Analytical expressions for the reconstructed image of a homogeneous cylindrical sample exhibiting a beam hardening artifact in X-ray computed tomography.

BACKGROUND: Cylindrical phantoms are often imaged by X-ray computed tomography (CT) to evaluate the extent of beam hardening (or cupping artifact) resulting from a polychromatic X-ray source. OBJECTIVE: Our goal was to derive analytical expressions for the reconstructed image of a homogeneous cylindrical phantom exhibiting a cupping artifact, to permit a quantitative comparison with experimental cupping data. METHODS: A filtered backprojection method was employed to obtain the analytical cupping profile for the phantom, assuming that the projection data could be approximated as a power series with respect to the sample penetration thickness. RESULTS: The cupping profile was obtained analytically as a series of functions by employing Ramachandran filtering with an infinite Nyquist wavenumber. The quantitative relationship between the power series of the projection and the nth moment of the linear attenuation coefficient spectrum of the phantom was also determined. Application of the obtained cupping profile to the evaluation of the practical reconstruction filters with a finite Nyquist wavenumber and to the best choice of the contrast agent was demonstrated. CONCLUSIONS: The set of exact solutions derived in this work should be applicable to the analysis of cylindrical phantom experiments intended to evaluate CT systems.

Development of a Single-Sided Nuclear Magnetic Resonance Scanner for the In Vivo Quantification of Live Cattle Marbling.

Non-invasive in vivo marbling quantification helps owners to choose the optimum nutritional management for growing cattle and buyers to more precisely evaluate grown cattle at auctions. When using time-domain proton nuclear magnetic resonance (NMR) relaxometry, it is possible to quantify muscle and fat separately by taking advantage of the difference in the spin-spin relaxation time (T2) between water molecules in muscles and fat molecules, which would contribute to the non-invasive and objective determination of marbling scores. With this in mind, we developed a prototype NMR scanner (4.1 MHz for protons) using an original single-sided magnetic circuit and a plane radio frequency (RF) coil for use in the non-invasive quantification of water and fat in live cattle. The sensed region of the developed scanner is compact and almost cubical (19 × 19 × 16 mm3) while the investigation depth (the distance from the RF coil to the center of the sensed region) has been lengthened to 30 mm, which is sufficient for the in vivo trapezius muscle measurement of live cattle. Measurements of 17 samples of beef meat blocks kept at 39 °C were taken in a laboratory to successfully obtain the calibration lines used to convert the NMR signals into water and fat weight fractions at correlation coefficients in excess of 0.9. We also showed that each meat sample could be measured in about 10 s with a measurement error as small as approximately 10 wt%. Accordingly, we believe that our prototype scanner would be useful for in vivo marbling measurements of live cattle trapezius muscles.

Optimizing contrast agents with respect to reducing beam hardening in nonmedical X-ray computed tomography experiments.

Iodine is commonly used as a contrast agent in nonmedical science and engineering, for example, to visualize Darcy flow in porous geological media using X-ray computed tomography (CT). Undesirable beam hardening artifacts occur when a polychromatic X-ray source is used, which makes the quantitative analysis of CT images difficult. To optimize the chemistry of a contrast agent in terms of the beam hardening reduction, we performed computer simulations and generated synthetic CT images of a homogeneous cylindrical sand-pack (diameter, 28 or 56 mm; porosity, 39 vol.% saturated with aqueous suspensions of heavy elements assuming the use of a polychromatic medical CT scanner. The degree of cupping derived from the beam hardening was assessed using the reconstructed CT images to find the chemistry of the suspension that induced the least cupping. The results showed that (i) the degree of cupping depended on the position of the K absorption edge of the heavy element relative to peak of the polychromatic incident X-ray spectrum, (ii) (53)I was not an ideal contrast agent because it causes marked cupping, and (iii) a single element much heavier than (53)I ((64)Gd to (79)Au) reduced the cupping artifact significantly, and a four-heavy-element mixture of elements from (64)Gd to (79)Au reduced the artifact most significantly.

Diffusivity measurement of heavy ions in Wyoming montmorillonite gels by X-ray computed tomography.

Medical X-ray computed tomography (CT) was applied to the measurement of the diffusion coefficients of heavy ions in an artificial barrier material for the disposal of nuclear wastes. Cs(+), Sr(2+), I(-), and Br(-) are the heavy ions measured and the barrier used is the water-rich gel of Wyoming montmorillonite (86.5-100 wt.% H(2)O). X-ray CT yields an inevitable artifact (beam-hardening) in the obtained images. Before the diffusion experiments, the polychromatic primary X-ray spectrum of the CT scanner was measured by a CdZnTe detector, and the effects of the artifact were examined for an aqueous CsCl solution sample. The results show that the beam-hardening artifact derived from the polychromatic photon energy distribution can be suppressed by applying a special image reconstruction method assuming the chemical composition of samples. The transient one-dimensional diffusion of heavy ions in a plastic container filled with the gel was imaged nondestructively by the X-ray CT scanner with an in-plane resolution of 0.31 mm and slice thickness of 2 mm. The results show that diffusivities decrease with increasing clay weight fraction. The degree of the diffusivity decrease was high for cations (Cs(+) and Sr(2+)) and low for anions (I(-) and Br(-)). The quantitative decomposition of the contribution of the geometrical tortuosity and of the sorption to the diffusivity was performed by subtracting the diffusivity of nonsorbing I(-) from the measured diffusivities. The results show that the contribution of the sorption is large for Cs(+), Sr(2+) and small for Br(-). Because X-ray CT allows nondestructive and quick measurements of diffusivities, the technique would be useful particularly for measuring the diffusive migration of harmful radioactive elements.

