The Basics of Magnetic Resonance Imaging (MRI)

1. Dr. Tanveer Ahmad PhD., PostDoctorate(Nano Physics) Department of Physics And Energy Sciences KNU, South Korea / AWKUM, Pakistan. The Basics of Magnetic Resonance Imaging (MRI)

2. Contents • Introduction • Magnetic properties of nuclei • Larmour Frequency • Net magnetization • 90° Pulse And 180° Pulse • Resonance • Excitation • Relaxation -Longitudinal Relaxation (T1 Relaxation time) -Transverse Relaxation (T2 Relaxation time) Differences Between T2 And T2* *Key concepts

3. Introduction • Magnetic moment is defined as the strength of magnetic property an object has, and is directly proportional to the object's total angular momentum. • Total angular momentum equals the vector sum of rotation and spin angular momenta. • Nuclear magnetic moment derives mainly from the collective spin motion of nuclei, the same way that electronic magnetic moment derives from the collective angular motion of electrons. • Only atoms whose total angular momentum is not zero are magnetic. • In general, atoms with filled electronic shell have zero angular momentum, and thus are nonmagnetic. • For example, transition metals have unfilled inner shell, and are magnetic. • On the same line, atoms whose nuclear angular momentum is not zero have nuclear magnetic moment, and thus are nuclear magnetic.

4. Magnetic properties of nuclei • In MRI, we exploit the magnetic property of the proton in hydrogen. Hydrogen has nuclear magnetic moment due to the spin motion of the proton in the nucleus. Human organs consist of water molecules, which, in turn, consist of two hydrogens and one oxygen. Thus, if we exploit the nuclear magnetic property of hydrogen in MRI imaging, large MR signal can be obtained, the human body being a huge reservoir of hydrogen. The nuclear magnetic moment of hydrogen is called the proton spin or more often, shortly, the proton. • Hydrogen nuclei (protons) have magnetic properties, called nuclear spin. • They behave like tiny rotating magnets, represented by vectors. Magnetic moment of proton, is related to the angular momentum, as Here, is the gyro-magnetic ratio, and has the value of for hydrogen proton.

5. Magnetic properties of nuclei • A proton in the hydrogen atom has a total angular momentum of j=1/2. • A particle with total angular momentum of j=1/2 has two possible magnetic quantum numbers: mj=1/2 and -1/2. • This means that if a hydrogen atom is placed in the magnetic field, there are two possible orientations for the proton: parallel (mj=1/2) and anti-parallel (mj=-1/2) to the field.

6. In “field free” space randomly oriented Magnetic properties of nuclei • The sum of all the tiny magnetic fields of each spin is called net magnetization or macroscopic magnetization. • Normally, the direction of these vectors is randomly distributed. Thus, the sum of all the spins gives a null net magnetization.

7. Inside magnetic field M Applied Magnetic Field (B0) oriented with or against B0 M = net magnetization Magnetic properties of nuclei • Within a large external magnetic field (called B0), nuclear spins align with the external field. • Some of the spins align with the field (parallel) and some align against the field (anti-parallel). • There is a small difference (10:1 million) in the number of protons in the low and high energy states – with more in the low state leading to a net magnetization (M)

8. Magnetic properties of nuclei • If a magnet with a magnetic moment of μ is placed in a magnetic field, it experiences a torque of τ =μ X B , where τ and B represent torque and magnetic field, respectively. Newton's second law expresses the angular motion as dJ/dt = τ . • A proton can also be considered as a small magnet with a magnetic moment of μ . • Thus a proton with a magnetic moment of μprecesses about the axis of magnetic field, B , with an angular frequency of ω =γB, as depicted in Fig. • The angular frequency, ω =γB , is called Larmour frequency. We can see that Larmour precession frequency increases as the strength of magnetic field increases. Spins wobble (or precess) about the axis of the B0 field so as to describe a cone. This is called precession.

9. Magnetic properties of nuclei • Spinning protons are like dreidles spinning about their axis. • Precession corresponds to the gyration of the rotating axis of a spinning body about an intersecting axis. • Spinning proton in a magnetic field (or a spinning top in a gravitational field) will "precess” at a speed determined by the strength of the magnetic field : f = B0

10. Larmor Frequency

11. Larmor Frequency f = B0  = 42.58 MHz/T At 1.5T, f = 63.76 MHz At 4T, f = 170.3 MHz • The resonance frequency, called Larmor frequency (w0) or precessional frequency, is proportional to the main magnetic field strength. 170.3 Resonance Frequency for 1H 63.8 1.5 4.0 Field Strength (Tesla)

12. Net magnetization • The magnetic vector of spinning protons can be broken down into two orthogonal components: a longitudinal or Z component, and a transverse component, lying on the XY plane. • Precession corresponds to rotation of the transverse component about the longitudinal axis.

13. Net magnetization By Boltzmann distribution, we can calculate the ratio of lower energy state protons to higher energy state protons. • Within the B0magnetic field, there are more spins aligned with the field (parallel - low energy state) than spins aligned against the field (anti-parallel - high energy state). • Due to this slight excess of parallel spins, net magnetization (macroscopic magnetization) has a longitudinal component (along the Z axis) aligned with B0.

14. Net magnetization • As spins do not rotate in phase, the sum of all the microscopic transverse magnetizations of each spin is a null transverse macroscopic magnetization.

