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Patients undergoing
Magnetic Resonance Imaging (MRI) are exposed to strong, non-uniform static magnetic fields outside of the central imaging region, in which the movement of the body may induce electric currents in tissues which could possibly be harmful. The purpose of this study was to re-evaluate existing clinical protocols by determining the induced electromagnetic (EM) fields in MRI spine examinations. The study covered 120 MRI spine examinations at the MRI Unit of a hospital in Accra, Ghana. A numerical model based on Faraday’s equation was developed using the finite difference method (FDM) and MATLAB software to compute, first, a test simulation of induced EM field intensities and then actual measurements of induced fields on the spine. The simulation results were peak induced electric field, 0.39 V/m and current density, 0.039 A/m^{2}. Patient results were; calculated maximum velocity, 0.29 m/s; peak induced electric field strength, 0.44 V/m, and current density, 0.043 A/m^{2}. The levels of induced EM-fields were such that they would not pose any potential health hazards to the patients as these values were well below the recommended guidance levels set by the Directive IEC 60601-2-33 of the European Parliament.

Magnetic Resonance Imaging (MRI) of patients undergoing investigations, are exposed to strong, non-uniform static magnetic fields outside the central imaging region, in which the movement of the body may induce electric currents in tissues which could possibly be harmful [

In Ghana, most patients undergoing MRI investigations are as a result of spinal related injuries. The human spine is one of the delicate organs of the human body because it contains the spinal cord that controls coordination and movement of the human body. As a result, any effect on the spine will have an adverse effect on the body. Hospital data indicate that these injuries may be due to their nature of work―the building industry (carpentry, masonry, laborers), motor mechanics, poor sitting postures, road accidents, carrying of loads on the head, a bad fall, and other such activities. All these activities in one way or the other affect the spine, with the lumbar spine being the most affected because the majority of patients who undergo MRI of the spine complain of lower back pain.

The number of MRI centers in Ghana increased from one in 2008 to ten in 2013. With the increasing number of MRI examinations in Ghana, it is therefore, a quality control measure to ensure that EM field exposure to workers is well below the acceptable maximum limit of 3.8 V/m according to EU Directive 2004/40/EC [

Patient participation was voluntary. The procedures involved in the study were verbally explained to patients using an acceptable language of the patient and their written consent sort. Data were anonymously collected and the procedures met the Ethical and Protocol Review Committees of the 37 Military Hospital, Accra, and Ministry of Health, Accra, Ghana which was approved on 12th September, 2012.

The MRI instrument used was a Philips MR Systems Achieva, (Model No. 43000-574; PHILIPS, Eindhoven, The Netherlands), with a 1.50 T superconducting magnet. The range of magnetic field strength used for medical imaging is typically from 0.15T to 3T [

A simulation test was first performed using the mathematical software MATLAB, Mathworks [

A numerical model based on Faraday’s equation and experimental data from MRI spine examinations were used to compute the induced EM fields of the human spine. The computation was carried out using the finite difference method (FDM). The FDM is ideally suited for modeling of electromagnetic waves scattering from complex non-canonical objects [

The computation method was developed as follows:

The expression for a patient’s motion, v is

v = d t (1)

where, v is the velocity of the motion, d is distance and t is time.

Static magnetic fields effects are likely to be caused by the magnetic field

vector, B, the gradient or the magnetic field, ∂ B ∂ z , the “force product”, P_{F} may

be expressed as:

P F = B ∂ B ∂ z (2)

where, z is taken as the direction of B.

Flow induced electric field, E_{F}, depends on the product of the flow velocity, v, the magnetic field vector, B and the angle θ between them, given as:

E F = v B sin θ (3)

The motion-induced electric field depends on the geometry and the time rate of change of the magnetic field.

∮ E _ ⋅ d l _ = − ∫ s d B _ d t ⋅ d s _ (4)

The length vector of the body part enclosing the changing magnetic field is dl and ds the normal vector to the incremental area dA.

Transforming the Faraday‘s equation from Maxwell’s time-dependent equations into difference equations with respect to specific field positions on an elementary lattice, the FD technique provides a simple and effective technique for the modeling of a field distribution within the spine of an MRI patient. The system is then solved in a time marching sequence by alternately calculating the electric and magnetic fields in an interlaced spatial grid cell. Given the location of an electromagnetic source and a complete description of the environment in terms of its dielectric parameters; permittivity (ε), permeability (μ), conductivity (σ), this method provides the ability to assess the electric and magnetic fields.

