Physics in Clinical Magnetic Resonance Spins, Images, Spectra, and Dynamic Nuclear Polarization

Transcription

1 Physics in linical Magnetic Resonance Spins, Images, Spectra, and Dynamic Nuclear Polarization Kevin M Koch, PhD GE Healthcare Applied Science Laboratory, MR Physics Group

2 Outline linical Magnetic Resonance 1. MR spin physics 2. Signal detection 3. Imaging 4. Advanced applications Hyperpolarized MR 1. Importance 2. Methods 3. Application: Liquid state in vivo DNP

3 MR Physics in linical Diagnostics

4 Magnetic Resonance: Spin Magnetic resonance is a measurement of subatomic spin Electrons and nucleons have spin Electron (spin ½) magnetic resonance Electron Paramagnetic Resonance (EPR) Nuclear magnetic resonance (NMR) can only be measured from nuclei with non-zero net spin m N 1 H nucleus: spin ½ DOES have NMR signal 12 nucleus: spin 0 does NOT have NMR signal nucleus: spin ½ DOES have NMR signal 17 O nucleus: spin 5/2 DOES have NMR signal m = γs S N S m

5 Magnetic Resonance: Spin Dynamics Single spin in a magnetic field Remove global phase Larmor equation

6 Magnetic Resonance: Spin Dynamics Important note (from the physics side) Spin precession is a mixed quantum state (Shroedinger cat state )

7 Magnetic Resonance: Spin Polarization At room temperature, the behavior of spin populations follow the laws of Boltzman Statistics - We want to work with spins in the ground state - Energy difference between the states: E = m. B - Probability ratio between the number of up and down states: N + /N - = e - E/kT - N + -N - ~ 7 parts per million!! at 1T for room temperature 1H nuclei -At any given moment, due to high levels of thermal energy being dispersed across the spin ensemble, we have very few spins in the ground state to work with -Would be nice to work at lower temperatures.but we like to work with living organisms! -We therefore typically use stronger applied magnetic fields to build maximal polarization

8 Magnetic Resonance: Spin Polarization E for electrons is much larger (orders of magnitude) than for NMR visible nucleons electron polarization is much larger Then why is NMR more widely used compared to EPR? The electron orbital structures alter the local magnetic field environment around the nuclei this provides a unique degree of freedom in signal detection We are able to distinguish nuclei in different chemical environments

9 Nuclear Magnetism: Spin Ensembles In room-temperature magnetic resonance, we therefore need to work with large spin ensembles (a high density of NMR visible spins) We measure the ensemble-averaged macroscopic magnetization, or expectation value of the quantum mechanical state r M N + = m i= 1 i = γ Ψ r S Ψ

10 Spin Flips: RF Perturbation 1. Spin precession is actually an unobservable superposition state of spin-up and spin-down quantum states if a spin is in either state, it is not precessing 2. NMR is largely a game of placing spins in precessing states that we can measure: We cannot measure useful signal in the unperturbed steady state 3. So, how do we take spins from the ground state and put them into the superposition precession states? 4. We increase the probability of the spin flipping to the excited state using input radiofrequency energy ω 1 = γb 1

11 Spin Flips: RF Perturbation Spin state probability determines observable ensemble averaged M B 0 Application of magnetic field rotating in x-y plane at Larmor frequency (radio frequencies for most MR) increases quantum probability of spin flip alters probability distribution Mz Mxy called a 90 o pulse B 1 = 0 B 0 B 1 = 0 (90 o Flip Angle) Further application of RF at Larmor frequency further increases probability of spin flip alters probability distribution Mz Mxy -Mz - called a 180 o pulse B 0 B 1 = 0 (180 o Flip Angle)

12 Spin Flips: Detection We detect macroscopic ensemble magnetization in the transverse plane When RF is applied at a frequency near the Larmor frequency, spins initially in the ground state will begin to have a probability to populate the excited state. The result is a net expectation of the precessing transverse state, which we detect through Faraday induction This is the resonance of magnetic resonance: an increase in detected transverse magnetization as a function of the applied RF frequency.

