Gantry rotational motion-induced blur in cone-beam computed tomography

Abstract

As neuro-endovascular image-guided interventions (EIGIs) make use of higher resolution detectors, gantry rotational motion-induced blur becomes more noticeable in acquired projections as well as reconstructed images by reducing the visibility of vascular and device features whose visualization could be critical in the treatment of vascular pathology. Motion-induced blur in projections views is a function of an object’s position in the field-of-view (FOV), gantry rotational speed, and frame capture or exposure time. In this work different frame rates were used to investigate the effects of blurring from individual projections on the reconstructed image. To test the effects of these parameters on reconstructed images, a regular pattern phantom of small objects was simulated and projection views were generated at various different frame rates for a given simulated rotational velocity. The reconstruction was made using a linear interpolation of filtered backprojections. Images reconstructed from lower frame rates showed significant blurring in the azimuthal direction, increasingly worse towards the periphery of the image. However, those reconstructed from higher frame rates showed significantly less blur throughout the entire FOV. While lower frame rates could be used with slower gantry speeds this would increase the risk of voluntary or involuntary patient motion contributing to blur over the entire FOV. A high frame rate used with high gantry speeds could reliable provide images without gantry-motion blur while reducing the risk of patient-motion blur. Frame rates exceeding 2000 fps available with photon counting detectors such as the X-counter Actaeon¹ are available.

1. INTRODUCTION

Neuro-endovascular image-guided interventions require the use of high-resolution images to view the subtle details of different pathologies and for evaluating the deployment of vascular treatment devices. Visualization of small endovascular devices by high-resolution detectors has less tolerance for blur due to motion. To reduce the risk of patient motion the highest gantry rotational speed available is preferred for cone beam computed tomography (CBCT). However, gantry rotational motion during exposure induces blur related to gantry rotational speed. If suitable images are to be reproduced at high gantry speeds, then effective exposure times or image capture times must be reduced, potentially through use of higher frame rates than those currently available on many commercial imaging detectors but becoming available with new photon counting imagers, or, in pulsed mode, through the use of shorter exposure pulses. To demonstrate the benefits of higher frame rates, a regular pattern phantom was simulated, forward projections were acquired, and the sinogram was blurred by averaging projections together. The blurred sinograms were then used to reconstruct the image using filtered back projection. These simulations give a qualitative and quantitative method for comparing different frame rates or effective exposure times.

2. MATERIALS AND METHODS

A 2-D phantom was simulated consisting of a pattern of squares, three pixels by three pixels, the centers of which were spaced 32 pixels apart in an image measuring 1024 by 1024 pixels. Simulated pixel size was set to 100 microns. The 9-pixel squares were assigned a value of one on a background assigned to a value of zero. The pattern was limited to a radius of 512 pixels to prevent artifacts in the reconstruction due to objects outside the field of view.

The phantom was rotated by tenths of a degree using a rotation matrix. Pixel values were assigned using the nearest neighbor method. Following the rotation, each column was summed to give a single detector element projection reading in the simulated detector using parallel beams for this demonstration. This process was repeated over a full 360-degree rotation to produce 3600 projection views. The resulting data was stored in a 1024 by 3600 sinogram.

To simulate blurring, N projections were averaged together simulating a continuous ‘on’ exposure with no dead time in the frame acquisition. N was determined from the simulated rotational speed of the gantry divided by the simulated frame rate and the angular step size (set at one tenth of a degree as stated above). The blurred projections were then stored in a separate sinogram whose dimensions were 1024 by 3600/N.

For reconstruction, the projections were convolved with a Shepp-Logan filter before being backprojected. New angles corresponding to each blurred projection were calculated and the filtered backprojections were added to the reconstructed image using a linear interpolation, or nearest pixel, method.

Simulated images were qualitatively compared for blur and the measured blur was compared to the maximum predicted blur of individual projections². The blur for a projection can be predicted quantitatively with the help of the diagram in Figure 1.

Figure 1.

