Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

Low-dimensional hydrogen-bonded structures in the 1:1 and 1:2 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine

The structures of proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine, namely triethylaminium 2-carboxy-4,5-dichlorobenzoate C~6~H~16~N^+^ C~8~H~3~Cl~2~O~4~^-^ (I), diethylaminium 2-carboxy-4,5-dichlorobenzoate C~4~H~12~N^+^ C~8~H~3~Cl~2~O~4~^-^ (II), bis(n-butylaminium) 4,5-dichlorophthalate monohydrate 2(C~4~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (III) and bis(piperidinium) 4,5-dichlorophthalate monohydrate 2(C~5~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (IV)have been determined at 200 K. All compounds have hydrogen-bonding associations giving in (I) discrete cation-anion units, linear chains in (II) while (III) and (IV) both have two-dimensional structures. In (I) a discrete cation-anion unit is formed through an asymmetric R2/1(4) N+-H...O,O' hydrogen-bonding association whereas in (II), one-dimensional chains are formed through linear N-H...O associations by both aminium H donors. In compounds (III) and (IV) the primary N-H...O linked cation-anion units are extended into a two-dimensional sheet structure via amide N-H...O(carboxyl) and ...O(carbonyl) interactions. In the 1:1 salts [(I) and (II)], the hydrogen 4,5-dichlorophthalate anions are essentially planar with short intramolecular carboxylic acid O-H...O(carboxyl) hydrogen bonds [O...O, 2.4223(14) and 2.388(2)A respectively]. This work provides a further example of the uncommon zero-dimensional hydrogen-bonded DCPA-Lewis base salt and the one-dimensional chain structure type, while even with the hydrate structures of the 1:2 salts with the primary and secondary amines, the low dimensionality generally associated with 1:1 DCPA salts is also found.

Three-dimensional imaging for a very large excavator

In this paper we describe the development of a three-dimensional (3D) imaging system for a 3500 tonne mining machine (dragline).Draglines are large walking cranes used for removing the dirt that covers a coal seam. Our group has been developing a dragline swing automation system since 1994. The system so far has been `blind' to its external environment. The work presented in this paper attempts to give the dragline an ability to sense its surroundings. A 3D digital terrain map (DTM) is created from data obtained from a two-dimensional laser scanner while the dragline swings. Experimental data from an operational dragline are presented.

Repair of calvarial defects with customized tissue-engineered bone grafts - I. Evaluation of osteogenesis in a three-dimensional culture system

Bone generation by autogenous cell transplantation in combination with a biodegradable scaffold is one of the most promising techniques being developed in craniofacial surgery. The objective of this combined in vitro and in vivo study was to evaluate the morphology and osteogenic differentiation of bone marrow derived mesenchymal progenitor cells and calvarial osteoblasts in a two-dimensional (2-D) and three-dimensional (3-D) culture environment (Part I of this study) and their potential in combination with a biodegradable scaffold to reconstruct critical-size calvarial defects in an autologous animal model [Part II of this study; see Schantz, J.T., et al. Tissue Eng. 2003;9(Suppl. 1):S-127-S-139; this issue]. New Zealand White rabbits were used to isolate osteoblasts from calvarial bone chips and bone marrow stromal cells from iliac crest bone marrow aspirates. Multilineage differentiation potential was evaluated in a 2-D culture setting. After amplification, the cells were seeded within a fibrin matrix into a 3-D polycaprolactone (PCL) scaffold system. The constructs were cultured for up to 3 weeks in vitro and assayed for cell attachment and proliferation using phase-contrast light, confocal laser, and scanning electron microscopy and the MTS cell metabolic assay. Osteogenic differentiation was analyzed by determining the expression of alkaline phosphatase (ALP) and osteocalcin. The bone marrow-derived progenitor cells demonstrated the potential to be induced to the osteogenic, adipogenic, and chondrogenic pathways. In a 3-D environment, cell-seeded PCL scaffolds evaluated by confocal laser microscopy revealed continuous cell proliferation and homogeneous cell distribution within the PCL scaffolds. On osteogenic induction mesenchymal progenitor cells (12 U/L) produce significantly higher (p < 0.05) ALP activity than do osteoblasts (2 U/L); however, no significant differences were found in osteocalcin expression. In conclusion, this study showed that the combination of a mechanically stable synthetic framework (PCL scaffolds) and a biomimetic hydrogel (fibrin glue) provides a potential matrix for bone tissue-engineering applications. Comparison of osteogenic differentiation between the two mesenchymal cell sources revealed a similar pattern.