13 Signal Detection: RF oils Transmit and pickup coils r µ dm V = 4π V dt r M xy B Transmit r ' 0 3 B coil d r r The same coil that was used for excitation can be used for detection. r B Transmit r = B oil xy r = B 1 ( ) oil field direction B 1 is perpendicular to B 0 to detect spins in transverse plane RF Field (B 1 ) Direction RF oil Magnetic Field (B 0 ) Direction y x M x,y Rotating magnetization vector M x,y in x,y plane

14 Signal Detection: Spectral properties Nuclei of a single species do not necessarily precess at a single frequency Small variations in magnetic field caused by electronic and nuclear environments result in frequency changes (chemical shift) Measuring these frequency shifts is the fundamental basis of spectroscopy Proton spectrum in the human brain frequency

15 Signal Detection: Spectral and Temporal Domains an measure a spectrum by W.change the applied RF frequency and measure the signal response OR..can utilize the linearity of the spin response to impulse RF perturbation Amp ( t ) = Amp ( t ) = A i cos ω t dω A( ω ) cos ω t i A ( ω ) = FT [ Amp ( t )] 1 ppm = (γb 0 )/10 6 Hz At 1.5 T 1 ppm = 64 Hz V(t) = Multi-Frequency Free Induction Decay (FID) orresponding Spectrum

16 MR Imaging : Spatial Encoding Static magnetic field gradients, G = (<0,0,G x >,<0,0,G y >,<0,0,G z >) B(r) = B 0 +G.r Larmor frequencies are given a spatial dependence If a gradient is turned on during signal acquisition: S ( t ) = ρ ( x ) e dx iγgxt Inverse Fourier Transformation gives ρ ( x ) = FT 1 [ S ( t )] alled frequency or readout encoding Gradients can be used to spatially encode the MR signal

17 MR Imaging : Slice Selection ω ( z ) = γg z z z = ω γ G z z 1250 Hz Selective RF RF in Freq. Domain If gradient and RF are applied together: ω Hz Hz ω Hz RF pulse in time domain Signal comes from the slice only.

18 MR Imaging : 2D Encoding Now that we have a 2D slice to work with, how do we encode both dimensions? We can frequency encode 1 direction (call it x ) The second dimension is phase-encoded by applying second orthogonal gradient for a set amount of time before signal acquisition S ( t, j) = ρ ( x, y ) e 1 iγ [ G x xt + G j y yt P ] dx dy ρ ( x, y ) = FT 2 D [ S ( t, j)] Each j value is a separate readout acquired after a different phase from G yj is accumulated

19 Relaxation: T1: Spin-Lattice Nearly all MR imaging measures in a liquid-state Liquids at room temperature have complicated molecular motion associated with them rotation, translation, tumbling Motion creates extra A magnetic fields that can induce spin flips Thus, excited spin states eventually decay back to the steady state configuration T1 decay only deals with spin flips and thus only effects net magnetization along the z axis T1 is the time constant of the characteristic exponential decay caused by these processes M z 1 ( t) = M (1 e 0 t T )

20 Relaxation: T2: Spin-Spin Spins also interact with each other via a local dipole interaction This effectively tweaks the precession of the spins relative to one another and reduces the coherence of the precessing spin ensemble oherence: In NMR, this refers to whether spins are at the same stage of precession (which also correlates to a quantum state coherence) when the spin ensemble is not coherent, the observed macroscopic magnetization reduces in amplitude T2 is also follows an exponential decay model T2 only impacts the x-y, or transverse magnetization M xy = M xy( t= 0) e t T 2

21 Relaxation: Importance T2 ontrast Relaxation properties of water molecules are highly dependent on the tissue they are embedded in Thus, relaxation is heavily used in MR to develop tissue contrast This enables clear identification of pathology lesions, tumors, etc.. pathological conditions create different tissue properties thus changing the contrast Tissue T1 (ms) T2 (ms) Grey Matter (GM) White Matter (WM) Muscle erebrospinal Fluid (SF) Fat Blood

