1. Introduction

In recent years an x-ray diffraction imaging (XDI) scanner has been developed for security screening applications by MorphoDetection GmbH in Hamburg, Germany (Harding et al., 2012). The main rationale for developing this XDI scanner is the existence of explosive materials whose densities overlap those of common materials, such as water, leading to unacceptably high false alarm rates for scanners employing merely transmission x-ray data. As x-ray diffraction probes molecular structure, XDI yields more features for material identification than transmission x-rays, leading to higher detection rates and lower false alarm rates.

The scanner at a major European airport is depicted in Figure 1 and will be referred to below simply as the XDI scanner.

Figure 1

Photograph of an XDI scanner for Checkpoint Baggage Screening applications (CBS) at a major European airport, courtesy of MorphoDetection GmbH Hamburg, Germany

The XDI scanner has the following characteristics, which may suit it for applications in medical diagnostic radiology:

• The object under investigation is 3-D spatially-resolved into a complete set of voxels filling the object space, each having a volume of approximately 1 cm3 (see Figure 4);
• The XDI scanner object space of 600 mm width (Y) and 425 mm height (X) is dimensionally comparable with the patient opening of medium-bore medical CT scanners having 650 mm diameter (see Figure 5);
• For an extended, inhomogeneous object, the momentum transfer profile of small-angle coherent scatter is measured for each voxel with energy-resolving detectors (see Figure 7);
• The XDI scanner exemplifies direct scatter tomography, rather than reconstruction from transmission projections. It is thus suited to imaging and analysing rapidly-moving organs;
• The inherent contrast of molecular coherent scatter from body tissues is much greater than that originating in the linear attenuation coefficient accessed by transmission radiation, when the momentum dimension is included in tissue discrimination (see Figure 10);
• As each voxel is irradiated from several directions, a modest degree of transmission tomosynthesis can be reconstructed from the transmission data;
• The fusion of data from scatter and transmission sensors allows a significant improvement in image quality relative to that obtained when each is separately depicted (see section 3.1);
• The conveyor belt speed is sufficient to allow an anatomical region, such as head, thorax or abdomen, to be scanned in only a few seconds;
• The measured dose imparted in an XDI scan is negligible compared with that of the natural radiation background, taken as ~ 3 mGy / year (see section 4).

2. Description of XDI scanner

The XDI scanner employs the Multiple Inverse Fan-Beam (MIFB) topology (Harding et al, 2012). The MIFB topology is a multiple-focus, multiple-beam, multiple-detector extension of that originally described by Harding et al., (1990). These extensions increase the photon throughput by over five orders of magnitude relative to that of the original system.

The MIFB topology features an x-ray multisource, visible at the top of Figure 2, comprising a linear array of 16 focal spots that are sequentially irradiated by a magnetically-deflected electron beam. The accelerating voltage is 140 kV; whereas the tube DC power is 6 kW and the beam dwell time for each focus is 200 µs. The multiple aperture primary collimator extracts from each focus a series of 17 well-collimated x-ray beams directed to fixed target points in the detector plane. As the x-ray foci are sequentially activated, the primary rays to each of the fixed target points trace out a set of fans, each having a vertex at the corresponding target point. The fan of the rightmost target point is illustrated by the dashed lines in Figure 2. As each fan has its vertex at the detector plane, rather than at the focus, it exhibits the so-called “Inverse Beam” topology. The Multiple Inverse Fan Beam (MIFB) terminology arises from the fact that there are multiple fans, one for each of the target points. 

These fans together completely cover the object space, eliminating any dead regions of the object, from which no signal would be measured. 

Figure 2

Schematic illustration of x-ray diffraction imaging (XDI) scanner implementing the MIFB topology. System is viewed along direction of conveyor belt movement, representing the Z direction. Only half of the primary beams are shown, for clarity. Dual energy transmission detectors are located in the plane of the primary beams at the vertex points; whereas the spectroscopic scatter detectors are displaced from the vertex points at distances corresponding to the fixed angle of scatter of the secondary collimator. A full description of the MIFB topology and its technological realization is to be found elsewhere (Harding et al., 2012).

