Physics of Relaxation. Outline

Transcription

1 Physis of Relaxation Weiguo Li Outline Fundamental relaxation Mehanisms Magneti dipole-dipole oupling» Stati oupling» Dynami oupling Frequeny dependene of relaxation Rate Temperature dependene of relaxation rate BPP theory of relaxation» Nonvisous liquids» Solids» Visous liquids Compartmentalization Maromoleular hydration effets» Three fration model Cross-relaxation Moleular weight dependene of relaxation Determinants of tissue T1 and T2 Mehanism of proton relaxation enhanement 1

2 Review T1 and T2 relation times How T1 and T2 happens? T2* Relaxation rate (RR) 1/T1 or 1/T2 Why relaxation again? Moleular basis of relaxation is better understood Predit the ontrast hange for pathologi ondition. Prospetive selet pulse sequene to optimize imaging Tissue are omplex moleular systems with omplex MR properties. Relations of T1,T2 to properties of tissue are imperfetly understood. 2

3 Fundamental relaxation mehanisms Dipole oupling Nulear magneti dipole interat with loal eletri and magneti fields reated by the neighboring nulei and atoms ->indue relaxation Five major interations Magneti dipole-dipole oupling Eletri quadrupole oupling Chemial shift anisotropy Salar oupling Spin-rotation interation Magneti dipole-dipole oupling Proton b inrease ΔB H 2 O rotates Magnitude and diretion hange Loal perturbation an be -10~10 gauss 3

4 Stati oupling If H 2 O moleule is fixed (ie) ΔB is fixed Fixed (stati) magneti field inhomogeneity ause proton on different moleules to preess at different frequenies.( what is the Δω?) Differenes in resonant frequeny result in Dephasing in x-y plane Shortening T2 Not affet T1 Dephasing time A proton proess 2 πin 20 gauss 1.2 *10-5 se Correlation time Correlation time τ is the minimum time required for a moleule to rotate one radian(1/ 2π ) If τ >10-5 se, fixed long enough for stati dephasing of M xy Any moleule large enough to have τ ~ 10-5 se (rotating so slow), its magneti field is essentially fixed with respet to MR measurement. 4

5 motional narrowing If the water moleules are moving rapidly in an isotropi fashion (as in bulk water τ ~10-12 se), positive and negative ontributions to the stati phase shift of a given proton is averaged to zero; this is referred to as motional averaging or motional narrowing. Uniform rates of preession, slow dephasing, long T2 Dynami oupling Rapid moleular tumbling motion is the soure. In bulk water, moleule rotate from 0 (fixed) to max freq (1/τ ) Rotation exposes eah proton to a hanging magneti field similar to MR exitation proess. at resonant frequeny, hanging spin state (low to high, absorb energy) Soure of hanging magneti field: B1 during exitation During relaxation, relative motion of proton magneti moments attahed to rotating moleule (soure of dynami omponent of dipole-dipole oupling) Spin exhange: interation of two protons One lose and one gain energy 5

6 Dynami oupling Spin exhange -> random orientation of the dipole moments ->random dephasing in x-y plane-> T2 deay (true sample-related) During spin exhange, if exess energy are transferred to moleule motion (both spins end up in lower energy state), -> regrowth of longitudinal magnetization-> T1 relaxation. So T1,T2 deay are the result of dipole-dipole oupling. Why energy an be transferred to H2O? Moleule tumbling at the resonant frequeny The more, the higher relaxation rate, the shorter T1. What determine the moleule tumbling rate? Moleular weight, temperature, shape of the moleule Frequeny dependene of relaxation rates Moleules rotate from 0(fixed)~ max freq (1/τ ) Relaxation rate (RR) depends on the fration of protons at the seleted ω 0, relative all other available frequenies. If the population J(ω) is a funtion of frequeny, then hange of B0 will hange RR. 6

