ELECTROMAGNETIC DOSIMETRY in MRI. Luca ZILBERTI

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1 ELECTROMAGNETIC DOSIMETRY in MRI Luca ZILBERTI

2 Effects of Electromagnetic Fields

3 Main Interaction Mechanisms Electromagnetic Fields Non-Ionizing Radiations Electric component interacts with electric charges and makes them move conductive/dielectric currents Magnetic component interacts with structures having an own magnetic moment & induces electric fields & produces magnetohydrodynamic effects

4 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/m 2 ) & - 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

5 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) σ 2πε f??? 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.

6 Thermal effects of RF fields A field propagating through a biological tissue transfers power to it and 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) generates heat 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: CEM n 43 Ti 43 = tir i= 1 0.5 @ T 43 C R = 0.

7 Thermal dose: CEM43 (Sapareto and Dewey, 1984) CEM43 = Cumulative Equivalent Minutes at 43 C: CEM n 43 Ti 43 = tir i= 1 T 43 C R = T < 43 C temperature ( C) (data deduced from experiments on cells of chinese hamster ovary) interval duration (minutes) Increasing CEM43 increasing damage Same CEM43 (with different temperature-duration) same damage

8 CEM43: a graphical example ( C) 30 minutes at 44 C produces (are equivalent to) CEM43 = 60 minutes (minutes)

9 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

Electric field At LF the body behaves as a conductor Interaction of LF fields Typically, the induced field is about five orders of magnitude smaller than the external electric field; the strongest

10 Electric field At LF the body behaves as a conductor Interaction of LF fields Typically, the induced field is about five orders of magnitude smaller than the external electric field; the strongest induced fields occur for the human body in perfect contact with the ground. Oscillating charges are induced on the body surface. The total current flowing through a body in contact with the ground is determined by the body size and posture. The distribution of induced currents is determined by the conductivity. Magnetic field The human body does not significantly perturb the field (magnetic permeability µ 0 ). The induction of electric currents can be due to time-varying fields or to the motion through a stationary field. For time-varying fields, the induced currents as a whole are greatest when the fields are aligned from the front (or back) of the body, but for some individual organs the highest values 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 the induced electric field is affected by the conductivity of the tissues.

11 Acute effects of LF fields Direct stimulation of nervous fibres when the internal electric field exceeds a few volt per metre (but much weaker fields can affect synaptic transmission in neural networks) unintentional muscle stimulation for exposure to external fields above 10 kv/m or 5 mt. Magnetophosphenes: flickering light sensation due to nerve and retina stimulation by strong magnetic fields. Sensory effects (experiences of vertigo, nausea, magnetophosphenes) and transient decrements in the performance of some behavioural tasks when moving through strong stationary magnetic fields. Metric Induced Electric Field (V/m)

12 Long-term effects IARC - International Agency for Research on Cancer RF fields 2B (main reference towards brain cancer and the use of mobile phones, hence above 500 MHz) LF magnetic fields 2B IARC classification: - carcinogenic (1) - probably carcinogenic (2A) - possibly carcinogenic (2B) - not classificable as to its carcinogenicity (3) - probably not carcinogenic (4) Static and LF electric fields; stationary magnetic fields 3

13 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 Translational forces Proportional to B (including saturation) and to the spatial gradient B Maximum values just outside the bore For modern systems

14 Stationary field and ferromagnetic objects 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 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.

15 Human Body Models

16 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 to evaluate detailed characteristics.

17 Examples of models Analytical solution adopted at standard level Stylized model High-resolution, anatomical, VOXEL models 3D version of the reference man (2300 elements) O. Bottauscio, M. Chiampi, L. Zilberti

Virtual Population (http://www.itis.ethz.

0 mm³ in the torso and limbs (version 1.0) to 0.5 0.

