Realistic Model Research Articles

Influence of muscle packing on the three-dimensional architecture of rabbit M. plantaris

In their physiological condition, muscles are surrounded by connective tissue, other muscles and bone. These tissues exert transverse forces that change the three-dimensional shape of the muscle compared to its isolated condition, in which all surrounding tissues are removed. A change in shape affects the architecture of a muscle and therefore its mechanical properties. The rabbit M. plantaris is a multi-pennate calf muscle consisting of two compartments. A smaller, bi-pennate inner muscle compartment is embedded in a larger, uni-pennate outer compartment (Böl et al., 2015). As part of the calf, the plantaris is tightly packed between other muscles. It is unclear how packing affects the shape and architecture of the plantaris. Therefore, we examined the isolated and packed plantaris of the contralateral legs of three rabbits to determine the influence of the surrounding muscles on its shape and architectural properties using photogrammetric reconstruction and manual digitization, respectively. In the packed condition, the plantaris showed a 27% increase in fascicle pennation and a 54% increase in fascicle curvature compared to the isolated condition. Fascicle length was not affected by muscle packing. The change in muscle architecture occurred mainly in the outer compartment of the plantaris. Furthermore, the isolated plantaris showed a more circular shape and a reduced width of its muscle belly. It can be concluded that the packed plantaris is flattened by the forces exerted by the surrounding muscles, causing a complex architectural change. The data provided improve our understanding of muscle packages in general and can be used to develop and validate realistic three-dimensional muscle models.

Bitemporal Radiative Transfer Modeling Using Bitemporal 3D-Explicit Forest Reconstruction from Terrestrial Laser Scanning

Radiative transfer models (RTMs) are often used to retrieve biophysical parameters from earth observation data. RTMs with multi-temporal and realistic forest representations enable radiative transfer (RT) modeling for real-world dynamic processes. To achieve more realistic RT modeling for dynamic forest processes, this study presents the 3D-explicit reconstruction of a typical temperate deciduous forest in 2015 and 2022. We demonstrate for the first time the potential use of bitemporal 3D-explicit RT modeling from terrestrial laser scanning on the forward modeling and quantitative interpretation of: (1) remote sensing (RS) observations of leaf area index (LAI), fraction of absorbed photosynthetically active radiation (FAPAR), and canopy light extinction, and (2) the impact of canopy gap dynamics on light availability of explicit locations. Results showed that, compared to the 2015 scene, the hemispherical-directional reflectance factor (HDRF) of the 2022 forest scene relatively decreased by 3.8% and the leaf FAPAR relatively increased by 5.4%. At explicit locations where canopy gaps significantly changed between the 2015 scene and the 2022 scene, only under diffuse light did the branch damage and closing gap significantly impact ground light availability. This study provides the first bitemporal RT comparison based on the 3D RT modeling, which uses one of the most realistic bitemporal forest scenes as the structural input. This bitemporal 3D-explicit forest RT modeling allows spatially explicit modeling over time under fully controlled experimental conditions in one of the most realistic virtual environments, thus delivering a powerful tool for studying canopy light regimes as impacted by dynamics in forest structure and developing RS inversion schemes on forest structural changes.

The Use of Patient-Derived Organoids in the Study of Molecular Metabolic Adaptation in Breast Cancer

Around 13% of women will likely develop breast cancer during their lifetime. Advances in cancer metabolism research have identified a range of metabolic reprogramming events, such as altered glucose and amino acid uptake, increased reliance on glycolysis, and interactions with the tumor microenvironment (TME), all of which present new opportunities for targeted therapies. However, studying these metabolic networks is challenging in traditional 2D cell cultures, which often fail to replicate the three-dimensional architecture and dynamic interactions of real tumors. To address this, organoid models have emerged as powerful tools. Tumor organoids are 3D cultures, often derived from patient tissue, that more accurately mimic the structural and functional properties of actual tumor tissues in vivo, offering a more realistic model for investigating cancer metabolism. This review explores the unique metabolic adaptations of breast cancer and discusses how organoid models can provide deeper insights into these processes. We evaluate the most advanced tools for studying cancer metabolism in three-dimensional culture models, including optical metabolic imaging (OMI), matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI), and recent advances in conventional techniques applied to 3D cultures. Finally, we explore the progress made in identifying and targeting potential therapeutic targets in breast cancer metabolism.

