Localising functionalised gold-nanoparticles in murine spinal cords by X-ray fluorescence imaging and background-reduction through spatial filtering for human-sized objects

Accurate in vivo localisation of minimal amounts of functionalised gold-nanoparticles, enabling e.g. early-tumour diagnostics and pharmacokinetic tracking studies, requires a precision imaging system offering very high sensitivity, temporal and spatial resolution, large depth penetration, and arbitrarily long serial measurements. X-ray fluorescence imaging could offer such capabilities; however, its utilisation for human-sized scales is hampered by a high intrinsic background level. Here we measure and model this anisotropic background and present a spatial filtering scheme for background reduction enabling the localisation of nanoparticle-amounts as reported from small-animal tumour models. As a basic application study towards precision pharmacokinetics, we demonstrate specific localisation to sites of disease by adapting gold-nanoparticles with small targeting ligands in murine spinal cord injury models, at record sensitivity levels using sub-mm resolution. Both studies contribute to the future use of molecularly-targeted gold-nanoparticles as next-generation clinical diagnostic and pharmacokinetic tools.


Results
Localisation of L1-functionalised gold-nanoclusters in murine spinal cords. As a pilot study towards XFI-based PK studies, we first present results of experiments using gold L-shell excitation XFI in murine models with spinal cord injury, and their subsequent treatment with GNPs functionalised with a short peptide derived from the neuronal cell adhesion molecule L1 and thiolated poly(ethylene glycol) (PEG) 20,21 see Fig. 1.
We assessed the diffusive behaviour of L1-GNPs using a clinically relevant in vivo model of spinal cord compression [22][23][24][25] . To this end, thoracic spinal cord injury was performed on adult female mice using well-established paradigms. L1-GNPs were applied 500 µm proximal to the lesion site via an ultra-thin capillary to stimulate neural regeneration. PEGylated GNP probes were used as controls. Following serial assessments as long as over a 48-hour time interval (i.e., 0, 2, 48 hours), injured mice were transcardially perfused, and the spinal cords subjected to XFI using highly-brilliant synchrotron radiation. Mock-injured spinal cords in the absence and presence of L1-GNPs were used for comparison. The aim here is to explore the sensitivity limit of XFI with respect to detecting an unprecedented minimum amount of locally confined tissue-bound biomarkers of high specificity, in addition to achieving sub-mm spatial resolution.
We detected local GNP-masses down to 72 picogram in the scanning pencil beam volume with a diameter of only 0.2 mm (Fig. 2A).
The statistical significance Z (in units of one standard deviation) of this record minimum detection limit in GNP-weight (i.e., 0.0017 wt% or weight-percentage) was Z = 4.3. The main aim of this experiment was to explore the XFI sensitivity limit in the localisation of GNPs, but we also benchmarked the XFI-detectable local GNP masses against inductively coupled plasma mass spectrometry (ICP-MS). Uncertainties in the XFI measurements have been thoroughly studied, and the results from ICP-MS and XFI are in close agreement, noting that no spinal cord was completely scanned, leaving the XFI-signal below ICP-MS values (Fig. 2B). The findings imply that for all post-injection times the entire GNP-mass remains concentrated in the region around the lesion positions, indicating a stable binding of the L1-functionalised GNPs to stressed neurons. On the basis of the XFI-scan obtained at those positions, we deduce an uptake of 0.6% to 1.0% of the total injected GNP-amounts. The transverse scanning (in one plane) along the spinal cords ( Fig. 2A) demonstrated strong localisation of the L1-functionalised GNPs at the injection positions ( Fig. 2C), an information not available from ICP-MS measurements.