7 Temperature dependene of relaxation rates T <25ºC, T = 25ºC, T > 25ºC Area under the urves is same and proportional to the total number of protons Shaded area is proportional to the number in resonane What is the relation of T1 with temperature? How about T2s? T1 <T1 <T1 T2 < T2 <T2 (why?) +temperature -> -τ -> - relaxation rate -> + T1,T2 1 T1 BPP theory and relaxation τ K ω τ 4τ ω0τ = T 2 K 5τ 2τ 3τ ω0τ 1+ 4ω0τ = 4 K = μ h γ /160π r 7

8 BPP theory and relaxation MRI freq range 1~100MHz, ω 0 = 2πf 0 = 6.4*10 6 ~10 8 /se Nonvisous liquids For bulk water, τ ~ se ω 0 τ << 1 T1=T2 Solids τ ~ 10-5 se; ω 0 τ >>1 T1 very large 1 τ 4τ = T1 = K + 5Kτ 1 K 5τ 2τ 1 1 = 3τ = 5Kτ T T2 small, 3 τ, stati magneti field inhomogeneity In ie, no motional narrowing -> dephasing like the magneti inhomogeneity in spin eho sequene, But diffusion so fast, that 180º pulse annot rephase it. Visous liquids (as lipids) τ ~ 10-9 se, ω 0 τ ~1 T1 and T2 more nearly equal than for solid. T1,T2 frequeny dependent Suesses and problems of BPP theory Suesses Explained the relaxation of monomoleular solvents and solids Problems Inadequate to desribe multiomponent solutions, suh as human tissue 8

9 Fast exhange model MR relaxation of tissue an be better explained if: a small fration of ell water is highly immobilized on the surfae of maromoleules with orrelation time on the order of that of ie (τ ~ τ of ie) Water moleules in this layer undergo rapid turnover or fast exhange with bulk water moleules free in solution. 1 1 = P i i T1 T1i Most investigators aept the fast exhange, but disagree over the extent and number of water ompartments and their relaxation harateristis ->3 ompartments model is suffiient for measurement on protein solution. Three-fration model MR relaxation rate of tissue is determined by the fast hemial exhange of water moleules between various sites on maromoleule surfaes Bulk water Hydration water Strutured water Bound water Rotationally bound water Irrotationally bound water Most fat free tissues 9

10 Three-fration model Fration one Bulk water and strutured water Mass: M w = f w X (solvent mass) R w relaxation rate Fration two Rotationally bound water Mass fration f r R r Fration three Irrotationally bound water Mass fration f i R i Ri >>Rr>Rw, irrotationally bond water dominate relaxation f w + fr + fi = 1 R 1 = 1 = fwrw + frrr + fir T1 i Cross-relaxation Protons of solids have wide ranges of resonane frequenies -> exhange exited spin energy. spin diffusion: If a proton nuleus on one end of a hain is exited, it an pass the exitation energy to a neighbor down the hain until only proton on the other end of the hain remains exited. This motion of spin energy is all spin diffusion. Ours in solids but not in mobile liquids Proteins move slowly -> This allows spin diffusion to side hain (possible bound water) whih move rapidly and relax faster-> promote the spin-lattie relaxation of the whole moleule. 10

11 Moleular weight dependene of relaxation Cross-relaxation make the relaxation of water in a protein solution dependent on maromoleular solute motion Solvent proton spin-lattie relaxation rate depend on the moleular weight of the solute protein at 10kHz~50MHz Relaxation of solvent responds to maromoleular motion via ross-relaxation between protein and water. Tumbling rate is determined by the moleular weight and the shape of the protein. Large proteins tumble slowly; small ones tumble rapidly At lower freq (roughly < 1MHz),maromoleular motion dominate relaxation harateristis of the solution. At high freq, water motion will be of primary importane. Determinants of tissue T1 and T2 In tissue, Inreasing size and mass of maromoleular struture -> anisotropi motion. Anisotropi rotation Isotropi motion (motional average/narrowing) Anisotropi motion of water -> shorten T2 In ollagen, regular parallel moleular arrangement of ollagen moleule surfae -> bonded water is rotating anisotropially and display strong orientational dependane.->shorter T2 11