From fundamental theory to realistic modeling of the birth of solar eruptions

From fundamental theory to realistic modeling of the birth of solar eruptions

Regression-based model predicting cost contingencies for road network projects

Cost contingencies represent a significant markup percentage for construction projects. Many construction projects experience cost overruns due to unexpected events before or during the construction phase. Determining the cost contingency for construction projects is one of the most frequent and widespread financial problems many countries face. Since the amount included in the estimates is always insufficient to absorb the actual cost overruns of the project. The main objective of this paper is to develop a simple realistic regression model for predicting the appropriate contingency amount for road network projects before the bidding stage. The regression model has been developed based on data from real case studies for 75 road network projects to adequately consider all potential risks may face the project. Good-of-fit tests were used to select the best-fitting statistical distribution for a given dataset. Based on the analysis of selected data, the log-logistic probability distribution function is the best-fit curve representing cost overrun behavior, and the cumulative distribution function has been used to determine the realistic probability of incurred cost overrun. Based on the analysis of real case studies, it is suggested that an average of 59.722% be used as a cost overrun contingency amount for road network projects. The study outcomes will help practitioners and researchers improve future accuracy/calculations of contingency amount for road construction projects and improve the decision-making process.

Improving surgical technical skills for emergency fixation of unstable pelvic ring fractures: an experimental study using a pelvic ring fracture simulator

BackgroundThe management of hemodynamically unstable pelvic ring injuries necessitates surgical intervention, often involving procedures such as external fixation and percutaneous screw placement. Given the infrequent performance of these procedures, regular training is imperative to ensure readiness for emergencies. Our pre- post simulation study aimed to adapt and validate a realistic simulation model for stabilizing unstable pelvic ring injuries, facilitating participants’ knowledge retention and procedural confidence enhancement.MethodsA standardized simulator of an unstable pelvic ring utilizing synthetic pelvic bones featuring complete disruption of the symphysis and sacroiliac joint was developed. Trauma surgeons of a level one academic hospital were invited to perform external fixation and emergency sacroiliac screw application under C-arm guidance. Prior to and following the simulation session, participants completed a subjective questionnaire assessing their confidence in emergency interventions on a 10-point Likert scale (10-LS). Objective parameters, such as intraoperative imaging quality, reduction accuracy, and the positioning of screws, wires, and external fixators, were also evaluated as secondary outcome measures.ResultsFifteen trauma surgeons (10 residents, 5 consultants) participated in the simulation over the course of one day. The mean total operation time was 20.34 ± 6.06 min, without significant differences between consultants and residents (p = 0.604). The confidence for emergency SI-Screw placement increased significantly after the simulator (10-LS: Before = 3.8 ± 3.08 vs. After = 5.67 ± 2.35; p = 0.002) as well as after external fixation (10-LS: Before = 3.93 ± 2.79 vs. After = 6.07 ± 2.52; p = 0.002). In addition, confidence in (intraoperative) pelvic imaging increased significantly (10-LS: Before = 4.60 ± 3.0 vs. After = 6.53 ± 2.39; p = 0.011). Overall, the model was rated as a realistic simulation of clinical practice (10-LS = 7.87 ± 1.13).ConclusionsOur unstable pelvis fracture model is a tool to practice emergency interventions such as external fixation and percutaneous techniques. Participants benefitted from this in terms of technical instrumentation as well as intraoperative imaging. Further studies are required to validate the objective benefits and improvements that participants undergo through frequent training.

Anatomically-detailed segmented representative adult and pediatric nasal models for assessing regional drug delivery and bioequivalence with suspension nasal sprays

In vitro nasal models can potentially facilitate development and approval of nasal drug products. This study aims to evaluate the potential for using regional deposition measurements from in vitro nasal models to evaluate nasal spray performance across several products. To accomplish this, the posterior regions of six anatomically realistic nasal airway models of adult and pediatric subjects, representing Low (L), Mean (M) and High (H) posterior drug deposition (PD) for each of the two age groups, were segmented with high anatomical precision into five regions of interest. These models were previously developed with the goal of quantifying the range of intersubject variability of PD following administration of inhaled corticosteroids. The in vitro regional drug deposition values were measured for the reference listed drug (RLD) product for triamcinolone acetonide and two corresponding generic (test) nasal spray products, as well as an RLD product for fluticasone furoate nasal spray. In general, the pediatric models mostly demonstrated higher PD compared to the adult models. The majority (>85 %) of PD was confined to the front and the inferior meatus regions. Subsequent population bioequivalence (PBE) analyses of the regional nasal deposition suggested that the anatomical differences among subjects may impact the nasal spray performance across different nasal products.

