Dieter Schwarzenbach (1936-2024).

Obituary for Dieter Schwarzenbach.

Effect of the Agglomerate Geometry on the Effective Electrical Conductivity of a Porous Electrode.

The study of the microstructure of random heterogeneous materials, related to an electrochemical device, is relevant because their effective macroscopic properties, e.g., electrical or proton conductivity, are a function of their effective transport coefficients (ETC). The magnitude of ETC depends on the distribution and properties of the material phase. In this work, an algorithm is developed to generate stochastic two-phase (binary) image configurations with multiple geometries and polydispersed particle sizes. The recognizable geometry in the images is represented by the white phase dispersed and characterized by statistical descriptors (two-point and line-path correlation functions). Percolation is obtained for the geometries by identifying an infinite cluster to guarantee the connection between the edges of the microstructures. Finally, the finite volume method is used to determine the ETC. Agglomerate phase results show that the geometry with the highest local current distribution is the triangular geometry. In the matrix phase, the most significant results are obtained by circular geometry, while the lowest is obtained by the 3-sided polygon. The proposed methodology allows to establish criteria based on percolation and surface fraction to assure effective electrical conduction according to their geometric distribution; results provide an insight for the microstructure development with high projection to be used to improve the electrode of a Membrane Electrode Assembly (MEA).

Effect of An Image Resolution Change on the Effective Transport Coefficient of Heterogeneous Materials.

Electrochemical electrodes comprise multiple phenomena at different scales. Several works have tried to model such phenomena using statistical techniques. This paper proposes a novel process to work with reduced size images to reconstruct microstructures with the Simulated Annealing method. Later, using the Finite Volume Method, it is verified the effect of the image resolution on the effective transport coefficient (ETC). The method can be applied to synthetic images or images from the Scanning Electron Microscope. The first stage consists of obtaining the image of minimum size, which contains at least 98% of the statistical information of the original image, allowing an equivalent statistical study. The image size reduction was made by applying an iterative decimation over the image using the normalized coarseness to compare the amount of information contained at each step. Representative improvements, especially in processing time, are achieved by reducing the size of the reconstructed microstructures without affecting their statistical behavior. The process ends computing the conduction efficiency from the microstructures. The simulation results, obtained from two kinds of images from different materials, demonstrate the effectivity of the proposed approach. It is important to remark that the controlled decimation allows a reduction of the processor and memory use during the reconstruction and ETC computation of electrodes.

Multiparametric statistical quantification of pH heterogeneity by 1 H MRS and MRSI of extracellular pH markers: Proof of principle.

Acid production and transport in numerous biological tissues and medical conditions are active areas of research. Heterogeneity of pH within a given homogeneous-appearing tissue volume has been reported, but none of the conventional methods currently available for measuring tissue pH provides quantitative parameters describing the frequency of occurrence of pH values within such a volume. We have previously presented a multiparametric noninvasive in vivo approach, providing at least 10 different statistical descriptors of pH heterogeneity based on a novel type of line shape analysis developed for pH-sensitive 31 P MRS resonances. However, this method suffers from lack of sensitivity, thus making rapid and spatially resolved measurements difficult. We present here the proof of principle of a new, more sensitive approach to statistical characterization of extracellular pH heterogeneity based on 1 H MRS, with the potential of being combined with spatial resolution. We experimentally study a range of test solutions of a reporter molecule that has previously been shown to possess a 1 H MRS resonance whose chemical shift varies with pH, including when injected intravenously into experimental animals (imidazole ethoxycarbonylpropionic acid, [IEPA]). Statistical pH heterogeneity descriptors are determined for phantoms mimicking tissue pH heterogeneity. To this end, the pH-sensitive 1 H MRS resonance is transformed into a pH curve. Subsequently, the digital points of this pH profile are used to build a histogram using dedicated algorithms. The following descriptors are computed from this histogram: weighted mean pH and median pH, pH standard deviation, pH range, pH mode(s), pH kurtosis, pH skewness and pH entropy. Our new method is also validated by analyzing previously published in vivo MRSI spectra. The proof of principle provided in this work should form the basis of further in vivo studies in physiology and medicine, eg in cancer research, but also in other fields such as kidney and muscle research.

Modeling clustered activity increase in amyloid-beta positron emission tomographic images with statistical descriptors.

BACKGROUND: Amyloid-beta (Aß) imaging with positron emission tomography (PET) holds promise for detecting the presence of Aß plaques in the cortical gray matter. Many image analyses focus on regional average measurements of tracer activity distribution; however, considerable additional information is available in the images. Metrics that describe the statistical properties of images, such as the two-point correlation function (S2), have found wide applications in astronomy and materials science. S2 provides a detailed characterization of spatial patterns in images typically referred to as clustering or flocculence. The objective of this study was to translate the two-point correlation method into Aß-PET of the human brain using 11C-Pittsburgh compound B (11C-PiB) to characterize longitudinal changes in the tracer distribution that may reflect changes in Aß plaque accumulation. METHODS: We modified the conventional S2 metric, which is primarily used for binary images and formulated a weighted two-point correlation function (wS2) to describe nonbinary, real-valued PET images with a single statistical function. Using serial 11C-PiB scans, we calculated wS2 functions from two-dimensional PET images of different cortical regions as well as three-dimensional data from the whole brain. The area under the wS2 functions was calculated and compared with the mean/median of the standardized uptake value ratio (SUVR). For three-dimensional data, we compared the area under the wS2 curves with the subjects' cerebrospinal fluid measures. RESULTS: Overall, the longitudinal changes in wS2 correlated with the increase in mean SUVR but showed lower variance. The whole brain results showed a higher inverse correlation between the cerebrospinal Aß and wS2 than between the cerebrospinal Aß and SUVR mean/median. We did not observe any confounding of wS2 by region size or injected dose. CONCLUSION: The wS2 detects subtle changes and provides additional information about the binding characteristics of radiotracers and Aß accumulation that are difficult to verify with mean SUVR alone.