Spatial Deformation Research Articles

METHOD OF SELF-DEFENSE OF GROUND (SURFACE) OBJECTS FROM HIGH-PRECISION RADAR MEANS OF AIR SURVEILLANCE

Context it is caused by the need to search for scientific and technical ways to ensure the effectiveness of protecting ground (surface) objects from high-precision guided missile weapons.
 Objective it is a necessity to ensure effective self-defense of objects from radar homing means.
 Method. Electrodynamic modeling of Echo signals from spatially distributed objects, taking into account the features of their design and related operational limitations.
 Results. Based on the analysis of the shortcomings of the well-known method of protecting stationary objects from radar surveillance and damage, based on the simulation of an effective reflection center outside the physical dimensions of the object, a new method of countering high-precision measurement of coordinates of stationary and mobile ground (surface) objects is proposed. The technique is based on the spatial deformation of the location of the effective target reflection center with dynamics that exceed the inertial capabilities of the auto-observation contour of the attacking missile (projectile). A structural and functional scheme of technical implementation of the methodology based on the first proposed relationship of simple design and technological solutions is proposed and justified.
 Conclusions. The analytical model of Echo signals of spatially distributed ground (surface) objects was further developed, which takes into account the specifics of their design, and on its basis, for the first time, a universal method of self-defense of objects from radar home-leading devices was developed, which is implemented in a patented method and complex to exclude damage to protected objects.

Ordinary Kriging Interpolation Method Combined with FEM for Arch Dam Deformation Field Estimation

The deformation characteristic of the arch dam can directly reflect its service performance, which can be analyzed on the basis of the dam deformation field. However, restricted by the limited number of dam monitoring points and the inhomogeneity of materials, an accurate measurement of arch dam deformation field is difficult to estimate by using the existing common methods, such as the spatial interpolation methods and the finite element method (FEM). With the aim of ensuring arch dam structure safety, the ordinary kriging interpolation method, combined with FEM, is proposed for arch dam deformation field estimation, in this study. Given the inversion of the computation parameters of the arch dam, FEM is used to calculate the basic arch dam deformation. Subsequently, the ordinary kriging interpolation method is introduced to estimate the spatial variance deformation at each point of the arch dam. One superhigh arch dam in China is selected as a case study; two additional methods are introduced as comparisons that are based on a numerical experiment and the actual monitoring data. The experimental results show that the proposed method considerably improves the accuracy and computational efficiency of the arch dam deformation field estimation and that it is of great practical importance for characterizing the deformation behavior of arch dams.

Point Cloud Registration Methods for Long-Span Bridge Spatial Deformation Monitoring Using Terrestrial Laser Scanning

In recent years, efforts have been devoted to utilizing terrestrial laser scanning for bridge spatial performance inspection, but they are still restricted to small or medium-span bridges, like some historical heritages. Due to the large-scale dimensional features of long-span bridges, applications of 3D point cloud techniques still remain challenging, such as the extra-long scan range and extreme-small incidence angle when scanning a bridge with a span over 1000 m. Moreover, rare attempts can be found for the performance evaluation of point cloud registration methods for long-span bridges as well, which is a critical basis for further spatial deformation recognition on the point cloud data. Hence, in this study, a cross-evaluation of three iterative closest point (ICP) registration methods is conducted for long-span suspension bridges, namely, traditional ICP, kd-tree-based ICP, and feature point-based ICP algorithms. We conducted field laser scanning on the Ma’anshan Yangtze Bridge, an 1880 m long suspension bridge located in China. The results show that the feature point-based ICP algorithm outperforms the other two in terms of convergence rate and execution time for a single iteration due to the smaller number of registration points compared to the other two algorithms. Moreover, it also gives more precise values in terms of bridge tower spatial deformation identification. Meanwhile, due to efficient data organization, the kd-tree-based ICP algorithm takes less time for a single iteration than the traditional ICP algorithm. Finally, two suggestions for algorithm improvement in terms of efficiency optimization and accuracy improvement of long-span bridge deformation analysis are proposed based on the assessment results.

