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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.

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COVID-19 (Coronavirus), an acute respiratory disorder, is caused by SARS-CoV-2 (coronavirus severe acute respiratory syndrome). The high prevalence of COVID-19 infection has drawn attention to a frequent illness symptom: olfactory and gustatory dysfunction. The primary purpose of this manuscript is to create a Computer-Assisted Diagnostic (CAD) system to determine whether a COVID-19 patient has normal, mild, or severe anosmia. To achieve this goal, we used fluid-attenuated inversion recovery (FLAIR) Magnetic Resonance Imaging (FLAIR-MRI) and Diffusion Tensor Imaging (DTI) to extract the appearance, morphological, and diffusivity markers from the olfactory nerve. The proposed system begins with the identification of the olfactory nerve, which is performed by a skilled expert or radiologist. It then proceeds to carry out the subsequent primary steps: (i) extract appearance markers (i.e., 1 s t and 2 n d order markers), morphology/shape markers (i.e., spherical harmonics), and diffusivity markers (i.e., Fractional Anisotropy (FA) & Mean Diffusivity (MD)), (ii) apply markers fusion based on the integrated markers, and (iii) determine the decision and corresponding performance metrics based on the most-promising classifier. The current study is unusual in that it ensemble bags the learned and fine-tuned ML classifiers and diagnoses olfactory bulb (OB) anosmia using majority voting. In the 5-fold approach, it achieved an accuracy of 94.1%, a balanced accuracy (BAC) of 92.18%, precision of 91.6%, recall of 90.61%, specificity of 93.75%, F1 score of 89.82%, and Intersection over Union (IoU) of 82.62%. In the 10-fold approach, stacking continued to demonstrate impressive results with an accuracy of 94.43%, BAC of 93.0%, precision of 92.03%, recall of 91.39%, specificity of 94.61%, F1 score of 91.23%, and IoU of 84.56%. In the leave-one-subject-out (LOSO) approach, the model continues to exhibit notable outcomes, achieving an accuracy of 91.6%, BAC of 90.27%, precision of 88.55%, recall of 87.96%, specificity of 92.59%, F1 score of 87.94%, and IoU of 78.69%. These results indicate that stacking and majority voting are crucial components of the CAD system, contributing significantly to the overall performance improvements. The proposed technology can help doctors assess which patients need more intensive clinical care.

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An innovative method for synthesizing optimum difference patterns of the spherical sensor array is introduced, along with a sidelobe tapering technique. Firstly, we suggest employing the spherical harmonics of degree ±1 to synthesize the spherical array difference pattern; secondly, we study the mapping relationship between the difference pattern of the spherical sensor array and the difference pattern of the uniformly spaced linear array (ULA) with odd-numbered elements; finally, we enhance the Zolotarev difference pattern, which is a counterpart to the Dolph-Chebyshev sum pattern that traditionally allows synthesis only for ULA with even-numbered elements. Our modification extends its applicability to synthesize difference patterns for ULA with odd-numbered elements. Leveraging the optimal difference pattern, a generalized Bayliss difference pattern synthesis method designed for the ULA with odd-numbered elements is further proposed. To illustrate the effectiveness of our approach, we present several design examples through experimental simulation.

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Data harmonization is necessary for removing confounding effects in multi-site diffusion image analysis. One such harmonization method, LinearRISH, scales rotationally invariant spherical harmonic (RISH) features from one site ("target") to the second ("reference") to reduce confounding scanner effects. However, reference and target site designations are not arbitrary and resultant diffusion metrics (fractional anisotropy, mean diffusivity) are biased by this choice. In this work we propose MidRISH: rather than scaling reference RISH features to target RISH features, we project both sites to a mid-space. We validate MidRISH with the following experiments: harmonizing scanner differences from 37 matched patients free of cognitive impairment, and harmonizing acquisition and study differences on 117 matched patients free of cognitive impairment. We find that MidRISH reduces bias of reference selection while preserving harmonization efficacy of LinearRISH. Users should be cautious when performing LinearRISH harmonization. To select a reference site is to choose diffusion metric effect-size. Our proposed method eliminates the bias-inducing site selection step.

