Control algorithms for dynamic attenuators
S. S. Hsieh, N. J. Pelc
Medical Physics, vol. 41, no. 6, p. 061907, 2014
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 requirea 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.
A multi-source inverse-geometry CT system: initial results with an 8 spot x-ray source array
J. Baek, B. De Man, J. Uribe, R. Longtin, D. Harrison, J. Reynolds, B. Neculaes, K. Frutschy, L. Inzinna, A. Caiafa, R. Senzig, N. J. Pelc
Physics in Medicine & Biology, vol. 59, no. 5, pp. 1189-1202, 2014
We present initial experimental results of a rotating-gantry multi-source inverse-geometry CT (MS-IGCT) system. The MS-IGCT system was built with a single module of 2 × 4 x-ray sources and a 2D detector array. It produced a 75 mm in-plane field-of-view (FOV) with 160 mm axial coverage in a single gantry rotation. To evaluate system performance, a 2.5 inch diameter uniform PMMA cylinder phantom, a 200 µm diameter tungsten wire, and a euthanized rat were scanned. Each scan acquired 125 views per source and the gantry rotation time was 1 s per revolution. Geometric calibration was performed using a bead phantom. The scanning parameters were 80 kVp, 125 mA, and 5.4 µs pulse per source location per view. A data normalization technique was applied to the acquired projection data, and beam hardening and spectral nonlinearities of each detector channel were corrected. For image reconstruction, the projection data of each source row were rebinned into a full cone beam data set, and the FDK algorithm was used. The reconstructed volumes from upper and lower source rows shared an overlap volume which was combined in image space. The images of the uniform PMMA cylinder phantom showed good uniformity and no apparent artifacts. The measured in-plane MTF showed 13 lp cm(-1) at 10% cutoff, in good agreement with expectations. The rat data were also reconstructed reliably. The initial experimental results from this rotating-gantry MS-IGCT system demonstrated its ability to image a complex anatomical object without any significant image artifacts and to achieve high image resolution and large axial coverage in a single gantry rotation.
Efficacy of fixed filtration for rapid kVp-switching dual energy x-ray systems
Y. Yao, A. S. Wang, N. J. Pelc
Medical Physics, vol. 41, no. 3, pp. 03191, 2014
Purpose: Dose efficiency of dual kVp imaging can be improved if the two beams are filtered to remove photons in the common part of their spectra, thereby increasing spectral separation. While there are a number of advantages to rapid kVp‐switching for dual energy, it may not be feasible to have two different filters for the two spectra. Therefore, the authors are interested in whether a fixed added filter can improve the dose efficiency of kVp‐switching dual energy x‐ray systems.
Methods: The authors hypothesized that a K‐edge filter would provide the energy selectivity needed to remove overlap of the spectra and hence increase the precision of material separation at constant dose. Preliminary simulations were done using calcium and water basis materials and 80 and 140 kVp x‐ray spectra. Precision of the decomposition was evaluated based on the propagation of the Poisson noise through the decomposition function. Considering availability and cost, the authors chose a commercial Gd2O2S screen as the filter for their experimental validation. Experiments were conducted on a table‐top system using a phantom with various thicknesses of acrylic and copper and 70 and 125 kVp x‐ray spectra. The authors kept the phantom exposure roughly constant with and without filtration by adjusting the tube current. The filtered and unfiltered raw data of both low and high energy were decomposed into basis material and the variance of the decomposition for each thickness pair was calculated. To evaluate the filtration performance, the authors measured the ratio of material decomposition variance with and without filtration.
Results: Simulation results show that the ideal filter material depends on the object composition and thickness, and ranges across the lanthanide series, with higher atomic number filters being preferred for more attenuating objects. Variance reduction increases with filter thickness, and substantial reductions (40%) can be achieved with a 2× loss in intensity. The authors’ experimental results validate the simulations, yet were overall slightly worse than expectation. For large objects, conventional (non‐K‐edge) beam hardening filters perform well.
