Phase retrieval through a one-dimensional ptychographic engine.

Ptychographic techniques are currently the subject of increasing scientific interest due to their capability to retrieve the complex transmission function of an object at very high resolution. However, they impose a substantial burden in terms of acquisition time and dimension of the scanned area, which limits the range of samples that can be studied. We have developed a new method that combines the ptychographic approach in one direction with Fresnel propagation in the other by employing a strongly asymmetric probe. This enables scanning the sample in one direction only, substantially reducing exposure times while covering a large field of view. This approach sacrifices ptychographic-related resolution in one direction, but removes any limitation on the probe dimension in the direction orthogonal to the scanning, enabling the scan of relatively large objects without compromising exposure times.

Characterization of Surfactant Spheroidal Micelle Structure for Pharmaceutical Applications: A Novel Analytical Framework.

We introduce an innovative theoretical framework tailored for the analysis of Pair Distribution Function (PDF) data derived from Small-Angle X-ray Scattering (SAXS) measurements of core-shell micelles. The new approach involves the exploitation of the first derivative of the PDF and the derivation of analytical equations to solve the core-shell micelle structure under the hypothesis of a spheroidal shape. These analytical equations enable us to determine the micelle's aggregation number, degree of ellipticity, and contrast in electron density between the core-shell and shell-buffer regions after having determined the whole micelle size and its shell size from the analysis of the first derivative of the PDF. We have formulated an overdetermined system of analytical equations based on the unknowns that characterize the micelle structure. This allows us to establish a Figure of Merit, which is utilized to identify the most reliable solution within the system of equations.

Small Angle X-Ray Scattering Data Analysis and Theoretical Modelling for the Size and Shape Characterization of Drug Delivery Systems Based on Vitamin E TPGS Micelles.

We developed a simple two-dimensional/two-components theoretical model that describes the structure and functionality of a VitE-TPGS system of micelles assuming a hydrophobic inner core and an outer hydrated hydrophilic shell. We then conceptually applied the developed methodology to a simple system of VitE-TPGS micelles unloaded and loaded with an active pharmaceutical ingredient, eltrombopag, to verify if the model could reliably monitor the size change of the micelle upon loading. The fit of laboratory Small Angle X-Ray Scattering data against such model allows us to extract absolute values of the micelles size under a spherical shape hypothesis as well as the distribution within the system between components and level of hydration. The intensity scale of the SAXS experimental data needs to be normalized to a reference standard (pure water) to get absolute scattered intensities. The mathematical model which has been developed under a general hypothesis of ellipsoidal micelles, is applied to our experimental data under the simplified spherical assumption, which suitably fits our experimental data.

Travelling through the Natural Hierarchies of Type I Collagen with X-rays: From Tendons of Cattle, Horses, Sheep and Pigs.

Type I collagen physiological scaffold for tissue regeneration is considered one of the widely used biomaterials for tissue engineering and medical applications. It is hierarchically organized: five laterally staggered molecules are packed within fibrils, arranged into fascicles and bundles. The structural organization is correlated to the direction and intensity of the forces which can be loaded onto the tissue. For a tissue-specific regeneration, the required macro- and microstructure of a suitable biomaterial has been largely investigated. Conversely, the function of multiscale structural integrity has been much less explored but is crucial for scaffold design and application. In this work, collagen was extracted from different animal sources with protocols that alter its structure. Collagen of tendon shreds excised from cattle, horse, sheep and pig was structurally investigated by wide- and small-angle X-ray scattering techniques, at both molecular and supramolecular scales, and thermo-mechanically with thermal and load-bearing tests. Tendons were selected because of their resistance to chemical degradation and mechanical stresses. The multiscale structural integrity of tendons' collagen was studied in relation to the animal source, anatomic location and source for collagen extraction.

Raman, WAXS, and Solid-State NMR Characterizations of Regenerated Silk Fibroin Using Lanthanide Ions as Chaotropic Agents.

