Prospects for transcranial temporal interference stimulation in humans: A computational study.

Transcranial alternating current stimulation (tACS) is a noninvasive method used to modulate activity of superficial brain regions. Deeper and more steerable stimulation could potentially be achieved using transcranial temporal interference stimulation (tTIS): two high-frequency alternating fields interact to produce a wave with an envelope frequency in the range thought to modulate neural activity. Promising initial results have been reported for experiments with mice. In this study we aim to better understand the electric fields produced with tTIS and examine its prospects in humans through simulations with murine and human head models. A murine head finite element model was used to simulate previously published experiments of tTIS in mice. With a total current of 0.776 mA, tTIS electric field strengths up to 383 V/m were reached in the modeled mouse brain, affirming experimental results indicating that suprathreshold stimulation is possible in mice. Using a detailed anisotropic human head model, tTIS was simulated with systematically varied electrode configurations and input currents to investigate how these parameters influence the electric fields. An exhaustive search with 88 electrode locations covering the entire head (146M current patterns) was employed to optimize tTIS for target field strength and focality. In all analyses, we investigated maximal effects and effects along the predominant orientation of local neurons. Our results showed that it was possible to steer the peak tTIS field by manipulating the relative strength of the two input fields. Deep brain areas received field strengths similar to conventional tACS, but with less stimulation in superficial areas. Maximum field strengths in the human model were much lower than in the murine model, too low to expect direct stimulation effects. While field strengths from tACS were slightly higher, our results suggest that tTIS is capable of producing more focal fields and allows for better steerability. Finally, we present optimal four-electrode current patterns to maximize tTIS in regions of the pallidum (0.37 V/m), hippocampus (0.24 V/m) and motor cortex (0.57 V/m).

Computationally optimized ECoG stimulation with local safety constraints.

Direct stimulation of the cortical surface is used clinically for cortical mapping and modulation of local activity. Future applications of cortical modulation and brain-computer interfaces may also use cortical stimulation methods. One common method to deliver current is through electrocorticography (ECoG) stimulation in which a dense array of electrodes are placed subdurally or epidurally to stimulate the cortex. However, proximity to cortical tissue limits the amount of current that can be delivered safely. It may be desirable to deliver higher current to a specific local region of interest (ROI) while limiting current to other local areas more stringently than is guaranteed by global safety limits. Two commonly used global safety constraints bound the total injected current and individual electrode currents. However, these two sets of constraints may not be sufficient to prevent high current density locally (hot-spots). In this work, we propose an efficient approach that prevents current density hot-spots in the entire brain while optimizing ECoG stimulus patterns for targeted stimulation. Specifically, we maximize the current along a particular desired directional field in the ROI while respecting three safety constraints: one on the total injected current, one on individual electrode currents, and the third on the local current density magnitude in the brain. This third set of constraints creates a computational barrier due to the huge number of constraints needed to bound the current density at every point in the entire brain. We overcome this barrier by adopting an efficient two-step approach. In the first step, the proposed method identifies the safe brain region, which cannot contain any hot-spots solely based on the global bounds on total injected current and individual electrode currents. In the second step, the proposed algorithm iteratively adjusts the stimulus pattern to arrive at a solution that exhibits no hot-spots in the remaining brain. We report on simulations on a realistic finite element (FE) head model with five anatomical ROIs and two desired directional fields. We also report on the effect of ROI depth and desired directional field on the focality of the stimulation. Finally, we provide an analysis of optimization runtime as a function of different safety and modeling parameters. Our results suggest that optimized stimulus patterns tend to differ from those used in clinical practice.

Calculation of the cross-sectional shape of a fibril from equatorial scattering.

