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There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.
Superparamagnetic iron oxide nanoparticles (SPION) are extensively used for magnetic resonance imaging (MRI) and magnetic particle imaging (MPI), as well as for magnetic fluid hyperthermia (MFH). We here describe a sequential centrifugation protocol to obtain SPION with well-defined sizes from a polydisperse SPION starting formulation, synthesized using the routinely employed co-precipitation technique. Transmission electron microscopy, dynamic light scattering and nanoparticle tracking analyses show that the SPION fractions obtained upon size-isolation are well-defined and almost monodisperse. MRI, MPI and MFH analyses demonstrate improved imaging and hyperthermia performance for size-isolated SPION as compared to the polydisperse starting mixture, as well as to commercial and clinically used iron oxide nanoparticle formulations, such as Resovist® and Sinerem®. The size-isolation protocol presented here may help to identify SPION with optimal properties for diagnostic, therapeutic and theranostic applications.
SHEMAT-Suite: An open-source code for simulating flow, heat and species transport in porous media
(2020)
SHEMAT-Suite is a finite-difference open-source code for simulating coupled flow, heat and species transport in porous media. The code, written in Fortran-95, originates from geoscientific research in the fields of geothermics and hydrogeology. It comprises: (1) a versatile handling of input and output, (2) a modular framework for subsurface parameter modeling, (3) a multi-level OpenMP parallelization, (4) parameter estimation and data assimilation by stochastic approaches (Monte Carlo, Ensemble Kalman filter) and by deterministic Bayesian approaches based on automatic differentiation for calculating exact (truncation error-free) derivatives of the forward code.
Safety of subjects during radiofrequency exposure in ultra-high-field magnetic resonance imaging
(2020)
Magnetic resonance imaging (MRI) is one of the most important medical imaging techniques. Since the introduction of MRI in the mid-1980s, there has been a continuous trend toward higher static magnetic fields to obtain i.a. a higher signal-to-noise ratio. The step toward ultra-high-field (UHF) MRI at 7 Tesla and higher, however, creates several challenges regarding the homogeneity of the spin excitation RF transmit field and the RF exposure of the subject. In UHF MRI systems, the wavelength of the RF field is in the range of the diameter of the human body, which can result in inhomogeneous spin excitation and local SAR hotspots. To optimize the homogeneity in a region of interest, UHF MRI systems use parallel transmit systems with multiple transmit antennas and time-dependent modulation of the RF signal in the individual transmit channels. Furthermore, SAR increases with increasing field strength, while the SAR limits remain unchanged. Two different approaches to generate the RF transmit field in UHF systems using antenna arrays close and remote to the body are investigated in this letter. Achievable imaging performance is evaluated compared to typical clinical RF transmit systems at lower field strength. The evaluation has been performed under consideration of RF exposure based on local SAR and tissue temperature. Furthermore, results for thermal dose as an alternative RF exposure metric are presented.
The Rothman–Woodroofe symmetry test statistic is revisited on the basis of independent but not necessarily identically distributed random variables. The distribution-freeness if the underlying distributions are all symmetric and continuous is obtained. The results are applied for testing symmetry in a meta-analysis random effects model. The consistency of the procedure is discussed in this situation as well. A comparison with an alternative proposal from the literature is conducted via simulations. Real data are analyzed to demonstrate how the new approach works in practice.
Robust estimators for free surface turbulence characterization: A stepped spillway application
(2020)
Robust estimators are parameters insensitive to the presence of outliers. However, they presume the shape of the variables’ probability density function. This study exemplifies the sensitivity of turbulent quantities to the use of classic and robust estimators and the presence of outliers in turbulent flow depth time series. A wide range of turbulence quantities was analysed based upon a stepped spillway case study, using flow depths sampled with Acoustic Displacement Meters as the flow variable of interest. The studied parameters include: the expected free surface level, the expected fluctuation intensity, the depth skewness, the autocorrelation timescales, the vertical velocity fluctuation intensity, the perturbations celerity and the one-dimensional free surface turbulence spectrum. Three levels of filtering were utilised prior to applying classic and robust estimators, showing that comparable robustness can be obtained either using classic estimators together with an intermediate filtering technique or using robust estimators instead, without any filtering technique.
