1. Department of Radiology and Imaging Sciences
Estimation of Displacement Forces of Metallic Foreign Bodies Based on Screening Radiographs eP-193
Blair Winegar, M.D.
Ulrich Rassner, M.D.
University of Utah
Department of Radiology and Imaging Sciences

2. Disclosures Blair Winegar, M.D. – None
Ulrich Rassner, M.D. – Speaker at Siemens meetings, Author for Amirsys/Elsevier

3. Purpose
Metallic foreign bodies are commonly observed on screening radiographs of patients scheduled to undergo MRI
The presence of metallic foreign bodies within the orbit or adjacent to other critical structures may preclude the ability to perform an MRI secondary to safety concerns
The radiologist is responsible for determining if MRI can be performed in the setting of a metallic foreign body
The purpose of this study is to determine a conservative estimate of displacement forces exerted on a metallic foreign body produced by an MRI magnet based on measurements obtained on screening radiographs

4. Approach/Methods
The observed displacement forces of eight different ferromagnetic foreign bodies (five pieces of nails and three ball bearing) were obtained by measuring the force needed to pull the object from the entrance of the bore of a 1.5T scanner (Avanto, Siemens)
These eight different ferromagnetic foreign bodies were placed on a skull phantom and radiographed in the PA, AP, left lateral, and right lateral projections using a source to image distance (SID) of 72 inches
A formula for estimated displacement force was obtained by using length measurements of these objects in 3 orthogonal dimensions of linear metallic foreign bodies and diameter measurements of spherical metallic foreign bodies from the screening radiographs

5. Images of eight different metallic foreign bodies8 6 7 1 2 3 4 5

6. Observed displacement forces
The observed displacement forces were obtained by the force needed to pull the foreign object from the top edge of the bore of a 1.5T MRI (Avanto, Siemens)
The mass of each metallic foreign body was measured
The metallic foreign body was placed in a silk tea bag weighing less than 0.25 g and positioned on the magnetic bore
The silk tea bag was coupled to another silk tea bag by fishing line on a pulley system
Weights were placed in the second silk tea bag until the metallic foreign body was displaced from the magnetic bore, measured to the nearest gram
Metallic foreign body (yellow arrow) on MRI edge of MRI bore and weights (blue arrow) coupled on pulley system

7. Metallic foreign bodies placed on skull phantom
The eight foreign bodies were taped to the left face of a skull phantom prior to screening radiographs
The 5 linear nail pieces and 3 different sized ball bearing were radiographed separately
Radiographs were performed in the PA, AP, left lateral, and right lateral positions

8. Measurements performed on radiographsPA L PA

9. Measurements performed on radiographsPA L PA

10. Table of Measurements
As would be expected, there was a linear relationship between the mass of the foreign body and mass of weights needed to counteract the magnetic force applied to the metallic foreign body at the edge of the MRI bore
Equivalent weight is calculated as Eqweight= Forcemagnetic / gravity (the magnetic force pulls with the same force on the test object as gravity would on a object with the equivalent weight)
Material number
Material shape
Weight (g)
Equivalent Weight (g) 1
Small linear nail
0.043
9.71 2
Short linear nail
0.141
31.39 3
Fat short nail
0.283
64.93 4
Long nail piece
0.694
148.91 5
Longest nail piece
0.948
210.19 6
Small ball bearing
0.507
91.19 7
Medium ball bearing
1.042
196.77 8
Large ball bearing
3.525
587.7

11. Mass versus equivalent mass produced by the magnetic force
Plots of the measured mass of the foreign bodies versus the mass of weights needed to counteract the magnetic force applied to the foreign body
Equivalent mass is the weight at which the gravitational force would equal the magnetic force applied to the foreign body
The linear (nail pieces) and spherical (ball bearings) were calculated separately given different alloy compositions and magnetic properties
An average of the slopes of the linear regression curves yielded an average of 190
In other words, the magnetic displacement force experienced by the metallic foreign bodies averaged 190 x gravitational force

12. Estimated displacement forces
The three orthogonal length measurements for linear foreign bodies or diameter measurement for spherical foreign bodies can be used to estimate the volume of the foreign body
Linear:
V (cm3) ≈ X (cm) * Y (cm) * Z (cm)
Spherical:
V (cm3) = 4/3 * π * (D (cm)/2)3 ≈ ½ * D3 PA PA

