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X-Ray Tomographic Reconstruction

TL;DR: In this article, a program employing iterative methods based on the inverse Radon transform was written to correct the data in order to obtain the most accurate images from which element concentrations and internal structure can be determined.
Abstract: Tomographic scans have revolutionized imaging techniques used in medical and biological research by resolving individual sample slices instead of several superimposed images that are obtained from regular x-ray scans. X-Ray fluorescence computed tomography, a more specific tomography technique, bombards the sample with synchrotron x-rays and detects the fluorescent photons emitted from the sample. However, since x-rays are attenuated as they pass through the sample, tomographic scans often produce images with erroneous low densities in areas where the x-rays have already passed through most of the sample. To correct for this and correctly reconstruct the data in order to obtain the most accurate images, a program employing iterative methods based on the inverse Radon transform was written. Applying this reconstruction method to a tomographic image recovered some of the lost densities, providing a more accurate image from which element concentrations and internal structure can be determined.

Summary (2 min read)

1. INTRODUCTION

  • X-Ray fluorescence computed tomography (XFCT) is a synchrotron-based imaging technique used for mapping the distribution of elements within a sample.
  • In XFCT, a sample is bombarded with x-rays that excite k-shell electrons.
  • These photons are collected by a solid state silicon detector that records multiple energies simultaneously.
  • Previous reconstruction techniques required a known attenuation at each fluorescence energy, which necessitated the time-consuming process of rescanning the sample at all the relevant energies [1].
  • The presence of metals and other trace elements drastically affect intracellular processes in any organism [3].

2. MATERIALS AND METHODS

  • Once the code was completed, data was collected at the Stanford Synchrotron Radiation Lightsource.
  • Because elements have signature fluorescence energies, a fluorescent photon detector that can distinguish different photon energy levels is used.
  • Applying an inverse Radon transform with the proper attenuation coefficient produces Figure 2(b), the reconstructed image.
  • Otherwise, this technique only works for very small attenuation coefficients on the order of µ = 0.01.
  • This method was translated into a code that processes images from tomographic scans.

3. RESULTS

  • The initial scan is shown in Figure 4a, and its inverse Radon transform is shown in Figure 4b.
  • The tomographic image with the applied reconstruction is shown in Figure 4c, and while the elimination of attenuation artifacts is not immediately noticed, data analysis showed an improvement.
  • In order to quantitatively measure the effect of the reconstruction program, the original data was subtracted from the corrected data, providing a matrix of absorption corrections that had been made.
  • The pixels in the back of the sample had lost at least 16% of their original density, which was added back during the reconstruction.
  • Because there are still attenuation artifacts present in the corrected image, the inputted attenuation coefficient was not high enough.

4. DISCUSSION

  • The proposed method yields accurate images that provide more detailed information about the sample.
  • Miqueles and De Pierro [4] found that using several iterations will limit the attenuation coefficients and further improve the data.
  • These functions can be added to any module that processes tomographic scans.
  • The sample used was brought to SSRL by Tracy Punshon from Dartmouth College.
  • This is significant for the current interest in trying to figure out ways to encourage iron transport in other plants, such as rice.

5. CONCLUSION

  • XFCT has the potential to provide incredibly informative images once a reconstruction has been applied to the data.
  • An effective reconstruction technique employs the inverse Radon transform and accounts for changing attenuation coefficients and the variance of fluorescence energies.
  • The attenuation coefficient map is the key input for a successful reconstruction, and its creation can be perfected by using iterative methods.
  • By correcting for the attenuation effects, the inaccuracies associated with XFCT become nearly irrelevant, which makes it very attractive, especially to the biological and medical communities.
  • This method has become vital for the analysis and mapping of elemental content in cells and tissues.