Conclusions: This study demonstrates the potential of fixed K‐edge filtration to improve the dose efficiency and material decomposition precision for rapid kVp‐switching dual energy systems.
Dose reduction using a dynamic, piecewise-linear attenuator MEDICAL PHYSICS
Hsieh, S. S., Fleischmann, D., Pelc, N. J.
2014; 41 (2)
The authors recently proposed a dynamic, prepatient x-ray attenuator capable of producing a piecewise-linear attenuation profile customized to each patient and viewing angle. This attenuator was intended to reduce scatter-to-primary ratio (SPR), dynamic range, and dose by redistributing flux. In this work the authors tested the ability of the attenuator to reduce dose and SPR in simulations. The authors selected four clinical applications, including routine full field-of-view scans of the thorax and abdomen, and targeted reconstruction tasks for an abdominal aortic aneurysm and the pancreas. Raw data were estimated by forward projection of the image volume datasets. The dynamic attenuator was controlled to reduce dose while maintaining peak variance by solving a convex optimization problem, assuminga prioriknowledge of the patient anatomy. In targeted reconstruction tasks, the noise in specific regions was given increased weighting. A system with a standard attenuator (or “bowtie filter”) was used as a reference, and used either convex optimized tube current modulation (TCM) or a standard TCM heuristic. The noise of the scan was determined analytically while the dose was estimated using Monte Carlo simulations. Scatter was also estimated using Monte Carlo simulations. The sensitivity of the dynamic attenuator to patient centering was also examined by shifting the abdomen in 2 cm intervals. Compared to a reference system with optimized TCM, use of the dynamic attenuator reduced dose by about 30% in routine scans and 50% in targeted scans. Compared to the TCM heuristics which are typically used withouta priori knowledge, the dose reduction is about 50% for routine scans. The dynamic attenuator gives the ability to redistribute noise and variance and produces more uniform noise profiles than systems with a conventional bowtie filter. The SPR was also modestly reduced by 10% in the thorax and 24% in the abdomen. Imaging with the dynamic attenuator was relatively insensitive to patient centering, showing a 17% increase in peak variance for a 6 cm shift of the abdomen, instead of an 82% increase in peak variance for a fixed bowtie filter. A dynamic prepatient x-ray attenuator consisting of multiple wedges is capable of achieving substantial dose reductions and modest SPR reductions.
Recent and Future Directions in CT Imaging ANNALS OF BIOMEDICAL ENGINEERING
Pelc, N. J.2014;
42 (2): 260-268
Computed tomography (CT) has made enormous technical advances since its introduction into clinical use. The engineering improvements have in turn led to important clinical applications and large impact in patient care. This paper reviews the technology development trends in CT since its introduction and uses these trends to help illuminate likely future progress. The prediction is that significant further improvements in speed, spatial resolution and dose efficiency can be expected in the next decade.
Enabling Photon Counting Detectors with Dynamic Attenuators MEDICAL IMAGING 2014: PHYSICS OF MEDICAL IMAGING
Hsieh, S. S., Pelc, N. J.
Photon-counting x-ray detectors (PCXDs) are being investigated as a replacement for conventional x-ray detectors because they promise several advantages, including better dose efficiency, higher resolution and spectral imaging. However, many of these advantages disappear when the x-ray flux incident on the detector is too high. We recently proposed a dynamic, piecewise-linear attenuator (or beam shaping filter) that can control the flux incident on the detector. This can restrict the operating range of the PCXD to keep the incident count rate below a given limit. We simulated a system with the piecewise-linear attenuator and a PCXD using raw data generated from forward projected DICOM files. We investigated the classic paralyzable and nonparalyzable PCXD as well as a weighted average of the two, with the weights chosen to mimic an existing PCXD (Taguchi et al, Med Phys 2011). The dynamic attenuator has small synergistic benefits with the nonparalyzable detector and large synergistic benefits with the paralyzable detector. Real PCXDs operate somewhere between these models, and the weighted average model still shows large benefits from the dynamic attenuator. We conclude that dynamic attenuators can reduce the count rate performance necessary for adopting PCXDs.