Bombyx mori silk fibroin (SF) has been reported as a convenient natural material for regenerative medicine, optoelectronics, and many other technological applications. SF owes its unique features to the hierarchical organization of the fibers. Many efforts have been made to set up protocols for dissolution since many applications of SF are based on regenerated solutions and fibers, but chaotropic conditions required to disassemble the packing of the polymer afford solutions with poor crystalline behavior. Our previous research has disclosed a dissolution and regeneration process of highly crystalline fibers involving lanthanide ions as chaotropic agents, demonstrating that each lanthanide has its own unique interaction with SF. Herein, we report elucidation of the structure of Ln-SF fibers by the combined use of Raman spectroscopy, wide-angle X-ray scattering (WAXS), and solid-state NMR techniques. Raman spectra confirmed the coordination of metal ions to SF, WAXS results highlighted the crystalline content of fibers, and solid-state NMR enabled the assessment of different ratios of secondary structures in the protein.

Why a Diffusing Single-Molecule can be Detected in Few Minutes by a Large Capturing Bioelectronic Interface.

Single-molecule detection at a nanometric interface in a femtomolar solution, can take weeks as the encounter rate between the diffusing molecule to be detected and the transducing nanodevice is negligibly small. On the other hand, several experiments prove that macroscopic label-free sensors based on field-effect-transistors, engaging micrometric or millimetric detecting interfaces are capable to assay a single-molecule in a large volume within few minutes. The present work demonstrates why at least a single molecule out of a few diffusing in a 100 µL volume has a high probability to hit a large capturing and detecting electronic interface. To this end, sensing data, measured with an electrolyte-gated FET whose gate is functionalized with 1012 capturing anti-immunoglobulin G, are here provided along with a Brownian diffusion-based modeling. The EG-FET assays solutions down to some tens of zM in concentrations with volumes ranging from 25 µL to 1 mL in which the functionalized gates are incubated for times ranging from 30 s to 20 min. The high level of accordance between the experimental data and a model based on the Einstein's diffusion-theory proves how the single-molecule detection process at large-capturing interfaces is controlled by Brownian diffusion and yet is highly probable and fast.

Deconvolution by finite-size-source effects of x-ray phase-contrast images.

PURPOSE: In the hard x-ray region, the cross sections for the phase shift of low-Z elements are about 1000 times larger than the absorption ones. As a consequence, phase contrast is detectable even when absorption contrast is minimal or absent. Therefore, phase-contrast imaging could become a valid alternative to absorption contrast without delivering high dose to tissue/human body parts. METHODS: To enhance the quality of phase-contrast images without increasing the dose, a possible approach could be the partial deconvolution of the finite source size effects by experimental phase-contrast images. The deconvolution procedure, the authors propose, employs the acquisition of two images on a suitable well-known test sample, one in contact and the other in phase-contrast conditions. Both acquired images are used along with a simulated phase-contrast image (obtained from the test sample in ideal conditions of pointlike source illumination) to correctly retrieve the experimental source distribution function. This information allows a generic experimental phase-contrast image, acquired in the same conditions, to be partially deconvolved by finite source size effects. RESULTS: The performed experimental tests indicate that deconvolved images are equivalent to those which would be obtained with a source 40% smaller than the actual size. In turn, this finding is equivalent to an increase of the "effective" lateral spatial coherence length. The corresponding quality improvement of the phase-contrast imaging is directly deducible by the presence of many Fresnel fringes, much better visible with respect to the original experimental phase-contrast images. CONCLUSIONS: The use of a test standard sample, always possible in every experimental setup, to partially deconvolve the finite-size-source blurring effects shows that higher quality phase-contrast images could be readily available, making easier diagnoses and tissue/sample analyses. The method could give, in the future, the possibility to further lower the delivered dose to patients, organs, and tissues when compact room-sized and brilliant microfocus x-ray sources will be available for clinical applications in hospitals.

Time scale of glycation in collagen of bovine pericardium-derived bio-tissues.

