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

Electric potential energy optimized 3D radial sampling trajectories for MRI

A novel method for creating "golden" 3D center-out radial MRI sampling trajectories was developed and analyzed. This method, called ELECTRO (ELECTRic potential energy Optimized), uses repulsive forces to minimize electric potential energy. An objective function [Formula: see text], the electric potential energies of all subsets of consecutive readouts in a 3D radial trajectory, and its reduced form were minimized using a multi-stage optimization strategy. A metric called normalized mean nearest neighbor angular distance (NMNA) was proposed for describing distributions of points on a sphere. ELECTRO and other relevant golden trajectories were compared in silico using NMNA and point spread function analysis. Consecutive readouts from an ELECTRO trajectory were well spread out, with consistent NMNA values across sphere sizes (σNMNA = 0.005) and between regions on the sphere (NMNA ≈ 1.49). Conversely, the supergolden trajectory had poor consistency in NMNA values (σNMNA = 0.090) and clustering (NMNA = 1.28 at the pole with 40,000 readouts) that lead to artifact in the point spread function. Multi-stage optimization was faster than single-stage and obtained lower values of [Formula: see text] (e.g., 0.87 vs. 0.91, for a sphere size of 40). In conclusion, ELECTRO trajectories are more golden than other 3D center-out radial trajectories, making them a suitable candidate for dynamic 3D MR imaging.

Modeling nonlinear optical microscopy in scattering media, part II. Radiation from focal volume to far-field: tutorial

The development and application of nonlinear optical (NLO) microscopy methods in biomedical research has experienced rapid growth over the past three decades. Despite the compelling power of these methods, optical scattering limits their practical use in biological tissues. This tutorial offers a model-based approach illustrating how analytical methods from classical electromagnetism can be employed to comprehensively model NLO microscopy in scattering media. In Part I, we quantitatively model focused beam propagation in non-scattering and scattering media from the lens to focal volume. In Part II, we model signal generation, radiation, and far-field detection. Moreover, we detail modeling approaches for major optical microscopy modalities including classical fluorescence, multi-photon fluorescence, second harmonic generation, and coherent anti-Stokes Raman microscopy.

Modeling nonlinear optical microscopy in scattering media, part I. Propagation from lens to focal volume: tutorial

The development and application of nonlinear optical (NLO) microscopy methods in biomedical research have experienced rapid growth over the past three decades. Despite the compelling power of these methods, optical scattering limits their practical use in biological tissues. This tutorial offers a model-based approach illustrating how analytical methods from classical electromagnetism can be employed to comprehensively model NLO microscopy in scattering media. In Part I, we quantitatively model focused beam propagation in non-scattering and scattering media from the lens to focal volume. In Part II, we model signal generation, radiation, and far-field detection. Moreover, we detail modeling approaches for major optical microscopy modalities including classical fluorescence, multi-photon fluorescence, second harmonic generation, and coherent anti-Stokes Raman microscopy.

Optimizing Diffusion Imaging Protocols for Structural Connectomics in Mouse Models of Neurological Conditions

Network approaches provide sensitive biomarkers for neurological conditions, such as Alzheimer's disease (AD). Mouse models can help advance our understanding of underlying pathologies, by dissecting vulnerable circuits. While the mouse brain contains less white matter compared to the human brain, axonal diameters compare relatively well (e.g., ~0.6 μm in the mouse and ~0.65-1.05 μm in the human corpus callosum). This makes the mouse an attractive test bed for novel diffusion models and imaging protocols. Remaining questions on the accuracy and uncertainty of connectomes have prompted us to evaluate diffusion imaging protocols with various spatial and angular resolutions. We have derived structural connectomes by extracting gradient subsets from a high-spatial, high-angular resolution diffusion acquisition (120 directions, 43-μm-size voxels). We have simulated protocols with 12, 15, 20, 30, 45, 60, 80, 100, and 120 angles and at 43, 86, or 172-μm voxel sizes. The rotational stability of these schemes increased with angular resolution. The minimum condition number was achieved for 120 directions, followed by 60 and 45 directions. The percentage of voxels containing one dyad was exceeded by those with two dyads after 45 directions, and for the highest spatial resolution protocols. For the 86- or 172-μm resolutions, these ratios converged toward 55% for one and 39% for two dyads, respectively, with <7% from voxels with three dyads. Tractography errors, estimated through dyad dispersion, decreased most with angular resolution. Spatial resolution effects became noticeable at 172 μm. Smaller tracts, e.g., the fornix, were affected more than larger ones, e.g., the fimbria. We observed an inflection point for 45 directions, and an asymptotic behavior after 60 directions, corresponding to similar projection density maps. Spatially downsampling to 86 μm, while maintaining the angular resolution, achieved a subgraph similarity of 96% relative to the reference. Using 60 directions with 86- or 172-μm voxels resulted in 94% similarity. Node similarity metrics indicated that major white matter tracts were more robust to downsampling relative to cortical regions. Our study provides guidelines for new protocols in mouse models of neurological conditions, so as to achieve similar connectomes, while increasing efficiency.

