ELECTROMAGNETIC DOSIMETRY in MRILuca ZILBERTI

(l.zilberti@inrim.it)

Effects of Electromagnetic Fields

Main Interaction Mechanisms

• Electric componentinteracts with electric charges and makes them move⇒ conductive/dielectric currents

• Magnetic componentinteracts with structures having an own magnetic moment

& induces electric fields

&produces magnetohydrodynamic effects

Electromagnetic Fields Non-Ionizing Radiations

Classification of effects

Physical Effects can give rise to (harmless/favourable/harmful) Biological Effects

Biological Effects becomes Health Effects when producing stress for the organism (even if reversible!)

Terms of comparison:- physiological current density (1 - 10 mA/m2)

&

- thermoregulation(whole-body metabolic heat production around 1 W/kg at rest and 10 W/kg for heavy work)

NB: artificial fields may be far higher than natural fields

Dielectric behaviour of tissues• The biological tissues behave as a complex collection of conductive and

dielectric elements

• The frequency of the EMF acts as a discriminating parameter

• Typically, tissues exhibit a dispersive behavior:

⇒ the permittivity (ε) decreases with frequency (the electronic and atomic polarizations are almost “instantaneous”, but the orientation of molecular dipoles and the motion of ions towards interfaces can be slow with respect to the period of a RF wave)

⇒ the conductivity (σ) increases with frequency (the equivalent conductivity also increases because the capacitive susceptance of the cell membrane raises too, allowing a conduction not limited to the extracellular tissue but involving the whole cytoplasm)

On the whole, in biological tissues conduction mechanisms prevail at low frequency, while the dielectric behavior becomes more and more

predominant with the increase of the frequency.

???2 fσπ ε

Thermal effects of RF fields

A field propagating through a biological tissue transfers power to it and generates heat

NOTES:• Below 10 GHz the penetration depth in relatively high• In general, a “flat layer model” is not applicable and wave reflections can cause hot spots • In the range 20 MHz – 300 MHz resonance phenomena can arise in some parts (e.g. the head)

Metric ⇒ SAR – Specific Absorption Rate (W/kg) (energy absorbed by the organic tissue for a unit mass in a unit of time)

Up to now, at standard level, SAR has been used as a surrogate for temperature.

From recent simulations: - a 2 hours exposure at whole-body averaged SAR = 4 W/kg produces ΔT ≈ 0.5 °C- a local SAR = 10 W/kg (averaged over 10 g of contiguous tissue) typically results in ΔT ≤ 2 °C

Thermal dose: CEM43(Sapareto and Dewey, 1984)

CEM43 = Cumulative Equivalent Minutes at 43 °C:

43

143 i

nT

ii

CEM t R −

=

=∑

duration (minutes)interval

temperature (°C)

0.5 @ 43 °C0.25 @ 43 °C

TR

T≥

= <(data deduced from experiments oncells of chinese hamster ovary)

Increasing CEM43 ⇒ increasing damage

Same CEM43 (with different temperature-duration) ⇒ same damage

CEM43: a graphical example

(°C)

(minutes)

30 minutes at 44 °C produces (are equivalent to)

CEM43 = 60 minutes

CEM43 – Some comments

• CEM43 is not a good metric for very low and very high temperatures

• Thresholds are tissue-dependent

• The values for R and the breakpoint are still under discussion

• Data obtained on animals cannot be easily

extrapolated to humans ?

Magnetic field

Electric field

Interaction of LF fields

• At LF the body behaves as a conductor

• Typically, the induced field is about five orders of magnitude smaller than the externalelectric field; the strongest induced fields occur for the human body in perfect contactwith the ground.

• Oscillating charges are induced on the body surface.

• The total current flowing through a body in contact with the ground is determined bythe body size and posture. The distribution of induced currents is determined by theconductivity.

• The human body does not significantly perturb the field (magnetic permeability ≈ µ0).

• The induction of electric currents can be due to time-varying fields or to the motionthrough a stationary field.

• For time-varying fields, the induced currents as a whole are greatest when the fields arealigned from the front (or back) of the body, but for some individual organs the highestvalues occur for the field aligned from side to side.

• Higher electric fields are induced in a body of a larger size. The local distribution of theinduced electric field is affected by the conductivity of the tissues.

Acute effects of LF fields

• Direct stimulation of nervous fibres when the internal electric field exceeds afew volt per metre (but much weaker fields can affect synaptic transmission inneural networks) ⇒ unintentional muscle stimulation for exposure to externalfields above 10 kV/m or 5 mT.

