Development, validation, and simplification of a scanner-specific CT simulator

Abstract

Background: Simulated computed tomography (CT) images allow for knowledge of the underlying ground truth and for easy variation of imaging conditions, making them ideal for testing and optimization of new applications or algorithms. However, simulating all processes that affect CT images can result in simulations that are demanding in terms of processing time and computer memory. Therefore, it is of interest to determine how much the simulation can be simplified while still achieving realistic results.

Purpose: To develop a scanner-specific CT simulation using physics-based simulations for the position-dependent effects and shift-invariant image corruption methods for the detector effects. And to investigate the impact on image realism of introducing simplifications in the simulation process that lead to faster and less memory-demanding simulations.

Methods: To make the simulator realistic and scanner-specific, the spatial resolution and noise characteristics, and the exposure-to-detector output relationship of a clinical CT system were determined. The simulator includes a finite focal spot size, raytracing of the digital phantom, gantry rotation during projection acquisition, and finite detector element size. Previously published spectral models were used to model the spectrum for the given tube voltage. The integrated energy at each element of the detector was calculated using the Beer-Lambert law. The resulting angular projections were subsequently corrupted by the detector modulation transfer function (MTF), and by addition of noise according to the noise power spectrum (NPS) and signal mean-variance relationship, which were measured for different scanner settings. The simulated sinograms were reconstructed on the clinical CT system and compared to real CT images in terms of CT numbers, noise magnitude using the standard deviation, noise frequency content using the NPS, and spatial resolution using the MTF throughout the field of view (FOV). The CT numbers were validated using a multi-energy CT phantom, the noise magnitude and frequency were validated with a water phantom, and the spatial resolution was validated with a tungsten wire. These metrics were compared at multiple scanner settings, and locations in the FOV. Once validated, the simulation was simplified by reducing the level of subsampling of the focal spot area, rotation and of detector pixel size, and the changes in MTFs were analyzed.

Results: The average relative errors for spatial resolution within and across image slices, noise magnitude, and noise frequency content within and across slices were 3.4%, 3.3%, 4.9%, 3.9%, and 6.2%, respectively. The average absolute difference in CT numbers was 10.2 HU and the maximum was 22.5 HU. The simulation simplification showed that all subsampling can be avoided, except for angular, while the error in frequency at 10% MTF would be maximum 16.3%.

Conclusion: The simulation of a scanner-specific CT allows for the generation of realistic CT images by combining physics-based simulations for the position-dependent effects and image-corruption methods for the shift-invariant ones. Together with the available ground truth of the digital phantom, it results in a useful tool to perform quantitative analysis of reconstruction or post-processing algorithms. Some simulation simplifications allow for reduced time and computer power requirements with minimal loss of realism.

Keywords: CT; computer simulations; system characterization.

FIGURE 1

Scanner-specific computed tomography (CT) simulation pipeline.

FIGURE 2

Schematic drawing of the focal spot and detector elements subsampling.

FIGURE 3

Schematic drawing of the angular subsampling.

FIGURE 4

MECT phantom, measured with 135 kV, used for computed tomography (CT) number validation, with a window level (WL) of 200 HU and a window width (WW) of 1000 HU.

FIGURE 5

Computed tomography (CT) numbers of the real and simulated MECT phantom images at 135 kV. Note that the B stands for blood ρ= 1.03 g/cm.³

FIGURE 6

Modulation transfer function of measured and simulated wires in radial (left) and tangential (right) direction for the large focal spot.

FIGURE 7

Slice sensitivity profile of measured and simulated wires for both focal spots present in the system.

FIGURE 8

Water phantom used for nNPS validation (140 mA, 135 kV) with a WL of 0 HU and a WW of 400 HU. The squares indicate the ROIs used to determine the nNPSs.

FIGURE 9

2D nNPS in the center region of measured (left) and simulated (middle) water phantom, and the difference between both nNPSs (right). Difference = simulation − measurement.

FIGURE 10

2D nNPS in the periphery region of measured (left) and simulated (middle) water phantom, and the difference between both nNPSs (right). Difference = simulation − measurement.

FIGURE 11

2D unstructured nNPS in the center region of measured (left) and simulated (middle) water phantom, and the difference between both nNPSs (right). Difference = simulation − measurement.

FIGURE 12

2D unstructured nNPS in the periphery region of measured (left) and simulated (middle) water phantom, and the difference between both nNPSs (right). Difference = simulation − measurement.

FIGURE 13

Radially averaged center nNPS (left) and nNPS across slices (right), for 135 kV and 140 mA.

FIGURE 14

Averaged slices of simulated water phantom with indicated ROIs used for obtaining the line profiles.

FIGURE 15

Line profiles of the measurement with 160 mm collimation, the measurement with 20 mm collimation, and the simulation.

FIGURE 16

Noiseless simulations of a lesion at 14 cm from the CoR. (Left) Full simulation (WW: 100, WL: 85). (Middle) Simplified simulation, 1 source sample using the MTF measured in the CoR, 2 angular subsamples and 1 detector sample, time and memory consumption potentially reduced by a factor 216 (WW: 100, WL: 85). (Right) Difference between the two simulations (WW: 40, WL: 0).

FIGURE 17

(Left) Line profile of the full and simplified simulation of the lesion in Figure 16. (Right) Difference between simplified simulation and full simulation (simplified simulation − full simulation).