Three-dimensional diffusion of non-sorbing species in porous sandstone: computer simulation based on X-ray microtomography using synchrotron radiation.

The diffusion pathways of porous sandstone were examined by a three-dimensional (3-D) imaging technique based on X-ray computed tomography (CT) using the SPring-8 (Super Photon ring-8 GeV, Hyogo, Japan) synchrotron radiation facility. The analysis was undertaken to develop better understanding of the diffusion pathways in natural rock as a key factor in clarifying the detailed mechanism of the diffusion of radionuclides and water molecules through the pore spaces of natural barriers in underground nuclear waste disposal facilities. A cylindrical sample (diameter 4 mm, length 6 mm) of sandstone (porosity 0.14) was imaged to obtain a 3-D image set of 450(3) voxels=2.62(3) mm(3). Through cluster-labeling analysis of the 3-D image set, it was revealed that 89% of the pore space forms a single large pore-cluster responsible for macroscopic diffusive transport, while only 11% of the pore space is made up of isolated pores that are not involved in long-range diffusive transport. Computer simulations of the 3-D diffusion of non-sorbing random walkers in the largest pore cluster were performed to calculate the surface-to-volume ratio of the pore, tortuosity (diffusion coefficient in free space divided by that in porous rock). The results showed that (i) the simulated surface-to-volume ratio is about 60% of the results obtained by conventional pulsed-field-gradient proton nuclear magnetic resonance (NMR) laboratory experiments and (ii) the simulated tortuosity is five to seven times larger than the results of laboratory diffusion experiments using non-sorbing I(-) and Br(-). These discrepancies are probably attributed to the intrinsic sample heterogeneity and limited spatial resolution of the CT system. The permeability was also estimated based on the NMR diffusometry theory using the results of the random walk simulations via the Kozeny-Carman equation. The estimated permeability involved an error of about 20% compared with the permeability measured by the conventional method, suggesting that the diffusometry-based NMR well logging with gradient coils is applicable to the in-situ permeability measurement of strata. The present study demonstrated that X-ray CT using synchrotron radiation is a powerful tool for obtaining 3-D pore structure images without the beam-hardening artifacts inevitable in conventional CT using X-ray tubes.

Nondestructive quantitative analysis of a heavy element in solution or suspension by single-shot computed tomography with a polychromatic X-ray source.

X-ray computed tomography (CT) images obtained with a polychromatic X-ray source were simulated by computer for homogeneous solutions and suspensions containing a heavy element. When the K-edge of the element was near the peak energy of the polychromatic X-ray spectrum, the degree of beam hardening in the simulated CT image strongly depended on the atomic number and molar concentration of the heavy element. We analyzed the beam hardening of a single measured CT image of a CeCl(3) aqueous solution sample, and successfully estimated the atomic number and the molar concentration of Ce simultaneously within a certain error. This single-shot, or single-energy (as opposed to dual-energy), CT method permits quick, nondestructive screening of a hazardous heavy element in a solution or suspension confined in a container.

Non-destructive Analysis of Oil-Contaminated Soil Core Samples by X-ray Computed Tomography and Low-Field Nuclear Magnetic Resonance Relaxometry: a Case Study.

Non-destructive measurements of contaminated soil core samples are desirable prior to destructive measurements because they allow obtaining gross information from the core samples without touching harmful chemical species. Medical X-ray computed tomography (CT) and time-domain low-field nuclear magnetic resonance (NMR) relaxometry were applied to non-destructive measurements of sandy soil core samples from a real site contaminated with heavy oil. The medical CT visualized the spatial distribution of the bulk density averaged over the voxel of 0.31 × 0.31 × 2 mm(3). The obtained CT images clearly showed an increase in the bulk density with increasing depth. Coupled analysis with in situ time-domain reflectometry logging suggests that this increase is derived from an increase in the water volume fraction of soils with depth (i.e., unsaturated to saturated transition). This was confirmed by supplementary analysis using high-resolution micro-focus X-ray CT at a resolution of ∼10 µm, which directly imaged the increase in pore water with depth. NMR transverse relaxation waveforms of protons were acquired non-destructively at 2.7 MHz by the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The nature of viscous petroleum molecules having short transverse relaxation times (T2) compared to water molecules enabled us to distinguish the water-saturated portion from the oil-contaminated portion in the core sample using an M(0)-T2 plot, where M(0) is the initial amplitude of the CPMG signal. The present study demonstrates that non-destructive core measurements by medical X-ray CT and low-field NMR provide information on the groundwater saturation level and oil-contaminated intervals, which is useful for constructing an adequate plan for subsequent destructive laboratory measurements of cores.