22 Image ontrast : How TR Repetition time time between RF excitations Determines T1 contrast Flip Angle TR TE Echo Time Time between RF excitation and signal detection Determines T2 contrast Flip Angle Area under RF pulse Provides T1 contrast TE

23 Image ontrast : Results T1 ontrast T E = 14 ms T R = 400 ms T2 ontrast T E = 100 ms T R = 1500 ms Proton Density T E = 14 ms T R = 1500 ms

24 Imaging: Advanced Applications 1cm

25 NMR Spectroscopy linical use of in vivo spectroscopy is a recent and explosive frontier challenging due to poor temporal and spatial resolutions sufficient SNR requires lengthy averaging procedures Strong clinical interest due to dense information in spectral data Metabolite concentrations, fluxes in time ancer screening based on molecular composition Molecule-specific pathology diagnosis. Brain proton spectrum where dominant water resonance has been suppressed

26 NMR Spectroscopy Presence of choline in breast proton spectra is indicative of malignancy (85-100% specificity) Avoids unnecessary biopsy invasive cancer University of Hull: M. Lowry, L. Turnbull

27 NMR Spectroscopy

28 NMR Spectroscopy: Imaging Gain spectral information with spatial resolution: This is ultimately the clinical takeoff point Apply two phase-encodes (kx and ky), then readout to acquire spectra from each voxel map chemical compositions of voxels on a spatial basis 1cm

29 NMR Spectroscopy: Improvements Analysis: quantification (modeling) Technique: faster (signal strength, sequence design) higher spatial resolution (signal strength) cleaner (pulse sequence design) Breadth work with low abundance nuclei to visualize new pathways, mechanisms, and pathologies Hyperpolarized

30 Frontiers: In Vivo Hyperpolarized MR

31 Magnetic Resonance: Signal strength Inherent MR signal is dependent on ability to polarize spin states: N = N + -N - Recall that the population difference is given by Boltzmann statistics: signal~ ρ N = ρ tanh(γb/kt) depends on applied magnetic field, B gyromagnetic ratio, γ spin density, ρ temperature, T AN WE BEAT THIS LIMITATION to image low abundance nuclei at room temperature at feasible magnetic field strengths?

32 Hyperpolarization: Perturbing Thermal Equilibrium Spin ensemble thermal equilibrium: steady state of transitions between the ground and excited states through energy exchange with thermal reservoir the more spins we keep in the ground state, the higher the degree of polarization Dynamic (or hyper) Polarization: use hyperfine interaction between electrons and nucleons to alter nuclear transition probabilities, thus changing the effective nuclear polarization, or spin temperature.

33 Hyperpolarization: Perturbing Thermal Equilibrium S N S N S N S E Hyperfine interaction between electrons and nuclei splits electronic energy levels Use electron transitions to alter nuclear equilibrium Nuclear state can flip only if electron flips in opposite direction e e p

34 Hyperpolarization: Perturbing Thermal Equilibrium If nuclear T 1 is far longer than electronic T 1 : electron-coupled relaxation can be considered only relaxation mechanism for nuclei during irradiation of electron resonance nuclei are pinned into ground state e e p n + /n - = exp[hb(γ e -γ N )/(2πkT)], which is a polarization enhancement of the thermal solution n + /n - = exp[-hbγ N /(2πkT)] by exp(-hb γ e /(2πkT) This is the Overhouser effect

35 DNP Technology: Solids DNP effect predicted (Overhauser) DNP effect Demonstrated (arver and Slichter) Extended to Non-Metals (Abragam) DNP Solid Effect Described (Jeffries) Organic Polarized to 46% (De Boer) DNP Preserved Outside of Polarizer in Aqueous solution (Ardenkjaer-Larsen et al) Hyperpolarized (DNP) Metabolic Imaging (Golman et al) Metals doped solids liquid In solids, Overhouser effect still observed, but is far a more complicated analysis Requires the concept of spin diffusion i.e. polarization migrating across nuclear ensemble through dipole-dipole interaction of nuclear spins