A Method for Evaluating Brain Deformation Under Sagittal Blunt Impacts Using a Half-Skull Human-Scale Surrogate.

Physical head models consisting of a half, sagittal plane skull, brain, and neck were constructed and subjected to crown and frontal impacts at two impact speeds. All tests were recorded with a high-speed camera at 1000 frames per second. Motion of visual markers within brain surrogates were used to track deformations and calculate spatial strain histories in 6 brain regions of interest. Principal strains, strain rates and strain impulses were calculated and reported. Higher impact velocities corresponded to higher strain values across all impact scenarios. Crown impacts were characterized by high, long duration strains distributed across the parietal, frontal and hippocampal regions whereas frontal impacts were characterized by sharply rising and falling strains primarily found in the parietal, frontal, hippocampal and occipital regions. High strain rates were associated with short durations and impulses indicating fast but short-lived strains. 2.23 m/s (5 mph) crown impacts resulted in 53% of the brain with shear strains higher than 0.15 verses 32% for frontal impacts. The results reveal large differences in the spatial and temporal strain responses between crown and forehead impacts. Overall, the results suggest that for the same speed, crown impact leads to higher magnitude strain patterns than a frontal impact. The data provided by this model provides unique insight into the spatial and temporal deformation patterns that have not been provided by alternate surrogate models. The model can be used to investigate how anatomical, material and loading features and parameters can affect deformation patterns in specific regions of interest in the brain.

Land Subsidence Assessment of an Archipelago Based on the InSAR Time Series Analysis Method

The lack of resources on islands leads to their extremely rapid development, and this can result in frequent geological disasters involving island subsidence. These disasters not only destroy the ecological environment and landscape of islands but also pose massive threats to the safety of residents’ lives and property and can even affect the country’s maritime rights and interests. To meet the demands of island stability and safety monitoring, in this study, we propose a large-area, full-coverage deformation monitoring method using InSAR technology to assess island subsidence based on a comprehensive analysis of conventional monitoring techniques. The working principle and unique advantages of InSAR data are introduced, and the SBAS InSAR key interpretation processing flow are described in detail. The GPU-assisted InSAR processing method is used to improve the processing efficiency. The monitoring results showed that the southern island group of the Miaodao Archipelago was relatively stable overall, with an annual average deformation rate of 3 mm. Only a few areas experienced large-magnitude surface deformation, and the maximum annual deformation magnitude was 45 mm. The time series deformation results of the characteristic points of the five inhabited islands in the southern island group showed that the subsidence trends of the two selected points on Beichangshan Island (P1 and P2) were slowly declining. The P3 point on Nanchangshan Island experienced a large deformation, while the P4 point experienced a relatively small deformation. The selected points (P5, P6 and P7) on Miaodao Island, Xiaoheishan Island and Daheishan Island were stable during the monitoring period. InSAR data can be used to accurately identify the millimetre-scale microdeformations experienced by island groups, thus demonstrating the high-precision deformation monitoring capability of these data. In addition, the accuracy of these data can meet the needs of island and archipelago subsidence monitoring, and the proposed method is an effective means to monitor the spatial deformation of island targets. This study is conducive to further enriching and improving island stability and safety monitoring technology systems in China and to providing data and technical support for identifying and mastering potential island risks, protecting and utilizing islands and preventing and reducing disasters.

Assembly accuracy analysis of cylindrical parts based on skin model shapes considering form deviations and local surface deformations

