A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields.

Objective.Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or 'whole' finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.Approach.Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.Main Results.Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh.Significance.Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

A semi-automated pipeline for finite element modeling of electric field induced in nonhuman primates by transcranial magnetic stimulation.

BACKGROUND: Transcranial magnetic stimulation (TMS) is used to treat a range of brain disorders by inducing an electric field (E-field) in the brain. However, the precise neural effects of TMS are not well understood. Nonhuman primates (NHPs) are used to model the impact of TMS on neural activity, but a systematic method of quantifying the induced E-field in the cortex of NHPs has not been developed. NEW METHOD: The pipeline uses statistical parametric mapping (SPM) to automatically segment a structural MRI image of a rhesus macaque into five tissue compartments. Manual corrections are necessary around implants. The segmented tissues are tessellated into 3D meshes used in finite element method (FEM) software to compute the TMS induced E-field in the brain. The gray matter can be further segmented into cortical laminae using a volume preserving method for defining layers. RESULTS: Models of three NHPs were generated with TMS coils placed over the precentral gyrus. Two coil configurations, active and sham, were simulated and compared. The results demonstrated a large difference in E-fields at the target. Additionally, the simulations were calculated using two different E-field solvers and were found to not significantly differ. COMPARISON WITH EXISTING METHODS: Current methods segment NHP tissues manually or use automated methods for only the brain tissue. Existing methods also do not stratify the gray matter into layers. CONCLUSION: The pipeline calculates the induced E-field in NHP models by TMS and can be used to plan implant surgeries and determine approximate E-field values around neuron recording sites.

Brain tumor detection using proper orthogonal decomposition integrated with deep learning networks.

BACKGROUND AND OBJECTIVE: The central organ of the human nervous system is the brain, which receives and sends stimuli to the various parts of the body to engage in daily activities. Uncontrolled growth of brain cells can result in tumors which affect the normal functions of healthy brain cells. An automatic reliable technique for detecting tumors is imperative to assist medical practitioners in the timely diagnosis of patients. Although machine learning models are being used, with minimal data availability to train, development of low-order based models integrated with machine learning are a tool for reliable detection. METHODS: In this study, we focus on comparing a low-order model such as proper orthogonal decomposition (POD) coupled with convolutional neural network (CNN) on 2D images from magnetic resonance imaging (MRI) scans to effectively identify brain tumors. The explainability of the coupled POD-CNN prediction output as well as the state-of-the-art pre-trained transfer learning models such as MobileNetV2, Inception-v3, ResNet101, and VGG-19 were explored. RESULTS: The results showed that CNN predicted tumors with an accuracy of 99.21% whereas POD-CNN performed better with about 1/3rd of computational time at an accuracy of 95.88%. Explainable AI with SHAP showed MobileNetV2 has better prediction in identifying the tumor boundaries. CONCLUSIONS: Integration of POD with CNN is carried for the first time to detect brain tumor detection with minimal MRI scan data. This study facilitates low-model approaches in machine learning to improve the accuracy and performance of tumor detection.

Electric Field Modeling in Personalizing Transcranial Magnetic Stimulation Interventions.

The modeling of transcranial magnetic stimulation (TMS)-induced electric fields (E-fields) is a versatile technique for evaluating and refining brain targeting and dosing strategies, while also providing insights into dose-response relationships in the brain. This review outlines the methodologies employed to derive E-field estimations, covering TMS physics, modeling assumptions, and aspects of subject-specific head tissue and coil modeling. We also summarize various numerical methods for solving the E-field and their suitability for various applications. Modeling methodologies have been optimized to efficiently execute numerous TMS simulations across diverse scalp coil configurations, facilitating the identification of optimal setups or rapid cortical E-field visualization for specific brain targets. These brain targets are extrapolated from neurophysiological measurements and neuroimaging, enabling precise and individualized E-field dosing in experimental and clinical applications. This necessitates the quantification of E-field estimates using metrics that enable the comparison of brain target engagement, functional localization, and TMS intensity adjustments across subjects. The integration of E-field modeling with empirical data has the potential to uncover pivotal insights into the aspects of E-fields responsible for stimulating and modulating brain function and states, enhancing behavioral task performance, and impacting the clinical outcomes of personalized TMS interventions.