Large scale central receiver systems typically deploy between thousands to more than a hundred thousand heliostats. During solar operation, each heliostat is aligned individually in such a way that the overall surface normal bisects the angle between the sun’s position and the aim point coordinate on the receiver. Due to various tracking error sources, achieving accurate alignment ≤1 mrad for all the heliostats with respect to the aim points on the receiver without a calibration system can be regarded as unrealistic. Therefore, a calibration system is necessary not only to improve the aiming accuracy for achieving desired flux distributions but also to reduce or eliminate spillage. An overview of current larger-scale central receiver systems (CRS), tracking error sources and the basic requirements of an ideal calibration system is presented. Leading up to the main topic, a description of general and specific terms on the topics heliostat calibration and tracking control clarifies the terminology used in this work. Various figures illustrate the signal flows along various typical components as well as the corresponding monitoring or measuring devices that indicate or measure along the signal (or effect) chain. The numerous calibration systems are described in detail and classified in groups. Two tables allow the juxtaposition of the calibration methods for a better comparison. In an assessment, the advantages and disadvantages of individual calibration methods are presented.
Purpose
Globally, a detrimental shift in cardiovascular disease risk factors and a higher mortality level are reported in some black populations. The retinal microvasculature provides early insight into the pathogenesis of systemic vascular diseases, but it is unclear whether retinal vessel calibers and acute retinal vessel functional responses differ between young healthy black and white adults.
Methods
We included 112 black and 143 white healthy normotensive adults (20–30 years). Retinal vessel calibers (central retinal artery and vein equivalent (CRAE and CRVE)) were calculated from retinal images and vessel caliber responses to flicker light induced provocation (FLIP) were determined. Additionally, ambulatory blood pressure (BP), anthropometry and blood samples were collected.
Results
The groups displayed similar 24 h BP profiles and anthropometry (all p > .24). Black participants demonstrated a smaller CRAE (158 ± 11 vs. 164 ± 11 MU, p < .001) compared to the white group, whereas CRVE was similar (p = .57). In response to FLIP, artery maximal dilation was greater in the black vs. white group (5.6 ± 2.1 vs. 3.3 ± 1.8%; p < .001).
Conclusions
Already at a young age, healthy black adults showed narrower retinal arteries relative to the white population. Follow-up studies are underway to show if this will be related to increased risk for hypertension development. The reason for the larger vessel dilation responses to FLIP in the black population is unclear and warrants further investigation.
Masked hypertension is known to induce microvascular complications. However, it is unclear whether early microvascular changes are already occurring in young, otherwise healthy adults. We therefore investigated whether retinal microvascular calibers and acute responses to a flicker stimulus are related to masked hypertension. We used the baseline data of 889 participants aged 20–30 years who were taking part in the African Prospective study on the Early Detection and Identification of Cardiovascular Disease and Hypertension. Clinic and 24-h ambulatory blood pressure were measured. The central retinal artery equivalent (CRAE) and central retinal vein equivalent were calculated from fundus images, and retinal vessel dilation was determined in response to flicker light-induced provocation. A smaller CRAE was observed in those with masked hypertension vs. those with normotension (157.1 vs. 161.2 measuring units, P < 0.001). In forward multivariable-adjusted regression analysis, only CRAE was negatively related to masked hypertension [adjusted R² = 0.267, β = −0.097 (95% CI = −0.165; −0.029), P = 0.005], but other retinal microvascular parameters were not associated with masked hypertension. In multivariable logistic regression analyses, masked hypertension [OR = 2.333, (95% CI = 1.316; 4.241), P = 0.004] was associated with a narrower CRAE. In young healthy adults, masked hypertension was associated with retinal arteriolar narrowing, thereby reflecting early microvascular alterations known to predict cardiovascular outcomes in later life.