• Magnetophosphenes: flickering light sensation due to nerve and retinastimulation by strong magnetic fields.

• Sensory effects (experiences of vertigo, nausea, magnetophosphenes) andtransient decrements in the performance of some behavioural tasks whenmoving through strong stationary magnetic fields.

Metric ⇒ Induced Electric Field (V/m)

Long-term effects

IARC - International Agency for Research onCancer

• RF fields ⇒ 2B(main reference towards brain cancer and the use of mobile phones, hence above 500 MHz)

• LF magnetic fields ⇒ 2B

• Static and LF electric fields; stationary magneticfields ⇒ 3

IARC classification:

- carcinogenic (1)

- probably carcinogenic (2A)- possibly carcinogenic (2B)

- not classificable as to itscarcinogenicity (3)

- probably not carcinogenic (4)

Other effects(not considered within electromagnetic dosimetry)

• Consequences of electric contact

• Interference with active implanted medical devices (e.g. pacemakers)

• Mechanical effects, mainly due to strong stationary magnetic fields (translational forces, torques, “missile effect”,…)

Stationary field and ferromagnetic objects

Torque Proportional to B

Maximum values inside the scanner

For elongated objects, the maximum restraining force can reach 30 times the

maximum translational force

For a given torque, it is more difficult for surrounding tissues to prevent a small

implant (e.g. a clip) from twisting compared to a longer one.

Translational forces Proportional to B (including saturation) and to the

spatial gradient |∇B|

Maximum values just outside the bore

For modern systems (exceeding 10 T/m), may be as high

as 250 times the object weight

Human Body Models

Human models

• Analytical methods with simple human models were used in the past to evaluate general characteristics.

• Currently, numerical simulations with realistic voxel human models are used toevaluate detailed characteristics.

Examples of modelsAnalytical solution adopted at standard level

3D version of the “reference man” (2300 elements)O. Bottauscio, M. Chiampi, L. Zilberti - 2009

Stylized model High-resolution, anatomical, VOXEL models

Virtual Population (http://www.itis.ethz.ch/itis-for-health/virtual-population/overview/)

• Imaging in 1.5 T whole-body MRI scanner• Resolution: up-sampling from 0.5 × 0.5 × 1.0 mm³ in the head and 0.9 × 0.9 × 2.0 mm³ in the torso

and limbs (version 1.0) to 0.5 × 0.5 × 0.5 mm³ (version 3.0)

• Some animal models (rat, rat with tumors, pregnant rat, pig) also available

Dielectric Parameters of Tissues • In general, in a passive medium, both conductive and dielectric effects take place.

• In an ideal insulator there are no losses, σ = 0 and P is in phase with E⇒ D = ε0E + P = εE

• In a good conductor, P is negligible and σ is “high” (it is the only source of losses)

• In a generic medium, there are both ohmmic losses (represented by σ) and dielectric losses (polarization implies “collisions” between dipoles and, at the increase of frequency, P is no longer in phase with E) ⇒ permittivity is represented as a complex quantity

NOTE: from the phenomenological (and therefore experimental!) side, we cannot distinguish ohmic losses from dielectric losses.

E: electric field D: dielectric inductionP: polarization J: current densityε: permittivity σ: electric conductivity ω: angular frequency

( )

( )

' ''

'' ' ' ' '' 'eq

T

eqeq

j j j

j

j j j jσ

σ

= σ + ωε = σ + ω ε − ε ωε

σσ σ = σ+ωε + ωε σ + ωε ε = ε − ε + = ε − ω ω

EJ E E E E =

E

=

Total current density:

Complex conductivity: Complex permittivity:

Dispersive behavior

Relative «static» permittivityof water (liquid) vs

temperature

0 °C 88

20 °C 80

100 °C 55

• Conductivity and permittivity (sometimes called “dielectric constant”) are NOT constant.

• They can be strongly influenced by environmental variables (humidity, pressure, temperature,…) and by the magnitude of the electric field itself.

