Chemical Exchange. Spin-interactions External interactions Magnetic field Bo, RF field B1

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1 Chemical Exchange Spin-interactions External interactions Magnetic field Bo, RF field B1 Internal Interactions Molecular motions Chemical shifts J-coupling Chemical Exchange 1

2 Outline Motional time scales Motional line shapes Two site exchange Time scales Reaction rates: Bloch equations Steady state solutions Exchange regimes Examples Chemical exchange saturation transfer Principle Glutamate and Creatine CEST Ex vivo and In vivo Results Motional time scales Very Slow Slow fast Very fast ultra fast Slow s ms µs ns ps fs Fast Macroscopic diffusion, flow Chemical Exchange Molecular rotations Molecular vibrations Relaxation Spectral Larmor Malcolm Levitt s Book 2

3 Motinal time scales Three times scales of the nuclear spin system. Larmor time scale, τ The time required for the spins to precess through 1 radian in the magnetic field. ω ο τ l ~1 (at 100 MHz, ω ο /2π =100 ΜΗz, τ l =1.6 ns) Spectral time scale t spec Spin system with two spins with CS at ω 1 and ω 2. If the CS interactions are dominant, then the spectral time scale τ spec : ω 1 - ω 2 τ spec ~1 (at 100 MHz, two protons have CS difference δω/2π = 5ppm(=500 Hz), then, τ spec = 330 µs) Relaxation time scale: Spin-lattice relaxation time T 1 (in the order of seconds) Motional Lineshapes and Two-site exchange Motional processes on the spectral timescale affect NMR line shapes. Consider an isolated nuclear spin is transported between two different chemical environments, with different chemical shifts but identical free energies k A -----> <----- B k 3

4 Chemical Exchange O CH 3 N H CH 3 k -----> <----- k O CH 3 N H CH 3 N,N -Dimethyl-formamide O - R C N + CH 3 CH 3 Exchange regimes If the chemical shift difference between Δω=-δω/2 Δω=δω/2 two states is δω, Δω=ο and chemical exchange rate constant is k then K< δω/2 slow int. exchange regime K~ δω/2 Intermediate exchange regime K> δω/2 fast int. exchange regime 4

5 Precesssion frequency and exchange process Change in the precession frequency on a molecular exchange (A <--->B) process Superposition of transverse magnetization oscillations for exchanging molecules Total transverse magnetization for many exchanging molecules ω a /2π=10kHz, ω b /2π=11kHz, and k=500s -1 Simulations of precessing transverse magnetization Slow intermediate exchange regime K< δω/2 Faster the exchange, faster the decay Leads to broadened NMR line Motional broadening Simulation parameters: ω a /2π = 2kHz, ω b /2π = 4kHz 5

6 Simulation of fast exchange Simulation of Transverse magnetization Fast intermediate exchange regime K> δω/2 As the exchange rate k increases, magnetization decays slowly Rapid molecular jumps leads to motional narrowing Simulation parameters: ω a /2π = 2kHz, ω b /2π = 4kHz Two-site exchange time scale Spectral line shape change as one goes from slow to fast exchange K= δω/2 Malcolm Levitt s Book 6

7 NMR and reaction rates Consider nuclei at sites a and b M a = M x +im y for nuclei at site a k M b = M x +im y "for nuclei at site b M 0 = Thermal equilibrium magnetization of the sum of two sites Δω=ω-ω 0 ; δω= splitting between the two lines Nuclei at sites a and b obey the following two differential equations: dm a = M a dt + i Δω + δω T 2 2 M M a + iω A k -----> <----- B dm b dt = M b + i Δω δω T 2 2 M M b + iω Sclichter s Book Steady-state solutions At steady state, dm a dt and steady state solutions give two Lorentzian lines Δω=-δω/2 and other at Δω=δω/2 = 0 dm b dt = 0 Δω=-δω/2 Δω=δω/2 Δω=0 7

8 Exchanging spins Consider that molecule reorients, taking spins from a to b-site and vice versa. Jumping of spins from b ---> a site (in time δt) will add δm a to a magnetization δm a = C 1 M b δt C 1 =constant will diminish δm b from b magnetization δm b = -C 1 M b δt C 1 =constant Exchanging spins Similarly, jumping of spins from a ---> b site (in time δt) will add δm b to b magnetization δm b = C 2 M a δt C 2 =constant will diminish δm a from a magnetization δm a = -C 2 M a δt C 2 =constant 8

9 Exchanging spins dm a dt = C 1 M b C 2 M a dm b = C 2 M a C 1 M b dt Adding these rates to the rates without spin jumps dm a dt dm b dt = M a + i Δω δω T 2 2 = M b + i Δω δω T 2 2 M M a + iω C M C M 1 b 2 a M M b + iω C M C M 2 a 1 b Exchanging spins since whenever a molecule reorients a spins ---> b spins and b spins ---> a spins ----> C 1 =C 2 =C The rate equations are solved in the steady state and the resulting total complex magnetization M x +im y is given by 9