Conventional dual-energy transmission detectors are located in the XY plane at the target point positions to measure the energy-dependent transmission of each of the fans through the object. Knowledge of the transmission characteristics of the object allows a correction to be made for the energy-dependent attenuation of the scatter radiation, which is assumed to follow the same path through the object as the primary beam. This “small angle attenuation approximation” is justified by the small value (a few tens of milliradians) of the mean angle of scatter. In addition to the transmission detectors, room-temperature energy-resolving detectors record (mainly coherent) x-rays scattered at small angle out of the XY plane. These photon counting detectors have a mean energy resolution of 3% at 60 keV.

3. Characterization of XDI scanner

A test phantom was constructed to measure various parameters of the XDI scanner. It comprised two trays of adjustable heights for receiving arbitrary test objects supported in a wooden frame. The wooden frame is depicted in Figure 3 and has a section of the wall cut out to reveal the trays. It is shown on the conveyor belt prior to entry into the XDI scanner.

Figure 3

Test phantom comprising wooden box with trays for receiving various test objects

The test phantom was constructed with a slant angle of 30° in the direction of motion (Z) of the conveyor belt. This tilt matches the gantry angle of the XDI scanner, which is also 30°. Two bottles of 500 ml volume were placed on the top tray. One of the bottles was filled with water; the second with an aqueous liquid. An XDI perspective image of the test phantom loaded with the two bottles is depicted in Figure 4. The displayed parameter is the spatially-resolved scatter strength, defined as the scattered x-ray counts per voxel summed over all measured momentum values.

Figure 4

Perspective XDI image of test phantom showing wooden frame and a tray positioned centrally in the object space for receiving a variety of test objects, in this case two 500 ml bottles filled with aqueous liquids. The axes are given in cm units.

As noted in section 2, the XDI scanner simultaneously measures scatter and transmission data from the irradiated slice. The data from the scatter and transmission sensors can be fused to improve image quality. The fusion procedure involves the following steps, which can only be briefly summarised here. First, the XDI profiles are reduced to several significant features important for material recognition. Based on these features, an accurate representation of the voxel-specific photoelectric and Compton components of the linear attenuation coefficient are derived. These are then combined with the transmission projections through the object space of the photoelectric and Compton components to determine the object that best satisfies both the scatter and transmission sensor data. Finally, the voxel-specific scatter strength is calculated as a weighted sum of the photoelectric and Compton components for the tissue types present in the human body. A thorough description of the data fusion procedure is to be found in Isernhagen (2017).

A cross-sectional slice in the XY plane of a 250 ml bottle in the object space, obtained as described in the previous paragraph, is depicted in Figure 5.

Figure 5

Cross-sectional XY slice through object space containing 250 ml plastic bottle filled with water

The bottle had dimensions of 60 mm diameter and 125 mm overall height. The cap of the bottle is nominally ~ 17 mm high. To ensure closure of the bottle contents, the neck has a flared region of ~ 1 mm thickness against which the cap mates as it is screwed down. This joint of cap and neck is possibly indicated in Figure 5 as a region of enhanced scatter strength in the neck region.

An enlarged image of the water bottle is reproduced in Figure 6. The parameter depicted is once again the scatter strength as defined above. The cross-sectional dimensions of the bottle are indicated by the white lines superimposed on the scatter strength image. This figure gives an impression of the spatial resolution of the XDI scanner.

