Stochastic Invariants for Probabilistic Termination

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page

X-Ray Phase-Contrast Tomography of Renal Ischemia-Reperfusion Damage

Purpose: The aim of the study was to investigate microstructural changes occurring in unilateral renal ischemia-reperfusion injury in a murine animal model using synchrotron radiation. Material and Methods: The effects of renal ischemia-reperfusion were investigated in a murine animal model of unilateral ischemia. Kidney samples were harvested on day 18. Grating-Based Phase-Contrast Imaging (GB-PCI) of the paraffin-embedded kidney samples was performed at a Synchrotron Radiation Facility (beam energy of 19 keV). To obtain phase information, a two-grating Talbot interferometer was used applying the phase stepping technique. The imaging system provided an effective pixel size of 7.5 mu m. The resulting attenuation and differential phase projections were tomographically reconstructed using filtered back-projection. Semi-automated segmentation and volumetry and correlation to histopathology were performed. Results: GB-PCI provided good discrimination of the cortex, outer and inner medulla in non-ischemic control kidneys. Post-ischemic kidneys showed a reduced compartmental differentiation, particularly of the outer stripe of the outer medulla, which could not be differentiated from the inner stripe. Compared to the contralateral kidney, after ischemia a volume loss was detected, while the inner medulla mainly retained its volume (ratio 0.94). Post-ischemic kidneys exhibited severe tissue damage as evidenced by tubular atrophy and dilatation, moderate inflammatory infiltration, loss of brush borders and tubular protein cylinders. Conclusion: In conclusion GB-PCI with synchrotron radiation allows for non-destructive microstructural assessment of parenchymal kidney disease and vessel architecture. If translation to lab-based approaches generates sufficient density resolution, and with a time-optimized image analysis protocol, GB-PCI may ultimately serve as a non-invasive, non-enhanced alternative for imaging of pathological changes of the kidney

In-vivo dark-field and phase-contrast x-ray imaging.

Novel radiography approaches based on the wave nature of x-rays when propagating through matter have a great potential for improved future x-ray diagnostics in the clinics. Here, we present a significant milestone in this imaging method: in-vivo multi-contrast x-ray imaging of a mouse using a compact scanner. Of particular interest is the enhanced contrast in regions related to the respiratory system, indicating a possible application in diagnosis of lung diseases (e.g. emphysema)

Visualization of subcutaneous insulin injections by x-ray computed tomography

We report how the three-dimensional structure of subcutaneous injections of soluble insulin can be visualized by x-ray computed tomography using an iodine based contrast agent. The injections investigated are performed ex vivo in porcine adipose tissue. Full tomography scans carried out at a laboratory x-ray source with a total acquisition time of about 1 min yield CT-images with an effective pixel size of 109 x 109 mu m(2). The depots are segmented using a modified Chan-Vese algorithm and we are able to observe differences in the shape of the injection depot and the position of the depot in the skin among equally performed injections. To overcome the beam hardening artefacts, which affect the quantitative prediction of the volume injected, we additionally present results concerning the visualization of two injections using synchrotron radiation. The spatial concentration distribution of iodine is calculated to show the dilution of the insulin drug inside the depot. Characterisation of the shape of the depot and the spatial concentration profile of the injected fluid is important knowledge when improving the clinical formulation of an insulin drug, the performance of injection devices and when predicting the effect of the drug through biomedical simulations

Visualization of subcutaneous insulin injections by x-ray computed tomography

We report how the three-dimensional structure of subcutaneous injections of soluble insulin can be visualized by x-ray computed tomography using an iodine based contrast agent. The injections investigated are performed ex vivo in porcine adipose tissue. Full tomography scans carried out at a laboratory x-ray source with a total acquisition time of about 1 min yield CT-images with an effective pixel size of 109 × 109 μm2. The depots are segmented using a modified Chan–Vese algorithm and we are able to observe differences in the shape of the injection depot and the position of the depot in the skin among equally performed injections. To overcome the beam hardening artefacts, which affect the quantitative prediction of the volume injected, we additionally present results concerning the visualization of two injections using synchrotron radiation. The spatial concentration distribution of iodine is calculated to show the dilution of the insulin drug inside the depot. Characterisation of the shape of the depot and the spatial concentration profile of the injected fluid is important knowledge when improving the clinical formulation of an insulin drug, the performance of injection devices and when predicting the effect of the drug through biomedical simulations

Microbubbles as a scattering contrast agent for grating-based x-ray dark-field imaging