Assembly accuracy analysis plays a very important role in verifying whether the design scheme of geometric accuracy in the product design stage can meet the functional requirements of mechanical product. Form deviations, position and orientation deviation are inevitable in manufactured parts, and must be considered during assembly accuracy analysis. With regard to the representation of form deviations, it is verified that skin model shapes are effective. However, the existing simulation approaches of skin model shapes for cylindrical parts are mainly based on gaussian random field, without considering the spatial distribution characteristics of form deviations in dealing with the relationship between geometrical and dimensional deviation for cylindrical parts. Especially, when considering local surface deformations of cylindrical mating surfaces generated during the assembly process, the form deviations with different distribution characteristics leads to different contact deformation, which may have further influence on assembly accuracy analysis of cylindrical parts. To address above problems, this paper proposes a simulation method of skin model shapes of cylindrical parts based on Non-Gaussian random field considering the spatial distribution characteristics of form deviations, and the local surface deformations are analyzed with a boundary element method. Based on above, the relative positioning deviation of cylindrical mating surfaces is obtained considering the influence of form deviations and local surface deformations. Finally, the effectiveness of the proposed method is verified with case studies. Specifically, the results of case study reveal that the influences of form deviations considering spatial distribution characteristics and local surface deformations cannot be ignored for assembly accuracy analysis of cylindrical parts. In addition, for the relative positioning deviation of cylindrical mating surfaces for loose fit, the influence of local surface deformations on translational deviations along the x-axis and y-axis is greater than that on rotational deviations around the x-axis and y-axis.

Calculating the ground-state energy of benzene under spatial deformations with noisy quantum computing

In this paper we calculate the ground-state energy of benzene under spatial deformations by using the variational quantum eigensolver. The primary goal of the study is to estimate the feasibility of using quantum computing Ans\"atze on near-term devices to solve problems with a large number of orbitals in regions where classical methods are known to fail. Furthermore, by combining our advanced simulation platform with real quantum computers, we provide an analysis of how the noise, inherent to quantum computers, affects the results. At the center of our study are the hardware efficient and quantum unitary coupled-cluster (QUCC) Ans\"atze. First, we find that the hardware efficient Ansatz has the potential to outperform mean-field methods for extreme deformations of benzene. However, key problems remain at equilibrium, preventing real chemical application. Moreover, the hardware efficient Ansatz yields results that strongly depend on the initial guess of parameters (in both noisy and noiseless cases) and optimization issues have a higher impact on their convergence than noise. This is confirmed by comparison with real quantum computing demonstrations. On the other hand, the QUCC Ansatz alternative exhibits deeper circuits. Therefore, noise effects increase and are so extreme that the method never outperform mean-field theories. Our dual simulator, (8--16)-qubit QPU computations of QUCC Ansatz appears to be much more sensitive to hardware noise than shot noise, which further indicates where the noise-reduction efforts should be directed. Finally, the study shows that the QUCC method better captures the physics of the system as the QUCC method can be utilized together with the H\"uckel approximation. We discussed how going beyond this approximation sharply increases the optimization complexity of such a difficult problem.

Displacement response characteristics of different sand tunnel excavation faces under true triaxial loading

During the construction of subway tunnels, the geotechnical body is affected by excavation to produce three-dimensional spatial deformation. The deformation of geotechnical bodies is an important safety hazard for project advancement, so it is important to understand the excavation disturbance range and deformation mechanism. The current related research is mainly about the theory of land subsidence and the two-dimensional plane displacement of the stratum, and there are few studies on the specific three-dimensional disturbance mode and its mechanism. In order to better understand the three-dimensional displacement characteristics of the tunnel excavation soil, a tunnel excavation model test was established based on a true triaxial stress loading system combined with three-dimensional scanning technology for a superimposed sandy soil. Based on the established model, the vector displacement response range and three-dimensional deformation characteristics of the excavation face were studied in the main displacement affected area around the excavation face. Meanwhile, the deformation characteristics, such as vertical settlement and horizontal displacement of the stratum in the main influence area were analyzed. The results show that the main influence area of tunnel excavation is elliptical and distributed within a range of twice the diameter of the tunnel axis. The main influence range is bell-shaped in the vertical direction and inverted wedge-shaped in the horizontal direction. The three-dimensional space presents a “W” deformation distribution. The three-dimensional deformation theoretical model of the excavation face established in this paper can provide some references for the excavation engineering of superimposed sand-soil tunnels.

