RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Master‘s Program in Medical Physics 11/26/2020 | Page 1 Physics of Imaging Systems Basic Principles of Magnetic Resonance Imaging III Prof. Dr. Lothar Schad Chair in Computer Assisted Clinical Medicine Faculty of Medicine Mannheim University of Heidelberg Theodor-Kutzer-Ufer 1-3 D-68167 Mannheim, Germany [email protected] www.ma.uni-heidelberg.de/inst/cbtm/ckm/ RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Relaxation 11/26/2020 | Page 2 Relaxation Seite 1 1 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Magnetization: M and M 11/26/2020 | Page 3 z xy longitudinal magnetization: Mz transversal magnetization: Mxy transversal magnetization: Mxy - phase synchronization after a 90°-pulse - the magnetic moments of the probe start to precede around B1 leading to a synchronization of spin packages → Mxy - after 90°-pulse Mxy = M0 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Movie: M and M 11/26/2020 | Page 4 z xy source: Schlegel and Mahr. “3D Conformal Radiation Therapy: A Multimedia Introduction to Methods and Techniques" 2007 Seite 2 2 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Longitudinal Relaxation Time: T1 11/26/2020 | Page 5 thermal equilibrium excited state after 90°-pulse: -N-1/2 = N+1/2 and Mz = 0, Mxy = M0 after RF switched off: - magnetization turns back to thermal equilibrium - Mz = M0, Mxy = 0 → T1 relaxation longitudinal relaxation time T1 spin-lattice-relaxation time T1 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Physical Model of T1 Relaxation 11/26/2020 | Page 6 J() B0 - in a real spin system (tissue) every nuclei is surrounded by intra- and intermolecular magnetic moments - thermal motion (rotation, translation, oscillation) leads to an additional fluctuating magnetic field Bloc(t) with typical spectral distribution J() - longitudinal components of J() at 0 allow energy transfer 0 from the spin system to the “lattice” → T1 relaxation - trajectory of the tip of magnetization vector in the laboratory system source: Liang and Lauterbur. “Principles of Magnetic Resonance Imaging” 2000 Seite 3 3 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Phenomological Description of T1 B 11/26/2020 | Page 7 0 the longitudinal magnetization Mz relaxes exponential to the equilibrium state Mz = M0 with a typical time constant T1 dMz/dt = (M0 x B)z + (M0 – Mz)/T1 : Bloch equation with T1 with Mz = 0 at t = 0: Mz(t) = M0 (1 – exp(-t/T1)) → solution of Bloch equation 1.0 (t) (t) / z 0.63 0.5 -t/T1 typical T1-values in (1-e ) tissue:100 - 2000 ms 0 normalized normalized signal: M M repetition time TR [s] 0T1 1 2 3 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Movie: T1 Relaxation 11/26/2020 | Page 8 © Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada Seite 4 4 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Transversal Relaxation Time: T2 11/26/2020 | Page 9 after 90°-pulse: -N-1/2 = N+1/2 and Mz = 0, Mxy = M0 after RF switched off: - magnetization Mxy starts to rotate in the x,y-plane at Larmor frequency - all transversal components J() of the fluctuating magnetic field Bloc(t) result in a dephasing of Mxy → spin-spin interaction - mainly static frequency components J() of the fluctuating magnetic field Bloc(t) at = 0 are contributing - no energy transfer in the spin system (entropy ) - no influence of T2 on T1, they are independent ! J() B0 → T2 relaxation transversal relaxation time T2 spin-spin-relaxation time T2 J(=0) - although technical inhomogeneities of B0 cause dephasing of Mxy → T2* (effective relaxation) RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Physical Model of T2 Relaxation 11/26/2020 | Page 10 Mxy thermal equilibrium signal intensitysignal time z z z z Mz M = 0 Mxy Mxy xy y y y y x x x x RF B0 90°- pulse Seite 5 5 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Movie: Spin Dephasing 11/26/2020 | Page 11 © Plewes DB, Plewes B, Kucharczyk W. The Animated Physics of MRI, University Toronto, Canada RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Phenomological Description of T2 B 11/26/2020 | Page 12 0 the transversal magnetization Mxy relaxes exponential to Mxy = 0 with a typical time constant T2 dMxy/dt = (M0 x B)xy – Mxy/T2 : Bloch equation with T2 with Mxy = M0 