In clinically established-absorption-based-biomedical x-ray imaging, contrast agents with high atomic numbers (e.g. iodine) are commonly used for contrast enhancement. The development of novel x-ray contrast modalities such as phase contrast and dark-field contrast opens up the possible use of alternative contrast media in x-ray imaging. We investigate using ultrasound contrast agents, which unlike iodine-based contrast agents can also be administered to patients with renal impairment and thyroid dysfunction, for application with a recently developed novel x-ray dark-field imaging modality. To produce contrast from these microbubble-based contrast agents, our method exploits ultra-small-angle coherent x-ray scattering. Such scattering dark-field x-ray images can be obtained with a grating-based x-ray imaging setup, together with refraction-based differential phase-contrast and the conventional attenuation contrast images. In this work we specifically show that ultrasound contrast agents based on microbubbles can be used to produce strongly enhanced dark-field contrast, with superior contrast-to-noise ratio compared to the attenuation signal. We also demonstrate that this method works well with an x-ray tube-based setup and that the relative contrast gain even increases when the pixel size is increased from tenths of microns to clinically compatible detector resolutions about up to a millimetre

Improved diagnosis of pulmonary emphysema using <em>in vivo</em> dark-field radiography.

OBJECTIVES: The purpose of this study was to assess whether the recently developed method of grating-based x-ray dark-field radiography can improve the diagnosis of pulmonary emphysema in vivo. MATERIALS AND METHODS: Pulmonary emphysema was induced in female C57BL/6N mice using endotracheal instillation of porcine pancreatic elastase and confirmed by in vivo pulmonary function tests, histopathology, and quantitative morphometry. The mice were anesthetized but breathing freely during imaging. Experiments were performed using a prototype small-animal x-ray dark-field scanner that was operated at 35 kilovolt (peak) with an exposure time of 5 seconds for each of the 10 grating steps. Images were compared visually. For quantitative comparison of signal characteristics, regions of interest were placed in the upper, middle, and lower zones of each lung. Receiver-operating-characteristic statistics were performed to compare the effectiveness of transmission and dark-field signal intensities and the combined parameter &quot;normalized scatter&quot; to differentiate between healthy and emphysematous lungs. RESULTS: A clear visual difference between healthy and emphysematous mice was found for the dark-field images. Quantitative measurements of x-ray dark-field signal and normalized scatter were significantly different between the mice with pulmonary emphysema and the control mice and showed good agreement with pulmonary function tests and quantitative histology. The normalized scatter showed a significantly higher discriminatory power (area under the receiver-operating-characteristic curve [AUC], 0.99) than dark-field (AUC, 0.90; P = 0.01) or transmission signal (AUC, 0.69; P &lt; 0.001) alone did, allowing for an excellent discrimination of healthy and emphysematous lung regions. CONCLUSIONS: In a murine model, x-ray dark-field radiography is technically feasible in vivo and represents a substantial improvement over conventional transmission-based x-ray imaging for the diagnosis of pulmonary emphysema

Small-animal dark-field radiography for pulmonary emphysema evaluation

Chronic obstructive pulmonary disease (COPD) is one of The leading causes of morbidity and mortality worldwide and emphysema is one of its main components. The disorder is characterized by irreversible destruction of The alveolar walls and enlargement of distal airspaces. Despite The severe changes in The lung Tissue morphology, conventional chest radiographs have only a limited sensitivity for The detection of mild To moderate emphysema. X-ray dark-field is an imaging modality That can significantly increase The visibility of lung Tissue on radiographic images. The dark-field signal is generated by coherent, small-Angle scattering of x-rays on The air-tissue interfaces in The lung. Therefore, morphological changes in The lung can be clearly visualized on dark-field images. This is demonstrated by a preclinical study with a small-Animal emphysema model. To generate a murine model of pulmonary emphysema, a female C57BL/6N mouse was Treated with a single orotracheal application of porcine pancreatic elastase (80 U/kg body weight) dissolved in phosphate-buffered saline (PBS). Control mouse received PBS. The mice were imaged using a small-Animal dark-field scanner. While conventional x-ray Transmission radiography images revealed only subtle indirect signs of The pulmonary disorder, The difference between healthy and emphysematous lungs could be clearly directly visualized on The dark-field images. The dose applied To The animals is compatible with longitudinal studies. The imaging results correlate well with histology. The results of This study reveal The high potential of dark-field radiography for clinical lung imaging