10 Steady-state solutions M x + im y = M a + M b = iγh 1 M 0τ[2 + τ(α a + α b )/2] (1 + α a τ)(1 + α b τ) 1 where α a = 1 + i ω T o ω δω 2 2 α b = 1 + i ω T o ω + δω 2 2 1/τ = C=k, and the absorption signal is given by My the imaginary part of the above equation Simulated spectra Two-site exchange in the slow intermediate regime K< δω/2 ( 6.3kHz) Simulation parameters ω a /2π = -1kHz ω b /2π = 1kHz Crossover point is K= δω/2 ( 6.3kHz) 10

11 Fast int. exchange K> δω/2 ( 6.3kHz) fast int. exchange regime Simulation parameters ω a /2π = -1kHz ω b /2π = 1kHz Two-site exchange time scale Spectral line shape change as one goes from slow to fast exchange K= δω/2 11

12 13 C Spectra of N,N - dimethylformamide 13 C enriched spectra of N,N - dimethylformamide gas at different temperatures in a field of 4.7T 1 H spectrum of N,N -dimethyltrichloroacetamide 1 H spectrum of N,N - dimethyltrichloroacetamide (DMTCA) as a function of temperature at 60 MHz. O CH 3 N R CH 3 k -----> <----- k O CH 3 N R CH 3 O - R C N + CH 3 CH 3 -R: H, CH 3 or CCl 3 12

13 Chemical exchange saturation transfer (CEST) Biological tissues, exchange of solute spins with water Can we exploit the CE to detect solute spins? Chemical Exchange Saturation Transfer (CEST) Solute Pool H k sw Water Pool O O O H H H H H H O O O H H H H k H H ws O O H H H H 13

14 MRS at 7T Glu 3.00ppm Excitatory neurotransmitter Sensitivity comparison between CEST and MRS Cai et al. Nat. Med. (2012) GluCEST ~700 fold higher sensitivity than MRS 28 14

15 Potential overlap of other brain metabolites with GluCEST CEST (%) CEST (%) 7T B1rms 150Hz 2s Ø Physiological concentrations of major brain metabolites at 37C Ø Glu & GABA contribute to GluCEST 29 GluCEST in MCAO rat brain 1.0 hour 4.5 hour >24 Contralateral ipsilateral <4 9.4T B 1rms 250Hz 1s Cai et al. Nat. Med. (in press) 30 15

16 Glu modulation in vivo 1 H Image GluCEST (%) 30 Baseline 2 Hr 0 In vivo GluCEST A. The axial view of the human brain. B. Difference image (CEST image at -3ppm CEST image at +3ppm); C. GluCEST contrast map; F. Map of distribution volumes (DVs) of metabotropic Glu receptor subtype 5 from the PET image (With permission, extracted from Ametamey Simon M et al, J. Cereb Blood flow Metab, J Nucl Med 2007; 48: ) Cai et al. Nat. Med. (2012) 16

17 Enzymatic inter-conversion of PCr and ATP CK facilitates high energy phosphate metabolism Current Methods 31 P MRS: measures PCr and ATP 1 HMRS: measures total creatine No noninvasive method For measuring free Cr Myocardial and skeletal muscle energetics CREST SENSITIVITY AND SPECIFICITY (3T) Haris et al., NMR in Biomed (2012) CrEST has two-three orders of magnitude higher sensitivity Than 1HMRS. Amine/amide groups on PCr, ATP and ADP have an order of magnitude slower exchange rate than Cr Hence they don t contribute to CrEST 17

18 In vivo Human Skeletal Muscle CrEST Before and After Exercise at 7T [a] (%) [b] exercise Kogan et al., Magn. Reson. Med. (in press) Plantar flexion exercise data for subject 1. (a) CrCEST asym maps of a human calf muscle before and every 48 seconds after (in order by number) 2 minutes of plantar flexion exercise. (b) MTR and (c) T 2 maps before and every 56 seconds after (in order by number) the same exercise protocol. (d) plot of the average CrCEST asym as function of time in 4 different muscles of the calf segmented from anatomical images. Error bars represent the standard deviation in the CrCEST asym in each region. 31 P MRS OF CALF MUSCLE- IN MAGNET EXERCISE Healthy human calf muscle exercise Pressing of a pedal connected to pneumatic piston for 1 minute. Kogan et al., Magn. Reson. Med. (in press) 18

19 CEST imaging Exchangeable groups on other endogenous molecules Myoinositol (Alzheimer s disease) Creatine (CK metabolism in heart) Aggrecan (Osteoarthritis) Requirement for CEST The chemical shift Δω > k A large ω reduces direct water saturation Increases the CEST sensitivity Δω < k Δω k Δω > k Ward et al. J. Magn. Reson. 143 (2000):