Analytically exact spiral scheme for generating uniformly distributed points on the unit sphere

NPCoronaPredict: A Computational Pipeline for the Prediction of the Nanoparticle-Biomolecule Corona

The corona of a nanoparticle immersed in a biological fluid is of key importance to its eventual fate and bioactivity in the environment or inside live tissues. It is critical to have insight into both the underlying bionano interactions and the corona composition to ensure biocompatibility of novel engineered nanomaterials. A prediction of these properties in silico requires the successful spanning of multiple orders of magnitude of both time and physical dimensions to produce results in a reasonable amount of time, necessitating the development of a multiscale modeling approach. Here, we present the NPCoronaPredict open-source software package: a suite of software tools to enable this prediction for complex multicomponent nanomaterials in essentially arbitrary biological fluids, or more generally any medium containing organic molecules. The package integrates several recent physics-based computational models and a library of both physics-based and data-driven parametrizations for nanomaterials and organic molecules. We describe the underlying theoretical background and the package functionality from the design of multicomponent NPs through to the evaluation of the corona.

Optimal uniform guide star catalog using a genetic algorithm

To achieve optimal and reliable star sensors and overcome some onboard hardware and software limitations, this study aimed to make an optimal uniform guide star catalog. For this purpose, the objective function was defined by the field of view (FOV) and magnitude threshold, and then design variables were optimized. The optimal uniform guide star catalog was obtained by a genetic algorithm alongside the Latinized stratified sampling method and by a novel, to the best of our knowledge, spherical density determination algorithm based on the minimum number of stars required for a star identification algorithm. Finally, Monte Carlo simulation was used to validate the results, which indicate a dramatic improvement, including a reduction in the number of stars in the uniform catalog and an increase in the probability of observing the minimum required stars for the star identification algorithm (at least 5 stars) in 98.34% of all possible optimal FOVs (about 12°).

Modeling impedance boundary conditions and acoustic barriers using the immersed boundary method: The three-dimensional case

One of the main challenges in time domain wave-based acoustics is the accurate simulation of both boundary conditions and barriers capable of reflecting and transmitting energy. Such scattering structures are generally of irregular geometry and characterised in terms of frequency-dependent reflectances and transittances. Conditions for numerical stability can be difficult to obtain in either case. Immersed boundary methods, which are heavily used in computational fluid dynamics applications, replace boundaries by discrete driving terms, avoiding volumetric meshing and staircasing approaches altogether. The main contribution of this article is a unified numerical treatment of both impedance boundary conditions and barriers capable of transmitting energy and suitable for use in the setting of wave-based acoustics. It is framed in terms of the immersed boundary method within a finite difference time domain scheme, using a dual set of matched discrete driving terms in both the conservation of mass and momentum equations that can be tuned against a desired reflectance or transmittance. Numerical results in three dimensions are presented, illustrating non-porous barriers and impedance boundary conditions, and highlight important features such as spurious leakage through an immersed boundary. A brief demonstration of conditions for numerical stability of the immersed boundary method in this context is provided in an appendix.

A Permanent Magnet Synchronous Spherical Motor for High-Mobility Servo-Actuation

The development of direct-drive spherical motors offers a potential solution to the limitations of conventional multiple degree-of-freedom (DOF) actuators, which typically utilize single-DOF joints (rotational and/or prismatic), arranged in series or parallel and powered by multiple single-DOF actuators. These configurations can be accompanied by kinematic singularities, backlash, limited power density and efficiency, and computationally expensive inverse kinematics. This paper details the design, fabrication and experimental testing of permanent magnet synchronous spherical motors (PMSSM) for multi-DOF servo-actuation. Its stator-pole arrangement is based on a Goldberg polyhedron, with each pole comprised of hexagonal or pentagonal inner and outer plates. The stator geometry and winding configurations are optimized using electromagnetic finite element analysis. A custom-made controller board includes a microcontroller, servo drivers, a wireless serial interface, and a USB PC interface. Angular orientation is sensed using an inertial measurement unit in wireless communication with the microcontroller. A PID controller is implemented and demonstrated for time-varying reference trajectories.

Immersed boundary methods in wave-based virtual acoustics

Volumetric wave-based simulation methods for room and virtual acoustics, such as the finite difference time domain method, are computationally intensive; for large volumes, operation over a regular grid is desirable for the sake of efficiency. In coping with realistic irregular geometries (such as enclosures or scattering objects), form-fitting meshing can disturb grid regularity and introduce new difficulties in terms of maintaining numerical stability. An alternative is the immersed boundary method, allowing for the representation of an irregular boundary over a regular grid through additional forcing terms in the dynamical system. While heavily used in fluid-structure interaction problems, such methods have seen less application in virtual acoustics. In this article, a simplified form of the immersed boundary method tailored to virtual acoustics is presented. Under appropriate passivity-preserving discretisation techniques, simple numerical stability conditions can be proved, and in particular, impedance boundaries may be incorporated easily without any risk of numerical instability. In addition, the method retains a largely explicit character with a small linear system solution required over the immersed boundary surface. Numerical results in two and three dimensions, illustrating various interior and exterior problem scenarios, are presented.

