The Public Multi-Coil Information (PUMCIN) Policy

Abstract

Purpose

Multi-coil (MC) magnetic field modeling has emerged as a viable alternative to conventional field generation based on spherical harmonic shapes, and an active MC community is forming. While all MC applications share the same modeling concept, the specific MC designs can largely differ due to disparities in region of interest (e.g., human vs. rodent), intended MR application (e.g., B₀ shimming vs. spatial encoding), or other experimental constraints (e.g., available bore space or integration with radio-frequency technology). To date, a lack of detailed information on existing MC designs complicates their assessment and precludes a meaningful comparison.

Methods

Here, we suggest that future publications involving the MC technique not only report the benefits for the application at hand but also include an explicit description of the MC wire pattern employed.

Results

This PUblic Multi-Coil INformation (PUMCIN) policy represents a voluntary commitment to promoting free public access to the details necessary for reproducing and benefiting from MC research.

Conclusions

The PUMCIN policy is expected to initiate a paradigm shift with respect to the way MC innovation is reported. Setting an example ourselves, we hope to encourage the evolving MC community to maximize the benefits for science and society by embracing it.

INTRODUCTION

Lessons Learned from Spherical Harmonic Coil Design

The shape and magnitude of the magnetic field produced by an electrical current through a conducting wire are well-described by Biot-Savart’s Law. Forming the wire pattern provides a handle on the current path and, consequently, the magnetic field created. This principle is exploited to produce magnetic fields resembling the shapes of spherical harmonic (SH) functions by dedicated, current-driven wire patterns (1,2). A set of SH coils – one for each term – is nested inside the scanner bore as an SH coil system to generate the required B₀ magnetic fields for spatial selection, spatial encoding and B₀ magnetic field homogenization. X, Y and Z gradients coils producing the three first-order SH functions are standard components in every MR scanner, and comprise the workhorse for the wealth of existing MR imaging (MRI) and spectroscopy applications.

Modern gradient coils are the result of decades of scientific innovation and represent works of engineering art. Gradient coil design aims to generate accurate gradient fields at maximal strength and efficiency while minimizing coil inductance to allow fast current switching, i.e., maximum slew rates, while considering other aspects like physical strength and vibrational modes. Advanced designs based on the target field approach (3), self-shielding (4), or 3D current geometries (5) have replaced the relatively simple Golay-type gradient systems (2,6–8).

Unfortunately, the underlying expertise is concentrated within a few academic and industrial research sites. More importantly, only a fraction of the existing knowledge on gradient technology is available to the wider MR community and the public. It appears practically impossible to obtain the wire pattern of any gradient coil employed in modern MR systems. To our knowledge, not a single coil design is publically available. Researchers and engineers are continuously pushing the envelope in this active field of research, developing increasingly novel concepts and even publishing parts thereof. The released information, however, inherently excludes derived wire patterns as a key outcome. The level of confidentiality typical of the field of gradient coil design makes it largely impossible for the MR community to appreciate the quality of new inventions, compare performance, and benefit from innovation. This protectionism likely results from concerns about releasing relevant details to competitors and aspects of intellectual property. These reservations are understandable and justified. However, a level of secrecy has resulted that leaves active researchers no choice but to also keep meaningful details confidential when reporting new innovations to prevent handing rivals a one-sided competitive advantage. Valuable developments vanish into thin air, and the wheel has to be reinvented by every research group separately. The resultant redundancy appears to retard novel innovation and to lessen potential scientific and clinical benefits. In practice, the inaccessibility of this knowledge poses a major discouraging and perhaps sometimes even insurmountable hurdle. The field of SH coil design is stuck in a rut, and this Gordian knot seems to have no solution in sight.

B₀ Shaping with the Multi-Coil Technique

For the longest time B₀ magnetic field modeling relied on a framework of orthogonal field shapes generated case-by-case by dedicated wire patterns (1,2). We have demonstrated recently that basis function orthogonality is not a requirement for successful field shaping and that a set of generic, localized coils can be converted to a powerful field modeling system when each of the electrical coils is driven individually (9). This multi-coil (MC) concept allows for the flexible and accurate synthesis of simple and complex magnetic fields via the superposition of generic non-orthogonal basis fields. B₀ shimming with static and especially dynamic (DYNAmic Multi-CoIl Technique or DYNAMITE) MC techniques have been shown to substantially enhance B₀ homogeneity in the mouse (10,11), the rat (12) and the human (13,14) brain. MC-based MRI with linear (9,15) and non-linear (16) encoding has been demonstrated, and the benefits of MC techniques for efficient spatial selection and SAR reduction have been described (17). The generalized MC concept has emerged as a viable alternative to conventional SH field generation. The application of MC techniques enjoys continuously growing interest in the scientific community, precipitating an active field of research (18–30).

