1. G16.4427 Practical MRI 1 – 2 nd April 2015 G16.4427 Practical MRI 1 Volume and Surface Coils

2. G16.4427 Practical MRI 1 – 2 nd April 2015 MR Coils An MR coil is an inductor capable of producing and/or detecting a time-varying magnetic field – It can be represented as an inductance L, with a series resistance R L, driven by an alternating current source (in Tx) or by the received MR signal “Circuit for AC-drive realistic inductor”

3. G16.4427 Practical MRI 1 – 2 nd April 2015 Coil Impedance When a voltage is applied, the current will be inversely proportional to the impedance – In Tx, power must be delivered efficiently to the inductor with minimum current at given impedance – In Rx, the induced current must encounter minimum resistance in the MR inductor circuit – For optimum performance the impedance is minimized and matches the Tx/Rx (source) system impedance

4. G16.4427 Practical MRI 1 – 2 nd April 2015 Coil Impedance When a voltage is applied, the current will be inversely proportional to the impedance – In Tx, power must be delivered efficiently to the inductor with minimum current at given impedance – In Rx, the induced current must encounter minimum resistance in the MR inductor circuit – For optimum performance the impedance is minimized and matches the Tx/Rx (source) system impedance The coil impedance can be expressed as: – Z coil = Z L = R L + iX L = R L + iωL – Typically a receive coil will have R L ~ 1 Ω and variable inductance depending on size and configuration

5. G16.4427 Practical MRI 1 – 2 nd April 2015 Tuned Circuits The inductor circuit need to operate efficiently at the MR frequency of the spin of interest – Tune the circuit with a capacitive-reactive element to provide the appropriate impedance “Series tuning” “Parallel tuning”

6. G16.4427 Practical MRI 1 – 2 nd April 2015 Problem Given: R L = 0.320 Ω L = 0.110 μH Find the value of the series capacitor that will make the circuit to resonate at the proton resonance frequency at 3 Tesla

7. G16.4427 Practical MRI 1 – 2 nd April 2015 Parallel-Tune Coil Has a resistive impedance at resonance that depends on the value of C and L – Can be used to transform the circuit resistance Parallel tuning effectively transforms the resistance of the circuit

8. G16.4427 Practical MRI 1 – 2 nd April 2015 Impedance Matching The coil circuit must have the impedance matched to the Tx/Rx (source) impedance – However, the series resistance of an MR coil is ~ 1 Ω, much less than the typical source impedance of 50 Ω A combination of series- and parallel-tuned circuit is used to allow both resonance and impedance matching

9. G16.4427 Practical MRI 1 – 2 nd April 2015 Impedance Matching The coil circuit must have the impedance matched to the Tx/Rx (source) impedance – However, the series resistance of an MR coil is ~ 1 Ω, much less than the typical source impedance of 50 Ω A combination of series- and parallel-tuned circuit is used to allow both resonance and impedance matching

10. G16.4427 Practical MRI 1 – 2 nd April 2015 Expression for the Impedance Using the series-equivalent representation: Substituting: must be zero (2 valid solutions) must be equal to 50 Ω The desired frequency response can be determined by requiring that the impedance be pure resistive and equal to the source impedance at the frequency of interest

11. G16.4427 Practical MRI 1 – 2 nd April 2015 Example Let’s look at the simulated performance of a surface coil modeled with the circuit we saw, tuned at 200 MHz and matched at 50 Ω

12. G16.4427 Practical MRI 1 – 2 nd April 2015 Example Let’s look at the simulated performance of a surface coil modeled with the circuit we saw, tuned at 200 MHz and matched at 50 Ω Real part of the impedance (resistance) Imaginary part of the impedance (reactance) Note that the reactance has two zeros (200 MHz and 205 MHz) and the lower frequency represents the appropriate one because it corresponds to a resistance of 50 Ω

