1. LORENTZ FORCE ELECTRICAL IMPEDANCE TOMOGRAPHY
Numerical Analysis and Scientific Computing: Workshop in Honour of Bülent Karasözen's 67th Birthday, 24 November 2017
LORENTZ FORCE ELECTRICAL IMPEDANCE TOMOGRAPHY
Nevzat Güneri Gençer
METU Bioelectromagnetism Research Group (METU BERG)
Department of Electrical and Electronics Engineering, Middle East Technical University (METU)
06800, Çankaya, Ankara, TURKEY

2. Bioelectromagnetism Research Group
Electromagnetic Source Imaging (EMSI)
Bioelectromagnetism Research Group
Lorentz Force Electrical Impedance Tomography (LFEIT)
Magnetic Induction Tomography (MIT)
Biomedical electronics, Signal processing, Numerical Modelling
Implantable Neurostimulators
Harmonic Motion Microwave Doppler Imaging (HHMDI)

3. LFEIT Research Group

4. Medical Imaging
Energy Types:
X-ray
Nuclear (radio-isotope) sources,
Ultrasonic waves,
Magnetic fields,
Electrical currents,
Mechanical,
Optical waves etc.
Collection of techniques, developed to measure and display distribution of a physical property in living subjects, specifically in humans.
Physical properties:
X-ray absorption coefficient,
Radionuclide concentration,
Ultrasonic properties,
Spin density and spin relaxation,
Electromagnetic properties,
Mechanical properties,
Optical properties.
It is used for diagnosis, to assist in treatment planning, and for monitoring the treatment

5. Medical Imaging Modalities
SPECT CT
DUAL
ULTRASOUND
MRI

6. Diagnosis of breast cancer
MAMMOGRAPHY 2
Women check breast for
any sign of breast cancer. 1
ULTRASONOGRAPHY 3 4

7. Facts and Acts
About 1 in 8 U.S. women (about 12%) will develop invasive breast cancer over the course of her lifetime.
In 2017, an estimated 252,710 new cases of invasive breast cancer are expected to be diagnosed in women in the U.S.
About 40,610 women in the U.S. are expected to die in 2017 from breast cancer.
As of March 2017, there are more than 3.1 million women with a history of breast cancer in the U.S. (US Breast Cancer Statistics)
New imaging modalities must be developed
for early stage diagnosis of breast cancer.
These modalities should
Have high resolution,
Have better contrast in soft tissues,
Be portable,
Use non-ionizing energy,
Not provide disconfort during application
Be economical (lower device cost and lower
service cost)
Be fast (should acquire data in shortest time)

8. Electrical Properties of body tissues
Advantages:
Electrical properties change from tissue to tissue.
Contrast among tissues is superior.
Tissues can be better distinguished.
Electrical properties change depending on the health
of the tissue.
Electrical impedance images can be used for diagnosis.
Electrical properties are a function of frequency.
Several electrical impedance images of the same body
can be generated depending on the applied frequency.
Devices proposed to image electrical properties are cheap
most of them are portable. F

9. Electrical Impedance Imaging techniquesV
𝐼 𝑒 𝑗𝑤𝑡 
Induced Current EIT V 
Applied Current EIT
𝐼 𝑒 𝑗𝑤𝑡  𝐵
Magnetic Induction Tomography (MIT)
In some clinical applications EIT is used as:
Monitoring of lung function
Detection of cancer in skin and breast
Location of some epileptic foci.
Monitoring of cerebral ischemia and hemorrhage
All these techniques are slow
and produce low resolution
images!

10. Other techniques that use MRI
MREIT
To improve spatial resolution magnetic resonance electrical impedance tomography (MREIT) has been proposed (İder and Birgül, 1998). Similar to EIT, current is injected into the body through surface electrodes. Magnetic fields generated inside the body are measured using MRI.
Major limitation is the amount of current applied to the body. The required current may stimulate the muscles and nerves during examination.
MREPT
Magnetic resonance electrical properties tomography (MREPT) has been recently proposed to image electrical properties at the Larmour frequency of an MRI system (Katscher et. Al, 2009). This method has advantages over the MREIT that no electrode is attached to the body, no other hardware is required.

11. Lorentz Force Electrical Impedance Imaging
This technique is based on electrical current induction using ultrasound together with an applied static magnetic field (Wen 1998).
The magnetic field intensity generated due to induced currents is sensed using coils nearby the body surface (Zengin and Gencer, 2016).
A time-varying voltage is picked-up and recorded while the acoustic wave propagates along its path.
The forward problem of this imaging modality is defined as calculation of the pick-up voltages due to a given acoustic excitation and known body properties. 
p : pressure (Pa)
V : particle velocity
E : electric field (V/m)
B : magnetic field intensity (T)
B0 : static magnetic field (T)
 : electrical conductivity
V : body volume
S : surface

12. Multiphysics Forward Problem
Acoustic Problem
Electromagnetic Problem
Solution of potential and current density distribution in the conductive body due to Lorentz currents
Solution of pressure distribution inside the body due to surface acceleration