Determining the charge distribution and the direction of bond cleavage with femtosecond anisotropic x-ray liquidography

Energy, structure, and charge are fundamental quantities characterizing a molecule. Whereas the energy flow and structure change in chemical reactions are experimentally characterized, determining the atomic charges of a molecule in solution has been elusive, even for a triatomic molecule such as triiodide ion, I3-. Moreover, it remains to be answered how the charge distribution is coupled to the molecular geometry; which I-I bond, if two I-I bonds are unequal, dissociates depending on the electronic state. Here, femtosecond anisotropic x-ray solution scattering allows us to provide the following answers in addition to the overall rich structural dynamics. The analysis unravels that the negative charge of I3- is highly localized on the terminal iodine atom forming the longer bond with the central iodine atom, and the shorter I-I bond dissociates in the excited state, whereas the longer one in the ground state. We anticipate that this work may open a new avenue for studying the atomic charge distribution of molecules in solution and taking advantage of orientational information in anisotropic scattering data for solution-phase structural dynamics.

On the collision of rods in a quiescent fluid

Rods settling under gravity in a quiescent fluid can overcome the bottleneck associated with aggregation of equal-size spheres because they collide by virtue of their orientation-dependent settling velocity. We find the corresponding collision kernel Γrods=lβ1ΔρVrodg/(16Aμ), where l, A, and Vrod are the rods’ length, aspect ratio (length divided by width), and volume, respectively, Δρ is the density difference between rods and fluid, μ is the fluid’s dynamic viscosity, g is the gravitational acceleration, and β1(A) is a geometrical parameter. We apply this formula to marine snow formation following a phytoplankton bloom. Over a broad range of aspect ratios, the formula predicts a similar or higher encounter rate between rods as compared to the encounter rate between (equal volume) spheres aggregating either by differential settling or due to turbulence. Since many phytoplankton species are elongated, these results suggest that collisions induced by the orientation-dependent settling velocity can contribute significantly to marine snow formation, and that marine snow composed of elongated phytoplankton cells can form at high rates also in the absence of turbulence.

The analytical subtraction approach for solving the forward problem in EEG

OBJECTIVE

The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists of computing integrals of singular kernels over the discretised domain, usually referred to as potential integrals. Several techniques have been proposed for dealing with such integrals, all of them approximating the results at the expense of reducing the accuracy of the solution. In this paper, we derive analytic formulas for the potential integrals, reducing approximation errors to a minimum.

APPROACH

Based on volume coordinates and Gauss theorems, we obtained parametric expressions for all the element matrices needed in the formulation assuming first order basis functions defined on a tetrahedral mesh. This included solving potential integrals over triangles and tetrahedra, for which we found compact and efficient formulas.

MAIN RESULTS

Comparison with numerical quadrature schemes allowed us to test the advantages of the methodology proposed, which were found of great relevance for highly-eccentric sources, as those found in the somatosensory and visual cortices. Moreover, the availability of compact formulas allowed for an efficient implementation of the technique, which resulted in similar computational cost than the simplest numerical scheme.

SIGNIFICANCE

The analytical subtraction approach is the optimal subtraction-based methodology with regard to accuracy. The computational cost is similar to that obtained with the lowest order numerical integration scheme, making it a competitive option in the field. The technique is highly relevant for improving electromagnetic source imaging results utilising individualised head models and anisotropic electric conductivity fields without imposing impractical mesh requirements.

A Finite Element Solution of the Forward Problem in EEG for Multipolar Sources

Multipolar source models have been presented in the context of electro/magnetoencephalography (E/MEG) to compensate for the limitations of the classical equivalent current dipole to represent realistic generators of brain activity. Although there exist several reports accounting for the advantages of multipolar components over single dipoles, there is still no available numerical implementation in fully personalized scenarios. In this paper, we present, for the first time, a finite element framework for simulating EEG signals generated by multipolar current sources in individualized, heterogeneous, and anisotropic head models. This formulation is based on the subtraction approach, guaranteeing the existence and uniqueness of the solution. In particular, we analyze the cases of monopolar, dipolar, and quadrupolar source components, for which we study their performance in idealized and realistic head models. Numerical solutions are compared with analytical formulas in multi-layered spherical models. Such formulas are available in the case of monopolar and dipolar sources, and here derived for the quadrupolar components. We finally illustrate their advantages in the description of extended current generators using a realistic head model. The framework presented here enables further analysis towards the estimation of biophysically principled source parameters from standard E/MEG experiments.