Anhydrous 1:1 proton-transfer compounds of isonipecotamide with picric acid and 3,5-dinitrosalicylic acid: 4-carbamoylpiperidinium 2,4,6-trinitrophenolate and two polymorphs of 4-carbamoylpiperidinium 2-carboxy-4,6-dinitrophenolate

The structures of the anhydrous 1:1 proton-transfer compounds of isonipecotamide (4-carbamoylpiperidine) with picric acid and 3,5-dinitrosalicylic acid, namely 4-carbamoylpiperidinium 2,4,6-trinitrophenolate, C6H13N2O8+ C6H2N3O7- (I) and 4-carbamoylpiperidinium 2-carboxy-4,6-dinitrophenolate, C6H13N2O8+ C7H3N2O7-: two forms, the monoclinic alpha-polymorph (II) and the triclinic beta-polymorph (III) have been determined at 200 K. All compounds form hydrogen-bonded structures, one-dimensional in (II), two-dimensional in (I) and three-dimensional in (III). In (I), the cations form centrosymmetric cyclic head-to-tail hydrogen-bonded homodimers [graph set R2/2(14)] through lateral duplex piperidinium N---H...O(amide) interactions. These dimers are extended into a two-dimensional network structure through further interactions with anion phenolate-O and nitro-O acceptors, including a direct symmetric piperidinium N-H...O(phenol),O(nitro) cation--anion association [graph set R2/1(6)]. The monoclinic polymorph (II) has a similar R2/1(6) cation-anion hydrogen-bonding interaction to (I) but with an additional conjoint symmetrical R1/2(4) interaction as well as head-to-tail piperidinium N-H...O(amide) O hydrogen bonds and amide N-H...O(carboxyl) hydrogen bonds, give a network structure which include large R3/4(20) rings. The hydrogen bonding in the triclinic polymorph (III) is markedly different from that of monoclinic (II). The asymmetric unit contains two independent cation-anion pairs which associate through cyclic piperidinium N-H...O,O'(carboxyl) interactions [graph set R2/1(4)]. The cations also show the zig-zag head-to-tail piperidinium N-H...O(amide) hydrogen-bonded chain substructures found in (II) but in addition feature amide N-H...O(nitro) and O(phenolate) and amide N-H...O(nitro) associations. As well there is a centrosymmetric double-amide N-H...O(carboxyl) bridged bis(cation-anion) ring system [graph set R2/4(8)] in the three-dimensional framework. The structures reported here demonstrate the utility of the isonipecotamide cation as a synthon with previously unrecognized potential for structure assembly applications. Furthermore, the structures of the two polymorphic 3,5-dinitrosalicylic acid salts show an unusual dissimilarity in hydrogen-bonding characteristics, considering that both were obtained from identical solvent systems.

Order and disorder in the structures of two crystal polymorphs of the adduct bis(quinolinium-2-carboxylate) DL-malic acid