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The shape of the talus, its internal structure, and its mechanical properties are important in determining talar behavior during loading, which may be significant for the design of surgical tools and implants. Although recent studies using statistical shape modeling have described quantitative talar external shape variation, no similar quantitative study exists to describe the density distribution of internal talar structure. The goal of this study is to quantify statistical variation in talar shape and density to benefit the design of talar implants. To this end, weight-bearing computed tomography (CT) scans of the ankle were collected in neutral, bilateral standing posture, and three-dimensional models were generated for each talus. Local density derived from the Hounsfield unit of each CT voxel was extracted. A weighted spherical harmonic analysis was performed to quantify the talar external shape. One hundred and seventy-nine volumes of interest were placed in the same relative position within each talus to quantify the talar density. Additionally, a finite element analysis (FEA) was conducted on a talus with both heterogeneous and homogeneous material properties to observe the effect of these properties on the stress and strain response. Significant differences were found in the talar density in sex and age, as well as in the stress and strain response between homogeneous and heterogeneous FEA. These differences show the importance of considering heterogeneity when examining the load response of tarsal bones.

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This study aims to examine geometric models of the corneal surface that can be used to reduce in reasonable time the dimensionality of datasets of normal anterior corneas. Polynomial models (P) like Zernike polynomials (ZP) and spherical harmonic polynomials (SHP) were obvious candidates along with their rational function (R) counterparts, namely Zernike rational functions (ZR) and spherical harmonic rational functions (SHR, new model). Knowing that both SHP and ZR were more accurate than ZP for the modeling of normal and keratoconus corneas, it was expected that both spherical harmonic (SH) models (SHP and SHR) would be more accurate than their Zernike (Z) counterparts (ZP and ZR, respectively), and both rational (R) models (SHR and ZR) more accurate than their polynomial counterparts (SHP and ZP, respectively) for a low dimensional space (coefficient number J < 30). This was the case. The SH factor contributed more to accuracy than the R factor. Considering the corneal processing time as a function of J, P models were processed in quasi-linear time with a quasi-null slope and rational models in polynomial time. Z models were faster than SH models, and increasingly so in their R version. In sum, for corneal dimensionality reduction, SHR is the most accurate model, but its processing time is increasingly prohibitive unless the best coefficient combination is identified beforehand. ZP is the fastest model and is reasonably accurate with normal corneas for exploratory tasks. SHP is the best compromise between accuracy and speed.

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Spheroids are one of the least understood lithic items yet are one of the most enduring, spanning from the Oldowan to the Middle Palaeolithic. Why and how they were made remains highly debated. We seek to address whether spheroids represent unintentional by-products of percussive tasks or if they were intentionally knapped tools with specific manufacturing goals. We apply novel three-dimensional analysis methods, including spherical harmonics and surface curvature, to 150 limestone spheroids from 'Ubeidiya (ca 1.4 Ma), presently the earliest Acheulean occurrence outside of Africa, to bring a new perspective to these enigmatic artefacts. We reconstruct the spheroid reduction sequence based on trends in their scar facets and geometry, finding that the spheroid makers at 'Ubeidiya followed a premeditated reduction strategy. During their manufacture, the spheroids do not become smoother, but they become markedly more spherical. They approach an ideal sphere, a feat that likely required skilful knapping and a preconceived goal. Acheulean bifaces are currently thought to represent the earliest evidence of hominins imposing a premeditated, symmetrical shape on stone. The intentional production of sphere-like objects at 'Ubeidiya similarly shows evidence of Acheulean hominins desiring and achieving intentional geometry and symmetry in stone.

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Objective: Data harmonization is necessary for removing confounding effects in multi-site diffusion image analysis. One such harmonization method, LinearRISH, scales rotationally invariant spherical harmonic (RISH) features from one site ("target") to the second ("reference") to reduce confounding scanner effects. However, reference and target site designations are not arbitrary and resultant diffusion metrics (fractional anisotropy, mean diffusivity) are biased by this choice. In this work we propose MidRISH: rather than scaling reference RISH features to target RISH features, we project both sites to a mid-space. Methods: We validate MidRISH with the following experiments: harmonizing scanner differences from 37 matched patients free of cognitive impairment, and harmonizing acquisition and study differences on 117 matched patients free of cognitive impairment. Conclusion: MidRISH reduces bias of reference selection while preserving harmonization efficacy of LinearRISH. Significance: Users should be cautious when performing LinearRISH harmonization. To select a reference site is to choose diffusion metric effect-size. Our proposed method eliminates the bias-inducing site selection step.

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Objective.Our objective is to formulate the problem of the magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements.Approach.We use the vector spherical harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array ofmperfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise.Main results.We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of 'high-quality' MEG sensor arrays, e.g. high channel information capacity.Significance.Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.