Online Uniformly Inserting Points on the Sphere

Uniformly inserting points on the sphere has been found useful in many scientific and engineering fields. Different from the offline version where the number of points is known in advance, we consider the online version of this problem. The requests for point insertion arrive one by one and the target is to insert points as uniformly as possible. To measure the uniformity we use gap ratio which is defined as the ratio of the maximal gap to the minimal gap of two arbitrary inserted points. We propose a two-phase online insertion strategy with gap ratio of at most 3.69 . Moreover, the lower bound of the gap ratio is proved to be at least 1.78 .

Sensitivity of the Projected Subtraction Approach to Mesh Degeneracies and Its Impact on the Forward Problem in EEG

OBJECTIVE

Subtraction-based techniques are known for being theoretically rigorous and accurate methods for solving the forward problem in electroencephalography (EEG-FP) by means of the finite-element method. Within them, the projected subtraction (PS) approach is generally adopted because of its computational efficiency. Although this technique received the attention of the community, its sensitivity to degenerated elements is still poorly understood. In this paper, we investigate the impact of low-quality tetrahedra on the results computed with the PS approach.

METHODS

We derived upper bounds on the relative error of the element source vector as a function of geometrical features describing the tetrahedral discretization of the domain. These error bounds were then utilized for showing the instability of the PS method with regards to the mesh quality. To overcome this issue, we proposed an alternative technique, coined projected gradient subtraction (PGS) approach, that exploits the stability of the corresponding bounds.

RESULTS

Computer simulations showed that the PS method is extremely sensitive to the mesh shape and size, leading to unacceptable solutions of the EEG-FP in case of using suboptimal tessellations. This was not the case of the PGS approach, which led to stable and accurate results in a comparable amount of time.

CONCLUSION

Solutions of the EEG-FP computed with the PS method are highly sensitive to degenerated elements. Such errors can be mitigated by the PGS approach, which showed better performance than the PS technique.

SIGNIFICANCE

The PGS is an efficient method for computing high-quality lead field matrices even in the presence of degenerated elements.

Quantitative comparison of measured crystallographic texture

A new approach for the determination of a quantitative measure to compare pole figures for different specimens is presented. The suggested approach is based on the Kolmogorov–Smirnov test. A new quantitative similarity measure between the textures of different specimens is suggested. This measure is verified by means of numerical models for both cubic and hexagonal crystalline symmetry, and it is applied to real experimental data for railway wheel steel. A comparison between the existing RP value and the introduced KSP value is presented to illustrate the specific character of the latter.

Pseudometrically constrained centroidal voronoi tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to diffusion and three-dimensional radial MRI

PURPOSE

The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role in image quality when the raw data and image data are related through the Fourier relationship. Currently, it is extremely challenging to generate large and uniform antipodally symmetric point sets suitable for three-dimensional radial MRI. A novel approach is proposed to solve this long-standing problem in a unique and optimal way.

METHODS

The proposed method is based on constrained centroidal Voronoi tessellations of the upper hemisphere with a novel pseudometric.

RESULTS

The time complexity of the proposed tessellations was shown to be effectively linear, i.e., on the order of the number of sampling measurements. For small sample size, the proposed method was comparable with the state-of-the-art method (a direct iterative minimization of the electrostatic potential energy of a collection of electrons antipodal-symmetrically distributed on the unit sphere) in terms of the sampling uniformity. For large sample size, in which the state-of-the-art method is infeasible, the reconstructed images from the proposed method has less streak and ringing artifacts, when compared with those of the commonly used methods.

CONCLUSION

This work proposed a unique and optimal approach to solving a long-standing problem in generating uniform sampling points for three-dimensional radial MRI.

lop-DWI: A Novel Scheme for Pre-Processing of Diffusion-Weighted Images in the Gradient Direction Domain

We describe and evaluate a pre-processing method based on a periodic spiral sampling of diffusion-gradient directions for high angular resolution diffusion magnetic resonance imaging. Our pre-processing method incorporates prior knowledge about the acquired diffusion-weighted signal, facilitating noise reduction. Periodic spiral sampling of gradient direction encodings results in an acquired signal in each voxel that is pseudo-periodic with characteristics that allow separation of low-frequency signal from high frequency noise. Consequently, it enhances local reconstruction of the orientation distribution function used to define fiber tracks in the brain. Denoising with periodic spiral sampling was tested using synthetic data and in vivo human brain images. The level of improvement in signal-to-noise ratio and in the accuracy of local reconstruction of fiber tracks was significantly improved using our method.