Molecular Subtyping and Prognostic Assessment Based on Tumor Mutation Burden in Patients with Lung Adenocarcinomas

The distinct molecular subtypes of lung cancer are defined by monogenic biomarkers, such as EGFR, KRAS, and ALK rearrangement. Tumor mutation burden (TMB) is a potential biomarker for response to immunotherapy, which is one of the measures for genomic instability. The molecular subtyping based on TMB has not been well characterized in lung adenocarcinomas in the Chinese population. Here we performed molecular subtyping based on TMB with the published whole exome sequencing data of 101 lung adenocarcinomas and compared the different features of the classified subtypes, including clinical features, somatic driver genes, and mutational signatures. We found that patients with lower TMB have a longer disease-free survival, and higher TMB is associated with smoking and aging. Analysis of somatic driver genes and mutational signatures demonstrates a significant association between somatic RYR2 mutations and the subtype with higher TMB. Molecular subtyping based on TMB is a potential prognostic marker for lung adenocarcinoma. Signature 4 and the mutation of RYR2 are highlighted in the TMB-High group. The mutation of RYR2 is a significant biomarker associated with high TMB in lung adenocarcinoma.

Optimization of q-space sampling for mean apparent propagator MRI metrics using a genetic algorithm

Mean Apparent Propagator (MAP) MRI is a recently introduced technique to estimate the diffusion probability density function (PDF) robustly. Using the estimated PDF, MAP MRI then calculates zero-displacement and non-Gaussianity metrics, which might better characterize tissue microstructure compared to diffusion tensor imaging or diffusion kurtosis imaging. However, intensive q-space sampling required for MAP MRI limits its widespread adoption. A reduced q-space sampling scheme that maintains the accuracy of the derived metrics would make it more practical. A heuristic approach for acquiring MAP MRI with fewer q-space samples has been introduced earlier with scan duration of less than 10 minutes. However, the sampling scheme was not optimized systematically to preserve the accuracy of the model metrics. In this work, a genetic algorithm is implemented to determine optimal q-space subsampling schemes for MAP MRI that will keep total scan time under 10 min. Results show that the metrics derived from the optimized schemes more closely match those computed from the full set, especially in dense fiber tracts such as the corpus callosum.

Postmortem diffusion MRI of the entire human spinal cord at microscopic resolution

The human spinal cord is a central nervous system structure that plays an important role in normal motor and sensory function, and can be affected by many debilitating neurologic diseases. Due to its clinical importance, the spinal cord is frequently the subject of imaging research. Common methods for visualizing spinal cord anatomy and pathology include histology and magnetic resonance imaging (MRI), both of which have unique benefits and drawbacks. Postmortem microscopic resolution MRI of fixed specimens, sometimes referred to as magnetic resonance microscopy (MRM), combines many of the benefits inherent to both techniques. However, the elongated shape of the human spinal cord, along with hardware and scan time limitations, have restricted previous microscopic resolution MRI studies (both in vivo and ex vivo) to small sections of the cord. Here we present the first MRM dataset of the entire postmortem human spinal cord. These data include 50 μm isotropic resolution anatomic image data and 100 μm isotropic resolution diffusion data, made possible by a 280 h long multi-segment acquisition and automated image segment composition. We demonstrate the use of these data for spinal cord lesion detection, automated volumetric gray matter segmentation, and quantitative spinal cord morphometry including estimates of cross sectional dimensions and gray matter fraction throughout the length of the cord.

