placed on the patient's skin at the central axis of three beams: AP, left lateral (Lt Lat) and right lateral (Rt Lat). To avoid the ring artefacts centred in the prostate, the treatment couch was dropped 3 cm from the patient's tattoo (central axis). The measured AP skin doses ranged 3-6 cGy for 20-33 cm separation. The larger the patient size the less the AP skin dose. Lateral doses did not change much with patient size. The Lt Lat dose was approximately 4.0 cGy, which was approximately 40% higher than the Rt Lat dose of approximately 2.6 cGy. To verify this dose asymmetry, surface doses on an IMRT QA phantom (oval shaped, 30 cm x 20 cm) were measured at the same three sites using TLD capsules with 3 cm table-drop. The dose asymmetry was due to: (1) kV source rotation which always starts from the patient's Lt Lat and ends at Lt Lat. Gantry rotation gets much slower near the end of rotation but dose rate stays constant and (2) 370 degrees scan rotation (10 degrees scan overlap on the Lt Lat side). In vivo doses were measured inside a Rando pelvic heterogeneous phantom using TLDs. The left hip (femoral head and neck) received the highest doses of approximately 10-11 cGy while the right hip received approximately 6-7 cGy. The surface and in vivo doses were also measured for phantoms at the central-axis setup. The difference was less than approximately 12% to the table-drop setup.

This study aims to determine the settings that provide the optimal clinical accuracy and consistency for the registration of megavoltage CT (MVCT) with planning kilovoltage CT image sets on the Hi-ART tomotherapy system. The systematic offset between the MVCT and the planning kVCT was determined by registration of multiple MVCT scans of a head phantom aligned with the planning isocentre. Residual error vector lengths and components were used to quantify the alignment quality for the phantom shifted by 5 mm in different directions obtained by all 27 possible combinations of MVCT inter-slice spacing, registration techniques and resolution. MVCT scans with normal slices are superior to coarse slices for registration of shifts in the superior-inferior, lateral and anterior-posterior directions. Decreasing the scan length has no detrimental effect on registration accuracy as long as the scan lengths are larger than 24 mm. In the case of bone technique and fine resolution, normal and fine MVCT scan slice spacing options give similar accuracy, so normal mode is preferable due to shorter procedure and less delivered dose required for patient set-up. A superior-inferior field length of 24-30 mm, normal slice spacing, bone technique, and fine resolution is the optimum set of registration settings for MVCT scans of a Rando head phantom acquired with the Hi-ART tomotherapy system, provided the registration shifts are less than 5 mm.

The long object problem is practically important and theoretically challenging. To solve the long object problem, spiral cone-beam CT was first proposed in 1991, and has been extensively studied since then. As a main feature of the next generation medical CT, spiral cone-beam CT has been greatly improved over the past several years, especially in terms of exact image reconstruction methods. Now, it is well established that volumetric images can be exactly and efficiently reconstructed from longitudinally truncated data collected along a rather general scanning trajectory. Here we present an overview of some key results in this area.

Experiments were conducted to confirm the isotropic spatial resolution of multislice CT with a 0.5 mm slice thickness. Isotropic spatial resolution means that the spatial resolution in the transaxial plane (X-Y plane) and that in the longitudinal direction (Z direction) are equivalent. To obtain point spread function (PSF) values in the X-Y-Z directions, three-dimensional voxel data were obtained by helical scanning of a bead phantom. The modulation transfer function (MTF) values were then obtained by three-dimensional Fourier transform of the PSF. Evaluation of the spatial resolution in the X-Y-Z directions by the MTF values showed that the spatial resolution in the Z direction does not depend on the reconstruction kernel used. It was also found that the spatial resolution in the Z direction, as compared with that in the X-Y plane, is superior with the standard kernel for the abdomen and is inferior with the high-definition kernel for the ears/bones. By performing sharpening filter processing in the Z direction with a high-definition kernel, comparable spatial resolution could be obtained in the X-Y-Z directions. It was confirmed that adjusting the spatial resolution in the Z direction with the reconstruction kernel used is an effective method for isotropic imaging.

