Towards a framework for rapid prototyping of iterative parallel-in-time algorithms

MotivationWith growing interest in parallel-in-time methods many different and new solvers for ordinary differential equations have gained the attention of researchers from various fields. In order to clearly estimate the potential and limitations of these mostly iterative solvers, a modular prototyping framework not only helps to understand their properties and various facets but also allows to easily implement and test new ideas.As an example, the “parallel full approximation scheme in space and time” (PFASST) and its serial counterpart, multi-level spectral deferred corrections (MLSDC) are composed of multiple levels and even types of spectral deferred correction sweeps which are coupled by space-time restriction and interpolation operators. These modular and interchangeable combinations of different techniques already generate a vast amount of variations with different effects on solvability and efficiency towards a diverse set of problems.PyPinTFor a thorough and systematic analysis of methods like PFASST or Parareal we take the path of a well-planned and fully modular implementation of these algorithms. By following the object-oriented programming paradigm we create an abstract decomposition of the methods’ functional components combined in a framework for parallel-in-time algorithms. Different methods implemented in a single framework using a unified base functionality enables detailed qualitative and quantitative analysis without paying too much attention to underlying implementation details.As a proof of concept and intermediate step, we show results for a two-dimensional parabolic test equation solved with a MLSDC solver coupled with a multigrid algorithm in space.Due to its flexibility, extensibility and rather comfortable learning curve Python has an ever growing world-wide community within science, academia and industry. For PyPinT, it provides the building block for a flexible and unified framework, allowing fast prototyping of iterative parallel-in-time algorithms. Well-maintained and open-source third party modules such as NumPy and SciPy offer high-level interfaces to performant low-level functionalities for matrix and vector arithmetics, common mathematical methods and plotting capabilities. In addition, current efforts leave the door open for enabling PyPinT to be applied on HPC clusters.GoalsAccompanying the development of parallel-in-time algorithms, new ideas can be implemented in PyPinT immediately. Utilizing the framework’s analysis tools such as calculation and plotting of stability regions, runtime and characteristic values (e.g. residuals), new algorithms can easily be studied in detail. Clearly defined interfaces, a strictly modular concept and different levels of abstraction enable the user to exchange certain parts of the algorithms and add his or her own methods to enrich the whole framework.Students, undergraduate and graduate, with a basic knowledge of iterative solvers and some programming skills will be able to use and extend PyPinT and discover, learn and understand the mechanics of parallel-in-time methods. PyPinT is open-source licensed and available on GitHub, thus fostering collaboration and ease contribution of amplifications by interested people.Ultimately, PyPinT should not only represent a package for applying and studying parallel-in-time methods but also provide a development environment for enhancing existing and inventing new methods. Finally, PyPinT can also provide valuable insight and guidance for future, performance-oriented implementations in other programming languages

Spatial heterogeneity of hepatic fibrosis in primary sclerosing cholangitis vs. viral hepatitis assessed by MR elastography

Spatial heterogeneity of hepatic fibrosis in primary sclerosing cholangitis (PSC) in comparison to viral hepatitis was assessed as a potential new biomarker using MR elastography (MRE). In this proof-of-concept study, we hypothesized a rather increased heterogeneity in PSC and a rather homogeneous distribution in viral hepatitis. Forty-six consecutive subjects (PSC: n=20, viral hepatitis: n=26) were prospectively enrolled between July 2014 and April 2017. Subjects underwent multifrequency MRE (1.5 T) using drive frequencies of 35-60 Hz and generating shear-wave speed (SWS in m/s) maps as a surrogate of stiffness. The coefficient of variation (CV in %) was determined to quantify fibrosis heterogeneity. Mean SWS and CV were 1.70 m/s and 21% for PSC, and 1.84 m/s and 18% for viral hepatitis. Fibrosis heterogeneity was significantly increased for PSC (P=0.04) while no difference was found for SWS of PSC and viral hepatitis (P=0.17). Global hepatic stiffness was similar in PSC and viral hepatitis groups, but spatial heterogeneity may reveal spatial patterns of stiffness changes towards enhanced biophysics-based diagnosis by MRI

Prostate cancer assessment using MR elastography of fresh prostatectomy specimens at 9.4 T

Purpose: Despite its success in the assessment of prostate cancer (PCa), in vivo multiparametric MRI has limitations such as interobserver variability and low specificity. Several MRI methods, among them MR elastography, are currently being discussed as candidates for supplementing conventional multiparametric MRI. This study aims to investigate the detection of PCa in fresh ex vivo human prostatectomy specimens using MR elastography. Methods: Fourteen fresh prostate specimens from men with clinically significant PCa without formalin fixation or prior radiation therapy were examined by MR elastography at 500 Hz immediately after radical prostatectomy in a 9.4T preclinical scanner. Specimens were divided into 12 segments for both calculation of storage modulus (G ' in kilopascals) and pathology (Gleason score) as reference standard. Sensitivity, specificity, and area under the receiver operating characteristic curve were calculated to assess PCa detection. Results: The mean G ' and SD were as follows: all segments, 8.74 ± 5.26 kPa; healthy segments, 5.44 ± 4.40 kPa; and cancerous segments, 10.84 ± 4.65 kPa. The difference between healthy and cancerous segments was significant with P ≤ .001. Diagnostic performance assessed with the Youden index was as follows: sensitivity, 69%; specificity, 79%; area under the curve, 0.81; and cutoff, 10.67 kPa. Conclusion: Our results suggest that prostate MR elastography has the potential to improve diagnostic performance of multiparametric MRI, especially regarding its 2 major limitations: interobserver variability and low specificity. Particularly the high value for specificity in PCa detection is a stimulating result and encourages further investigation of this method