Real-Time Computation of Brain E-Field for Enhanced Transcranial Magnetic Stimulation Neuronavigation and Optimization.

Transcranial Magnetic Stimulation (TMS) coil placement and pulse waveform current are often chosen to achieve a specified E-field dose on targeted brain regions. TMS neuronavigation could be improved by including real-time accurate distributions of the E-field dose on the cortex. We introduce a method and develop software for computing brain E-field distributions in real-time enabling easy integration into neuronavigation and with the same accuracy as 1st -order finite element method (FEM) solvers. Initially, a spanning basis set (< 400) of E-fields generated by white noise magnetic currents on a surface separating the head and permissible coil placements are orthogonalized to generate the modes. Subsequently, Reciprocity and Huygens' principles are utilized to compute fields induced by the modes on a surface separating the head and coil by FEM, which are used in conjunction with online (real-time) computed primary fields on the separating surface to evaluate the mode expansion. We conducted a comparative analysis of E-fields computed by FEM and in real-time for eight subjects, utilizing two head model types (SimNIBS's 'headreco' and 'mri2mesh' pipeline), three coil types (circular, double-cone, and Figure-8), and 1000 coil placements (48,000 simulations). The real-time computation for any coil placement is within 4 milliseconds (ms), for 400 modes, and requires less than 4 GB of memory on a GPU. Our solver is capable of computing E-fields within 4 ms, making it a practical approach for integrating E-field information into the neuronavigation systems without imposing a significant overhead on frame generation (20 and 50 frames per second within 50 and 20 ms, respectively).

Fast and accurate computational E-field dosimetry for group-level transcranial magnetic stimulation targeting.

Transcranial magnetic stimulation (TMS) is used to study brain function and treat mental health disorders. During TMS, a coil placed on the scalp induces an E-field in the brain that modulates its activity. TMS is known to stimulate regions that are exposed to a large E-field. Clinical TMS protocols prescribe a coil placement based on scalp landmarks. There are inter-individual variations in brain anatomy that result in variations in the TMS-induced E-field at the targeted region and its outcome. These variations across individuals could in principle be minimized by developing a large database of head subjects and determining scalp landmarks that maximize E-field at the targeted brain region while minimizing its variation using computational methods. However, this approach requires repeated execution of a computational method to determine the E-field induced in the brain for a large number of subjects and coil placements. We developed a probabilistic matrix decomposition-based approach for rapidly evaluating the E-field induced during TMS for a large number of coil placements due to a pre-defined coil model. Our approach can determine the E-field induced in over 1 Million coil placements in 9.5 h, in contrast, to over 5 years using a brute-force approach. After the initial set-up stage, the E-field can be predicted over the whole brain within 2-3 ms and to 2% accuracy. We tested our approach in over 200 subjects and achieved an error of <2% in most and <3.5% in all subjects. We will present several examples of bench-marking analysis for our tool in terms of accuracy and speed. Furthermore, we will show the methods' applicability for group-level optimization of coil placement for illustration purposes only. The software implementation link is provided in the appendix.

Fast And Accurate Population Level Transcranial Magnetic Stimulation via Low-Rank Probabilistic Matrix Decomposition (PMD).