Nonlinear calculation of structural elements according to transforming design schemes

An approach to the calculation of the processes of structural elements deformation and their environments in the case of a complex phased erection of building objects is proposed. On the basis of consistent equations of the geometrically nonlinear theory elasticity within the finite element approach to the geometry description, a technique for solving three-dimensional statics problems of concrete and reinforced concrete structural elements is implemented. On the basis of calculation by transforming calculation schemes new computational models of spatial elements deformation of building structures during their interaction with soil media have been developed. On the basis of the proposed methods the underground elements deformation problem of building structures was solved when carrying out technological measures related to the local strengthening of already erected underground facilities. The calculation results showed that the use of the proposed methodology makes it possible to implement the determination of the stress-strain state and displacement fields in the phased construction zone in a single design scheme.

3D Point-Voxel Correlation Fields for Scene Flow Estimation.

In this paper, we propose Point-Voxel Correlation Fields to explore relations between two consecutive point clouds and estimate scene flow that represents 3D motions. Most existing works only consider local correlations, which are able to handle small movements but fail when there are large displacements. Therefore, it is essential to introduce all-pair correlation volumes that are free from local neighbor restrictions and cover both short- and long-term dependencies. However, it is challenging to efficiently extract correlation features from all-pairs fields in the 3D space, given the irregular and unordered nature of point clouds. To tackle this problem, we present point-voxel correlation fields, proposing distinct point and voxel branches to inquire about local and long-range correlations from all-pair fields respectively. To exploit point-based correlations, we adopt the K-Nearest Neighbors search that preserves fine-grained information in the local region, which guarantees the scene flow estimation precision. By voxelizing point clouds in a multi-scale manner, we construct pyramid correlation voxels to model long-range correspondences, which are utilized to handle fast-moving objects. Integrating these two types of correlations, we propose Point-Voxel Recurrent All-Pairs Field Transforms (PV-RAFT) architecture that employs an iterative scheme to estimate scene flow from point clouds. To adapt to different flow scope conditions and obtain more fine-grained results, we further propose Deformable PV-RAFT (DPV-RAFT), where the Spatial Deformation deforms the voxelized neighborhood, and the Temporal Deformation controls the iterative update process. We evaluate the proposed method on the FlyingThings3D and KITTI Scene Flow 2015 datasets and experimental results show that we outperform state-of-the-art methods by remarkable margins. The code is available at https://github.com/weiyithu/PV-RAFT.

Determination of Monitoring Control Value for Concrete Gravity Dam Spatial Deformation Based on POT Model

Deformation can directly reflect the working behavior of the dam, so determining the deformation monitoring control value can effectively monitor the safety of dam operation. The traditional dam deformation monitoring control value only considers the single measuring point. In order to overcome the limitation, this paper presents a new method to determine the monitoring control value for concrete gravity dam based on the deformations of multi-measuring points. A dam’s comprehensive deformation displacement is determined by the measured values at different measuring points on the positive inverted vertical line and the corresponding weight of each measuring point. The projection pursuit method (PPM) combined with the grey wolf optimization (GWO) algorithm is used to determine the weight of each measuring point according to the spatial correlation distribution characteristics of dam deformation. The peaks over threshold (POT) model based on the extreme value theory is adopted to determine the monitoring control value with the obtained dam comprehensive deformation displacement. In addition, the POT model is improved with the automatic threshold determination method based on the criterion in probability theory and the GWO algorithm, which can avoid subjectivity and randomness in determining the threshold. The results of the engineering application show the feasibility and applicability of the proposed method.

