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Current characterization methods of the so-called Bulk Heterojunction (BHJ), which is the main material of Organic Photovoltaic (OPV) solar cells, are limited to the analysis of global fabrication parameters. This reduces the efficiency of the BHJ design process, since it misses critical information about the local performance bottlenecks in the morphology of the material. In this paper, we propose a novel framework that fills this gap through visual characterization and exploration of local structure-performance correlations. We also propose a formula that correlates the structural features with the performance bottlenecks. Since research into BHJ materials is highly multidisciplinary, our framework enables a visual feedback strategy that allows scientists to build intuition about the best choices of fabrication parameters. We evaluate the usefulness of our proposed system by obtaining new BHJ characterizations. Furthermore, we show that our approach could substantially reduce the turnaround time.
The structure of Bulk-Heterojunction (BHJ) materials, the main component of organic photovoltaic solar cells, is very complex, and the relationship between structure and performance is still largely an open question. Overall, there is a wide spectrum of fabrication configurations resulting in different BHJ morphologies and correspondingly different performances. Current state- of-the-art methods for assessing the performance of BHJ morphologies are either based on global quantification of morphological features or simply on visual inspection of the morphology based on experimental imaging. This makes finding optimal BHJ structures very challenging. Moreover, finding the optimal fabrication parameters to get an optimal structure is still an open question. In this paper, we propose a visual analysis framework to help answer these questions through comparative visualization and parameter space exploration for local morphology features. With our approach, we enable scientists to explore multivariate correlations between local features and performance indicators of BHJ morphologies. Our framework is built on shape-based clustering of local cubical regions of the morphology that we call patches. This enables correlating the features of clusters with intuition-based performance indicators computed from geometrical and topological features of charge paths.
Many real world problems can be mapped onto graphs and solved with well-established efficient algorithms studied in graph theory. One such problem is to find large sets of points satisfying some mutual relationship. This problem can be transformed to the problem of finding all cliques of an undirected graph by mapping each point onto a vertex of the graph and connecting any two vertices by an edge whose corresponding points satisfy our desired relationship. Clique detection has been widely studied and there exist efficient algorithms. In this paper we study a related problem, where all points have a set of binary attributes, each of which is either 0 or 1. This is only a small limitation, since all discrete properties can be mapped onto binary attributes. In our case, we want to find large sets of points not only satisfying some mutual relationship; but, in addition, all points of a set also need to have at least one common attribute with value 1. The problem we described can be mapped onto a set of induced subgraphs, where each subgraph represents a single attribute. For attribute $i$, its associated subgraph contains those vertices corresponding to the points with attribute $i$ set to 1. We introduce the notion of a maximal clique of a family, $\mathcal{G}$, of induced subgraphs of an undirected graph, and show that determining all maximal cliques of $\mathcal{G}$ solves our problem. Furthermore, we present an efficient algorithm to compute all maximal cliques of $\mathcal{G}$. The algorithm we propose is an extension of the widely used Bron-Kerbosch algorithm.
In this paper we describe a new algorithm for multiple semi-flexible superpositioning of drug-sized molecules. The algorithm identifies structural similarities of two or more molecules. When comparing a set of molecules on the basis of their three-dimensional structures, one is faced with two main problems. (1) Molecular structures are not fixed but flexible, i.e., a molecule adopts different forms. To address this problem, we consider a set of conformers per molecule. As conformers we use representatives of conformational ensembles, generated by the program ZIBMol. (2) The degree of similarity may vary considerably among the molecules. This problem is addressed by searching for similar substructures present in arbitrary subsets of the given set of molecules. The algorithm requires to preselect a reference molecule. All molecules are compared to this reference molecule. For this pairwise comparison we use a two-step approach. Clique detection on the correspondence graph of the molecular structures is used to generate start transformations, which are then iteratively improved to compute large common substructures. The results of the pairwise comparisons are efficiently merged using binary matching trees. All common substructures that were found, whether they are common to all or only a few molecules, are ranked according to different criteria, such as number of molecules containing the substructure, size of substructure, and geometric fit. For evaluating the geometric fit, we extend a known scoring function by introducing weights which allow to favor potential pharmacophore points. Despite considering the full atomic information for identifying multiple structural similarities, our algorithm is quite fast. Thus it is well suited as an interactive tool for the exploration of structural similarities of drug-sized molecules.
Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.
Many natural objects contain pores and cavities that are filled with the same material that also surrounds the object. When such objects are imaged using, for example, computed tomography, the pores and cavities cannot be distinguished from the surrounding material by considering gray values and texture properties of the image. In this case, morphological operations are often used to fill the inner region. This is efficient, if the pore and cavity structures are small compared to the overall size of the object and if the object’s shape is mainly convex. If this is not the case, the segmentation might be very difficult and may result in a lot of noise. We propose the usage of ambient occlusion for the segmentation of pores and cavities. One nice property of ambient occlusion is that it generates smooth scalar fields. Due to this smoothness property, a segmentation based on those fields will result in smooth boundaries at the pore and cavity openings. This is often desired, particularly when dealing with natural objects.