Transcranial magnetic stimulation (TMS) is used to study brain function and treat mental health disorders. During TMS, a coil placed on the scalp induces an E-field in the brain that modulates its activity. TMS is known to stimulate regions that are exposed to a large E-field. Clinical TMS protocols prescribe a coil placement based on scalp landmarks. There are inter-individual variations in brain anatomy that result in variations in the TMS-induced E-field at the targeted region and its outcome. These variations across individuals could in principle be minimized by developing a large database of head subjects and determining scalp landmarks that maximize E-field at the targeted brain region while minimizing its variation using computational methods. However, this approach requires repeated execution of a computational method to determine the E-field induced in the brain for a large number of subjects and coil placements. We developed a probabilistic matrix decomposition-based approach for rapidly evaluating the E-field induced during TMS for a large number of coil placements. Our approach can determine the E-field induced in over 1 Million coil placements in 9.5 hours, in contrast, to over 5 years using a bruteforce approach. After the initial set-up stage, the E-field can be predicted over the whole brain within 2-3 milliseconds and to 2% accuracy. We tested our approach in over 200 subjects and achieved an error of < 2% in most and < 3.5% in all subjects. We will present several examples of bench-marking analysis for our tool in terms of accuracy and speed across and its applicability for population level optimization of coil placement. Highlights: A method for practical E-field informed population-level TMS coil placement strategies is developed.This algorithm enables the determination of E-field informed optimal coil placement in seconds enabling it’s use for close-loop and on-the-fly reconfiguration of TMS.After the initial set-up stage of less than 10 hours, the E-field can be predicted for any coil placement across the whole brain within in 2-3 milliseconds.

Evidence of contamination-associated damage in blue sharks (Prionace glauca) from the Northeast Atlantic.

Top predators such as most shark species are extremely vulnerable to amassing high concentrations of contaminants, but not much is known about the effects that the contaminant body burden imparts on these animals. Species like the blue shark (Prionace glauca) are very relevant in this regard, as they have high ecological and socioeconomic value, and have the potential to act as bioindicators of pollution. This work aimed to assess if differences in contaminant body burden found in blue sharks from the Northeast Atlantic would translate into differences in stress responses. Biochemical responses related to detoxification and oxidative stress, and histological alterations were assessed in the liver and gills of 60 blue sharks previously found to have zone-related contamination differences. Similar zone-related differences were found in biomarker responses, with the sharks from the most contaminated zone exhibiting more pronounced responses. Additionally, strong positive correlations were found between contaminants (i.e., As, PCBs, and PBDEs) and relevant biomarkers (e.g., damaged DNA and protective histological alterations). The present results are indicative of the potential that this species and these tools have to be used to monitor pollution in different areas of the Atlantic.

Fast computational E-field dosimetry for transcranial magnetic stimulation using adaptive cross approximation and auxiliary dipole method (ACA-ADM).

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation technique that uses a coil to induce an electric field (E-field) in the brain and modulate its activity. Many applications of TMS call for the repeated execution of E-field solvers to determine the E-field induced in the brain for different coil placements. However, the usage of solvers for these applications remains impractical because each coil placement requires the solution of a large linear system of equations. We develop a fast E-field solver that enables the rapid evaluation of the E-field distribution for a brain region of interest (ROI) for a large number of coil placements, which is achieved in two stages. First, during the pre-processing stage, the mapping between coil placement and brain ROI E-field distribution is approximated from E-field results for a few coil placements. Specifically, we discretize the mapping into a matrix with each column having the ROI E-field samples for a fixed coil placement. This matrix is approximated from a few of its rows and columns using adaptive cross approximation (ACA). The accuracy, efficiency, and applicability of the new ACA approach are determined by comparing its E-field predictions with analytical and standard solvers in spherical and MRI-derived head models. During the second stage, the E-field distribution in the brain ROI from a specific coil placement is determined by the obtained rows and columns in milliseconds. For many applications, only the E-field distribution for a comparatively small ROI is required. For example, the solver can complete the pre-processing stage in approximately 4 hours and determine the ROI E-field in approximately 40 ms for a 100 mm diameter ROI with less than 2% error enabling its use for neuro-navigation and other applications. Highlight: We developed a fast solver for TMS computational E-field dosimetry, which can determine the ROI E-field in approximately 40 ms for a 100 mm diameter ROI with less than 2% error.

DeeptDCS: Deep Learning-Based Estimation of Currents Induced During Transcranial Direct Current Stimulation.

