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Elastography 47499 BME 47500 ME Tuesdays & Thursdays 3:30 pm - 4:45 pm; LH 312 Instructor: Dieter Klatt, Ph.D., Associate Prof., Email: dklatt@uic.edu Office hours: with appointment Office location: West Campus, BME Area NMRL 110B. TA: Jimit Kapadia Email: jkapad4@uic.edu Office hours: Thursdays, 12:30 – 2:30 pm. Office location: SEO, Rm 219 B
Schedule Draft – Work in Progress 1. Introduction. Why Elastography? What is stiffness? 2. Viscoelasticity and propagation of mechanical waves. 3. Overview on modalities for measuring the mechanical properties of biological tissue. 4. MR Elastography I: Data acquisition (From conventional MRI to MRE). 5. MR Elastography II: Data processing and viscoelastic parameter reconstruction. 6. MR Elastography III: New developments. 7. Final Project Practice. Week Topic Tuesday Topic Thursday 1: August 22, 24 1 1 2: Aug. 29, 31 1 2 HW 1 Assignment 3: September 5, 7 2 2 HW 1 Due 4: September 12, 14 2 2 HW 2 Assignment 5: September 19, 21 2 2/3 HW 2 Due 6: September 26, 28 3 HW 3 Assignment 3 7: October 3, 5 3 4 HW 3 Due 8: October 10, 12 4 4 9: October 17, 19 4 4 HW 4 Assignment 10: October 24, 26 4 4 HW 4 Due 11: Oct. 31, Nov. 2 4 4 12: November 7, 9 5 HW 5 Assignment 5 13: November 14, 16 5 HW 5 Due 6 Final Project Assignment 14: November 21, 23 7 No Class: Thanksgiving Day 15: November 28, 30 RSNA 7 December 1 st , 11:59pm Due Friday: Final Project
Bloch equations – Excitation of M T B 0 x y M 0 Β e 1 , Β 1 : envelope and amplitude of RF-pulse 1: frequency of RF-pulse Β 0 : magnetic field from MRI magnet α In case of rectangular pulse: α=γΒ 1 τ τ : duration of RF-pulse resonance condition: 1 =γΒ 0 radiofrequency (RF) pulse M T RF pulse must have frequency according to resonance condition in order to flip the magnetization Flip angle is determined by amplitude and duration of RF-pulse 𝛼𝛼 = 0 𝜏𝜏 𝛺𝛺 1 𝑡𝑡 𝑑𝑑𝑡𝑡 = 𝛾𝛾 � 0 𝜏𝜏 𝐵𝐵 𝑒𝑒 1 𝑡𝑡 𝑑𝑑𝑡𝑡 flip angle α
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M y M z M x M y M x M z ( ) 1 0 2 T e M e M T e M e M B M dt M d z z z y y x x + × = γ Bloch equations – Summary (I) t
M y M z M x M y M x M z Bloch equations – Summary (II) 𝑀𝑀 𝑇𝑇 = 𝑀𝑀 𝑥𝑥 𝑒𝑒 𝑥𝑥 + 𝑀𝑀 𝑦𝑦 𝑒𝑒 𝑦𝑦 Solution - expressed in complex plane 𝑀𝑀 𝑇𝑇 𝑡𝑡 = 𝑀𝑀 0 sin 𝛼𝛼 exp −𝑖𝑖 𝜔𝜔𝑡𝑡 + 𝜙𝜙 0 𝑡𝑡 𝑇𝑇 2 𝑀𝑀 𝐿𝐿 = 𝑀𝑀 𝑧𝑧 𝑒𝑒 𝑧𝑧 𝑀𝑀 𝐿𝐿 𝑡𝑡 = 𝑀𝑀 0 1 + cos 𝛼𝛼 1 exp 𝑡𝑡 𝑇𝑇 1 Larmor frequency: ω flip angle: α equilibrium magnetization: M 0 transverse magnetization: M T initial phase of M T : φ 0 longitudinal magnetization: M L relaxation times: T 1 , T 2 t
t Signal ) / exp( 2 0 T t S S = Spin dephasing due to spin-spin interactions T2-relaxation describes the dephasing of individual magnetic moments due to spin-spin interactions.
