WO2012029039A1

WO2012029039A1 - Beam hardening correction for phase-contrast imaging

Info

Publication number: WO2012029039A1
Application number: PCT/IB2011/053819
Authority: WO
Inventors: Thomas Koehler
Original assignee: Koninklijke Philips Electronics N.V.; Philips Intellectual Property&Standards Gmbh
Priority date: 2010-09-03
Filing date: 2011-08-31
Publication date: 2012-03-08

Abstract

The present invention relates to differential phase-contrast imaging of an object. Polychromatic X-ray radiation (114) penetrating an object (108) is attenuated non-uniformly by the tissue structure of the object (108), known as beam hardening. Accordingly, it may be beneficial to consider the effect of beam hardening when generating X-ray image information from differential phase-contrast image data. Thus, a method (400) for generating image data of an object (108) employing phase-contrast imaging is provided employing receiving (402) an X-ray projection of an object (108) to be examined, generating (404) differential phase contrast image data of the object (108) and storing (406) generated differential phase contrast image data image data of the object (108). The generation of differential phase contrast image data of the object comprises a correction for beam hardening of X-ray radiation the object (108).

Description

BEAM HARDENING CORRECTION FOR PHASE-CONTRAST IMAGING

FIELD OF THE INVENTION

The present invention relates to X-ray imaging technology in general.

More particularly, the present invention relates to differential phase-contrast imaging.

In particular, the present invention relates to a method for generating image data of an object employing phase-contrast imaging, an apparatus for generating image data of an object employing phase-contrast imaging, an X-ray system comprising an apparatus according to the present invention, the use of an apparatus according to the present invention in one of an X-ray system and a CT system, a computer-readable medium as well as a program element.

BACKGROUND OF THE INVENTION

An object to be examined, e.g., a patient, of which an X-ray image is to be acquired, is arranged between an X-ray generating device and an X-ray detector element in the path of X-ray radiation. Said X-ray radiation is penetrating the object emanating from the X-ray generating device. An inner structure or tissue structure of the object to be examined provides a spatial attenuation of the X-ray beam arriving at the X-ray detector after passage through the object. The X-ray radiation spatially attenuated by the object is detected by the X-ray detector. Attenuation information of the X-ray radiation is subsequently employed for generating X-ray image information of the object.

However, a certain object, in particular its inner structure with regard to different types of tissue, may not provide sufficient attenuation of the X-ray radiation for obtaining image information with high contrast. Rather, in case the inner structure of an object has a low variability of the X-ray attenuation coefficient, resulting in rather uniformly attenuated image information the structure of the object may not be revealed with sufficient detail.

While an object may substantially uniformly attenuate X-ray radiation, a phase of X-ray radiation penetrating the object may be influenced to a larger extent.

Accordingly, phase-contrast imaging may be employed for gaining information about an object by determining, in particular the relative phase of X-ray radiation after penetrating said object. At least partly spatially coherent X-ray radiation may allow for a subsequent retrieval of phase information. While a phase of X-ray radiation may not be measured directly, the phase-shift of a wave front may be converted to an intensity modulation by interference of two or more waves. In one particular setup for phase-contrast imaging, a so-called phase grating element is arranged between the object to be examined and an X-ray detector.

While the phase grating element provides means for generating an interference pattern, a spatial resolution of a current X-ray detector may not be sufficient for detecting said interference pattern with sufficient detail. To resolve this problem, a further grating element, a so-called analyzer grating element, is arranged between the phase grating element and the X-ray detector, subsequently providing an interference pattern, which is large enough to be detectable by current X-ray detectors.

To obtain appropriate image information, a so-called phase stepping is performed. In phase stepping, one of the source grating, employed for generating the at least partly spatial coherent X-ray radiation, the phase grating, and the analyzer grating is displaced laterally with respect to the other gratings and the X-ray detector element by a fraction of its respective grating pitch, e.g., a fourth, sixth, or eighth of the grating pitch of the respective grating element constituting a phase stepping state. Image acquisition and lateral displacement is repeated, e.g., four, six, or eight times, for acquiring a plurality of phase contrast projections, constituting together a phase stepping series.