The combination of circular CT with a helical trajectory segment results in a mathematically complete data set. We present a reconstruction algorithm which is mathematically exact and of the filtered back-projection type. The algorithm ensures that only Radon planes which are not covered along the circle are taken into account, when data from the helical segment are back-projected. Therefore, the helical segment contributes only to low-frequency parts of trans-axial slices. Data along the helix can be obtained with a very low acquisition dose.

In recent years, image reconstruction methods for cone-beam computed tomography (CT) have been extensively studied. However, few of these studies discussed computing parallel-beam projections from cone-beam projections. In this paper, we focus on the exact synthesis of complete or incomplete parallel-beam projections from cone-beam projections. First, an extended central slice theorem is described to establish a relationship between the Radon space and the Fourier space. Then, data sufficiency conditions are proposed for computing parallel-beam projection data from cone-beam data. Using these results, a general filtered backprojection algorithm is formulated that can exactly synthesize parallel-beam projection data from cone-beam projection data. As an example, we prove that parallel-beam projections can be exactly synthesized in an angular range in the case of circular cone-beam scanning. Interestingly, this angular range is larger than that derived in the Feldkamp reconstruction framework. Numerical experiments are performed in the circular scanning case to verify our method.

Reconstruction algorithms for cone-beam CT have been the focus of many studies. Several exact and approximate reconstruction algorithms were proposed for step-and-shoot and helical scanning trajectories to combat cone-beam related artefacts. In this paper, we present a new closed-form cone-beam reconstruction formula for tilted gantry data acquisition. Although several algorithms were proposed in the past to combat errors induced by the gantry tilt, none of the algorithms addresses the scenario in which the cone-beam geometry is first rebinned to a set of parallel beams prior to the filtered backprojection. We show that the image quality advantages of the rebinned parallel-beam reconstruction are significant, which makes the development of such an algorithm necessary. Because of the rebinning process, the reconstruction algorithm becomes more complex and the amount of iso-centre adjustment depends not only on the projection and tilt angles, but also on the reconstructed pixel location. In this paper, we first demonstrate the advantages of the row-wise fan-to-parallel rebinning and derive a closed-form solution for the reconstruction algorithm for the step-and-shoot and constant-pitch helical scans. The proposed algorithm requires the 'warping' of the reconstruction matrix on a view-by-view basis prior to the backprojection step. We further extend the algorithm to the variable-pitch helical scans in which the patient table travels at non-constant speeds. The algorithm was tested extensively on both the 16- and 64-slice CT scanners. The efficacy of the algorithm is clearly demonstrated by multiple experiments.

Helical cone-beam CT is used widely nowadays because of its rapid scan speed and efficient utilization of x-ray dose. Recently, an exact reconstruction algorithm for helical cone-beam CT was proposed (Zou and Pan 2004a Phys. Med. Biol. 49 941-59). The algorithm is referred to as a backprojection-filtering (BPF) algorithm. This BPF algorithm for a helical cone-beam CT with a flat-panel detector (FPD-HCBCT) requires minimum data within the Tam-Danielsson window and can naturally address the problem of ROI reconstruction from data truncated in both longitudinal and transversal directions. In practical CT systems, detectors are expensive and always take a very important position in the total cost. Hence, we work on an exact reconstruction algorithm for a CT system with a detector of the smallest size, i.e., a curved PI detector fitting the Tam-Danielsson window. The reconstruction algorithm is derived following the framework of the BPF algorithm. Numerical simulations are done to validate our algorithm in this study.

The combination-weighted Feldkamp algorithm (CW-FDK) was developed and tested in a phantom in order to reduce cone-beam artefacts and enhance cranio-caudal reconstruction coverage in an attempt to improve image quality when utilizing cone-beam computed tomography (CBCT). Using a 256-slice cone-beam CT (256CBCT), image quality (CT-number uniformity and geometrical accuracy) was quantitatively evaluated in phantom and clinical studies, and the results were compared to those obtained with the original Feldkamp algorithm. A clinical study was done in lung cancer patients under breath holding and free breathing. Image quality for the original Feldkamp algorithm is degraded at the edge of the scan region due to the missing volume, commensurate with the cranio-caudal distance between the reconstruction and central planes. The CW-FDK extended the reconstruction coverage to equal the scan coverage and improved reconstruction accuracy, unaffected by the cranio-caudal distance. The extended reconstruction coverage with good image quality provided by the CW-FDK will be clinically investigated for improving diagnostic and radiotherapy applications. In addition, this algorithm can also be adapted for use in relatively wide cone-angle CBCT such as with a flat-panel detector CBCT.