Since the isotropic XFI-signal was measured by a detector with an extremely small fraction of the entire (4π) solid angle, the applied dose was found to be very high. Setting the physical dose limit to 11 mGy (corresponding to 10 6 incident photons) for 4π-detection and a statistical significance limit of Z = 3, we find a minimum detectable GNP-mass of 2.3( ± 0.7) ng, corresponding to 0.055 wt%. These computed GNP-mass and concentration values are effectively more than one to two orders of magnitude lower than those previously published, taking into account the much smaller scanning beam diameter and the use of significantly lower dose levels than used for other probes, especially in XFI-Computed-Tomography (XFI-CT) schemes (ref. 26 and references therein). The critical factor needed to attain high XFI-sensitivity for the low dose administered was the usage of highly brilliant X-ray beams, whose mono-chromaticity allows for quasi background-free measurements. Solution of "background problem" for large objects. While the above L-shell XFI-experiment demonstrated a quasi background-free setup, its relatively low photon energy makes it impractical for in vivo imaging of objects larger than small animals. On the other hand, K-shell XFI in human-sized objects is expected to suffer from a large intrinsic background [27][28][29] (Fig. 3a).
We have set up analytical and numerical studies of the signal and background behaviour. In order to minimise intrinsic background contributions to the measured signal without concomitant signal losses, a scheme utilizing advanced spatial and spectral filtering was developed, derived from the anisotropy of the background. In this work we treat the anisotropy in case of human-sized objects, both for monochromatic polarised and polychromatic unpolarised X-ray photons, both in numerical and experimental studies, and provide an explanation from an analytical model.
In order to address size scales relevant for future XFI-applications on human patients, we simulated a (soft-tissue) sphere with a diameter as large as 30 cm. In its centre, a small sphere with radius of only 0.5 mm has been placed containing gold at the same concentration of 0.23 wt% as that reported in XFI-experiments using tumour-bearing mice 26 , i.e. from a small-animal model. However, this reported concentration was detected (with a polychromatic benchtop X-ray source) in a cubic voxel of length 2.5 mm, while here we aim to detect the same concentration in just a 1-mm-diameter sphere -a volume, and hence, GNP-mass, a factor of 30 times smaller, i.e.  in our case only 1.2 μg. Note that the scheme in ref. 26 could not detect this GNP-amount in a 30-cm-object. In our simulation, the large-size phantom was scanned with a pencil beam of 1 mm diameter, defining the spatial resolution of 1 mm, with an average physical dose, i.e. absorbed energy within the scanning beam volume, set to be only 10 mGy. Our ability to determine both the photon detection scheme with maximum background reduction and optimum incident photon energy is based upon an analysis of the energy-dependent spatial distribution of the multiple Compton scattering background. Since we propose to quantify the signal quality as the combined significance of both the Kα 1 and Kα 2 lines of the GNPs, we apply spectral filtering around these two lines (within a range of ± 3σ det around each line, with a detector energy resolution of σ det ). The manifold of all possible combinations of multiple Compton scatter angles with final energies falling into the range around these two fluorescence lines results in a strongly anisotropic background (Fig. 4a).
Due to this anisotropic background in large objects, a detector covering the full solid angle -similar to the 4π-detection extrapolation of our spinal cord measurements -does not automatically imply an optimised setup (see the corresponding spectrum in Fig. 3a), despite its maximum signal counts.
The two basic constraints, which our detection scheme fulfils, are to (i) allow the GNP-loaded subvolume to be anywhere along the scanning beam volume and (ii) exclude higher-order Compton scattered photons from the scanning pencil beam volume. The first constraint, aimed at maintaining a minimum dose level and time by requiring only a single exposure per scanning direction, rules out any collimators for which GNP position must be known a priori, as assumed e.g. in ref. 30 or our own previous work 31 . The second constraint is realised by using a set of molybdenum leaves, radially arranged around the beam, such that detected photons can only arise from within the scanning beam volume, effectively excluding higher-order Compton photons. The simulated X-ray beam is linearly polarised and chosen to be monochromatic, as would be expected from synchrotron or laser-driven sources -two principle sources that allow a sufficiently fast XFI-scanning time.