The phase-shift of the X-rays may be considered to be directly related to the integral of the electron density along the path of X-ray radiation. Grating-based differential phase-contrast imaging may allow employing a relatively broad-banded X-ray source, e.g., with ΔΕ/Ε~10%. In other words, polychromatic X-ray radiation rather than monochromatic X-ray radiation having substantially only a single wavelength may be employed for phase- contrast imaging.

Though X-ray radiation comprises more than a single dedicated wavelength, regularly for calculating the phase-shift, in particular the phase gradient, for calculation X-ray radiation having a design energy and thus a single dedicated wavelength is assumed. It may further be assumed that the design energy of a particular X-ray system is well-known and thus a spectrum of X-ray radiation arriving at the object to be examined.

However, the spectrum is subject to change while penetrating the object to be examined. In other words, the intensity distribution of a dedicated X-ray system, though known for X-ray radiation arriving at the object to be examined, may be influenced by the object and its inner structure resulting in a dynamic change of the spectrum during the penetration of the object.

This effect is referred to as beam hardening since the X-ray beam becomes more penetrating or harder, as it passes through the object.

Different aspects of phase-contrast imaging are described in Weitkamp T., Diaz A., David C. et al.: "X-ray phase imaging with a grating interferometer"; Optics Express 6296, 8. August 2005/vol. 13, no. 16, Bartl P., Durst J., Haas W. et al. "Simulation of X-ray phase-contrast computed tomography of a medical phantom comprising particle and wave contributions", Proc of SPIE vol. 7622 76220Q-1, Wang Z., Huang Z., Zhang Li et al: "New solutions for reconstruction problem about grating-based dark field computed tomography", 10^th international meeting on fully three-dimensional image reconstruction in radiology and nuclear medicine, Beijing, China, 2009, pages 438-441, and Huang Z. Zhang Li, Wang Z. et al.: "Grating-based Multiple Information Computed Tomography", 10^th international meeting on fully three-dimensional image reconstruction in radiology and nuclear medicine, Beijing, China, 2009, pages 446-448.

SUMMARY OF THE INVENTION

Since the determination of a phase gradient employed for differential phase- contrast imaging depends on the knowledge of the spectrum of X-ray radiation employed for generating image information, it may be beneficial to determine or at least consider a change in the spectrum in differential phase-contrast imaging.

One aspect of the present invention may be seen as taking into account beam hardening in the determination or calculation of a phase gradient employed for differential phase-contrast imaging when reconstructing image information.

Accordingly, a method for generating images of an object employing phase- contrast imaging, an apparatus for generating image data of an object employing phase- contrast imaging, an X-ray system comprising an apparatus according to the present invention, the use of an apparatus according to the present invention in one of an X-ray system and a CT system, a computer-readable medium and a program element according to the independent claims are provided.

Preferred embodiments may be taken from the dependent claims.

These and other aspects of the present invention will become apparent from and elucidated with reference to the embodiments described hereinafter. Exemplary embodiments of the present invention will be described below with reference to the following drawings.

The illustration in the drawings is schematic. In different drawings, similar or identical elements are provided with similar or identical reference numerals.

The figures are not drawn to scale, however may depict qualitative

proportions.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 shows an exemplary embodiment of an X-ray system according to the present invention;

Fig. 2 shows an exemplary embodiment of a differential phase-contrast

imaging system according to the present invention;

Fig. 3 shows an exemplary embodiment of an apparatus for generating image data of an object employing phase-contrast imaging according to the present invention; and

Fig. 4 shows an exemplary embodiment of the method for generating image data of an object employing phase-contrast imaging according to the present invention. DETAILED DESCRIPTION OF EMBODIMENTS

The aspect of X-ray radiation becoming regularly harder when passing through tissue of an object may be relevant when processing differential phase-contrast image information for reconstruction, since both attenuation and phase shift of X-ray radiation may be considered to be energy-dependent.