Based on the structure of the original helical FDK algorithm, a three-dimensional (3D)-weighted cone beam filtered backprojection (CB-FBP) algorithm is proposed for image reconstruction in volumetric CT under helical source trajectory. In addition to its dependence on view and fan angles, the 3D weighting utilizes the cone angle dependency of a ray to improve reconstruction accuracy. The 3D weighting is ray-dependent and the underlying mechanism is to give a favourable weight to the ray with the smaller cone angle out of a pair of conjugate rays but an unfavourable weight to the ray with the larger cone angle out of the conjugate ray pair. The proposed 3D-weighted helical CB-FBP reconstruction algorithm is implemented in the cone-parallel geometry that can improve noise uniformity and image generation speed significantly. Under the cone-parallel geometry, the filtering is naturally carried out along the tangential direction of the helical source trajectory. By exploring the 3D weighting's dependence on cone angle, the proposed helical 3D-weighted CB-FBP reconstruction algorithm can provide significantly improved reconstruction accuracy at moderate cone angle and high helical pitches. The 3D-weighted CB-FBP algorithm is experimentally evaluated by computer-simulated phantoms and phantoms scanned by a diagnostic volumetric CT system with a detector dimension of 64 x 0.625 mm over various helical pitches. The computer simulation study shows that the 3D weighting enables the proposed algorithm to reach reconstruction accuracy comparable to that of exact CB reconstruction algorithms, such as the Katsevich algorithm, under a moderate cone angle (4 degrees) and various helical pitches. Meanwhile, the experimental evaluation using the phantoms scanned by a volumetric CT system shows that the spatial resolution along the z-direction and noise characteristics of the proposed 3D-weighted helical CB-FBP reconstruction algorithm are maintained very well in comparison to the FDK-type algorithms. Moreover, the experimental evaluation by clinical data verifies that the proposed 3D-weighted CB-FBP algorithm for image reconstruction in volumetric CT under helical source trajectory meets the challenges posed by diagnostic applications of volumetric CT imaging.

Recently, several exact cone-beam reconstruction algorithms, such as the generalized filtered-backprojection (FBP) and backprojection-filtration (BPF) methods, have been developed to solve the long object problem. Although the well-known 3D Shepp-Logan phantom (SLP) is often used to validate these algorithms, it is deficient due to the discontinuity of the SLP. In this paper, we first construct a differentiable polynomial function to approximate the unit rectangular function on [-1, 1]. Then, we use this function to obtain a differentiable ellipsoid phantom, whose x-ray transform is differentiable for any smooth scanning trajectory. Finally, we propose a differentiable Shepp-Logan phantom (DSLP) for numerical simulation of the exact cone-beam CT algorithms. Our numerical simulation shows that the reconstructed DSLP has a better image quality than the reconstructed SLP, and is complementary to the traditional SLP for evaluation of the exact cone-beam CT algorithms.

While respiration-correlated CT is gaining acceptance in clinical radiotherapy, the effect of scanning parameters on the image quality has yet to be addressed. The intent of this study was to characterize the effects of gantry rotation and table speed on various image quality characteristics in multi-slice, helical, retrospectively-gated CT images. Images of stationary and moving phantoms were obtained in helical mode on a 20-slice CT scanner. Motion was generated by a computer-controlled platform capable of moving simultaneously in two dimensions. Motion was monitored using a pressure gauge inserted inside an adjustable belt. Selected scans were retrospectively gated into ten phases based on the monitored motion. Gantry rotation speeds of 0.5 s and 1.0 s were evaluated with pitches ranging from 0.1 to 0.45. Several parameters, including calculated object volumes, trajectory (movement from peak to trough), deformation (actual volume divided by volume created with the maximum diameter of contoured object) and z-axis resolution, were used to characterize image quality. These studies indicate that for objects in the peak phase of a movement pattern that simulates breathing, retrospectively gated scans using fast gantry rotation speeds produce volume, trajectory, deformation and z-axis resolution results comparable with those of a stationary object.