Glycosyl-ation is the process of combining one or more glucose molecules (or other monosaccharides) with molecules of a different nature (which are therefore glycosyl-ated). In biochemistry, glycosyl-ation is catalyzed by several specific enzymes, and assumes considerable importance since it occurs mainly at the expense of proteins and phospho-lipids which are thus transformed into glycoproteins and glycolipids. Conversely, in diabetes and aging, glycation of proteins is a phenomenon of non-enzymatic nature and thus not easily controlled. Glycation of collagen distorts its structure, renders the extracellular matrix stiff and brittle and at the same time lowers the degradation susceptibility thereby preventing renewal. Based on models detailed in this paper and with parameters determined from experimental data, we describe the glycation of type 1 collagen in bovine pericardium derived bio-tissues, upon incubation in glucose and ribose. With arginine and lysine/hy-droxy-lysine amino acids as the primary sites of glycation and assuming that the topological polar surface area of the sugar molecules determines the glycation rates, we modelled the glycation as a function of time and determined the glycation rate and thus the progression of glycation as well as the resulting volume increase.

Decellularized pericardium tissues at increasing glucose, galactose and ribose concentrations and at different time points studied using scanning X-ray microscopy.

Diseases like widespread diabetes or rare galactosemia may lead to high sugar concentrations in the human body, thereby promoting the formation of glycoconjugates. Glycation of collagen, i.e. the formation of glucose bridges, is nonenzymatic and therefore cannot be prevented in any other way than keeping the sugar level low. It relates to secondary diseases, abundantly occurring in aging populations and diabetics. However, little is known about the effects of glycation of collagen on the molecular level. We studied in vitro the effect of glycation, with d-glucose and d-galactose as well as d-ribose, on the structure of type 1 collagen by preparing decellularized matrices of bovine pericardia soaked in different sugar solutions, at increasing concentrations (0, 2.5, 5, 10, 20 and 40 mg ml-1), and incubated at 37°C for 3, 14, 30 and 90 days. The tissue samples were analyzed with small- and wide-angle X-ray scattering in scanning mode. We found that glucose and galactose produce similar changes in collagen, i.e. they mainly affect the lateral packing between macromolecules. However, ribose is much faster in glycation, provoking a larger effect on the lateral packing, but also seems to cause qualitatively different effects on the collagen structure.

Analysis of tapered front-coupling X-ray waveguides.

The coupling and propagation of electromagnetic waves through planar X-ray waveguides (WG) with vacuum gap and Si claddings are analyzed in detail, starting from the source and ending at the detector. The general case of linearly tapered WGs (i.e. with the entrance aperture different from the exit one) is considered. Different kinds of sources, i.e. synchrotron radiation and laboratory desk-top sources, have been considered, with the former providing a fully coherent incoming beam and the latter partially coherent beams. It is demonstrated that useful information about the parameters of the WG can be derived, comparing experimental results with computer simulation based on analytical solutions of the Helmholtz equation which take into account the amplitude and phase matching between the standing waves created in front of the WG, and the resonance modes propagating into the WG.

Combined mixed approach algorithm for in-line phase-contrast x-ray imaging.