As the contents of the bottle are liquid, it can be assumed that the XDI momententum profiles of all voxels in the bottle are the same. Using standard object segmentation techniques, it is possible to identify automatically all voxels belonging to the same object and to aggregate them together. In analogy to the H-unit scale widespread in transmission computed tomography, the H-value of water on the XDI scatter strength scale is set to zero; whereas the scatter strength of air in these H units is set to -1000. The scatter strength is defined as the voxel-specific XDI momentum profile distribution summed over all momentum values. The H-scale mean scatter strength of the water bottle voxels in Figure 5 is zero and has a standard deviation of 27 H units. The scatter strengths in H units of some common materials are shown in Table 1. The scatter strength is used as a feature enabling object segmentation.

Table 1

Scatter strength in H units of some common materials

Contrary perhaps to expectations, the H scatter strength values of crystalline materials as reproduced in Table 1 are lower than those of amorphous samples. The maximum H intensity, defined as the scatter strength per unit momentum interval, is however significantly greater for crystalline than for amorphous materials. The explanation of this dichotomy is that the coherent scatter for crystalline objects is concentrated in narrow momentum bands centred on the major Bragg peaks of the material; whereas the coherent scatter from amorphous samples is distributed over a wide range of momenta.

The momentum profile of the water bottle aggregated over all voxels in 3D belonging to it is shown in Figure 7. The aggregation technique increases the number of counts constituting the momentum profile, thus improving its signal-to-noise ratio. As expected, the profile shown in Figure 7 is broad, characteristic of amorphous and liquid samples, and reaches a peak at ~ 1.5 nm-1. This accords, as expected, with the diffraction profile of water as measured with a conventional angular-dispersive diffractometer (Harding et al 1987).

Figure 7

Momentum profile of water as measured from the bottle depicted in Figure 5

The momentum resolution of the XDI scanner was measured by placing a packet of table salt powder in the test phantom depicted in Figure 3. The result of this measurement is shown in Figure 8. The most prominent Bragg peak at ~ 1.7 nm-1 arises owing to interference from the {200} planes of salt. The momentum resolution is estimated from this figure at 5%, in accordance with the XDI scanner design specifications.

Figure 8

Momentum profile of salt powder as measured with the XDI scanner

4. Radiation dose

The radiation dose imparted by the XDI scanner was repeatedly measured with a PTW Diados E dosimeter inserted into the centre of a D100 QRM thorax phantom. The measurement arrangement is illustrated in Figure 9.

The thorax phantom, visible to the right of the picture, was inserted in a luggage bin that was moved by conveyor belt through the scanner. The dosimeter signal was read out through the cable shown in the figure. As the dosimeter was inserted into the centre of the phantom, it was shielded from radiation emitted by the x-ray multisource owing to overlying material; hence the skin dose will be significantly higher.

Figure 9

Arrangement used to measure dose to a thorax phantom imparted by the XDI scanner

The arrangement of Figure 9 was used in 50 separate scans of the luggage bin containing the dosimeter through the XDI scanner. The mean value of dose used to obtain the scan results displayed in Figure 5 and Figure 7 was measured to be 126 nGy. It is thus, remarkably, insignificant relative to the natural background radiation dose of ~ 3 mGy per year (NCRP 2009), which is itself of the same order of magnitude as the dose administered in a volume CT investigation of the thorax as reported by Yu et al., (2009).

The main reasons for the low dose in the XDI scanner are that: the primary beam is very highly collimated (sub-millimetre width) in the direction of the patient couch movement (Z), so the time over which a point in the object is irradiated during a volume scan is very small (a few milliseconds); each focus produces a fan beam with a fill factor, relative to a complete fan beam, of only 20% in the Y direction; and the tube power is moderate regarding that routinely used in volume CT investigations.

5. Base-tissue decomposition

As remarked above, XDI (3D spatially-resolved x-ray diffraction imaging) permits the XDI profiles of individual voxels, parts of body organs, body organs and groups of body organs to be acquired in vivo. This capability suggests the potential of XDI for a novel type of diagnostic radiology, in which morphological information, such as local density, is supplemented by the x-ray diffraction profile of tissue at that locality. Differences between healthy and diseased tissue reflect, at the molecular level, differences in the molecular composition and spatial order of atoms of which the molecules are composed. X-ray diffraction is sensitive to such differences. At the molecular level, the function of a tissue type is related to its molecular structure.

