Not sure if you have seen these Curt....
Use of Diffraction Enhanced Imaging to Determine the X-ray Refractive Indices of Various Tissues at Biologically-Relevant Energies
Matthew Teng
Cornell University
Advisor: Zhong Zhong, Ph.D.
Brookhaven National Laboratory
Article ToolsEmail this article
Print article
Articles in the current issue...
Research Articles
--------------------------------------------------------------------------------
Prey Selection by Chaoborus in the Field and Laboratory
Nocturnal vs. Diurnal Insect Diversity Within the Tropical Montane Forest Canopy
Most PopularViewing the most popular Research from the past 30 days
REVIEW: Mechanisms of Bacterial Pathogenesis and Targets for Vaccine Design
REVIEW: Advanced Glycation End-products (AGEs) in Hyperglycemic Patients
Targeting the HIV-1 Reverse Transcriptase, Integrase, P27, By Expression of RNAi Oligonucleotides from Engineered Human Artificial Chromosome
Beta-catenin Mediated Wnt Signaling as a Marker for Characterization of Human Bone Marrow-Derived Connective Tissue Progenitor Cells
Literature Review - A 21st Century Epidemic: Childhood Obesity in North America
Sponsored Ad
This experiment used diffraction enhanced imaging (DEI) to investigate the refractive indices of various organic tissues and water at X-ray energies similar to the energies of medical X-rays. We employed Silicon 333 reflection, which is typically used in DEI. In order to measure the small change in refractive index accurately across different samples and different energies, we constructed a sample holder which confined the sample to a 90-degree wedge. We analyzed the experimental data to determine the refractive indices for several organic tissues and water, and then we fitted them to a theoretical model. Clearly, each substance has a different refractive index. However, all substances showed the same inverse relationship between the energy and refractive index. This information will aid integration of DEI into clinical medicine in terms of optimization of DEI parameters in a clinical setting.
Introduction
Diffraction enhanced imaging (DEI) is a relatively new X-ray imaging technique which provides a very high contrast X-ray image of a subject using a single, monochromatic X-ray energy (Johnston et al. 1996). We used diffraction enhanced imaging in a research program aimed at studying the refractive indices of various organic tissues. This project was undertaken in order to further understand and investigate the possible introduction of DEI into a clinical medical imaging modality. This research was conducted at the X15A beamline at the National Synchrotron Light Source (NSLS) at the Brookhaven National Laboratory (BNL).
The underlying basis for DEI functionality exploits the unique atomic structure of perfect crystals. Synchrotron X-ray radiation produces high-powered X-rays covering an energy range of a few keV to a few hundred keV. A crystal monochromator is placed in the path of the X-ray beam, which is used to select a small energy range from the incident white X-ray radiation (Zhong et al. 2002). As a result, only X-rays with appropriate wavelength and energy are selected by the monochromator. Furthermore, an additional crystal, the analyzer crystal, is placed behind the sample. The purpose of the analyzer crystal is to reduce the scattering of the X-ray beam, which results from the elastic and inelastic (including Comption) scattering of the beam as it passes through the subject. The analyzer crystal also converts the differences in refraction angle, which result from the interaction of the electrons in the subject with the X-rays that pass through the sample, into a difference in intensity. As the radiation diffracted by the analyzer strikes the detector, it forms an image that is sensitive to the X-ray refraction. This difference in intensity permits a much greater degree of image contrast of the sample. As the X-rays strike the varying internal structure of the sample, differences in intensity result due to the varying thicknesses and densities of internal structure.
The DEI experimental setup allows for an improved radiological image with increased contrast when compared to the standard X-ray imaging techniques currently employed throughout the medical field. As a consequence, with the use of DEI, it is possible to image and distinguish among various types of soft tissue. The current X-ray imaging technology does not possess high enough contrast (at reasonable X-ray dosages) to distinguish among the relatively density-similar soft tissues. When the X-ray beam strikes the sample, there are two possible results that are relevant to DEI. That is, the X-rays can be absorbed, scattered, or refracted (Chapman et al. 1997). If the radiation is absorbed, then the intensity difference due to differences in sample absorption creates the absorption contrast. This contrast mechanism is the only contrast in conventional X-ray imaging, is well understood and provides one mechanism of contrast between different substances. However, as stated before, the X-rays can also be refracted. X-ray refraction properties are only measured and reported for a few inorganic materials, typically for 8 keV X-rays, which are too low for clinical imaging. Thus, in order to properly integrate DEI technology into clinical use, the refractive indices at high X-ray energies are needed to accurately build a digital model of various organic tissues. This could possibly provide an easier method of imaging soft tissue.
