The physical factors that govern 2D and 3D imaging performance may be understood from quantitative analysis of the spatial-frequency-dependent signal and noise transfer characteristics ͓e.g., modulation transfer function ͑MTF͒, noise-power spectrum ͑NPS͒, detective quantum efficiency ͑DQE͒, and noise-equivalent quanta ͑NEQ͔͒ along with a task-based assessment of performance ͑e.g., detectability index͒. This paper advances a theoretical framework based on cascaded systems analysis for calculation of such metrics in cone-beam CT ͑CBCT͒. The model considers the 2D projection NPS propagated through a series of reconstruction stages to yield the 3D NPS and allows quantitative investigation of tradeoffs in image quality associated with acquisition and reconstruction techniques. While the mathematical process of 3D image reconstruction is deterministic, it is shown that the process is irreversible, the associated reconstruction parameters significantly affect the 3D DQE and NEQ, and system optimization should consider the full 3D imaging chain. Factors considered in the cascade include: system geometry; number of projection views; logarithmic scaling; ramp, apodization, and interpolation filters; 3D back-projection; and 3D sampling ͑noise aliasing͒. The model is validated in comparison to experiment across a broad range of dose, reconstruction filters, and voxel sizes, and the effects of 3D noise correlation on detectability are explored. The work presents a model for the 3D NPS, DQE, and NEQ of CBCT that reduces to conventional descriptions of axial CT as a special case and provides a fairly general framework that can be applied to the design and optimization of CBCT systems for various applications.
Purpose: Design and optimization of medical imaging systems benefit from accurate theoretical modeling that identifies the physical factors governing image quality, particularly in the early stages of system development. This work extends Fourier metrics of imaging performance and detectability index ͑dЈ͒ to tomosynthesis and cone-beam CT ͑CBCT͒ and investigates the extent to which dЈ is a valid descriptor of task-based imaging performance as assessed by human observers. Methods:The detectability index for tasks presented in 2D slices ͑d slice Ј ͒ was derived from 3D cascaded systems analysis of tomosynthesis and CBCT. Anatomical background noise measured in a physical phantom presenting power-law spectral density was incorporated in the "generalized" noise-equivalent quanta. Theoretical calculations of d slice Ј were performed as a function of total angular extent ͑ tot ͒ of source-detector orbit ranging 10°-360°under two acquisition schemes: ͑i͒ Constant angular separation between projections ͑constant-⌬͒, giving variable number of projections ͑N proj ͒ and dose vs tot and ͑ii͒ constant number of projections ͑constant-N proj ͒, giving constant dose ͑but variable angular sampling͒ with tot . Five simple observer models were investigated: Prewhitening ͑PW͒, prewhitening with eye filter and internal noise ͑PWEi͒, nonprewhitening ͑NPW͒, nonprewhitening with eye filter ͑NPWE͒, and nonprewhitening with eye filter and internal noise ͑NPWEi͒. Human observer performance was measured in 9AFC tests for five simple imaging tasks presented within uniform and power-law clutter backgrounds. Measurements ͑from 9AFC tests͒ and theoretical calculations ͑from cascaded systems analysis of d slice Ј ͒ were compared in terms of area under the ROC curve ͑A z ͒ Results: Reasonable correspondence between theoretical calculations and human observer performance was achieved for all imaging tasks over the broad range of experimental conditions and acquisition schemes. The PW and PWEi observer models tended to overestimate detectability, while the various NPW models predicted observer performance fairly well, with NPWEi giving the best overall agreement. Detectability was shown to increase with tot due to the reduction of out-of-plane clutter, reaching a plateau after a particular tot that depended on the imaging task. Depending on the acquisition scheme, however ͑i.e., constant-N proj or ⌬͒, detectability was seen in some cases to decline at higher tot due to tradeoffs among quantum noise, background clutter, and view sampling. Conclusions: Generalized detectability index derived from a 3D cascaded systems model shows reasonable correspondence with human observer performance over a fairly broad range of imaging tasks and conditions, although discrepancies were observed in cases relating to orbits intermediate to 180°and 360°. The basic correspondence of theoretical and measured performance supports the 1754 1754 Med. Phys. 38 "4…,
Purpose:The authors previously developed the 4D extended cardiac-torso (XCAT) phantom for multimodality imaging research. The XCAT consisted of highly detailed whole-body models for the standard male and female adult, including the cardiac and respiratory motions. In this work, the authors extend the XCAT beyond these reference anatomies by developing a series of anatomically variable 4D XCAT adult phantoms for imaging research, the first library of 4D computational phantoms. Methods: The initial anatomy of each phantom was based on chest-abdomen-pelvis computed tomography data from normal patients obtained from the Duke University database. The major organs and structures for each phantom were segmented from the corresponding data and defined using nonuniform rational B-spline surfaces. To complete the body, the authors manually added on the head, arms, and legs using the original XCAT adult male and female anatomies. The structures were scaled to best match the age and anatomy of the patient. A multichannel large deformation diffeomorphic metric mapping algorithm was then used to calculate the transform from the template XCAT phantom (male or female) to the target patient model. The transform was applied to the template XCAT to fill in any unsegmented structures within the target phantom and to implement the 4D cardiac and respiratory models in the new anatomy. Each new phantom was refined by checking for anatomical accuracy via inspection of the models. Results: Using these methods, the authors created a series of computerized phantoms with thousands of anatomical structures and modeling cardiac and respiratory motions. The database consists of 58 (35 male and 23 female) anatomically variable phantoms in total. Like the original XCAT, these phantoms can be combined with existing simulation packages to simulate realistic imaging data. Each new phantom contains parameterized models for the anatomy and the cardiac and respiratory motions and can, therefore, serve as a jumping point from which to create an unlimited number of 3D and 4D variations for imaging research. Conclusions: A population of phantoms that includes a range of anatomical variations representative of the public at large is needed to more closely mimic a clinical study or trial. The series of anatomically variable phantoms developed in this work provide a valuable resource for investigating 3D and 4D imaging devices and the effects of anatomy and motion in imaging. Combined with Monte Carlo simulation programs, the phantoms also provide a valuable tool to investigate patient-specific dose and image quality, and optimization for adults undergoing imaging procedures.
The complex tradeoffs among anatomical background, quantum noise, and electronic noise in projection imaging, tomosynthesis, and CBCT can be described by generalized cascaded systems analysis, providing a useful framework for system design and optimization.
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