Take as an example the liver. It is well-known that above a certain amount of fatty tissue in the liver, generally considered as ≥ 5% of the liver mass, the function of the liver is impaired (Kleiner et al 2005). Hence an XDI profile analysis of the liver revealing the quantitative amount of fat present will lead to improved diagnosis relative to other radiological modalities. Moreover, in osteoporotic bone there is a direct correlation between the onset of diseased bone and the weight proportion of body fat (Crepaldi et al, 2007). Finally, the composition of kidney stones significantly affects the diagnosis of renal failure (Davidson et al., 2005).

These examples indicate that a base-tissue decomposition of body tissues into such types as: fat; bone matrix (hydroxyapatite); urinary tract and gall bladder stones having various chemical compositions and crystalline structures; connective tissue (collagen); and water etc., yielding the weighting coefficients with which the local tissue composition is represented in terms of the base tissues types, may be a useful supplement to morphology for determining tissue health in diagnostic radiology performed with the XDI scanner.

Base-tissue decomposition of x-ray diffraction profiles has been proposed by Tartari et al., (2002) to improve the accuracy of photon transport calculations, which must necessarily include not only atomic form factors but also molecular structure functions. As there are many different types of body tissues, Tartari et al., (2002) proposed to simplify existing photon transport codes by representing each body tissue as a weighted sum of four base tissues: namely fat, water, collagen and calcium hydroxyapatite. These four base tissues were chosen for several reasons, including: simplicity; good representation of both soft and bony tissues; and the fact that their x-ray diffraction profiles are markedly different. For more details and further literature citations the interested reader is referred to the article of Tartari et al., (2002).

The main difference between the present work and that of Tartari et al., (2002) is the application of the Non-Negative Matrix Factorization (NNMF) data processing technique to determine the number of base-tissue profiles needed for accurate representation of the body tissues present in healthy and diseased individuals. NNMF is a standard data processing and reduction technique, akin to principal component analysis. NNMF factorizes a large matrix into a product of two smaller matrices. NNMF obviates the need for measurements of pure, isolated, homogenous tissue samples. Instead it decomposes all the measured profiles into their underlying base tissue functions.

In the present case, the large matrix under consideration is comprised of column elements referring to the momentum-dependent diffraction profile intensity for a certain tissue; whereas the row elements describe the tissue variations in diffraction profile intensity at constant momentum. In the case at hand, there are 512 rows per column corresponding to the regularly-spaced momentum grid; and 12 columns representing the various tissue types. Non-Negative matrix Factorization (NNMF), as its name implies, permits only a factorization into positive base functions. This condition corresponds to the fact that intensities of scattered photons must necessarily be non-negative.

Although NNMF is applied here to diffraction profiles from small in vitro tissue samples, it can be extended readily to in vivo XDI scans of material in each voxel. NNMF numerically sub-divides diffraction profiles from each of the tissue samples, or material in each of the voxels, into base-tissue functions. NNMF seeks the minimum number of base-tissue profiles needed for accurate representation of all tissue profiles. For this purpose the base-functions are multiplied by tissue-dependent weighting coefficients. Considering the original 512 x 12 large data matrix, this is factorized by NNMF into a 512 x P matrix multiplied by a P x 12 matrix. P is the number of base-tissue profiles determined by NNMF and the latter matrix contains the weighting coefficients. NNMF often effects a significant reduction in the number of elements comprising the original data matrix. This is often taken as evidence of redundancy in the original data.

NNMF proceeds iteratively, beginning with just one base function and gradually increasing the number of functions employed. At each iteration step a cost function is minimized, representing how well different base function solutions reconstruct the original matrix. The cost function used here is the mean square error between the original matrix and its NNMF representation.

