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Iron oxide nano-particles have very different x-ray diffraction properties from tissue. They can be clearly visualized against suppressed tissue background in a single-shot x-ray diffraction imaging technique. This technique is able to acquire both diffraction and absorption images from a single grating-modulated projection image through analysis in the spatial frequency domain. We describe the use of two orthogonal transmission gratings to selectively retain diffraction signal from iron oxide particles that are larger than a threshold size, while eliminating the background signal from soft tissue and bone. This approach should help the tracking of functionalized particles in cell labeling and targeted therapy.
©2010 Optical Society of America
1. Introduction
In the current realm of diagnostic radiography and computed tomography, a contrast agent is necessary to differentiate between tissue types of similar absorptions. The most common radiographic contrast agents such as iodine and barium are efficient x-ray absorbers. However, they often cannot be separated from the surrounding tissue without the subtraction of a reference image. Temporal subtraction with and without contrast is susceptible to registration errors, while dual-energy subtraction is limited by the broadband nature of x-ray tubes. Scattering or diffraction contrast is an alternative to absorption. X-ray diffraction arises from elastic scattering of photons by microscopic structures which are too small to be visible in absorption images. Full-field diffraction images can be obtained in laboratory settings with phase-grating based Talbot interferometry [1–6]. To shorten the imaging time for in vivo applications, we developed a variant single-shot technique [7,8], which we call the spatial harmonic method. Here, a single projection image containing a transmission grating (grid) will have several distinct harmonic peaks in the spatial frequency domain. Inverse Fourier transformation of these peaks results in harmonic images. The relative weight between absorption and diffraction-caused attenuations differs among these images, and therefore provide us with sufficient information to extract separate absorption and diffraction images.
A double-grid version of the spatial harmonic method offers the opportunity to separate particle-based contrast agents from the background tissue in a single image. In the following, we show that by placing two orthogonal linear grids at different distances from the x-ray camera, the ratio between the harmonic images from the two grids only contain diffraction from scatterers above a threshold size. If we choose an appropriate threshold size where the diffraction signal from bone and soft tissue is minimal, then particles larger than the threshold can be visualized without interference from surrounding biological structures. Such particles can then serve as contrast agents, while anatomical information is still available from the absorption image. We demonstrate the effectiveness of this method with iron oxide nano-particles injected into tissue samples, and confirm the elimination of the background soft tissue and bone with ultra-small angle x-ray scattering (USAXS) measurements obtained at a synchrotron beam line.
2. Methods and materials
2.1 Imaging device description
The imager is illustrated in Fig. 1 . The x-ray source was a 50 Watt tungsten-target tube of 50 µm focal spot size, operating at 50 kVp/1.0 mA. The exposure time for a single experiment was 28 seconds and delivered 0.61 mSv surface radiation dose to the imaged object. The x-ray camera was a 16 bit water-cooled CCD array of 4090 × 4096 matrix operating at 2 × 2 binned mode and 30 µm pixel size, coupled to a Gd2O2S:Tb phosphor screen via a 1:1 fiberoptic taper (PI-SCX-4096, Princeton Instruments, Trenton, NJ, USA). The distance between the x-ray tube and the camera was 100 cm. The imaged object was placed midway between the two at 50 cm from the camera. The two transmission gratings were commercially available linear radiography grids (Bucky grids). Each grid had different periods, but both had projected lines on the camera with a period of approximately 250 µm. The first, “object”, grid had a period of 127 µm and was placed 46 cm from the camera, close to the imaged object, with the grid lines oriented horizontally. The second, “camera”, grid had a period of 250 µm and was placed 2.4cm from the camera with the grid lines oriented vertically.
Fig. 1 The double-grid diffraction imaging setup. After passing through the sample, the x-ray cone beam is spatially modulated by a horizontal, object grid and a vertical, camera grid before detection by a camera.
2.2 Retrieval and interpretation of double-grid diffraction images
Image analysis is performed in the spatial frequency domain (Fig. 2 ). The raw image is first converted into the spatial frequency domain by 2D Fourier transformation. A lattice of distinct peaks can be seen in the resulting spectrum, which corresponds to the frequency contents of the projected grid pattern on the camera surface. When the grid overlays the sample, the spectrum of the projection image of the sample itself is duplicated at each peak. The zeroth order peak at the center is not modulated by the grids and is only affected by absorption. The higher order harmonic peaks, however, represent the amplitude of the grid lines and will be affected by both absorption and diffraction. An nth order harmonic image In is obtained by inverse Fourier transforming the area surrounding the nth peak. Since both the harmonic image and the zeroth order image share the same absorption attenuation, the ratio between their magnitudes retains only diffraction-related attenuation in the harmonic image. The intensity of a pure diffraction image is then given by the logarithm of this ratio, which is proportional to the depth of x-ray penetration through the material:
It is important to note that the image resolution resulting from the above procedure is the period of the grid.Fig. 2 Process to extract absorption and diffraction images from a single raw image. The sample includes a vial of black watercolor paint on the left which is a suspension of black iron oxide nano-particles, and a vial of 150 mg/ml KI solution on the right. (a) A grid-masked raw image is acquired and (b) 2D Fourier transformed into the spatial frequency domain. The spectrum contains a number of peaks corresponding to the frequencies of the grids. (c) An absorption image is obtained from the inverse Fourier transform of the segment around the zeroth order peak. (d,e) Harmonic images from the camera and object grids are obtained from the inverse Fourier transform of the segments surrounding the first order harmonic peaks on the X and Y axes. They are shown in log scale. (f) The final double-grid diffraction image is the ratio of the two single-grid harmonic images. Note that the stripe pattern in the raw image (a) is not the actually grid lines but a Moire effect from the low resolution of the graph.
