Active B 1 Imaging Using Polar Decomposition RF-CDI

Transcription

1 Active B 1 Imaging Using Polar Decomposition RF-CDI Weijing Ma, Nahla Elsaid, Dinghui Wang, Tim DeMonte, Adrian Nachman, Michael Joy Department of Electrical and Computer Engineering University of Toronto

2 Outline t Background t Methodology t Magnetic field measurement t Current density field calculation t Experimental Validations t Active B 1 measurement and comparison with double-angle B 1 mapping t Phantom experiments with disturbance pulses t Phantom experiment with injected currents t Conclusions and Discussions 2

3 Background: Current Density Imaging t Current Density Imaging (CDI) is a technique that non-invasively measures current densities in a volume using Magnetic Resonance Imaging (MRI). t Current is applied externally. t Low Frequency Source (5-1 Hz) -LFCDI t Radio Frequency Source (64 MHz) -RFCDI 3

4 Background: Current Density Imaging t Current Density Imaging (CDI) is a technique that non-invasively measures current densities in a volume using Magnetic Resonance Imaging (MRI). t Current is applied externally. t Low Frequency Source (5-1 Hz) -LF-CDI t Radio Frequency Source (64 MHz) -RF-CDI 4

5 Background: Polar Decomposition RF-CDI t RF-CDI Methods: RF-CDI Rotary Echo RF-CDI Polar Decomposition RF-CDI t Limitations of Rotary Echo RF-CDI t Magnitude of the injected current is restricted; t Inevitable systematic artifacts and high SAR. t Limitations of previous Polar Decomposition RF-CDI t Low SNR due to phase-wrapping and axis flips. 5

6 Flowchart: How PD-RFCDI works Injected Current Density J Induced Magnetic Field H Changes in Local Magnetic Fields Magnetization variations w.r.t. Position Reconstructed J with J = H Reconstructed Magnetic Field H Encoded MRI Images 6

7 Polar Decomposition RF-CDI: Methodology PD-RFCDI consists of two important reconstruction steps: t Part 1: to measure the magnetic field from the rotation of magnetization measured by MRI; t Part 2: to compute current density field from the measured magnetic field. 7

8 Flowchart: How PD-RFCDI works Injected Current Density J Induced Magnetic Field H Changes in Local Magnetic Fields Magnetization variations w.r.t. Position Reconstructed J with J = H Reconstructed Magnetic Field H Encoded MRI Images 8

9 Polar Decomposition RF-CDI: Methodology (part 1) How to measure the magnetic field from the rotation of magnetization? t Bloch s Equation: M M x M y M H t T T T = γ M z M z ( µ L ) z x y Current-induced Magnetic Field Component t Physical Interpretation: Magnetization Mrotating about the rotation axis: t Magnitude of H determines the rotation angle; t Orientation of H determines the rotation axis. 9

10 Polar Decomposition RF-CDI: Methodology (part 1) How to measure the magnetic field from the rotation of M? t Answer: to measure the rotation angle and axis of M. How to measure the rotation angle and axis of M? t Answer: three steps 1. Polar Decomposition; 2. Quaternion operation; 3. Dual-unwrapping. 1

11 Polar Decomposition RF-CDI: Methodology (part 1) How to measure the magnetic field from the rotation of M? t Answer: to measure the rotation angle and axis of M. How to measure the rotation angle and axis of M? t Answer: three steps 1. Polar Decomposition; 2. Quaternion operation; 3. Dual-unwrapping. 11

12 Polar Decomposition RF-CDI: Methodology (part 1) t Polar Decomposition: to extract rotation matrix from snapshots of the starting and ending positions of M. M M M M x y z x x x C x y z M D M y M y M y x y z M M z M z M z 12

13 Polar Decomposition: Rotation and Relaxation Decoupling wtop: The x and y components of M from the Maxwell- Bloch simulation. wbottom: The x and y components of M after polar decomposition. w9% decrease in the discontinuity between the left and right halves after the polar decomposition.

14 Polar Decomposition RF-CDI: Methodology (part 1) How to measure the magnetic field from the rotation of M? t Answer: to measure the rotation angle and axis of M. How to measure the rotation angle and axis of M? t Answer: three steps 1. Polar Decomposition; 2. Quaternion operation; 3. Dual-unwrapping. 14

15 Polar Decomposition RF-CDI: Methodology (part 1) t Quaternion operation: t Extracts rotation angle and rotation axis information from the rotation matrix. t Introduces phase wraps and axis false-flips in regions where rotation angles reach multiples of π. t Dual-unwrapping: t Unwraps the rotation angle and rotation axis that have been falsely interpreted in quaternion conversion. 15

16 Dual-unwrapping: unwrapping: Flood-fill algorithm t Start from initial seed point A t remove false flips and phase wrapsin the neighborhood t Find the next pixel with the highest quality value t Set it to be the next seed point t Probe the neighbourhood of the new seed point, remove false flips and phase wraps 1 1 A 1 B

17 Dual-unwrapping: unwrapping: simulations Rotation angle x y z components of rotation axis 17-1

18 Flowchart: How PD-RFCDI works Injected Current Density J Induced Magnetic Field H Changes in Local Magnetic Fields Magnetization variations w.r.t. Position Reconstructed J with J = H Reconstructed Magnetic Field H Encoded MRI Images 18

