Gyroscope Movie Nuclear Magnetic Resonance NMR Nuclear Magnetic

Gyroscope Movie

Nuclear Magnetic Resonance (NMR) • Nuclear Magnetic Resonance (NMR) is a powerful technique for the investigation of chemical and physical properties at the molecular level. • Precession of the Proton that allows magnetic resonance imaging. • Proton in a magnetic field will precess about the magnetic field because it has spin angular momentum and a magnetic dipole moment.

Angular Momentum •

Angular Momentum

Spin

Angular Momentum •

Angular Momentum

Orbital Momentum

Angular Momentum •

Angular Momentum

Angular Momentum

Magnetic Dipole Moment (MDM) • The Magnetic field is generated from the motion of electric charges (electric current). • If we set a point charge moving in a circle then we have a current loop which will generate a magnetic field in turn.

Magnetic Dipole Moment (MDM)

Magnetic Dipole Moment (MDM) • Proton is a sphere like and its charge is distributed on its volume and this charge is spinning (moving charge). • The motion of proton’s charge will generate a magnetic field.

Magnetic Dipole Moment (MDM)

Magnetic Dipole Moment (MDM)

Magnetic Dipole Moment (MDM)

Magnetic Dipole Moment (MDM)

Magnetic Dipole Moment MDM Gyroscope Movie

Magnetic Resonance Imaging MRI • How we can employ the property of Magnetic Dipole Moment of protons in the field of Imaging?

Magnetic Resonance Imaging MRI • Protons like electrons they rotate in shell but inside the nucleus and according to Pauli exclusion principle each proton will be in a state different from other protons. • As a whole if the nucleus has odd number of protons then it said that this nucleus has a magnetic dipole moment

Proton Spin • • • In absence of a magnetic field, protons spin at random A magnetic field is used to align them (B 0) Current MRI fields run at 0. 5 and 3. 0 Teslas 1 Tesla is equal to 10, 000 Gauss Earth's magnetic field varies from between 0. 3 - 0. 7 Gauss. • Refrigerator magnet ~10 -100 Gauss

Alignment of Nuclear MDM in a Magnetic Field

Magnetic Dipole Moment (MDM) There are only three kinds of nuclei as far as the spin is concerned. 1 - If the number of neutrons and the number of protons are both even, then the nucleus has NO spin. 2 - If the number of neutrons plus the number of protons is odd, then the nucleus has a half-integer spin (i. e. 1/2, 3/2, 5/2) 3 - If the number of neutrons and the number of protons are both odd, then the nucleus has an integer spin (i. e. 1, 2, 3)

Alignment of Nuclear MDM in a Magnetic Field • The term MDM can be translated to “tiny magnet” • When tiny magnets placed in an external magnetic field (Bo) they will try to align in the direction of the external magnetic field. • We have alluded to the idea that MRI is based on the interaction of a nuclear spin with an external magnetic field, Bo. The dominant nucleus in MRI is the proton in hydrogen and its interaction with the external field results in the precession of the proton spin about the field direction.

Alignment of Nuclear MDM in a Magnetic Field

Alignment of Nuclear MDM in a Magnetic Field

Alignment of Nuclear MDM in a Magnetic Field

Alignment of Nuclear MDM in a Magnetic Field MDM Alignment Movie

Alignment of Nuclear MDM in a Magnetic Field •

Alignment of Nuclear MDM in a Magnetic Field • The magnetic moment, vector for a typical proton is prevented from relaxing fully to an alignment, along the external magnetic field because of thermal energy associated with the absolute temperature T. For a proton with only two quantum spin states, there are only two possible alignments. 1 - Parallel alignment (lower energy). 2 - Anti-parallel alignment (higher energy).

Alignment of Nuclear MDM in a Magnetic Field

Alignment of Nuclear MDM in a Magnetic Field

Alignment of Nuclear MDM in a Magnetic Field

Alignment of Nuclear MDM in a Magnetic Field • The number of protons with spin up (parallel to the magnetic field or low energy state) is little greater than the number of protons with spin down (anti parallel to the magnetic field or high energy state) around 1 per million. • The ratio of the number of protons in the low energy state to protons in the high energy is determined by 1 - the difference in energy between the two states. 2 - The magnetic field. 3 - The temperature.

Magnetization • The magnetization is defined as the sum of the magnetic dipole moment of protons. • The net magnetic dipole moment (magnetization) in the presence of external magnetic field is Not zero.

Alignment of Nuclear MDM in a Magnetic Field

Alignment of Nuclear MDM in a Magnetic Field

Magnetization • In a population of 2, 000 nuclei, 1, 000 + 1 might go to the lower energy state, while 1, 000 – 1 might go the higher energy state. • For a sample of 1023 nuclei, the difference in the population of the two states would be 1017 nuclei. • The NMR signal is produced only by the 1023 excess nuclei.

Larmor Frequency • The frequency of precession, is called Larmor frequency, is of fundamental importance in NMR. • Larmor frequency depends on 1 - The magnetic field B. 2 - The gyromagnetic ratio, γ.

Larmor Frequency • ω = γB • Where • ω: is Larmor frequency. • γ: Gyromagnetic ratio. • B: is the total magnetic field.

Larmor Frequency • The gyromagnetic ratio is the ratio of the MDM to the nuclear spin angular momentum. • γ = μ/Jħ • with • μ: magnetic dipole moment (MDM). • ħ = h/2π = 1. 05 x 10 -34 J. s • J: nuclear spin. • And Jħ is the nuclear spin angular momentum.