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Work supported in part by US Department of Energy contract DE-AC02-76SF00515.
X-Ray Tomographic Reconstruction
Bonnie Schmittberger
Science Undergraduate Laboratory Internship Program
Bryn Mawr College
SLAC National Accelerator Laboratory
Menlo Park, California
August 14, 2009
Prepared in partial fulfillment of the requirement of the Department of Energy's Science
Undergraduate Laboratory Internship program under the direction of Samuel Webb at the
Stanford Synchrotron Radiation Lightsource at SLAC National Accelerator Laboratory.
Participant: _______________________________
Signature
Project Advisor: ______________________________
Signature
SLAC-TN-10-015

2
Table of Contents
Abstract……………………………………………………………………………………3
Introduction………………………………………………………………………………..4
Materials and Methods……………………………………………………………………5
Results……………………………………………………………………………………10
Discussion…………………………………………………………………………….….10
Conclusion……………………………..………………………………………………...12
Acknowledgments………………………………………………………………………..12
References………………………………………………………………………………..13
Figure 1: Schematic of Detector Setup…………………………………………………..14
Figure 2: Calcium and Iron Tomographic Scans……………………………………...…15
Figure 3: Schematic of Axis Setup………………………………………………………16
Figure 4: Tomographic Scan and Reconstruction of Arabidopsis Thaliana………….….17
Appendix: Copy of Reconstruction Code…………………...……………...……………18

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ABSTRACT
X-Ray Tomographic Reconstruction. BONNIE SCHMITTBERGER (Bryn Mawr
College, Bryn Mawr, PA, 19010) DR. SAMUEL WEBB (Stanford Synchrotron
Radiation Laboratory at SLAC National Acceleratory Laboratory, Menlo Park, CA
94025)
Tomographic scans have revolutionized imaging techniques used in medical and
biological research by resolving individual sample slices instead of several superimposed
images that are obtained from regular x-ray scans. X-Ray fluorescence computed
tomography, a more specific tomography technique, bombards the sample with
synchrotron x-rays and detects the fluorescent photons emitted from the sample.
However, since x-rays are attenuated as they pass through the sample, tomographic scans
often produce images with erroneous low densities in areas where the x-rays have already
passed through most of the sample. To correct for this and correctly reconstruct the data
in order to obtain the most accurate images, a program employing iterative methods
based on the inverse Radon transform was written. Applying this reconstruction method
to a tomographic image recovered some of the lost densities, providing a more accurate
image from which element concentrations and internal structure can be determined.

4
1. INTRODUCTION
X-Ray fluorescence computed tomography (XFCT) is a synchrotron-based
imaging technique used for mapping the distribution of elements within a sample. In
XFCT, a sample is bombarded with x-rays that excite k-shell electrons. When these
atoms return to their stable state, they emit fluorescent x-rays at energies characteristic of
the element. These photons are collected by a solid state silicon detector that records
multiple energies simultaneously. The total number of photons recorded is a function of
the sum of the various element concentrations along the line of the incident beam. By
rotating the object and compiling horizontal scans, it is possible to obtain a complete
tomographic reconstruction of the distribution of the elements within a sample.
Since the incident beam is attenuated through the sample and part of the emission
is absorbed by the sample, attenuation correction is necessary in order to obtain accurate
results. If reconstruction techniques are not employed, the image of the center of the
sample is blurred, and its density, as recorded by the scan, is much lower than its true
density. Previous reconstruction techniques required a known attenuation at each
fluorescence energy, which necessitated the time-consuming process of rescanning the
sample at all the relevant energies [1]. Tomographic reconstruction is also possible by a
series of mathematical corrections based on the inverse Radon transform, which is a
faster and simpler method.
These reconstruction techniques have attracted numerous scientific disciplines to
XFCT. In particular, the high sensitivity and sub-micrometer resolution of this method is
useful in medicine [2]. The presence of metals and other trace elements drastically affect
intracellular processes in any organism [3]. XFCT is the only sub-micrometer technique

5
that can map these elements within cells and search for abnormal quantities and
distributions accompanying the development of certain diseases [3].
2. MATERIALS AND METHODS
i. Data Collection
Once the code was completed, data was collected at the Stanford Synchrotron
Radiation Lightsource. X-Rays obtained from the synchrotron are sent through an ion
chamber to measure the energy of the incident beam. The x-rays are then directed into a
helium-purged chamber where they are focused down to a 2 µm diameter by two
elliptical mirrors. This focused beam is then sent out to the sample, which is scanned by
moving completely across the incident beam, then rotating by a certain small angle,
typically 1 to 3 degrees, and repeating until 180 degrees are covered. This is called a full
translation, half rotation tomographic scan. If the scan were to cover a full rotation, the
amount of attenuation correction would be minimized because the image would only
contain artifacts towards the center of the sample, but that process doubles the scanning
time, generally requiring three to four extra hours.
The detector is placed behind the sample to collect the transmitted x-rays, and
another is placed at 90 degrees to the incident beam to collect the fluorescent photons, as
depicted in Figure 1. A uniform fluorescence around the sample is assumed, so that one
fluorescent photon detector is sufficient. Because elements have signature fluorescence
energies, a fluorescent photon detector that can distinguish different photon energy levels
is used. This detector counts the number of photons that it receives at each energy level,
so the concentrations of different elements in the sample can be determined.