OBJECTIVE: Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique used to generate conduction currents in the head and disrupt brain functions. To rapidly evaluate the tDCS-induced current density in near real-time, this paper proposes a deep learning-based emulator, named DeeptDCS. METHODS: The emulator leverages Attention U-net taking the volume conductor models (VCMs) of head tissues as inputs and outputting the three-dimensional current density distribution across the entire head. The electrode configurations are also incorporated into VCMs without increasing the number of input channels; this enables the straightforward incorporation of the non-parametric features of electrodes (e.g., thickness, shape, size, and position) in the training and testing of the proposed emulator. RESULTS: Attention U-net outperforms standard U-net and its other three variants (Residual U-net, Attention Residual U-net, and Multi-scale Residual U-net) in terms of accuracy. The generalization ability of DeeptDCS to non-trained electrode configurations can be greatly enhanced through fine-tuning the model. The computational time required by one emulation via DeeptDCS is a fraction of a second. CONCLUSION: DeeptDCS is at least two orders of magnitudes faster than a physics-based open-source simulator, while providing satisfactorily accurate results. SIGNIFICANCE: The high computational efficiency permits the use of DeeptDCS in applications requiring its repetitive execution, such as uncertainty quantification and optimization studies of tDCS.

A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields.

Objective: Commonly used cable equation-based approaches for determining the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or "whole" finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons. Methods: Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios. Main Results: Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is made computationally tractable, and the relative placement of devices and cells can be varied without the need to generate a new mesh. Significance: Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis.

A butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the O(N log 2 N) construction cost of the HOD-BF-compressed system matrix and O(N 1.5 log N) inversion cost for the preconditioner, where N is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a H matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.

Store-Operated Calcium Entry and Its Implications in Cancer Stem Cells.

Tumors are composed by a heterogeneous population of cells. Among them, a sub-population of cells, termed cancer stem cells, exhibit stemness features, such as self-renewal capabilities, disposition to differentiate to a more proliferative state, and chemotherapy resistance, processes that are all mediated by Ca2+. Ca2+ homeostasis is vital for several physiological processes, and alterations in the patterns of expressions of the proteins and molecules that modulate it have recently become a cancer hallmark. Store-operated Ca2+ entry is a major mechanism for Ca2+ entry from the extracellular medium in non-excitable cells that leads to increases in the cytosolic Ca2+ concentration required for several processes, including cancer stem cell properties. Here, we focus on the participation of STIM, Orai, and TRPC proteins, the store-operated Ca2+ entry key components, in cancer stem cell biology and tumorigenesis.

Uncertainty quantification of TMS simulations considering MRI segmentation errors.

Objective.Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation method that is used to study brain function and conduct neuropsychiatric therapy. Computational methods that are commonly used for electric field (E-field) dosimetry of TMS are limited in accuracy and precision because of possible geometric errors introduced in the generation of head models by segmenting medical images into tissue types. This paper studies E-field prediction fidelity as a function of segmentation accuracy.Approach.The errors in the segmentation of medical images into tissue types are modeled as geometric uncertainty in the shape of the boundary between tissue types. For each tissue boundary realization, we then use an in-house boundary element method to perform a forward propagation analysis and quantify the impact of tissue boundary uncertainties on the induced cortical E-field.Main results.Our results indicate that predictions of E-field induced in the brain are negligibly sensitive to segmentation errors in scalp, skull and white matter (WM), compartments. In contrast, E-field predictions are highly sensitive to possible cerebrospinal fluid (CSF) segmentation errors. Specifically, the segmentation errors on the CSF and gray matter interface lead to higher E-field uncertainties in the gyral crowns, and the segmentation errors on CSF and WM interface lead to higher uncertainties in the sulci. Furthermore, the uncertainty of the average cortical E-fields over a region exhibits lower uncertainty relative to point-wise estimates.Significance.The accuracy of current cortical E-field simulations is limited by the accuracy of CSF segmentation accuracy. Other quantities of interest like the average of the E-field over a cortical region could provide a dose quantity that is robust to possible segmentation errors.

Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries.