A ConvLSTM Neural Network Model for Spatiotemporal Prediction of Mining Area Surface Deformation Based on SBAS-InSAR Monitoring Data

The surface deformation caused by underground mining leads to damage to surface buildings and brings potential safety hazards and property losses. The demand for reliable prediction methods of surface deformation in mining areas is becoming increasingly significant. At present, most prediction methods are based on sampling points; however, these methods neglect to consider local and overall spatial features, and this oversight affects the spatial accuracy of prediction results. The data form of the prediction output is often discontinuous and not intuitive. In order to solve this problem, the spatiotemporal prediction method of surface deformation in mining areas is a very effective proposal. However, few scholars have proposed a solution based on this idea. In this study, a convolution long short-term memory (ConvLSTM) neural network for surface deformation spatiotemporal prediction based on time-series interferometric synthetic aperture radar (InSAR) is proposed to directly predict the overall spatial deformation of the surface in the mining area. First, based on Sentinel-1A images of the Jinchuan Mining Area, Jinchang, Gansu province, China, the time-series InSAR surface deformation data of the study area from January 2018 to October 2020 (81 scenes) are obtained using small baseline subset InSAR (SBAS-InSAR) technology. Because of the large value scale of surface deformation in the mining area, we propose a method to fit the maximum and minimum values of time-series deformation, respectively, and carry out piecewise numerical compression. Then, based on the ConvLSTM neural network layer, construct the spatiotemporal prediction model of time-series InSAR surface deformation. Support vector regression (SVR), multilayer perceptron (MLP) regression, and the gray model [GM (1,1)] are used as benchmark methods. The prediction results of our models are compared with the three benchmark methods. The comparison results show that the prediction effect of the ConvLSTM model with optimal input time steps is significantly better than the benchmark methods in the comprehensive performance of various evaluation metrics, especially for the metrics used to evaluate the error. This shows that the ConvLSTM model has relatively fine spatiotemporal prediction performance for time-series InSAR surface deformation. Based on the InSAR time-series deformation monitoring results of the Jinchuan Mining Area, we carry out the spatiotemporal prediction of surface deformation in the subsequent 50 time steps (600 days). The results agree with the natural deformation development law in band collection statistics and 3-D representation of deformation; moreover, the reliability of numerical spatial distribution is relatively high. This result can be used to intuitively evaluate the overall surface deformation of the mining area in the monitoring range, find potential hazards in time, and take measures to address these hazards quickly. At the same time, this research process also provides a new concept design for such problems.

Spatial deformations and transverse vibrations in the cutting mechanisms of big band saw machines: Investigation and analysis

Spatial deformations and transverse vibrations in the cutting mechanisms of big band saw machines: Investigation and analysis

Spatial deformations and transverse vibrations in the cutting mechanisms of big band saw machines: Investigation and analysis

In this paper, the influence of static and dynamic loads on the cutting mechanisms of big band saw machines is analyzed. For this purpose, functions describing the static deformations of the upper shaft in two mutually perpendicular planes were obtained. The influence of dynamic loads is also analyzed. In this case, the transverse vibrations and the dynamic deformations are studied. Functions describing the vibrations and deformations of the upper shaft have been received. Diagrams showing the type of elastic lines from static loading are built. Diagrams and surfaces, showing the type of the dynamic deformations are also built. The proposed theoretical expressions, diagrams and surfaces can be used to design new band saw machines, as well as to study the influence of various dynamic processes on the operation of machines in operating mode.

Kinematic Calibration Method for Large-Sized 7-DoF Hybrid Spray-Painting Robots

Large-sized seven-degrees-of-freedom (7-DoF) hybrid spray-painting robots combine ample working space and high flexibility, making them lucrative for the spray painting of aircraft and rocket surfaces. However, their kinematic calibration is hindered by gravitational deformation, which problem is addressed in this study by introducing a rigid-flexible coupling error modeling method. The latter combines the finite element method (FEM) and stiffness matrix method to assess the spatial gravitational deformation of a hybrid robot, which is then introduced into a geometric error model to establish the rigid-flexible coupling error identification model. Given many redundant parameters in the identification model for 7-DoF robots, these parameters are classified and simplified using the nonlinear least-square regularization method for parameter identification. Combining the inverse solution of 7-DoF spray-painting robots with dynamic characteristics considered, an error compensation method for 7-DoF robots is proposed. The kinematic calibration test results strongly indicate that position errors are significantly reduced with gravity compensation taken into consideration, and error convergence speed increases, demonstrating that the kinematic calibration method is feasible and can effectively improve the accuracy of spray-painting robots. The mean errors in the X- and Y-directions are reduced by 20 and 17%, respectively, compared to the conventional method. The proposed method is instrumental in the accurate kinematic calibration of large-sized 7-DoF hybrid robots.

