Biomedical Imaging. Nuclear Magnetic Resonance. Patrícia Figueiredo IST,

Transcription

1 Biomedical Imaging Nuclear agneic Resonance Parícia Figueiredo IST,

2 The wide specrum of medical imaging echniques (F. Deconinck, Vrije Universi, Belgium).

3 Overview Nuclear magneism Precession: ineracion wih a saic magneic field Eciaion: ineracion wih a ime-varing magneic field Relaaion: reurn o equilibrium Pulse-acquire eperimens

4 Nuclear magneic resonance (NR) Nuclei wih a non-ero spin number spins (paricularl 1 H in H 2 ) are polaried b ineracion wih a srong saic magneic field B Precession around B a he Larmor frequenc L = γb Polaried nuclear spins are ecied b varing magneic fields B 1 applied a he nuclei s Larmor frequenc Eciaion Reurn of he ecied nuclear spins o equilibrium: Relaaion Inducion of a curren on a receive coil according o Farada s law: Free Inducion Deca (FID) This signal depends on he densi of nuclear spins, as well as on he properies of he medium refleced on he relaaion ime consans.

5 Nuclear magneism Nuclear spins A proon is a elecric charge roaing => magneic momenum Isoope Spin I γ [H/T] Naural abundance [%] 1 H 1/ H F 1/ P 1/ Na 3/ N C 1/ Spin number I Spin operaor I Spin angular momenum S Dipolar magneic momen µ Gromagneic raio γ [H/T] S = " I µ = γs 17 O 5/ Roaing veloci

6 Precession Ineracion wih a polariing magneic field B Zeeman ineracion (energ): Quanied energ levels (ineracion energ wih B o ) he ineracion onl occur along Nuclear magneic quanum number, m: The value of I depends on he number of proons and neurons in he nucleus Proons: 2 energ levels 2 orienaions I = 1/ 2 m = ±1/ 2 µ = ±γ 3 2 µ = ±γ 2 E ±1/2 = γb 2 ΔE = γb $ θ ±1 2 = ±cos 1 µ ' $ & ) = ±cos 1 γ 2 ' & ) % µ ( % γ 3 2( θ ±1 2 = ±54.7 # B o is aligned wih he ais E = µ B E = µ B B = B ẑ µ = γm m = I I 1 " I I = spin number

7 Precession Ineracion wih a polariing magneic field B Proons: I=1/2 E ±1/2 = γb 2 " θ ±1 2 = ±cos 1 µ % $ ' # µ & " ΔE = γb = ±cos 1 γ 2 % $ ' # γ 3 2& θ ΔE B ±1 2 = ±54.7 " m = ½ µ = γh 3 2 The proons are pariall aligned wih Bo because µ = γs = γhm I B θ B E=+½γħB m =+½ ΔE E= ½ γħb

8 Precession Ineracion wih a polariing magneic field B wih a populaion of proons Bolmann disribuion: N 1 2 N+ 1 2 = e T=37º, B =1.5T N -1/2 /N +1/2 = ΔE kt The populaion difference is abou: 1-4 % ΔE = γb = L Larmor (resonance) frequenc: L = γb B ~ 1 1 T L ~ 4 5 H [RF] N -1/2 = ΔE, L, ΔN B B N +1/2 =.549

9 Precession Ineracion wih a polariing magneic field B agneiaion: (for an ensemble of nuclei) = µ ( N ) γ = N B 2 2 γ B N 4kT N s = oal number of proons proon densi s B B

10 Precession Classical descripion Free Precession: d S = µ d B d µ = γµ d B µ roaes abou he ais, wih frequenc: Larmor (resonance) frequenc = γb = L µ,s θ B φ Longiudinal ais: Transverse place:

11 Precession Classical descripion B d d γ = L B B B ˆ = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = 1 cos sin sin cos = B B d d d d d d γ γ Equaions of moion: roaion abou he ais, clockwise, wih frequenc L B γ = = = ˆ Vecor model: L Bloch equaion:

12 Precession Classical descripion Laboraor reference frame: Roaing reference frame: B L L " = Lˆ = γb ˆ = saionar in he roaing reference frame.

13 Precession Classical descripion Effecive field (for a general applied field B and associaed magneiaion ): d d = = γb d d = γ B = γ B + = γ B eff γ Effecive field: B eff = B + γ In general, he magneiaion precesses around he effecive field B eff in he roaing frame, jus as i precesses around he applied magneic field B in he laboraor frame.