Computed tomography (CT) scanners are usually described by their in-plane resolution and slice-sensitivity profile (SSP). Other imaging systems are characterized by their point spread function (PSF). The PSF is an excellent basis for the analysis, design and enhancement of imaging systems. The 3D PSF of CT systems has rarely been considered, and has usually been approximated by a 3D Gaussian. We present mathematical analysis of the PSF of single-slice and multi-slice fan-beam and cone-beam CT, for major reconstruction algorithms. We show that the PSF has a complicated, non-separable 3D shape. It is anisotropic in the xy plane and twisted in the z direction. Furthermore, the PSF is space variant in all three axes. In particular, it rotates as the input impulse function moves in the z direction. The PSF may also have effective discontinuities that can lead to streaking artefacts. Indirect measurements of the PSF can be misleading. We support the theoretical results by direct experimental measurements of the PSF.

An x-ray computed tomography (CT) simulator based on the Monte Carlo N-particle radiation transport computer code (MCNP4C) was developed for simulation of both fan- and cone-beam CT scanners. A user-friendly interface running under Matlab 6.5.1 creates the scanner geometry at different views as MCNP4C's input file. The full simulation of x-ray tube, phantom and detectors with single-slice, multi-slice and flat detector configurations was considered. The simulator was validated through comparison with experimental measurements of different nonuniform phantoms with varying sizes on both a clinical and a small-animal CT scanner. There is good agreement between the simulated and measured projections and reconstructed images. Thereafter, the effects of bow-tie filter, phantom size and septa length on scatter distribution in fan-beam CT were studied in detail. The relative difference between detected total, primary and scatter photons for septa length varying between 0 and 95 mm is 11.2%, 1.9% and 84.1%, respectively, whereas the scatter-to-primary ratio decreases by 83.8%. The developed simulator is a powerful tool for evaluating the effect of physical, geometrical and other design parameters on scanner performance and image quality in addition to offering a versatile tool for investigating potential artefacts and correction schemes when using CT-based attenuation correction on dual-modality PET/CT units.

Proposed is an exact shift-invariant filtered backprojection algorithm for the circle-and-arc trajectory. The algorithm has several important features. First, it allows for the circle to be incomplete. Second, axial truncation of the cone beam data is allowed. Third, the length of the arc is determined only by the region of interest and is independent of the size of the entire object. The algorithm is quite flexible and can be used for even more general trajectories that consist of several circular segments and arcs. The algorithm applies also in the case when the circle (or, circles) is complete. A numerical experiment with the clock phantom demonstrated good image quality.

In this paper, Novikov's inversion formula of the attenuated two-dimensional (2D) Radon transform is applied to the reconstruction of attenuated fan-beam projections acquired with equal detector spacing and of attenuated cone-beam projections acquired with a flat planar detector and circular trajectory. The derivation of the fan-beam algorithm is obtained by transformation from parallel-beam coordinates to fan-beam coordinates. The cone-beam reconstruction algorithm is an extension of the fan-beam reconstruction algorithm using Feldkamp-Davis-Kress's (FDK) method. Computer simulations indicate that the algorithm is efficient and is accurate in reconstructing slices close to the central slice of the cone-beam orbit plane. When the attenuation map is set to zero the implementation is equivalent to the FDK method. Reconstructed images are also shown for noise corrupted projections.

For applications in bolus-chasing computed tomography (CT) angiography and electron-beam micro-CT, the backprojection-filtration (BPF) formula developed by Zou and Pan was recently generalized by Ye et al to reconstruct images from cone-beam data collected along a rather flexible scanning locus, including a nonstandard spiral. A major implication of the generalized BPF formula is that it can be applied for n-PI-window-based reconstruction in the nonstandard spiral scanning case. In this paper, we design an n-PI-window-based BPF algorithm, and report the numerical simulation results with the 3D Shepp-Logan phantom and Defrise disk phantom. The proposed BPF algorithm consists of three steps: cone-beam data differentiation, weighted backprojection and inverse Hilbert filtration. Our simulated results demonstrate the feasibility and merits of the proposed algorithm.

