IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011 Magnetic Resonance Electrical Impedance Tomography (MREIT) As Electromagnetic Tissue Property Imaging Modality Eung Je Woo Department of Biomedical Engineering Impedance Imaging Research Center (IIRC) Kyung Hee University Korea [email protected]
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IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Magnetic Resonance ElectricalImpedance Tomography (MREIT)As Electromagnetic Tissue Property Imaging Modality
Eung Je Woo
Department of Biomedical EngineeringImpedance Imaging Research Center (IIRC)
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Acoustic impedance Proton density and MR phenomena Oxygen and water diffusion Optical absorption, scattering, and emission X-ray attenuation γ-ray emission
Image Contrast
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Acoustic impedance Proton density and MR phenomena Oxygen and water diffusion Optical absorption, scattering, and emission X-ray attenuation γ-ray emission Electrical conductivity Electrical permittivity Magnetic susceptibility Neural activity Biochemistry
Image Contrast
Electromagnetic Tissue Property
Electromagnetic Source
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Medical Imaging Modality Ultrasound MRI OCT X-ray PET
Source Imaging MRE MREIT EIT MAT-MI MIT MREPT QSM Microwave Tomography Terahertz Imaging DOT
What are differences?
- Linear vs. nonlinear
- High vs. low sensitivity
- Well- vs. ill-posedness
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Electromagnetic Tissue Property Imaging
Electrical Impedance Tomography (EIT) Admittivity (conductivity and permittivity) imaging Frequency range: 10 Hz to 1 MHz Difference imaging
Magnetic Induction Tomography (MIT) Microwave Tomography Magneto-Acoustic Tomography – Magnetic Induction (MAT-MI)
MR Electrical Property Tomography (MREPT) Admittivity (conductivity and permittivity) imaging Frequency : Larmor frequency (128 MHz at 3 T) Static imaging
Quantitative Susceptibility Mapping (QSM)
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Conductivity and Resistance
V -Cl
-e
-e
+Na
I
I
V
-eI
-eI
-Cl+Na
dc=J vd µ=v E c uµ σ σ= = = − ∇J E Eu= −∇E q=F E
L
S
, ,
1 , 1
V V VE J E I JS SL L L
L L VV I I RIS S
LI
RS
σ σ σ
ρσ σ
= = = = =
= = = = =
Mobile Ions
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Permittivity and Capacitance
V+-+-
+-+-
+-+-
+-+-
+-+-
+-+-
+-+-
+-+-
+-+-
V-+-+
-+-+
-+-+
-+-+
-+-+
-+-+
-+-+
-+-+
-+-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-e
-e- - - - - - - - -
+ + + + + + + + +
-e
-e+ + + + + + + + +
- - - - - - - - -+Q
-Q +Q
-Q
L
S
( ) ( )( )
Q V V
dQ t dv ti t Cdt
SC
dt
Lε= =
= =
( ) sin( ), ( ) cos( )10, 90 ,
v t V t i t V C t
V V Cj C
ω ω ω
ωω
= =
= ∠ = ∠ = =VV I ZI
PolarizationImmobile Polar Molecules
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
i(t) ~
Cell and Bio-impedance
1
1
2
2
RCCR
1 21 2
1 1R jX R Rj C j Cω ω
= + = + + +Z
-Cl+Na
-Cl+Na
+Na -Cl
+ + + + + + +
+ + + + + + +
_ _ _ _ _ _ _
_ _ _ _ _ _ _
Cell Membrane
Extra-cellular Fluid
Intra-cellular Fluid
cos , sinR jX Z
R Z X Zθ
θ θ= + = ∠= =
Z( )( )
( ) sin and
( ) sinm
m
i t I t
v t I Z t
ω
ω θ
=
= +
i(t) ~
+
v(t)
−
+
v(t)
−
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Cell Structures in TissuesExtra-cellular
Fluid
Intra-cellularFluid
CellularMembrane
( , ) ( , )( , )
(, ) (( , )) c
ω ω
σ
σ
µω
ω
ω
=
=
J r E r
r
r
r r
• Ion Concentration
• Ion Mobility
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Simple Case 1
Homogeneous Object
I
I
LowFrequency
Current
HighFrequency
Current
Macroscopic Conductivity Seen by the Current
(( ), () ) ,cσ µ ωω = r rr
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Simple Case 2
Insulating MembraneFilled with the Same Saline
I
I
LowFrequency
Current