The present invention in particular relates to data processing or image data enhancement on an early, low level of the data processing chain in X-ray image acquisition. E.g., during phase contrast image acquisition, for each phase stepping step or phase stepping state during a phase stepping series, X-ray projection data is acquired by the X-ray detector. Each phase stepping state corresponds to a particular alignment of grating elements. In each phase stepping state, the X-ray detector is acquiring a single X-ray projection. A plurality of X-ray projections of a phase stepping series is subsequently processed for obtaining, thus, generating, a single differential phase contrast image. In other words, depending on the number of phase stepping steps, e.g., four, six, or eight, in a single phase stepping series, the same number of individual X-ray projections are processed for generating a single differential phase contrast image. The differential phase contrast image may subsequently be employed for obtaining X-ray image information.

The present invention employs the method generating image data of an object after receiving the phase stepping series of X-ray projections for correction of beam hardening.

X-ray radiation in an energy range corresponding to a higher attenuation coefficient of the object to be penetrated may be attenuated to a larger extent than energy of a further energy range with a lower attenuation coefficient. Regularly, the energy of X-ray radiation is divided in and referred to as soft X-rays and hard X-rays. Soft X-rays are more strongly attenuated than hard X-rays. In other words, when X-ray radiation is penetrating an object, the tissue of the object more easily removes soft X-rays from an X-ray beam than hard X-rays.

This results in the X-ray beam shifting its intensity spectrum to hard X-rays since soft X-rays are more strongly removed. Accordingly, for a measured intensity of X-ray radiation at the X-ray detector and a single detector element respectively, beam hardening has to be considered for obtaining reasonable meaningful results. In other words, although the X- ray spectrum generated by an X-ray source may be well peaked and thus known at the design energy E_d of the detection system, said peak may have shifted and thus be well above E_d after penetration of the object.

Beam hardening may in particular cause an underestimation of a phase gradient, since a phase-shift decreases with energy and may thus create inconsistencies in a differential projection of the phase front. Beam hardening may be considered to be typically varying from a single detector pixel to a further detector pixel.

For considering beam hardening, the present invention employs equation 1 for determining a measured intensity / for each detector pixel as a function of the position x of the analyzer grating G₂. f(x) = j dE · I₀ (E) · _e - J>(t^f.0^di + j dE · C(E) · V(E) · 1(E) · cos(2?z: ^ + φ (Ε_α) · )

Equation 1

E being the energy of the X-ray radiation, Io(E) being the incoming intensity spectrum and 1(E) the transmitted intensity spectrum of the X-ray radiation. V(E) is the visibility function of the X-ray generating device, p is the pitch of the analyzer grating G₂, and μ is the X-ray attenuation coefficient. The integration over / is performed along the line from the X-ray source, i.e., the focal spot of an X-ray tube, to a single detector pixel element of the X-ray detector. The incoming intensity spectrum h(E) and the visibility function V(E) may be considered to be known. h(E) may either be measured for a dedicated X-ray system or may be determined by calculation or simulation. The visibility function V(E) may be calculated as well, e.g., as described in Weitkamp et al.

Function C(E) models the loss in visibility of the interference pattern. For a particular energy, e.g., the design energy E , the loss in visibility C(E ) is related to the second moment (variance) of the scatter angle distribution S²(E_d) at the design energy E_d according to equation 2 as described in Wang et al. and Huang et al.

Equation 2

Small angle scattering, i.e., Thomson scattering, has an energy dependence as 1/E², which is then also related to the energy dependence of the second moment of the angular distribution, in accordance with equation 3

Equation 3

Consequently, the energy dependence of the visibility may be modelled by equation 4

C(E) = _e -2^² <5² (¾)^/£² = C{E_d) ^E '^E2

Equation 4

Depending on the energy range of X-rays used during the measurement, other physical effect like Compton scattering may contribute to the loss of visibility. In this case, the energy dependence of C may be modelled differently.