Previous MC work focused mainly on the benefits for the MR application at hand which has been reflected in detailed descriptions of the MC methodology and achieved performance. The exact details of the employed MC designs, however, have typically not been reported. Notably, to date, this also holds true for our own work. The newly established MC community is therefore about to repeat the shortcomings that led to the aforementioned deadlock in the field of SH coil design.

SH wire patterns largely provide the corresponding SH shapes, e.g., linear gradients, and SH coils can be directly applied without knowing the underlying technical details. By contrast, the average MC user can and probably must tailor his or her MC setup to the immediate application. This aspect of MC field modeling is distinctly different from the application of SH coils, and detailed knowledge of the employed wire pattern is therefore essential.

Researchers invest significant effort in the development of novel MC designs and the resultant intellectual property. There is arguably no perfect solution that respects all related academic and commercial concerns. Optimal scientific progress is only possible, however, if results are not withheld but publicized. Most of us receive public funding of various forms and, as such, society arguably deserves to access the derived knowledge and to benefit from the investment. In our opinion, the expected advantages promise to outweigh the concerns, and there seems no alternative to full transparency for the sake of science. We as a research community are in the unique position to define the scientific climate ourselves, and it is up to us to establish the policies to shape it.

METHODS

Public Multi-Coil Information (PUMCIN) Policy

Increasingly, the scientific community is actively promoting public access to knowledge. For instance, data sharing through the Human Connectome Project initiative has enabled unprecedented research on the human brain (31). Limited access to scientific reports has long been recognized as problematic by the National Institutes of Health (NIH), and a Public Access Policy was passed in 2008 to make NIH-funded research open-access (32). Moreover, the NIH has recently pushed to enhance reproducibility in part through increased rigor and transparency (33). As such, both scientific communities and regulatory agencies have begun to appreciate the importance of information sharing to both the usefulness and integrity of science.

Here, we propose to apply these principles to the field of MC field modeling and suggest that future publications involving the MC technique not only report the benefits for the immediate application but also explicitly describe the MC wire pattern employed. This PUblic MC INformation (PUMCIN) policy will be a voluntary commitment that aims to promote free public access to MC-related knowledge and expertise. Notably, the explicit data sharing demanded by the PUMCIN policy is in line with the NIH’s recent initiatives and is expected to initiate a paradigm shift with respect to the way MC-related innovation is reported.

RESULTS

We first introduced the PUMCIN policy at the ISMRM workshop on Ultra-High Field MRI: Technological Advances & Clinical Applications (34). Here, we will further define practical aspects and propose a format for reporting the defining characteristics of MC setups. We will set an example for this new PUMCIN policy by publicizing the defining characteristics of our own five most influential MC setups along with this Note. More specifically, the 24-coil setup of the first MC publication (Figure 1A, (9)), and the 48-coil setups for MC applications in mice (Figure 1B, (10)), rats (Figure 1C, (12)) and humans (Figure 1D, (13)) are reported in the Supporting Tables A–D, respectively. The MC setup employed in the analysis of fundamental MC strategies and performance parameters (11) is given in Supporting Table E, but not explicitly shown due to its similarity with the mouse setup of Figure 1B. Note that the color coding of the individual coils has variable meaning, and the reader is referred to the original work for further details on each. The description of the MC setups is followed by a basic MATLAB (MathWorks, Natick, MA, USA) routine, i.e. a Supporting Script, to read and visualize MC wire paths that have been saved to file in the format outlined below.

FIG. 1. MULTI-COIL SETUPS.

Selection of miniature and human-sized coil setups for MC B₀ shimming and MRI in phantoms (A, (9)), mice (B, (10)), rats (C, (12)) and humans (D, (13)). Note that the physical dimensions of the MC setups differ significantly and have been adapted in this figure for presentation purposes. The color coding of the individual coils has varying meaning and the reader is referred to the original work for further details.