Algorithms for Optimizing CT Fluence Control MEDICAL IMAGING 2014: PHYSICS OF MEDICAL IMAGING
Hsieh, S. S., Pelc, N. J.
The ability to customize the incident x-ray fluence in CT via beam-shaping filters or mA modulation is known to improve image quality and/or reduce radiation dose. Previous work has shown that complete control of x-ray fluence (ray-by-ray fluence modulation) would further improve dose efficiency. While complete control of fluence is not currently possible, emerging concepts such as dynamic attenuators and inverse-geometry CT allow nearly complete control to be realized. Optimally using ray-by-ray fluence modulation requires solving a very high-dimensional optimization problem. Most optimization techniques fail or only provide approximate solutions. We present efficient algorithms for minimizing mean or peak variance given a fixed dose limit. The reductions in variance can easily be translated to reduction in dose, if the original variance met image quality requirements. For mean variance, a closed form solution is derived. The peak variance problem is recast as iterated, weighted mean variance minimization, and at each iteration it is possible to bound the distance to the optimal solution. We apply our algorithms in simulations of scans of the thorax and abdomen. Peak variance reductions of 45% and 65% are demonstrated in the abdomen and thorax, respectively, compared to a bowtie filter alone. Mean variance shows smaller gains (about 15%).
Use of depth information from in-depth photon counting detectors for X-ray spectral imaging: a preliminary Simulation study MEDICAL IMAGING 2014: PHYSICS OF MEDICAL IMAGING
Yao, Y., Bornefalk, H., Hsieh, S. S., Danielsson, M., Pelc, N. J.
Purpose: Photon counting x-ray detectors (PCXD) may improve dose-efficiency but are hampered by limited count rate. They generally have imperfect energy response. Multi-layer ("in-depth") detectors have been proposed to enable higher count rates but the potential benefit of the depth information has not been explored. We conducted a simulation study to compare in-depth detectors against single layer detectors composed of common materials. Both photon counting and energy integrating modes were studied. Methods: Polyenergetic transmissions were simulated through 25cm of water and 1cm of calcium. For PCXD composed of Si, GaAs or CdTe a 120kVp spectrum was used. For energy integrating x-ray detectors (EIXD) made from GaAs, CdTe or CsI, spectral imaging was done using 80 and 140kVp and matched dose. Semi-ideal and phenomenological energy response models were used. To compare these detectors, we computed the Cramér-Rao lower bound (CRLB) of the variance of basis material estimates. Results: For PCXDs with perfect energy response, depth data provides no additional information. For PCXDs with imperfect energy response and for EIXDs the improvement can be significant. E.g., for a CdTe PCXD with realistic energy response, depth information can reduce the variance by ~50%. The improvement depends on the x-ray spectrum. For a semi-ideal Si detector and a narrow x-ray spectrum the depth information has minimal advantage. For EIXD, the in-depth detector has consistent variance reduction (15% and 17%~19% for water and calcium, respectively). Conclusions: Depth information is beneficial to spectral imaging for both PCXD and EIXD. The improvement depends critically on the detector energy response.
Segmented Targeted Least Squares Estimator for Material Decomposition in Multi-Bin PCXDs MEDICAL IMAGING 2014: PHYSICS OF MEDICAL IMAGING
Rajbhandary, P. L., Hsieh, S. S., Pelc, N. J.
