Finite‐length shim coil design using a fourier series minimum inductance and minimum power algorithm
Bibliographic record
Abstract
Abstract High field magnetic resonance (MR) imaging and spectroscopy are sensitive to magnetic field inhomogeneities caused by susceptibility differences between tissues, bone, and air. These inhomogeneities cause MR image artifacts and line broadening in MR spectra. To correct for these inhomogeneities, specialized shim coils are used in combination with the usual gradient systems. To produce realistic coils for use in human or small‐animal studies, direct control over the length of the coils is necessary. In this article, a simple method for the design of shim coils of arbitrary order and with predetermined length is presented. The method is based on a simple Fourier series expansion of the current density and either power or inductance can be minimized subject to a series of field constraints. The method is mathematically simple, easy to implement and computationally fast. A quantitative comparison of figures of merit for inductance and resistance was made as a function of shim coil length. Coils of 40 cm diameter were designed with lengths of 50, 60, 80, and 100 cm. Comparison of results obtained using the two design methods across all shim axes and coil lengths indicate very little performance difference between the two methods. The decreased complexity of the minimum power designs appears to outweigh any small benefits obtainable using the minimum inductance algorithm for the range of coils investigated. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 245–253, 2010.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".