Dual-source CT

Mathias Sebastian Palm, 23.07.2014

Artikel auf Deutsch

Dual-source computed tomography as an three-dimensional imaging radiography method

In contrast to conventional computed tomography (CT), two series of X-ray images each with different X-ray spectra are recorded in dual-source computed tomography. This takes place by simultaneously using two X-ray tubes in a scanner or by using scanners with a X-ray source to record two successive images. Thus, for example, the density and chemical atomic number of the material being testing can be determined non-destructively or the contrast can be increased by applying special algorithms.

History

For the history of X-rays, please refer to the article on radiography.

The fundamental mathematical principles of CT in the form of Radon transformation were developed by an Austrian mathematician Johann Radon in 1917. Between 1957 and 1963, Allan M. Cormack carried out studies in ignorance of Radon's work and worked out mathematical methods. The realisation of CT scanners only became possible with the progressive development of computers. In 1969, the electrical engineer Godfrey Hounsfield built prototypes for the EMI Group and developed these into a model ready for the market. He also had to develop fundamental mathematical principles of image reconstruction himself as he did not know about the work of Cormack. In 1972, the EMI Group's first commercial CT scanner was installed. CT was instantly accepted as a new technology and was in demand due to the new medical possibilities created by representing body structures three-dimensionally. In 1979, Cormack and Hounsfield were awarded the Nobel Prize for "Physiology or Medicine" for the work on developing CT. ^[1]

Since the 1990s, commercial scanners for dual-source CT have been on the market. The advantages of these scanners in medicine are decreased artefacts in the images and the ability to precisely measure bone density. ^[1]

Just like many other methods of non-destructive testing, conventional CT and dual-source CT were initially used for medical purposes before being used for testing of industrial components. ^[2] The high-resolution three-dimensional images created make it possible to visibly detect and quantitatively assess even the smallest defect and interior structures in components. ^[3] In particular, CT offers several advantages in testing fibre re-enforced components and this forms an increasingly larger proportion of non-destructive testing. ^[2]

Physical fundamentals and operating methods

Physically, each CT measurement proceeds according to the principles of radiography, where the object being tested is exposed to X-rays - electromagnetic radiation created by the rapid acceleration of electrons and their subsequent braking at the anode. The remaining intensity of the X-rays transmitted through the object are measured pixel-by-pixel with a detector (normally a flat-panel detector or an array detector). Using attenuation through the object, density difference within an object can be made qualitatively visible. However, no direct density information is supplied. Attenuation in the material results from the absorption and scattering of photons, which X-rays consist of. For extensive information about X-rays and attenuation of rays, please refer to the article X-ray tomography. ^[4]

Either the X-ray source and the detector or the object itself has to be rotated 180° or 360° for a complete CT measurement. Here, X-ray images, termed projections, are taken at various rotational angles. Owing to a computerised reconstruction algorithm (usually a Feldkamp algorithm or an iterative image reconstruction), the X-ray images at various rotational angles are processed into a volume model of the object. In this, the attenuation of the X-rays for every voxel, which is equivalent to a three-dimensional pixel, can be visualised and tested using relevant software. In particular, the difficulty in this process are the mathematics needed for finding a suitable reconstruction algorithm that can be implemented on a computer. The necessity of a computer for reconstructing data distinguishes CT from methods such as X-ray tomography. ^[1]

In dual-source CT, this method is carried out by using two different acceleration energies of electrons between the cathode and anode, as well as suitable preliminary filters (e.g. Al, Cu, Sn), which results in two different X-ray spectra. By using thin metal plates as preliminary filters, a desirable, even more limited X-ray spectrum is created. Thus, a spectrum with a high energy level and one with a low energy level are used. This generation takes place between two different X-ray tubes. ^[5] Similarly, it is possible to carry out two successive images with differing measurement parameters.

Heismann theory

The two volume scans created are ultimately overlapped using software, for example, according to Heismann theory. ^[6] In contrast to classic CT, with this method it is possible to obtain not only comparative and qualitative, but also quantitative evidence regarding the atomic number and density of the tested material. This can be determined using the ρZ-projection described below. ^[6] Thus, it is also possible to obtain results regarding sizes difficult to capture such as the porosity of composite materials. ^[7]

According to Heismann, the linear attenuation coefficient $//<![CDATA[ \begin{array}{l}μ\end{array} //]]>$ from the Beer–Lambert law calculated as follows with the intensity $//<![CDATA[ \begin{array}{l}I\end{array} //]]>$, the total intensity of the X-ray spectrum $//<![CDATA[ \begin{array}{l}I_0\end{array} //]]>$ and the distance $//<![CDATA[ \begin{array}{l}d\end{array} //]]>$ though the object. This term can be converted and as a result, $//<![CDATA[ \begin{array}{l}μ\end{array} //]]>$ can be determined with $//<![CDATA[ \begin{array}{l}d\end{array} //]]>$, the x-ray spectrum $//<![CDATA[ \begin{array}{l}S(E)\end{array} //]]>$, the detector sensitivity $//<![CDATA[ \begin{array}{l}D(E)\end{array} //]]>$ and the linear attenuation coefficient $//<![CDATA[ \begin{array}{l}κ(E)\end{array} //]]>$.