36 an also be accomplished in noble gases

37 Primary Hyperpolarization push at GE: DNP Preserved Outside of Polarizer in Aqueous solution (Ardenkjaer-Larsen et al) Hyperpolarized (DNP) Metabolic Imaging (Golman et al) liquid

38 Dynamic Nuclear Polarizer Technology 3.35 Tesla magnetic field and cryostat at ~1.2K amorphous solid material doped with unpaired electrons e - e - e - Take nuclei from % polarization at (3T,310K) to 42% as a solid at (3.35T, 1.2K), to 20% as a liquid at 310K. 200 mw 94kHz microwave source

39 Dynamic Nuclear Polarizer Technology Polarization steps: 1. solution/mixture (40-50 mg) frozen as pellets in liquid Nitrogen 2. Holder is loaded with frozen sample and placed in center of 3.35 T magnetic field 3. Sample is cooled to 1.2K and irradiated with microwaves for > 1Hr to build polarization 4. Dissolution (taking hyperpolarized solid and taking it to a liquid state) process was the lynch-pin to in-vivo application A. Water (7ml) is heated to boiling in a pressurized tube B. The sample is pulled 10 cm out of the center of the magnetic field (but still at ~3T) and connected to the tube. The boiling water is rapidly (<1 sec) flushed over the sample D. The sample is dissolved and the liquid (pressurized from the input water jet side) liquid follows an outtake tube to the collection vessel E. ollection vessel is pre-cooled to result in hyperpolarized liquid temperature of ~40 o at time of in-vivo injection Ardenkjaer-Larsen, PNAS, 100, , 2003

40 DNP polarization build-up time -pyruvate, 20 mm trityl radical NMR enhancement polarisation build-up time constant: τ = (20.7 ± 0.8) min time (min)

41 T 1 relaxation in the solid state T 1 decreases with increasing temperature relaxation time (min) T 2.0T 1.5T Temperature (K)

42 After Dissolution: How Long Does the Added Polarization Last? o 1-2 T1 s o 3-6 T1 s Enhancement Multiples of T 1

43 Why Pyruvate? Pyruvate is a crucial molecule in energy metabolism dynamics. Output of glycolysis An input in the Krebs cycle (cellular oxygen respiration process) labeled nuclei in pyruvate can be tracked through to a number of reaction products, including lactate, alanine, and bicarbonate nuclei in pyruvate have a long T1 (~45 seconds), so a hyperpolarized ensemble can be given time to reach a certain metabolic pathway Why do we care about metabolic dynamics? Pathology can often be linked to metabolic dynamics Increasing the signal strength of a widely metabolized nuclei can allow increased spectral coverage with greater temporal resolution stronger signal less/no averaging of the MR signal to gain decent spectral quality and spatial resolution

44 Pyruvate Metabolism 4x

45 MRSI Spatial overage (rat) proton lac ala pyr bicarb pyr.h2o pyr intra pyr-h 2 O kidney lac ala bicarb liver muscle 5 mm resolution, 17 second scan time Kohler et al, Magn. Res. Med., 58, 65-69, 2007

46 Dynamic MRS (rat) lac ala pyr-h 2 O pyr bicarb 3 Second Resolution T= 0 s Kohler et al, Magn. Res. Med., 58, 65-69, 2007

47 linical Impact : Prostate ancer spectra from TRAMP mouse Elevated lactate levels in TRAMP mouse prostate tumors hen et al, Magn. Res. Med., 58, , 2007

48 Will Delivery in Humans be Fast Enough? Enhancement Time (min)

49 GE Hyperpolarized Development: Jan-Henrik Ardenkjaer-Larsen Ralph Hurd Y-Fen Yen Jim Tropp