Lab 1: Earth s Field NMR

Transcription

1 Lab 1: Earth s Field NMR March 1, 213 Galen Reed (GSI), Miki Lustig (Prof) 1 Introduction In this lab, we will acquire spectra using an Earth s field spectrometer. This lab will cover basic NMR concepts such as acquiring free induction decas (FID), transmitter strength & flip angle calibration, B strength and homogeneit, and basic NMR eperiments such as pulse / acquire, spin echoes, and relaation parameter measurements. 1.1 Hardware The spectrometer consists of concentric B 1, gradient, and polariation coils (Fig 1). It is a pre-polaried MRI sstem in which a stronger, but inhomogeneous electromagnet is used to polarie the sample, and another, weaker and ver homogeneous field is used for the signal detection. We will utilie the earth s field for signal detection, which at Berkele s latitude, make an approimatel a 65 inclination angle with the vertical and has a strength of about Gauss. Our detection frequenc is f = γb e /2π 2 kh (1) We are calling the ais of this field, analogous to the B in standard NMR / MRI sstems; the solenoidal ais is defined as (Fig 2). Notice how all of the coils are concentric and point along (Figs 1, 2). In this respect this sstem is different from standard NMR / MRI sstems in that the detection field (Earth s magnetic field) is perpendicular to the longitudinal () ais of the sstem (most sstems use the detection field parallel to the solenoid ais). Recall that when we drive current through a solenoid, we produce a longitudinal magnetic field (use the right hand rule with our fingers wrapping around the coils in the direction of the current). The strength of this field is approimatel B = µ NI ˆ (2) where I is the current and N number of coil turns per length (along ). 1

2 1 INTRODUCTION RF Coil When we drive a low frequenc AC field though the coil, we generate a field along that also oscillates at the driving frequenc. In the lab frame, this field can be written as B 1 = B 1 (t) cos ωt ˆ, (3) where ω is a tunable parameter and B 1 (t) is the amplitude modulation. The B 1 field can also be written in terms of comple eponentials as, B 1 = 1 2 B 1(t) ( e iωt + e iωt). (4) In this case, it is onl the right circular polariation is going to interact with the magnetiation (The other component is off-resonance ) so the effective field that interacts with the magnetiation is, B 1 = 1 2 B 1(t)e iωt. (5) For this eperiment, B 1 (t) is just an on/off control (i.e. a rect function in time). This is how we generate our RF pulses (Note, that RF is not reall the right terminolog here. 2KH is well within the audio range). Recall the rotating frame treatment of RF pulses where we are allowed to epress the pulse simpl as B 1,rot = 1 2 B 1(t) ˆ. (6) We lose a factor of 2 in field strength per current because we use a linearl polaried RF field in ˆ, but this is unimportant in this case where efficienc is not a great issue. Figure 1: The concentric coils of the Terra Nova unit

3 1 INTRODUCTION 3 Figure 2: Basic geometr of the NMR spectrometer. The solenoidal ais is defined as. 1.3 Polariing Coil The Terra Nova unit has a polariing coil, which is just another solenoid along. We appl a switchable DC current through this coil, and turn it on for some period and switch it off before we pla the B 1 pulse and perform signal detection. The need for this coil is evident when we look at the Curie magnetiation induced b a field with strength B : ( ) µb M = Nµ tanh (7) kt This epression is specific to spin S = 1/2 particles. µ is the magnetic moment of a single nucleus (µ = γs), N is the number of nuclei in the sample, k is the Boltmann constant, and T is the temperature in Kelvin. The tanh term (sometimes called P for polariation) just describes the fraction of the spins aligned with the B vector, so equation 7 just sas ( ) magnetic moment total magnetiation = (# nuclei) (frac aligned with B ) (8) single nucleus P = tanh(µb /kt ) is for B = (no field, no polariation), linearl increases with B for a bit, and asmptoticall approaches 1 when µb kt. For most NMR applications, this is no where near the case, and we are making all our images with µb /kt patheticall small. The polariation coil operates with a peak current of 6 A generating a peak B p = 18.8 mt giving P = For comparison the Earth s field B e = 5µT, and P = A standard clinical scanner operating a 1.5 T will give P = 5 1 6, a big gain but sadl 6 orders of magnitude sh of 1% polariation. We use B p to make P = instead of which translates directl to a 3 fold SN R increase over using the earth s field for polariation. However, we are performing all B 1 ecitation and signal detection with B p switched off, so how do we etract this gain from the polariation coil? It turns out the increased polariation will live for a little while after B p is switched off. The component of the Bloch equation is dm dt = 1 T 1 (M M ), (9)