Published data suggest that tissues crossing the demarcation line from healthy to diseased are characterized by alterations in the underlying molecular structure and hence by changes in the weighting coefficients of the base-tissue profiles.

The NNMF algorithm used to reduce the measured data to a set of base functions is based on the work presented by Berry et al., (2007).

6. X-ray diffraction profiles

Numerous authors have published compilations of medical tissue x-ray diffraction profiles, assumed isotropic. Among these, in chronological order, are the following: Kosanetzky et al., (1987); Royle and Speller (1995); Peplow and Verghese (1998); Kidane et al., (1999); Tartari et al., (2002); Johns and Wismayer (2004); Geraki et al., (2004); Ryan and Farquharson (2007); Griffiths et al., (2007); and Theodorakou and Farquharson (2008).

In the majority of these publications, small homogenous tissue samples were measured by commercial x-ray diffractometers implementing angular-dispersive analysis. In this form of XRD, quasi-monochromatic radiation (such as Cu Ka) scattered by the sample is measured in dependence on the scatter angle. They provide excellent momentum resolution; however they lack tomographic (depth) sensing capability and feature long scan times. These will be referred to in this publication as XRD profiles.

In the other cases the diffraction profiles were measured in the XDI scanner, implementing energy-dispersive analysis of broad-band x-radiation. Although the momentum resolution is essentially determined by the energy-resolution of the detectors and is therefore inferior to that of angular-dispersive technique, it offers direct tomographic analysis capability and is much faster. There are merely differences between the two in their technological implementation.

For the sake of clarity, the diffraction profiles acquired by the XDI scanner will be referred to as XDI profiles; whereas those acquired in an x-ray diffractometer will be referred to XRD profiles. Naturally, the underlying physical phenomenon is the same. Differences in technological implementation and data correction are responsible for differences between XRD and XDI profiles of the same material. King and Johns (2010) have pointed out that data correction for energy-dispersive equipment is more straightforward than that for angular-dispersive devices. The equivalence of XRD and XDI profiles has been demonstrated for amorphous substances such as water and acrylic plastic to within the applicable error bars e.g. by King and Johns (2010).

7. Results

In presenting results of the NNMF factorization technique applied to x-ray diffraction profiles, the intention here is to emphasise more the methodology than its precise output. The main reason for this emphasis is that in the course of time, as more tissues are included in the analysis, the number of base-tissue profiles derived from NNMF is expected to increase. Moreover, the input data is a mixture of XRD and XDI profiles. Thus changes both in the number and form of the base profiles are expected when only XDI data are analyzed. Finally, the statistical accuracy of a small set of only twelve diffraction profiles is questionable. As noted earlier, the XDI scanner provides the unique chance to apply NNMF in vivo to very many voxels containing healthy and diseased tissues.

Figure 10 depicts the six base-tissue profiles needed to represent accurately the twelve input profiles. It is not possible to relate uniquely base-tissue profiles to those known from the literature. For instance, profile 1 appears to represent that of water; whereas profile 4 is similar to that of calcium hydroxyapatite. For reasons outlined above it does not appear worthwhile to delve too deeply into the precise identification of the base-tissue functions depicted in Figure 10 until a more comprehensive study with the XDI scanner has been performed.

The NNMF algorithm employed here presumes that no a priori knowledge is available concerning the presence or otherwise of known base-tissue functions. In the numerical technique known as “Constrained NNMF”, it is possible to “prime” the NNMF decomposition process with one (e.g. water) or more known base functions (Liu et al., 2012). An investigation of NNMF and some of its more modern derivatives is envisaged in Section 8.