Peer-Review, Accountability and Public Availability of Knowledge

SH functions can be analytically derived from the underlying associated Legendre polynomials and, as such, are unquestionably accessible to the public. Under the approximation of an ideal SH coil system producing clean (without cross-terms) SH shapes, the suitability of SH-based approaches for B₀ shimming can be readily predicted both qualitatively and quantitatively (35).

The complexity of numerical MC procedures is increased compared to SH approaches due to the lack of orthogonality. While some basic aspects of the MC approach can be conceptualized qualitatively, any meaningful assessment of the MC performance must be based on a quantitative analysis. Such analysis inherently relies on detailed knowledge of the defining characteristics of the MC setup, i.e., its wire pattern. This level of detail is furthermore essential for comparing a given MC design with other field modeling approaches, both MC- or SH-based. The lack of publicly available information on the existing MC designs might therefore also be perceived as a strategic disadvantage for researchers advocating other, e.g., SH-based, methods. Moreover, if the details of an MC design are not included in a manuscript, peer review becomes challenging as no direct means exist to verify the presented work. In principle, this issue can be addressed by a coherent stream of data including both theoretical predictions and experimental validation. If experimental validation is lacking and results rest solely upon simulations, however, the reviewers are doomed to trust the claims made in a manuscript.

Given the relative infancy of the MC field, the window of opportunity for redefining its publication conventions is still open. Releasing the details of MC setups under the PUMCIN policy is expected to overcome the above shortcomings and to define a new accountability standard. The PUMCIN policy will ensure that the MC community benefits from new innovation and will also enable competitors to confirm or potentially refute published work. The proposed transparency may lead to some purifying scientific dispute and arguably raise the bar for publication.

Proposed Format of Multi-Coil Definition Files

As mentioned, MC setups consist of a set of individual coils that act together to synthesize a target B₀ field shape. The definition of this overall wire pattern must therefore include information on position, length and orientation of each of the differential (straight) elements representing, piecewise, each of the individual coils. We describe the format with which we lay out the MC wire patterns published in the Supporting Tables of this Note (Figures 1A–D, Supporting Tables A–E). Moreover, we hope that the described convention can serve as a standard for the communication of MC setups in the future.

The wire path of an MC setup is saved as a regular text file (Figure 2A), describing all defining characteristics of the contributing coils (Figure 2B). The example MC file contains a set of three independent coils: A green rectangular loop (coil #1), a red triangular loop (coil #2) and a blue octagonal loop (coil #3). Individual wire pieces are hereby expressed as pairs of Cartesian x-, y- and z-coordinates representing the start and the end positions of each wire piece (columns 2–4, unit: millimeter). More specifically, every row contains one serially numbered spatial position defined as x-, y- and z-coordinates (first column). Closed structures, e.g., the rectangular loop of coil #1, share the coordinates of the first and last points (points 1 & 5: −25/−70/0 mm). The number of spatial points needed to define an enclosed wire path therefore exceeds the number of wire pieces by one. For instance, five spatial points are needed to describe the four wire pieces of coil #1 (green). The last column contains the multiplicity of the wire piece defined by the spatial position of that and the previous row (fifth column). There thus exists no weighting for position 1. Weighting is employed to describe the number of turns or multiplicity of a coil element, thereby reducing the computational burden of the Biot-Savart calculation. Zero entries indicate the beginning of a new coil (black arrows). As such, the last column of an MC design consists of a series of positive integers and zeros, and the number of entries is one smaller than the number of points (here: 18 points, 17 weightings). Additional information, e.g., the type of MC setup or the creation date, can be added as comments indicated by leading percentage signs (here: first three lines, black). Note that cable connections can be easily incorporated into this format. They are typically neglected, however, as the fields from twisted wires with opposing currents cancel. According to common convention, the scanner’s B₀ field is assumed to be oriented along the z-axis.

FIG. 2. MULTI-COIL FILE FORMAT.

Format of MC definition file. A wire trace is expressed as a numbered series of coordinate triplets for a piecewise definition of the contributing wire segments (columns 1: counting variable, columns 2–4: x-, y- and z-coordinates). The number of turns per wire pattern and the separation of MC channels are represented by weighting factors (column 5). See text for details.

