Scott S. Hsieh

The feasibility of an inverse geometry CT system with stationary source arrays.

PURPOSE Inverse geometry computed tomography (IGCT) has been proposed as a new system architecture that combines a small detector with a large, distributed source. This geometry can suppress cone-beam artifacts, reduce scatter, and increase dose efficiency. However, the temporal resolution of IGCT is still limited by the gantry rotation time. Large reductions in rotation time are in turn difficult due to the large source array and associated power electronics. We examine the feasibility of using stationary source arrays for IGCT in order to achieve better temporal resolution. We anticipate that multiple source arrays are necessary, with each source array physically separated from adjacent ones. METHODS Key feasibility issues include spatial resolution, artifacts, flux, noise, collimation, and system timing clashes. The separation between the different source arrays leads to missing views, complicating reconstruction. For the special case of three source arrays, a two-stage reconstruction algorithm is used to estimate the missing views. Collimation is achieved using a rotating collimator with a small number of holes. A set of equally spaced source spots are designated on the source arrays, and a source spot is energized when a collimator hole is aligned with it. System timing clashes occur when multiple source spots are scheduled to be energized simultaneously. We examine flux considerations to evaluate whether sufficient flux is available for clinical applications. RESULTS The two-stage reconstruction algorithm suppresses cone-beam artifacts while maintaining resolution and noise characteristics comparable to standard third generation systems. The residual artifacts are much smaller in magnitude than the cone-beam artifacts eliminated. A mathematical condition is given relating collimator hole locations and the number of virtual source spots for which system timing clashes are avoided. With optimization, sufficient flux may be achieved for many clinical applications. CONCLUSIONS IGCT with stationary source arrays could be an imaging platform potentially capable of imaging a complete 16-cm thick volume within a tenth of a second.

Dynamic bowtie for fan-beam CT

A bowtie is a filter used to shape an x-ray beam and equalize its flux reaching different detector channels. For development of spectral CT with energy discriminating photon-counting (EDPC) detectors, here we propose and evaluate a dynamic bowtie for performance optimization based on a patient model or a scout scan. With a mechanical rotation of a dynamic bowtie and an adaptive adjustment of an x-ray source flux, an x-ray beam intensity profile can be modulated. First, a mathematical model for dynamic bowtie filtering is established for an elliptical section in fan-beam geometry, and the contour of the optimal bowtie is derived. Then, numerical simulation is performed to compare the performance of the dynamic bowtie in the cases of an ideal phantom and a realistic cross-section relative to the counterparts without any bowtie and with a fixed bowtie respectively. Our dynamic bowtie can equalize the expected numbers of photons in the case of an ideal phantom. In practical cases, our dynamic bowtie can effectively reduce the dynamic range of detected signals inside the field of view. Although our design is optimized for an elliptical phantom, the resultant dynamic bowtie can be applied to a real fan-beam scan if the underlying cross-section can be approximated as an ellipse. Furthermore, our design methodology can be applied to specify an optimized dynamic bowtie for any cross-section of a patient, preferably using rapid prototyping technology.

Optimized control of a dynamic, prepatient attenuator

Dynamic attenuators are beam shaping filters that can customize the x-ray illumination field to the clinical task and for each view. These dynamic attenuators replace traditional attenuators (or “bowtie filters”) and decrease radiation dose, dynamic range, and scatter when compared to their static counterparts. We propose a one-dimensional dynamic attenuator that comprises multiple wedges with axially-dependent triangular cross-sections, and which are translated in the axial direction. These wedges together produce a time-varying, piecewise-linear attenuation function. We investigate different control methods for this attenuator and estimate the ability of the dynamic attenuator to reduce dose while maintaining the peak variance of the scan. With knowledge of the patient anatomy, the dynamic attenuator can be controlled by solving a convex optimization problem. This knowledge could be determined from a low dose pre-scan. Absent this information, various heuristics can be used. We simulate the dynamic attenuator on datasets of the thorax, abdomen, and a targeted scan of an abdominal aortic aneurysm. The dose and scatter-to-primary ratio (SPR) are estimated using Monte Carlo simulations, and the noise is calculated analytically. Compared to a system using the standard bowtie with typical mA modulation, dose reductions of 50% are observed. Compared to an optimized, patientspecific mA modulation, the typical dose reduction is 30%. If the dynamic attenuator is controlled with a heuristic, typical dose reductions are also 30%. The gains are larger in the targeted scan. The SPR is also reduced by 20% in the abdomen. We conclude that the dynamic attenuator has significant potential to reduce dose without increasing the peak variance of the scan.

