3D Algebraic Iterative Reconstruction for Cone-Beam X-Ray Differential Phase-Contrast Computed Tomography

Due to the potential of compact imaging systems with magnified spatial resolution and contrast, cone-beam x-ray differential phase-contrast computed tomography (DPC-CT) has attracted significant interest. The current proposed FDK reconstruction algorithm with the Hilbert imaginary filter will induce severe cone-beam artifacts when the cone-beam angle becomes large. In this paper, we propose an algebraic iterative reconstruction (AIR) method for cone-beam DPC-CT and report its experiment results. This approach considers the reconstruction process as the optimization of a discrete representation of the object function to satisfy a system of equations that describes the cone-beam DPC-CT imaging modality. Unlike the conventional iterative algorithms for absorption-based CT, it involves the derivative operation to the forward projections of the reconstructed intermediate image to take into account the differential nature of the DPC projections. This method is based on the algebraic reconstruction technique, reconstructs the image ray by ray, and is expected to provide better derivative estimates in iterations. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a mini-focus x-ray tube source. It is shown that the proposed method can reduce the cone-beam artifacts and performs better than FDK under large cone-beam angles. This algorithm is of interest for future cone-beam DPC-CT applications.     

New types of X-ray computed tomography (CT) with synchrotron radiation: fluorescent X-ray CT and phase-contrast X-ray CT using interferometer.

New types of X-ray computed tomography (CT), fluorescent X-ray CT and phase-contrast X-ray CT are being developed for biomedical research. While fluorescent scanning X-ray CT (FXCT) can detect specific contrast elements, or endogenous iodine, at very low content (less than 400 pg iodine of tissue in a volume of 8 x 10(-6) ml), the phase-contrast X-ray CT (PCCT) is a highly sensitive imaging technique to differentiate between different biological tissue types (based on their specific gravity variation) without the use of a contrast agent. Therefore, we can expect functional diagnosis with FXCT, and high contrast, high resolution biological imaging with PCCT. In this paper, a human thyroid gland imaged by FXCT, and a metastatic human cancerous lesion depicted using PCCT are presented. The latter method used a newly manufactured, large, monolithic, X-ray interferometer, which is described in this paper in detail.     

Imaging Liver Lesions Using Grating-Based Phase-Contrast Computed Tomography with Bi-Lateral Filter Post-Processing

X-ray phase-contrast imaging shows improved soft-tissue contrast compared to standard absorption-based X-ray imaging. Especially the grating-based method seems to be one promising candidate for clinical implementation due to its extendibility to standard laboratory X-ray sources. Therefore the purpose of our study was to evaluate the potential of grating-based phase-contrast computed tomography in combination with a novel bi-lateral denoising method for imaging of focal liver lesions in an ex vivo feasibility study. Our study shows that grating-based phase-contrast CT (PCCT) significantly increases the soft-tissue contrast in the ex vivo liver specimens. Combining the information of both signals – absorption and phase-contrast – the bi-lateral filtering leads to an improvement of lesion detectability and higher contrast-to-noise ratios. The normal and the pathological tissue can be clearly delineated and even internal structures of the pathological tissue can be visualized, being invisible in the absorption-based CT alone. Histopathology confirmed the presence of the corresponding findings in the analyzed tissue. The results give strong evidence for a sufficiently high contrast for different liver lesions using non-contrast-enhanced PCCT. Thus, ex vivo imaging of liver lesions is possible with a polychromatic X-ray source and at a spatial resolution of ∼100 µm. The post-processing with the novel bi-lateral denoising method improves the image quality by combining the information from the absorption and the phase-contrast images.     

Hybrid framework for feasible modeling of an edge illumination X-ray phase-contrast imaging system at a human scale