Optimizing large-scale CO2 pipeline networks using a geospatial splitting approach

CO2 transport infrastructure is the backbone of carbon capture and storage (CCS) technology for the mitigation of carbon emissions and project deployment viability. In conventional large-scale CO2 pipeline network designs, the storage sites are generally assumed as the centroids of the major geologic basins, however, this approach might provide suboptimal solutions since the large extension of some storage formations significantly increases the length of the CO2 transportation networks. To address this situation and obtain optimal pipeline routes, we present a novel geospatial splitting framework that partitions large basins into multiple sub-sinks. In our approach, we used a large number of reservoir models varying petrophysical properties and CO2 injection rates to compute pressure plumes through numerical simulations, leading to the calculation of the number of subregions for each basin as a function of the extension of pressure interference areas and boundaries. Finally, we applied K-means clustering and Voronoi polygon algorithms to partition large basins into subregions and obtain their sink coordinates. To demonstrate the capability of the developed workflow, we investigated two CO2 pipeline network modeling case studies using our splitting approach: one regional case study focusing on the Intermountain West (I-West) region and one nationwide case study covering the lower 48 states in the U.S. In both case studies, we compared the optimal pipeline routes using the original and new storage locations and examined the major differences. The use of the developed geospatial approach resulted in both cases in a shortening of the total pipeline network length by 13% and 10%, compared to the pipeline modeling with the original basins, leading to cost reductions of 25% and 17%, respectively, demonstrating that the location of point sinks has a critical impact on the length and expenses of pipelines to efficiently transport CO2 to distant storage sites. Therefore, the workflow presented here contributes to the proper and realistic modeling of case studies that support decision-making in CCS deployment.

Exploring Nonlinear Dynamics In Brain Functionality Through Phase Portraits And Fuzzy Recurrence Plots.

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.

Gaia BH1 and BH2 — Evolutionary Models with Overshooting of the Black Hole Progenitors within the Present-Day Binary Separation

Abstract Three black holes (BHs) in wide binaries — Gaia BH1, BH2 and BH3 — were recently discovered. The likely progenitors of the BHs were massive stars that experienced a supergiant phase, reaching radii of ∼1000R⊙, before collapsing to form the BH. Such radii are difficult to accommodate with the present-day orbits of BH1 and BH2 — with semi-major axes of 1.4 and 3.7 au, respectively. In this letter, we show that the maximal radii of the supergiants are not necessarily so large, and realistic stellar evolution models, with some assumed overshooting above the convective core into the radiative stellar envelope, produce substantially smaller maximal radii. The limited expansion of supergiants is consistent with the empirical Humphreys-Davidson limit — the absence of red supergiants above an upper luminosity limit, notably lower than the highest luminosity of main-sequence stars. We propose that the evolution that led to the formation of Gaia BH1 and BH2 simply did not involve an expansion to the cool supergiant phase.

Lieb-Schultz-Mattis theorems for symmetry-protected topological phases

The Lieb-Schultz-Mattis (LSM) theorem and its generalizations are a class of powerful no-go theorems that rule out any short-range-entangled (SRE) symmetric ground state irrespective of the specific Hamiltonian, based only on certain microscopic inputs, such as symmetries and particle filling numbers. In this work, we introduce and provide physical arguments for a new class of LSM-type theorems, where any symmetry-allowed SRE ground state must be a symmetry-protected topological (SPT) phase with robust gapless edge states, such as topological insulators and superconductors. The key ingredient is to replace the lattice translation symmetry in usual LSM theorems by the magnetic translation symmetry. These theorems provide new insights into realistic models and experimental realizations of SPT phases in interacting bosons and fermions.