HighFrequency
Current
(( ), () ) ,cσ µ ωω = r rr
Macroscopic Conductivity Seen by the Current
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Simple Case 3
I
I
LowFrequency
Current
HighFrequency
Current
Insulating Membrane with HolesFilled with the Same Saline
(( ), () ) ,cσ µ ωω = r rr
Macroscopic Conductivity Seen by the Current
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Simple Case 4
I
I
LowFrequency
Current
HighFrequency
Current
Insulating Membrane with HolesFilled with the Same Saline
(( ), () ) ,cσ µ ωω = r rr
Macroscopic Conductivity Seen by the Current
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Simple Case 5
Solid Anomaly withConductivity Contrast
I
I
LowFrequency
Current
HighFrequency
Current
(( ), () ) ,cσ µ ωω = r rr
Macroscopic Conductivity Seen by the Current
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Admittivity of Biological Tissue
Molecular composition of cells Shape and direction of cells Density and structure of cells Intra- and extra-cellular fluids Concentration and mobility of ions Temperature Probing method including frequency and
electrode configuration
( ) ( ) ( ), , j ,γ ω σ ω ωε ω= +r r r
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Breast Tissues
A. J. Surowiec, S. S. Stuchly, J. R. Barr, and A. Swarup, ”Dielectric properties of breast carcinoma and the surroundingtissues,” IEEE Trans. Biomed. Eng., vol. 35, no. 4, pp. 257–263, 1988.
NormalTissue
LobularCarcinoma
DuctalCarcinoma
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Liver Tissues
D. Haemmerich, S.T. Staelin, J. Z. Tsai,S. Tungjitkusolmun,D. M. Mahvi and J.G. Webster, “In vivoelectricalconductivity ofhepatic tumours,”Physiol. Meas., vol.24, pp. 251–260,2003.
Normal Cells Tumor
NecrosisFibrosis
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Conductivity and Neural Activity Cole K S and Curtis H J 1939 Electrical impedance of the squid giant axon during
activity J. Gen. Physiol. 22 649-670 Cole K S 1949 Dynamic electrical characteristics of squid axon membrane Arch.
Sci. Physiol. 3 253-258 Adey W, Kado R and Didio J 1962 Impedance measurements in brain tissue of
animals using microvolt signals Exp. Neruol. 5 47-66 Van-Harreveld A and Schade J 1962 Changes in the electrical conductivity of
cerebral cortex during seizure activity Exp. Neurol. 5 383-400 Rank J B 1963 Specific impedance of rabbit cerebral cortex Exp. Neurol. 7 144-152 Aladjolova N A 1964 Slow electrical processes in the brain Prog. Brain Res. 7 155-
237 Geddes L A and Baker L E 1967 The specific resistance of biological material: a
compendium of data for the biomedical engineer and physiologist Med. Biol. Eng. 5 271-293
Meister M, Pine J, Baylor, DA 1994 Multi-neuronal signals from the retina: acquisition and analysis J. Neurosci. Meth. 51 95-106
Neural activity produces 1-5% local conductivity changes at low frequency.
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Action Potential
-+
Current Source
Crab Nerve V1 V2
Action Potential
-5
0
5
10
mV
2245
2250
2255
2260
2265
Time (msec)
R (o
hms)
Resistance0 10 20 30 40 50
-2
0
2
4
6
8
CA
P [m
V]
0 10 20 30 40 50-1
0
1
2
Time [ms]
∆σ
[%]
CAP
∆σ
Conductivity of Crab Nerve
From D. Holder and T. I. Oh
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
( ) ( )( )( ) ( )
0 in on
uu g
σσ
∇⋅ ∇ = Ω− ∇ ⋅ = ∂Ω
r rr r n
( ) ( ) ( ) ( ) ( )uσ σ== − ∇J r r r r E r
( ) ( ) ( )03
' ''4 '
dµπ Ω
× −=
−∫
J r r rB r r
r r
1E2EΩ
∂Ω
I I
n
L− L+
a
(σ, u, J, B)
(g)
Probing by Injecting Current
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Numerical Example using FEM
B. I. Lee, S. H. Oh, E. J. Woo, S. Y. Lee, M. H. Cho, O. Kwon, J. K. Seo, J. Lee, and W. S. Baek, “Three-dimensional forward solver and its performance analysis for MREIT using recessed electrodes," Phys. Med. Biol., vol. 48, 1972-1986, 2003.