Comparison of non-invasive assessment of liver fibrosis in patients with alpha1-antitrypsin deficiency using magnetic resonance elastography (MRE), acoustic radiation force impulse (ARFI) Quantification, and 2D-shear wave elastography (2D-SWE)

Purpose: Although it has been known for decades that patients with alpha1-antitrypsin deficiency (AATD) have an increased risk of cirrhosis and hepatocellular carcinoma, limited data exist on non-invasive imaging-based methods for assessing liver fibrosis such as magnetic resonance elastography (MRE) and acoustic radiation force impulse (ARFI) quantification, and no data exist on 2D-shear wave elastography (2D-SWE). Therefore, the purpose of this study is to evaluate and compare the applicability of different elastography methods for the assessment of AATD-related liver fibrosis. Methods: Fifteen clinically asymptomatic AATD patients (11 homozygous PiZZ, 4 heterozygous PiMZ) and 16 matched healthy volunteers were examined using MRE and ARFI quantification. Additionally, patients were examined with 2D-SWE. Results: A high correlation is evident for the shear wave speed (SWS) determined with different elastography methods in AATD patients: 2D-SWE/MRE, ARFI quantification/2D-SWE, and ARFI quantification/MRE (R = 0.8587, 0.7425, and 0.6914, respectively; P <= 0.0089). Four AATD patients with pathologically increased SWS were consistently identified with all three methods-MRE, ARFI quantification, and 2D-SWE. Conclusion: The high correlation and consistent identification of patients with pathologically increased SWS using MRE, ARFI quantification, and 2D-SWE suggest that elastography has the potential to become a suitable imaging tool for the assessment of AATD-related liver fibrosis. These promising results provide motivation for further investigation of non-invasive assessment of AATD-related liver fibrosis using elastography

Altered energy partitioning across terrestrial ecosystems in the European drought year 2018

Drought and heat events, such as the 2018 European drought, interact with the exchange of energy between the land surface and the atmosphere, potentially affecting albedo, sensible and latent heat fluxes, as well as CO(2)exchange. Each of these quantities may aggravate or mitigate the drought, heat, their side effects on productivity, water scarcity and global warming. We used measurements of 56 eddy covariance sites across Europe to examine the response of fluxes to extreme drought prevailing most of the year 2018 and how the response differed across various ecosystem types (forests, grasslands, croplands and peatlands). Each component of the surface radiation and energy balance observed in 2018 was compared to available data per site during a reference period 2004-2017. Based on anomalies in precipitation and reference evapotranspiration, we classified 46 sites as drought affected. These received on average 9% more solar radiation and released 32% more sensible heat to the atmosphere compared to the mean of the reference period. In general, drought decreased net CO(2)uptake by 17.8%, but did not significantly change net evapotranspiration. The response of these fluxes differed characteristically between ecosystems; in particular, the general increase in the evaporative index was strongest in peatlands and weakest in croplands. This article is part of the theme issue 'Impacts of the 2018 severe drought and heatwave in Europe: from site to continental scale'

Entwicklung und Anwendung der Mehrfrequenz-Magnetresonanzelastographie

Magnetresonanzelastographie (MRE) bietet die Möglichkeit, über die Aufnahme mechanischer Scherwellen im Körper auf die mechanischen Eigenschaften lebender Gewebe zu schließen. Dabei werden in der klassischen MRE Wellen mittels Einkopplung externer Vibrationen einer einzelnen Frequenz angeregt. Wegen der starken Absorption der Vibrationsenergie in biologischen Geweben und der damit verbundenen Dispersion der Phasengeschwindigkeit sowie der Dämpfung der Wellen können mit dieser Methode nur frequenzabhängige Größen, jedoch keine Materialkonstanten bestimmt werden. Die in dieser Arbeit entwickelte Methode erlaubt die synchrone Einkopplung und Aufnahme multipler Gewebeschwingungen, wodurch viskoelastische Gewebekenngrößen in einer zeitlich-zyklisierten MRE-Untersuchung erfasst werden können. Diese Technik wird in Phantomstudien, an Gewebeproben sowie am Menschen evaluiert. Mittels verschiedener rheologischer Modelle werden erstmalig die viskoelastischen Eigenschaften der Leber und des Gehirns in ihrem intakten, lebenden Umfeld bestimmt. Dabei zeigt sich die Überlegenheit eines zweiparametrischen Modells, mit dessen Hilfe die gewonnene, spektrale Information des komplexen Moduls des Gewebes in eine einzige diagnostisch-relevante Kenngröße zusammengefasst werden kann.Magnetic resonance elastography (MRE) is capable of measuring the mechanical properties of living tissue by using externally introduced vibrations and phase contrast magnetic resonance imaging techniques. Until now, monofrequency shear wave excitation techniques have been used in conventional MRE. However, since biological tissue is highly dispersive due to its strong damping characteristics, the study of tissue rheology requires knowledge of wave propagation at multiple frequencies. The multifrequency-MRE method, which was engineered in this thesis, applies a superposition of multiple harmonics as the shear wave excitation signal. All vibrations are acquired simultaneously, which enables the determination of viscoelastic tissue parameters in one time-resolved MRE experiment. This technique is evaluated in studies on gel phantoms and excised tissue samples, as well as in human in-vivo studies. The viscoelastic properties of human brain and liver are determined in their in-vivo environment using several rheological models. A two-parameter fractional model demonstrates excellent stability and allows for combining the spectral information of the complex modulus acquired by multifrequency-MRE, which then results in a single viscoelastic parameter that is diagnostically relevant