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Quantitative CT and tomosynthesis

Currently, most modeling metrics for diagnostic imaging are employed to investigate detection performance. However, it is clear that the clinical imaging tasks often encompass other types of tasks. As illustrated in Fig. 1 the clinical imaging tasks can be divided into detection tasks, discrimination tasks, and estimations tasks. An example of a detection task would be the task to determine whether a lesion is present or not, a discrimination task would be that to determine whether that lesion is malignant or benign, and an estimation tasks would be that to determine its size. As shown in the diagram, it is clear that there is some overlap between these tasks. For example, it would be difficult to estimate the size of a lesion without the ability to detect it. It should also be noted that within the context of this proposal, quantitative imaging falls mostly under the category of estimation tasks.

Figure 1: Diagram illustrating the various task encompassed in a clinical imaging task.

Currently there is a void in terms of metrics developed specifically for predicting performance in terms of estimation tasks for quantitative imaging. Several useful metrics have been developed for assessing and modeling imaging device performance. Examples include signal-to-noise ratio (SNR) and noise equivalent quanta (NEQ) for image quality or detective quantum efficiency (DQE) for system efficiency. These metrics provide powerful tools for system design and evaluation, and in general, are expected to correlate with quantitative imaging performance. However, they don’t address any specific task for quantitative imaging.

It is clear with current, more advanced imaging systems that have more “knobs” to adjust and optimize that optimal settings will depend on the type of quantitative task at hand. A simple example would be the task of determining the size of a lesion in terms of its diameter, which can generally be achieved on a 2D radiograph; however, determining its volume would require a volumetric imaging system such as CT. Therefore, an example of a research question that motivates this work would be the following: can the partial volume information obtained in tomosynthesis be sufficient to determine the volume and if so, how accurate and precise would the measurement be?

Briefly, quantitative imaging generally involves the estimation of one or more parameters from the image data. It is known from estimation theory that a parameter, can be estimated by computing the maximum likelihood (ML) estimator.(1)  Therefore we are using the ML estimator to provide a useful framework for computing estimation performance metrics, such as bias, for quantifying the system’s accuracy and the mean square error (MSE) for quantifying the system’s precision.

Applications to Breast tomosynthesis:

Volumetric breast imaging holds great potential for quantitative imaging for several reasons, including: 1) high–spatial resolution, which makes it ideal for determining distances, areas, and volumes; and 2) estimation of linear x-ray attenuation (e.g., Hounsfeld units), which enables tissue characterization (2, 3). Quantitative information obtained from volumetric breast imaging could offer valuable information for improved diagnosis and treatment performance.

Dr. Samei’s group is working on simulating an imaging system for investigating detection and estimation task performance in volumetric breast imaging. The imaging system models an isocentric flat-panel based system as depicted in Fig. 2. The bare-beam incident signal is computed from the incident fluence and detector gain using CSA.(4)  Projections can be acquired over a range of acquisition angle for modeling projection, tomosynthesis, and CT imaging, while keeping the total glandular dose constant.

Figure 2: (a) Schematics of the volumetric breast imaging system depicting the 10 inserted masses in the breast. (b) Projection of the of the computerized breast phantom at 0°.

Figure 3: Detectability index computed for detection task. (b) Precision in the MLE size estimation identifying an optimal acquisition angle of 105° for volume estimation. (c) Precision in the MLE localization. Green highlights correspond to regions of optimal acquisition angle for each task.

The system was used to investigate detection and estimation performance for a small spherical target. The detection performance is plotted in Fig. 3(a) as a function of acquisition angle. Note that “acquisition angle” denotes the total angle spanned by the tube during acquisition. The detection was optimal at an acquisition angle of ~85 degrees, where reconstructed images using a smaller acquisition angle exhibited increased anatomical noise and reconstructed images using a larger acquisition angle exhibited increased quantum and electronic noise. In comparison, performance of size estimation is plotted in terms of precision (i.e., the inverse of the MSE scaled to arbitrary units) [Fig. 3(b)]. Volume estimation is maximized between 100° and 125°. Furthermore, precision for the localization in 3D is shown in Fig. 3(c). Localization in the x- and in the y-direction (i.e., localization in the coronal plane) exhibited similar trends as a function of acquisition angle, whereas precision in the z-direction was significantly lower and required a larger angle to achieve optimal performance (~165°). Overall, precision for a localization task was found to require a larger acquisition angle compared to both detection and size estimation tasks. This is expected as larger acquisition angles provide better three-dimensional definition of the anatomy - demonstrating the task-dependent optimization that needs to be accounted for when investigating advanced imaging systems.

This ongoing research suggests that the ML estimator can provide a useful metric for assessing estimation task performance - identifying clear optima for system performance. Larger angles are required for estimation and localization tasks compared to detection task. These observations point to tomographic imaging techniques with larger acquisition angles than currently employed in breast tomosynthesis and points to further investigation for other optimal acquisition and reconstruction techniques that may also depend on imaging task.


Applications to chest computed tomography:

Work at RAI Labs is also providing a better understanding of what factor affects estimation performance in chest CT. The goal is to tune the various CT acquisition parameters to yield high performance CT images for quantitative chest imaging applications at the lowest possible dose.

Figure 5: (left) Axial slice of the Kyoto Kagaku anthropomorphic chest phantom, (middle) software rendering and (right) segmentation of nodule for volume estimation.

Figure 6: Precision measurements (MSE) of an 8 mm lung nodule volume estimation task in chest CT as a function of (a) kVp and (b) pitch.

For example, the precision for estimating the volume of 8 mm nodule inserted in a chest phantom (fig. 5) was investigated as a function of kVp [80, 100, 120, and 140 kVp] and pitch [20, 40, and 55 mm] while holding the CTDI fixed. We generated volume estimates from a clinically available segmentation program. As shown in fig. 6, precision was found to have little dependence on kVp but increases with pitch. Other factors such as slice thickness and reconstruction parameters are currently being investigated as important factors for quantitative imaging performance.


  1. H. H. Barrett, J. L. Denny, R. F. Wagner and K. J. Myers, "Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance," J Opt Soc Am A Opt Image Sci Vis 12, 834-852 (1995).
  2. J. M. Boone, "Radiological interpretation 2020: toward quantitative image assessment," Med Phys 34, 4173-4179 (2007).
  3. D. C. Sullivan, "Imaging as a quantitative science," Radiology 248, 328-332 (2008).
  4. S. Richard, J. H. Siewerdsen, D. A. Jaffray, D. J. Moseley and B. Bakhtiar, "Generalized DQE analysis of radiographic and dual-energy imaging using flat-panel detectors," Med Phys 32, 1397-1413 (2005).
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