Notably, analytical B₀ descriptions exist for selected wire geometries when driven with electrical current, e.g. planar circular coils, and the integration of Biot Savart’s Law is not strictly necessary. In these cases, the resultant B₀ field behavior of the entire coil can also be described by a handful of parameters defining the coil’s spatial position along with information on its angulation (9,36,37). However, the existence of analytical solutions is the exception rather than the rule for the calculation of B₀ feld shapes, and the piecewise integration of Biot-Savart’s Law is typically necessary. The multi-coil approach does not rely on given basis field shapes or individual coil geometries and coils with non-planar and/or non-circular geometry. In reality, most coils exhibit a certain curvature, e.g., when tailored to a cylindrical surface, or they deviate from a circular geometry in other ways (e.g. (13)). We chose to express the employed wire geometry as a piecewise discretized path, capturing arbitrary MC scenarios with maximal flexibility and reproducing the resultant B₀ results, thereby fulfilling the primary motivation of the PUMCIN policy.

Proposed Elements of Multi-Coil Publications

Successful MC field modeling relies on the availability of a repertoire of meaningful spatial features and amplitudes in the region of interest (ROI). B₀ shimming of the human ventral prefrontal cortex (vPFC), for instance, requires basis shapes with localized spatial features to resemble and cancel apparent focal B₀ inhomogeneities. Among others, this can be achieved by placing a single circular coil with a normal vector perpendicular to the main B₀ field at the subject’s chin-level (36) or with an MC system using one or more such coils (13). Notably, the same coil placed in front of the eyes, corresponding to the height or z-position of the vPFC artifact, is largely inefficient in the vPFC. Such a coil, therefore, does not contribute to B₀ shimming in the vPFC and is ineffective in this specific part of the brain. Maximal proximity of the coils to the ROI is not generally desirable with the MC technique, a design principle that is not shared with radio-frequency (RF) setups.

Such issues can be considered, and potential ambiguities avoided, by rational study design. We therefore also propose a basic structure for future MC publications that will help to ensure comparability with previous MC and SH-based methods. We propose 1) the publication of the wire pattern together with MC results according to the PUMCIN policy along with a detailed description of the employed MC geometries in the text body, 2) the comparison of attained MC performance with SH approaches as they represent a standard and generally available reference, and, 3) if possible, comparison with select previously published MC designs.

The design of novel MC setups is commonly based on a combination of physical reasoning and quantitative optimization. The appropriate consideration of practical aspects like space requirements and physical mounting, or the characteristics of the amplifier system driving the coils, is crucial. Along the same lines, the positioning of an MC setup relative to the ROI, e.g., the human brain, is an important aspect for the optimization and assessment of MC hardware. MR is still an experimental science, and any innovation that cannot be applied in reality has to be labeled redundant. As such, 4) experimental validation consistent with theoretical claims is preferable to pure simulation studies. If equivalent performance for the primary functionality is achieved in a meaningful sample, e.g., B₀ homogeneity in the brains of a reasonable group of subjects of mixed sex and race with MC B₀ shimming, 5) secondary characteristics such as current behavior, space requirement, or generation efficiency, can be compared. A generalized metric to report the generation of B₀ field shapes considering the employed coil currents and MC wire lengths has been introduced previously (11) and can be potentially extended by the coil inductances to account for the switching behavior of the MC setup. Other potentially important aspects include the electrical field distribution and the corresponding thresholds for peripheral nerve or cardiac stimulation during fast switching. 6) Potential extensions include example data (contingent Institutional Review Board approach for release) to allow the validation of specific results such as ROI-specific B₀ distributions addressed with MC B₀ shimming or encoding fields for DYNAMITE MRI, i.e. the B₀ field shape to be produced along with the best MC field modeling result.

While beyond the scope of this publication, the facilitation of public access to MC optimization routines and software represents the logical extension of the present effort and deserves genuine consideration once the PUMCIN policy has been adopted by the MC community.

DISCUSSION

All MC setups share the same modeling approach for shaping B₀ fields. MC designs can largely differ in appearance, however, due to differences in ROI geometry (e.g., human vs. rodent), the intended MR application (e.g., B₀ shimming vs. spatial encoding), or other experimental constraints (e.g., bore space or integration with RF technology). To date, the lack of detailed information on existing MC designs renders their comprehensive assessment difficult and prevents their meaningful comparison.

Here, we introduce the PUMCIN policy to promote the public availability of MC-related knowledge. Detailed access to MC information is expected to promote the evaluation of MC-related innovation and to expedite future developments. The PUMCIN policy represents a proactive and voluntary commitment expected to accelerate MC development. Setting an example ourselves, we hope to encourage the evolving MC community to optimize the benefits for science and society by embracing it.