13. Acoustic Problem Wave equation taking into account Lorentz forces:
(Current density)
Boundary condition:
acceleration
particle velocity

14. Electromagnetic Problem
Operation frequency f = 1 MHz
Maximum field distance R = 0.1 m
Displacement currents are much
small compared to conduction
currents
Inductive effects are negligible,
Propagation effects are negligible
Arbitrary time dependence
Time Harmonic Excitation

15. t=10 s
t=25 s
Pressure distribution
Velocity current density

16. Numerıcal sımulatıons

17. Reciprocal Problem formulation
The relation between the magnetic measurements and acoustic waves was obtained as (Zengin and Gencer, 2016):
𝑣 𝑎𝑏 𝑡 = 𝑣 𝑏𝑜𝑑𝑦 𝜕 𝜕𝑡 𝜎 𝑣 𝑡 × 𝐵 ∙ 𝐸 𝑅 0 (𝜎) dV
𝑣 𝑎𝑏 𝑡 : induced voltage in the detector coil
𝜎: conductivity of the tissues
𝑣 𝑡 : particle velocity
𝐵 : magnetic flux density
𝐸 𝑅 0 𝜎 : the reciprocal electric field
The magnetic field measurement approach of MAET problem1. 𝐼 𝑅 𝑡 is the reciprocal current.
1 R. Zengin and N. G. Gencer, Lorentz force electrical impedance tomography using magnetic field measurements,
IOP Physics in Medicine and Biology, 61 (16), 2016,

18. (Karadaş, 2014)

19. Alternative coil configurations
(Zengin and Gencer, 2016)

20. The receiver voltages are calculated using two methods:
using the derived lead field equation, and
using the time derivatives of the flux density inside the coil area.
There are two peaks in the induced voltage at about 15 μs and 18 μs. These two time instants match with the travel time from the LPA transducer to the upper and bottom edge of the tumorous tissue.
(Zengin and Gencer, 2016)

21. Inverse Problem

22. İleri Problemin doğrusallaştırılması
Around an initial conductivity distribution (0) :
Conductive body is discretized and represented by N elements:
M samples are acquired in the data acquisition period:
S MxN sensitivity matrix

23. Numerical Model Transducer Excitation:
Mesh view
Transducer Excitation:
A Linear Phased Array (LPA) ultrasonic transducer with 16-element PZT-5H material
A sinusoidal Voltage (𝑉 𝑡 =100𝑠𝑖𝑛(2𝜋𝑓𝑡)) with a period of resonance frequency 𝑓=1 𝑀𝐻𝑧 is applied to the surface of each piezoelectric crystal.

24. System configuration
Body is a 5×5 cm square area divided into 0.5 mm × 0.5 mm elements yielding pixels.
LPA is assumed at two positions, namely, the upper and the left edges of the body.
For each transducer position, data is acquired for eleven steering angles (-25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25).
The data acquisition period for each steering angle is 32.8 s.
Data are sampled with 0.1 s intervals.
At a given steering angle, 328 measurements are acquired by each receiver coil.
For the two transducer positions and a single receiver coil, the resultant sensitivity matrix S is of dimension 7216x10000.

25. Body geometry and transducer positions

26. Reconstructed images Rectangular coil xy coil
Rectangular and xy coil
(Zengin and Gencer, 2016)
S/N = 80 dB

27. Image sensitivity maps
(Zengin and Gencer, 2016)

28. Simulations on breast model
Simplified 2D Breast geometry2.
2 M. N. Sudarshan, E. Y. Ng, and S. L. Teh, Surface temperature distribution of a breast with and without tumour, Computer Methods in Biomechanics and Biomedical Engineering, 2 (3), 1995,

29. Image Reconstruction rectangular loop coil, 80 dB SNR
Truncated singular decomposition (SVD) method for image reconstruction
Image
Sensitivity
Map

30. ExperImental StudIes

31. Measurement of magnetic LFEIT signals: First attempt (Karadaş, 2014, METU BERG)
Coil Type
Turn Numbers
Core
Mean Diameter
(cm)
Phantom
Oil
Conductivity
(S/m)
Saline Water Conductivity
Disk Multiple Layer Coil 70
Air Cored 2
Oil-saline Water
0.6
0.2
Mursel: In an experimental study for LFEIT using magnetic field measurements, a simple set up was established and experiments were conducted using a simple phantom. A low amplitude burst sinusoidal signal (5 cycle, 1 MHz) with repetition period of 1 ms was applied to an ultrasound transducer (Olympus A-303-SU) yielding a pressure level of 0.6 MPa in the body. A custom made Neodymium magnet configuration was used to apply a static magnetic field of 0.2 T. A multilayer (70 turns) air coil sensor of diameter 2 cm was employed for measurements. However, measurements from an oil ((2-10)× 10-9 S/m)-saline water (2-4 S/m) phantom did not show any evidence of LFEIT signals [11].
Amplitude (Vpp)
Signal Type
Cycle
Frequency (MHz)
TR (ms)
Transducer Type
Pressure Level (kPa)
B0 (T)
300
Burst 5 1
Single Element
Olympus A-303-SU
600
0.2

32. Recent Work (Kaboutari et. al., 2017, METU BERG)

33. Static magnetic field (B0) generation
A new permanent magnet configuration is used to obtain a stronger magnetic field.
Generated magnetic field distribution in the central plane. Neodymium magnets (grade N45) are used for magnetic field generation.
Magnets setup with iron core.