19 Polar Decomposition RF-CDI: Methodology (part 2) How to compute current density field from the magnetic field?. t Current Density field Jis calculated by taking the curl of magnetic field H: J = H. t When single orientation assumption H z z J z is met, current densities can be computed through l l l l H% j z y H ϕ H% x H% % x y J z = jze = j + x y x y t Conclusion: only the transverse magnetic field components are required to compute the longitudinal component of RF current density vectors. 19

20 Outline t Background t Methodology t Magnetic field measurement t Current density field calculation t Experimental Validations t B 1 measurement and comparison with doubleangle B 1 mapping t Phantom experiments with disturbance pulses t Phantom experiment with injected currents t Conclusions and Discussions 2

21 B + 1 Validations: Double Angle vs. PD-RFCDI t Double angle B 1 mapping method: t Conceptually simple t Straightforward implementation t One of the gold standards for active B 1 mapping t Experiment settings: t A GE manufactured acrylic phantom was used. t GE bird cage head coil used as transmit/receive. t Flip angles α 1 = 2 ο and α 2 = 4 ο t Excitation pulse of PD-RFCDI was calibrated to match the parameters in the double angle method. 21

22 B + 1 Validations: PD-RFCDI v.s. Double Angle Comparison of the measured flip angle using polar decomposition method (left) and the double angle mapping methods (right) 22

23 B + 1 Validations: Double Angle vs. PD-RFCDI PD-RFCDI is able to measure the phase information of the active B 1 field 23

24 Polar Decomposition RF-CDI with Disturbance Pulses t A hard 9 pulse was applied to the RF excitation coil to create a 9-degree tip angle. t The experiment was conducted on a GE manufactured acrylic phantom Rotation angle x y z components of rotation axis 24-1

25 Polar Decomposition RF-CDI with Disturbance Pulses t A disturbance pulse was applied to the gradient X coil to create a linearly increasing magnetic field along the x-axis. t Pulse duration was 8.2 ms and the relative pulse amplitude was Rotation angle x y z components of rotation axis 25-1

26 Polar Decomposition RF-CDI with Injected Current t Experiment settings RF pre-amplifier RF excitation pulse MRI scan system trigger signal SSR control switch trigger signal imaging pulses RF current control box Saline filled phantom Turn on/off injected current RF amplifier Matching network Feeding wires of the phantom 26

27 Polar Decomposition RF-CDI: Phantom Experiment t Phantom settings t Three-chamber phantom; t Copper electrodes covering only the inner two chambers; t Center chamber filled with conductive saline; t Outer two chambers filled with CuSO 4 doped water. 27

28 Polar Decomposition RF-CDI with injected current t Current magnitude and phase vary from the inner to the outer chamber; t Consistent reconstruction results with comparison to the FDTD simulation Current magnitude Current phase -3 28

29 Updated Flowchart: How RF-CDII works Injected Current Density J Induced Magnetic Field H Changes in Local Magnetic Fields Impedance distribution 18 rotation RF-CDII formula Magnetization variations w.r.t. Position Reconstructed J with J = H Reconstructed Magnetic Field H Encoded MRI Images 29

30 Conclusions and Discussions In this work, we have: t compared PD-RFCDI with the double angle B1 mapping method to confirm the validity of PD-RFCDI measurements. t conducted the phantom experiments that showed PD-RFCDI is able to detect disturbances applied through RF and gradient coils; t performed the phantom experiment with injected currents on a commercial scanner; t proved that the new, improved PD-RFCDI is able to reconstruct currents of a much larger dynamic range. Future work includes: t to perform full vector PD-RFCDI experiment with 18 rotations; t to implement RF impedance imaging algorithm (RF-CDII) with the measured RF current information. 3

31 References G. C. Scott, PhD thesis, Univ. of Toronto, M. L. G. Joy, G. C. Scott, R. M. Henkelman, In-Vivo Detection of Applied Electric Currents by Magnetic Resonance Imaging, Magn. Reson. Imag., vol. 7, pp , W. Ma, PhD thesis, Univ. of Toronto, 21. E. K. Insko et al, Mapping of the Radiofrequency Field, J. Magn. Reson. 13:82 85, R. Stollberger, et al, Imaging of the Active B1 Field in Vivo. Magn. Reson. Med. 35: , D.I. Hoult et al, Sensitivity and power deposition in a high-field imaging experiment, J Magn Reson Imag. 12(1): 46 67, 2. A. Nachman, et al, "A Local Formula for Inhomogeneous Complex Conductivity as a Function of the RF Magnetic Field", in Proceedings of 15th ISMRM Conference, Berlin, Germany, 27. D. Wang, et al, "Radio Frequency Current Density Imaging Based on a 18-degree Rotation with Feasibility Study of Full Current Density Vector Reconstruction. IEEE Trans. Med. Imag. 3(2):327-37, 211. U. Katscher, et al, In vivo determination of electric conductivity and permittivity using a standard MR system, in proceedings of13th Int. Conf. on Elec.Bioimped. and 8th Conf. on Elec. Imped. Tomog., pp ,

32 Acknowledgements Dr. Michael Joy, University of Toronto Dr. Adrian Nachman, University of Toronto Dr. Greig Scott, Stanford University Dr. Dinghui Wang, Center for Imaging Innovation at Barrow Neurological Institute Tim DeMonte, Field Metrica Inc. Nahla Elsaid, University of Toronto Funding support Mitacs Elevate NSERC University of Toronto 32

33 For More Information on CDI, RFCDI, PD-RFCDI t Software downloads; t Reference papers; t Projects overviews; t Contact information. 33

34 Thanks for your attention! 34