13. G16.4427 Practical MRI 1 – 2 nd April 2015 Circular Loop Coil The field from the circular loop can be found from Biot-Savart law: In the case of thin wires ( J(x) = Idl ): Haacke et al. (1999) Magnetic Resonance Imaging

14. G16.4427 Practical MRI 1 – 2 nd April 2015 Sensitivity Profile of the Loop Coil An elementary calculation can be made to find the on-axis field: Maximum SNR at depth d is obtained with loop of radius:

15. G16.4427 Practical MRI 1 – 2 nd April 2015 Example of Surface Coils Receiver system brought closer to patients Detect noise from a limited volume Has good SNR for superficial tissues Surface coils are placed on or around the surface of a patients. Question: what are the advantages of surface coils?

16. G16.4427 Practical MRI 1 – 2 nd April 2015 Whole-Volume Coils Can be used for surrounding either the whole body or a specific region Allow imaging bigger volumes Have better magnetic field homogeneity than surface coils

17. G16.4427 Practical MRI 1 – 2 nd April 2015 Helmholtz Coils An initial step to produce a magnetic field that is more homogeneous than that shown for the single loop is two combine two coaxial loops and find the ration of their separation to radii which gives optimal field homogeneity The optimal arrangement is found by doing a Taylor expansion of the field along the z axis and eliminate the second- order derivative, which yields: a = 2s Haacke et al. (1999) Magnetic Resonance Imaging

18. G16.4427 Practical MRI 1 – 2 nd April 2015 Magnetic Field for an Helmholtz Coil

19. G16.4427 Practical MRI 1 – 2 nd April 2015 Problem German physician and physicist 31 st August 1821 - 8 th September 1894 Hermann von Helmholtz z = 0 Using the following expression, derived with the Biot-Savart law, for the B z of each coil, compute the value of B at the mid point between the two coils

20. G16.4427 Practical MRI 1 – 2 nd April 2015 Maxwell Coils A variation of the Helmholtz coil for improved field homogeneity (at the expenses of more material and complexity) Haacke et al. (1999) Magnetic Resonance Imaging

21. G16.4427 Practical MRI 1 – 2 nd April 2015 Classic Solenoid A solenoid is a coil wound into a tightly packed helix From Ampere’s law: number of turnscurrent length of solenoid

22. G16.4427 Practical MRI 1 – 2 nd April 2015 Solenoid Uniformity for Body Coil A classic uniformly wound solenoid is not the best choice for an MRI main magnet – Good uniformity at the center requires its length to be large compared to its radius For B z to be constant near the origin, then α 1 and α 2 need to be approximately constant  length much greater than radius Haacke et al. (1999) Magnetic Resonance Imaging

23. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage Coils One of the most popular coil configuration – Quadrature design – Excellent radial field homogeneity over the imaging volume The axial current paths are referred to as the legs The azimuthal paths are referred to as the endrings Haacke et al. (1999) Magnetic Resonance Imaging

24. G16.4427 Practical MRI 1 – 2 nd April 2015 Field in a Birdcage Coil If the current in the legs if the coil is of the form: then the field produced in the imaging region is extremely uniform and rotates its direction with angular frequency ω Nearly all of the fields produced are used for imaging – The birdcage coil is very efficient

25. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage Coil Circuit Analysis Each conductor is modeled as an inductance and a resistance An N leg birdcage has N/2 + 2 resonant modes - Using Kirchhoff law we can find all the resonant frequency and calculate the corresponding magnetic field

26. G16.4427 Practical MRI 1 – 2 nd April 2015 Different Types of Birdcage Coils Low Pass BirdcageHigh Pass BirdcageHybrid Birdcage

27. G16.4427 Practical MRI 1 – 2 nd April 2015 Examples of Birdcage Coils High Pass BirdcageHybrid Birdcage

28. G16.4427 Practical MRI 1 – 2 nd April 2015 Uniform Mode The magnetic flux lines inside and outside a cylindrical shell carrying a z-directed surface current with sin( ϕ ) variation ϕ

29. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage Modes Uniform Mode: I = I 0 sin( ϕ ) Unwrap ϕ

30. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage Modes Uniform Mode: I = I 0 sin( ϕ ) Unwrap ϕ Gradient Mode: I = I 0 sin(2 ϕ )

31. G16.4427 Practical MRI 1 – 2 nd April 2015 B 1 Distribution (Oil Phantom) Uniform ModeGradient Mode

32. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage Coil: Linear Drive 0° Port

33. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage Coil: Linear Drive 90° Port

34. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage Coil: Quadrature Drive 0° Port90° Port

35. G16.4427 Practical MRI 1 – 2 nd April 2015 Limitations of the Birdcage Coil For a finite birdcage the field uniformity decay axially The currents in the endrings do not produce uniform fields within the imaging volume – If the coil’s length is approximately equal to its diameter, then the coil has good homogeneity over a spherical volume The current has to flow all the way around the coil (through the endrings) making the inductance of the circuit very high

36. G16.4427 Practical MRI 1 – 2 nd April 2015 TEM Coil The TEM coil is a cavity resonator – A space bounded by an electrically conducting surface and in which oscillating electromagnetic energy is stored The significant current return path is on the cavity wall, in the z direction – There are no endrings Size scaling of TEM coils is easy Better sensitivity than birdcage

37. G16.4427 Practical MRI 1 – 2 nd April 2015 Birdcage vs. TEM Shielded LP BirdcageTEM Coil

38. G16.4427 Practical MRI 1 – 2 nd April 2015 Current Paths Shielded LP BirdcageTEM Coil

39. G16.4427 Practical MRI 1 – 2 nd April 2015 Ideal Current Patterns at Low Field

40. G16.4427 Practical MRI 1 – 2 nd April 2015 Ideal Current Patterns at 1.5 Tesla Ideal current patterns appear to form two distributed loops separated by 180 degrees, which precess at the Larmor frequency around the axis of the cylinder. The amplitude of current varies sinusoidally in the azimuthal direction, completing one full cycle around the circumference Resemblance with a birdcage coil (with smooth distributed currents and narrower along z)

41. G16.4427 Practical MRI 1 – 2 nd April 2015 Ideal Current Patterns at 7 Tesla Ideal current patterns become more complex and the circumferentially-directed portions near the edges of the axial FOV, which at 1.5 T resemble end-ring return currents, seem to disappear Possible resemblance with a TEM coil

42. G16.4427 Practical MRI 1 – 2 nd April 2015 TEM Resonator at 8 Tesla Linear-element TEM volume coil FDTD calculated polarization vector Vaughan JT et al., in Ultra High Field Magnetic Resonance Imaging, chapter 6 (Springer). Vaughan JT et al., in Ultra High Field Magnetic Resonance Imaging, chapter 6 (Springer). Ibrahim T, in Ultra High Field Magnetic Resonance Imaging, chapter 7 (Springer). Ibrahim T, in Ultra High Field Magnetic Resonance Imaging, chapter 7 (Springer).

43. G16.4427 Practical MRI 1 – 2 nd April 2015 Body Imaging at 7 Tesla Vaughan JT et al., 2009, MRM 61:244-248

44. G16.4427 Practical MRI 1 – 2 nd April 2015 Simulated Body Imaging at 7 Tesla FDTD models of relative B 1 magnitude (T/m) FDTD models of SAR (W/kg) Vaughan JT et al., 2009, MRM 61:244-248

45. G16.4427 Practical MRI 1 – 2 nd April 2015 Any questions?

46. G16.4427 Practical MRI 1 – 2 nd April 2015 Acknowledgments The slides describing the birdcage modes and the comparison between birdcage and TEM coils are courtesy of Dr. Graham Wiggins

47. G16.4427 Practical MRI 1 – 2 nd April 2015 See you next week!