Basics of Bioimpedance and Admittivity Imaging

1. Basics of Bioimpedance and Admittivity Imaging Eung Je Woo Impedance Imaging Research Center (IIRC) Department of Biomedical Engineering, Kyung Hee University KOREA http://iirc.khu.ac.kr

2. Fundamental Quantity • Length (dimension or size) in meter (m) • Time (sequence or duration or interval) in second (s) • Mass in kilogram (kg) • Charge in coulomb (C) • Temperature in kelvin (K) • Amount of substance in mole (mol) • Luminous intensity in candela (cd) • Mechanics • Electromagnetics • Optics • Thermodynamics • Chemistry

3. Charged Particle and Charge Density • Free electron and hole are mobile • Unbounded ion and molecule are mobile • Bounded atom and molecule are immobile but may vibrate • Polar molecule hasno net charge but dipole moment and may rotate • Mass • Charge • Size • Position

4. Field • Space with nothing • Space with a single charged particle • Space with two charged particles • Space with multiple charged particles • Space with a charge density distribution Qr z r y x Q 0

5. Potential or Voltage • Space with electric field E(r) • Put a point charge at r1 from the infinity (a reference point) • Move the point charge from r1 to r2 E(r) Qr Qr r1 r2

6. Conductivity and Resistance I I S l I I

7. Permittivity and Capacitance +Q -Q S - - - - - - - - - + + + + + + + + + l - - - - - - - - - + + + + + + + + + -Q +Q

8. Polarization, Permittivity and Capacitance +Q -Q S - - - - - - - - - + + + + + + + + + l - - - - - - - - - + + + + + + + + + -Q +Q

9. Cell and Bio-impedance Extra-cellular Fluid Cell Membrane + + + + + _ _ _ + _ + _ _ _ + + _ + _ + + + + _ _ _ _ _ Intra-cellular Fluid

10. Conductivity and Permittivity of Tissues Extra-cellular Fluid Intra-cellular Fluid Cell Membrane

11. Conductivity and Permittivity of Tissues • Tissues themselves • Molecular composition of cells • Shape and density of cells • Direction of cells • Concentration and mobility of ions • Amounts of intra- and extra-cellular fluids • Amplitude and frequency of current • Temperature

12. Hepatic Tumor Conductivity Necrosis Fibrosis Normal Cells Tumor D. Haemmerich, S. T. Staelin, J. Z. Tsai, S. Tungjitkusolmun, D. M. Mahvi and J. G. Webster, “In vivo electrical conductivity of hepatic tumours,” Physiol. Meas., vol. 24, pp.251–260, 2003.

13. Breast Tumor Conductivity Normal Tissue Lobular Carcinoma Ductal Carcinoma A. J. Surowiec, S. S. Stuchly, J. R. Barr, and A. Swarup, ”Dielectric properties of breast carcinoma and the surrounding tissues,” IEEE Trans. Biomed. Eng., vol. 35, no. 4, pp. 257–263, 1988.

14. 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 3-5% local conductivity changes at low frequency.

15. Amplifier ECG Bio-electric Signal and Source Imaging Medical Instrumentation: Application and Design, 3rd ed., by J. G. Webster

16. Bio-magnetic Signal and Source Imaging MEG f(r;t) J(r;t) W

17. Defibrillation and Cardioversion R. S. Yoon, T. P. DeMonte, and M. L. G. Joy, “Measurement of thoracic current flow in pigs for the study of defibrillation and cardioversion,” IEEE Trans. Biomed. Eng., vol. 50, no. 10, pp. 1167-1173, 2003.

18. Transcranial Electrical Stimulation M. L. G. Joy,V. P. Lebedev, and J. S. Gati, “Imaging of current density and current pathways in rabbit brain during transcranial electrostimulation,” IEEE Trans. Biomed. Eng., vol. 46, no. 9, pp. 1138-1148, 1999.