In the double grid setting, after the Fourier transformation, the horizontal object grid produces harmonic peaks along the y axis and the vertical camera grid produces harmonic peaks along the x axis. If we consider the first-order peaks from both sets and recognize that they are affected by the same absorption factors, then absorption is negated after computing the ratio of the magnitude of the harmonic images from the two peaks. We call the ratio a double-grid diffraction image. The intensity of the double-grid diffraction image in log scale is in fact the difference between the two single-grid diffraction images:
To interpret the double-grid diffraction image, we first look at the relationship between a single-grid diffraction image and the size of the scatterers that give rise to the diffraction effect. For this purpose we modeled the idealized case of elastic scattering in a random suspension of cylindrical particles in a homogeneous medium. The first Born approximation was used to calculate the angular scattering distribution [9]. The particles had uniform diameter and length l, and were all aligned with the x-ray beam. The diffraction image intensity from the 1st-order harmonic image was then given by the expression:
where f is the volume fraction of the particles, λ is the x-ray wavelength, Δn is the index of refraction difference between the particle and the surrounding medium, and L is a length scale determined by the grid period and position:Equation (3) shows that the diffraction signal increases linearly with the particle size until the length scale L (Fig. 3a ).
Fig. 3 (a) Calculated single-grid diffraction image intensities from a random suspension of cylindrical particles for the camera (blue) and object (red) grids. The scattering length scales of the grids are 4 nm and 87 nm. (b) Calculated double-grid diffraction image intensity. The vertical lines mark the scattering length scales of the two grids. This graph shows that the double-grid image is a highpass filter on the particle size.
Based on Eq. (2) and (3), the double-grid diffraction image can be shown to exclude particles below the smaller of the length scales of the two grids, and includes mostly particles at or above the larger length scale (Fig. 3b). In our device, the value of L differs for each grid due to the difference in grid to camera distance: 4 nm for the camera grid and 87 nm for the object grid. Figure 3a shows the diffraction intensity from both the camera and object grids independently using Eq. (3). Figure 3b shows the difference between these two curves, which is the expected signal intensity in the double grid image. Therefore, the double-grid image acts as a highpass filter on the size of the scatterer.
2.3 Sample details
Rat tissue samples were taken according to Institutional Animal Care and Use Committee guidelines. An adult male Sprague-Dawley rat was euthanized and a hind leg was excised for imaging. Rat tibia bone samples and beef muscle samples were also obtained for USAXS measurements.
To determine the possibilities of a suitable nano-particle agent, we experimented with various particles. One promising material is iron oxide. Iron oxide is produced in multiple forms for a multitude of purposes, including paint pigments, magnetic tapes and MRI contrast agents. Black iron oxide pigments have a typical diameter of 100-600 nm. This size was suitable for our device based on the modeling results shown in Fig. 3. The specific sample we used was a black paint (Liquitex Heavy body Mars Black). The paint contains iron oxide pigments Pbk11. In a chicken wing we injected 0.05 ml of the iron oxide paint and the same amount of a 150mg/ml concentration potassium iodide (KI) solution for comparison.
3. Results
3.1 Double grid imaging experiments
Figure 4 shows the absorption, single-grid diffraction, and double-grid diffraction images of a rat leg. It is evident that both bone and soft tissue are nulled in the double-grid image.
Fig. 4 Absorption and diffraction images of a rat leg. (a) Absorption, (b) object grid diffraction, (c) camera grid diffraction and (d) double grid diffraction images. Both bone and soft tissue are effectively nulled in the double grid diffraction image.
Figure 5 shows the set of images from the chicken wing injected with iron oxide particles and potassium iodide. In the absorption image (Fig. 5a), the bone, soft tissue, iron oxide particles, and iodine are all clearly visible. In each single-grid diffraction image (Fig. 5b and 5c), the cortical bone and iodine have similar diffraction intensities. However, there is a clear difference between the iron oxide particle diffraction levels in the two images. In Fig. 5b, the diffraction from the particles is low because the scattering length scale of the corresponding grid is small (4 nm). Conversely, in Fig. 5c, the particles have higher diffraction intensity because the scattering length scale of the corresponding grid is 87 nm, over 20 times larger than the first grid. In the double-grid diffraction image (Fig. 5d), the bone and soft tissue are absent and only the particle contrast agent is visible. Additionally, the injected iodine is also absent.