Therefore, the total magnetic flux passing through a loop is,

ϕ m ( t ) = ∫ s B × d s (5)

Electric potential can also be expressed as;

v ( t ) = ∮ E × d l (6)

But from Faraday’s law;

v ( t ) = − d ϕ m ( t ) d t (7)

where, ϕ m ( t ) is the total time varying magnetic flux passing through the surface.

Considering a close cylindrical loop, substituting Equation (5) into Equation (7),

v ( t ) = − ∫ B d t × d s (8)

v ( t ) = − d d t ∫ B × d s (9)

where, ds = Area (A).

The differential equation of

∂ 2 A ∂ r 2 = 2 π r 2 h

Therefore, Equation (9) becomes

v ( t ) = − d d t ∫ B × A (10)

= − ∂ B ∂ t × ∂ A ∂ t (11)

From Equations (6) and (9)

∮ E × d l = − d d t ∫ B × d s (12)

Equation (11) is the integral form of the Faraday’s Law.

Using Stokes’ theorem [

∮ E _ × d l = ∫ s ( ∇ _ × E _ ) × d a (13)

Therefore, the differential form of the Faraday’s law of induction is;

∇ _ × E _ = − ∂ B _ ∂ t (14a)

∇ _ × E _ = ( 1 r ∂ E z ∂ θ − ∂ E θ ∂ z ) r ^ + ( ∂ E r ∂ z − ∂ E z ∂ r ) θ ^ + 1 r ( ∂ ∂ r ( r E θ ) − ∂ E r ∂ θ ) z ^ (14b)

Note that the determinant;

∇ _ × E _ = [ r ^ r θ ^ z ^ ∂ ∂ r ∂ ∂ θ ∂ ∂ z E r r E θ E z ]

Formulating EM wave equation of the spine from Maxwell’s equation;

∇ × B = ϕ ∇ × E = 0 (15)

∇ _ × E _ = − ∂ B _ ∂ t ∇ _ × B _ = ε ∘ μ ∘ ∂ E _ ∂ t (16)

∇ _ × ∇ _ × E _ = − ∇ _ × ∂ B _ ∂ t (17)

∇ _ × ∇ _ × E _ = ∇ _ ( ∇ _ ⋅ E ) − ∇ _ 2 E _ (18)

− ∂ ∂ t ∇ _ × ∇ _ = ∇ _ ( ∇ _ . ∇ _ ) − ∇ _ 2 E _ (19)

− ∂ B _ ∂ t ∇ _ × B _ = ε ∘ μ ∘ ∂ 2 E _ ∂ t 2 (20)

Combing Equations (19) and (20);

∇ _ ( ∇ _ × ∇ _ ) − ∇ _ 2 E _ = − ε o μ o ∂ 2 E _ ∂ t 2 (21)

where, ∇ ( ∇ × E ) = 0

− ∇ _ 2 E _ = − ε o μ o ∂ 2 E _ ∂ t 2 (22)

Equation (22) indicates the modified Maxwell’s equation, where, ε ∘ μ ∘ = 1 v 2 .

Therefore, Equation (22) becomes

− ∇ _ E _ = − 1 v 2 ∂ 2 E ∂ t 2 (23)

Since the EM field is polarized in the y direction, the induced EM field in the 3D plane within the spine becomes;

From Equation (14) ϕ m ( t ) = ∫ s B × d s

∂ 2 ϕ m ∂ r 2 + ∂ 2 ϕ m ∂ z 2 = 1 2 π r h ∂ 2 ϕ m ∂ t 2 (24)

The discretization of Equation (25) yields the EM field within various positions of the spine.

2 π h ( ∂ 2 ϕ m ∂ r 2 + ∂ 2 ϕ m ∂ z 2 ) = ∂ 2 ϕ m ∂ t 2 (25)

where, h is the length of the spine.