Here, we present a hybrid approach for simulating an edge illumination X-ray phase-contrast imaging (EIXPCi) set-up using graphics processor units (GPU) with a high degree of accuracy. In this study, the applicability of pixel, mesh and non-uniform rational B-splines (NURBS) objects to carry out realistic maps of X-ray phase-contrast distribution at a human scale is accounted for by using numerical anthropomorphic phantoms and a very fast and robust simulation framework which integrates total interaction probabilities along selected X-ray paths. We exploit the mathematical and algorithmic properties of NURBS and describe how to represent human scale phantoms in an edge illumination X-ray phase-contrast model. The presented implementation allows the modeling of a variety of physical interactions of x-rays with different mathematically described objects and the recording of quantities, e.g. path integrals, interaction sites and deposited energies. Furthermore, our efficient, scalable and optimized hybrid Monte Carlo and ray-tracing projector can be used in iterative reconstruction algorithms on multi GPU heterogeneous systems. The preliminary results of our innovative approach show the fine performance of an edge illumination X-ray phase-contrast medical imaging system on various human-like soft tissues with noticeably reduced computation time. Our approach to the EIXPCi modeling confirms that building a true imaging system at a human scale should be possible and the simulations presented here aim at its future development.     

Atherosclerotic plaque imaging using phase-contrast X-ray computed tomography

Reliable, noninvasive imaging modalities to characterize plaque components are clinically desirable for detecting unstable coronary plaques, which cause acute coronary syndrome. Although recent clinical developments in computed tomography (CT) have enabled the visualization of luminal narrowing and calcified plaques in coronary arteries, the identification of noncalcified plaque components remains difficult. Phase-contrast X-ray CT imaging has great potentials to reveal the structures inside biological soft tissues, because its sensitivity to light elements is almost 1,000 times greater than that of absorption-contrast X-ray imaging. Moreover, a specific mass density of tissue can be estimated using phase-contrast X-ray CT. Ex vivo phase-contrast X-ray CT was performed using a synchrotron radiation source (SPring-8, Japan) to investigate atherosclerotic plaque components of apolipoprotein E-deficient mice. Samples were also histologically analyzed. Phase-contrast X-ray CT at a spatial resolution of 10-20 mum revealed atherosclerotic plaque components easily, and thin fibrous caps were detected. The specific mass densities of these plaque components were quantitatively estimated. The mass density of lipid area was significantly lower (1.011 +/- 0.001766 g/ml) than that of smooth muscle area or collagen area (1.057 +/- 0.001407 and 1.080 +/- 0.001794 g/ml, respectively). Moreover, the three-dimensional assessment of plaques could provide their anatomical information. Phase-contrast X-ray CT can estimate the tissue mass density of atherosclerotic plaques and detect lipid-rich areas. It can be a promising noninvasive technique for the investigation of plaque components and detection of unstable coronary plaques.     

Visualizing Typical Features of Breast Fibroadenomas Using Phase-Contrast CT: An Ex-Vivo Study

Background

Fibroadenoma is the most common benign solid breast lesion type and a very common cause for histologic assessment. To justify a conservative therapy, a highly specific discrimination between fibroadenomas and other breast lesions is crucial. Phase-contrast imaging offers improved soft-tissue contrast and differentiability of fine structures combined with the potential of 3-dimensional imaging. In this study we assessed the potential of grating-based phase-contrast CT imaging for visualizing diagnostically relevant features of fibroadenomas.

Materials and Methods

Grating-based phase-contrast CT was performed on six ex-vivo formalin-fixed breast specimens containing a fibroadenoma and three samples containing benign changes that resemble fibroadenomas using Talbot Lau interferometry and a polychromatic X-ray source. Phase-contrast and simultaneously acquired absorption-based 3D-datasets were manually matched with corresponding histological slices. The visibility of diagnostically valuable features was assessed in comparison with histology as the gold-standard.

Results

In all cases, matching of grating-based phase-contrast CT images and histology was successfully completed. Grating-based phase-contrast CT showed greatly improved differentiation of fine structures and provided accurate depiction of strands of fibrous tissue within the fibroadenomas as well as of the diagnostically valuable dilated, branched ductuli of the fibroadenomas. A clear demarcation of tumor boundaries in all cases was provided by phase- but not absorption-contrast CT.

Conclusions

Pending successful translation of the technology to a clinical setting and considerable reduction of the required dose, the data presented here suggest that grating-based phase-contrast CT may be used as a supplementary non-invasive diagnostic tool in breast diagnostics. Phase-contrast CT may thus contribute to the reduction of false positive findings and reduce the recall and core biopsy rate in population-based screening. Phase-contrast CT may further be used to assist during histopathological workup, offering a 3D view of the tumor and helping to identify diagnostically valuable tissue sections within large tumors.     

