X-ray phase contrast imaging

Comparison of conventional (left) and phase-contrast-based (right) X-rays from in-ear headphones. The plastic structures inside can be seen more clearly in the phase contrast, while the strongly absorbing metal parts of the loudspeaker create a strong contrast in the conventional image.

X-ray phase contrast imaging refers to a number of technical methods that use the phase shift of the X-rays as they pass through matter for imaging. Since the phase shift cannot be measured directly ( phase problem ), various arrangements of diffractive and absorbing optics must be used to convert the phase change into a measurable, lateral intensity modulation through interference . Using coherent radiation sources and high-resolution detectors, phase images can also be obtained by reconstructing the wave propagation.

The decisive advantage of the phase-sensitive methods is that they can image X-ray transparent objects such as soft tissue more sensitively. In addition, scattering objects such as lung tissue can be imaged with high contrast. This makes use of the fact that small-angle X-ray scattering of the illuminated object causes a weakening of the generated interference pattern. Due to the similarities to dark field microscopy , the image created by scattering is also referred to as an X-ray dark field . Conventional X-ray imaging such as B. radiography or computed tomography are based until today only on the weakening of the beam intensity ( Lambert-Beer law ) by the object to be imaged and thus only generate a low contrast between objects of similar material composition.

The various technical implementations for generating X-ray phase contrast images are developed especially for applications in medicine, biology and materials science. Potential clinical applications are currently being developed in preclinical studies.

Physical principle

Illustration of absorption and phase shift of the X-ray wave when passing through vacuum and matter with the complex refractive index . ${\displaystyle n=1-\delta +i\beta }$

The interaction of X-rays with matter is described in the mathematical treatment as a wave through the complex refractive index . The notation for the real part has become established because it deviates only very slightly from 1 for X-rays and the notation of the deviation is more advantageous. An X-ray wave in the medium can thus be described by the following wave function: ${\displaystyle n=1-\delta +i\beta }$ ${\displaystyle 1-\delta }$ ${\displaystyle \delta }$

${\displaystyle \Psi (z)=E_{0}e^{inkz}=E_{0}e^{i(1-\delta )kz}e^{-\beta kz}}$

Here, the intensity at the entrance into the medium, the complex refractive index, the wave number and the depth of penetration or the propagation coordinate. In the factored representation it can be seen immediately that the imaginary part produces the weakening of the wave intensity when passing through matter and the real part produces the phase shift. Of particular interest is the dependence on and on the energy of the radiation used and the material properties of the object being irradiated. For energies and elements of the atomic number (which is in the diagnostically relevant range) approximations result: ${\displaystyle E_{0}}$ ${\displaystyle n}$ ${\displaystyle k}$ ${\displaystyle z}$ ${\displaystyle \beta }$ ${\displaystyle 1-\delta }$ ${\displaystyle \beta }$ ${\displaystyle \delta }$ ${\displaystyle >20keV}$ ${\displaystyle Z<40}$

${\displaystyle \delta ={\frac {\rho _{a}\sigma _{p}}{k}}={\frac {2\pi \rho _{a}Zr_{0}}{k^{2}}}\propto {\frac {Z}{E^{2}}}}$

${\displaystyle \beta ={\frac {\rho _{a}\sigma _{a}}{2k}}\propto {\frac {Z^{3-4}}{E^{4}}}}$

Thereby is the particle density , the cross section of the phase shift, the cross section of the photo absorption and the classical electron radius . It is crucial that matter of low density and atomic number, as is the case with organic substances, is about three orders of magnitude higher than . The phase thus reacts much more sensitively to small differences in density and is better suited for generating contrast in soft tissue. In addition, the energy dependency of and results in a further advantage for the generation of phase contrast. With increasing energy, it decreases much faster than and thus the possibility arises to use radiation of higher energy without strong loss of contrast. This is diagnostically advantageous because at higher energies a smaller fraction of the radiation is absorbed by the body and the radiation dose is reduced. ${\displaystyle \rho _{a}}$ ${\displaystyle \sigma _{p}}$ ${\displaystyle \sigma _{a}}$ ${\displaystyle r_{0}}$ ${\displaystyle \sigma _{p}}$ ${\displaystyle \sigma _{a}}$ ${\displaystyle \beta }$ ${\displaystyle \delta }$ ${\displaystyle \beta }$ ${\displaystyle \delta }$