at t = 0: Mxy(t) = M0 exp(-t/T2)) → solution of Bloch equation 0 1.0 (t) (t) M / xy -t/T2 e typical T2-values in 0.5 tissue: 50 - 100 ms 0.37 water: ~1000 ms normalized normalized signal: M T2 echo time TE [ms] 0 50 100 150 200 Seite 6 6 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Simultaneous T1 and T2 Relaxation 11/26/2020 | Page 13 T1- and T2*- relaxation are simultaneous processes T2* < T1 T1-recovery time T2*-decay longitudinal: longitudinal: relaxation to thermalequilibrium transversal: dephasing of spin ensemble RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Movie: T1 and T2 Relaxation 11/26/2020 | Page 14 source: Schlegel and Mahr. “3D Conformal Radiation Therapy: A Multimedia Introduction to Methods and Techniques" 2007 Seite 7 7 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad T1 and T2 Relaxation Times in-vivo 11/26/2020 | Page 15 tissue T2 [ms] T1 [s] at T1 [s] at T1 [s] at 0.5 T 1.0 T 1.5 T skeletal 47 ± 13 0,55 ± 0,10 0,73 ± 0,13 0,87 ± 0,16 muscle myocardium 57 ± 16 0,58 ± 0,09 0,75 ± 0,12 0,87 ± 0,14 liver 43 ± 14 0,33 ± 0,07 0,43 ± 0,09 0,50 ± 0,11 kidney 58 ± 24 0,50 ± 0,13 0,59 ± 0,16 0,65 ± 0,18 spleen 62 ± 27 0,54 ± 0,10 0,68 ± 0,13 0,78 ± 0,15 fata 84 ± 36 0,21 ± 0,06 0,24 ± 0,07 0,26 ± 0,07 grey matter 101 ± 13 0,66 ± 0,11 0,81 ± 0,14 0,92 ± 0,16 white matter 92 ± 22 0,54 ± 0,09 0,68 ± 0,12 0,79 ± 0,13 a more than one exponential component - T1 increases with B0 - T2 nearly independent of B0 Bottomley et al. Med Phys 1984 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad NMR History: Relaxation Times 11/26/2020 | Page 16 excitation refocusing pulse pulse Harvard Nicolaas Bloembergen 1948 Robert Pound excitation refocusing pulse pulse Edward Purcell • characterized the relaxation times of the nuclear response signal in detail © Yves De Deene. University of Gent, Belgium Seite 8 8 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Comparison: CT and MRI 11/26/2020 | Page 17 CT CT WM: 1025 Hu GM: 1035 Hu } = 1% CSF: 1000 Hu r T2 T1 T2 T1 MRI WM: 90 ms 550 ms GM: 100 ms 1000 ms } = 100% CSF: >1000 ms 2000 ms patient: astrocytoma grade II - no bones + best soft tissue contrast + no radiation RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Bloch Equations with T1 and T2 11/26/2020 | Page 18 dMz/dt = (M0 x B)z + (M0 – Mz)/T1 dMxy/dt = (M0 x B)xy – Mxy/T2 rotating system: laboratory system: complex signal: M = Mx + iMy M = M0 exp(-iLt – t/T2) Seite 9 9 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Complex Signal: Simulated FID 11/26/2020 | Page 19 exp(-t/T2) FID complex FT 2 T2 absorption dispersion 2 L Mx: real part FT T2 My: imaginary part FT 2 Mx() = M0 T2 My() = M0 T2 ( - L) 2 2 L 2 2 1 + ( - L) T2 1 + ( - L) T2 light dispersion source: Liang and Lauterbur. “Principles of Magnetic Resonance Imaging” 2000 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Macroscopic Effect: Diamagnetism 11/26/2020 | Page 20 - Lenz’s law: the induced current produces an own magnetic moment in a conductor opposite to B0 - most of biological tissues have diamagnetic properties since the electron magnetization Me of the electron sheath is opposite to B0 due to Lenz’s law: B = 0(H + Me) Me = H -6 with 0 = 1.257 10 Vs/A magnetic field constant -6 H2O = -0.72 10 magnetic susceptibility - weaker B-field inside a diamagnetic sphere due to e--shielding which is very effective since e- = 658 p - intersection of different tissues creates additional local field inhomogeneities of B0 can be “homogenized” by additional shim coils Seite 10 10 RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof. Dr. Lothar Schad Microscopic Effect: Chemical Shift 11/26/2020 | Page 21 1H spectrum of ethanol - precession frequency of nuclei bound in a specific molecule is determined by the local magnetic field Bloc: Bloc = B - B loc = Bloc = (1 - )B 6 with = 10 ( - ref)/0 the relative chemical shift [ppm] - ~ 10 ppm for 1H MRS ~ 100 ppm for 13C, 19F, and 31P - high resolution spectrum at B0 > 1.5 T with B/B0 < 0.1 - 0.5 ppm show multiplet splitting due to spin-spin coupling → domain of MRS - in MRI only protons of water are imaged, chemical shift is not relevant ! exception: fat = 3.5 ppm (220 Hz) at 1.5 T RUPRECHT-KARLS- UNIVERSITY HEIDELBERG Computer Assisted Clinical Medicine Prof.