4 2 EXPERIMENTS 4 where T 1 is a time constant, M is the current component of M, and M is the equilibrium M (given b eq 7) that depends on the current B. Therefore, we have a time T 1 before the polaried magnetiation dies off back to the induced b the earth s field. This is also wh we have to leave B p on for a few seconds before we do an detection: the magnetiation will take T 1 seconds to approach the higher polariation induced b B p. Another concern with the polariation coil is that it generates the polariation in the wrong direction (we want it along, but it generates it along ). However, this turns out to be not a big deal provided that B p is switched off slow enough (or adiabaticall). Specificall, as long as the rate of change of B p is much less than the Larmor frequenc, the magnetiation will track the field and will end up lined up with B e, i.e. along b the time we pla the B 1 pulse. 2 Eperiments 2.1 Pulse / Acquire FID The most basic NMR eperiment is the pulse / acquire, or pulse collect eperiment consisting of an RF ecitation followed b a data acquisition period. Our version of this basic sequence is slightl complicated due to the need for a polariation pulse. Fig 3 shows this sequence as we ll implement it. Following the polariation pulse, we pla the ecitation, and this is followed b a data acquisition period. B p 9 B 1 M Figure 3: The pulse / acquire eperiment. The magnetiation response after during readout is easil described b a Larmor frequenc oscillation term and a deca envelope. The deca term is a combination of the native deca constant T 2 and another term which depends on the homogeneit of the sample. This term is called T2, and is defined as 1/T 2 = 1/T 2 + 1/T 2, (1)

5 2 EXPERIMENTS 5 where T 2 B is proportional to the spread (inhomogeneit) of the field strength B. Epression 1 is almost alwas dominated b the second term, so we can almost alwas ignore the T 2 contribution to the deca envelope of pulse / acquire eperiments. The signal encoded immediatel following an RF ecitation is S(t) = e i2πf t e t/t 2, (11) where we ve defined f = γb /2π as the Larmor frequenc. Magnetic field inhomogeneit increases the damping, and also affects the spectral appearance. We can calculate the spectra analticall b taking a (half-sided) Fourier transform: S(f) = = S(t)e i2πft dt 1 1/T 2 + i2π (f f ) This curve is called the Lorentian line shape, and it has some ke characteristics which are more readil visible in magnitude: S(f) = T (2πT 2 ) 2 (f f ) 2 (12) This is just a spike centered at f with some width which is due to damping. Note that the peak signal on resonance is T2, and the full width at half maimum (F W HM) 1/T2 (see Fig 4, right). Therefore, we can see how magnetic field inhomogeneit B directl affects the data qualit. For a well shimmed magnetic field, B is small, so T2 is big, so the F W HM of the spectra is narrow and the spike is tall. When the homogeneit diminishes, our peak is blurred out (Fig 5). MRI image qualit is alwas improved with long T2 / small B since the integrated signal over the readout (and thus the SNR efficienc) is higher Figure 4: Pulse acquire FID with a long T 2 : a well shimmed magnet The Terra Nova uses the fact that the height of the spectra is proportional to T2 to perform automatic shimming. In other words, it automaticall iterates the current in shim coils (DC coils that spatiall alter B ) in order to minimie B between pulse / acquire eperiments.