Phase-Contrast Hounsfield Units of Fixated and Non-Fixated Soft-Tissue Samples

X-ray phase-contrast imaging is a novel technology that achieves high soft-tissue contrast. Although its clinical impact is still under investigation, the technique may potentially improve clinical diagnostics. In conventional attenuation-based X-ray computed tomography, radiological diagnostics are quantified by Hounsfield units. Corresponding Hounsfield units for phase-contrast imaging have been recently introduced, enabling a setup-independent comparison and standardized interpretation of imaging results. Thus far, the experimental values of few tissue types have been reported; these values have been determined from fixated tissue samples. This study presents phase-contrast Hounsfield units for various types of non-fixated human soft tissues. A large variety of tissue specimens ranging from adipose, muscle and connective tissues to liver, kidney and pancreas tissues were imaged by a grating interferometer with a rotating-anode X-ray tube and a photon-counting detector. Furthermore, we investigated the effects of formalin fixation on the quantitative phase-contrast imaging results.     

X-Ray Phase-Contrast CT of a Pancreatic Ductal Adenocarcinoma Mouse Model

To explore the potential of grating-based x-ray phase-contrast computed tomography (CT) for preclinical research, a genetically engineered mouse model of pancreatic ductal adenocarcinoma (PDAC) was investigated. One ex-vivo mouse specimen was scanned with different grating-based phase-contrast CT imaging setups covering two different settings: i) high-resolution synchrotron radiation (SR) imaging and ii) dose-reduced imaging using either synchrotron radiation or a conventional x-ray tube source. These experimental settings were chosen to assess the potential of phase-contrast imaging for two different types of application: i) high-performance imaging for virtual microscopy applications and ii) biomedical imaging with increased soft-tissue contrast for in-vivo applications. For validation and as a reference, histological slicing and magnetic resonance imaging (MRI) were performed on the same mouse specimen. For each x-ray imaging setup, attenuation and phase-contrast images were compared visually with regard to contrast in general, and specifically concerning the recognizability of lesions and cancerous tissue. To quantitatively assess contrast, the contrast-to-noise ratios (CNR) of selected regions of interest (ROI) in the attenuation images and the phase images were analyzed and compared. It was found that both for virtual microscopy and for in-vivo applications, there is great potential for phase-contrast imaging: in the SR-based benchmarking data, fine details about tissue composition are accessible in the phase images and the visibility of solid tumor tissue under dose-reduced conditions is markedly superior in the phase images. The present study hence demonstrates improved diagnostic value with phase-contrast CT in a mouse model of a complex endogenous cancer, promoting the use and further development of grating-based phase-contrast CT for biomedical imaging applications.     

Imaging of Metastatic Lymph Nodes by X-ray Phase-Contrast Micro-Tomography

Invasive cancer causes a change in density in the affected tissue, which can be visualized by x-ray phase-contrast tomography. However, the diagnostic value of this method has so far not been investigated in detail. Therefore, the purpose of this study was, in a blinded manner, to investigate whether malignancy could be revealed by non-invasive x-ray phase-contrast tomography in lymph nodes from breast cancer patients. Seventeen formalin-fixed paraffin-embedded lymph nodes from 10 female patients (age range 37–83 years) diagnosed with invasive ductal carcinomas were analyzed by X-ray phase-contrast tomography. Ten lymph nodes had metastatic deposits and 7 were benign. The phase-contrast images were analyzed according to standards for conventional CT images looking for characteristics usually only visible by pathological examinations. Histopathology was used as reference. The result of this study was that the diagnostic sensitivity of the image analysis for detecting malignancy was 100% and the specificity was 87%. The positive predictive value was 91% for detecting malignancy and the negative predictive value was 100%. We conclude that x-ray phase-contrast imaging can accurately detect density variations to obtain information regarding lymph node involvement previously inaccessible with standard absorption x-ray imaging.     