The solution to the "background problem" is to consider it as an optimisation problem. To that end, the entire cylindrical detector surface is divided into a set of pixels. For any given incident photon energy, our algorithm determines that subset of pixels whose sum spectrum exhibits the maximum statistical signal significance Z. The single spectrum of each pixel alone does not show a significant signal, hence the spectra of many pixels are added to a sum spectrum. Our algorithm discards those pixels with the largest yields from the adding to a sum spectrum until this sum spectrum shows a statistically significant signal. Once this signal is found, the algorithm then removes further pixels as long as the resulting significance of the remaining sum spectrum reaches a maximum. We have found that this algorithm proves to be robust for arbitrary locations of the gold-distributions inside the object. The sum spectrum of this optimal subset allows the detection of the desired small gold concentration of 0.23 wt%, i.e. 1.2 μg, with a minimum statistical significance limit of Z = 3. We have tested our algorithm with many different incident photon energies and have found that 85 keV delivers the maximum significance Z over all other incident energies. This finding of optimum incident photon energy close to the K-edge energy of gold can be understood in terms of our optimisation solution: the smaller the difference between incident photon energy and the K-edge, the more dominant is single Compton scattering, while higher order Compton scattering becomes more important at higher incident energies. The background of single Compton scattering exhibits the highest degree of anisotropy, which is the basis for the solution presented here. Thus, at higher incident energies, higher Compton order scattering leads to a less and less anisotropic background, precluding the presented spatial filtering. In (a) no spatial filtering is applied, while (b) shows spatial filtering exhibiting the highest overall signal significance with the optimum of 85 keV incident energy, using spherical detector coordinates. One can also see the influence of linear polarisation in the azimuthal angle Φ (Φ and cos(Θ) are given with respect to the beam direction). Note that the colour scale varies from (a) to (b) by almost three orders of magnitude, with the total entries reduced by a factor of 570. A white colour means "discarded pixel", i.e. such a pixel is removed from contributing to the sum spectrum.  Figure 4b shows the result of our solution for a polarised X-ray source. If one would use an unpolarised source, the "wave-like" pattern would be transformed into Φ-independent vertical columns. However, we have simulated both cases and have seen that Z pol = 13.62( ± 0.22) and Z unpol = 13.66 ± (0.33).
In order to decrease radiation dose and exposure time, our scheme does not require a full CT because particle localisation can simply be inferred from the intersections of two, e.g. orthogonal, scanning pencil beams (if both indicate a signal). Furthermore, (projection) absorption images along these two directions can be obtained without further exposure.

Validation of background photon distribution.
In order to experimentally validate the above solution, which is particularly based on the anisotropic distribution of the scattered photons, we have measured the flux of these background photons emitted from a 30-cm-diameter cylindrical phantom. In addition, for studying the effect of finite bandwidths, we utilised an industrial X-ray tube source with beam collimators and filters, delivering a pencil beam with 3 mm diameter, average photon energy of 90 keV, and 24% Full-Width-at-Half-Maximum (FWHM) bandwidth. Figure 5 shows measured and simulated photon counts for various detection angles, as well as the comparison with estimates from a simplified mathematical model described below, exhibiting clear overall agreement. In order to validate our claim also with a monochromatic and polarised source, we have performed the same angular scan at a DESY-synchrotron-beamline with 82.8 keV photons. Figure 6 shows the comparison between the measured counts of photons in the signal region with the simulated ones, showing again a very good agreement.
This simplified model is able to explain the angular distribution of the anisotropic Compton-background and is based upon the assumption that most of the photons that are detected by any pixel have taken the shortest path from the entry point to a scatter position z along the incident beam direction and from there directly to the detector pixel. The model thus adds up the yields from all scattering positions along the beam direction. For each scatter position z we have used the (weak) angular dependence a(z) of Compton scattering, but neglect any energy-variation due to scattering. Furthermore, for each position z we take the fraction f(z) of the pixel's solid angle and the projection p(z) of its area with respect to that position into account, as well as the total transmission T(z) over such shortest paths. For the polychromatic source the mean photon energy was used. We then simply sum up all contributions y(z) over all z-positions to the total yield Y of a given