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Diffusion MRI (dMRI) is a non-invasive tool for assessing the white matter region of the brain by approximating the fiber streamlines, structural connectivity, and estimation of microstructure. This modality can yield useful information for diagnosing several mental diseases as well as for surgical planning. The higher angular resolution diffusion imaging (HARDI) technique is helpful in obtaining more robust fiber tracts by getting a good approximation of regions where fibers cross. Moreover, HARDI is more sensitive to tissue changes and can accurately represent anatomical details in the human brain at higher magnetic strengths. In other words, magnetic strengths affect the quality of the image, and hence high magnetic strength has good tissue contrast with better spatial resolution. However, a higher magnetic strength scanner (like 7T) is costly and unaffordable to most hospitals. Hence, in this work, we have proposed a novel CNN architecture for the transformation of 3T to 7T dMRI. Additionally, we have also reconstructed the multi-shell multi-tissue fiber orientation distribution function (MSMT fODF) at 7T from single-shell 3T. The proposed architecture consists of a CNN-based ODE solver utilizing the Trapezoidal rule and graph-based attention layer alongwith L1 and total variation loss. Finally, the model has been validated on the HCP data set quantitatively and qualitatively.

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One of the main purposes of CryoEM Single Particle Analysis is to reconstruct the three-dimensional structure of a macromolecule thanks to the acquisition of many particle images representing different poses of the sample. By estimating the orientation of each projected particle, it is possible to recover the underlying 3D volume by multiple 3D reconstruction methods, usually working either in Fourier or in real space. However, the reconstruction from the projected images works under the assumption that all particles in the dataset correspond to the same conformation of the macromolecule. Although this requisite holds for some macromolecules, it is not true for flexible specimens, leading to motion-induced artefacts in the reconstructed CryoEM maps. In this work, we introduce a new Algebraic Reconstruction Technique called ZART, which is able to include continuous flexibility information during the reconstruction process to improve local resolution and reduce motion blurring. The conformational changes are modelled through Zernike3D polynomials. Our implementation allows for a multiresolution description of the macromolecule adapting itself to the local resolution of the reconstructed map. In addition, ZART has also proven to be a useful algorithm in cases where flexibility is not so dominant, as it improves the overall aspect of the reconstructed maps by improving their local and global resolution.

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We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from only axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

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In diffusion weighted MRI (DW-MRI), hardware nonlinearities lead to spatial variations in the orientation and magnitude of diffusion weighting. While the correction of these spatial distortions has been well established for analyses of DW-MRI, the existing voxel-wise empirical correction for gradient nonlinearities requires reimplementation of existing models, as the resultant gradients vary by voxel. Herein, we propose a two-step signal approximation after voxel-wise correction of gradient nonlinearity effects in DW-MRI. The proposed technique (1) scales the diffusion signal and (2) resamples the gradient orientations. This results in uniform gradients across the corrected image and provides the key advantage of seamless integration into current diffusion workflows. We investigated the validity of our technique by fitting a multi-compartment neurite orientation dispersion and density imaging (NODDI) model to the empirical correction and proposed approximation in five subjects from the MASiVar pediatric dataset. We evaluated intra-cellular volume fraction (iVF), CSF volume fraction (cVF), and orientation dispersion index (ODI) from NODDI. The Cohen's d of iVF, cVF and ODI between the techniques was <0.2 indicating the proposed technique does not exhibit significant differences from the voxel-wise correction technique. Our two-step signal approximation is an efficient representation of the voxel-wise gradient table correction. Using this approximation, correction of gradient nonlinearities can be easily incorporated into existing diffusion preprocessing pipelines and is implemented in "PreQual: An automated pipeline for integrated preprocessing and quality assurance of diffusion weighted MRI images".