Prospective comparison of panoramic tomography (zonography) and helical computed tomography in the diagnosis and operative management of mandibular fractures

This prospective study compared the sensitivity of panoramic tomography (zonography) and helical computed tomography (CT) in diagnosing 73 mandibular fractures in 42 consecutive patients and correlated the results with known surgical findings. The purpose of the study was to determine the optimal radiologic examination for the diagnosis and operative management of mandibular fractures. The attending surgeons' interpretations of panoramic tomograms and helical CT images in the axial plane were compared with the patients' known surgical findings. A series of questions assessed the relative contribution of these two radiologic examinations in formulating an optimal operative plan for each patient. In the 42 patients studied, the sensitivity of helical CT was 100 percent in diagnosing mandibular fractures; this compared with 86 percent (36 of 42) for panoramic tomography, in which significantly more fractures were missed (p = 0.0412). In the six patients with fractures not visualized, the operative management was altered because of the new fracture visualized on helical CT. Of the seven missed fractures, six were in the posterior portion of the mandible. Comparing fracture detection by region, seven fractures found on helical CT were not visualized on panoramic tomography. Helical CT improved the understanding of the nature of mandibular fractures by providing additional information regarding fracture displacement and comminution and by locating injuries missed using panoramic tomography. This study suggests that helical CT alone may be more diagnostic than panoramic tomography alone in evaluating mandibular fractures. Helical CT sufficiently demonstrated details of fractures in 41 of 42 patients; in one patient, the nature of a dental root fracture was better delineated by panoramic tomography.     

Helical flows and asymmetry of blood jet in dilated ascending aorta with normally functioning bicuspid valve

Bicuspid aortic valve (BAV) is associated with aortic dilatation and aneurysm. Several studies evidenced an eccentric systolic flow in ascending aorta associated with increased wall shear stresses (WSS) and the occurrence of an helical systolic flow. This study seeks to elucidate the connections between jet asymmetry and helical flow in patients with normally functioning BAV and dilated ascending aorta. We performed a computational parametric study by varying, for a patient-specific geometry, the valve area and the flow rate entering the aorta and drawing also a tricuspid valve (TAV). We considered also phase-contrast magnetic resonance imaging of four BAV and TAV patients. Measurement of normalized flow asymmetry index, systolic WSS and of a new index (positive helix fraction, PHF) quantifying the presence of a single a single helical flow were performed. In our computation, BAV cases featured higher values of all indices with respect to TAV in both numerical and imaged-based results. Moreover, all indices increased with decreasing valve area and/or with increasing flow rate. This allowed to separate the BAV and TAV cases with respect to the jet asymmetry, WSS localization and helical flow. Interestingly, these results were obtained without modeling the leaflets.     

Measuring skin dose in CT examinations under complex geometries: Instruments,methods and considerations

ObjectiveTo investigate skin dose in Computed Tomography (CT) and its dependence on scanning geometry.Materials and methodsMeasurements of entrance surface air kerma (ESAK) in free air and entrance skin dose (ESD) on an anthropomorphic phantom were performed in a 64-slice CT scanner, using two different instruments: the Dose Profiler (DP) and the QED skin diode (QEDSD). Using DP and QEDSD, the ESAK rate profiles at the isocenter and at different distances from it, were measured using axial scans. Using DP and helical scans the ESAK rate profile in the Z-axis was acquired. The same profile was acquired with the QEDSD also, using many axial scans and manual table translation. ESD measurements were performed with the DP and QEDSD, in axial and helical scan mode.ResultsESAK measurements with DP and QEDSD were in good agreement, for both point dose and profile measurements. The agreement was also good for ESD measurements but not for helical scans, due to variable X-ray beam overlapping and different tube angular positions at each scan start. It was observed that the ESD values at different Y-axis offsets were comparable to the respective ESAK values recorded at the same Y-axis offset distances without the phantom.ConclusionsBoth DP and QEDSD were proven suitable for performing point ESD measurements. However, calculating the skin dose distribution in CT examinations is a very challenging task. A practical approach would be for CT scanners to provide a conservative estimate of the peak skin dose using the isocenter ESAK value.     