Multi-Objective Short-Term Operation of Hydro–Wind–Photovoltaic–Thermal Hybrid System Considering Power Peak Shaving, the Economy and the Environment

In recent years, renewable, clean energy options such as hydropower, wind energy and solar energy have been attracting more and more attention as high-quality alternatives to fossil fuels, due to the depletion of fossil fuels and environmental pollution. Multi-energy power systems have replaced traditional thermal power systems. However, the output of solar and wind power is highly variable, random and intermittent, making it difficult to integrate it directly into the grid. In this context, a multi-objective model for the short-term operation of wind–solar–hydro–thermal hybrid systems is developed in this paper. The model considers the stability of the system operation, the operating costs and the impact in terms of environmental pollution. To solve the model, an evolutionary cost value region search algorithm is also proposed. The algorithm is applied to a hydro–thermal hybrid system, a multi-energy hybrid system and a realistic model of the wind–solar–hydro experimental base of the Yalong River Basin in China. The experimental results demonstrate that the proposed algorithm exhibits superior performance in terms of both convergence and diversity when compared to the reference algorithm. The integration of wind and solar energy into the power system can enhance the economic efficiency and mitigate the environment impact from thermal power generation. Furthermore, the inherent unpredictability of wind and solar energy sources introduces operational inconsistencies into the system loads. Conversely, the adaptable operational capacity of hydroelectric power plants enables them to effectively mitigate peak loads, thereby enhancing the stability of the power system. The findings of this research can inform decision-making regarding the economic, ecological and stable operation of hybrid energy systems.

3D printing of realistic body phantoms: Comparison of measured and simulated organ doses on the example of a CT scan on a pregnant woman

AbstractBackgroundMedical examinations or treatment of pregnant women using ionizing radiation are sometimes unavoidable. In such cases, the risk of harm to the embryo and fetus after exposure to ionizing radiation must be carefully estimated. However, no commercially available anthropomorphic body phantoms of pregnant women are available for dose measurements. A promising possibility for the production of body phantoms for patient groups that are not adequately represented by the phantoms of reference persons is 3D printing. However, this approach is still in the evaluation phase.PurposeTo print the abdomen of a woman in the late stage of pregnancy and compare the dose distribution measured using thermoluminescence dosimeters (TLDs) in the printed phantom for two different computed tomography (CT) protocols with the corresponding results of Monte Carlo simulations on voxel models of the pregnant woman.Materials and methodsThe physical phantom was produced through multi‐material extrusion printing using different print materials identified in previous studies to simulate homogeneous soft tissues and the mean compositions of maternal and fetal bones. The 3D printed abdomen was combined with a conventionally produced anthropomorphic female phantom to obtain a whole‐body phantom of a pregnant woman. Dose values resulting from two different CT scans acquired at tube voltages of 80 and 120 kV were measured using TLDs positioned in the physical phantom and cross‐validated with the results of Monte Carlo simulations performed for two different voxel models. The first was a voxelized model of the produced phantom itself and the second a realistic digital model of a pregnant woman. Representative CT values of the materials used in the printed phantom were determined from the acquired CT images.ResultsThe CT values of maternal and fetal tissue structures in the phantom are comparable to CT values of real human tissues. The difference between most organ doses measured in the 3D printed phantom and simulated in the voxel models was below 20% and equivalent within the measurement uncertainties. Only the dose to the fetal head was up to 50% higher and not equivalent for the realistic model and the 80 kV‐protocol. As expected, the agreement was better for the voxelized than for the realistic model. For both models a slight energy dependence was observed, with larger deviations for the 80‐kV protocol especially for organs located in the pelvic region.ConclusionIndividualized physical body phantoms, such as that of a pregnant woman, can be produced using 3D printing. The good agreement between measured and simulated doses to the fetus cross‐validates both dosimetric methods. Therefore, this study demonstrates the suitability of 3D printing phantoms for patients not adequately represented by commercially available body phantoms of reference persons.