$//<![CDATA[ \begin{array}{l}\mu = \lim_{d \to 0}\left [- \frac{1}{d}\ln \left ( \frac{I}{I_0} \right ) \right ] = \lim_{d \to 0}\left [- \frac{1}{d}\ln \left ( \frac{\int S(E)D(E)e^{-\kappa(E)d}dE}{\int S(E)D(E)dE} \right ) \right]\end{array} //]]>$

Through the definition of the elementary weighting function for dual-source CT ^{[6] $//<![CDATA[ \begin{array}{l}w(E) = \frac{S(E)D(E)}{\int S(E)D(E)dE}\end{array} //]]>$} the formula above as per ^[6] can be simplified to:

$//<![CDATA[ \begin{array}{l}\mu = \int w(E)\kappa(E)dE\end{array} //]]>$

This results in the following system in matrix notation as per ^[6] for both measurements:

$//<![CDATA[ \begin{array}{l}\binom{\mu_1}{\mu_2} = \rho * \binom{\int w_1(E)\left ( \frac{\kappa}{\rho} \right )(E,Z)dE }{\int w_2(E)\left ( \frac{\kappa}{\rho} \right )(E,Z)dE}\end{array} //]]>$

By inverting this system, density $//<![CDATA[ \begin{array}{l}ρ\end{array} //]]>$ and the chemical atomic number $//<![CDATA[ \begin{array}{l}Z\end{array} //]]>$ can be determined as per ^[6].

$//<![CDATA[ \begin{array}{l}\binom{\mu_1(\rho,Z)}{\mu_2(\rho,Z)}\to \binom{\rho(\mu_1,\mu_2)}{Z(\mu_1,\mu_2)}\end{array} //]]>$

The mass attenuation coefficient $//<![CDATA[ \begin{array}{l}\frac {\kappa}{ρ}\end{array} //]]>$ can be taken from National Institute of Standards and Technology (NIST) tables. ^[8]

Advantages and disadvantages

The application of CT in non-destructive testing has a range of advantages. Components can be tested for interior defects which can then be made visible three-dimensionally and recorded quantitatively. Depending on the test situation, the high resolution obtained with micro-CT scanners make even the smallest defect in the μm range visible. ^[9] Thus, CT is often used in non-destructive testing as a reference method in order to test the suitability of other methods.

In dual-source CT, differences in density and thus different materials can often be distinguished more effectively than by using conventional CT. There is even a reduction in the number of resulting artefacts in the images created. ^[10]

The major drawback of CT is the high cost of the measuring equipment and that a lot of effort is needed to carry out the measurements. Owing to the often necessarily high number of projections for a CT image, the required time is heavily dependent on the exposure time of each individual measurement. Dual-source CT increases this effect even more as double the amount of measurements need to be carried out in comparison to conventional CT. In addition, the scanners are bulky and heavy, and the component being tested has to fit into the scanner and be attached so that it can rotate. This disadvantage means that CT as a testing method is usually only economical for small, very expensive components in the aerospace industry. ^[3]

Literature

1. Computertomographie. German Wikipedia, accessed on 13.7.2014.
2. Oster, R.: Herausforderungen an die ZfP bei Ihrer Anwendung an Faserverbundbauteilen. 2012.
3. Läpple, R.: Analyse von Rotorblättern mit CT-Software – Auf die Fasern kommt es an. 2012.
4. Große, C.U.: Grundlagen der Zerstörungsfreien Prüfung. Arbeitsblätter im Rahmen der Lehrveranstaltung des Lehrstuhls für Zerstörungsfreie Prüfung der Technischen Universität München. Kapitel 10 Durchstrahlungsprüfung. 2014.
5. Hassler, U.; Fuchs, T.; Mohr, S.; Firsching, M.; Scholz, G.: Study on CFRP Porosity Determination Based on Dual Energy CT. 2012.
6. Heismann, B.J.; Leppert, J.; Stierstorfer, K.: Density and atomic number measurements with spectral x-ray attenuation method. 2002.
7. Hanke, R.: Computertomographie in der Materialprüfung - Stand der Technik und aktuelle Entwicklungen. 2010.
8. X-Ray Mass Attenuation Coefficients. The National Institute of Standards and Technology (NIST). 2011, accessed on 20.7.2014.
9. Bossi, R. H.; Iddings, F. A.; Wheeler, G. C.: Nondestructive Testing Handbook. Third edition: Volume 4, Radiographic Testing. 2002.
10. Heinzl, C.; Kastner, J.; Gröller, E.: Geometriebestimmung von Multimaterialbauteilen und reproduzierbare Oberflächenextraktion. 2008.