Introduction to Medical Imaging Week 4: Introduction to Medical Imaging Week 4: MRI – Magnetic Resonance Imaging (part I) Guy Gilboa Course

MRI invention Several involved: ◦ Raymond Damadian – 1971, idea still very sketchy, no images produces. ◦ Paul Lauterbur – , mature technique for 2D and 3D imaging. Produced first image of a living mouse. ◦ Peter Mansfield - developed a mathematical technique where scans take seconds rather than hours also producing clearer images. Nobel prize 2003, ◦ Paul Lauterbur ◦ Sir Peter Mansfield ◦ (Damadian left out, protests of him and colleagues). From top: Damadian, Lauterbur, Mansfield.

MRI scanner The lecture is based mainly on: [1] [2] Ch. 5 of the book by N. B. Smith and A. Webb, Introduction to Medical Imaging, Cambridge University Press, 2011.

Typical brain MRI

MRI – basic operation principle The MRI is comprised of 3 main components: A superconducting primary magnet 3 magnetic field gradient coils RF transmitter and receiver Taken from -+MRI+Radio+Frequency+Coils -+MRI+Radio+Frequency+Coils

Movie – how MRI works (8.5 min.)

Lorentz force

Faraday induction

Magnetic Fields used in MR: 1) Static main field B o 2) Radio frequency (RF) field B 1 3) Gradient fields G x, G y, G z

Very strong magnets used in MRI Ohio Akron Children’s Hospital: 3T MRI (Magnetom Skyra, Siemens). Weight ~7,500kg. Cost $3.5M (2011).

Over 3T magnets  very large and expensive 7T (Stanford) 9.4T (Siemens)

Gradient coils Create a weak magnetic field in any direction in space. Magnetic field strength approximately 100 times lower than the main field.

Reference Frame z x y

Magnetic Moments MR is exhibited in atoms with odd # of protons or neutrons. Spin angular momentum creates a dipole magnetic moment Intuitively current, but nuclear spin operator in quantum mechanics Planck’s constant / 2  Model proton as a ring of current. Which atoms have this phenomenon? 1 H - abundant, largest signal 31 P 23 Na = gyromagnetic ratio : the ratio of the dipole moment to angular momentum

Nuclei spin states There are two populations of nuclei: n + - called parallel n - - called anti parallel n+n+ n-n- lower energy higher energy Which state will nuclei tend to go to? For B= 1.0T Boltzman distribution: Slightly more will end up in the lower energy state. We call the net difference “aligned spins”. Only a net of 7 in 2*10 6 protons are aligned for H + at 1.0 Tesla. (consider 1 million +3 in parallel and 1 million -3 anti-parallel. But...

There is a lot of a water! 18 g of water is approximately 18 ml and has approximately 2 moles of hydrogen protons Consider the protons in 1mm x 1 mm x 1 mm cube. 2*6.62*10 23 *1/1000*1/18 = 7.73 x10 19 protons/mm 3 If we have 7 excesses protons per 2 million protons, we get.25 million billion protons per cubic millimeter!!!!

Torque – mechanical analogy Spins in a magnetic field are analogous to a spinning top in a gravitational field. (gravity - similar to B o ) Top precesses about Magnetic Torque

Precession – Movie (7 min.)

RF Magnetic field The RF Magnetic Field, also known as the B 1 field To excite nuclei, apply rotating field at  o in x-y plane. (transverse plane) B 1 radiofrequency field tuned to Larmor frequency and applied in transverse ( xy ) plane induces nutation (at Larmor frequency) of magnetization vector as it tips away from the z -axis. - lab frame of reference

RF general excitation (rotating frame) By design, In the rotating frame, the frame rotates about z axis at  o radians/sec 1) B 1 applies torque on M 2) M rotates away from z. (screwdriver analogy) 3) Strength and duration of B 1 determines flip angle. This process is referred to as RF excitation. x y z

Coils diagram Simplified Drawing of Basic Instrumentation. Body lies on table encompassed by coils for static field B o, gradient fields (two of three shown), and radiofrequency field B 1. Image, caption: copyright Nishimura, Fig. 3.15

Detection - Switch RF coil to receive mode. Precession of M induces EMF in the RF coil. (Faraday’s Law) EMF time signal - Lab frame t Voltage (free induction decay) x y z M for 90 degree excitation

T1 and T2 relaxation times Application of RF pulse creates non- equilibrium state (adding energy to the system). After the pulse is switched off, the system is relaxed back to equilibrium. There are 2 relaxation times which govern the return to equilibrium: ◦ T1 (spin-lattice), equilibrium of z component. ◦ T2 (spin-spin), x and y components.