pixel and plot the result versus detector angle. Note that all mentioned functions vary only with the scatter position z: , with µ being the (incident energy dependent) linear attenuation coefficient and z 0 the entry position along the beam direction. Note that one could use also the energy dependence for the attenuation coefficient, but its variation is relatively small, which is also the case for the angular dependence and pixel area projection. As it turns out, only T(z) and f(z) vary strongly with z. Since the agreement with both experiments (polychromatic unpolarised X-ray tube source vs monochromatic polarised synchrotron radiation) and corresponding simulations is convincing (s. Figs 5 and 6), it seems as if the underlying principle of this simplified Figure 5. Comparison between measured, simulated, and analytically derived Compton peak heights for an unpolarised X-ray source and the 30cm-diameter phantom. Varying the detection angle Θ (same Θ as in Fig. 4) shows good agreement of the Compton-peak heights of the experiment (red), simulation (blue), and mathematical model (black). Note the logarithmic scale over more than two orders of magnitude. model reflects indeed the basic reason for the found angular distribution of the anisotropic Compton-background, namely the interplay between total path attenuation and relative solid angle which both lead to strong background yields for large detection angles, but "suppress" the yield for forward-angles. In order to also demonstrate a concrete XFI-measurement with the large 30cm-diamater phantom, we have drilled a vertical hole into the centre of it for placing a high-Z material solution in it. Since we only had a single detector (so to speak only one pixel) available with a correspondingly small effective solid angle, the concentration of the solution must be relatively large to keep measurement times low. Therefore, instead of gold solutions, we have used a Gadolinium-solution with a concentration of 78 mg/ml, which was placed within a 3 mm Eppendorf tube. Fig. 7 shows a direct comparison of the measured and simulated spectrum around the Gd-signal region. The agreement is quite convincing, when keeping in mind that both data sets are not scaled to each other. The (constant) difference between both by about 14% can be mainly attributed to the uncertainty in the measured incoming photon flux (determined by using a photo diode).
Although fluorescence is a non-resonant excitation process, our spatial filtering scheme shows an energy dependence, because the optimum "map" (s. e.g. Fig. 4b) varies slightly with energy, hence one can expect a limit Figure 6. Comparison between measured, simulated, and analytically derived background photon counts in the Gold-signal region for a polarised synchrotron source and the 30cm-diameter phantom. Like in Fig. 5, also here is a good agreement of the photon counts in the signal region when experimental data (red) are compared with simulation (blue), and mathematical model (black). for the bandwidth of the incident X-ray beam. Further simulations revealed a critical X-ray bandwidth of about 15% FWHM, above which the significance Z starts decreasing (by more than 10%). In addition, we have shown that when using the filtered spectrum of the conventional X-ray source, which was used for the data in Fig. 5, the significance Z drops only to 50% of the value for the (simulated) monochromatic case. Hence, our method does not require strictly monochromatic X-ray sources, but depends on sources that deliver synchrotron-like pencil beams.

Translation into clinical application.
While pilot studies at large-scale synchrotron facilities are helpful in developing XFI-technology towards scanning of human patients, their sheer size and costs preclude clinical applications. One pathway for translating our XFI-method into clinics is to use compact, laser-based, brilliant X-ray sources [16][17][18][19] . Here, electrons with relativistic energies oscillate in the field of a counter-propagating laser-pulse. Due to the relativistic energies, the X-ray emission is confined to small forward angles, hence allowing effective collimation for scanning pencil beams 32 . This collimation, together with the periodic oscillation of the electrons in the laser field, keeps the resulting bandwidths in the above-mentioned limit. The time needed per scanning direction is fully determined by two factors: (i) the number of photons per second that the used X-ray source can generate within a pencil beam solid angle and (ii) the number of photons per second that the used detector can handle. Synchrotrons can easily produce more than the required 10 9 photons/ sec/mrad 2 per scanning direction. Our used Amptek detector can handle an input count rate of about 50 kHz. For measurements where the X-ray beam flux was originally too large, we have used attenuators in the beamline. However, note that the larger the object the smaller the solid angle of each detector and the less restriction from the detector count rate. Our solution to the background problem requires a large area pixelated detector which could be simply realized by an arrangement of many independent detectors of the kind as used in our experiment.