15. 90° Pulse And 180° Pulse • In MRI, two pulses are widely used. Those are the 900 and 1800 pulses which make the magnetization vector rotate to the Y-axis and –Z axis, respectively.

16. 90° Pulse • The pulse that causes the 90° flip is called a 90° RF pulse. • After applying an RF pulse If the entire vector M0 flips into the x-y plane, then the magnitude of Mxy equals the magnitude of the vector M0. This is called a 90° flip.

17. 180° Pulse A 180° RF pulse can rephase spins and reverse static field inhomogeneities. After a 90° RF pulse, spins dephase and transverse magnetization decreases. If we apply a 180° RF pulse, spins rephase and transverse magnetization reappears. • A 180° Pulse has twice the power or twice the duration of a 90° Pulse. • After a 180° Pulse, the longitudinal magnetization vector is inverted and spins begins to recover from –M0 . We can calculate the RF

18. Resonance • Exchange of energy between two systems at a specific frequency is called resonance. • Magnetic resonance corresponds to the energetic interaction between spins and electromagnetic radio frequency (RF).

19. Resonance • Only protons that spin with the same frequency as the electromagnetic RF pulse will respond to that RF pulse. • There is a modification of spin equilibrium and absorption of electromagnetic energy by atomic nuclei, which is called excitation. • When the system returns from this state of imbalance to equilibrium (relaxation), there is an emission of electromagnetic energy.

20. Excitation • Excitation modifies energy levels and spin phases. • At the quantum level, a single proton jumps to a higher energy state (from parallel to anti-parallel). • The consequence on the macroscopic net magnetization vector is a spiral movement down to the XY plane.

21. B0 B1 Excitation • the net magnetization vector tips down during excitation. • The flip angle is in function of the strength and duration of the electromagnetic RF pulse. • final angle between B0 and B1 is the flip angle

22. Excitation • The net magnetization vector can be broken down into a longitudinal component (along the Z axis, aligned with B0), and a transverse component, lying on the XY plane. • During excitation, longitudinal magnetization decreases and a transverse magnetization appears (except for a 180° flip angle). • Longitudinal magnetization is due to a difference in the number of spins in parallel and anti-parallel state. • Transverse magnetization is due to spins getting into phase coherence.

23. Excitation • If we consider an excitation with a 90° flip angle, when the RF transmitter is turned off: • There is no longitudinal magnetization (equal proportion of parallel and anti-parallel spins) • A transverse magnetization exists (all spins are in phase : complete phase coherence)

24. Excitation • The key points • The net magnetization vector tips down during excitation but the microscopic spin magnetization vectors do not. • Modifications of the energy state and phase of spins depend on intensity, waveform and duration of RF pulse. • Longitudinal magnetization is due to a difference in the number of spins in parallel and anti-parallel state. • Transverse magnetization is due to spins getting more or less into phase.

25. Relaxation • Return to equilibrium of net magnetization is called Relaxation. • During relaxation, electromagnetic energy is retransmitted: this RF emission is called the NMR signal.

26. Relaxation Relaxation combines 2 different mechanisms: • Longitudinal relaxation corresponds to longitudinal magnetization recovery • Transverse relaxation corresponds to transverse magnetization decay

27. Longitudinal Relaxation • Longitudinal relaxation is due to energy exchange between the spins and surrounding lattice (spin-lattice relaxation), re-establishing thermal equilibrium. • As spins go from a high energy state back to a low energy state, RF energy is released back into the surrounding lattice.

28. Longitudinal Relaxation(T1) • The recovery of longitudinal magnetization follows an exponential curve. • The recovery rate is characterized by the tissue-specific time constant T1. • After time T1, longitudinal magnetization has returned to 63 % of its final value. • With a 1.5 T field strength, T1 values are about 200 to 3000 ms.T1 values are longer at higher field strengths.

29. Transverse Relaxation(T2) • Transverse relaxation results from spins getting out of phase. As spins move together, their magnetic fields interact (spin-spin interaction), slightly modifying their precession rate. • These interactions are temporary and random. Thus, spin-spin relaxation causes a cumulative loss in phase resulting in transverse magnetization decay.

30. Transverse Relaxation • Transverse magnetization decay is described by an exponential curve, characterized by the time constant T2. • After time T2, transverse magnetization has lost 63 % of its original value. • T2 is tissue-specific and is always shorter than T1. • Transverse relaxation is faster than longitudinal relaxation. • T2 values are unrelated to field strength.

31. T2 Relaxation Transverse magnetization Time

32. Differences Between T2 And T2* T2* is always shorter than T2. T2* signal decay is lower than pure T2 signal decay.

33. Key concepts • Within a magnetic field B0, the sum of spins is a net magnetization aligned with B0. • This macroscopic magnetization results from a slight excess of spins in parallel state and a null transverse magnetization due to spins being out of phase. • Precession frequency (Larmor frequency) of protons is proportional to field strength intensity. • A RF pulse that matches the precession frequency affects the spin equilibrium : there is an exchange of energy and a tip down of the net magnetization vector. • Flip angle depends on intensity, waveform and duration of RF pulse.

34. Key concepts • Relaxation is the dynamic physical process in which the system of spins returns to equilibrium. • Relaxation can be broken down into:1. Recovery of longitudinal magnetization, aligned with B0, following an exponential curve characterized by time constant T1

35. Key concepts 2. Decay of transverse magnetization, due to spins getting out of phase, according to an exponential curve characterized by time constant T2.

36. Surface Coil