18 Virtual Population ( Imaging in 1.5 T whole-body MRI scanner Resolution: up-sampling from mm³ in the head and mm³ in the torso and limbs (version 1.0) to mm³ (version 3.0) Some animal models (rat, rat with tumors, pregnant rat, pig) also available

19 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 = ε 0 E + P = εe E: electric field D: dielectric induction P: polarization J: current density ε: permittivity σ: electric conductivity ω: angular frequency 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 Total current density: Complex conductivity: σ σ σ = ( σ + ωε '') + jωε' = σ eq + jωε' ε = ε' j ε '' + = ε' j ω ω σ eq σ E JT =σ E+ jωε E=σ E+ jω( ε' jε'' ) E= j ωε E Complex permittivity: NOTE: from the phenomenological (and therefore experimental!) side, we cannot distinguish ohmic losses from dielectric losses. eq

20 Dispersive behavior 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. Relative «static» permittivity of water (liquid) vs temperature dispersive parameters 0 C C C 55 Electronic and atomic polarizations can be considered instantaneous at LF and RF

21 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 D i = ε E appears instantaneously - a second contribution D d increases gradually After a relatively long time, the final value is: D(t ) = ε E + D d (t ) = ε s E ε = lim ε ε = lim ε ("static" permittivity) s ω ω 0 The delayed component D d follows approximately the response of a 1 st order dynamical system: D d (t) = A + Be -t/τ D D d d ( t = 0) = A+ B= 0 ( ) = = ( ε ε ) t A s E D d t ( t) = E( ε ε )( 1 e τ ) u( t) ( ) where u t s is the unit step function The complete response of the system to a unit step of electric field results to be: D ( t) = ε + εs ε E t ( )( 1 e τ ) u( t) ε s ε

22 Debye Model From the response to the unit step, we can get the response to the unit pulse δ(t): d dt { ( )( ) ( )} t 1 t τ τ ε + εs ε 1 e u t =ε δ ( t) + ( εs ε ) e u( t ) τ The Fourier transform of the response to the unit pulse provides the transfer function of the system: ( j ) ( j ) ( ) D ω εs ε εs ε εs ε ε( jω ) = =ε + ε( jω ) =ε' jε '' = ε + j 2 2 ωτ 2 2 E ω 1+ jωτ 1+ω τ 1+ω τ ε reduces monotonically from ε s to ε ε goes to zero for both low and high frequencies; it has a maximum for ωτ = 1, where ε s +ε ε ' ωτ= 1 = 2 εs ε ε '' ωτ= 1 = 2 Debye model for liquid water at 0 C ε s = 88 ε = 5 τ = 18 ps

Advanced models 1) For many materials, the Debye model does not fit the experimental results very well Cole-Cole model ( εs ε ) σ j 0 1 ( j ) 1 δ + ωτ ω ε=ε + δ 1 2) Most real materials

23 Advanced models 1) For many materials, the Debye model does not fit the experimental results very well Cole-Cole model ( εs ε ) σ j 0 1 ( j ) 1 δ + ωτ ω ε=ε + δ 1 2) Most real materials exhibit a distribution of macroscopic relaxation times ε1 ε2 ε( jω ) =ε jωτ 1+ jωτ 1 2 Gabriel model ε 4 ε=ε + i ( ) ( 1 ) j δi i= 1 1+ jωτ ω i σ Phys. Med. Biol. (41), 1996.

Electromagnetic Simulations A P P R O X I M A T I O N S Basic ingredients (geometry, ) Problem description Formulation and domain discretization Numerical solution RESULTS Body model Field sources

24 Electromagnetic Simulations A P P R O X I M A T I O N S Basic ingredients (geometry, ) Problem description Formulation and domain discretization Numerical solution RESULTS Body model Field sources Environment Electromagnetic equations Material properties Boundary conditions Finite Element Method (FEM) Boundary Element Method (BEM) Finite Difference Time Domain (FDTD) Finite Integration Technique (FIT) D =ρ B = 0 B E = t D H = J + t

25 Thermal models Thermal phenomena in a living body are typically described through Pennes bioheat equation (local thermal balance, applied to the volume power density) Thermal conduction Metabolic heat ( ) ( ) λ T + p + p + h T T = c met g b b V Additional heat source (e.g. electromagnetic field) Blood perfusion T t Heat storage under Robin boundary conditions T λ = h T T ( ) b amb amb n bound T : temperature λ : thermal conductivity c V : volume specific heat capacity T, h : blood temperature and perfusione coefficient T b amb b, h : external temperature and heat exchange coefficient amb Along internal interfaces, conservation of both temperature and thermal flux is enforced