σ
u
1E
2E
yx
yx
[S/m]
Bx
By
Bz
yx
yx
yx
Jx
Jy
Jz
yx
yx
yx
[mV]
[Tesla]
[Tesla]
[Tesla]
[mA/mm2]
[mA/mm2]
[mA/mm2]
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
EIT and MREIT
EIT (Electrical Impedance Tomography)- Admittivity imaging from 10 Hz to 1 MHz- Boundary current-voltage measurement- Time- or frequency-difference imaging- Low spatial resolution- High temporal resolution- Functional imaging
MREIT (Magnetic Resonance EIT)- Conductivity imaging below 1 kHz- Internal magnetic flux density measurement- Absolute or contrast imaging- High spatial resolution- Low temporal resolution- Static and functional imaging
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
EIT
( ) sin( )p mi t I tω=
( ) sin( )q pq mv t Z I tω θ= +
Ip=Im∠0
Vq=ZpqIm∠θ
Zpq=Zpq∠θp
q
i
V
( ) ( )( )( ) ( )
0 in on
uu g
ω ω
ω ω
γγ
∇⋅ ∇ = Ω− ∇ ⋅ = ∂Ω
r rr r n
( ) ( ) ( )jωγ σ ωε= +r r r
(Electrical Impedance Tomography)
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Data Collection Protocol
Neighboring Method
(10-4-10-6V)
(10-3-10-4A)
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Difference Imaging in EIT
If admittivity changes as
boundary voltage changes accordingly as
When δγ is small, by a linearization.
A difference image is by tSVD, for example.
2 1 ,γ γ δγ= +
2 1.u u uγ γ δ= +
u γδ δγ= S† uγδγ δ= S
2 1T Tu u uδ= +
Time-difference (tdEIT)
2 1T Tγ γ δγ= +2 1u u uω ω δ= +
Frequency-difference (fdEIT)
2 1ω ωγ γ δγ= +
( ) ( )( )( ) ( )
0 in on .
uu g
γγ
∇⋅ ∇ = Ω− ∇ ⋅ = ∂Ω
r rr r n
The relation between voltage u and admittivity γ is nonlinear since
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
EIT System Current Source
Digital waveform generation and DAC
Balanced current source using Howland circuit
Generalized impedance converter
Voltmeter Differential voltage
amplifier and ADC Digital phase-
sensitive demodulation using FPGA
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Imaging Experiments
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Regional Lung Ventilation
Sitting
R
X
Right Lateral Left Lateral
Sitting
RightLateral
LeftLateral
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
( ) ( )( )( ) ( )
0 in on
uu g
σσ
∇⋅ ∇ = Ω− ∇ ⋅ = ∂Ω
r rr r n
( ) ( ) ( ) ( ) ( )uσ σ== − ∇J r r r r E r
( ) ( ) ( )03
' ''4 '
dµπ Ω
× −=
−∫
J r r rB r r
r r
1E2EΩ
∂Ω
I I
n
L− L+
a
(σ, u, J, B)
(g)
Probing by Injecting Current
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Numerical Example using FEM
B. I. Lee, S. H. Oh, E. J. Woo, S. Y. Lee, M. H. Cho, O. Kwon, J. K. Seo, J. Lee, and W. S. Baek, “Three-dimensional forward solver and its performance analysis for MREIT using recessed electrodes," Phys. Med. Biol., vol. 48, 1972-1986, 2003.
σ
u
1E
2E
yx
yx
[S/m]
Bx
By
Bz
yx
yx
yx
Jx
Jy
Jz
yx
yx
yx
[mV]
[Tesla]
[Tesla]
[Tesla]
[mA/mm2]
[mA/mm2]
[mA/mm2]
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
B0
Electrode
Lead Wire
( )( , )( , )( , ) ( , ) x yz c j xm k yn kj B x y Tj x yS m n M x y e e e dxdyγδ∞ ∆ + ∆±±
−∞= ∫ ∫
MRI for MREIT
M. L. G. Joy, G. C. Scott, and R. M. Henkelman, “In vivo detection of applied electric currents bymagnetic resonance imaging,” Mag. Reson. Imag., vol. 7, pp. 89-94, 1989.