The discretization of the partial differential equation, Equation (25) is illustrated in

ϕ i , j , k = ∑ m = 0 1 ( ϕ i − m , j , k − 2 ϕ i , j , k + ϕ i + m , j , k ) Δ r 2 + ∑ m = 0 1 ( ϕ i , j − m , k − 2 ϕ i , j , k + ϕ i , j + 1 , k ) Δ z 2 (26)

Therefore, the final discretized EM-field equation from the Faraday’s equation becomes;

⇒ ϕ i , j n + 1 − 2 ϕ i , j n + ϕ i , j n − 1 ( Δ t 2 ) = v 2 ω [ ϕ i + 1 , j n − 2 ϕ i , j n + ϕ i − 1 , j n ( Δ h ) 2 + ϕ i , j + 1 n − 2 ϕ i , j n + ϕ i , j − 1 n ( Δ h ) 2 ] (27)

where, ϕ^{n}, ϕ^{n}^{+1} represent the iterated EM fields within the spatial grids of the spine and Δ h is the step size.

The induced EM fields were computed for the three sections of the spine as the patients underwent the MRI examinations using FDM and MATLAB. The simulated results of the induced electric field (0.39 V/m) and current density (0.039 A/m^{2}) were lower than the measured results (0.44 V/m and 0.043 A/m^{2}, respectively) and this was due to the fact that during the simulation an assumed length of the spine (41.0 cm) was assumed for all patients.

A total of 120 patients were MRI examined of which 75 patients ranging in ages from 8 to 90 years underwent lumbar spine examinations (

The lumbar spine had the highest duration with a mean of 5.98 ± 0.48 s compared with the cervical spine, 5.92 ± 0.40 s and the thoracic spine, 5.88 ± 0.67 s.

Gender | Cervical | Thoracic | Lumbar |
---|---|---|---|

Male | 20 | 7 | 44 |

Female | 10 | 8 | 31 |

Total | 30 | 15 | 75 |

Mean age (years) | 51.22 ± 15.71 | 43.87 ± 19.85 | 51.88 ± 15.06 |

Mean height (m) | 1.63 ± 0.13 | 1.62 ± 0.14 | 1.65 ± 0.11 |

Mean weight (kg) | 75.60 ± 19.89 | 71.40 ± 15.37 | 76.40 ± 12.19 |

Parameters | Cervical | Thoracic | Lumbar |
---|---|---|---|

Mean Distance (m) | 1.10 ± 0.10 | 1.33 ± 0.36 | 1.46 ± 0.06 |

Mean Time (s) | 5.92 ± 0.40 | 5.88 ± 0.67 | 5.98 ± 0.48 |

The results showed that, a maximum velocity of 0.29 m/s, with peak induced electric field and current density of 0.44 V/m and of 0.043 A/m^{2} were recorded, respectively. The results of the induced electric field were compared to the limits given in the directive IEC 60601-2-33 standard [^{2}. The result of the induced current densities in the spinal cord was 0.043 A/m^{2} which as much lower than the limit of 3 A/m^{2}. Similarly, the induced current densities in the skin and spine were lower than the Directive 2013/35/EU exposure limit [

Solutions to the discretized partial differential equations obtained with the finite difference method showing the variations in induced EM fields for male (

From this study, the simulated results of the induced electric field (0.39 V/m) and current density (0.039 A/m^{2}) the experimental results; induced electric field (0.44 V/m) and current density (0.043 A/m^{2}) were much lower compared with the report by Liu et al. [^{2} respectively) and the experimental results (1.8 V/m and 0.21 A/m^{2} respectively). Here, a lower magnetic field strength of 1.5 T was used as compared with the 4.0 T used for simulation, with the maximum current of about 220 mA/m^{2} in the report by Liu et al., [^{2} [

The results of the level of induced EM-fields were such that they might not pose any potential health hazards to the patients as these values were well below the recommended guidance levels set by Directives 2013/35/EU [

We also recommend periodic reviews of such protocols of newer NMR instruments to help shape safety policies for both patients and workers.

The authors declare that there are no conflicts of interests regarding the study and publication of this paper.

We would like to express our sincere thanks to Prof. AWK Kyere, Head of Medical Physics Department, Graduate School of Nuclear and Allied Sciences, Legon, Ghana, the staff of the MRI Unit at 37 Military Hospital and Ghana Standards Authority.

Acheampong, F., Dery, T., Appiah, R. and Abaye, D.A. (2018) Induced Electromagnetic Fields Estimation in Spine Examinations of MRI Patients: A Re-Evaluation of Existing Clinical Protocols at a Hospital in Accra, Ghana. Journal of Applied Mathematics and Physics, 6, 1065-1075. https://doi.org/10.4236/jamp.2018.65092