6 2 EXPERIMENTS Figure 5: Pulse acquire FID with a short T 2 : a badl shimmed magnet 2.2 Coil Capacitance Calibration We can use some linear circuit analsis to optimie the efficienc of the transmitter (B 1 coil). The coil is itself a resonant circuit, and can be loosel approimated as a series LRC circuit. L is the inductor, which is just the coil itself. The circuit has a resonance with some width (proportional to R), and a resonant frequenc centered at ω = 1 LC. (13) In order to maimie the efficienc of the transmitter, we will want to first measure the resonant frequenc (via a pulse acquire eperiment). The spectrometer automaticall generates an ω versus C curve, and we manuall set C to the proper resonance frequenc. This is a tunable parameter b necessit since B e can var significantl as a function of geograph Pulse Calibration We ignored the amplitude of the signal response in our treatment in the pulse / acquire section, but the amplitude actuall is a function of the polariation and flip angle: where θ is the RF pulse flip angle. Recall that this is just S(t) = e i2πf t e t/t 2 M sin θ, (14) θ = γ T B 1 (t) dt (15) which is the pulse area. For our spectrometer, the pulse is just a square function ( ) t B 1 (t) = B 1 t so θ = γb 1 t To calibrate the 9 pulse, the spectrometer plas pulse/acquire eperiments at varing values of the pulse width t. What should the maimum value of the spectrum S(f) look like as a function of t? Once we find the 9 pulse, then we know what a 18 is too: we just double t.

7 2 EXPERIMENTS The Spin Echo Sa we want a measurement of the actual sample-specific T 2 (which varies with molecular structure, temperature, solvent viscosit, and a million other interesting parameters), and not the B inhomogeneit-dominated parameter T2 which the pulse/acquire eperiment gives us. It turns out we can etract this parameter with a 2-pulse eperiment called the spin echo. A second RF pulse placed T E/2 after the first refocuses the magnetiation dephased b T2, and we get the signal back again at T E/2 after the second pulse. The echo is not full amplitude; it s actuall modulated b the pure T 2 deca curve (but the echo grows and dies on either side b the old T2 envelope). The second pulse does not necessaril have to be a 18, but this is the angle that maimies the response. B p 9 18 B 1 M ep(-t/t 2* ) ep(-t/t 2 ) TE/2 TE/2 Figure 6: The spin echo eperiment. Figure 6 shows the basic spin echo eperiment. As before, we use B p to boost the SNR. Onl the data after the second pulse is acquired. A single spin echo eperiment doesn t give us a T 2 estimate, however. We have to repeat the eperiment with multiple T E values in order to generate an eponential deca curve of the echo amplitudes. The spin echo signal is a smmetric echo; what does this impl about the phase detection of the spectrum S(f)? It turns out there are man reasons to perform spin echoes besides estimating T 2. We can use the T 2 as a contrast generating mechanism for MRI. For materials with long T 2 (and sstems with short T2 such as ours), there are large SNR benefits to acquiring spin echo versus pulse/acquire data. 2.5 The Carr Purcell Meiboom Gill (CPMG) Sequence The CPMG eperiment is a modification of the spin echo eperiment. This time we pla a spin echo train, and between each refocusing pulse we acquire the echo. Since each echo is modulated b a T 2 deca, we can perform a T 2 measurement in a single acquisition. However, there is a price to be paid for acquiring the measurement in a single scan, and it is sensitivit to flip angle. For a 9, 18, 18, 18,... sequence, the 18s must be calibrated perfectl to generate a T 2 curve. As the blue dotted line in Figure 8 shows, when we are onl 2 awa from a perfect 18 (a 1% error in RF calibration), the signal response curve is vastl different from the pure T 2 deca curve after onl a few echoes. This is because the error propagates between each echo. What do ou think the actual % error in RF calibration is? A clever wa to address this instabilit is to pla the 18 pulses with a phase advance of π/2 with respect to the initial pulse; i.e the are pulses. In this wa, the RF amplitude

8 2 EXPERIMENTS 8 B p B 1 ep(-t/t 2 ) M... Figure 7: The CPMG eperiment. error does not corrupt the signal response (see Figure 8) since the errors are not cumulative in echo number. The CPMG eperiment is the basis for the commercial fast spin echo (FSE) or turbo spin echo (TSE) scans which are used to obtain high resolution T 2 -weighted images in nearl ever clinical eam = 18!,,,...,,,,... ep(t/t2) = 178!,,,...,,,,... ep(t/t2) = 165!,,,...,,,,... ep(t/t2) t [ms] t [ms] t [ms] Figure 8: The ideal T 2 deca curve (red) is plotted with the signal response of the 9, 18, 18, 18,... sequence using phase modulation,,,... (blue) and,,,,... (green)