PURPOSE: In the past decade, phase-contrast imaging (PCI) has been applied to study different kinds of tissues and human body parts, with an increased improvement of the image quality with respect to simple absorption radiography. A technique closely related to PCI is phase-retrieval imaging (PRI). Indeed, PCI is an imaging modality thought to enhance the total contrast of the images through the phase shift introduced by the object (human body part); PRI is a mathematical technique to extract the quantitative phase-shift map from PCI. A new phase-retrieval algorithm for the in-line phase-contrast x-ray imaging is here proposed. METHODS: The proposed algorithm is based on a mixed transfer-function and transport-of-intensity approach (MA) and it requires, at most, an initial approximate estimate of the average phase shift introduced by the object as prior knowledge. The accuracy in the initial estimate determines the convergence speed of the algorithm. The proposed algorithm retrieves both the object phase and its complex conjugate in a combined MA (CMA). RESULTS: Although slightly less computationally effective with respect to other mixed-approach algorithms, as two phases have to be retrieved, the results obtained by the CMA on simulated data have shown that the obtained reconstructed phase maps are characterized by particularly low normalized mean square errors. The authors have also tested the CMA on noisy experimental phase-contrast data obtained by a suitable weakly absorbing sample consisting of a grid of submillimetric nylon fibers as well as on a strongly absorbing object made of a 0.03 mm thick lead x-ray resolution star pattern. The CMA has shown a good efficiency in recovering phase information, also in presence of noisy data, characterized by peak-to-peak signal-to-noise ratios down to a few dBs, showing the possibility to enhance with phase radiography the signal-to-noise ratio for features in the submillimetric scale with respect to the attenuation-based imaging. CONCLUSIONS: It has been shown that phase-retrieved radiographies can be used both to have quantitative phase information about soft tissues, complementary to the attenuation information, and to enhance the visibility of details inside soft tissues, with higher efficiency with respect to phase radiography.

X-ray ptychographic mode of self-assembled CdSe/CdS octapod-shaped nanocrystals in thick polymers.

This work describes the application of X-ray ptychography for the inspection of complex assemblies of highly anisotropic nanocrystals embedded in a thick polymer matrix. More specifically, this case deals with CdSe/CdS octapods, with pod length L = 39 ± 2 nm and pod diameter D = 12 ± 2 nm, dispersed in free-standing thick films (24 ± 4 µm) of polymethyl methacrylate and polystyrene, with different molecular weights. Ptychography is the only imaging method available to date that can be used to study architectures made by these types of nanocrystals in thick polymeric films, as any other alternative direct method, such as scanning/transmission electron microscopy, can be definitively ruled out as a result of the large thickness of the free-standing films. The electron density maps of the investigated samples are reconstructed by combining iterative difference map algorithms and a maximum likelihood optimization algorithm. In addition, post image processing techniques are applied to both reduce noise and provide a better visualization of the material morphological details. Through this process, at a final resolution of 27 nm, the reconstructed maps allow us to visualize the intricate network of octapods inside the polymeric matrices.

Sub- and Supramolecular X-Ray Characterization of Engineered Tissues from Equine Tendon, Bovine Dermis, and Fish Skin Type-I Collagen.

Collagen represents one of the most widely used biomaterial for scaffolds fabrication in tissue engineering as it represents the mechanical support of natural tissues. It also provides physical scaffolding for cells and it influences their attachment, growth, and tissue regeneration. Among all fibrillary collagens, type I is considered one of the gold standard for scaffolds fabrication, thanks to its high biocompatibility, biodegradability, and hemostatic properties. It can be extracted by chemical and enzymatic protocols from several collagen-rich tissues, such as tendon and skin, of different animal species. Both the extraction processes and the manufacturing protocols for scaffolds fabrication provide structural and mechanical changes that can be tuned in order to deeply impact the properties of the final biomaterial. The aim of this review is to discuss the role of X-rays to study structural changes of type I collagen from fresh collagen-rich tissues (bovine, equine, fish) to the final scaffolds, with the aim to screen across available collagen sources and scaffolds fabrication protocols to be used in tissue regeneration.

A theoretical study on phase-contrast mammography with Thomson-scattering x-ray sources.