An Online Multiobject Tracking Network for Autonomous Driving in Areas Facing Epidemic

Multi-object tracking is of great importance in autonomous driving. However, with the outbreak of COVID-19, multi-object tracking faces new challenges in areas gripped by epidemics because of complex motion blur, frequent occlusions, and appearance deformations. To reliably improve object trajectory association in epidemic-plagued areas, we propose a temporal-spatial aggregation embedding network (TSAEN) for multi-object tracking. Our embedding network contains a temporal-aware correlation module (TACM) and spatial-aggregate embedding module (SAEM) that can fully obtain and aggregate appearance clues related to moving objects in previous frames. The TACM learns the temporal homogeneity features of the current and previous frames to perceive features with correlated appearance cues. Then, the SAEM adjusts the spatial deformation for each perceived temporal homogeneity feature and aggregates them for re-ID embedding learning. The experimental results demonstrate that our proposed method is able to achieve excellent overall performance.

Development and systematic evaluation of high resolution PD‐weighted, T2‐weighted, and T2 map templates of the MIITRA atlas for use in studies on older adults

AbstractBackgroundAtlas based MRI investigations involving PD‐weighted (PDw), T2‐weighted (T2w) MRI sequences on older adults typically utilized younger adult templates such as those of the ICBM. Additionally, a thorough quantitative assessment of how available standardized PDw and T2w templates perform on aging population has not yet been performed. Here a new standardized high resolution PDw, T2w and T2 map templates of the MIITRA atlas dedicated for studies on older adults was developed using concepts of super‐resolution and sparse‐representation and compared to other available standardized templates in terms of image quality, inter‐subject spatial normalization accuracy and representativeness of the older adult brain.MethodT2‐weighted multi‐echo spin‐echo brain MRI (0.5mmx0.5mmx3mm isotropic, TE=20,40,60,80,100ms) and its corresponding T1‐weighted (isotropic 1mm) data obtained from the 400 non‐demented older adults (65‐95 age range, male:female=1:1) participating in the construction of the MIITRA atlas were used in this work. Additionally, subject T2 maps were constructed by fitting the T2 decay equation. The template construction involved reconstruction of high resolution voxels of T2‐weighted data utilizing nonlocal super‐resolution upsampling technique, mapping of each of the five echo (TE=20,40,60,80,100ms) separately using combined iterative T1‐weighted and DTI spatial normalization based transformations on a super‐resolution grid followed by patch‐based sparse representation to construct our T2‐weighted templates of the MIITRA atlas (Fig.1).The first echo PD‐weighted and the third echo T2‐weighted templates were compared to other available templates in terms of image sharpness and inter‐subject spatial normalization accuracy achieved when used as references for normalization of 30 ADNI PD‐weighted and T2‐weighted participants.ResultThe new PD and T2 weighted templates of the MIITRA atlas demonstrated higher image sharpness compared to the other templates, as exhibited by larger high spatial frequency content in the normalized power spectra (Fig. 2A,B,C,D). Inter‐subject spatial normalization was higher when using the new templates compared to the other templates (Fig.3,4). The new templates required the least spatial deformation for normalizing ADNI data (Fig.5A,B).ConclusionWe conclude that the new PD‐weighted and T2‐weighted templates of the MIITRA atlas are characterized by superior image quality, require lower deformation and allow for higher spatial normalization accuracy for use in studies on older adults such as the ADNI datasets.