The structures of two polymorphs of the anhydrous cocrystal adduct of bis(quinolinium-2-carboxylate) DL-malic acid, one triclinic the other monoclinic and disordered, have been determined at 200 K. Crystals of the triclinic polymorph 1 have space group P-1, with Z = 1 in a cell with dimensions a = 4.4854(4), b = 9.8914(7), c = 12.4670(8)Å, α = 79.671(5), β = 83.094(6), γ = 88.745(6)deg. Crystals of the monoclinic polymorph 2 have space group P21/c, with Z = 2 in a cell with dimensions a = 13.3640(4), b = 4.4237(12), c = 18.4182(5)Å, β = 100.782(3)deg. Both structures comprise centrosymmetric cyclic hydrogen-bonded quinolinic acid zwitterion dimers [graph set R2/2(10)] and 50% disordered malic acid molecules which lie across crystallographic inversion centres. However, the oxygen atoms of the malic acid carboxylic groups in 2 are 50% rotationally disordered whereas in 1 these are ordered. There are similar primary malic acid carboxyl O-H...quinaldic acid hydrogen-bonding chain interactions in each polymorph, extended into two-dimensional structures but in l this involves centrosymmetric cyclic head-to-head malic acid hydroxyl-carboxyl O-H...O interactions [graph set R2/2(10)] whereas in 2 the links are through single hydroxy-carboxyl hydrogen bonds.

Optimal fluid injection strategies for in situ mineral leaching in two-dimensions

This paper examines the ground-water flow problem associated with the injection and recovery of certain corrosive fluids into mineral bearing rock. The aim is to dissolve the minerals in situ, and then recover them in solution. In general, it is not possible to recover all the injected fluid, which is of concern economically and environmentally. However, a new strategy is proposed here, that allows all the leaching fluid to be recovered. A mathematical model of the situation is solved approximately using an asymptotic solution, and exactly using a boundary integral approach. Solutions are shown for two-dimensional flow, which is of some practical interest as it is achievable in old mine tunnels, for example.

User behaviour modelling in a multi-dimensional environment for personalization and recommendation

Handling information overload online, from the user's point of view is a big challenge, especially when the number of websites is growing rapidly due to growth in e-commerce and other related activities. Personalization based on user needs is the key to solving the problem of information overload. Personalization methods help in identifying relevant information, which may be liked by a user. User profile and object profile are the important elements of a personalization system. When creating user and object profiles, most of the existing methods adopt two-dimensional similarity methods based on vector or matrix models in order to find inter-user and inter-object similarity. Moreover, for recommending similar objects to users, personalization systems use the users-users, items-items and users-items similarity measures. In most cases similarity measures such as Euclidian, Manhattan, cosine and many others based on vector or matrix methods are used to find the similarities. Web logs are high-dimensional datasets, consisting of multiple users, multiple searches with many attributes to each. Two-dimensional data analysis methods may often overlook latent relationships that may exist between users and items. In contrast to other studies, this thesis utilises tensors, the high-dimensional data models, to build user and object profiles and to find the inter-relationships between users-users and users-items. To create an improved personalized Web system, this thesis proposes to build three types of profiles: individual user, group users and object profiles utilising decomposition factors of tensor data models. A hybrid recommendation approach utilising group profiles (forming the basis of a collaborative filtering method) and object profiles (forming the basis of a content-based method) in conjunction with individual user profiles (forming the basis of a model based approach) is proposed for making effective recommendations. A tensor-based clustering method is proposed that utilises the outcomes of popular tensor decomposition techniques such as PARAFAC, Tucker and HOSVD to group similar instances. An individual user profile, showing the user's highest interest, is represented by the top dimension values, extracted from the component matrix obtained after tensor decomposition. A group profile, showing similar users and their highest interest, is built by clustering similar users based on tensor decomposed values. A group profile is represented by the top association rules (containing various unique object combinations) that are derived from the searches made by the users of the cluster. An object profile is created to represent similar objects clustered on the basis of their similarity of features. Depending on the category of a user (known, anonymous or frequent visitor to the website), any of the profiles or their combinations is used for making personalized recommendations. A ranking algorithm is also proposed that utilizes the personalized information to order and rank the recommendations. The proposed methodology is evaluated on data collected from a real life car website. Empirical analysis confirms the effectiveness of recommendations made by the proposed approach over other collaborative filtering and content-based recommendation approaches based on two-dimensional data analysis methods.