Tissue relaxation times for 1.5 Tesla Table: 5.1 from [2] TissueT 1 (ms)T 2 (ms) White matter79090 Gray matter Liver50050 Skeletal muscle87060 Lipid (מסיס שומן) Cartilage (סחוס)106042

Bloch Equation Solution: Longitudinal Magnetization Relaxation Component The greater the difference from equilibrium, the faster the change Solution: Initial Mz Doesn’t have to be 0! Return to Equilibrium

Transverse time constant T2 - spin-spin relaxation T 2 values: < 1 ms to 250 ms What is T 2 relaxation? - z component of field from neighboring dipoles affects the resonant frequencies. - spread in resonant frequency (dephasing) happens on the microscopic level. - low frequency fluctuations create frequency broadening. Image Contrast: Longer T2’s are brighter in T2-weighted imaging, darker in T1-weighted imaging

MR: Relaxation: Some sample tissue time constants - T 1 Image, caption: Nishimura, Fig. 4.2 fat liver kidney Approximate T 1 values as a function of B o white matter gray matter muscle

Gradient Fields - key for imaging - Paul Lauterbur Gradient coils are designed to create an additional B field that varies linearly across the scanner as shown below when current is driven into the coil. The slope of linear change is known as the gradient field and is directly proportional to the current driven into the coil. The value of B z varies in x linearly. z BzBz BoBo slope = G z Whole Body Scanners: |G| = 1-4 G/cm (10-40 mT/m) Gz can be considered as the magnitude of the gradient field, or as the current level being driven into the coil.

Basic Procedure 1)Selectively excite a slice (  z) - time?.4 ms to 4 ms - thickness?2 mm to 1 cm 2) Record, control G x and G y - time?1 ms to 50 ms 3) Wait for recovery - time?5 ms to 3s 4)Repeat for next measurement. - measurements?128 to in just 1 flip 5) Next: More on spatial encoding

Phase and frequency encoding It is not important which dimension encodes frequency and which phase. We assume: ◦ X encodes frequency ◦ Y encodes phase

Frequency encoding

Phase encoding

K-space formalism (5.10)

Image recovery

Phase Direction Frequency Direction One line of k-space acquired per TR k-Space Acquisition Phase Encode DAQ Sampled Signal kxkx kyky Taken from [1]

Fast Fourier Transform  FFT

8 x x 512

16 x x 512

32 x x 512

64 x x 512

128 x x 512

256 x x 512

Multiple slice imaging The TR time required between successive RF excitations for each phase encoding step is much longer than TE. In this time other adjacent slices are usually acquired (maximum of TR/TE) Usually this is done in an interlacing fashion – od numbered slices are followed by even-numbered slices.

Spin-echo imaging sequence SS – Slice selection, PE – Phase encoding, FE – Frequency encoding, TR – Time of repetition, TE – Time of echo.

T1, T2, PD A long TR and short TE sequence is usually called Proton Density (PD) –weighted. A short TR and short TE sequence is usually called T1- weighted A long TR and long TE sequence is usually called T2-weighted Taken from

MR angiography Increase signal difference between flowing blood and tissue Based on TOF (time-of-flight) technique, shorter effective T1 due to flow if the slice is oriented perpendicular to the direction of flow.

Functional MRI Determines which areas of the brain are involved in cognitive tasks and brain functions such as speech and sensory motion. Based on the fact that MRI signal intensity changes depending upon the level of oxygenation of the blood in the brain (indicating increased neuronal activity). Uses fast scans which can cover the brain in a few seconds.

Example of fMRI Brain activity changes of teenagers playing violent video games. Taken from