Note that it is also possible to retrieve the gradient of the phase front by stepping the phase grating instead of the analyser grating. In this case, equation 1 still holds true, but x is then the position of Gi and p is the pitch of G_\ . Furthermore, in a setup with an additional source grating Go, it is also possible to perform the stepping by moving Go. Again, equation 1 is still valid if x is considered to be the position of Go and p is the pitch of Go. The first term of equation 1 may relate to the total mean intensity over the phase stepping, i.e., with regard to a single phase stepping state or step. In the second term, in accordance with the present invention, the expression 1/E as the energy dependence of the phase-shift has been included.

Phase <p(i¾) is the value to be determined by and derived from equation 1 in particular by employing a set of N samples flxj); j=l , .. . ,N with N being an integer as well as the number of phase steps during a dedicated phase stepping acquisition, e.g. 4, 6, or 8.

The phase <p(i¾) is related to the desired gradient of the wave front δΦ/dx of the X-ray beam behind the object by the relation given in Weitkamp et al. according to

δΦΙδχ=φ(Ε_ά) p₂l d)

Equation 5 where /¾ is the pitch of the grating G₂ and λ is the wavelength of the X-rays at the design energy E_d. Since there is this linear relationship between the desired gradient of the wave front δΦ/δχ and the phase <p(i¾), only the determination of phase <p(i¾) is discussed in the following.

Phase <p(i¾) may not be determined directly by solving equation 1. Rather, further methods for solving equation 1 may be employed, e.g., the Newton method or other algorithms for numerical approximation.

A rather accurate approximation of beam hardening may be to assume that all attenuation of X-ray radiation was caused by water only. Thus, the path lengths of the X-ray radiation travelling through water that would result in the same total transmitted intensity of X-ray radiation is referred to as /water- This length is defined as the length for which equation 6 holds true.

Equation 6 μ water(E) being the attenuation coefficient of water as a function of the energy E of X-ray radiation.

Accordingly, employing /_water, the transmitted intensity spectrum 1(E) may be determined according to equation 7.

1 E) = I_Q (E) · e ^~lwater^^water^

Equation 7 For a preferred determination and calculation of the phase (p(E_d), further approximations may be employed.

In a first embodiment, a mean energy approximation may be conducted, i.e., the energy Es is determined for which the product of the visibility function V(E) and the transmitted intensit spectrum 1(E) is maximal, thus V(E)-I(E)=max.

When employing the mean energy approximation, the measured intensity may be approximated by equation 9.

When employing the mean energy approximation according to equation 9, a conventional phase retrieval may be employed for determining the desired phase gradient at the design energy as

Equation 10

A further embodiment for approximation, which may be considered a more accurate embodiment than the mean energy approximation, may be obtained by substituting, thus approximating the second integral term of equation 1 by a finite sum, obtaining equation

1 1.

Equation 1 1

The number M of energy bins may be selected according to the energy dependence of the integrand C(E)- V(E)-I(E). Normally, this function is rather smooth so that only few energy bins, e.g., four to six bins, are sufficient.

Again, having a set of measurements flxj), the desired quantity, the phase

(p(E ) may be obtained by a numerical fit.

Now referring to Fig. 1 , an exemplary embodiment of an X-ray system according to the present invention is depicted.

In Fig. 1 , an X-ray system 100, exemplarily a CT system 100, is depicted. X- ray system 100 comprises an X-ray generating device 102, e.g. an X-ray tube, as well as an X-ray detector 104. X-ray generator 102 is generating X-ray radiation 1 14, which is travelling from X-ray generating device 102 to X-ray detector element 104. X-ray radiation 1 14 may in particular be a spatially coherent X-ray beam, collimated to the dimension and shape of the X-ray detector 104, in Fig. 1 exemplarily depicted as a two-dimensional array of detector pixel elements 1 16.