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Objective.We provide a systematic framework for quantifying the effect of externally applied weak electric fields on realistic neuron compartment models as captured by physiologically relevant quantities such as the membrane potential or transmembrane current as a function of the orientation of the field.Approach.We define a response function as the steady-state change of the membrane potential induced by a canonical external field of 1 V m-1as a function of its orientation. We estimate the function values through simulations employing reconstructions of the rat somatosensory cortex from the Blue Brain Project. The response of different cell types is simulated using the NEURON simulation environment. We represent and analyze the angular response as an expansion in spherical harmonics.Main results.We report membrane perturbation values comparable to those in the literature, extend them to different cell types, and provide their profiles as spherical harmonic coefficients. We show that at rest, responses are dominated by their dipole terms (ℓ=1), in agreement with experimental findings and compartment theory. Indeed, we show analytically that for a passive cell, only the dipole term is nonzero. However, while minor, other terms are relevant for states different from resting. In particular, we show howℓ=0andℓ=2terms can modify the function to induce asymmetries in the response.Significance.This work provides a practical framework for the representation of the effects of weak electric fields on different neuron types and their main regions-an important milestone for developing micro- and mesoscale models and optimizing brain stimulation solutions.

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BACKGROUND AND OBJECTIVE: Diffusion MRI (dMRI) has been considered one of the most popular non-invasive techniques for studying the human brain's white matter (WM). dMRI is used to delineate the brain's microstructure by approximating the WM region's fiber tracts. The achieved fiber tracts can be utilized to assess mental diseases like Multiple sclerosis, ADHD, Seizures, Intellectual disability, and others. New techniques such as high angular resolution diffusion-weighted imaging (HARDI) have been developed, providing precise fiber directions, and overcoming the limitation of traditional DTI. Unlike Single-shell, Multi-shell HARDI provides tissue fractions for white matter, gray matter, and cerebrospinal fluid, resulting in a Multi-shell Multi-tissue fiber orientation distribution function (MSMT fODF). This MSMT fODF comes up with more precise fiber directions than a Single-shell, which helps to get correct fiber tracts. In addition, various multi-compartment diffusion models, including as CHARMED and NODDI, have been developed to describe the brain tissue microstructural information. This type of model requires multi-shell data to obtain more specific tissue microstructural information. However, a major concern with multi-shell is that it takes a longer scanning time restricting its use in clinical applications. In addition, most of the existing dMRI scanners with low gradient strengths commonly acquire a single b-value (shell) upto b=1000s/mm2 due to SNR (Signal-to-noise ratio) reasons and severe imaging artifacts. METHODS: To address this issue, we propose a CNN-based ordinary differential equations solver for the reconstruction of MSMT fODF from under-sampled and fully sampled Single-shell (b=1000s/mm2) dMRI. The proposed architecture consists of CNN-based Adams-Bash-forth and Runge-Kutta modules along with two loss functions, including L1 and total variation. RESULTS: We have shown quantitative results and visualization of fODF, fiber tracts, and structural connectivity for several brain regions on the publicly available HCP dataset. In addition, the obtained angular correlation coefficients for white matter and full brain are high, showing the proposed network's utility.Finally, we have also demonstrated the effect of noise by adjusting SNR from 5 to 50 and observed the network robustness. CONCLUSION: We can conclude that our model can accurately predict MSMT fODF from under-sampled or fully sampled Single-shell dMRI volumes.

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PURPOSE: Identifying optimal machine learning pipelines for computer-aided diagnosis is key for the development of robust, reproducible, and clinically relevant imaging biomarkers for endometrial carcinoma. The purpose of this study was to introduce the mathematical development of image descriptors computed from spherical harmonics (SPHARM) decompositions as well as the associated machine learning pipeline, and to evaluate their performance in predicting deep myometrial invasion (MI) and histopathological high-grade in preoperative multiparametric magnetic resonance imaging (MRI). PATIENTS AND METHODS: This retrospective study included 128 women with histopathology-confirmed endometrial carcinomas who underwent 1.5-T MRI before hysterectomy between January 2011 and July 2015. SPHARM descriptors of each tumor were computed on multiparametric MRI images (T2-weighted, diffusion-weighted, dynamic contrast-enhanced-MRI and apparent diffusion coefficient maps). Tensor-based logistic regression was used to classify two-dimensional SPHARM rotationally-invariant descriptors. Head-to-head comparisons with radiomics analyses were performed with DeLong tests with Bonferroni-Holm correction to compare diagnostic performances. RESULTS: With all MRI contrasts, SPHARM analysis resulted in area under the curve, sensitivity, specificity, and balanced accuracy values of 0.94 (95% confidence interval [CI]: 0.85, 1.00), 100% (95% CI: 100, 100), 74% (95% CI: 51, 92), 87% (95% CI: 78, 98), respectively, for predicting deep MI. For predicting high-grade tumor histology, the corresponding values for the same diagnostic metrics were 0.81 (95% CI: 0.64, 0.90), 93% (95% CI: 67, 100), 63% (95% CI: 45, 79) and 78% (95% CI: 64, 86). The corresponding values achieved via radiomics were 0.92 (95% CI: 0.82, 0.95), 82% (95% CI: 65, 93), 80% (95% CI: 51, 94), 81% (95% CI: 70, 91) for deep MI and 0.72 (95% CI: 0.58, 0.83), 93% (95% CI: 65, 100), 55% (95% CI: 41, 69), 74% (95% CI: 52, 88) for high-grade histology. The diagnostic performance of the SPHARM analysis was not significantly different (P = 0.62) from that of radiomics for predicting deep MI but was significantly higher (P = 0.044) for predicting high-grade histology. CONCLUSION: The proposed SPHARM analysis yields similar or higher diagnostic performance than radiomics in identifying deep MI and high-grade status in histology-proven endometrial carcinoma.