Estimation and validation of elastic constants in fused filament fabrication 3D printing: From mesoscale to macroscale

Evaluating the mechanical properties of 3D-printed parts is a cumbersome task. This study poses an approach based on computational homogenization to estimate the elastic constants of fused filament fabrication 3D-printed parts. A whole methodology for characterization and experimental validation is necessary to improve finite element numerical models.Samples are characterized both mechanically and geometrically. To improve the characterization, novel algorithms based on micro-computed tomography images and image segmentation techniques are implemented. Thereafter, elastic constants are estimated, informed by the characterization results. The method’s effectiveness is assessed through a deep comparison, based on the digital image correlation technique, between different experimental samples and finite element models.Results show that the numerical estimation provided in this work is accurate enough to develop realistic finite element models, including anisotropy of the structures. However, defects and voids developed during 3D printing are an important source of error for these numerical models.This work provides an estimation and validation of elastic constants in 3D-printed parts, including geometrical characterization, numerical homogenization and experimental validation. The results of this work provide valuable information encompassing techniques to improve the characterization of 3D-printed parts, tendencies on elastic constants, and main sources of error.

A Computer Model of a Marx Generator Charging a Coaxial Switched Wave Oscillator

The paper describes an axisymmetric Finite-Difference Time-Domain computer model of a coaxial Switched Wave Oscillator integrated with a dipole antenna. The model analyzes the operation of a realistic circuit model of a multistage Marx generator that charges the oscillator to a high voltage. The initial field distribution is calculated with an electrostatic finite-difference method solver to speed up the time-domain analysis. The work presents the results of our circuit model of a Marx generator’s simulations of the charging phase, followed by the results from the discharge phase, using our axisymmetric Finite-Difference Time-Domain model. Our work describes new and fast numerical solvers that can observe the operation of Switched Wave Oscillator systems (also considering the connected antenna). The codes could be used in the process of designing such a system. Advanced boundary conditions modeling the spark gap and oscillator’s excitation set our work apart from the other attempts in the literature.

Analysis of the optical performance of intraocular lenses using profilometric measurements.

The aim of this study was to develop a methodology, based on profilometer measurements to assess the optical behaviour of Intraocular Lenses (IOls). The "Modulation Transfer Function through-object" (MTF through-object) based on vergence object displacement was calculated for different pupil sizes and pseudophakic eyes. Tilt and decentration were also analysed in a realistic cornea eye model. For comparison between the different IOLs, an optical quality criterion based on a minimum value the MTF through-object and the recognition of simulated vision optotypes was introduced. Five IOLs were used in this study: Tecnis Eyhance, Mini Well, Tecnis Symfony, Tecnis Synergy and RayOne EMV. The technique was validated with previous methodologies. A general narrowing of the through-object MTF curve compared to the through-focus MTF curve was shown, resulting in greater distances between near and intermediate points and less depth of field around the far peak. The comparison between the IOLs showed that variations in corneal aberrations, pupil size and decentration caused relevant changes in IOL performance. A decrease of the SA produced a hypermetropic shift of the far focus between + 0.3 D and + 0.4 D. Most of IOLs worsen the optical quality as pupil size increased, even the MTF through-object shape changed. Decentration was an important factor in IOL implantation, causing a significant change in MTF through-object shape in most of IOLs. This study highlights the need to evaluate pre-operative patients for corneal aberrations and pupillary size to have the best optical success after cataract surgery in multifocal or extended depth of focus IOLs. What is known MTF(Modulation Transfer Function)through-focus curves (calculated in image space by moving the detector plane) can be obtained from optical bench assembly or from commercial devices. Recently, some studies proposed to characterize the lens surface design based on the profilometric measurements What is new A novel methodology based on profilometer measurements to assess the optical behaviour of Intraocular Lenses (IOls) was shown. The "Modulation Transfer Function through-object" based on vergence object displacement was introduced in order to analyse five premium IOLs. MTF through-object curve is more appropriate for studying clinical behaviour, as it provides further near and intermediate points distances and lower depth of focus around far peak compare to MTF through-focus curves. The optical behaviour of the five IOLs can vary considerably depending on the eye model and pupil size. The effect of tilt and decentration on the MTF through-object the IOLs was analysed.

Age truncation due to disease shrinks metapopulation viability for amphibians.