Effect of scattering on coherent anti-Stokes Raman scattering (CARS) signals

We develop a computational framework to examine the factors responsible for scattering-induced distortions of coherent anti-Stokes Raman scattering (CARS) signals in turbid samples. We apply the Huygens-Fresnel wave-based electric field superposition (HF-WEFS) method combined with the radiating dipole approximation to compute the effects of scattering-induced distortions of focal excitation fields on the far-field CARS signal. We analyze the effect of spherical scatterers, placed in the vicinity of the focal volume, on the CARS signal emitted by different objects (2μm diameter solid sphere, 2μm diameter myelin cylinder and 2μm diameter myelin tube). We find that distortions in the CARS signals arise not only from attenuation of the focal field but also from scattering-induced changes in the spatial phase that modifies the angular distribution of the CARS emission. Our simulations further show that CARS signal attenuation can be minimized by using a high numerical aperture condenser. Moreover, unlike the CARS intensity image, CARS images formed by taking the ratio of CARS signals obtained using x- and y-polarized input fields is relatively insensitive to the effects of spherical scatterers. Our computational framework provide a mechanistic approach to characterizing scattering-induced distortions in coherent imaging of turbid media and may inspire bottom-up approaches for adaptive optical methods for image correction.

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.

A Diffusion MRI Tractography Connectome of the Mouse Brain and Comparison with Neuronal Tracer Data

Interest in structural brain connectivity has grown with the understanding that abnormal neural connections may play a role in neurologic and psychiatric diseases. Small animal connectivity mapping techniques are particularly important for identifying aberrant connectivity in disease models. Diffusion magnetic resonance imaging tractography can provide nondestructive, 3D, brain-wide connectivity maps, but has historically been limited by low spatial resolution, low signal-to-noise ratio, and the difficulty in estimating multiple fiber orientations within a single image voxel. Small animal diffusion tractography can be substantially improved through the combination of ex vivo MRI with exogenous contrast agents, advanced diffusion acquisition and reconstruction techniques, and probabilistic fiber tracking. Here, we present a comprehensive, probabilistic tractography connectome of the mouse brain at microscopic resolution, and a comparison of these data with a neuronal tracer-based connectivity data from the Allen Brain Atlas. This work serves as a reference database for future tractography studies in the mouse brain, and demonstrates the fundamental differences between tractography and neuronal tracer data.

4D hyperspherical harmonic (HyperSPHARM) representation of surface anatomy: a holistic treatment of multiple disconnected anatomical structures

Image-based parcellation of the brain often leads to multiple disconnected anatomical structures, which pose significant challenges for analyses of morphological shapes. Existing shape models, such as the widely used spherical harmonic (SPHARM) representation, assume topological invariance, so are unable to simultaneously parameterize multiple disjoint structures. In such a situation, SPHARM has to be applied separately to each individual structure. We present a novel surface parameterization technique using 4D hyperspherical harmonics in representing multiple disjoint objects as a single analytic function, terming it HyperSPHARM. The underlying idea behind HyperSPHARM is to stereographically project an entire collection of disjoint 3D objects onto the 4D hypersphere and subsequently simultaneously parameterize them with the 4D hyperspherical harmonics. Hence, HyperSPHARM allows for a holistic treatment of multiple disjoint objects, unlike SPHARM. In an imaging dataset of healthy adult human brains, we apply HyperSPHARM to the hippocampi and amygdalae. The HyperSPHARM representations are employed as a data smoothing technique, while the HyperSPHARM coefficients are utilized in a support vector machine setting for object classification. HyperSPHARM yields nearly identical results as SPHARM, as will be shown in the paper. Its key advantage over SPHARM lies computationally; HyperSPHARM possess greater computational efficiency than SPHARM because it can parameterize multiple disjoint structures using much fewer basis functions and stereographic projection obviates SPHARM's burdensome surface flattening. In addition, HyperSPHARM can handle any type of topology, unlike SPHARM, whose analysis is confined to topologically invariant structures.

Rapid computation of the amplitude and phase of tightly focused optical fields distorted by scattering particles

We develop an efficient method for accurately calculating the electric field of tightly focused laser beams in the presence of specific configurations of microscopic scatterers. This Huygens-Fresnel wave-based electric field superposition (HF-WEFS) method computes the amplitude and phase of the scattered electric field in excellent agreement with finite difference time-domain (FDTD) solutions of Maxwell's equations. Our HF-WEFS implementation is 2-4 orders of magnitude faster than the FDTD method and enables systematic investigations of the effects of scatterer size and configuration on the focal field. We demonstrate the power of the new HF-WEFS approach by mapping several metrics of focal field distortion as a function of scatterer position. This analysis shows that the maximum focal field distortion occurs for single scatterers placed below the focal plane with an offset from the optical axis. The HF-WEFS method represents an important first step toward the development of a computational model of laser-scanning microscopy of thick cellular/tissue specimens.

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.