26 Temperature increase In absence of electromagnetic exposure, at steady-state, Pennes equation reduces to ( ) ( ) λ T + p + p + h T T = c met g b b V ( T ) h ( T T ) p 0 λ + + = s b b s met T t T λ = h T T ( ) b amb amb n bound T λ = h T T ( ) s b amb amb s n bound Subtracting and introducing we get ( xyz,, ) T( xyz,, ) T( xyz,, ) θ = s θ λ θ + h θ + p = b hamb ( ) 0 b g λ = θ n bound Thermal simulations are typically applied to voxel-based models, through a suitable formulation (e.g. the Finite Element Method)

27 Exposure Limits

28 ICNIRP Guidelines International Commission on Non-Ionizing Radiation Protection 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

29 Directive 2013/35/EU (workers) European Law Exposure Limit Values (ELVs) Basic Restrictions Health effects ELVs (avoid health effects) Sensory effects ELVs (avoid sensory effects) High ALs (respect of health effects ELVs) Action Levels (ALs) Reference Levels Low ALs (respect of sensory effects ELVs) Limb ALs Recommendation 1999/519/EC (general public) Exceptions for medical purposes Some derogations (e.g. MRI)

30 EN/IEC , 2010, +AMD1:2013+AMD2:2015 Medical electrical equipment Part 2-33: Particular requirements for the safety of magnetic resonance equipment for medical diagnosis Exposure to the stationary magnetic field Exposure to slowly-varying magnetic fields Primary concern about cardiac fibrillation and peripheral nerve stimulation (PNS). The scanner shall be designed so that cardiac stimulation is automatically prevented. Exposure to radiofrequency fields Scanning of PATIENTs with active or passive implants (device labelled as MR safe or MR conditional) 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 cause physiological 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 produce significant risk for patients, for which explicit ethical approval is required The limits for the MR WORKERS are in excess of those permitted by ICNIRP

EN/IEC 60601-2-33 Protection against PNS Modified version of Reilly s model for nerve stimulation threshold (*) E TH = r 1+ c t s t s : stimulus duration r: rheobase (threshold for long t s ) c:

31 EN/IEC Protection against PNS Modified version of Reilly s model for nerve stimulation threshold (*) E TH = r 1+ c t s t s : stimulus duration r: rheobase (threshold for long t s ) c: chronaxie (characteristic reaction time) Limits related to peripheral nerve stimulation (, ) L01< 0.8 r t s eff (, ) L12 < 1 r t s eff (Limit for normal operating mode) (Limit for first level controlled operating mode) r = 2.2 V/m (for E) Rheobase: r = 20 T/s (for db/dt) 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

32 EN/IEC Protection against RF energy deposition whole 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

33 Other standards for protection in case of implants ISO/TS 10974, 2012, Requirements for the safety of magnetic resonance imaging for patients with an active implantable medical device. ASTM Standards F2503: Practice for Marking Medical Devices and Other Items for Safety in the Magnetic Resonance Environment MR safe MR conditional MR unsafe Non-conductive, non-metallic and non-magnetic components F2182: Test Method for Measurement of Radio Frequency Induced Heating On or Near Passive 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

34 Some (hopefully interesting) examples of dosimetric computations

35 Maximum local SAR SAR vs Temperature O. Bottauscio et al., A GPU Computational Code for Eddy-Current Problems in Voxel-Based Anatomy, IEEE T. Magn., MHz bird-cage coil 1 µt B 1+ field in the coil center without the head Maximum temperature elevation at steady state

Frequency dependence (anatomical head model) Anatomical head model in a shielded birdcage head coil driven in the circularly polarized mode, from 64 to 500 MHz 10g-averaged SAR distribution in a

36 Frequency dependence (anatomical head model) Anatomical head model in a shielded birdcage head coil driven in the circularly polarized mode, from 64 to 500 MHz 10g-averaged SAR distribution in a transversal and a sagittal slice Plots normalized to the individual maximum. At 64 MHz the SAR distribution is similar to eddy current patterns in quasi-static approximations maximum SAR located in superficialtissues With the frequency increase, local SAR elevations occur deeper in the head T. M. Fiedler, M. E. Ladd, A. K. Bitz, SAR Simulations & Safety, NeuroImage, 2018.