PURPOSE: The x-ray transmitted beam from any material/tissue depends on the complex refractive index (n= 1-delta+ibeta), where delta is responsible for the phase shift and beta is for the beam attenuation. Although for human tissues, the delta cross section is about 1000 times greater than the beta ones in the x-ray energy range from 10 to 150 keV, the gain in breast tumor visualization of phase-contrast mammography (PCM) with respect to absorption contact imaging (AI) is limited by the maximum dose that can be delivered to the patient. Moreover, in-line PC imaging (PCI) is the simplest experimental mode among all available x-ray PCI techniques since no optics are needed. The latter is a fundamental requirement in order to transfer the results of laboratory research into hospitals. Alternative to synchrotron radiation sources, the implementation of relativistic Thomson-scattering (TS) x-ray sources is particularly suitable for hospital use because of their high peak brightness within a relatively compact and affordable system. In this work, the possibility to realize PCM using a TS source in a hospital environment is studied, accounting for the effect of a finite deliverable dose on the PC visibility enhancement with respect to AI. METHODS: The contrast-to-noise ratio of tumor-tissue lesions in PCM has been studied on the bases of a recent theoretical model, describing image contrast formation by means of both wave-optical theory and the mutual coherence formalism. The latter is used to describe the evolution, during wave propagation, of the coherence of the wave field emitted by a TS source. The contrast-to-noise ratio for both PCI and AI has been analyzed in terms of tumor size, beam energy, detector, and source distances, studying optimal conditions for performing PCM. Regarding other relevant factors which could influence "tumor" visibility, the authors have assumed simplified conditions such as a spherical shape description of the tumor inclusion, a constant surrounding background, ideal conditions for the calculus of the contrast-to-noise ratio. RESULTS: The results show the possibility to enhance with PCI the signal-to-noise ratio for features in the submillimeter scale. This finding could give PCM a great advantage with respect to AI, opening the possibility to decrease the number of wrong diagnoses before histological exams. The results agree with experimental evidences obtained by Dreossi et al. [D. Dreossi et al., "The mammography project at the SYRMEP beamline," Eur. J. Radiol. 68, S58-S62 (2008)] with real PCM using synchrotron radiation. CONCLUSIONS: The challenging characteristics of TS sources, suitable for PCM, should be fluxes of at least 10(11) photons/s emitted by very small sources of about 10 microm, together with moderate energy spreads (less than 10%) in order to realize both sufficient spatial coherence and enough fluence on the patient, collecting images in reasonable exposure times. These fluxes will be achieved by next generation TS sources which are already under development.

Investigations of Processing-Induced Structural Changes in Horse Type-I Collagen at Sub and Supramolecular Levels.

The aim of this work is to evaluate the effects of different extraction and material processing protocols on the collagen structure and hierarchical organization of equine tendons. Wide and Small Angle X-ray Scattering investigations on raw powders and thin films revealed that not only the extraction and purification treatments, but also the processing conditions may affect the extent of the protein crystalline domain and induce a nanoscale "shield effect." This is due to the supramolecular fiber organization, which protects the atomic scale structure from the modifications that occur during fabrication protocols. Moreover, X-ray analyses and Fourier Transform Infrared spectroscopy performed on the biomaterial sheds light on the relationship between processing conditions, triple helical content and the organization in atomic and nanoscale domains. It was found that the mechanical homogenization of the slurry in acidic solution is a treatment that ensures a high content of super-organization of collagen into triple helices and a lower crystalline domain in the material. Finally, mechanical tensile tests were carried out, proving that the acidic solution is the condition which most enhances both mechanical stiffness and supramolecular fiber organization of the films.

In-line phase-contrast imaging for strong absorbing objects.

Phase-contrast imaging is one of the most important emerging x-ray imaging techniques. In this work we analyse, from a theoretical point of view, the in-line phase-contrast image formation under general assumptions. The approach is based on wave-optical theory (Fresnel/Kirchoff diffraction integrals) and on the formalism of the mutual coherence function for the evolution of the coherence wavefield properties. Our theoretical model can be applied to phase-contrast imaging realized both by using highly coherent synchrotron radiation and micro-focus x-ray laboratory sources. Thus, the model is suitable for widespread applications, ranging from material science to medical imaging of human body parts. However, it cannot be applied to polychromatic sources, although the validity of the model does not require particularly demanding characteristics of monochromaticity. In addition, for moderate phase gradients, a useful analytical formula of the phase-contrast visibility is derived, based on the a priori knowledge of source size and distance, pixel detector size, defocus distance, material/tissue dielectric susceptibility and characteristic scales of transversal and longitudinal non-uniformities of the material/tissue dielectric susceptibility. Comparisons both with experimental results published by other authors and with simulations based on a Fourier optics approach have been reported, to confirm the validity of the proposed analytical formula

The (Fo-Fc) Fourier synthesis: a probabilistic study.