Virtual bronchoscopy and 3D spiral CT reconstructions in the management of patient with bronchial cancer--our experience with Syngo 3D postprocessing software

Multislice helical CT generated virtual bronchoscopy (VB) represents one of the most recent developments in three-dimensional computer aided visualisation techniques. VB allows non-invasive and relatively accurate 3D evaluation of tracheobronchal tree. We performed virtual bronchoscopy and in-space 3D volume analysis on CT-data set acquired from sixty-four-year old male with bronchial cancer in order to demonstrate advantages and disadvantages of these methods in diagnostics and preoperative management of metastatic bronchial cancer. Siemens Somatom Emotion 16 helical CT scanner was used for data acquisition. Data post-processing was done with 3D Syngo 2006G software package from Siemens medical systems. CT scanning of the thorax was performed in heavy smoker with an expansive T4N1M1 malignant process in a superior lobe of the right lung accompanied with large metastatic lesion attached on the right lateral chest wall. Metastatic lesions were also found in vertebral column. In-space 3D analysis followed with virtual bronchoscopy had revealed obstruction of apical branch of superior lobe segmental bronchus. External compression done by tumor to the superior segmental and right main bronchus was found. We concluded that multi-slice CT in connection with VB became a possible non-invasive alternative to bronchoscopy, if tissue samples are not required.     

Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study

The hemodynamics within the aorta of five healthy humans were investigated to gain insight into the complex helical flow patterns that arise from the existence of asymmetries in the aortic region. The adopted approach is aimed at (1) overcoming the relative paucity of quantitative data regarding helical blood flow dynamics in the human aorta and (2) identifying common characteristics in physiological aortic flow topology, in terms of its helical content. Four-dimensional phase-contrast magnetic resonance imaging (4D PC MRI) was combined with algorithms for the calculation of advanced fluid dynamics in this study. These algorithms allowed us to obtain a 4D representation of intra-aortic flow fields and to quantify the aortic helical flow. For our purposes, helicity was used as a measure of the alignment of the velocity and the vorticity. There were two key findings of our study: (1) intra-individual analysis revealed a statistically significant difference in the helical content at different phases of systole and (2) group analysis suggested that aortic helical blood flow dynamics is an emerging behavior that is common to normal individuals. Our results also suggest that helical flow might be caused by natural optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion. The approach here applied to assess in vivo helical blood flow could be the starting point to elucidate the role played by helicity in the generation and decay of rotating flows in the thoracic aorta.     

Quantitative Three-Dimensional Imaging of Lipid,Protein, and Water Contents via X-Ray Phase-Contrast Tomography

X-ray phase-contrast computed tomography is an emerging imaging technology with powerful capabilities for three-dimensional (3D) visualization of weakly absorbing objects such as biological soft tissues. This technique is an extension of existing X-ray applications because conventional attenuation-contrast images are simultaneously acquired. The complementary information provided by both the contrast modalities suggests that enhanced material characterization is possible when performing combined data analysis. In this study, we describe how protein, lipid, and water concentrations in each 3D voxel can be quantified by vector decomposition. Experimental results of dairy products, porcine fat and rind, and different human soft tissue types are presented. The results demonstrate the potential of phase-contrast imaging as a new analysis tool. The 3D representations of protein, lipid, and water contents open up new opportunities in the fields of biology, medicine, and food science.     

螺旋CT增强扫描对孤立性肺结节的诊断价值

目的:研究螺旋CT增强扫描时孤立性肺结节的诊断价值。方法:回顾分析经病理证实的恶性结节50例、炎性结节26例、结核瘤12例的螺旋CT增强扫描的表现。结果:恶性结节和炎性结节增强扫描的强化程度明显高于结核瘤(P＜0．05)。炎性结节强化峰值的时间较恶性结节延迟。恶性结节增强扫描出现点、条状及边缘强化。结论:螺旋CT增强扫描对孤立性肺结节的诊断具有重要临床应用价值。     

Evaluation of size,morphology, concentration,and surface effect of gold nanoparticles on X-ray attenuation in computed tomography

Increasing attention has been focused on the use of nanostructures as contrast enhancement agents in medical imaging, especially in computed tomography (CT). To date, gold nanoparticles (GNPs) have been demonstrated to have great potential as contrast agents for CT imaging. This study was designed to evaluate any effect on X-ray attenuation that might result from employing GNPs with a variety of shapes, sizes, surface chemistries, and concentrations. Gold nanorods (GNRs) and spherical GNPs were synthesized for this application. X-ray attenuation was quantified by Hounsfield unit (HU) in CT. Our findings indicated that smaller spherical GNPs (13 nm) had higher X-ray attenuation than larger ones (60 nm) and GNRs with larger aspect ratio exhibited great effect on X-ray attenuation. Moreover, poly ethylene glycol (PEG) coating on GNRs declined X-ray attenuation as a result of limiting the aggregation of GNRs. We observed X-ray attenuation increased when mass concentration of GNPs was elevated. Overall, smaller spherical GNPs can be suggested as a better alternative to Omnipaque, a good contrast agent for CT imaging. This data can be also considered for the application of gold nanostructures in radiation dose enhancement where nanoparticles with high X-ray attenuation are applied.     