An analytical tool that quantifies cellular morphology changes from three-dimensional fluorescence images

The most common software analysis tools available for measuring fluorescence images are for two-dimensional (2D) data that rely on manual settings for inclusion and exclusion of data points, and computer-aided pattern recognition to support the interpretation and findings of the analysis. It has become increasingly important to be able to measure fluorescence images constructed from three-dimensional (3D) datasets in order to be able to capture the complexity of cellular dynamics and understand the basis of cellular plasticity within biological systems. Sophisticated microscopy instruments have permitted the visualization of 3D fluorescence images through the acquisition of multispectral fluorescence images and powerful analytical software that reconstructs the images from confocal stacks that then provide a 3D representation of the collected 2D images. Advanced design-based stereology methods have progressed from the approximation and assumptions of the original model-based stereology(1) even in complex tissue sections(2). Despite these scientific advances in microscopy, a need remains for an automated analytic method that fully exploits the intrinsic 3D data to allow for the analysis and quantification of the complex changes in cell morphology, protein localization and receptor trafficking. Current techniques available to quantify fluorescence images include Meta-Morph (Molecular Devices, Sunnyvale, CA) and Image J (NIH) which provide manual analysis. Imaris (Andor Technology, Belfast, Northern Ireland) software provides the feature MeasurementPro, which allows the manual creation of measurement points that can be placed in a volume image or drawn on a series of 2D slices to create a 3D object. This method is useful for single-click point measurements to measure a line distance between two objects or to create a polygon that encloses a region of interest, but it is difficult to apply to complex cellular network structures. Filament Tracer (Andor) allows automatic detection of the 3D neuronal filament-like however, this module has been developed to measure defined structures such as neurons, which are comprised of dendrites, axons and spines (tree-like structure). This module has been ingeniously utilized to make morphological measurements to non-neuronal cells(3), however, the output data provide information of an extended cellular network by using a software that depends on a defined cell shape rather than being an amorphous-shaped cellular model. To overcome the issue of analyzing amorphous-shaped cells and making the software more suitable to a biological application, Imaris developed Imaris Cell. This was a scientific project with the Eidgenössische Technische Hochschule, which has been developed to calculate the relationship between cells and organelles. While the software enables the detection of biological constraints, by forcing one nucleus per cell and using cell membranes to segment cells, it cannot be utilized to analyze fluorescence data that are not continuous because ideally it builds cell surface without void spaces. To our knowledge, at present no user-modifiable automated approach that provides morphometric information from 3D fluorescence images has been developed that achieves cellular spatial information of an undefined shape (Figure 1). We have developed an analytical platform using the Imaris core software module and Imaris XT interfaced to MATLAB (Mat Works, Inc.). These tools allow the 3D measurement of cells without a pre-defined shape and with inconsistent fluorescence network components. Furthermore, this method will allow researchers who have extended expertise in biological systems, but not familiarity to computer applications, to perform quantification of morphological changes in cell dynamics.

Micromarrows—Three-dimensional coculture of hematopoietic stem cells and mesenchymal stromal cells

Hematopoietic stem cell (HSC) transplant is a well established curative therapy for some hematological malignancies. However, achieving adequate supply of HSC from some donor tissues can limit both its application and ultimate efficacy. The theory that this limitation could be overcome by expanding the HSC population before transplantation has motivated numerous laboratories to develop ex vivo expansion processes. Pioneering work in this field utilized stromal cells as support cells in cocultures with HSC to mimic the HSC niche. We hypothesized that through translation of this classic coculture system to a three-dimensional (3D) structure we could better replicate the niche environment and in turn enhance HSC expansion. Herein we describe a novel high-throughput 3D coculture system where murine-derived HSC can be cocultured with mesenchymal stem/stromal cells (MSC) in 3D microaggregates—which we term “micromarrows.” Micromarrows were formed using surface modified microwells and their ability to support HSC expansion was compared to classic two-dimensional (2D) cocultures. While both 2D and 3D systems provide only a modest total cell expansion in the minimally supplemented medium, the micromarrow system supported the expansion of approximately twice as many HSC candidates as the 2D controls. Histology revealed that at day 7, the majority of bound hematopoietic cells reside in the outer layers of the aggregate. Quantitative polymerase chain reaction demonstrates that MSC maintained in 3D aggregates express significantly higher levels of key hematopoietic niche factors relative to their 2D equivalents. Thus, we propose that the micromarrow platform represents a promising first step toward a high-throughput HSC 3D coculture system that may enable in vitro HSC niche recapitulation and subsequent extensive in vitro HSC self-renewal.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