In more general terms, the phase shift generated by the irradiated object along a path with the distribution relative to the propagation in the vacuum can be described by the integral : ${\displaystyle \delta (z')}$

${\displaystyle \Phi (z)={\frac {2\pi }{\lambda }}\int \limits _{0}^{z}\delta (z')dz}$

where denotes the wavelength of the incident radiation. Since the phase shift results from a projection of in the beam direction, a three-dimensional measurement of is accessible by reconstruction according to the tomographic principle . However, due to technical limitations, the phase is usually only measured modulo , which is why different deconvolution algorithms are used. ${\displaystyle \lambda }$ ${\displaystyle \delta }$ ${\displaystyle \delta }$ ${\displaystyle 2\pi }$

The difficulties in detecting the phase shift in X-rays arise due to several aspects, which is why various technical implementations have developed. In principle, only one intensity measurement is possible for the imaging, in which, however, the information about the phase position is lost. Therefore, the imaging system must either be able to resolve the extremely small angular deviations of the refraction of the beam directly or the phase shift must be converted interferometrically into a lateral intensity modulation, which can then be resolved by a detector. Both place high demands on the spatial coherence and monochromaticity of the radiation source and make it difficult to obtain the method in a cost- and time-efficient manner. By using X-ray optics such. B. grids, however, the requirements could be relaxed considerably, so that routine use in clinics and industry has become conceivable.

Individual evidence

1. ^ ^{A b c} R. A. Lewis: Medical phase contrast x-ray imaging: current status and future prospects . In: Physics in Medicine & Biology . tape 49 , no. 16 , 2004, ISSN  0031-9155 , p. 3573 , doi : 10.1088 / 0031-9155 / 49/16/005 .
2. ^ F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, EF Eikenberry: Hard-X-ray dark-field imaging using a grating interferometer . In: Nature Materials . tape 7 , no. 2 , 2008, ISSN  1476-4660 , p. 134-137 , doi : 10.1038 / nmat2096 .
3. ^ Andre Yaroshenko, Katharina Hellbach, Martin Bech, Susanne Grandl, Maximilian F. Reiser: Grating-based X-ray dark-field imaging: a new paradigm in radiography . In: Current Radiology Reports . tape 2 , no. 7 , July 1, 2014, ISSN  2167-4825 , p. 57 , doi : 10.1007 / s40134-014-0057-9 .
4. ↑ ^{a b} McMorrow, Des .: Elements of modern X-ray physics . 2nd ed. Wiley, Hoboken 2011, ISBN 978-0-470-97395-0 .
5. ↑ ^{a b} Martin Bech: X-ray imaging with a grating interferometer. (PDF) 2009, accessed on March 27, 2018 . 
6. ↑ Atsushi Momose: Recent Advances in X-ray Phase Imaging . In: Japanese Journal of Applied Physics . tape 44 , 9R, September 8, 2005, ISSN  1347-4065 , doi : 10.1143 / jjap.44.6355 / meta .
7. ↑ Grating-based X-ray phase contrast for biomedical imaging applications . In: Journal of Medical Physics . tape 23 , no. 3 , September 1, 2013, ISSN  0939-3889 , p. 176–185 , doi : 10.1016 / j.zemedi.2013.02.002 ( sciencedirect.com [accessed December 27, 2017]).
8. ^ Franz Pfeiffer, Timm Weitkamp, ​​Oliver Bunk, Christian David: Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources . In: Nature Physics . tape 2 , no. 4 , 2006, ISSN  1745-2481 , p. 258-261 , doi : 10.1038 / nphys265 .