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When red blood cells (RBCs) experience non-physiologically high stresses, e.g., in medical devices, they can rupture in a process called hemolysis. Directly simulating this process is computationally unaffordable given that the length scales of a medical device are several orders of magnitude larger than that of a RBC. To overcome this separation of scales, the present work introduces an affordable computational framework that accurately resolves the stress and deformation of a RBC in a spatially and temporally varying macroscale flow field such as those found in a typical medical device. The underlying idea of the present framework is to treat RBCs as one-way coupled tracers in the macroscale flow by capturing the effect of the flow on their dynamics but neglecting their effect on the flow at the macroscale. As a result, the RBC dynamics are simulated after those of the flow in a postprocessing step by receiving the fluid velocity gradient tensor measured along the RBC trajectory as the input. To resolve the fluid velocity in the immediate vicinity of the RBC as well as the motion of the membrane, we employ the boundary integral method coupled to a structural solver. The governing equations are discretized in space using spherical harmonics, yielding spectral integration accuracy. The predictions produced by this formulation are in good agreement with those obtained from simulations of spherical capsules in shear flows and optical tweezers experiments. The accuracy of the present method is evaluated using unbounded shear flow as a benchmark. Its computational cost grows proportional to p 5, where p is the degree of the spherical harmonic. It also exhibits a fast convergence rate that is approximately O ( p 6 ) for p ⪅ 20.

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Normal organogenesis cannot be recapitulated in vitro for mammalian organs, unlike in species including Drosophila and zebrafish. Available 3D data in the form of ex vivo images only provide discrete snapshots of the development of an organ morphology. Here, we propose a computer-based approach to recreate its continuous evolution in time and space from a set of 3D volumetric images. Our method is based on the remapping of shape data into the space of the coefficients of a spherical harmonics expansion where a smooth interpolation over time is simpler. We tested our approach on mouse limb buds and embryonic hearts. A key advantage of this method is that the resulting 4D trajectory can take advantage of all the available data while also being able to interpolate well through time intervals for which there are little or no data. This allows for a quantitative, data-driven 4D description of mouse limb morphogenesis.

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We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have [Formula: see text] complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity [Formula: see text] or [Formula: see text] if evaluated using a Fast Fourier Transform on a grid of size [Formula: see text]. Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the [Formula: see text] sphere and are intrinsically related to angular momentum operators. Concatenation of [Formula: see text] such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

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Increased static field inhomogeneities are a burden for human brain MRI at Ultra-High-Field. In particular they cause enhanced Echo-Planar image distortions and signal losses due to magnetic susceptibility gradients at air-tissue interfaces in the subject's head. In the past decade, Multi-Coil Arrays (MCA) have been proposed to shim the field in the brain better than the 2nd or 3rd order Spherical Harmonic (SH) coils usually offered by MRI manufacturers. Here we present a novel MCA, named SCOTCH, optimized for whole brain shimming. Based on a cylindrical structure, it features several layers of small coils whose shape, size and location are found from a principal component analysis of ideal stream functions computed from an internal 100-brain fieldmap database. From an Open-Access external database of 126 brains, our SCOTCH implementation is shown to be equivalent to a partial 7th-order SH system with unlimited power, outperforming all known existing MCA prototypes. This result is further confirmed by a low-cost  30-cm diameter SCOTCH prototype built with 48 coils on 3 layers, and tested on 7 volunteers at 7T with a parallel-transmit RF coil made to be inserted in SCOTCH. Echo-Planar images of the subject brains before and after SCOTCH shimming show large signal recoveries, especially in the prefrontal cortex.

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