Fluid-filled dynamic bowtie filter: a feasibility study

By varying its thickness to compensate for the different path length through the patient as a function of fan angle, a pre-patient bowtie filter modulates flux distribution to reduce patient dose, scatter, and detector dynamic range, and to improve image quality. A dynamic bowtie filter is superior to its traditional, static counterpart in its ability to adjust its thickness along different fan and view angles to suit a specific patient and task. Among the proposed dynamic bowtie designs, the piecewise-linear and the digital beam attenuators offer more flexibility than conventional filters, but rely on analog positioning of a limited number of wedges. In this work, we introduce a new approach with digital control, called the fluid-filled dynamic bowtie filter. It is a two-dimensional array of small binary elements (channels filled or unfilled with attenuating liquid) in which the cumulative thickness along the x-ray path contributes to the bowtie’s total attenuation. Using simulated data from a pelvic scan, the performance is compared with the piecewise-linear attenuator. The fluid-filled design better matches the desired target attenuation profile and delivers a 4.2x reduction in dynamic range. The variance of the reconstruction (or noise map) can also be more homogeneous. In minimizing peak variance, the fluid-filled attenuator shows a 3% improvement. From the initial simulation results, the proposed design has more control over the flux distribution as a function of both fan and view angles.

A Dynamic Attenuator Improves Spectral Imaging With Energy-Discriminating, Photon Counting Detectors

Energy-discriminating, photon counting (EDPC) detectors have high potential in spectral imaging applications but exhibit degraded performance when the incident count rate approaches or exceeds the characteristic count rate of the detector. In order to reduce the requirements on the detector, we explore the strategy of modulating the X-ray flux field using a recently proposed dynamic, piecewise-linear attenuator. A previous paper studied this modulation for photon counting detectors but did not explore the impact on spectral applications. In this work, we modeled detection with a bipolar triangular pulse shape (Taguchi , 2011) and estimated the Cramer-Rao lower bound (CRLB) of the variance of material selective and equivalent monoenergetic images, assuming deterministic errors at high flux could be corrected. We compared different materials for the dynamic attenuator and found that rare earth elements, such as erbium, outperformed previously proposed materials such as iron in spectral imaging. The redistribution of flux reduces the variance or dose, consistent with previous studies on benefits with conventional detectors. Numerical simulations based on DICOM datasets were used to assess the impact of the dynamic attenuator for detectors with several different characteristic count rates. The dynamic attenuator reduced the peak incident count rate by a factor of 4 in the thorax and 44 in the pelvis, and a 10 Mcps/mm2 EDPC detector with dynamic attenuator provided generally superior image quality to a 100 Mcps/mm 2 detector with reference bowtie filter for the same dose. The improvement is more pronounced in the material images.

An algorithm to estimate the object support in truncated images

PURPOSE Truncation artifacts in CT occur if the object to be imaged extends past the scanner field of view (SFOV). These artifacts impede diagnosis and could possibly introduce errors in dose plans for radiation therapy. Several approaches exist for correcting truncation artifacts, but existing correction algorithms do not accurately recover the skin line (or support) of the patient, which is important in some dose planning methods. The purpose of this paper was to develop an iterative algorithm that recovers the support of the object. METHODS The authors assume that the truncated portion of the image is made up of soft tissue of uniform CT number and attempt to find a shape consistent with the measured data. Each known measurement in the sinogram is interpreted as an estimate of missing mass along a line. An initial estimate of the object support is generated by thresholding a reconstruction made using a previous truncation artifact correction algorithm (e.g., water cylinder extrapolation). This object support is iteratively deformed to reduce the inconsistency with the measured data. The missing data are estimated using this object support to complete the dataset. The method was tested on simulated and experimentally truncated CT data. RESULTS The proposed algorithm produces a better defined skin line than water cylinder extrapolation. On the experimental data, the RMS error of the skin line is reduced by about 60%. For moderately truncated images, some soft tissue contrast is retained near the SFOV. As the extent of truncation increases, the soft tissue contrast outside the SFOV becomes unusable although the skin line remains clearly defined, and in reformatted images it varies smoothly from slice to slice as expected. CONCLUSIONS The support recovery algorithm provides a more accurate estimate of the patient outline than thresholded, basic water cylinder extrapolation, and may be preferred in some radiation therapy applications.