G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Measurement of nonuniformcurrent density by magnetic resonance,” IEEE Trans. Med. Imag., vol. 10, no. 3, pp. 362-374, 1991.
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Magnetic Flux Density (Bz) ImagingWe use both positive and negative injection currents.
Inverse Fourier Transform
Compute phase and unwrap phase
k-space data collection
Scaling and slice ordering
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Limitation in Injection Current Patient auxiliary current (IEC 601-1) : current flowing
in the patient in normal use between any patientconnection and all other patient connections and notintended to produce a physiological effect• 0 Hz – 0.1 Hz : 0.01 mArms
• 0.1 Hz – 1 kHz : 0.1 mArms
• 1 kHz – 100 kHz : 0.1 × f (in kHz) mArms
• Above 100 kHz : 10 mArms
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Limitation in Injection Current Therapeutic current (IEC 601-2-10) is defined as
functional current from nerve or muscle stimulator• 0 Hz – 0.1 Hz : 80 mArms
• 0.1 Hz – 400 Hz : 50 mArms
• 400 Hz – 1500 Hz : 80 mArms
• Above 1500 Hz : 100 mArms
• For pulse duration < 0.1 s, pulse energy < 0.3 J
• Pulse voltage < 500 V
Diagnostic current in dentistry and ophthalmology(IEC 601-2-10)• 10 mArms
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Limitation in Injection Current Threshold to stimulate a nerve with 20 µm diameter
(McRobbie and Foster, 1984)• 1 A/m2 below 1 kHz
• 2.5 mA through 5×5 cm2 uniform current density electrode
Conventional Electrode Uniform Current Density Electrode
(σ = 0.17 S/m) (σ = 0.17 S/m)
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Noise in MREIT Random Noise in MR Phase Image
Noise Standard Deviation in Bz, • Current injection time, Tc• Magnitude image SNR, ΨM
Typical Values
Factors Affecting sBz• Performance of current source• Performance of MRI scanner including RF coils• Pulse sequence• MR imaging parameters
12zB
c M
sTγ
=Ψ
6 2
1 3.4 [nT]2 41.065 10 [rad/s/T] 10 [s] 500zBs
−= =
× × × ×
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Applications Pathological changes related with conductivity
• Brain tumor• Breast tumor• Prostate tumor
Brain functions• Conductivity changes associated with neural activity• Conductivity changes related with brain injury, stroke,
epilepsy, tumor, and others Provide conductivity values to source imaging
problems in EEG, MEG, and ECG Planning and optimization of treatments using
electromagnetic energy Applications in biology and chemistry
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Directions Maximize signal and minimize noise
• Optimize current source • Optimize electrode configuration• Optimize pulse sequence and imaging parameters• Increase current pulse width• Increase averaging (low temporal resolution)• Increase pixel size (low spatial resolution)• Improve RF coil• Use high-field high-performance MRI system
Reduced FOV and ROI imaging
Denoising techniques and hybrid algorithms
Reduce Imaging Current!
