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.

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.