13. Estimated displacement forces
The mass of an object is equal to the volume times the density: m = V * ρ
The density of iron is approximately 8 g/cm3
Fest ≈ V * ρiron * 190 * g
V is volume estimated from the screening radiographs in cm3
ρiron = 8 g/cm3
190 * g is 190 times the acceleration of gravity
West = Fest/g
West is the estimated equivalent weight of an object in grams which experiences a gravitation force equivalent to the estimated magnetic force experienced by the foreign body
Linear foreign bodies
V ≈ X (cm) * Y (cm) * Z (cm)
Fest ≈ X * Y * Z * 1500 * g
West ≈ X * Y * Z * 1500
Spherical foreign bodies
V ≈ 4/3 * π * (D (cm)/2)3
V ≈ D3 * ½
Fest ≈ D3 * 750 * g
West ≈ D3 * 750
The volume measurements were performed on the PA and left lateral projections, as image size is more accurate when the object is closer to the detector

14. Estimated displacement forces

15. Findings/Discussion
The magnetic displacement force experienced by a ferromagnetic foreign body at the bore edge of a 1.5T magnet is conservatively estimated at 190x gravitational force
The equivalent weight of an object undergoing gravitational force equal to the magnetic force exerted on the ferromagnetic foreign body can be conservatively estimated by the following formulas using length measurements on screening radiographs:
Linear foreign bodies: West ≈ X * Y * Z * 1500
Spherical foreign bodies: West ≈ D3 * 750
The magnetic displacement force is strongest near the edge of the bore and none near the center of the bore
Therefore, ferromagnetic foreign bodies are not likely to experience the maximal displacement force produced by the magnet
Different ferromagnetic materials can have different magnetic susceptibilities and will experience different magnitude of forces
Issues from magnetic torque forces are not addressed by this estimation
The direction of applied magnetic displacement force and proximity to vital structures (e.g. retina) is not addressed by this estimation

16. Potential errors in estimated calculation
Dimensional measurements
Magnification and geometric unsharpness (increases the apparent size)
Obliquity of foreign body (decreases the apparent size)
Assumption of iron density of metallic foreign bodies
Metallic foreign bodies can vary in their magnetic susceptibility properties
Heterogeneity of the magnetic field
Between locations
Differences between MRI magnet spatial field gradients
Graph of measured spatial field gradients of different MRI magnets, including the 1.5T Avanto used in this presentation

17. Magnification
The farther the object is from the detector, the larger the object appears secondary to magnification
M = SID/SOD
M is magnification
SID is source to image distance
SOD is source to object distance
For lateral skull radiograph with object on skin surface closer to source, the magnification is approximately 1.09x
SID = 72 inches
SOD = 66 inches (lateral width of head ≈ 6 inches)

18. Geometric unsharpness
Marginal blurring resulting from geometry of the X-ray beam as a result of focal spot size and magnification
Can increase the apparent image size
G = F x (SID/SOD – 1)
G = Geometric unsharpness
F = Focal spot size
SID = Source to image distance
SOD = Source to object distance
SID/SOD = Magnification F
SID
SOD
OID

19. Magnification and Geometric unsharpnessPA AP
Magnification and geometric unsharpness increase image size as object is farther from the detector
The degree of geometric blurring is not affected by object size, so blurring will be proportionally greater for smaller objects
Three different sized ball bearing on left face of skull phantom demonstrate increased image sizes secondary to magnification and geometric unsharpness when farther from detector on AP view

20. Obliquity of object on AP and lateral radiographs
The obliquity of an object on frontal and lateral radiographs will decrease the observed maximal dimension
For two orthogonal (frontal and lateral) views, the maximal underestimation ≈ 0.7x the true length
Occurs when linear object is in the transverse plane with 45º angulation to frontal and lateral projections

21. Limitations Only two types of metallic foreign bodies were evaluated
Pieces of nails
Metallic ball bearing
The magnetic forces were calculated on a 1.5T system (Avanto, Siemens)
Potential differences between different 1.5T system
Limited evaluation on a 3.0T system (Verio, Siemens) demonstrated only a difference of up to 6% for measurements performed on ball bearing
The metallic foreign bodies were placed at the top edge of the bore, which is close, but not exactly at the site of highest spatial field gradient for all MRI systems

22. Conclusion Radiologists are responsible for MRI safety
Metallic foreign bodies differ in size, location, and content of ferromagnetic materials, which makes it difficult to determine the potential harm when placed in the magnetic field of an MRI
A conservative estimate of the equivalent weight of an object undergoing gravitational force equal to the magnetic force exerted on the ferromagnetic foreign body can be conservatively estimated by the following formulas using length measurements obtained in cm on screening radiographs:
Linear foreign bodies: West ≈ X * Y * Z * 1500
Spherical foreign bodies: West ≈ D3 * 750
With this data, a more informed decision can be made whether to proceed with an MRI in the setting of a foreign body

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