2.23 shows measurements of B and E in a phantom where significant amounts of both fields exist up to 60 cm beyond the end of a head only transmit coil, i.e. well beyond where we might otherwise consider the RF field to end [7] . This behavior has implications for patients with implants.
MYTHBUSTER:
With a patient lying in the bore, the RF field extends significantly beyond the confines of the transmit coil. This is consequence of Maxwell’s Equations.
λ/2 resonant length
A better‐known effect of the wavelength change in tissue is the creation of standing waves or resonances when a conductor length is close to one half wavelength λ/2. This has particular importance for the avoidance of heating in active implants with lead lengths equal to or close to λ/2. Often the resonant lengths 13 cm and 26 cm are cited, but different tissues have a range of values:
muscle λ/2 = 14.7 cm at 128 MHz
fat λ/2 = 33.3 cm at 128 MHz
cancellous bone λ/2 = 22.9 cm at 128 MHz
cortical bone λ/2 = 30.6 cm at 128 MHz.
MYTHBUSTER:
The resonant length differs from 13 or 26 cm for most tissues at 1.5 and 3 T, and much broader resonant behavior is likely.
The final zone, is the far field or Fraunhofer region which occurs at distances much greater than a wavelength. In this region, we have fully formed electromagnetic plane waves whose intensity decreases with the inverse square law. Their intensity is measured as power density (in W m−2), but in MRI is very low – only relevant in terms of EM interference on other equipment.
Example 2.11 RF wavelength at 1.5 T
What is the RF wavelength in bone, muscle and fat at 64 MHz?
From Equation 2.33,
εr values are 16.7, 72.2 and 6.5 – so the wavelenths are 1.12 m for bone, 55 cm for muscle and 1.84 m for fat.
CONCLUSIONS
The fields and forces associated with MRI and MRI equipment are not simple. They are all consequences of Maxwell’s equations. Forces on objects may be:
purely magnetic, relating to the shape and ferromagnetism of the material
related to electrical current flowing in the object
related to induction
or movement within a field gradient.
For ferromagnetic objects the attractive or projectile magnetic force is proportional to the spatial gradient of the B0 fringe field. The torque on an unsaturated object is proportional to the square of B0. Most ferromagnetic objects will be saturated close to the scanner in which case the attractive force is related to Bsat .dB/dz and the torque to Bsat 2.
Time‐varying magnetic fields from the gradients, RF, or movement within the static fringe field gradient will induce electric fields in tissue. These can lead to the stimulation of excitable tissues or to tissue heating. The RF field can exhibit unpredictable wave‐like behavior. The next three chapters will look at the biological effects of the static field, gradient fields, and RF field.
Revision Questions
1 If the magnetic susceptibility χ of a diamagnetic tissue is ‐10−3 the magnetic flux density within that tissue in a 1.5 T scanner will be:1.499 T1.5 T1.501 T1.51 T15 mT
2 The magnetic field strength H at the centre of a long solenoid of length 150 cm, with 1800 turns carrying 1000 A is1000 A m−1200 000 A m−1400 000 A m−1600 000 A m−11 200 000 A m−1
3 The magnetic flux density produced in question 2 is500 G0.5 T1.0 T1.5 T5000 G
4 Which of the following does not affect the magnetic force on a soft ferromagnetic material with a high magnetic susceptibility?The distance to the bore openingThe fringe field spatial gradient dB/dzThe exact value of susceptibility χThe size of the objectIts electrical conductivity.
5 A metal object saturates magnetically at 1 T. The maximum force as it approaches a 3T scanner with a spatial gradient of 5 T m−1 is proportional to1 T2 m−13 T2 m−15 T2 m−19 T2 m−115 T2 m−1
6 When a previously un‐magnetized ferromagnetic object is introduced into an external B field, the maximum torque occurs when the angle between the long axis of the object and the field lines is:0°30°45°60°90°
7 The induced electric field in a circular cross section of tissue from the z‐gradient is proportional to:The tissue conductivityThe area of the cross sectionThe rate of change of magnetic fieldThe radius of the cross sectionTissue density.
8 If the diameter of the heart is 8 cm, what current density would a uniform dB/dt of 100 T s−1 induce in it, assuming tissue conductivity of 0.2 Sm−1?1.6 mA m−2400 mA0.8 A m−20.4 A m−24.0 A m−2
9 If we change field strengths from 1.5T to 3T then (keeping our sequence the same)SAR will stay the same but B1 will halveSAR and B1 will both doubleSAR will double while B1 remains the sameBoth SAR and B1 will increase by four timesSAR will increase by a factor of 4 while B1 remains the same.
10 In a pulse sequence, if we halve the duration of the RF pulse whilst keeping the flip angle and TR the sameSAR will increaseSAR will not changeSAR will decreaseThe duty cycle is doubledWe cannot predict what will happen.
References
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3 3. Budinger, T.F. (1979). Thresholds for physiological effects due to RF and magnetic fields used in NMR imaging. IEEE Transactions on Nuclear Science NS‐26:2821–2825.
4 4. Payne, D., Klingenböck, A., and Kuster, N. (2018). IT’IS Database for thermal and electromagnetic parameters of biological tissues, Version 4.0, May 15, 2018. DOI: 10.13099/VIP21000‐04‐0.
5 5. Schaefer, D.J. (2014). Bioeffects of radiofrequency power deposition. In: MRI bioeffects, safety, and patient management (Ed. F.D. Shellock and J.V. Crues III) pp. 131–154. Los Angeles, C: Biomedical Research Publishing Group.
6 6. Hand, J.W. (2008). Modelling the interaction of electromagnetic fields (10 MHz–10 GHz) with the human body: methods and applications. Physics in Medicine and Biology 53:R 243–286.
7 7. Nagy, Z., Oliver‐Taylor