Three-dimensional modeling of steel portal frame buildings

The realistic strength and deflection behavior of industrial and commercial steel portal frame buildings are understood only if the effects of rigidity of end frames and profiled steel claddings are included. The conventional designs ignore these effects and are very much based on idealized two-dimensional (2D) frame behavior. Full-scale tests of a 1212 m steel portal frame building under a range of design load cases indicated that the observed deflections and bending moments in the portal frame were considerably different from those obtained from a 2D analysis of frames ignoring these effects. Three-dimensional (3D) analyses of the same building, including the effects of end frames and cladding, were carried out, and the results agreed well with full-scale test results. Results clearly indicated the need for such an analysis and for testing to study the true behavior of steel portal frame buildings. It is expected that such a 3D analysis will lead to lighter steel frames as the maximum moments and deflections are reduced.

Adhesive characteristics of low dimensional carbon nanomaterial on actin

The biosafety of carbon nanomaterial needs to be critically evaluated with both experimental and theoretical validations before extensive biomedical applications. In this letter, we present an analysis of the binding ability of two dimensional monolayer carbon nanomaterial on actin by molecular simulation to understand their adhesive characteristics on F-actin cytoskeleton. The modelling results indicate that the positively charged carbon nanomaterial has higher binding stability on actin. Compared to crystalline graphene, graphene oxide shows higher binding influence on actin when carrying positive surface charge. This theoretical investigation provides insights into the sensitivity of actin-related cellular activities on carbon nanomaterial.

Self-organized Au nanoarrays on vertical graphenes : an advanced three-dimensional sensing platform

A three-dimensional surface enhanced Raman scattering (SERS)/plasmonic sensing platform based on plasma-enabled, catalyst-free, few-layer vertical graphenes decorated with self-organized Au nanoparticle arrays is demonstrated. This platform is viable for multiple species detection and overcomes several limitations of two-dimensional sensors.

Purification of the major group 1 allergen from bahia grass pollen, Pas n 1

Background Group 1 grass pollen allergens are glycoproteins of the β-expansin family. They are a predominant component of pollen and are potent allergens with a high frequency of serum IgE reactivity in grass pollen-allergic patients. Bahia grass is distinct from temperate grasses and has a prolonged pollination period and wide distribution in warmer climates. Here we describe the purification of the group 1 pollen allergen, Pas n 1, from Bahia grass (Paspalum notatum), an important subtropical aeroallergen source. Methods Pas n 1 was purified from an aqueous Bahia grass pollen extract by ammonium sulphate precipitation, hydrophobic interaction and size exclusion chromatography, and assessed by one- and two-dimensional gel electrophoresis, immunoblotting and ELISA. Results Pas n 1 was purified to a single 29-kDa protein band containing two dominant isoforms detected by an allergen-specific monoclonal antibody and serum IgE of a Bahia grass pollen-allergic donor. The frequency of serum IgE reactivity with purified Pas n 1 in 51 Bahia grass pollen-allergic patients was 90.6%. Serum IgE reactivity with purified Pas n 1 was highly correlated with serum IgE reactivity with Bahia grass pollen extract and recombinant Pas n 1 (r = 0.821 and 0.913, respectively). Conclusions Pas n 1 is a major allergen reactive at high frequency with serum IgE of Bahia grass pollen-allergic patients. Purified natural Pas n 1 has utility for improved specific diagnosis and immunotherapy for Bahia grass pollen allergy.