Control algorithms for dynamic attenuators

PURPOSE The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. METHODS The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. RESULTS The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. CONCLUSIONS Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods.

Estimating scatter in cone beam CT with striped ratio grids: A preliminary investigation.

PURPOSE To propose a new method for estimating scatter in x-ray imaging. Conventional antiscatter grids reject scatter at an efficiency that is constant or slowly varying over the surface of the grid. A striped ratio antiscatter grid, composed of stripes that alternate between high and low grid ratio, could be used instead. Such a striped ratio grid would reduce scatter-to-primary ratio as a conventional grid would, but more importantly, the signal discontinuities at the boundaries of stripes can be used to estimate local scatter content. METHODS Signal discontinuities provide information on scatter, but are contaminated by variation in primary radiation. A nonlinear image processing algorithm is used to estimate the scatter content in the presence of primary variation. We emulated a striped ratio grid by imaging phantoms with two sequential CT scans, one with and one without a conventional grid. These two scans are processed together to mimic a striped ratio grid. This represents a best case limit of the striped ratio grid, in that the extent of grid ratio modulation is very high and the scatter contrast is maximized. RESULTS In a uniform cylinder, the striped ratio grid virtually eliminates cupping. Artifacts from scatter are improved in an anthropomorphic phantom. Some banding artifacts are induced by the striped ratio grid. CONCLUSIONS Striped ratio grids could be a simple and effective evolution of conventional antiscatter grids. Construction and validation of a physical prototype remains an important future step.

A limit on dose reduction possible with CT reconstruction algorithms without prior knowledge of the scan subject.

PURPOSE To find an upper bound on the maximum dose reduction possible for any reconstruction algorithm, analytic or iterative, that result from the inclusion of the data statistics. The authors do not analyze noise reduction possible from prior knowledge or assumptions about the object. METHODS The authors examined the task of estimating the density of a circular lesion in a cross section. Raw data were simulated by forward projection of existing images and numerical phantoms. To assess an upper bound on the achievable dose reduction by any algorithm, the authors assume that both the background and the shape of the lesion are completely known. Under these conditions, the best possible estimate of the density can be determined by solving a weighted least squares problem directly in the raw data domain. Any possible reconstruction algorithm that does not use prior knowledge or make assumptions about the object, including filtered backprojection (FBP) or iterative reconstruction methods with this constraint, must be no better than this least squares solution. The authors simulated 10,000 sets of noisy data and compared the variance in density from the least squares solution with those from FBP. Density was estimated from FBP images using either averaging within a ROI, or streak-adaptive averaging with better noise performance. RESULTS The bound on the possible dose reduction depends on the degree to which the observer can read through the possibly streaky noise. For the described low contrast detection task with the signal shape and background known exactly, the average dose reduction possible compared to FBP with streak-adaptive averaging was 42% and it was 64% if only the ROI average is used with FBP. The exact amount of dose reduction also depends on the background anatomy, with statistically inhomogeneous backgrounds showing greater benefits. CONCLUSIONS The dose reductions from new, statistical reconstruction methods can be bounded. Larger dose reductions in the density estimation task studied here are only possible with the introduction of prior knowledge, which can introduce bias.

Improving pulse detection in multibin photon-counting detectors

Abstract. Energy-discriminating, photon-counting (EDPC) detectors are attractive for their potential for improved detective quantum efficiency and for their spectral imaging capabilities. However, at high count rates, counts are lost, the detected spectrum is distorted, and the advantages of EDPC detectors disappear. Existing EDPC detectors identify counts by analyzing the signal with a bank of comparators. We explored alternative methods for pulse detection for multibin EDPC detectors that could improve performance at high count rates. The detector signal was simulated in a Monte Carlo fashion assuming a bipolar shape and analyzed using several methods, including the conventional bank of comparators. For example, one method recorded the peak energy of the pulse along with the width (temporal extent) of the pulse. The Cramer–Rao lower bound of the variance of basis material estimates was numerically found for each method. At high count rates, the variance in water material (bone canceled) measurements could be reduced by as much as an order of magnitude. Improvements in virtual monoenergetic images were modest. We conclude that stochastic noise in spectral imaging tasks could be reduced if alternative methods for pulse detection were utilized.