Larmor Frequency

Larmor Frequency • Each type of nucleus will precess at a unique frequency in a given magnetic field. • Two different nuclei will precess at two different frequencies in a given field. • Larmor precession (frequency) is a process that, for a given field, can distinguish between nuclear types. • ω/2π = 8. 5 MHz at 0. 2 Tesla for Hydrogen nucleus. • ω/2π = 42. 58 MHz at 1 Tesla for the same nucleus.

Larmor Frequency • The concept of identical nuclei in a slightly different magnetic fields is the concept on which a great deal on NMR work is based. • More interest in NMR imaging is the purposely varied field to help establish different Larmor frequencies for a given nuclear type (usually hydrogen) across the object to be imaged.

Larmor Frequency

Larmor Frequency • The torque produced from the interaction of MDM and the magnetic field and is required to precess the MDM around B is defined by • τ=μx. B • The torque on both the spin-up and spin-down nuclei, however, is the same. Therefore, both spin-up and spin-down nuclei precess in the same direction.

Larmor Frequency • When an MDM aligned with a magnetic field, it is energy (magnetic potential energy) is just • E = -μB (spin-up). • While in the reversed orientation • E = μB (spin-down). • The difference in energy between these two orientation is 2μB

Larmor Frequency

Larmor Frequency • For a nucleus to flip from the lower to the higher energy state, it must absorb this amount of energy from somewhere. • When the nucleus returns from the higher to the lower energy state, the energy is transformed to the lattice (the material structure surrounding the nucleus) usually in the form of heat Not in the form of electromagnetic radiation.

Larmor Frequency • A radio frequency (RF) pulse with a frequency equal to Larmore frequency is to transit the lower energy state to the higher energy state. • The basis of NMR is to induce transitions between these energy states by the absorption and transfer of energy.

Magnetization • Earlier we said that for a sample with 1023 nuclei would be involved in the NMR process. • 1017 are excess nuclei, it impossible to visualize what these nuclei are doing. • Normally, we replace all these individual nuclei having individual MDMs by a single vector termed the magnetization M

Magnetization

Magnetization • Each nucleus has a MDM. If we add up the MDM of all these nuclei the resulting sum is the magnetization, M, of the sample. • Because the MDM is a vector it has components parallel and perpendicular to the magnetic field B. • The excess nuclei in the lower energy state give a net magnetization parallel (along) the field. • For nuclei, the perpendicular components of MDM for both spin-up and spin-down add up to zero.

Magnetization

Magnetization MRI Principle 1 of 4 movie

Magnetization • The magnetization behaves like a magnet that has a spin angular momentum. That is, the magnetization can precess about a magnetic field if the magnetization and the magnetic field are Not parallel. • Because the magnetization M is exactly parallel to B. This means M cannot precess about B.

Radio Frequency Magnetic Field (RF) • Since M is not precess’ about B, we would like to displace M from its direction along B and watch M as it tries to go back to its alignment along B. • To have M precessing about B, another external magnetic field B 1 will be applied which will displace M from the direction of B. • B 1 is the radio frequency magnetic field (RF).

Properties of B 1 1 - B 1 must be perpendicular to B. If we assume that B is in the z-direction then B 1 will be in the xy-plane. 2 - B 1 is much smaller than B. 3 - B 1 is rotating about B at the Larmor frequency.

Precession of M • After applying B 1 the magnetization vector M is displaced from the direction of B. • M now has two different precession motions. 1 - it precess about B with Larmor frequency ω = γB 2 - it precess about B 1 with frequency ω1 = γB 1. Remember that M and B 1 are both precessing about B with Larmor frequency.

Precession of M MRI principle 1 of 4 movie

Precession of M

Precession of M

Precession of M

Precession of M

Precession of M • After applying the RF the magnetization M is moving toward the xy-plane, the angle at which M will flipped toward the xy-plane depends on the time of applying the RF (B 1). • This angle α = ω1 t. where t is the time of applying the RF.

Precession of M • Now M is moving from the direction of B toward the xy-plane, which means that M is varied with time. • so we can get a signal while M is moving down. • Because the MDM were precessing with different frequencies they were out of phase, after applying the RF these MDM will come close to each other to be in -phase.

Signal received from M • The RF is applied for a time enough to flip M into the xy-plane so M does not have any component in the zdirection, and all the MDMs are in-phase that is mean all the MDMs are precessing with the same frequency about B. After the Rf done the MDMs start to dephase again, so the M vector varies with time that is mean we can get a signal from de-phasing of the MDMs.

Signal received from M MRI principles 2 of 4 movie

Spin-spin relaxation time T 2 • The signal from de-phasing of MDMs is given by. • where • t: is the time after turning RF of. • T 2 is the spin-spin relaxation time. T 2 depends on spin interaction. • Mxy(0) is the component of M in the xy-plane prior to turn the RF off.

Spin-lattice relaxation time T 1 • The signal received when the magnetization goes back to the direction of B is given by. • where Mz(0) is the component of M in the direction of B just after turning the RF. • Mo is the equilibrium magnetization.

Signal received from M • Now M is going back to align with B, which means a signal from the change of M will produce a signal. • A change in the magnitude or direction of M will produce a n induced current in the coil detector.