Recent advances in X-ray imaging of breast tissue: From two- to three-dimensional imaging

Breast cancer is a globally widespread disease whose detection has already been significantly improved by the introduction of screening programs. Nevertheless, mammography suffers from low soft tissue contrast and the superposition of diagnostically relevant anatomical structures as well as from low values for sensitivity and specificity especially for dense breast tissue. In recent years, two techniques for X-ray breast imaging have been developed that bring advances for the early detection of breast cancer. Grating-based phase-contrast mammography is a new imaging technique that is able to provide three image modalities simultaneously (absorption-contrast, phase-contrast and dark-field signal). Thus, an enhanced detection and delineation of cancerous structures in the phase-contrast image and an improved visualization and characterization of microcalcifications in the dark-field image is possible. Furthermore, latest studies about this approach show that dose-compatible imaging with polychromatic X-ray sources is feasible. In order to additionally overcome the limitations of projection-based imaging, efforts were also made towards the development of breast computed tomography (BCT), which recently led to the first clinical installation of an absorption-based BCT system. Further research combining the benefits of both imaging technologies is currently in progress. This review article summarizes the latest advances in phase-contrast imaging for the female breast (projection-based and three-dimensional view) with special focus on possible clinical implementations in the future.     

Lung tumors on multimodal radiographs derived from grating-based X-ray imaging – A feasibility study

PurposeThe purpose of this study was to assess whether grating-based X-ray imaging may have a role in imaging of pulmonary nodules on radiographs.Materials and methodsA mouse lung containing multiple lung tumors was imaged using a small-animal scanner with a conventional X-ray source and a grating interferometer for phase-contrast imaging. We qualitatively compared the signal characteristics of lung nodules on transmission, dark-field and phase-contrast images. Furthermore, we quantitatively compared signal characteristics of lung tumors and the adjacent lung tissue and calculated the corresponding contrast-to-noise ratios.ResultsOf the 5 tumors visualized on the transmission image, 3/5 tumors were clearly visualized and 1 tumor was faintly visualized in the dark-field image as areas of decreased small angle scattering. In the phase-contrast images, 3/5 tumors were clearly visualized, while the remaining 2 tumors were faintly visualized by the phase-shift occurring at their edges. No additional tumors were visualized in either the dark-field or phase-contrast images. Compared to the adjacent lung tissue, lung tumors were characterized by a significant decrease in transmission signal (median 0.86 vs. 0.91, p = 0.04) and increase in dark-field signal (median 0.71 vs. 0.65, p = 0.04). Median contrast-to-noise ratios for the visualization of lung nodules were 4.4 for transmission images and 1.7 for dark-field images (p = 0.04).ConclusionLung nodules can be visualized on all three radiograph modalities derived from grating-based X-ray imaging. However, our initial data suggest that grating-based multimodal X-ray imaging does not increase the sensitivity of chest radiographs for the detection of lung nodules.     

Hidden termite coprolites revealed by Synchrotron microtomography inside Eocene–Oligocene filled wood-borings from the Malzieu Basin,Lozère,southern France

Fragments of filled wood-borings were recently discovered from the Eocene–Oligocene Conglomerate and Sandstone Formation of the Malzieu Basin (Lozère, southern France). Propagation phase-contrast X-ray synchrotron microtomography (PPC-SRμCT) was used to characterize their hidden inner structures. Virtual 2D sections and 3D reconstructions show that the inner microstructures of borings display a mudstone–wackestone siliceous matrix including tiny coprolites. The hexagonal cross-section of these coprolites is characteristic of termite faecal pellets. Morphology and dimensions of the coprolites share strong similarities with those of extant Kalotermitidae (drywood termites). The depositional environment is interpreted as a fluvial valley in which the lenticular sandstone and conglomerate lenses correspond to channels. This discovery complements the record of Palaeogene termites which remain poor in France and throughout the world.