Metapopulations often exist in a fragile balance between local extinctions and (re)colonisations, in which case emerging threats that alter species vital rates may drastically increase metapopulation extinction risk. We combined empirical data with metapopulation simulations to examine how demographic shifts associated with amphibian chytrid fungus (Batrachochytrium dendrobatidis, Bd) have altered metapopulation viability for threatened amphibians in Australia. Comparing the ages of museum specimens collected before Bd emerged in Australia with individuals from geographically matched remnant populations revealed significant truncation of age structures post-Bd, with a halving of annual adult survival probabilities. Spatially realistic metapopulation modelling demonstrated that reduced adult survival led to major reductions in the parameter space over which persistence was possible for the focal species, with contractions to landscapes with higher landscape connectivity, lower environmental stochasticity and considerably higher recruitment rates. Metapopulation persistence post-Bd required greater landscape connectivity than pre-Bd. This arises from a landscape-level analogue of compensatory recruitment at the population level, in which higher (re)colonisation rates can offset more frequent local extinctions, enabling persistence of amphibians susceptible to Bd. Interactions between recruitment rate, environmental stochasticity and landscape connectivity were also more important for metapopulation persistence post-Bd. Higher recruitment was required to mitigate the impacts of environmental stochasticity, and higher landscape connectivity was required to mitigate the impacts of environmental stochasticity and poor recruitment. Increased reliance on these interdependencies shrunk the parameter space over which metapopulations could persist post-Bd. Our study demonstrates that emerging threats that alter species vital rates can drastically reduce the capacity of certain environments to support metapopulations. For our focal species, reductions in adult survival rates due to Bd produced major reductions in the conditions under which persistence was possible, providing a mechanistic insight into the processes underpinning observed range and niche contractions of amphibians impacted by this pathogen. More broadly, our study illustrates how environmentally mediated host resilience can enable persistence following the emergence of novel pathogens. This pathway to persistence is worthy of greater attention on both conceptual and applied grounds.

Formation and retrieval of cell assemblies in a biologically realistic spiking neural network model of area CA3 in the mouse hippocampus

The hippocampal formation is critical for episodic memory, with area Cornu Ammonis 3 (CA3) a necessary substrate for auto-associative pattern completion. Recent theoretical and experimental evidence suggests that the formation and retrieval of cell assemblies enable these functions. Yet, how cell assemblies are formed and retrieved in a full-scale spiking neural network (SNN) of CA3 that incorporates the observed diversity of neurons and connections within this circuit is not well understood. Here, we demonstrate that a data-driven SNN model quantitatively reflecting the neuron type-specific population sizes, intrinsic electrophysiology, connectivity statistics, synaptic signaling, and long-term plasticity of the mouse CA3 is capable of robust auto-association and pattern completion via cell assemblies. Our results show that a broad range of assembly sizes could successfully and systematically retrieve patterns from heavily incomplete or corrupted cues after a limited number of presentations. Furthermore, performance was robust with respect to partial overlap of assemblies through shared cells, substantially enhancing memory capacity. These novel findings provide computational evidence that the specific biological properties of the CA3 circuit produce an effective neural substrate for associative learning in the mammalian brain.

Semi-analytic three-shell forward calculation for magnetoencephalography

In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.

A Physics-Informed Auto-Learning Framework for Developing Stochastic Conceptual Models for ENSO Diversity

Abstract Understanding ENSO dynamics has tremendously improved over past decades. The ENSO diversity in spatial pattern, peak intensity, and temporal evolution is however still poorly represented in conceptual ENSO models. In this paper, a physics-informed auto-learning framework is applied to derive ENSO stochastic conceptual models with varying degrees of freedom. The framework is computationally efficient and easy to apply. Once the state vector of the target model is set, causal inference is exploited to build the right-hand side of the equations based on a mathematical function library. Fundamentally different from standard nonlinear regression, the auto-learning framework provides a parsimonious model by retaining only terms that improve the dynamical consistency with observations. It can also identify crucial latent variables and provide physical explanations. This methodology successfully reconstructs the equations of a realistic six-dimensional reference ENSO model based on the recharge oscillator theory from its data. A hierarchy of lower-dimensional models is derived and their representation of ENSO (including its diversity) systematically assessed. The minimum model that represents ENSO diversity is four-dimensional, with three interannual variables describing the western Pacific thermocline depth, the eastern and central Pacific sea surface temperatures (SSTs), and one intraseasonal variable for westerly wind events. Without the intraseasonal variable, the resulting three-dimensional model underestimates extreme events and is too regular. The limited number of weak nonlinearities in the model are essential in reproducing the observed extreme El Niño events and the observed nonlinear relationship between eastern and western Pacific SSTs.