• They are also strongly influenced by frequency.

dispersive parameters

Electronic and atomic polarizations can be considered instantaneous at LF and RF

Description of Polarization• Consider a dielectric slab, with zero conductivity, among the armatures of a capacitor

• Apply a step of voltage (= step of electric field) directly to the capacitor (i.e. with null external resistance)

• The dielectric induction will vary with time:- a first contribution Di = ε∞E appears instantaneously- a second contribution Dd increases gradually

• After a relatively long time, the final value is:D(t→∞) = ε∞E + Dd(t→∞) = εsE

• The “delayed” component Dd follows approximately the response of a 1st–order dynamical system:Dd (t) = A + Be-t/τ

• The complete response of the system to a unit step of electric field results to be:

0

lim

lim ("static" permittivity)s

∞ ω→∞

ω→

ε = ε

ε = ε

( )( ) ( )

0 0d

d s

t A B

t A ∞

= = + =

→∞ = = ε − ε

D

D E

( ) ( )( ) ( )

( )

1

where is the unit step function

t

d st e u t

u t

− τ∞= ε − ε −D E

( ) ( )( ) ( )1t

st e u t− τ

∞ ∞ = ε + ε − ε −

DE ∞ε

sε

Debye Model• From the response to the unit step, we can get the response to the unit pulse δ(t):

• The Fourier transform of the response to the unit pulse provides the transfer function of the system:

⇒ ε′ reduces monotonically from εs to ε∞⇒ ε′′ goes to zero for both low and high frequencies; it has a maximum for ωτ = 1, where

( )( ) ( ){ } ( ) ( ) ( )11t t

s sd e u t t e u tdt

− −τ τ∞ ∞ ∞ ∞

ε + ε − ε − = ε δ + ε − ε τ

( ) ( )( )

( ) ( ) ' ''1 1 1

s s sjj j j j

j j∞ ∞ ∞

∞ ∞ 2 2 2 2

ω ε − ε ε − ε ε − ε ε ω = = ε + ⇒ ε ω = ε − ε = ε + − ωτ ω + ωτ +ω τ +ω τ

DE

1

1

'2

''2

s

s

∞ωτ=

∞ωτ=

ε + εε = ε − εε =

Debye model for liquid water at 0 °C

εs = 88ε∞ = 5

τ = 18 ps

Advanced models

1) For many materials, the Debye model does not fit the experimental results very well

Cole-Cole model

2) Most real materials exhibit a distribution of macroscopic relaxation times

( )( )1

0 11

s jj

∞∞ −δ

ε − ε σε = ε + − ≤ δ ≤

ω+ ωτ

( ) 1 2

2

...1 1

jj j∞

1

∆ε ∆εε ω = ε + + +

+ ωτ + ωτ

Gabriel model( )( )

4

11 1 i

i

i i

jj

∞ −δ=

∆ε σε = ε + −

ω+ ωτ∑

Phys. Med. Biol. (41), 1996.

Electromagnetic Simulations

Basic ingredients(geometry, …)

• Body model• Field sources• Environment

Problemdescription

• Electromagnetic equations• Material properties• Boundary conditions

Formulation and domain

discretization

• Finite Element Method (FEM)• Boundary Element Method (BEM)• Finite Difference Time Domain (FDTD)• Finite Integration Technique (FIT)• …

Numericalsolution

RESULTS

APPROXIMATIONS

0

D

B

BEt

DH Jt

∇ ⋅ = ρ

∇ ⋅ =

∂∇× = −

∂∂

∇× = +∂

Thermal models

Thermal phenomena in a living body are typically described throughPennes’ bioheat equation

(local thermal balance, applied to the volume power density)

( ) ( )met g b b VTT p p h T T ct

∂∇ ⋅ λ∇ + + + − =

∂

under Robin boundary conditions

( )b amb ambbound

T h T Tn

∂λ = −

∂

Thermal conduction

Metabolic heat

Heat storageAdditional heat source (e.g. electromagnetic field)

Blood perfusion

Along internal interfaces, conservation of bothtemperature and thermal flux is enforced

: temperature: thermal conductivity: volume specific heat capacity, : blood temperature and perfusione coefficient

, : external temperature and heat exchange coefficient

V

b b

amb amb

T

cT hT h

λ

Temperature increase

In absence of electromagnetic exposure, at steady-state, Pennes’ equation

reduces to

Subtracting and introducing we get

( ) ( )met g b b VTT p p h T T ct

∂∇ ⋅ λ∇ + + + − =

∂

Thermal simulations are typically applied to voxel-based models, through a suitableformulation (e.g. the Finite Element Method)

( ) ( ) 0s b b s metT h T T p∇⋅ λ∇ + − + =

( )b amb ambbound

T h T Tn

∂λ = −

∂

( )sb amb amb s

bound

T h T Tn

∂λ = −

∂

( ) ( ) ( ), , , , , ,sx y z T x y z T x y zθ = −

( ) 0b gh p∇⋅ λ∇θ + θ+ = b ambbound

hn∂θ

−λ = θ∂

Exposure Limits

ICNIRP Guidelines

• Electromagnetic fields 100 kHz – 300 GHz (1998)