12 Determinants of tissue T1 and T2 Fast exhange --- ellular suspensions Blood (a ellular suspension) is an example of the marosopi signifiane of fast exhange The linear relationship onfirm fast exhange between intraellular and extraellular water Beause of the fast exhange, Relaxation is a weighted average of the two frations of RBC and plasma. Determinants of tissue T1 and T2 Fast exhange---soft tissue Spin-lattie relaxation rate for most tissue organs are generally single omponent in harater, just as in blood. Mirostrutures -> widely varying water and maromoleule in different portion of the ell 12

13 Determinants of tissue T1 and T2 Fast exhange---soft tissue The observed relaxation rate is a weighted average of all the omponents within a diffusion radius, inluding one ell or more ells in most ases. The radius is determined by: Water diffusion haraters of tissue. Frequeny of MR devie. Determinants of tissue T1 and T2 Slow exhange --- soft tissue (fat). Lipids in adipose are hydrophobi moleules -> rejeted by water Lak of hydrogen bonding sites also limits the ross-relaxation possibilities between fat and water. Two omponents relax 13

14 Slow exhange --- soft tissue T1 relaxation is Biphasi in harater The relaxation rate of the water-protein fration of fat ell is nearly idential to that of musle The relaxation rate of the short omponent of the adipose tissue is idential to that of fat extrat Slow exhange --- soft tissue Separate fat and water. Distintly different loal magneti field ontribution ---Dixon Method Relaxation time differene. not make the lipid fration in brain visible Polar and organize in vivo into membranes. Bilayer sheet 14

15 Determinants of tissue T1 and T2 Water ontent Primary fator in determining the relaxation time Signifiant on ontrast Determinants of tissue T1 and T2 Lipid ontent High lipids ontent auses shorter net tissue T1 relaxation times Homework Fat relax rapidly ompared to water,why? Clue: Slower tumbling rate;12% w/w protons in fat ompared to 11% w/w in water T2 of nonpolar storage fat is longer than that of many other tissue, why? How about lipids in brain? 15

16 Determinants of tissue T1 and T2 Perturbed water motion The ability of tissue to perturb the motion of water on or near their moleular surfae is an important seondary soure of tissue T1 and T2 differene Paramagneti iron speies Don t play an important role in normal tissue ontrast exept iron ompounds in the brain at high field strength. Summary of MR ontrast parameters on moleular level Water ontent ontrast Perturbed water motion varying ability of the maromoleules of different tissue to bind and struture water in their viinity. Maromoleular motion Lipid ontent Paramagneti speies. 16

17 Mehanism of proton relaxation enhanement Enhanement: proesses that shorten either T1 or T2 are said to enhane protein relaxation. Paramagneti substane dissolved in water expose the water protons to flutuating magneti fields from unpaired eletrons flipping up and down. When these eletroni magneti moments flutuate at or near the Larmor frequeny, both T1 and T2 are shortened. In biologi substanes,t1 are 5~10 times longer than T2, -> T1 shortening is observed at lower onentration of paramagneti agent than are needed to produe T2 shortening. Next leture Contrast agents Definition and lassifiation Design requirements MR ontrast mehanisms Relaxivity theory of CA Gadolinium omplex Tissue speifi ontrast agents(appliation) MR Moleular imaging 17

18 Referene: Magneti resonane Imaging (2nd edition) David D. Stark, William G. Bradley, JR. Magneti resonane Imaging (3nd edition) David D. Stark, William G. Bradley, JR N. Bloembergen, E. M. Purell, and R. V. Pound. Relaxation Effets in Nulear Magneti Resonane Absorption. 1948,73: