Purpose

Preclinical micro-computed tomography (microCT, μCT) systems are used in many

different imaging applications. Many of these studies require imaging small anatomical structures with spatial resolutions that are sufficient to track subtle changes over the course of a longitudinal study and/or subtle changes between diseased and naïve subjects early in disease. Therefore, it is extremely important to understand the performance of in vivo imaging systems. This Technical Note describes the principles that govern 3D spatial resolution and provides a foundation for interpreting the physical performance of microCT imaging systems. Using these principles, the limiting spatial resolutions of the Quantum FX and Quantum GX microCT imaging systems were characterized.

Preclinical In Vivo Imaging

T E C H N I C A L N O T E

Image Resolution in MicroCT: Principles and Characterization of the Quantum FX and Quantum GX Systems

Authors:

Ali Behrooz, Ph.D.

Jen-Chieh Tseng, Ph.D.

Jeff Meganck, Ph.D.

PerkinElmer, Inc. Hopkinton, MA

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Methods

Phantom DesignTwo different phantoms were used in this study:

1. To look at discrete frequencies, a bar pattern phantom (QRM GmBH; http://www.qrm.de/content/products/microct/microct_barpattern.htm) was scanned.8 This phantom contains two separate chips with bar patterns etched into them; one chip is oriented parallel to the center of rotation and the other chip is perpendicular to the center of rotation.

2. To analytically characterize the complete MTF, a custom phantom was built to freely suspend a 1/8” acrylic cylindrical rod (McMaster Carr) within the imaging Field of View. (Figure 1)

Image Acquisition and FormationImages of both phantoms were acquired on the Quantum FX and the Quantum GX instruments using the longest supported scan times: 4.5 minute scan on the Quantum FX or 57 minute scan on the Quantum GX. The imaging modes selected used bin 1 on the detector. Gain calibrations were redone prior to imaging to minimize artifacts in the final images.

All images were reconstructed using a filtered back-projection algorithm with a Ram-Lak filter. A sinogram-based ring reduction filter was used to minimize rings inherent in CT scans. On the Quantum GX, a single transaxial slice was reconstructed at the best possible resolution (Figure 2A and 2B) of 4.5 μm in plane pixel size; the slice thickness selected was 36 μm. On the Quantum FX, the voxel size is directly linked to the FOV, so the smallest 5 mm FOV was used and reconstructed with an isotropic voxel size of 10 μm.

Introduction

With any in vivo imaging instrument, the goal is to create a perfect image of the object (e.g. animal, sample) being scanned. In practice, however, performance limitations and image artifacts result in an imperfect representation of the object. Many micro-computed tomography applications are intended to image small anatomical structures. Therefore, it is critically important to understand the limits of what can be visually captured in the image. This is often described in two different ways:

Voxel Size: The physical size of the 3D discrete volume element (‘Voxel’) in the image.

Spatial Resolution: The size of the smallest object visually detectable, usually defined as the smallest space between two isolated discrete objects.

Both terminologies are frequently used in the peer-reviewed scientific literature as well as in product literature. Understanding the distinction between voxel size and spatial resolution is essential to interpret data. In practice, the spatial resolution limit of every microCT system is degraded by image artifacts and blur. Artifacts can include physical sources such as beam hardening (a differential absorption of X-rays based on energy in a polychromatic beam), aliasing, partial voluming, photon starvation, and undersampling.1 Physical sources of blur include motion (both from the subject motion and mechanical motions), penumbral blur due to a finite focal spot size, and dispersion of light within the scintillator and detector.2 Filtering properties of the reconstruction algorithms can also affect image quality and resolution.

In light of these complexities, the 3D image spatial resolution can only be obtained by characterizing the imaging system. This is commonly presented as a modulation transfer function (MTF). Resolution is often thought of in terms of physical space. The simplest approach to measure MTF is often to scan a phantom which has a range of fixed line widths and determine what is visually detectable; phantoms for this purpose are commercially available.3,7 However, the limiting resolution commonly falls between the fixed frequencies used in these phantoms. When that is needed, the MTF can be analytically characterized from the point spread function. The purpose of this study is to formally characterize resolution in the Quantum FX and Quantum GX imaging system using both the measurement-based and analytical approaches.

Figure 1. Photograph of the custom built phantom to freely suspend an acrylic rod..

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Figure 3: Quantum FX images of the (A) QRM bar pattern target reconstructed and (B) an acrylic phantom with the ring reduction algorithm applied.

A B

Direct Resolution MeasurementsTo derive the resolution based on the bar pattern phantom, the images were imported into the image processing package Analyze (AnalyzeDirect, Overland Park, KS). A line profile plot was created by averaging multiple columns across the line pair pattern to reduce noise (Figure 2C). This data was then imported into MATLAB and a custom script was written to apply a baseline and calculate the MTF for each line pair phantom using the following equation

I PEAK_ I VALLEY

I PEAK+ I VALLEY

where IPEAK represents the mean grayscale value for all peaks and IVALLEY represents the mean grayscale value for all valleys.

MTF=

Analytical Characterization of Modulation Transfer Function (MTF) A Fourier-based analytical approach was developed based on previously described methods6 to accurately characterize the spatial resolution and MTF for the entire frequency range. In this approach, the acrylic rod is automatically segmented in the 3D microCT (μCT) volume, and projected (averaged) along its medial axis to render a 2D projected image as depicted in (Figure 4A). This 2D image is radially binned at sub-Nyquist intervals as shown in Figure 4B. The mean pixel values from the radial bins are used to produce an edge spread function (ESF), equivalent to the step response function widely used in the field of signal processing. The difference operator is applied to the ESF to arrive at the line spread function (LSF). This is conceptually equivalent to an impulse response. The fast Fourier transform of the LSF yields the MTF for the corresponding system.

Figure 2: (A) The initial Quantum GX acquisition was acquired for a 36 mm FOV and reconstructed with a 72 µm voxel size. A single slice for a subsection of the image corresponding to the bar pattern chip oriented in a transaxial plane was then selected and reconstructed to be 4.5 µm. (B) The smallest line pair section was cropped out of this image (yellow box). (C) A summed line profile was generated for each line pair pattern; averaging was performed along an axis orthogonal to the red line for the portion between the green lines. (D) Image of the acrylic phantom reconstructed with the ring reduction algorithm applied.

B C D

A

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Figure 5: Plots of the MTF curve for the (A) Quantum GX and (B) Quantum FX imaging systems analytically characterized from the acrylic rod. Asterisk marks indicate the fixed measurements taken from the bar pattern phantom.

Table 1: Tabulated results for the limiting resolution in the MTF curve.

Instrument Limiting MTF Target

Limiting Res (lp/mm)

Line Width (μm)

FX 10% 14.01 35.7

5% 15.71 31.8

3% 16.29 30.7

GX 10% 24.57 20.4

5% 27.66 18.1

3% 28.74 17.4

Results and Discussion

MTF curves for the Quantum FX and Quantum GX imaging systems show a good match between the analytically characterized MTF curves and the measured MTF values from the bar pattern phantom (Figure 5). As expected, the limiting resolution in the Quantum GX is better than in the Quantum FX due to smaller voxel size and improved system components in Quantum GX.

The smallest visually distinguishable line pair from the bar pattern target was a 15 μm line in the Quantum GX and a 50 μm in the Quantum FX. The spatial frequency correlating to 3%, 5% and 10%, three commonly used limits for the precise limiting resolution,9 were calculated from the MTF curves analytically characterized using the acrylic phantom (Table 1). The limiting resolutions of the Quantum FX and Quantum GX are 16.29 and 28.74 lp/mm respectively.

It should be noted that the MTF is not, in itself, a perfect metric for image characterization. Image quality is also related to the noise level in the image, so some investigators have proposed using the detective quantum efficiency metric (DQE) that accounts for both MTF and the noise power spectrum (NPS).10

Since the purpose of this study is primarily to characterize the limiting resolution, this generalization is not strictly necessary to interpret these results. It is still important to ensure that the methods used in this study accurately represent the limiting resolution. The 14.01 lp/mm at 10% MTF for the Quantum FX is comparable to the 12.56 lp/mm measured using a different technique,11 providing some reassurance that the methods used here provide a fair assessment of the performance.

A B C

Figure 4: Projected 2D image of the acrylic phantom is binned to produce the edge spread function. (A) 3D image of the acrylic phantom is projected along the medial axis (z-axis) to produce a 2D projected representation of the acrylic phantom. (B) The 2D projected image is radially binned, and the pixel values in each bin are averaged to form the edge spread function. (C) The edge spread function (1D signal) is computed using the mean pixel values from the radial bins attributed to the 2D projected image.

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Figure 6: Images of (A) mouse inner ear structure and (B) tumor vasculature in a murine tumor model obtained using the Quantum GX.

Conclusion

The limiting resolution of the Quantum GX and Quantum FX imaging systems is market leading. The theoretical limiting resolution of 9 μm in the Quantum GX and ability to visually identify a 15 μm line in a bar pattern phantom is better than any other system currently available. This resolution is quite sufficient relative to the common needs for small animal imaging applications. Small anatomical structures such as trabecular bone and small vessels can be easily resolved with the resolutions achieved on either imaging system.12, 13