14 Eciaion Ineracion wih a radiofrequenc field B 1 : Perurbaion awa from equilibrium, hrough resonance: Energ equal o he energ difference beween spin populaions will induce ransiions beween saes, reducing he magneiaion. Δ E = γ cb = L Classical descripion: Roaion of he magneiaion awa from equilibrium, owards he plane Applicaion of B 1 in he plane, wih oscillaing frequenc equal o = L γb B Circularl polaried magneic field (roaing clockwise): ( ) = B ( ) ˆ B sin( )ˆ 1 1 cos RF 1 RF = = γ RF L B T=37º, B =1.5T N -1/2 /N +1/2 = B ~ 1 1 T L ~ 4 5 H [RF]

15 Eciaion Ineracion wih a radiofrequenc field B 1 : Nuaion in he laboraor reference frame: B eff d d d B + B = 1 d d = d + γ ( γb ) ( γb ) γb 1 γb 1 B eff B 1 B -/γ B B B L RF B 1 B 1 B 1

16 Eciaion Ineracion wih a radiofrequenc field B 1 : Precession in he roaing reference frame: roaion abou wih frequenc ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = cos sin sin cos = γb ˆ B B B B eff " = = = γ B 1 L Δ Δ = B B d d d d d d 1 1 γ γ If off-resonance occurs: ( ) B B B eff ˆ ˆ 1 γ γ Δ + = + Δ = "

17 Eciaion Ineracion wih a radiofrequenc field B 1 : RF pulse: Flip angle / ip angle: B 1 = B 1 (), [,τ] θ = γ τ ( ) B1 d 1 = γb 1 9º pulse: eciaion/sauraion 18 º pulse: inversion/refocusing θ = 9 θ = 18 B 1 B 1 = = -

18 Eciaion Eciaion/ Sauraion 9º RF pulses: B 1 = = The effec of an RF pulse is o ransfer energ from he ransmiing coil o proons. This ecess energ resuls in a non- Bolman disribuion (non equilibrium) of he populaions of he parallel and ani-parallel energ saes. is reduced and and are no longer. θ = 9 = = B 1 θ = 9 Inversion/ Refocusing 18º RF pulses: θ = 18 θ = 18 - B 1 - B 1

19 Relaaion Reurn o hermal equilibrium: relaaion Following eciaion: Energ sae hermal equilibrium = = = = Longiudinal relaaionl 1- ep{-/t 1 } Loss of coherence Transverse relaaion ep{-/t 2 }

20 Relaaion Bloch equaions for relaaion: d d = T Following eciaion: 1 d d = ( ) = + ( ( ) ) ep T1 ( ) ( ) = ep T2 T 2 ( ) = ( ) = 1 ep T1 ( ) = ( ) = ep T2 Longiudinal relaaion 1- ep{-/t 1 } Transverse relaaion ep{-/t 2 }

21 Relaaion Relaaion mechanims: Relaaion resuls from energ echange hrough he flucuaing magneic fields eperienced b he nuclei as a consequence of heir hermal molecular moion. The dominan mechanisms of flucuaing magneic fields for nuclei of spin ½ are dipolar ineracions wih oher nuclei. Longiudinal relaaion or spin-laice relaaion: requires flucuaions a he Larmor frequenc o produce ransiions beween energ saes and hus resore polariaion and. Transverse relaaion or spin-spin relaaion: is also promoed b flucuaions a ero frequenc, which produce random dephasing of spins and hus loss of coherence and cancellaion of.

22 Relaaion Relaaion mechanims: Transverse relaaion or spin-spin relaaion: is also promoed b flucuaions a ero frequenc, which produce random dephasing of spins and hus loss of coherence and cancellaion of. Phase dispersion (roaing frame): ΔB = B B Δ = γδb ΔB Δφ = γ Δ

23 Relaaion Relaaion mechanims: olecular moion (roaions, ranslaions, vibraions) flucuaions in nuclear magneic fields J() Fas Low Viscosi High emperaure Specral densi funcion = frequenc specrum of flucuaing magneic fields of nuclei J τ c ( ) τc Slow High Viscosi Low emperaure L (low B ) τ c -1 L (high B ) τ c is he correlaion ime: characerisic ime scale of hermal molecular moion: τ c T -1

24 Relaaion Relaaion ime consans T 1 and T 2 : Relaaion ime consans for dipolar ineracions (spin 1/2): J() Longiudinal relaaion (spin-laice): slow fas 1 T γ r 4 c [ J ( L ) + J ( 2L )], J ( L ) τ τ c L Transverse relaaion (spin-spin): τ -1 c L 1/T 2 1/T 1 1 T 2 4 γ 6 r [ J( ) + J( L ) + J( 2L )], J( ) τc T 1 - T 2 is alwas shorer han T 1 - In soluion: T 1 ~T 2 (fas moion, shor τ c ) T 2 slow L fas τ c -1 - In vivo, T 1 up o ~1 T 2 (slow moion, long τ c ) - T 1 increases wih field srengh while T 2 is roughl independen.