In this paper, we present a new algorithm designed for a specific data truncation problem in fan-beam CT. We consider a scanning configuration in which the fan-beam projection data are acquired from an asymmetrically positioned half-sized detector. Namely, the asymmetric detector only covers one half of the scanning field of view. Thus, the acquired fan-beam projection data are truncated at every view angle. If an explicit data rebinning process is not invoked, this data acquisition configuration will reek havoc on many known fan-beam image reconstruction schemes including the standard filtered backprojection (FBP) algorithm and the super-short-scan FBP reconstruction algorithms. However, we demonstrate that a recently developed fan-beam image reconstruction algorithm which reconstructs an image via filtering a backprojection image of differentiated projection data (FBPD) survives the above fan-beam data truncation problem. Namely, we may exactly reconstruct the whole image object using the truncated data acquired in a full scan mode (2pi angular range). We may also exactly reconstruct a small region of interest (ROI) using the truncated projection data acquired in a short-scan mode (less than 2pi angular range). The most important characteristic of the proposed reconstruction scheme is that an explicit data rebinning process is not introduced. Numerical simulations were conducted to validate the new reconstruction algorithm.

We derive accurate and efficient reconstruction algorithms for helical, cone-beam CT that employ shift-invariant filtering. Specifically, a new backprojection-filtration algorithm is developed, and a minimum data filtered-backprojection algorithm is derived. These reconstruction algorithms with shift-invariant filtering can accept data with transverse truncation, and hence allow for minimum data image reconstruction.

Retrospectively gated cardiac volume CT imaging has become feasible with the introduction of heart rate adaptive cardiac CT reconstruction algorithms. The development in detector technology and the rapid introduction of multi-row detectors has demanded reconstruction schemes which account for the cone geometry. With the extended cardiac reconstruction (ECR) framework, the idea of approximate helical cone beam CT has been extended to be used with retrospective gating, enabling heart rate adaptive cardiac cone beam reconstruction. In this contribution, the ECR technique is evaluated for systems with an increased number of detector rows, which leads to larger cone angles. A simulation study has been carried out based on a 4D cardiac phantom consisting of a thorax model and a dynamic heart insert. Images have been reconstructed for different detector set-ups. Reconstruction assessment functions have been calculated for the detector set-ups employing different rotation times, relative pitches and heart rates. With the increased volume coverage of large area detector systems, low-pitch scans become feasible without resulting in extensive scan times, inhibiting single breath hold acquisitions. ECR delivers promising image results when being applied to systems with larger cone angles.

Convolution/superposition (C/S) is regarded as the standard dose calculation method in most modern radiotherapy treatment planning systems. Different implementations of C/S could result in significantly different dose distributions. This paper addresses two major implementation issues associated with collapsed cone C/S: one is how to utilize the tabulated kernels instead of analytical parametrizations and the other is how to deal with voxel size effects. Three methods that utilize the tabulated kernels are presented in this paper. These methods differ in the effective kernels used: the differential kernel (DK), the cumulative kernel (CK) or the cumulative-cumulative kernel (CCK). They result in slightly different computation times but significantly different voxel size effects. Both simulated and real multi-resolution dose calculations are presented. For simulation tests, we use arbitrary kernels and various voxel sizes with a homogeneous phantom, and assume forward energy transportation only. Simulations with voxel size up to 1 cm show that the CCK algorithm has errors within 0.1% of the maximum gold standard dose. Real dose calculations use a heterogeneous slab phantom, both the 'broad' (5 x 5 cm2) and the 'narrow' (1.2 x 1.2 cm2) tomotherapy beams. Various voxel sizes (0.5 mm, 1 mm, 2 mm, 4 mm and 8 mm) are used for dose calculations. The results show that all three algorithms have negligible difference (0.1%) for the dose calculation in the fine resolution (0.5 mm voxels). But differences become significant when the voxel size increases. As for the DK or CK algorithm in the broad (narrow) beam dose calculation, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 10% (7%) of the maximum dose. As for the broad (narrow) beam dose calculation using the CCK algorithm, the dose differences between the 0.5 mm voxels and the voxels up to 8 mm (4 mm) are around 1% of the maximum dose. Among all three methods, the CCK algorithm is demonstrated to be the most accurate one for multi-resolution dose calculations.