High-Throughput Segmentation of Tiled Biological Structures using Random-Walk Distance Transforms
(2019)
Various 3D imaging techniques are routinely used to examine biological materials, the results of which are usually a stack of grayscale images. In order to quantify structural aspects of the biological materials, however, they must first be extracted from the dataset in a process called segmentation. If the individual structures to be extracted are in contact or very close to each other, distance-based segmentation methods utilizing the Euclidean distance transform are commonly employed. Major disadvantages of the Euclidean distance transform, however, are its susceptibility to noise (very common in biological data), which often leads to incorrect segmentations (i.e. poor separation of objects of interest), and its limitation of being only effective for roundish objects. In the present work, we propose an alternative distance transform method, the random-walk distance transform, and demonstrate its effectiveness in high-throughput segmentation of three microCT datasets of biological tilings (i.e. structures composed of a large number of similar repeating units). In contrast to the Euclidean distance transform, this random-walk approach represents the global, rather than the local, geometric character of the objects to be segmented and, thus, is less susceptible to noise. In addition, it is directly applicable to structures with anisotropic shape characteristics. Using three case studies—stingray tessellated cartilage, starfish dermal endoskeleton, and the prismatic layer of bivalve mollusc shell—we provide a typical workflow for the segmentation of tiled structures, describe core image processing concepts that are underused in biological research, and show that for each study system, large amounts of biologically-relevant data can be rapidly segmented, visualized and analyzed.
In most vertebrates the embryonic cartilaginous skeleton is replaced by bone during development. During this process, cartilage cells (chondrocytes) mineralize the extracellular matrix and undergo apoptosis, giving way to bone cells (osteocytes). In contrast, sharks and rays (elasmobranchs) have cartilaginous skeletons throughout life, where only the surface mineralizes, forming a layer of tiles (tesserae). Elasmobranch chondrocytes, unlike those of other vertebrates, survive cartilage mineralization and are maintained alive in spaces (lacunae) within tesserae. However, the function(s) of the chondrocytes in the mineralized tissue remain unknown. Applying a custom analysis workflow to high-resolution synchrotron microCT scans of tesserae, we characterize the morphologies and arrangements of stingray chondrocyte lacunae, using lacunar morphology as a proxy for chondrocyte morphology. We show that the cell density is comparable in unmineralized and mineralized tissue from our study species and that cells maintain the similar volume even when they have been incorporated into tesserae. This discovery supports previous hypotheses that elasmobranch chondrocytes, unlike those of other taxa, do not proliferate, hypertrophy or undergo apoptosis during mineralization. Tessera lacunae show zonal variation in their shapes—being flatter further from and more spherical closer to the unmineralized cartilage matrix and larger in the center of tesserae— and show pronounced organization into parallel layers and strong orientation toward neighboring tesserae. Tesserae also exhibit local variation in lacunar density, with the density considerably higher near pores passing through the tesseral layer, suggesting pores and cells interact (e.g. that pores contain a nutrient source). We hypothesize that the different lacunar types reflect the stages of the tesserae formation process, while also representing local variation in tissue architecture and cell function. Lacunae are linked by small passages (canaliculi) in the matrix to form elongate series at the tesseral periphery and tight clusters in the center of tesserae, creating a rich connectivity among cells. The network arrangement and the shape variation of chondrocytes in tesserae indicate that cells may interact within and between tesserae and manage mineralization differently from chondrocytes in other vertebrates, perhaps performing analogous roles to osteocytes in bone.
An advantageous property of mesh-based geometric morphometrics (GM) towards landmark-based approaches, is the possibility of precisely examining highly irregular shapes and highly topographic surfaces. In case of spherical-harmonics-based GM the main requirement is a completely closed mesh surface, which often is not given, especially when dealing with natural objects. Here we present a methodological workflow to prepare 3D segmentations containing large cavity openings for the conduction of spherical-harmonics-based GM. This will be exemplified with a case study on claws of hermit crabs (Paguroidea, Decapoda, Crustacea), whereby joint openings – between manus and “movable finger” – typify the large-cavity-opening problem. We found a methodology including an ambient-occlusion-based segmentation algorithm leading to results precise and suitable to study the inter- and intraspecific differences in shape of hermit crab claws. Statistical analyses showed a significant separation between all examined diogenid and pagurid claws, whereas the separation between all left and right claws did not show significance. Additionally, the procedure offers other benefits. It is easy to reproduce and creates sparse variance in the data, closures integrate smoothly into the total structures and the algorithm saves a significant amount of time.