Figure 10

The six most significant x-ray diffraction profiles derived from NNMF analysis of 12 experimentally-measured XRD and XDI profiles of a selection of human tissues

Figure 11

Plot of the MS error in the representation of 12 input x-ray diffraction profiles by base profiles, in dependence on the number of base profiles derived from NNMF analysis

Figure 11 illustrates the development of the mean-square error between the original input data and their NNMF representation as the number of base profiles increases. As is common in such cases, the error cost function initially decreases as more base-functions are added. At some stage however, when the original data no longer support the use of too many base-functions, the error increases. From Figure 11 the minimum error between the original input data and their NNMF representation occurs when 6 base-functions are considered.

8. Future work

This section details three proposals for future work to enable the efficacy of the XDI scanner for extending the capabilities of diagnostic radiology with base-tissue decomposition to be assessed.

The XDI scanner permits diffraction profiles to be measured in vivo and with low dose from entities such as: individual voxels; groups of voxels; parts of body organs; body organs; and groups of body organs. This capability raises the intriguing possibility, when XDI scans of healthy and diseased individuals have been performed, of deriving correlations between the base-tissue function weighting coefficients and the health of the body entity to which these coefficients pertain. Naturally, such correlations can be refined by including the morphological structure of the scanned entity, as determined by the XDI scanner, in the correlation analysis.

Body organs such as liver, heart, brain etc. can be identified from XDI scans using the object segmentation algorithms that are routinely employed in XDI security screening applications.

It is proposed to embark with the XDI scanner on a measurement program of healthy and diseased individuals. The aim is to compile a library of XDI profiles that can be correlated with tissue health or otherwise. It is acknowledged that this program is ambitious in scope; nevertheless this proposal for future work is regarded as significant, novel and interesting as an option for extending the capabilities of diagnostic radiology.

The NNMF technique will be in future work critically compared to some of its more modern derivatives which allow a priori knowledge of base-tissue functions to be included. This technique is termed Constrained NNMF (Liu et al., 2012). It is known that the human body is mainly composed of the components water, fat, hydroxyapatite and collagen. As their XDI momentum profiles can be accurately measured, these four components can be used as input to the Constrained NNMF algorithm. This investigation will help determine the NNMF variant that is most suited to the XDI base-tissue decomposition procedure envisaged here.

The XDI scanner was developed, as noted above, for application in the security screening environment. There are several possible redesign options for optimizing it to the diagnostic radiology scenario. Apart from the obvious need to adapt the XDI scanner to patient investigations by replacing the conveyor belt with a moveable patient couch, these options aim to reduce the scan time whilst improving both the spatial and contrast resolution. The extremely low radiation dose associated with an XDI scan yields much room for manoeuvring in the optimization space.

9. Conclusions

An X-ray Diffraction Imaging (XDI) scanner has been introduced having the following characteristics: 3D spatial resolution; 1D momentum resolution; object opening having dimensions permitting whole-body scans; and short scan times. A measurement of radiation dose suggests that an XDI scan imparts an extremely low radiation dose, which is negligible compared with the yearly natural radiation background.

The Non-Negative matrix Factorization (NNMF) technique has been applied to a range of published and measured x-ray diffraction profiles. NNMF numerically sub-divides diffraction profiles from the sample, or the material in each XDI voxel, into base-tissue functions. Published data suggest that tissues crossing the demarcation line from healthy to diseased are characterized by alterations in molecular structure and hence by changes in the weighting coefficients of the base-tissue profiles.

Proposals for future work on this topic are made, including: XDI scans of healthy and diseased individuals to construct a tissue library; adaption of the XDI scanner for medical applications; and optimization of the NNMF technique to allow a priori knowledge of important base-tissue components to be incorporated into the analysis.

​Acknowledgements

The authors gladly acknowledge fruitful exchanges with their erstwhile colleagues in the XDI development group at MorphoDetection, Hamburg, led by Dr Jens-Peter Schlomka. The tissue samples measured with XDI were made available by Prof. Dr. med. Udo Schumacher of the Institute of Anatomy and Experimental Morphology at University Hospital Hamburg in Eppendorf.