25 Relaaion Off-resonance conribuions o relaaion mechanims - Chemical shifs, J-couplings, ec. specral peaks - Saic field inhomogeneiies T 2 * deca - Imperfec B uniformi - Inrinsic sample suscepibili differences - Eernall applied gradien fields

26 Relaaion Off-resonance conribuions o relaaion mechanims Chemical shif: - shif in he precessional frequenc of a nucleus due o he magneic field associaed wih he elecronic momen (elecron spin), of opposie polari o B : eff = γ B o (1 - σ), σ = shielding consan. - in order o allow direc comparison a differen field srenghs, he chemical shif is defined as he frequenc shif scaled o a reference peak: δ = 1 6 ( - ref )/ ref [ppm] (e.g., σ{η 2 Ο} = 1.3 ppm, σ{-cη 2 -} = 4.5 ppm - differen chemical compounds produce signals a differen precessional frequencies and a specrum is obained (RS). E: 1H - NR specrum of human brain (ppm)

27 Relaaion Off-resonance conribuions o relaaion mechanims: T 2 * deca T 2 * deca: Addiionall o spin-spin relaaion mechanisms, loss of coherence of he ransverse magneiaion also occurs as a resul of bulk magneic field effecs: saic field inhomogeneiies due o applied and/or inrinsic gradiens. ΔB Δ = γδb Δφ = γδb Δ Field inhomogenei Phase dispersion (roaing frame)

28 Inducion Signal deecion: Farada s Law of Inducion: For a solenoid wih N urns and surface area A: ε = Φ ( L) L B ε = NA sin L

29 Inducion Signal deecion: Farada s Law of Inducion: For a solenoid wih N urns and surface area A: Φ ε = = NA sin ε L ( L ) L B Quadraure deecion

30 Inducion Free Inducion Deca (FID): T 2 * deca: = + + T 2 * < T T * T T T * ( ) = ( ) e 2 signal ~1/T 2 ~1/T 2 * ~ep{-/t 2 } FT ime real L frequenc ~ep{-/t 2 *} T 2 * processes speed up signal deca and broaden specral linewidh.

31 Pulse-acquisiion eperimens Spin echo Eciaion Spin dephasing

32 Pulse-acquisiion eperimens Spin echo 18º RF pulse Spin refocusing

33 Pulse-acquisiion eperimens Spin echo Eciaion Spin dephasing

34 Pulse-acquisiion eperimens Spin echo 18º RF pulse Spin refocusing

35 Pulse-acquisiion eperimens Spin echo 18º RF pulse Spin refocusing

36 Pulse-acquisiion eperimens Spin echo pulse sequence (SE) RF eciaion 9 o refocusing 18 o TE = echo ime acquire Signal TE / 2 TE T 2 * T 2 FID echo

37 Pulse-acquisiion eperimens Spin echo pulse sequence (SE) A spin-echo can refocus spins ha are siing in a ime invarian (saic) B field, i.e., phase dispersion due o saic field inhomogenei (T 2 * processes). A spin-echo canno refocus spins ha have eperienced a ime varing B field, i.e., phase dispersion due o diffusion and T 2 processes.

38 Pulse-acquisiion eperimens Spin echo pulse sequence (SE) easuremen of T 2 b muliple spin-echo: T2 ( nte) = e nte T 2 * T TE/2 TE 2 TE 3 TE

39 Pulse-acquisiion eperimens Inversion recover pulse sequence (IR) easuremen of T 1 b inversion recover: ( TI ) n 1 2e TI = T 1 n T 1 TI 1 TI 2 TI 3

40 Pulse-acquisiion eperimens Sead-sae magneiaion ( ss ) and repeion ime (TR) Erns angle α Erns : maimies he ransverse magneiaion: α α α α cos α Erns α TR ep T = 1 TR ss

41 References Webb, Inroducion o Biomedical Imaging, Wile 23. Cho, Foundaions of edic E. ark Haacke, Rober W. Brown, ichael R. Thompson, Ramesh Venkaesan, agneic Resonance Imaging: Phsical Principles and Sequence Design, Wile 1993.