Homogeneous body model RF simulation at 300 MHz Voxel-based SAR distribution in an anatomical and a homogeneous head model Homogeneous body models do not provide realistic information on the local

37 Homogeneous body model RF simulation at 300 MHz Voxel-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, homogeneous phantoms 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.

Body Truncation Body model in a 7 T birdcage Magnetic field SAR Current density For the head only model, the currents in the head form a pseudo loop at the neck and the SAR distribution increases

38 Body Truncation Body model in a 7 T birdcage Magnetic field SAR Current density For the head only model, the currents in the head form a pseudo loop at the neck and the SAR distribution increases correspondingly. If the shoulders are part of the model, the field disturbances inside the head of the reduced model and full model are almost indistinguishable. 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.

Influence of body models Voxel-based SAR distribution 7 T 8-channel head coil in CP+ mode and input power of 1 W. Investigations of the effects of anatomical differences.

39 Influence of body models Voxel-based SAR distribution 7 T 8-channel head coil in CP+ mode and input power of 1 W. 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. T. M. Fiedler, M. E. Ladd, A. K. Bitz, SAR Simulations & Safety, NeuroImage, 2018.

to SAR wb = 2 W/kg) Ellipsoid (40/25 mm)

40 Enhancement of the local SAR in tissues surrounding the object Metallic object (handled as PEC), immersed in a tissue-like material and exposed to a rotating RF field (Results rescaled to SAR wb = 2 W/kg) Ellipsoid (40/25 mm) Ellipsoid (40/15 mm) Sphere (diameter = 40 mm) Ellipsoid (100/15 mm)

41 MRI Gradient coils & hip implants L. Zilberti, et al., Magn. Res. Imag. 74: (2015) Example: diffusion weighted single shot planar echo sequence G = 30 mt/m t slope = 125 μs t on = 40 ms CoCrMo implant T = 200 ms f = 1 khz On a gross time-scale, the temperature elevation approximately follows the response of a dynamic 1 st - order system. Results for a scanning time of 30 minutes

42 Motion-induced fields in MRI L. Zilberti, et al., IEEE Trans. Magnetics 52: (2016) Two trajectories (including acceleration, uniform speed and deceleration): 1) 180 rotation in 1 s, ω max = 3.83 rad/s 2) 1 m translation in 1 s, v max = 1.22 m/s 2 Trajectory Maximum exposure index computed via DFT 1: Rotation : Translation B map at brain height

43 MR-based Electric Properties Tomography (EPT)

44 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

45 Local EPT From Maxwell s equation in phasor notation: H = jωε E H = jω ε E jωε E ( ) H H = jωε ( jωµ 0) H H = ω µ 0ε H = 0 µ=µ everywhere 0 Assumption of local homogeneity Applying the equation to the rotating part of the field one gets σ ε=ε ' j = 2 eq 2 ω ωµ 0 + H H + H = H e + + jϕ whose real and imaginary parts give: H 2 + H ϕ ϕ ϕ ε= ' + σ = eq + ω µ 0 H ω µ 0 ωµ 0 ωµ 0 H + Fast and straightforward - Limited accuracy (approximations)

Global EPT The total field is seen as a superposition of the source field and the scattering

source field as known term and assigning tentative tissue properties to the body 2) Repeat,

agreement Initial guess Iteration 10 Iteration 100 Iteration 1000 Iteration 10000 + Good

46 Global EPT The total field is seen as a superposition of the source field and the scattering due to the body Source field Body effect Total field 1) Solve the total field using the source field as known term and assigning tentative tissue properties to the body 2) Repeat, changing the tissue properties, until measured and computed total fields are in good agreement Initial guess Iteration 10 Iteration 100 Iteration 1000 Iteration Good accuracy, additional outputs - Complex and computationally demanding Maps of electric conductivity in a human brain

Magnetic resonance imaging MRI

Magnetic resonance imaging MRI Introduction What is MRI MRI is an imaging technique used primarily in medical settings that uses a strong magnetic field and radio waves to produce very clear and detailed