The X-ray generating device 102 and X-ray detector 104 are arranged on a gantry 106, which is adapted for rotation about an axis. Both the X-ray generating device 102 and the X-ray detector element 104 are rotatable by gantry 106 with a fixed relation to one another.

A support 1 10 is provided for holding and situating an object 108 to be examined within the path of X-ray radiation 1 14. When object 108 is placed in the X-ray beam, image information of object 108 may be acquired by X-ray detector 104 and may subsequently be processed, e.g. reconstructed, for obtaining an X-ray image of object 108.

Processing system 1 12 is communicatively coupled to X-ray system 100 to allow control of X-ray system 100, e.g., control the image acquisition procedure and to possibly subsequently present or display acquired image information of object 108.

Presenting reconstructed image data of object 108 may thus be a display of image information to a user of the X-ray system 100. However, presenting may also comprise storing reconstructed image data for a later display, archival of reconstructed image data, thus permanent or temporal storage of image data and may also comprise providing image data to a further processing system for e.g., display, storage or further processing.

Individual grating elements like e.g., a source grating, a phase grating Gi and an analyzer grating G₂, are not depicted in Fig. 1 , however may be considered to be present to allow acquisition of differential phase-contrast image information. An exemplary setup of a differential phase-contrast imaging system may be taken from Fig. 2.

Now referring to Fig. 2, an exemplary embodiment of an apparatus 200, a differential phase-contrast imaging system, according to the present invention is depicted. In Fig. 2, X-ray source 102 is depicted having a source grating element 202 arranged adjacently. X-ray radiation 1 14 penetrating source grating element 202 may be considered to be at least partially spatially coherent. X-ray radiation 1 14 comprises individual wave fronts of which wave front 210a is depicted as a wave front before penetration of object 108 while wave front 210b is depicted after penetration of object 108, having an illustrated phase-shift.

Arranged after object 108 and spaced apart from both the detector element 104 and an analyzer grating G₂ 206 by distance d, is phase grating 204 having a pitch pi. Detector 104 with its individual detector pixel elements 1 16, subsequently detect an interference pattern of X-ray radiation 1 14, imposed by phase grating Gi 204 and analyzer grating G₂ 206.

Actuator element 208 is schematically illustrated being adapted to laterally displace analyzer grating G₂ 206 relative to X-ray tube 102 with source grating 202, phase grating Gi 204 and X-ray detector 104. However, actuator element 208 may be arranged at any of the grating elements 202, 204, 206 for displacement.

Now referring to Fig. 3, an exemplary embodiment of an apparatus for generating image data of an object employing phase-contrast imaging according to the present invention is depicted.

Processing system 1 12, exemplarily the processing system 1 12 of Fig. 1 , is depicted comprising a processing element 300 as well as a local storage element 302.

Processing system 1 12 is communicatively coupled to X-ray system 100, e.g., for control of X-ray system 100, for receiving and sending data.

Processing element 300 is adapted to execute the method (400) for generating image data of an object employing phase-contrast imaging according to the present invention. In particular, processing element 300 is adapted for generating differential phase contrast image data acquired by X-ray system 100 but also by a further X-ray system.

In particular, processing system 1 12 may be a processing system completely separate from the X-ray system employed for acquiring X-ray projection data, substantially being only adapted for receiving image information for subsequent processing and

reconstruction.

Processing element 300 may further be adapted to employ a correction for beam hardening when generating differential phase contrast image data. Received X-ray projection data as well as generated differential phase contrast image data may be stored in storage element 302. Storage element 302 may be a storage element for short-term or long- term storage of data. After the generation of the differential phase contrast image data, said data may be stored in storage element 302, may be provided to a separate, e.g. remote, storage system or to a further processing system for further image reconstruction. Image reconstruction may comprise generating an X-ray image of the object and may either be conducted by processing system 112 or by a further, e.g. remote, processing system.