References
More filters
Journal ArticleDOI
TL;DR: Characteristic X‐ray fluorescence is a technique that can be used to establish elemental concentrations for a large number of different chemical elements simultaneously in different locations in cell and tissue samples to gain insight into cellular processes.
Abstract: Characteristic X-ray fluorescence is a technique that can be used to establish elemental concentrations for a large number of different chemical elements simultaneously in different locations in cell and tissue samples. Exposing the samples to an X-ray beam is the basis of X-ray fluorescence microscopy (XFM). This technique provides the excellent trace element sensitivity; and, due to the large penetration depth of hard X-rays, an opportunity to image whole cells and quantify elements on a per cell basis. Moreover, because specimens prepared for XFM do not require sectioning, they can be investigated close to their natural, hydrated state with cryogenic approaches. Until several years ago, XFM was not widely available to bio-medical communities, and rarely offered resolution better then several microns. This has changed drastically with the development of third-generation synchrotrons. Recent examples of elemental imaging of cells and tissues show the maturation of XFM imaging technique into an elegant and informative way to gain insight into cellular processes. Future developments of XFM-building of new XFM facilities with higher resolution, higher sensitivity or higher throughput will further advance studies of native elemental makeup of cells and provide the biological community including the budding area of bionanotechnology with a tool perfectly suited to monitor the distribution of metals including nanovectors and measure the results of interactions between the nanovectors and living cells and tissues.

218 citations


"X-Ray Tomographic Reconstruction" refers background in this paper

  • ...5 that can map these elements within cells and search for abnormal quantities and distributions accompanying the development of certain diseases [3]....

    [...]

  • ...intracellular processes in any organism [3]....

    [...]

Journal ArticleDOI
TL;DR: In this article, a self-consistently estimated attenuation of the fluorescence radiation is used to estimate the attenuation inside the sample, which allows one to reconstruct relative concentrations.
Abstract: X-ray fluorescence microtomography allows one to map element distributions inside a sample with high sensitivity and resolutions in the micrometer range. Quantitative reconstruction of the element concentrations from the fluorescence data requires correction for the attenuation inside the sample. However, the attenuation of the fluorescence radiation is not directly accessible by experiment. The method described self-consistently estimates this attenuation and allows one to reconstruct relative concentrations. This is demonstrated on numerical as well as experimental data. A measure for the quality of the reconstruction is given.

119 citations


"X-Ray Tomographic Reconstruction" refers methods in this paper

  • ...In particular, the high sensitivity and sub-micrometer resolution of this method is useful in medicine [2]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors present a set of tools for scattering and fluorescence tomography, which they intend to present in the near future, together with an implementation of such an algorithm and also several examples.

31 citations


"X-Ray Tomographic Reconstruction" refers background in this paper

  • ...Figure 3, where the s and u axes are parallel to the translation direction and the beam, respectively [5]....

    [...]

Proceedings ArticleDOI
14 May 2008
TL;DR: Different reconstruction methods for XFCT, based on iteratively inverting the generalized attenuated Radon transform are proposed and compared, using simulated and real data as well.
Abstract: X-Ray fluorescence computed tomography (XFCT) aims at reconstructing fluorescence density from emission data given the measured X-Ray attenuation. In this paper, inspired by emission tomography (ECT) reconstruction literature, we propose and compare different reconstruction methods for XFCT, based on iteratively inverting the generalized attenuated Radon transform. We compare the different approaches using simulated and real data as well.

8 citations


"X-Ray Tomographic Reconstruction" refers background in this paper

  • ...and it can be shown that it is the adjoint operator of W R [6]....

    [...]

  • ...When 0 = = ! μ , W R is the general Radon transform [6]....

    [...]

  • ...elements whose fluorescence energies are lower [6]....

    [...]

  • ...a f d e k W k ) ( ) ( 1 R R ! = ! [6]....

    [...]

  • ...angle range ] , [ 2 1 ! ! at each emission point [6]....

    [...]