• Low-frequency electric and magnetic fields (2010)

• Stationary magnetic fields (2009)

• Motion-induced electric fields (2014)

Different limits for general public and workers

Limits on induced quantities (basic restrictions) and

unperturbed external fields (reference levels)

Weighted-peak approach for non-sinusoidal fields

International Commission on Non-Ionizing Radiation Protection

European Law

Directive 2013/35/EU (workers)

Exposure Limit Values (ELVs) ⇒ Basic Restrictions

Action Levels (ALs)⇒ Reference Levels

Health effects ELVs (avoid health effects)

Sensory effects ELVs (avoid sensory effects)

High ALs (respect of health effects ELVs)

Low ALs (respect of sensory effects ELVs)

Limb ALs

Some derogations (e.g. MRI)

Recommendation 1999/519/EC (general public)

⇒ Exceptions for medical purposes

EN/IEC 60601-2-33, 2010, +AMD1:2013+AMD2:2015 Medicalelectrical equipment – Part 2-33: Particular requirements for thesafety of magnetic resonance equipment for medical diagnosis

Three levels of operation:Normal Operating Mode ⇒ none of the outputs have a value that may cause physiological stress to patients

First Level Controlled Operating Mode ⇒ one or more outputs reach a value that may causephysiological stress to patients, which needs to be controlled by medical supervision

Second Level Controlled Operating Mode ⇒ one or more outputs reach a value that may producesignificant risk for patients, for which explicit ethical approval is required

•Exposure to the stationary magnetic field

•Exposure to slowly-varying magnetic fields

•Exposure to radiofrequency fields

•Scanning of PATIENTs with active or passive implants (device labelled as MR safe or MR conditional)

•…

The limits for the MR WORKERS are in excess of those permitted by ICNIRP

Primary concern about cardiac fibrillation and peripheral nerve stimulation(PNS). The scanner shall be designed so that cardiac stimulation isautomatically prevented.

EN/IEC 60601-2-33 – Protection against PNSModified version of Reilly’s model for nerve stimulation threshold (*)

r = 2.2 V/m (for E)

Rheobase:

r = 20 T/s (for dB/dt)

( ),01 0.8 1 0.36 s effL r t< ⋅ ⋅ +

( ),12 1 1 0.36 s effL r t< ⋅ ⋅ +

Limits related to peripheral

nerve stimulation

(Limit for normal operating mode)

(Limit for first level controlled operating mode)

1THs

cE rt

= +

• ts : stimulus duration• r: rheobase (threshold for long ts)• c: chronaxie (characteristic reaction time)

⇒ L12 corresponds to the PNS threshold; L01 has a 0.8 safety factor

(*) Peripheral nerve and cardiac excitation by time-varying magnetic fields: A comparison of thresholds. NY Acad. of Sci., 1992, 649, p.96-117.

EN/IEC 60601-2-33 – Protection against RF energy depositionwhole body coils, head coils or coils designed for homogeneous exposure of a specific part of the body

Mass to determine the local SAR: 10 g

Other standards for protection in case of implants

ISO/TS 10974, 2012, Requirements for the safety of magneticresonance imaging for patients with an active implantablemedical device.

ASTM StandardsF2503: Practice for Marking Medical Devices and Other Items for Safety in the MagneticResonance Environment

F2182: Test Method for Measurement of Radio Frequency Induced Heating On or NearPassive Implants During Magnetic Resonance Imaging

F2213: Test Method for Measurement of Magnetically Induced Torque on Medical Devices in the Magnetic Resonance Environment

F2052: Test Method for Measurement of Magnetically Induced Displacement Force on Medical Devices in the Magnetic Resonance Environment

MR safe MR conditional MR unsafe

Non-conductive, non-metallic and non-magnetic components

Some (hopefully interesting) examples of dosimetric computations

SAR vs Temperature

Maximum local SAR

Maximum temperature elevation at steady state

128 MHz bird-cage coil 1 µT B1

+ field in the coil center without the head

O. Bottauscio et al., “A GPU Computational Code for Eddy-Current Problems in Voxel-Based Anatomy”, IEEE T. Magn., 2015.

10g-averaged SAR distribution in a transversal and a sagittal slice Plots normalized to the individual maximum.