34. MAET experiment setup 48.4 cm Iron core 31 cm 11.06 cm 16 cm
LPA Transducer
31 cm
Permanent magnets
Phantom
11.06 cm
16 cm
Receiver sensor coil
9 cm
6.4 cm
5.85 cm
15 cm

35. LFEIT experiment setup: ultrasound system and data acquisition card

36. Receiver coil sensor Physical properties of the receiver coil Sensor I
Min
VInd.
(nV)
measurable B
(pT)
Coil sensor
44.73
0.13
Electrical properties of the receiver coil Sensor I B
(pT)
VInd.
(μV)
Vout
(mV)
VTh
(nV)
Sensitivity At
1 MHz
SNR at
Coil sensor 10
3.45
0.1
31.67
4.36 n 𝑽 𝑻
40.75 dB

37. Phantoms Phantoms Amount of materials in the agar-gel phantom
Water
(ml)
Agar
(mg)
Gelatin
100
1.5 3
Acoustic properties
of phantom’s materials
Oil
(m/s)
Solder
Graphite
1450 **
5120
4170
Phantoms
Layer one
Layer 2
Layer 3
Depth of boundary
(mm)
Object size
Conductivity
(S/m)
Phantom I
Oil
Solder disk
Agar-Gel
Paper 45
20 *
8 × 106
Phantom II
Graphite bar
5 × 5
Phantom III
15% Hydrochloric solution acid - 46 32 70
Phantom IV 48

38. LFEIT signal obtained from phantom III

39. LFEIT signal obtained from phantom IV

40. Construction of data profile from phantom IV
Ultrasound transducer steers acoustic wave front form -20 degree to 20 degree in 1 degree step.
Ultrasound transducer is excited 8000 times (5 periods, 1 MHz) sinusoidal wave for each angle.
In each angle, data acquisiton card (DAQ card) takes the average of 8000 received signal.
For each steering angle, there are 6144 samples.
Each signal is placed on a column with respect to its angle in an order. A 2D matrix whose size is 6144 × 41 is obtained (column wise data profile).
2D polar coordinate data profile is also obtained by placing each signal to the related angle position.

41. Obtained LFEIT signals from -20˚ to 18˚ by 2˚ step

42. Data profile of LFEIT and B-scan from phantom IV
Column wise data profile of LFEIT signal
Column wise data profile of B-scan

43. Data profile of LFEIT and B-scan from phantom IV
Polar data profile of LFEIT signal
Polar data profile of B-scan
Phantom IV geometry

44. Conclusion and Discussion
Theoretical and numerical studies
In this study, magnetic field measurement technique for LFEIT was investigated to image electrical conductivity of body tissues.
The initial phase of this study was to reveal the theory and basic assumptions behind the forward problem of MAET.
Integral expressions were derived relating pick-up voltages to the conductivity distribution of the body for two different excitations, namely, the time harmonic excitation and pulse type excitation.
To understand the feasibility of this imaging modality, the forward problem was investigated numerically using COMSOL Multiphysics software.
 In this computer simulation, a conducting body representing the breast fat and tumors were assumed. 

45. Conclusion and Discussion
A 16-element LPA transducer (1 MHz) was attached on the upper and left edge of the body surface and excited with a single cycle sinusoid (100 V peak). The body was assumed to be in 4 T static magnetic field. 
It can be concluded that with this imaging system a conductivity perturbation with 5 mm x 5 mm size up to 3.5 cm depth can be detected.
B) Experimental Studies
LFEIT measurement set up is developed using a 16 element LPA ultrasound transducer. A static magnetic field of 0.56 T is generated using permanent magnets.

46. Conclusion and Discussion
A static magnetic field of 0.56 T is generated using permanent magnets.
Design tools are developed to design coils for magnetic measurements.
Four phantoms were prepared to measure LFEIT signals.
LFEIT signals of a phantom whose conductivity was about 70 S/m (minimum conductivity difference), at a depth of 46 mm were detected by the realized coil sensor.
Minimum measured LFEIT magnetic field is 0.13 pT.
LFEIT signals were measured from top surface of the graphite phantom by steering acoustic wavefront from -20 to 20 degree. These signals were placed side by side to construct images showing the location of inhomogeneities.
By increasing gain of amplifier (120 dB) and quality factor of coil sensor, measurement of LFEIT signals from tissue mimicking phantoms seems possible.

47. Acknowledgement
The Scientific and Technological Research Council of Turkey (114E184)
COST Action BM1309: European network for innovative uses of EMFs in biomedical applications (EMF-MED)

48. Thank you for your attention.