Force balance in thermal quantum many-body systems from Noether’s theorem

We address the consequences of invariance properties of the free energy of spatially inhomogeneous quantum many-body systems. We consider a specific position-dependent transformation of the system that consists of a spatial deformation and a corresponding locally resolved change of momenta. This operator transformation is canonical and hence equivalent to a unitary transformation on the underlying Hilbert space of the system. As a consequence, the free energy is an invariant under the transformation. Noether’s theorem for invariant variations then allows to derive an exact sum rule, which we show to be the locally resolved equilibrium one-body force balance. For the special case of homogeneous shifting, the sum rule states that the average global external force vanishes in thermal equilibrium.

Determination of the stress-deformed state of a multilayer composite

An analytical determination algorithm was developed in the linear formulation, and a particular case of determining the stress-deformed state of a multilayer composite material was investigated. The algorithm is based on the use of the stress function (Ery) and the dependence of all indicators of the stress-deformed state of the material of each layer on its shape. Possible external factors affecting the composite structure are given. For the general case of building a composite structure, the sequence of adding the matrix of coefficients and the vector of free members of the system of linear algebraic equations is formed. The solution of the system of algebraic equations is proposed to be carried out by a method similar to the pre-race method, but for blocks of four equations supplemented by two equations of the influence of the previous layer in the calculation. As a result of actions similar to direct and reverse pre-race, we will obtain vectors of coefficient values of expressions of indicators of the stress-deformed state of the material of all layers as component sums.
 The acceptability of the algorithm for determining stresses and spatial deformations in a separate case of loading a composite sample with square layers is proven. The possibility of using the algorithm for the case of a significant (infinitely large) thickness the farthest from the loaded layer of the composite structure and single-layer (monolithic) material is shown. The following is established: characteristics of the distribution of normal stresses and displacements in the loaded layer of a two-layer composite material. They qualitatively coincide for different values of the Poisson coefficients of the layer materials. The amplitude of stress relief and displacements across the thickness of the loaded layer increases with a decrease in Poisson's ratio. The ratio of extreme values of normal stresses in the material of the loaded layer depends not only on the ratio of the shear moduli or the longitudinal elasticity moduli but also on the ratio of the values of the Poisson coefficients of the materials of the layers.

Modeling intracranial electrodes. A simulation platform for the evaluation of localization algorithms.

IntroductionIntracranial electrodes are implanted in patients with drug-resistant epilepsy as part of their pre-surgical evaluation. This allows the investigation of normal and pathological brain functions with excellent spatial and temporal resolution. The spatial resolution relies on methods that precisely localize the implanted electrodes in the cerebral cortex, which is critical for drawing valid inferences about the anatomical localization of brain function. Multiple methods have been developed to localize the electrodes, mainly relying on pre-implantation MRI and post-implantation computer tomography (CT) images. However, they are hard to validate because there is no ground truth data to test them and there is no standard approach to systematically quantify their performance. In other words, their validation lacks standardization. Our work aimed to model intracranial electrode arrays and simulate realistic implantation scenarios, thereby providing localization algorithms with new ways to evaluate and optimize their performance.ResultsWe implemented novel methods to model the coordinates of implanted grids, strips, and depth electrodes, as well as the CT artifacts produced by these. We successfully modeled realistic implantation scenarios, including different sizes, inter-electrode distances, and brain areas. In total, ∼3,300 grids and strips were fitted over the brain surface, and ∼850 depth electrode arrays penetrating the cortical tissue were modeled. Realistic CT artifacts were simulated at the electrode locations under 12 different noise levels. Altogether, ∼50,000 thresholded CT artifact arrays were simulated in these scenarios, and validated with real data from 17 patients regarding the coordinates’ spatial deformation, and the CT artifacts’ shape, intensity distribution, and noise level. Finally, we provide an example of how the simulation platform is used to characterize the performance of two cluster-based localization methods.ConclusionWe successfully developed the first platform to model implanted intracranial grids, strips, and depth electrodes and realistically simulate thresholded CT artifacts and their noise. These methods provide a basis for developing more complex models, while simulations allow systematic evaluation of the performance of electrode localization techniques. The methods described in this article, and the results obtained from the simulations, are freely available via open repositories. A graphical user interface implementation is also accessible via the open-source iElectrodes toolbox.