We present a stochastic modeling framework to represent and simulate spatially-dependent geometrical uncertainties on complex geometries. While the consideration of random geometrical perturbations has long been a subject of interest in computational engineering, most studies proposed so far have addressed the case of regular geometries such as cylinders and plates. Here, standard random field representations, such as Kahrunen-Loève expansions, can readily be used owing, in particular, to the relative simplicity to construct covariance operators on regular shapes. On the contrary, applying such techniques on arbitrary, non-convex domains remains difficult in general. In this work, we formulate a new representation for spatially-correlated geometrical uncertainties that allows complex domains to be efficiently handled. Building on previous contributions by the authors, the approach relies on the combination of a stochastic partial differential equation approach, introduced to capture salient features of the underlying geometry such as local curvature and singularities on the fly, and an information-theoretic model, aimed to enforce non-Gaussianity. More specifically, we propose a methodology where the interface of interest is immersed into a fictitious domain, and define algorithmic procedures to directly sample random perturbations on the manifold. A simple strategy based on statistical conditioning is also presented to update realizations and prevent self-intersections in the perturbed finite element mesh. We finally provide challenging examples to demonstrate the robustness of the framework, including the case of a gyroid structure produced by additive manufacturing and brain interfaces in patient-specific geometries. In both applications, we discuss suitable parameterization for the filtering operator and quantify the impact of the uncertainties through forward propagation.

Fast computational optimization of TMS coil placement for individualized electric field targeting.

BACKGROUND: During transcranial magnetic stimulation (TMS) a coil placed on the scalp is used to non-invasively modulate activity of targeted brain networks via a magnetically induced electric field (E-field). Ideally, the E-field induced during TMS is concentrated on a targeted cortical region of interest (ROI). Determination of the coil position and orientation that best achieve this objective presently requires a large computational effort. OBJECTIVE: To improve the accuracy of TMS we have developed a fast computational auxiliary dipole method (ADM) for determining the optimum coil position and orientation. The optimum coil placement maximizes the E-field along a predetermined direction or, alternatively, the overall E-field magnitude in the targeted ROI. Furthermore, ADM can assess E-field uncertainty resulting from precision limitations of TMS coil placement protocols. METHOD: ADM leverages the electromagnetic reciprocity principle to compute rapidly the TMS induced E-field in the ROI by using the E-field generated by a virtual constant current source residing in the ROI. The framework starts by solving for the conduction currents resulting from this ROI current source. Then, it rapidly determines the average E-field induced in the ROI for each coil position by using the conduction currents and a fast-multipole method. To further speed-up the computations, the coil is approximated using auxiliary dipoles enabling it to represent all coil orientations for a given coil position with less than 600 dipoles. RESULTS: Using ADM, the E-fields generated in an MRI-derived head model when the coil is placed at 5900 different scalp positions and 360 coil orientations per position (over 2.1 million unique configurations) can be determined in under 15 min on a standard laptop computer. This enables rapid extraction of the optimum coil position and orientation as well as the E-field variation resulting from coil positioning uncertainty. ADM is implemented in SimNIBS 3.2. CONCLUSION: ADM enables the rapid determination of coil placement that maximizes E-field delivery to a specific brain target. This method can find the optimum coil placement in under 15 min enabling its routine use for TMS. Furthermore, it enables the fast quantification of uncertainty in the induced E-field due to limited precision of TMS coil placement protocols, enabling minimization and statistical analysis of the E-field dose variability.

Comparison of immediate colposcopy, repeat conventional cytology and hrHPV testing for the clinical management of ASC-US cytology in routine health services of Medellin, Colombia: The ASCUS-COL Trial.