Now referring to Fig. 4, an exemplary embodiment of the method for generating image data of an object employing phase-contrast imaging according to the present invention is depicted. In Fig. 4, method 400 for generating image data of an object employing phase-contrast imaging is provided, comprising receiving 402 an X-ray projection of an object to be examined having a tissue structure and generating 404 differential phase contrast image data of the object. Generated differential phase contrast image data may subsequently be stored 406. The reconstruction comprises correction for beam hardening of X-ray radiation within the tissue structure of the object during acquisition of differential phase-contrast image data.

Storing may comprise long-time storage, i.e. for archival of data, but may also comprise short-time storage, e.g. in a memory element of processing element 300, for further processing, transmission of data to a further processing system or storage system or display of data on display element 304.

It should be noted that the term "comprising" does not exclude other elements or steps and that "a" or "an" does not exclude a plurality. Also, elements described in association with different embodiments may be combined.

It should also be noted, that reference numerals in the claims shall not be construed as limiting the scope of the claims.

LIST OF REFERENCE SIGNS

100 X-ray system

102 X-ray generating device/X-ray source

104 X-ray detector

106 Gantry

108 Object

1 10 Support

1 12 Processing system

1 14 X-ray radiation

200 Apparatus

202 Source grating

204 Phase grating Gi

206 Analyzer grating G₂

208 Actuator element

210a,b Wave front

300 Microprocessor

302 Storage element

304 Display element

400 Method for generating image data

402 Receiving X-ray projection data

404 Generating differential phase contrast image data

406 Storing generated differential phase contrast image data

Claims

CLAIMS:

1. Method (400) for generating image data of an object employing phase contrast imaging, comprising

receiving (402) an X-ray projection of an object (108) to be examined;

generating (404) differential phase contrast image data of the object (108); and storing (406) generated differential phase contrast image data of the object (108); wherein generating (404) differential phase contrast image data comprises correction for beam hardening of X-ray radiation within the object (108).

2. Method according to the preceding claim,

wherein a plurality of X-ray projections are employed for generating the differential phase contrast image data of the object; and

wherein the plurality of X-ray projections relate to a single phase stepping series.

3. Method according to at least one of the preceding claims,

wherein the correction for beam hardening comprises determining a phase φ (Ε_ά) at a design energy E_d employing the equation f(x) = j dE · I₀ (E) · e - f ^E.Ddi ₊ j _dE . _C(E) · V(E) · 1(E) · cos(2?z: ^ + φ (Ε_α) · )

4. Method according to at least one of claims 1 or 2,

wherein the correction for beam hardening comprises determining a phase gradient φ (Ε_ά) at a design energy E_d employing the equation

f(x) ~ j dE - 1(E) + C(E_S) · V(E_S) · I (E_S) · COS(2TT - + φ (Ε_α) · ¾

v

5. Method according to at least one of claims 1 or 2,

wherein the correction for beam hardening comprises determining a phase gradient φ (Ε_ά) at a design energy ^employing the equation f(x) * j dE - 1(E) + ^ C(E_t) · V(E_t) · l (E_t) · COS(2T^ + φ (Ε_α) · -)

6. Apparatus (200) for generating image data of an object employing phase contrast imaging, comprising

a storage element (302) for storing a received X-ray projection and generated differential phase contrast image data of an object (108); and

a processing element (300) for generating differential phase contrast image data of the object (108);

wherein the apparatus (200) is adapted to carry out the method (400) according to one of the preceding claims.

7. X-ray system (100) comprising an apparatus (200) according to the preceding claim.

8. Use of an apparatus (200) according to claim 7 in one of an X-ray system (100) and a CT system.

9. Computer-readable medium, in which a computer program for providing beam hardening correction for phase-contrast imaging is stored, which computer program, when being executed by a processor (300), is adapted to carry out the method (400) according to at least one of claims 1 to 5.

10. Program element for providing beam hardening correction for phase-contrast imaging, which program element, when being executed by a processor (300), is adapted to carry out the method (400) according to at least one of claims 1 to 5.