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Multi-echo Pulse Sequence
Tc2
Tc1
Tc2
Tc1
Tc2
Tc2
Tc2
Tc1
90° 180° Echo 180° Echo 180° Echo
Spin echo
ICNE
Multi -echo
Injection current
Data acquisition
TE/2 TE 2TE 3TE
90° 180° Echo
90° 180° Echo
TE/2 TE
TE/2 TE
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
b-SSFP Pulse Sequence
RF pulse
GS
GP
GR
I
TRα < 900
( ) ( )( ) ( ) ( ) ( )( ) ( ) ( )( ) ( )
( ) ( ) ( ) ( )
1 1 2 2
1 2 2 1 2
0 1 2
0 1 2
2 2 20 12 2
( )
exp / , exp /
1 cos 1 cos cos cos
1 sin 1 cos /
1 sin sin /
1 sin, 1 2 cos
( , ) ( , ) x y
y
x
x y
j xm k yn kj
E TR T E TR T
D E E E E E
M M E E D
M M E E D
M EM x y M M E E
D
S m n M x y e e dxdyφ
α θ α θ
θ α θ
θ α θ
αθ
∞ − ∆ + ∆
−∞
= − = −
= − − − − −
= − −
= −
−= + = + −
= ∫ ∫
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
High-sensitivity RF Coils• Sodickson D K and Manning W J 1997 Simultaneous
acquisition of spatial harmonics (SMASH): fastimaging with radiofrequency coil arrays Magn. Reson.Med. 38 591-603
• Wiggins G C, Polimeni J R, Potthast A, Schmitt M,Alagappan V and Wald L L 2009 96-channel receive-only head coil for 3 Tesla: design optimization andevaluation Magn. Reson. Med. 62 754-62
• Mekle R, van der Zwaag W, Joosten A and Gruetter R2008 Comparison of three commercially availableradio frequency coils for human brain imaging at 3Tesla Magn. Reson. Mater. Phy. 21 53-61
• Hiratsuka Y, Miki H, Kikuchi K, Kiriyama I, Mochizuki T,Takahashi S and Sadamoto K 2007 Sensitivity of aneight-element phased array coil in 3 Tesla MR imaging:a basic analysis Magn. Reson. Med. Sci. 6 177-81www.medical.siemens.com
32 channel 64 channel
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
New Techniques in MRI•Scheffler K 2004 Fast frequency mapping with balanced SSFP: theory and applicationto proton-resonance frequency shift thermometry Magn. Reson. Med. 51 1205-11
•Klarhofer M, Barth M, Moser E 2002 Comparison of multi-echo spiral and echo planarimaging in functional MRI Magn. Reson. Imaging 20 356-64
•Ge Y, Korogi Y, Sugahara T, Shigematsu Y, Hirai T, Kitajima M, Liang L, Dai J andTakahashi M 2001 Comparison between EPI and HASTE for ultra-fast MR imaging ofthe human brain Neuroradiol. 43 1046-55
•Candes E, Romberg J and Tao T 2006 Robust uncertainty principles: exact signalreconstruction from highly incomplete frequency information IEEE Trans. Inf. Theory52 489-509
•Donoho D 2006 Compressed sensing IEEE Trans. Inf. Theory 52 1289-1306•Santos J M, Cunningham C H, Lusting M, Hargreaves B A, Hu B S, Nishimura D Gand Pauly J M 2006 Single breadth-hold whole-heart MRA using variable-densityspirals at 3T Mag. Res. Med. 55 371-379
•Block K T, Uecker M and Frahm J 2007 Under-sampled radial MRI with multiple coils:iterative image reconstruction using a total variation constraint Mag. Res. Med. 571086-1098
•Lusting M, Donoho D and Pauly J M 2007 Sparse MRI: the application of compressedsensing for rapid MR imaging Mag. Res. Med. 58 1182-1195
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Towards Neuro-imaging
MRI-compatible EEG
MRI-compatible EIT
MREIT• Low-noise high-performance MRI system at 3 or 7 T• Uniform current density electrode, electrode configuration,
and low-noise current source• Sensitivity enhancement by improvements in RF coil and
pulse sequence • Fast imaging method• Denoising, image reconstruction, and anomaly detection
algorithms• Functional imaging protocol and statistical image analysis
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Outlook: Multi-modal Approach
MRI-MREIT-EIT-
EEG
Multi-modal
Neuro-imaging
• MR image
• Surface voltage map
• Magnetic flux
density image
• Conductivity image
• Current density
image
• Current source
image
Surface voltage (EEG)- Endogenous- Spontaneous or evoked- 10-6 – 10-5 V
Surface voltage (EIT)- Exogenous- Spontaneous or evoked- 10-4 – 10-3 V
Internal magneticflux density (MREIT)- Exogenous- Spontaneous or evoked- 10-10 – 10-8 T
Geometry andother information (MRI)- Endogenous- Spontaneous or evoked
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Collaborators at IIRC
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011
Acknowledgement
National Research Foundation (NRF) of Korea• Impedance Imaging Research Center (IIRC)
• Ion Conduction Imaging Group
Kyung Hee University
Researchers at IIRC• Mathematicians
• Engineers
• Biologists and clinicians
International Collaborators
IIRC, KHU Magnetic Resonance Electrical Impedance Tomography (MREIT) May 2011