Fig. 5 Absorption and diffraction images of a chicken wing injected with iron oxide particles and potassium iodide. (a) Absorption image showing the patch of iron oxide (single-line oval) and KI (double-line oval), (b) object grid diffraction image, (c) camera grid diffraction image and (d) double-grid diffraction image. The double-grid diffraction only retains the iron oxide particles.
3.2 USAXS measurements
In order to understand why in tissues there is little difference between the diffraction signal of the object and camera grids, we would like to know the actual small angle scattering profiles of bone and soft tissue. The USAXS measurements provided the angular dispersion profile of a collimated monochromatic beam after it was transmitted through the sample [10] (Fig. 6 ). The scattering angle θ is related to the scattering vector q as q = sin(θ/2)4π/λ. These measurements were performed in rat tibia and beef muscle samples on a synchrotron beam line of 16.85 keV energy (Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois, USA). To explain the absence of double-grid diffraction signal from tissue in light of the USAXS data, we note that if the scattering distribution is I(q) and it is isotropic, then the double grid diffraction signal can be expressed as [7]:
where LC and LO are the length scales of the camera and object grids, respectively. The multiplication term in Eq. (5) is the superposition of two cosine functions. Since LC << LO, the second cosine oscillates much more rapidly, while the first cosine provides a slow varying offset. The first band of generally positive values in the multiplication term occurs in the range of π/(2LO) < qx < π/(2LC). Thus for scattering distributions that decay rapidly with q, the double diffraction signal mainly comes from this first band.Fig. 6 The USAXS measurement from the cortical bone of a rat tibia. Based on Eq. (5) the double-grid diffraction signal mainly comes from the shaded band of q values, which is negligible in the bone sample.
USAXS measurements In both bone (Fig. 6) and soft tissue (not shown) showed that I(q) diminished beyond q = 10−4 Å−1. The amount of scattered x-rays in the band described above was only 0.002% of the total transmitted beam (Fig. 6). This level was undetectable by our device, resulting in the absence of double diffraction signal from the background tissue. It is worth noting that x-ray scattering from inter-molecular interference [11] gives a broad peak at q ~2 Å−1 in water. This peak is beyond the range of our USAXS measurements. It is sufficiently broad to cause equal attenuation in both single-grid diffraction images, and therefore no effect on the double grid diffraction image.
4. Conclusion
In this study we showed the feasibility of the double-grid spatial harmonic method to selectively image nano-particles above a threshold size. We demonstrated that by using two transmission gratings, it is possible to null the diffraction signal from biological structures and even iodine contrast agents. The synchrotron USAXS data from bone and soft tissue support this finding.
Although in this study the diffraction signal of the particles is 15% their absorption, it can be substantially amplified with high density gratings. Figure 3 shows that the diffraction signal is limited by the scattering length scale of the object grating, which increases linearly with the grating density. The gratings in our current device are commercial radiography grids and have densities of 4 to 8 lines per millimeter. Micro-fabricated gold gratings can reach more than 10-fold higher densities [4]. Such gratings should yield 10 times higher diffraction signals from the iron oxide particles, which would surpass their absorption signal. It is worth noting that for high energy human imaging above 80 keV, the aspect ratio of a gold transmission grating of 20 µm period should be greater than 7:1. Denser gratings will require higher aspect ratios.
However, the diffraction signal cannot increase infinitely with ever higher grating densities and larger particle sizes as one may expect from Eq. (2). This is because Eq. (2) was derived from the first Born approximation, which assumes that the scattered wave within the particle is negligible relative to the incident wave. For large particles, this picture should be replaced by wave propagation through compartments of different indexes of refraction. The transition particle size between these two scenarios is Δn*l/λ ~1, where Δn is the index of refraction difference between the material of the particle and the medium. For black iron oxide the transition size is approximately 10 µm at 30 keV and larger for higher energies. This transition size still leaves much room for higher diffraction contrast.
In the current experiment the object grid was placed immediately behind the sample in favor of the slightly higher magnification factor and resolution of the sample on the camera. However, for high dose applications such as CT, it is advantageous to put the object grid in front of the sample to intersect the beam first and reduce the dose on the sample by a factor of two [8].
The combination of the elimination of biological structures and the enhancement of contrast agents could be important for future clinical imaging. Sub-micron particles of interesting magnetic and fluorescence properties such as iron oxide and gold have been highly successful as MRI and fluorescent imaging labels for cells, and have been investigated for use in targeted therapy and diagnostic imaging [12]. MRI has demonstrated high sensitivity in detecting magnetic particles. However, it relies on their influence on the surrounding water signal, limiting the spatial resolution and efficacy in areas such as the lungs and bone. The current method provides a means to visualize such particles with x-rays without the need to acquire and subtract a background image. When compared to absorption contrast agents such as iodine, it may be particularly helpful when the targeted tissue is obscured by or within bones, or when the contrast uptake is slow making subtraction techniques difficult. Additionally, the single-shot feature of the spatial method makes it suitable for computed tomography to provide 3D visualization of the contrast agent. Because the absorption image can still be recovered, the pure contrast images can be precisely placed in the context of anatomic features.
Acknowledgements
Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.
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