Theoretically, it is possible to measure the refractive indices of X-rays by directly measuring the deviation of the beam as it passes through the sample (James 1948). Practically, since the deviation from unity of the X-ray refractive index is very small, on the order of 10-6, the deviation of the beam is too small to be accurately measured (on the order of microns). Thus, an experimental method was developed to take advantage of DEI analyzer’s high angular resolution, on the order of micro-radians, to accurately measure this small angular deviation. Using the DEI technique, along with the proper calibration procedure and algorithm, it was possible to determine the absolute value of refractive indices of a few different types of tissues. The method used in this investigation can be easily adapted to other tissues in future studies.
Methods and Materials
This investigation took place at the X15A beamline at NSLS at the Brookhaven National Laboratory. See Figure 1 for experimental setup (Zhong 2002).Figure 1. The most popular SCI model is the rodent contusion model, with a necrotic core surrounded by histologically normal-appearing myelinated fibers and portions of grey matter from both dorsal and ventral horns (left). Similar to human SCI pathophysiology, the cell loss continues radially in all directions, so that the lesion expands over time. By 60 days post-SCI, there remains only a thin rim of white matter (right). Massive cell death, causing irreversible damage, occurs immediately after the initial impact in the central core region. However, cell death continues to occur over several days and weeks and offers an opportunity for therapeutic intervention to rescue the neural cell populations that are at risk of dying after the first few hours (Hulsebosch 2002). (Click image for larger version)
The design of the sample holder is schematically shown in Figure 2. It consists of a rectangular cell culture dish, with each compartment measuring approximately 10 mm in width. We used a total of 7 compartments in this experiment, and each compartment was filled with a different material. Each divider was approximately 1 mm in width. Figure 2. Corticospinal tract (CST) sprouting across the midline in the spinal cord after adenoviral vector neurotrophin 3 (Adv.EF -NT3) transduction of motoneurons. Dark-field photomicrographs of spinal cord cross sections showed the unlesioned CST axons. (A) Section from a normal rat (sham surgery). (B) Section from an Adv.EF -LacZ-treated rat (control vector). (C) Section from an Adv.EF -NT3-treated rat. CST neurites can be seen arising from the intact CST, traversing the midline, and growing into the gray matter of the lesioned side of the spinal cord. (A'-C') Higher-power photomicrographs of the regions around the central canal (Zhou et al. 2003). (Click image for larger version)
The cell culture dish was set up in such a way that the dish’s edges were 45 degrees off of the horizontal and the X-ray beam (Figure 3).
The bottom edge of the dish and the support strut were fixed into place using Devcon 5-minute epoxy. After we set up the sample-containing apparatus, we placed it into the experimental chamber and subjected it to DEI rocking curve measurement. The X-ray imaging beam was approximately 80mm in width. The energy points that were used for this experiment were 30, 32, 34, and 36 keV. We calibrated the energy of the X-ray beam using the K-edge of Iodine (33.169 keV) and then set by precisely controlled motors that functioned to tune the monochromator and the analyzer crystal. The beam was passed through a gas ionization chamber, whose purpose was to monitor the intensity of the oncoming beam. We used a shutter to control the exposure time of the sample. The sample was supported on a platform, which could be adjusted by a vertically moving linear stage controlled by stepper motor to accurately position the object in the path of the X-ray beam.Figure 3. Remyelination of the rat spinal cord following transplantation of adult human precursor cells. Normal (A), demyelinated (B), and remyelinated axons (C) of the dorsal column. (D) Remyelinated axons at higher magnification. The anatomical pattern of myelination was similar to that produced by Schwann cells (arrows). (bar: A–C, 25 µm; D, 10 µm) (Akiyama et al. 2001). (Click image for larger version)
For each energy that was used, two data sets were taken. One of the data sets was taken with the sample in the direct path of the beam (referred to as the “sample” set) while the other data set was taken with a sample placement outside of the beam, known as the “air” set, allowing for calibration. In an algorithm written later, the rocking curve peak position data derived from the air set was essentially subtracted from the sample set, thus reducing to a minimum the electronic noise interference and systematic error due to monochromator and analyzer crystal non-uniformity. During the data extraction, 56 scan lines were taken for every data set; the first 5 scan lines were taken with the shutter closed to measure the detector dark current, and the remaining 51 scan lines were taken with the shutter opened. Each data line was taken at different analyzer positions ranging from –5 to 5 micro-radians at a step size of 0.2 micro-radians.