Discussion
In the present work, unprecedented gains in target tissue penetration and detection sensitivity, as well as the ability to precisely and rapidly interrogate disease-bearing tissues utilizing low-dose, molecularly-targeted GNPs, are distinct advantages offered by our novel XFI scheme for human-sized objects. Other XFI-schemes, which are either preferring measurements in certain small angle ranges and/or applying collimators with restricted fields of view on only parts of the entire beam volume, cannot present a low-dose solution to the intrinsic "background problem", while our spatial filtering opens the path for the background suppression factor demanded for bringing small-animal results from tumour-diagnostics onto size-scales of future human applications. Our optimisation approach is well-justified by experiments as well as by simulations and an analytical model. Furthermore, for a future utilisation as next-generation tool for monitoring in vivo pharmacokinetics, whereby the distribution of medical drugs to which GNPs are bound can be serially imaged, we have also studied the scaling of XFI with spatial resolution. Here, in contrast to the above-mentioned early small-tumour detection, the spatial resolution can be lowered, e.g. to a 1-cm-diameter sphere. In this case, the scaling of XFI-sensitivity, for the same physical dose and statistical signal significance, predicts that the minimum detectable GNP-mass inside a 1-cm-target-sphere is just 12 µg, while above it is 1.2 µg inside the 1-mm-target-sphere (both embedded in a 30-cm-diameter object), thus lowering the minimum detectable GNP-concentration by a factor of 100.
Outlook. More than 50% of all cancer patients receive radiotherapy (RT) during their treatment regimen 33 .
Despite advances in external beam RT that optimise dose delivery by e.g. beam shaping and real-time imaging, image-guided attenuation of therapy 34 for treating early stage cancers and tumour recurrence 35 , a significant number of patients experience relapse, metastases, and/or significant toxicities to normal tissue 36 . Such unfavourable outcomes underscore a critical need for new probe-device combinations that can overcome these limitations, e.g. by enhancing RT dose to tumour while sparing normal tissues 37,38 . The use of targeted high-atomic number radiosensitising materials, such as the GNPs, has served as a promising solution for further increasing RT efficacy 39 . Particles, initially adapted as cancer-specific imaging probes, localise to and accumulate within tissue targets of interest -and they can be further exploited as imaging agents for image-guided X-ray RT of the target site as they boost local dose deposition to target tumour volumes 40 . Hence, GNP-based XFI would allow for combining diagnostics and therapy with one and the same device.
As a further step on the path of GNP-technology research, newer generation (i.e., sub 10-nm diameter) GNPs 41 will be functionalised with tumour-targeting moieties and contrast labels to create molecularly-targeted cancer imaging probes, as in prior human clinical trials using fluorescent core-shell silica nanoparticles, referred to as Cornell dots, or simply C dots 42 . These "target-or-clear" sub-10 nm inorganic particle probes exhibit hallmarks of ideal diagnostic probes. Recent studies have shown that GNPs, ranging from 2 to 15 nm in diameter, penetrate and localise within cancer cells, multicellular spheroids, and in vivo tumours in a size-dependent manner 43 . Further, careful tuning of surface ligand and PEG chain densities to maintain sub-10 nm sizes has led to favourable in vivo biological profiles and radiation dosimetry 44 , paving the way for product translation in both surgical 45 and other oncological settings.
XFI can also be applied to other high-atomic number atoms, e.g. another future application of our XFI-method could be in vivo measuring of Gadolinium(Gd)-retention in human brains and bones from using Gd as a contrast agent in MRI-applications. First estimates, assuming a homogeneous distribution, reveal a sensitivity of about 1 µg per gram (brain/bone) tissue. The main difference between XFI of Gd versus GNP is the lower atomic number and K-shell excitation energy. A similar application could be pharmacokinetic studies for Platinum-based chemotherapeutics (e.g. Cisplatin) and also here we reach the same sensitivity as in the Gd-retention case.
Summing up, for early diagnostic evaluations, including the possibility of higher resolution pharmacokinetic assessments, our spatial filtering scheme presents a low-dose solution to the "background problem" with high spatial resolution for large objects. This solution is validated by experiments and explained by a simplified

Methods
Experimental Design. L1 peptides. A peptide derived from the third fibronectin type III domain of murine L1 with a lysine linker and a cysteine for coupling at the N-terminus was purchased from Schafer-N (Copenhagen, Denmark) and had the following sequence: H-CKKKKKPELEDITIFNSSTVLVRWRPVD-OH (L1-N-Lys). Poly(ethylene glycol) methyl ether with an average M w ~ 2000 g mol −1 was purchased from Fluka. All other chemicals and solvents (analytical grade) were ordered from Sigma-Aldrich (Taufkirchen, Germany). Ultrapure water (Millipore, Darmstadt, Germany) was used for all procedures.
