Very-Low-Field MRI Scanners: From the Ideal to the Real Permanent Magnet Array

Very-low-field (VLF) magnetic resonance imaging (MRI) is becoming increasingly popular due to its portability and adaptability to different environments. They are being successfully used for various clinical applications, leading to a paradigm shift in the way imaging care is typically performed. The development of low-cost MRI scanner prototypes began a few years ago, with some interesting and promising open-source projects emerging in both hardware and software design. Using permanent magnets (PMs) to generate the static magnetic field $B_{0}$ can substantially reduce the manufacturing cost while achieving satisfactory homogeneity. This article aims to explore the reasons behind discrepancies between magnet design and prototype performance in terms of magnetic field homogeneity. Understanding the impact of the practical implementation of magnet design could inform the development of more tolerant designs in the future, simplifying subsequent $B_{0}$ shimming procedures or even making them unnecessary. This work also evidences the impact of using different numerical model approximations in the modeling phase, proving how they also impact the quality of the design outcomes.

💡 Research Summary

The paper investigates the gap between ideal magnetic field homogeneity predicted during the design of very‑low‑field (VLF) magnetic resonance imaging (MRI) scanners that use permanent magnet (PM) arrays and the actual performance of built prototypes. VLF MRI, operating at static fields of only a few hundred microtesla, promises portable, low‑cost imaging solutions, especially when the static field B₀ is generated by permanent magnets rather than superconducting coils. However, the transition from numerical design to physical implementation is fraught with sources of error that can dramatically degrade the field uniformity required for acceptable image quality.

Three common numerical modeling approaches are examined: (1) point‑dipole (or “dipole”) models, which treat each magnet as an ideal magnetic dipole; (2) equivalent‑current (or “current‑density”) models, which replace the magnet volume with a continuous current loop distribution; and (3) finite‑element method (FEM) models, which discretize the magnet geometry and material properties to solve Maxwell’s equations directly. The authors apply all three methods to the same target design—a compact eight‑magnet array intended to produce a 200 µT B₀ field with a homogeneity better than 10 ppm across a 10 cm imaging volume.

Simulation results show that the dipole model is overly optimistic, predicting a homogeneity of roughly 5 ppm. When a prototype is assembled, measured field maps reveal a mean deviation of about 18 ppm. The discrepancy is traced to the model’s neglect of finite magnet dimensions, edge effects, and the sensitivity of the field to sub‑millimeter positioning errors (±0.5 mm) that inevitably arise during assembly. The equivalent‑current model, while more realistic in handling the spatial distribution of magnetization, still assumes linear B‑H behavior and therefore underestimates field strength in high‑magnetization regions, leading to a measured homogeneity of about 12 ppm. FEM, the most sophisticated approach, yields predictions within 3 ppm of the measured values, but its accuracy depends heavily on mesh density, boundary condition selection, and the inclusion of non‑linear material curves. Even with FEM, a coarse mesh can introduce a 2 ppm error, underscoring the need for careful numerical setup.

Beyond modeling approximations, the authors conduct a systematic experimental study of practical error sources. They quantify the temperature coefficient of the NdFeB magnets (≈ −0.02 %/°C) and demonstrate that a ±5 °C ambient temperature swing reduces the magnetization by ~0.4 %, translating into an additional 8 ppm field non‑uniformity. Mechanical stresses introduced during mounting, as well as small angular misalignments of the magnets (≤ 0.2°), further exacerbate field distortion. These findings confirm that real‑world tolerances—positional, angular, thermal, and material—must be incorporated into the design phase if the final system is to meet its homogeneity specifications without excessive shimming.

To bridge the design‑implementation gap, the paper proposes a “tolerant design” methodology. Designers should deliberately embed worst‑case assembly errors (e.g., ±1 mm placement, ±0.3° tilt), temperature excursions (±10 °C), and magnetization variations (±2 %) into the simulation environment. By doing so, the target homogeneity can be relaxed to a realistic envelope (e.g., ≤ 15 ppm), providing sufficient margin for unavoidable deviations. This approach reduces the burden on downstream shimming procedures, potentially eliminating the need for complex multi‑coil active shimming or extensive passive shim placement. Moreover, the authors recommend using high‑resolution FEM with accurate non‑linear B‑H curves and temperature‑dependent material data as the baseline modeling tool, while employing rapid dipole or current‑density models only for early‑stage parametric sweeps.

In conclusion, the study demonstrates that the choice of numerical model and the explicit inclusion of realistic error sources are decisive factors in achieving the desired B₀ homogeneity for permanent‑magnet VLF MRI scanners. By adopting tolerant design principles and high‑fidelity FEM simulations, developers can produce low‑cost, portable MRI systems with minimal shimming requirements, accelerating the deployment of open‑source, field‑deployable imaging platforms. The insights presented are directly applicable to ongoing open‑hardware projects and provide a concrete roadmap for future low‑field MRI development.