In the context of opportunistic cervical cancer screening settings of low-and-middle-income countries, little is known about the benefits of high-risk human papillomavirus (hrHPV) testing on high-grade cervical abnormality detection among women with atypical squamous cells of undetermined significance (ASC-US) cytology in routine clinical practice. We compared the effectiveness of immediate colposcopy (IC), conventional cytology at 6 and 12 months (colposcopy if ≥ASC-US) (RC), and hrHPV testing (colposcopy if hrHPV-positive) (HPV) to detect cervical intraepithelial neoplasia grade 2 or more severe diagnoses (CIN2+) among women aged 20-69 years with ASC-US in routine care. Participants (n=2,661) were evenly randomized into three arms (n=882 IC, n=890 RC, n=889 HPV) to receive services by routine healthcare providers and invited to an exit visit 24 months after recruitment. Histopathology was blindly reviewed by a quality-control external panel (QC). The primary endpoint was the first QC-diagnosed CIN2+ or CIN3+ detected during three periods: enrolment (≤6 months for IC and HPV, ≤12 months for RC), follow-up (between enrolment and exit visit), and exit visit. The trial is completed. Colposcopy was done on 88%, 42%, and 52% of participants in IC, RC, and HPV. Overall, 212 CIN2+ and 52 CIN3+ cases were diagnosed. No differences were observed for CIN2+ detection (p=0.821). However, compared to IC, only HPV significantly reduced CIN3+ cases that providers were unable to detect during the 2-year routine follow-up (relative proportion 0.35, 95% CI 0.09-0.87). In this context, hrHPV testing was the most effective and efficient management strategy for women with ASC-US cytology.

Conditions for numerically accurate TMS electric field simulation.

BACKGROUND: Computational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking. OBJECTIVE: To ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup. METHOD: We benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods. RESULTS: To achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled. CONCLUSION: BEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.

Antiproliferative and Antitumour Effect of Nongenotoxic Silver Nanoparticles on Melanoma Models.

During the last 3 decades, there has been a slow advance to obtain new treatments for malignant melanoma that improve patient survival. In this work, we present a systematic study focused on the antiproliferative and antitumour effect of AgNPs. These nanoparticles are fully characterized, are coated with polyvinylpyrrolidone (PVP), and have an average size of 35 ± 15 nm and a metallic silver content of 1.2% wt. Main changes on cell viability, induction of apoptosis and necrosis, and ROS generation were found on B16-F10 cells after six hours of exposure to AgNPs (IC50 = 4.2 µg/mL) or Cisplatin (IC50 = 2.0 µg/mL). Despite the similar response for both AgNPs and Cisplatin on antiproliferative potency (cellular viability of 53.95 ± 1.88 and 53.62 ± 1.04) and ROS production (20.27 ± 1.09% and 19.50 ± 0.35%), significantly different cell death pathways were triggered. While AgNPs induce only apoptosis (45.98 ± 1.88%), Cisplatin induces apoptosis and necrosis at the same rate (22.31 ± 1.72% and 24.07 ± 1.10%, respectively). In addition to their antiproliferative activity, in vivo experiments showed that treatments of 3, 6, and 12 mg/kg of AgNPs elicit a survival rate almost 4 times higher (P < 0.05) compared with the survival rate obtained with Cisplatin (2 mg/kg). Furthermore, the survivor mice treated with AgNPs do not show genotoxic damage determined by micronuclei frequency quantification on peripheral blood cells. These results exhibit the remarkable antitumour activity of a nongenotoxic AgNP formulation and constitute the first advance toward the application of these AgNPs for melanoma treatment, which could considerably reduce adverse effects provoked by currently applied chemotherapeutics.

TRP Channels in Angiogenesis and Other Endothelial Functions.

Angiogenesis is the growth of blood vessels mediated by proliferation, migration, and spatial organization of endothelial cells. This mechanism is regulated by a balance between stimulatory and inhibitory factors. Proangiogenic factors include a variety of VEGF family members, while thrombospondin and endostatin, among others, have been reported as suppressors of angiogenesis. Transient receptor potential (TRP) channels belong to a superfamily of cation-permeable channels that play a relevant role in a number of cellular functions mostly derived from their influence in intracellular Ca2+ homeostasis. Endothelial cells express a variety of TRP channels, including members of the TRPC, TRPV, TRPP, TRPA, and TRPM families, which play a relevant role in a number of functions, including endothelium-induced vasodilation, vascular permeability as well as sensing hemodynamic and chemical changes. Furthermore, TRP channels have been reported to play an important role in angiogenesis. This review summarizes the current knowledge and limitations concerning the involvement of particular TRP channels in growth factor-induced angiogenesis.