GNPs. The ligand a-methoxypoly(ethylene glycol)-w-(11-mercaptoundecanoate) (PEGMUA, M ~ 2000 g/mol) was synthesized. GNPs were synthesized by a seeded growth method; seed particles were synthesized by an optimized Turkevich protocol. GNP40s had a diameter of 37.7( ± 3.5) nm and a concentration of 0.3 nM. GNP30s had a diameter of 31.2( ± 2.0) nm and a concentration of 0.5 nM. GNP40s had a diameter of 37.7( ± 3.5) nm and a concentration of 0.3 nM. The as-synthesized GNPs were stabilized by citrate, which can be easily exchanged by thiols. Spinal cord compression injury and tissue preparation for XFI. Spinal cord compression injury was performed as described in ref. 25 using three-month-old female C57BL/6 J mice. Following intraperitoneal anesthesia with ketamin and xylazin (100 mg Ketanest, Parke-Davis/Pfizer, Karlsruhe, Germany, and 5 mg Rompun, Bayer, Leverkusen, Germany, per kg body weight), laminectomy at the T7-T9 spinal cord level was performed using a mouse spinal cord compression device to elicit compression force. The compression duration was controlled by an electromagnetic device: the spinal cord was maximally compressed for 1 second by a time-controlled current flow through the electromagnetic device. Two different concentrations of L1-functionalised and non-functionalised nanoparticles in a volume of 1-2 µl were then applied via a very thin pulled-out single barrel microfilament (outside diameter <500 µm, inside diameter <300 µm, AM Systems) into the spinal cord, 0.5 mm proximal to the lesion site. This method leads to a minimal lesion injury due to the fine geometry of the microcapillary. Muscles and skin were then closed using 6-10 nylon stitches (Ethicon, Norderstedt, Germany). After surgery, mice were kept on a heated pad (37 °C) for 24-48 hours to prevent hypothermia. Injured mice were then intraperitoneally anesthetized with sodium pentobarbital (Narcoren, Merial, Hallbergmoos, Germany, 5 µl/g body weight) and transcardially perfused with 4% formaldehyde in PBS buffer. The spinal cords were isolated and post-fixed overnight at 4 °C. The tissue was then immersed in a lubricating balsam (Bayer) and subjected to XFI.

Synchrotron-based XFI-experiments. XFI experiments of the spinal cords were performed at the
Bio-imaging and Diffraction beamline P11 at DESY's highly brilliant X-ray source PETRA III. The instrument provides linearly polarized photons tunable from 5.5 to 30 keV. Using KB mirrors, the monochromatic X-ray beam can be focused from (300·300) µm 2 down to a size of (4·9) µm 2 at the sample position (v × h, FWHM) with full flux from the source in the focal spot (2·10 13 ph/s at 12 keV). To reach optimal detector dead time aluminium filters were used for flux reduction up to 0.006%. For restricting the scanning time we have chosen 0.2 mm diameter aperture for our measurements. The used Vortex-EM (Hitachi) detector is mounted perpendicular to the incident photon beam and its energy resolution is about 100 eV (rms) around the fluorescence lines. For the reconstruction of gold masses in spinal cords, a silicon waver with a (20.8 ± 0.8) nm sputtered gold layer was used as a reference target. Measured spectra were normalized by this reference and corrected by the transmission factors of the spinal cord geometry, which was approximated by a cylinder having a length of 10 mm and a radius of 1 mm. Taking inbound and outbound transmission properties into account, the optimum incident photon energy was found to be 15 keV. Gaussian peaks were used to fit background and gold fluorescence peaks. For the Compton tail, an exponential function was used. Gold nanoparticle concentrations were determined by inductively coupled plasma mass spectrometry (ICP-MS) on a 7700x instrument (Agilent Technologies, Santa Clara, CA, USA). Standard solutions were prepared from a 1 g/l gold stock solution (Merck Millipore, Billerica, MA, USA). The method detection limit was determined with 1 ng/l. It should be noted that while ICP-MS probes the total GNP-mass per spinal cord, it does not provide any spatial information. The error bars in Fig. 2 are the statistical variation from three consecutive measurements of the same probe.