We present a fast, noise-efficient, and accurate estimator for material separation using photon-counting x-ray detectors (PCXDs) with multiple energy bin capability. The proposed targeted least squares estimator (TLSE) improves a previously proposed A-Table method by incorporating dynamic weighting that allows noise to be closer to the Cramér- Rao Lower Bound (CRLB) throughout the operating range. We explore Cartesian and average-energy segmentation of the basis material space for TLSE, and show that iso-average-energy contours require fewer segments compared to Cartesian segmentation to achieve similar performance. We compare the iso-average-energy TLSE to other proposed estimators - including the gold standard maximum likelihood estimator (MLE) and the A-Table 1 - in terms of variance, bias and computational efficiency. The variance and bias of this estimator between 0 to 6 cm of aluminum and 0 to 50 cm of water is simulated with Monte Carlo methods. Iso-average energy TLSE achieves an average variance within 2% of CRLB, and mean of absolute error of (3.68 ± 0.06) x 10-6 cm. Using the same protocol, MLE showed variance-to- CRLB ratio and average bias of 1.0186 ± 0.0002 and (3.10 ± 0.06) x 10-6 cm, respectively, but was 50 times slower in our simulation. Compared to the A-Table method, TLSE gives a more homogenous variance-to-CRLB profile in the operating region. We show that variance-to-CRLB for TLSE is lower by as much as ~36% than A-Table method in the peripheral region of operation (thin or thick objects). The TLSE is a computationally efficient and fast method for implementing material separation technique in PCXDs, with performance parameters comparable to the MLE.
To bin or not to bin? The effect of CT system limiting resolution on noise and detectability PHYSICS IN MEDICINE AND BIOLOGY
Baek, J., Pineda, A. R., Pelc, N. J.
2013; 58 (5): 1433-1446
We examine the noise advantages of having a computed tomography (CT) detector whose spatial resolution is significantly better (e.g. a factor of 2) than needed for a desired resolution in the reconstructed images. The effective resolution of detectors in x-ray CT is sometimes degraded by binning cells because the small cell size and fine sampling are not needed to achieve the desired resolution (e.g. with flat panel detectors). We studied the effect of the binning process on the noise in the reconstructed images and found that while the images in the absence of noise can be made identical for the native and the binned system, for the same system MTF in the presence of noise, the binned system always results in noisier reconstructed images. The effect of the increased noise in the reconstructed images on lesion detection is scale (frequency content) dependent with a larger difference between the high resolution and binned systems for imaging fine structure (small objects). We show simulated images reconstructed with both systems for representative objects and quantify the impact of the noise on the detection of the lesions based on mathematical observers. Through both subjective assessment of the reconstructed images and the quantification using mathematical observers, we show that for a CT system where the photon noise is dominant, higher resolution in the detectors leads to better noise performance in the reconstructed images at any resolution.
The feasibility of a piecewise-linear dynamic bowtie filter MEDICAL PHYSICS
Hsieh, S. S., Pelc, N. J.
2013; 40 (3)
The prepatient attenuator (or "bowtie filter") in CT is used to modulate the flux as a function of fan angle of the x-ray beam incident on the patient. Traditional, static bowtie filters are tailored only for very generic scans and for the average patient. The authors propose a design for a dynamic bowtie that can produce a time-dependent piecewise-linear attenuation profile. This dynamic bowtie may reduce dynamic range, dose or scatter, but in this work they focus on its ability to reduce dynamic range, which may be particularly important for systems employing photon-counting detectors.The dynamic bowtie is composed of a set of triangular wedges. Each wedge is independently moved in order to produce a time-dependent piecewise-linear attenuation profile. Simulations of the bowtie are conducted to estimate the dynamic range reduction in six clinical datasets. The control of the dynamic bowtie is determined by solving a convex optimization problem, and the dose is estimated using Monte Carlo techniques. Beam hardening artifacts are also simulated.The dynamic range is reduced by factors ranging from 2.4 to 27 depending on the part of the body studied. With a dynamic range minimization objective, the dose to the patient can be reduced from 6% to 33% while maintaining peak image noise. Further reduction in dose may be possible with a specific dose reduction objective. Beam hardening artifacts are suppressed with a two-pass algorithm.A dynamic bowtie producing a time-dependent, piecewise-linear attenuation profile is possible and can be used to modulate the flux of the scanner to the imaging task. Initial simulations show a large reduction in dynamic range. Several other applications are possible.