Diagram of a point object imaged using the geometry of CBCT

As the gantry rotates x, the projection’s lateral distance from the center of the detector, changes during the projection acquisition. The value of x can be calculated using equation 1 below.

$$x=\frac{\mathit{SID}\cdot r\cdot \sin (\theta )}{\mathit{SAD}-r\cdot \cos (\theta )}$$ (1)

The above equation was arrived at using similar triangles. Blur is caused by the change in x during a projection’s acquisition. Taking the difference in positions (calculated from the initial and final angles) and replacing the final angle with the initial angle plus the gantry speed (ω) multiplied by the projection’s time (t) gives equation 2.

$$\mathit{Blur}=\mathit{SID}\left(\frac{r\cdot \sin (\theta +\omega t)}{\mathit{SAD}-r\cdot \cos (\theta +\omega t)}-\frac{r\cdot \sin (\theta )}{\mathit{SAD}-r\cdot \cos (\theta )}\right)$$ (2)

Terms containing ωt can be expanded. By applying the small angle approximation, equation 2 takes the form longer below.

$$\mathit{Blur}=\mathit{SID}\cdot r\left(\frac{\sin (\theta )+\cos (\theta )\omega t)}{\mathit{SAD}-r\cdot (\cos (\theta )-\sin (\theta )\omega t)}-\frac{\sin (\theta )}{\mathit{SAD}-r\cdot \cos (\theta )}\right)$$ (3)

To further simplify, r·sin(θ)ωt is approximated to be much smaller than the other terms in the denominator. The reduced denominator gives the source to object distance. Since SID/SOD gives the projections magnification, the two terms can be replaced with m.

$$\mathit{Blur}=m\cdot r\cdot \omega \cdot t\cdot \cos (\theta )$$ (4)

Since the projections and reconstructions were made using a parallel beam geometry, for this demonstration the magnification is unity. Taking the derivative of the equation above with respect to θ gives the maximum blur occurring at 0 and 180 degrees. Therefore the maximum predicted blur occurs when an object lies along the central axis.

3. RESULTS

Gantry rotational speed was simulated at 60 degrees per second and three frame rates (30, 60 and 120 fps) were used. Use of different frame rates resulted in a different number of acquired projections for the different frame rates. For example, at 30 fps the sinogram would contain 180 projections and at 120 fps the sinogram would contain 720 projections. Continuous tube output was assumed for this simulation. Since the features of interest in the phantom are very small only the upper left quadrant of the original phantom and reconstructed images are displayed (Figures 2a – 2d).

Figure 2.

Upper left quadrants of simulated images: (a) pattern phantom, (b) reconstruction using 120 fps, (c) reconstruction using 60 fps. Full reconstructed image for acquisition at 30 fps is shown in (d).

The simulated images can be inspected for a qualitative assessment of the blur. As predicted from equation 4 the blur is much smaller for points near the center of the phantom and increases as the distance from the center of rotation increases. Furthermore, the blurring due to gantry motion is notably lower in the reconstructions simulated with a frame rate of 60 fps and lower still with a frame rate of 120 fps. Even higher frame rates are possible with photon counting detectors such as the X-counter Actaeon. With a pixel size of 100 um and lower noise due to the counting nature of the detector³, reconstructions using such detectors have less noise.

For a quantitative comparison, tangential line profiles were taken of blurred pixels in the central row of the reconstruction. Blur was estimated by plotting the line profile with the average background level of the reconstructed image, the intersection of the background and the line profile was interpolated, and the difference in the two points was taken to be the total width of the blurred point. Five points were selected from the central row for each reconstructed image. Below is a plot (Figure 3) comparing computed blur values to those predicted by equation 4. The average percent difference between predicted and computed blur was found to be 11.3%.

Figure 3.

Plot of computed blur vs objects distance from isocenter. The dashed line is the theoretical blur and the points are the estimates of the simulated blur.

4. DISCUSSION

The experiment demonstrates the ability to predict motion induced blur in CT reconstructions. Using this method imaging parameters can be selected beforehand that will minimize gantry motion induced blur.

Furthermore, the advantage of using high frame rates in acquiring projections has been demonstrated. This results in images with little to no blur which would enable visualization of small features in reconstructed images. As detectors capable of higher frame rates become commercially available the effect of gantry rotational motion-induced blur will become negligible.

Alternatively, pulse duration may be used to reduce image blurring. From equation 4 above it is seen that blur is linearly related to frame exposure duration.

5. CONCLUSIONS

High resolution imaging may be critical during neuro-vascular and other interventions. The problem of blur due to rotational motion of a c-arm during CBCT with high resolution imagers is analyzed and suggestions for the minimization or even elimination of this motion-induced blur are presented.

The simulations show the effectiveness of using high frame rates to reduce gantry rotational-motion-induced blur in computed tomography. It was also shown that the blur can be predicted quantitatively with some error due to pixelization and noise in the reconstructed image.

Further investigations will examine the effect of high frame rates on the noise of a reconstructed image and will make use of a new photon counting detector capable of very high frame rates (thousands of frames per second).