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t = 0 t = T E 180° t = T E /2- τ 180° /2 t = Τ E /2 y M T µ 2 µ 1 ∆Ω 2 ∆Ω 1 x y M T µ 2 µ 1 ∆Ω 2 ∆Ω 1 x y M T µ 2 µ 1 ∆Ω 2 ∆Ω 1 x y M T µ 2 µ 1 ∆Ω 2 ∆Ω 1 x t = T E /2+ τ 180° /2 Spin dephasing due to technical imperferctions and rephasing Spin dephasing due to static magnetic field inhomogeneity is reversible by applying 180° RF pulse.
Spin-Echo Source: Wikipedia http://en.wikipedia.org/wiki/File:HahnEcho_GWM.gif Spin dephasing due to static magnetic field inhomogeneity is reversible by applying 180° RF pulse.
t Signal ) / exp( 2 0 T t S S = Spin dephasing T2-relaxation describes the dephasing of individual magnetic moments due to spin-spin interactions. *) / exp( 2 0 T t S S = T2*-relaxation describes the T2-effects plus contributions due to static magnetic field inhomogeneity.
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~exp(-t/T2*) time [s] S FI ( t ) [V] time [s] S SE ( t ) [V] time [s] S GE ( t ) [V] T E 2T E RF-pulse RF-pulse Gradient [T/m] T E /2 3/2T E T E 2T E T E /2 3/2T E 0 0 0 5/2T E 180° 180° 90 90° ~exp(-t/T2*) ~exp(-t/T2) ~exp(-t/T2*) ~exp(-t/TG) MR signal MR signal is read out during an echo spin echos gradient echos free induction decay
• Introduction • MR physics Hardware • Image acquisition Magnetic Resonance Imaging (MRI)
Sketch of MRI hardware components @Shreyan Majumdar
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The magnet 9.4 T small animal MRI Human MRI system Superconducting electromagnet inside MRI casing involves a permanent, homogeneous field B 0 inside bore. B 0 is parallel to scanner axis.
Magnetic field strength in MRI Strong magnetic field involves contraindication for pacemakers, ferromagnetic implants, neurostimulators. 0.0001 Tesla 1.5 - 3.0 Tesla
Potential hazards in MRI environments No ferromagnetic objects ! No magnetic strip cards ! No phones !
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Magnet Preamplifier Control unit Gradient amplifier Compact table-top MRI on tissue samples Field strength 0.5 Tesla Field of view 9.6 x 9.6 mm 2 Slice thickness 5 mm Number of slices 1
RF receive coils in human systems abdomen head-chest lower extremities
Gradient coils and RF transmit coils 9.4 T small animal MRI Human MRI system inside bore inside MR casing
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• Introduction • MR physics • Hardware Image acquisition Magnetic Resonance Imaging (MRI)
x y z axial plane or transverse plane (xy-plane) saggital plane (yz-plane) coronal plane (xz-plane) Image orientation Axial plane and scanner axis are perpendicular to each other.
Magnetic field gradients x G y G y z x Magnetic field gradients describe a linear variation of B along a spatial dimension. z G B B B Magnetic field is equal to the main field B 0 in the magnet isocenter. 𝐵𝐵 = 𝐵𝐵 0 + 𝑟𝑟 � 𝐺𝐺 Magnetic field is parallel to the z-axis. 𝑟𝑟 = 𝑥𝑥 𝑦𝑦 𝑧𝑧
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Magnetic field gradients II x G y G y z x Magnetic field gradients describe a linear variation of B along a spatial dimension. This directly implies a linear variation of the Larmor frequency. z G B B B 𝐵𝐵 = 𝐵𝐵 0 + 𝑟𝑟 � 𝐺𝐺 𝑟𝑟 = 𝑥𝑥 𝑦𝑦 𝑧𝑧 𝜔𝜔 = 𝛾𝛾 𝐵𝐵 0 + 𝑟𝑟 � 𝐺𝐺
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