(F(o)-F(c)) and (2F(o)-F(c)) Fourier syntheses are considered the most powerful tools for recovering the remainder of a structure and for correcting crystal structure models. A probabilistic approach has been applied to derive the formula for the variance for the expected value of the coefficient (F(o)-F(c)). This has allowed a better understanding of the features of the difference Fourier synthesis; in particular, a subset of well phased reflections has been separated from the subset of reflections best phased by the standard F(o) Fourier synthesis. An iterative procedure, based on the electron-density modification of the difference Fourier map, has been devised which aims to improve phase and modulus estimates of the reflections with higher variance value, by using as lever arm the set of reflections with lower variance value. The new procedure (DEDM) has been implemented and verified on a wide set of test structures, the partial models of which were obtained by molecular replacement or by automatic model-building routines applied to experimental electron-density maps. Phase and modulus estimates of the difference Fourier syntheses improve in all the test cases; as a consequence, the quality of the difference Fourier maps also improves in the region where the target structure deviates from the partial model. A new procedure is suggested, combining DEDM with standard electron-density modification techniques, which leads to significant reduction of the phase errors. The procedure may be considered a starting point for further developments.

Atomic resolution studies detect new biologic evidences on the Turin Shroud.

We performed reproducible atomic resolution Transmission Electron Microscopy and Wide Angle X-ray Scanning Microscopy experiments studying for the first time the nanoscale properties of a pristine fiber taken from the Turin Shroud. We found evidence of biologic nanoparticles of creatinine bounded with small nanoparticles of iron oxide. The kind, size and distribution of the iron oxide nanoparticles cannot be dye for painting but are ferrihydrate cores of ferritin. The consistent bound of ferritin iron to creatinine occurs in human organism in case of a severe polytrauma. Our results point out that at the nanoscale a scenario of violence is recorded in the funeral fabric and suggest an explanation for some contradictory results so far published.

Facing the phase problem in Coherent Diffractive Imaging via Memetic Algorithms.

Coherent Diffractive Imaging is a lensless technique that allows imaging of matter at a spatial resolution not limited by lens aberrations. This technique exploits the measured diffraction pattern of a coherent beam scattered by periodic and non-periodic objects to retrieve spatial information. The diffracted intensity, for weak-scattering objects, is proportional to the modulus of the Fourier Transform of the object scattering function. Any phase information, needed to retrieve its scattering function, has to be retrieved by means of suitable algorithms. Here we present a new approach, based on a memetic algorithm, i.e. a hybrid genetic algorithm, to face the phase problem, which exploits the synergy of deterministic and stochastic optimization methods. The new approach has been tested on simulated data and applied to the phasing of transmission electron microscopy coherent electron diffraction data of a SrTiO3 sample. We have been able to quantitatively retrieve the projected atomic potential, and also image the oxygen columns, which are not directly visible in the relevant high-resolution transmission electron microscopy images. Our approach proves to be a new powerful tool for the study of matter at atomic resolution and opens new perspectives in those applications in which effective phase retrieval is necessary.

Ptychographic Imaging of Branched Colloidal Nanocrystals Embedded in Free-Standing Thick Polystyrene Films.

Research on composite materials is facing, among others, the challenging task of incorporating nanocrystals, and their superstructures, in polymer matrices. Electron microscopy can typically image nanometre-scale structures embedded in thin polymer films, but not in films that are micron size thick. Here, X-ray Ptychography was used to visualize, with a resolution of a few tens of nanometers, how CdSe/CdS octapod-shaped nanocrystals self-assemble in polystyrene films of 24 ± 4 µm, providing a unique means for non-destructive investigation of nanoparticles distribution and organization in thick polymer films.