Statistical methods for image reconstruction such as maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurate modelling of the photon transport and noise. Statistical reconstruction is prohibitively slow when applied to clinical x-ray cone-beam CT due to the large data sets and the high number of iterations required for reconstructing high resolution images. One way to reduce the reconstruction time is to use ordered subsets of projections during the iterations, which has been successfully applied to fan-beam x-ray CT. In this paper, we quantitatively analyse the use of ordered subsets in concert with the convex algorithm for cone-beam x-ray CT reconstruction, for the case of circular acquisition orbits. We focus on the reconstructed image accuracy of a 3D head phantom. Acceleration factors larger than 300 were obtained with errors smaller than 1%, with the preservation of signal-to-noise ratio. Pushing the acceleration factor towards 600 by using an increasing number of subsets increases the reconstruction error up to 5% and significantly increases noise. The results indicate that the use of ordered subsets can be extremely useful for cone-beam x-ray CT.

In this paper, a new image reconstruction scheme is presented based on Tuy's cone-beam inversion scheme and its fan-beam counterpart. It is demonstrated that Tuy's inversion scheme may be used to derive a new framework for fanbeam and cone-beam image reconstruction. In this new framework, images are reconstructed via filtering the backprojection image of differentiated projection data. The new framework is mathematically exact and is applicable to a general source trajectory provided the Tuy data sufficiency condition is satisfied. By choosing a piece-wise constant function for one of the components in the factorized weighting function, the filtering kernel is one dimensional, viz. the filtering process is along a straight line. Thus, the derived image reconstruction algorithm is mathematically exact and efficient. In the cone-beam case, the derived reconstruction algorithm is applicable to a large class of source trajectories where the pi-lines or the generalized pi-lines exist. In addition, the new reconstruction scheme survives the super-short scan mode in both the fan-beam and cone-beam cases provided the data are not transversely truncated. Numerical simulations were conducted to validate the new reconstruction scheme for the fan-beam case.

We have recently proposed a general formula (i.e., equations (9) to (11) in Zou and Pan (2004a Phys. Med. Biol. 49 941-59)) for image reconstruction from helical cone-beam data. On the basis of the formula, we have also developed two reconstruction algorithms, which are referred to as the backprojection filtration (BPF) algorithm (Zou and Pan 2004a) and the filtered backprojection (FBP) algorithm (Zou and Pan 2004b Phys. Med. Biol. 49 2717-31), respectively. The two algorithms have been implemented and evaluated in numerical studies. In this note, however, we point out that the data function previously used for proving the general formula in Zou and Pan (2004a) is incomplete and that, instead, an extended data function and its generalized backprojection, which are described in this note, should be used to complete the proof of the general formula. On the other hand, we also demonstrate in this note that the additional term in the extended data function has no effect on the previously developed BPF and FBP algorithms. The results can also be extended to general, smooth trajectories.

A circular scanning trajectory is and will likely remain a popular choice of trajectory in computed tomography (CT) imaging because it is easy to implement and control. Filtered-backprojection (FBP)-based algorithms have been developed previously for approximate and exact reconstruction of the entire image or a region of interest within the image in circular cone-beam and fan-beam cases. Recently, we have developed a 3D FBP-based algorithm for image reconstruction on PI-line segments in a helical cone-beam scan. In this work, we demonstrated that the 3D FBP-based algorithm indeed provided a rather general formulation for image reconstruction from divergent projections (such as cone-beam and fan-beam projections). On the basis of this formulation we derived new approximate or exact algorithms for image reconstruction in circular cone-beam or fan-beam scans, which can be interpreted as special cases of the helical scan. Existing algorithms corresponding to the derived algorithms were identified. We also performed a preliminary numerical study to verify our theoretical results in each of the cases. The results in the work can readily be generalized to other non-circular trajectories.