An alternate formulation of helical diffraction theory is used to generate cross-sectional shapes of fibrous structures from equatorial scattering. We demonstrate this approach with computationally generated scattering intensities and then apply it to scattering data from Tobacco Mosaic Virus (TMV) and in vitro assembled fibrils of Aß40 peptides. Refining the cross-sectional shape of TMV from SAXS data collected on a 26mg/ml solution resulted in a circular shape with outer diameter of ∼180Å and inner diameter of ∼40Å consistent with the known structure of TMV. We also utilized this method to analyze the equatorial scattering from TMV collected by Don Caspar from a concentrated (24% ∼295mg/ml) gel of TMV as reported in his Ph.D. thesis in 1955. This data differs from the SAXS data in having a sharp interference peak at ∼250Å spacing, indicative of strong interparticle interactions in the gel. Analysis of this data required consideration of interatomic vectors as long as 2000Å and resulted in generation of images that were interpreted as representative of local organization of TMV particles in the sample. Peaks in the images were separated, on average by about 250Å with a density consistent with Caspar's original measurements. Analysis of SAXS data from Aß fibrils resulted in a cross-sectional shape that could be interpreted in terms of structural models that have been constructed from ssNMR and cryoEM. These results demonstrate an unexpected use of the small-angle region of fiber diffraction patterns to derive fundamental structural properties of scattering objects.

FiXR: a framework to reconstruct fiber cross-sections from X-ray fiber diffraction experiments.

Ab initio reconstruction methods have revolutionized the capabilities of small-angle X-ray scattering (SAXS), allowing the data-driven discovery of previously unknown molecular conformations, exploiting optimization heuristics and assumptions behind the composition of globular molecules. While these methods have been successful for the analysis of small particles, their impact on fibrillar assemblies has been more limited. The micrometre-range size of these assemblies and the complex interaction of their periodicities in their scattering profiles indicate that the discovery of fibril structures from SAXS measurements requires novel approaches beyond extending existing tools for molecular discovery. In this work, it is proposed to use SAXS measurements, together with diffraction theory, to infer the electron distribution of the average cross-section of a fiber. This cross-section is modeled as a discrete electron density with continuous support, allowing representations beyond binary distributions. Additional constraints, such as non-negativity or smoothness/connectedness, can also be added to the framework. The proposed approach is tested using simulated SAXS data from amyloid ß fibril models and using measured data of Tobacco mosaic virus from SAXS experiments, recovering the geometry and density of the cross-sections in all cases. The approach is further tested by analyzing SAXS data from different amyloid ß fibril assemblies, with results that are in agreement with previously proposed models from cryo-EM measurements. The limitations of the proposed method, together with an analysis of the robustness of the method and the combination with different experimental sources, are also discussed.

Reporter Selection for Nanotags in Multiplexed Surface Enhanced Raman Spectroscopy Assays.

We report a quantitative evaluation of the choice of reporters for multiplexed surface-enhanced Raman spectroscopy (SERS). An initial library consisted of 15 reporter molecules that included commonly used Raman dyes, thiolated reporters, and other small molecules. We used a correlation matrix to downselect Raman reporters from the library to choose five candidates: 1,2-bis(4-pyridyl)ethylene, 4-mercaptobenzoic acid, 3,5-dichlorobenzenthiol, pentachlorothiophenol, and 5,5'-dithiobis(2-nitrobenzoic acid). We evaluated the ability to distinguish the five SERS reporters in a dipstick immunoassay for the biomarker human IgG. Raman nanotags, or gold nanostars conjugated to the five reporters and anti-human IgG polyclonal antibodies were constructed. A linear discriminant analysis approach was used to evaluate the separation of the nanotag spectra in mixtures of fixed ratios.

Design of SERS nanotags for multiplexed lateral flow immunoassays.

Surface enhanced Raman spectroscopy (SERS) has been attractive for enhancing the sensitivity of lateral flow immunoassays (LFA). A format that has enabled specific detection of biomarkers is to use Raman reporter molecules linked to gold nanoparticles (NPs), which are conjugated to antibodies specific for the target of interest. Many factors such as the NP and Ab properties and the method of signal readout impact the sensitivity of a SERS based immunoassay. To understand how to optimize assay sensitivity, we studied SERS readouts of multiplexed sandwich immunoassays for the zika and dengue non-structural protein 1 (NS1) biomarkers as a test case. We investigated the effect of NP shape on the SERS enhancement of the reporter molecules 1,2-bis(4-pyridyl)ethylene (BPE) and 4-mercaptobenzoic acid (MBA). We also performed SERS imaging of test lines to map the spatial distribution of signal in test lines on the nitrocellulose. Finally, we used a modified least squares analysis to differentiate reporter contributions.