Here f(•) and g(•) are functions that depend on the object's intrinsic susceptibility (χ), shape-dependent demagnetizing factors (Na and Nd), and angle the object makes with the external magnetic field (θ). The term μo ≈ 4π x 10−7 N/A² is the magnetic constant, also known as the permeability of free space. For paramagnetic and weakly ferromagnetic materials with χ < 1, f(•) = χ and g(•) = ¼ χ² sin2θ. Further modifications of these equations are needed for materials that reach magnetic saturation or are permanently magnetized.
As shown in the diagram, the object in question is suspended by a string near the edge of the scanner bore (where the spatial gradient product Bo•∇Bo is largest). The angular displacement from vertical is then measured, and the translational force along the z-axis (along the direction of the main magnetic field) based on the weight of the object can then be calculated. If the deflection angle is less than 45º, the magnetic force of the object is less than that of gravity, which ASTM considers conditionally safe for this parameter.
The ASTM method does not consider the shape of the object or the configuration in which it hangs. For example, an elongated object in a field below magnetic saturation will experience a stronger force when aligned with Bo than when perpendicular. Likewise, the magnetic torque on the object is not considered, but this will affect the angle of suspension.
In the Pulley Method, the implant is placed on a platform in near magnet isocenter which is free to rotate via a string and low-friction pulley apparatus. The string is pulled and the object rotated by 360° with the maximum force Fm noted. The object is removed and the rotation repeated to determine the maximum frictional force (Ff) of the pulley system alone. The Torque (T) then equals R(Fm−Ff) where R is the radius.
The final technique, the Torsion Spring Method, was the only torque measurement standard ASTM recognized up until the current (2017) edition. This method thus has a long history and is considered by many to be the most accurate for implants where an appreciable torque is expected. As shown in the illustration left, the implant is secured by strong tape to a tray suspended between two calibrated torsion springs (blue canisters) and placed at magnet isocenter. The apparatus is then rotated in 10° increments using a turning gear (not pictured) over a full 360° rotation and the maximum deflection angle (Δφ) recorded. The magnetically induced torque (T) equals kΔφ, where k is the torsional spring constant. The calibrated spring system thus allows a numerical value for torque to be obtained, in units such as N-m.
Advanced Discussion (show/hide)»
ASTM F2503-20, Standard Practice for Marking Medical Devices and Other Items for Safety in the Magnetic Resonance Environment, ASTM International, West Conshohocken, PA, 2020, www.astm.org
ASTM F2052-15, Standard Test Method for Measurement of Magnetically Induced Displacement Force on Medical Devices in the Magnetic Resonance Environment, ASTM International, West Conshohocken, PA, 2015, www.astm.org
ASTM F2213-17, Standard Test Method for Measurement of Magnetically Induced Torque on Medical Devices in the Magnetic Resonance Environment, ASTM International, West Conshohocken, PA, 2017, www.astm.org
ISO/TS 10974:2018. Assessment of the safety of magnetic resonance imaging for patients with an active implantable medical device. International Standards Organization, Geneva, 2018.
US Food and Drug Administration. Testing and labeling medical devices for safety in the magnetic resonance (MR) environment. Draft Guidance for Industry and Food and Drug Administration Staff. Distributed 2 August 2019.
Woods TO. Standards for medical devices in MRI: present and future. J Magn Reson Imaging 2007; 26:1186-1189. [DOI Link]
What are the risks of passive vs active implants in MRI?
How do you calculate the magnetic force pulling a piece of metal toward the scanner?