Data analysis was conducted using an algorithm, written in IDL programming language that determined the refractive index of the tissue.
Results
Examining the experimental setup, it is possible to see the method of determining the refractive index of the organic tissue of interest (Figure 4).Figure 4. Schematic of a piece of spinal cord that has sustained an initial injury (black central oval) that spreads progressively outward and radially (red circular region followed by orange circular region) in zones until it finally reaches the final lesion size (grey shaded area). Blue lines are axons, and green rectangles are the myelinating oligodendrocytes. Methods of intervention: 1) reduction of edema and free radical production, 2) rescue of neural tissue at risk of dying in secondary processes such as abnormally high extracellular glutamate concentrations, 3) control of inflammation, 4) rescue of neuronal/glial populations at risk of continued apoptosis; 5) repair of demyelination and conduction deficits, 6) promotion of neurite growth through improved extracellular environment, 7) cell replacement therapies,
efforts to bridge the gap with transplantation approaches, 9) efforts to retrain and relearn motor tasks, 10) restoration of lost function by electrical stimulation, and 11) relief of chronic pain syndromes (Hulsebosch 2002). (Click image for larger version)Considering the refraction at the left surface of the prism, it is apparent that
δΘ = Θ2 – Θ1
Using Snell’s Law:
n1 /n2 = sin Θ2 /sin Θ1
Therefore,
1/(1 – δ) = sin (Θ1+ ΔΘ)/(sin Θ1) [Equation 1]
where 1-δ is the refractive index of the material. The X-ray refractive index of the air is assumed to be 1.
Assuming for a small δ and δ Θ:
1 + δ = 1 + cot (Θ1)( ΔΘ) [Equation 2]
Therefore,
ΔΘ = [tan (Θ1)]( δ) [Equation 3]
Since the experimental apparatus was designed such that
Θ1 = 45 °
ΔΘ = δ
Considering this experiment, the X-ray beam was refracted at both the entering and exiting surfaces of the sample. Therefore,
ΔΘ = 2(δ)
Thus, the refractive index
δ = ½ (ΔΘ) [Equation 4]
As can be seen, the refractive index can be determined from simply measuring the angular deviation of the X-rays that pass through the material. This angle can be measured accurately by measuring the intensity-versus-angle curve (or rocking curve) of the analyzer crystal. As is known, the refractive index of any substance is energy dependent. In this investigation, we analyzed 7 substances at 4 different energies. These energies were 30, 32, 34, and 36 keV. This tunable energy range is similar to the X-ray energies that are generally used in clinical practice.
The first and second cells of the culture dish contained pork fat and chicken breast, respectively. The second, third, and fourth cells of the culture dish contained human breast parenchyma, human breast fat, and human breast fat along with skin, respectively. The tissues were provided by University of North Carolina Medical School with IRB approval. The sixth and seventh cells of the culture dish contained air and water, respectively. The data for the air chamber was used as a calibration to selectively eliminate the natural noise found in the experimental chamber. The deviation from unity, delta, of the refractive index was analyzed and determined for all substances (Table 1). Table 1. (Click image for larger version)
Discussion and Conclusions
Table 1 shows the absolute determined refractive index values of all the substances. Over the regulated energy range, the chicken breast has a higher index of refraction than the pork fat. This is to be expected, since chicken breast is a muscle tissue and muscle is typically more dense than fat.
These two tissues, chicken breast and pork fat, were used because they were the most generic muscle and fat tissues that were available. These results can be further used as models to serve future analysis. The composition of animal and human tissue is remarkably similar and thus the refractive index of those tissues can be assumed to be very similar and independent among species.