19. Motivation and Goal • Physiological functions and pathological changes alter conductivity and permittivity values. • Neural activity induces changes in conductivity. • Source imaging needs conductivity values. • Electromagnetic stimulations need conductivity values. Cross-sectional Imaging of Conductivity, Permittivity and Current Density Distribution

20. i Ip=Im0 p Vq=RpqIm0 Zpq=Rpq0 s q V Trans-resistance • Rpqdepends on • electrode configuration • conductivity distribution, s • geometry (boundary shape and size)

21. Ip=Im0 Zpq=Zpq Vq=ZpqIm i p q V s+jwe Trans-impedance • Zpqdepends on • electrode configuration • complex conductivity distribution, s+jwe • geometry (boundary shape and size)

22. KHU Mark1 mfEIT System 16-Channel System 32-Channel System T. I. Oh, E. J. Woo, and D. Holder, “ Multi-frequency EIT system with radially symmetric architecture: KHU Mark1,” Physiol. Meas., 28, pp. S183-96, 2007. T. I. Oh, K. H. Lee, S. M. Kim, W. Koo, E. J. Woo, and D. Holder, “Calibration methods for a multi-channel multi-frequency EIT system,” Physiol. Meas., 28, pp. 1175-88, 2007. T. I. Oh, W. Koo, K. H. Lee, S. M. Kim, J. Lee, S. W. Kim, J. K. Seo, and E. J. Woo, “Validation of a multi-frequency electrical impedance tomography (mfEIT) system KHU Mark1: impedance spectroscopy and time-difference imaging,” Physiol. Meas., 29, pp. 295-307, 2008.

23. KHU Mark2 mfEIT System • Multiple current sources • Multiple voltmeters • No pre-determined electrode configuration • Wide bandwidth • Compact design

24. Boundary Current and Voltage

25. Contact Impedance Two-electrode Method Four-electrode Method

26. Data Collection Protocol Neighboring Method

27. Reciprocity

28. Neumann-to-Dirichlet Data

29. Linearity and Nonlinearity • Linearity between current and voltage for a fixed g • Linearity between voltage and cg for a fixed g • What are nonlinear?

30. i p q V s+jwe Complex Conductivity Problem

31. i Ip=Im0 p Zpq=Zpq Vq=ZpqIm q V s+jwe Complex Conductivity Problem

32. Multi-frequency Data Collection jth Current i j j+1 k+1 kth Voltage V s+jwe k

33. Mathematical Expressions • Injection current, voltage and complex conductivity • Current density • Magnetic flux density

34. 2 [ Tesla] [ mA /mm ] Bx Jx x x y y [S/m] 2 [ Tesla] [ mA /mm ] By Jy x x y y [ Tesla] 2 [ mA /mm ] Bz Jz x x y y Forward Solver: Example using FEM s x y [ mV] u x y 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.

35. + + - - Forward Solver: Example using FEM • White lines are current stream lines. • Black lines are equipotential lines.

36. Forward Solver: Example using FEM • White lines are current stream lines. • Black lines are equipotential lines. + + - -

37. Equipotential Lines at 100 kHz Saline Banana v (real part) h (imaginary part)

38. Voltage and Current Density

39. EIT using Boundary Measurements Neumann (Boundary Current) Dirichlet (Boundary Voltage)

40. Problem Definition in EIT S I L

41. tdEIT Imaging: Human Thorax

42. Subject Computer Model Injection Current gk g* Data Acquisition System Forward Solver Image Reconstruction Algorithm Measured Boundary Voltage Computed Boundary Voltage Static Imaging in EIT

43. Static Imaging in EIT • Image of absolute value of complex conductivity (s + iwe) • Must overcome the following problems • Geometry is unknown and varying. • Electrode positions are unknown and varying. • Very accurate forward model is needed. • Higher degree of measurement accuracy is needed.

44. Difference Imaging in EIT • Image of change in complex conductivity with respect to time and/or frequency • Common systematic errors can be cancelled out • Unknown boundary geometry • Uncertainty in electrode position • Systematic artifacts • Applications are limited but there are enough of them

45. Difference Imaging in EIT • If conductivity changes as boundary voltage changes accordingly as • When dg is small, • Then, a difference image of dg is obtained as Time-difference (tdEIT) Frequency-difference (fdEIT)

46. tdEIT Algorithm • Linearization • Misfit Functional • Algorithm

47. : homogeneous complex conductivity at w1 and w2 : complex voltage with : frequency-difference image between w1 and w2 fdEIT Algorithm

48. Perturbation and Sensitivity qth Pixel gq= 1+1=2in Lq g = s+jwe = 1

49. Sensitivity and Linearization g = Dxin Lx g = Dyin Ly

50. Sensitivity Matrix and Lineariztion - E electrodes - Q pixels