T. M. Fiedler, M. E. Ladd, A. K. Bitz, “SAR Simulations & Safety”, NeuroImage, 2018.

Anatomical head model in a shielded birdcage head coil driven in the circularly polarized mode, from 64 to 500 MHz

At 64 MHz the SAR distribution is similar to eddy current patterns in quasi-staticapproximations ⇒ maximum SAR located in superficial tissuesWith the frequency increase, local SAR elevations occur deeper in the head

Frequency dependence (anatomical head model)

RF simulation at 300 MHzVoxel-based SAR distribution in an anatomical and a homogeneous head model

Homogeneous body models do not provide realistic information on the local SAR.

NOTE: If the RF coil determines the spatial resolution of the mesh, homogeneousphantoms do not necessarily result in a reduction of the computational costs(required amount of memory and computation time).

T. M. Fiedler, M. E. Ladd, A. K. Bitz, “SAR Simulations & Safety”, NeuroImage, 2018.

Homogeneous body model

Magnetic field

S. Wolf, D. Diehl, M. Gebhardt, J. Mallow, and O. Speck, “SAR Simulations for High-Field MRI: How Much Detail, Effort, and Accuracy Is Needed?”, Magnetic Resonance in Medicine, 2013.

For the head only model, the currents in the head form a pseudo loop at the neck and theSAR distribution increases correspondingly.If the shoulders are part of the model, the field disturbances inside the head of thereduced model and full model are almost indistinguishable.

Body model in a 7 T birdcage

SAR

Current density

Body Truncation

Investigations of the effects of anatomical differences. Variations of up to 54% in SAR and up to 63% in temperature increase.

A patient-specific assessment is an important target for dosimetry.

Voxel-based SAR distribution 7 T 8-channel head coil in CP+ mode and input power of 1 W.

T. M. Fiedler, M. E. Ladd, A. K. Bitz, “SAR Simulations & Safety”, NeuroImage, 2018.

Influence of body models

Enhancement of the local SAR in tissues surrounding the object

Sphere(diameter = 40 mm)

Ellipsoid(100/15 mm)

Ellipsoid(40/15 mm)

Ellipsoid(40/25 mm)

Metallic object (handled as PEC), immersed in a tissue-like material and

exposed to a rotating RF field(Results rescaled to SARwb = 2 W/kg)

Example: “diffusion weighted single shot planar echo sequence”

G = 30 mT/m

tslope = 125 μs

ton = 40 ms

T = 200 ms

f = 1 kHz

L. Zilberti, et al., Magn. Res. Imag. 74:272-279 (2015)

On a gross time-scale, the temperature elevationapproximately follows the response of a dynamic 1st-order system.

Results for a scanning time of 30 minutes

CoCrMoimplant

MRI Gradient coils & hip implants

L. Zilberti, et al., IEEE Trans. Magnetics 52:5000304 (2016)

1

2

B map at brain height

Trajectory Maximum exposure indexcomputed via DFT

1: Rotation 0.342: Translation 0.54

Two trajectories (including acceleration, uniform speed and deceleration):1) 180° rotation in 1 s, ωmax = 3.83 rad/s2) 1 m translation in 1 s, vmax = 1.22 m/s

Motion-induced fields in MRI

MR-basedElectric Properties Tomography (EPT)

EPT: What & Why

EPT is a family of techniques to get, non-invasively, the

electric properties of tissues.

EPT results can be used:

as a diagnostic tool

to predict local SAR distribution

to plan subject-specific therapies based on

electromagnetic fields

Local EPTFrom Maxwell’s equation in phasor notation:

( ) H j E H j E j E∇× = ωε ⇒ ∇×∇× = ω∇× ε ≅ ωε∇×

Assumption of local homogeneity

( )2 2 20 0

0 H H j j H H H

=

∇ ∇ ⋅ −∇ = ωε − ωµ ⇒ −∇ = ω µ ε

0µ = µ everywhere

Applying the equation to the rotating part of the field

one gets

jH H e+ + ϕ=2

20

' eq HjH

+

+

σ ∇ε = ε − = −

ω ω µ

whose real and imaginary parts give:22 2

220 00 0

' 2eq

H H

H H

+ +

+ +

∇ ∇ ⋅∇ϕ∇ϕ ∇ ϕε = − + σ = +

ω µ ωµω µ ωµ+ Fast and straightforward- Limited accuracy (approximations)

Global EPTThe total field is seen as a superposition of the source field andthe scattering due to the body

Source field

Body effect

Total field

+ Good accuracy, additional outputs- Complex and computationally demanding

Initialguess

Iteration10

Iteration100

Iteration1000

Iteration10000

1) Solve the total field using the source field asknown term and assigning tentative tissueproperties to the body

2) Repeat, changing the tissue properties, untilmeasured and computed total fields are in goodagreement

Maps of electric conductivity in a human brain