Over the regulated energy range, the breast fat and breast fat with skin refractive index values were comparable. This result is most likely due to the positioning of the skin in the compartment. The skin was placed alongside the closed end of the cell (Figure 5).Figure 5. (Click image for larger version)
The skin acts as a parallel plate, which serves to cancel the extra refraction due to the skin. Furthermore, human skin is very fibrous, and as a result, the skin is expected the scatter X-rays more than fat. However, since only the refractive index was measured in this experiment, we are not sensitive to scattering properties. Furthermore, the values of the refractive index of breast fat and pork fat are very similar. There is less than a 1.40% difference between the two different fats. This confirms the similarity in density, chemical composition and morphology of the same type of tissue among different species. The refractive index values of the breast tissue provide critical information for modeling a DEI system for mammography.
The refractive index of water under this energy range was very important to determine, since water constitutes nearly 70% of the human body and will almost always have an effect on the imaging procedure. The absolute refractive index values of water are considerably lower than every other organic tissue in this study. This is expected since water is much less dense than the organic tissues of interest in this study.
For low-Z materials, the deviation from unity, δ, of the refractive index is proportional to 1/E2. Z represents the number of electrons per atom. Using the measured values and a fitting procedure, it is possible to determine the refractive index value at any X-ray energy from the following formula.
δ = α * (1/E2) [Equation 5]
where α is a constant coefficient which is a unique property of the material. From Equation 5, it is apparent that δ is in a linear relationship with 1/E2. A linear regression analysis was applied to the experimental data and confirmed a statistically significant linear relationship between δ and 1/E2. The α value is proportional to the electron density of the specimen and E is the X-ray energy in keV.
Accordingly, taking all the obtained data from this experiment, it was possible to determine α for all substances used (Table 2). The α-values were determined by calculating the α-values of the individual experimental energies and averaging them to reduce experimental error. Averaging the α-values is a valid calculation because of the linear relationship of Equation 5.Table 2. (Click image for larger version)
Thus, using the determined α-values along with Equation 5, it is possible to predict the refractive index of an organic tissue at any desired energy. According to the theory, the refractive index, n, is (Zhong 2000)
1 – n = δ + iβ = (1/2π)reλ2 Σj (Nj + fj’ + ifj’’) [Equation 6]
where re = e2/mec2 = 2.818 x 10-15, which is the classic electron radius, and
λ is the X-ray wavelength.
Nj, zj, fj’ and fj’’ are the number density of atoms, the atomic number and the real and imaginary dispersion terms, respectively, for an atom j. The difference between the refractive index of the substance and that of a vacuum is (Guinier 1963)
δ = 1 – n = (1/2π)Nereλ2 [Equation 7]
where Ne = electron number density.
For the theoretical value, in the case of water,
Ne = 3.346 x 1023 electrons / cm3 = 3.346 x 1029 electron / m3
Using this value, it is possible to determine the theoretical α value of water by the following algebraic manipulation.
δ = 1 – n = (1/2π)Nereλ2 [Equation 7]
Using the approximation of λ = (12.4/E), in which λ is in Angstroms and E is energy in keV, we have
δ = 1 – n = (1/2π)Nere(12.4/E)2
δ = 1 – n = (1/2π)Nere(12.4)2*(1/E2) [Equation 8]
Previously stated,
δ = α * (1/E2) [Equation 5]
Thus,
α = (1/2π)Nere(12.4)2 [Equation 9]
Using Equation 9, the theoretical α-value of water is calculated as 2.31 x 10-4
Comparison of the theoretical water α-value with the experimental α-value led to a 26% discrepancy. This could be due to some experimental setup error. The experimental error was likely caused by the intrinsic variations of the samples. In other words, the samples were not homogenous throughout, which would affect the measurements. However, this error can be further minimized by averaging data over a larger area and by repeating measurements a few times to double-check the intrinsic texture variation.
The next step, which is already underway, is to incorporate the understanding of DEI contrast mechanisms into a clinical X-ray tube-based system. The currently employed X-ray conditioning (monochromator) and analyzer systems used at the National Synchrotron Light Source will be modified to suit an X-ray tube in order to deliver the flux necessary within a few minutes time. Brookhaven National Laboratory, in collaboration with the Illinois Institute of Technology, University of North Carolina, and Rush Medical School, is currently funded by the National Health Institute to carry out research to produce and test a prototype of a clinically-viable DEI system.