Sparse and optimal acquisition design for diffusion MRI and beyond

PURPOSE

Diffusion magnetic resonance imaging (MRI) in combination with functional MRI promises a whole new vista for scientists to investigate noninvasively the structural and functional connectivity of the human brain-the human connectome, which had heretofore been out of reach. As with other imaging modalities, diffusion MRI data are inherently noisy and its acquisition time-consuming. Further, a faithful representation of the human connectome that can serve as a predictive model requires a robust and accurate data-analytic pipeline. The focus of this paper is on one of the key segments of this pipeline-in particular, the development of a sparse and optimal acquisition (SOA) design for diffusion MRI multiple-shell acquisition and beyond.

METHODS

The authors propose a novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and a novel and effective semistochastic and moderately greedy combinatorial search strategy with simulated annealing to locate the optimum design or configuration. The goal of the optimality criteria is threefold: first, to maximize uniformity of the diffusion measurements in each shell, which is equivalent to maximal incoherence in angular measurements; second, to maximize coverage of the diffusion measurements around each radial line to achieve maximal incoherence in radial measurements for multiple-shell acquisition; and finally, to ensure maximum uniformity of diffusion measurement directions in the limiting case when all the shells are coincidental as in the case of a single-shell acquisition. The approach taken in evaluating the stability of various acquisition designs is based on the condition number and the A-optimal measure of the design matrix.

RESULTS

Even though the number of distinct configurations for a given set of diffusion gradient directions is very large in general-e.g., in the order of 10(232) for a set of 144 diffusion gradient directions, the proposed search strategy was found to be effective in finding the optimum configuration. It was found that the square design is the most robust (i.e., with stable condition numbers and A-optimal measures under varying experimental conditions) among many other possible designs of the same sample size. Under the same performance evaluation, the square design was found to be more robust than the widely used sampling schemes similar to that of 3D radial MRI and of diffusion spectrum imaging (DSI).

CONCLUSIONS

A novel optimality criterion for sparse multiple-shell acquisition and quasimultiple-shell designs in diffusion MRI and an effective search strategy for finding the best configuration have been developed. The results are very promising, interesting, and practical for diffusion MRI acquisitions.

A simple scheme for generating nearly uniform distribution of antipodally symmetric points on the unit sphere

A variant of the Thomson problem, which is about placing a set of points uniformly on the surface of a sphere, is that of generating uniformly distributed points on the sphere that are endowed with antipodal symmetry, i.e., if x is an element of the point set then -x is also an element of that point set. Point sets with antipodal symmetry are of special importance to many scientific and engineering applications. Although this type of point sets may be generated through the minimization of a slightly modified electrostatic potential, the optimization procedure becomes unwieldy when the size of the point set increases beyond a few thousands. Therefore, it is desirable to have a deterministic scheme capable of generating this type of point set with near uniformity. In this work, we will present a simple deterministic scheme to generate nearly uniform point sets with antipodal symmetry.

Extremely efficient and deterministic approach to generating optimal ordering of diffusion MRI measurements

PURPOSE

Diffusion MRI measurements are typically acquired sequentially with unit gradient directions that are distributed uniformly on the unit sphere. The ordering of the gradient directions has significant effect on the quality of dMRI-derived quantities. Even though several methods have been proposed to generate optimal orderings of gradient directions, these methods are not widely used in clinical studies because of the two major problems. The first problem is that the existing methods for generating highly uniform and antipodally symmetric gradient directions are inefficient. The second problem is that the existing methods for generating optimal orderings of gradient directions are also highly inefficient. In this work, the authors propose two extremely efficient and deterministic methods to solve these two problems.

METHODS

The method for generating nearly uniform point set on the unit sphere (with antipodal symmetry) is based upon the notion that the spacing between two consecutive points on the same latitude should be equal to the spacing between two consecutive latitudes. The method for generating optimal ordering of diffusion gradient directions is based on the idea that each subset of incremental sample size, which is derived from the prescribed and full set of gradient directions, must be as uniform as possible in terms of the modified electrostatic energy designed for antipodally symmetric point set.

RESULTS

The proposed method outperformed the state-of-the-art method in terms of computational efficiency by about six orders of magnitude.

CONCLUSIONS

Two extremely efficient and deterministic methods have been developed for solving the problem of optimal ordering of diffusion gradient directions. The proposed strategy is also applicable to optimal view-ordering in three-dimensional radial MRI.