Simulation tools. For the extrapolation onto human-sized phantoms we used simulations with the simulation toolkit GEANT4 46 . A "soft tissue" sphere with a diameter of 30 cm consisting of a GEANT4 material called "G4_ TISSUE_SOFT_ICRP" (Geant4 User's Guide for Application Developers Geant4 Collaboration Version: geant4 10.0, 6 December 2013) was considered.
The assumed detector resolution of σ det = 200 eV (rms) was chosen close to the value of a real detector, that is, from the Amptek XR-100T-CdTe detector, whose resolution at 60 keV is 255 eV (rms). Note that the significance Z scales inversely with the square root of the detector resolution (i.e. a resolution of 255 eV instead of 200 eV lowers Z by 13%).
The radial collimator leaves started at a radius R = 30 cm, ended at R = 60 cm, and extended axially along the entire detector. The detector had a radius of 60 cm and a length of 1.60 m. The need for a collimator was met before we found out the optimum incident photon energy to be close to the K-edge. Thus, the vast majority of background photons in the signal region are Compton1(!)-photons, for which the collimator has no effect. Using a collimator is still useful to reduce the detector input count rate from multiply-Compton-scatted photons.
Validation experiments. We used an YXLON X-ray tube, model MG160, operated with 100 kV voltage, 20 mA current, and "N150"-filters (consisting of 4 mm aluminium and 2.5 mm tin). The pencil beam geometry was realised by a collimator with diameter of 3 mm and 30 mm length. The phantom was a cylinder made out of PMMA, with diameter of 30 cm and a height of 6 cm. We used the XR-100T-CdTe detector from Amptek, which was positioned at various angle positions directly on the phantom's surface. Note that the simulation used the same number of incident photons as in the experiment and that we incorporated the detector geometry and the corresponding acceptance solid angle into the simulation. The synchrotron validation experiments were performed at the DESY P07 beamline, which satisfies high energy x-ray diffraction (XRD) and imaging techniques. It is tunable in the range 30 to 200 keV and optimised for micrometre focusing with Compound Refractive Lenses (CRLs).
For the experiments we have chosen 4·10 8 ph/s at 82.8 keV within a pencil beam of (100·100) µm 2 and horizontal polarisation. The Gadolinium solution had a concentration of 78 mg/ml and was placed within a 3 mm Eppendorf tube, embedded in the 30cm-diameter phantom. Also here we have used the Amptek-detector.
In order to correct the CdTe-detector signals for the so-called hole-tailing effect, we have calibrated the detector with a series of different radioactive source covering a wide range of incident photon energies, as well as two dedicated experiments at the DESY-synchrotron, one using a direct (strongly attenuated) beam on the detector, whereby the energies are tuned in a wide range, and another one with fixed beamline energy, but different thin scatter foils of different (high-Z) materials, hence tuning the incident energy by making use of the different energies of the singly-Compton-scattered photons. With these data we have studied the parameters for mathematical functions that "smear" out the simulated raw data (with an ideal detector) into data for the realistic detector. Since today there is no large area CdTe-detector available, it is clear that so far we can only move our single detector through the full 4π solid angle, thus mimicking the situation once such a large area detector version is available. The simplest technical solution would be to place many single detectors next to each other. Statistical Analysis. As the signals in the experiments and simulations consisted of two fluorescence peaks, we decided to use Significance (Z) as a measurement of signal quality instead of the usual Signal-to-Noise ratio. This significance Z is calculated from the p-value (probability that the measured level above background is not just a fluctuation), using the number of signal photons of both fluorescence peaks and the number of background photons in a region of ± 3σ det around the peaks, all numbers derived from Gaussian fits. Typically, Z is given in units of a standard deviation σ (sigma) of a normal distribution. A significance level of 3σ (i.e. 99.73%) was chosen to be the minimum signal strength.

Data Availability
All raw and processed data generated in this work, including the data for the figures provided in the manuscript, are available from the corresponding author on reasonable request.