MRI Physics: Chapter 1: Basic Principles (Book: MRI in Practice)

Pulse Timing Parameters

A very simplified pulse sequence is a combination of RF pulses, signals and intervening periods of relaxation The separate timing parameters used in more complicated sequences Repetition time (TR) Echo time (TE)

Out of phase / incohernet

Means that magnetic moments of hydrogen are at different places on the precessional path at a moment in time When the only influence is B0 (static field) the magnetic moments of the nuclei are out of phase with each other, and therefore the NMV does not precess

In phase / coherent

Means that magnetic moments of hydrogen are at the same place on the precessional path at a moment in time

Atoms are organized into?

Molecules, which are two or more atoms arranged together

Atoms consist of?

A central nucleus and orbiting electrons -The nucleus is very small, one millionth of a billionth of the total volume of the atom -It contains all of the atoms mass (the nucleus)

The laws of electromagnetic induction (Faraday) states that the induced emf:

(1) is proportional to the rate of change of magnetic field and the area of the circuit (2) is proportional to the number of turns in a coil of wire (3) is in a direction so that is opposes the change in magnetic field that cause is (Lenz's law)

Classical Theory

*Accredited by Sir Isaac Newton and often called Newtonian theory -Provides a mechanical view of how the universe (and therefore MRI) works

Quantum Theory

*Accredited to several individuals including Max Planck, Albert Einstein, and Paul Dirac -Operates at a much smaller, subatomic scale and refers to the energy levels of protons, neutrons and electrons

Things to remember: Excitation and Signal Generation

-Application of RF energy at the Larmor frequency causes a net absorption of energy (excitation) and changes the balance between the number of spins in the low and high energy populations -The orientation of the NMV to B0 depends on this balance. If there are a similar number of spins in each population, the NMV lies in a plane at 90° to B0 (transverse plane) -Resonance also causes the magnetic moments of all spins to precess in phase. The result is coherent transverse magnetization that precesses in the transverse plane -If a receiver coil (conductor) is placed in the transverse plane, the movement of the rotating coherent transverse magnetization causes a voltage in the coil -When the RF excitation pulse is removed, the magnetic moments of all spins de-phase and produce FID

Excitation

-Application of an RF pulse that causes resonance, means it is "energy giving"

MR-active nuclei

-Are characterized by their tendency to align their axis of rotation to an applied magnetic field -This occurs because they have angular momentum or spin and, as they contain positively charged protons, they posses an electrical charge -Have a net electrical charge (electric field) and are spinning (motion) thus automatically acquire a magnetic field This magnetic field is called a magnetic moment

The difference between these two states is proportional to the strength of the external magnetic field (B0)

-As B0 increases, the difference in energy between the two energy states increases, and nuclei therefore require more energy to align their magnetic moments in opposition to the main field. -Boltzmann's equation shows that the patient's temperature is an important factor that determines whether a spin is in the high or low energy population

Results of Resonance - Classical Theory

-As the B1 magnetic field associated with the RF excitation pulse is weak, the magnetic moments of spins precess at a much lower frequency than they do when they are aligned in the longitudinal place and experience the much larger B0 field -Another consequence of RF excitation pulse is that the magnetic moments of the spin-up and spin-down nuclei move into phase with each other -Magnetic moments that are in phase (coherent) are in the same place on their precessional path at any given time *When resonance occurs, all magnetic moments move into the same position on the precessional path and are then in phase

Low-Energy Nuclei

-Do not have enough energy to oppose the main B0 field -These are nuclei that align their magnetic moments parallel or spin-up to the main B0 field in the classical description

Precession

-Each hydrogen nucleus spins on its axis -The influence of B0 (static field in machine) produces an additional spin or wobble of the magnetic moments of hydrogen (in the body) around B0 -This is a secondary spin, and causes the magnetic moments to circle around B0

Gyromagnetic ratio

-Expresses the relationship between angular momentum and the magnetic moment of each MR-active nucleus. -It is constant and is expressed as the precessional frequency of the magnetic moment of a specific MR0active nucleus at 1 T (tesla) -Unit of measurement MHz/T -Gyromagnetic ratio of hydrogen 42.58 MHz/T *Other MR-active nuclei have different gyromagnetic ratios, so their magnetic moments have different precessional frequencies at the same field strength

Things to remember: Basics of the atom

-Hydrogen is the most abundant element in the human body -Nuclei that are available for MRI are those that exhibit a net spin -As all nuclei contain at least one positively charged proton, those that also spin have a magnetic field induced around them -An arrow called a magnetic moment denotes the magnetic field of a nucleus in classical theory

Examples of MR-active nuclei

-Hydrogen: 1H Protons: 1 Neutrons: 0 Nuclear Spin: 1/2 % Natural Abundance: 99.985 -Carbon: 13C Protons: 6 Neutrons: 7 Nuclear Spin: 1/2 % Natural Abundance: 1.10 -Nitrogen: 15N Protons: 7 Neutrons: 8 Nuclear Spin: 1/2 % Natural Abundance: 0.366 -Oxygen: 17O Protons: 8 Neutrons: 9 Nuclear Spin: 5/2 % Natural Abundance: 0.038 -Fluorine: 19F -Sodium: 23Na

Alignment

-In the absence of an applied magnetic field, the magnetic moments of hydrogen nuclei are randomly oriented and produce no overall magnetic effect -When placed in a strong static external magnetic field (B0) the magnetic moments of hydrogen nuclei orientate with this magnetic field. This is called alignment

Things to remember: Precession

-Magnetic moments of all the spins precess around B0 at the Larmor frequency that is proportional to B0 for a given MR-active nucleus. Frequency therefore refers to how fast magnetic moments of spins are precessing an is measured in MHz in MRI -For field strengths used in clinical imaging, the Larmor frequency of hydrogen is in the radio-frequency (RF) band of the electromagnetic spectrum -Phase refers to the position of a magnetic moment of a spin on its precessional path at nay moment in time -At equilibrium, the magnetic moments of the spins are out of phase with each other

Resonance

-Phenomenon that occurs when an object is exposed to an oscillating perturbation that has a frequency close to its own natural frequency of oscillation -When a nucleus is exposed to an external force that has an oscillation similar to the natural frequency of its magnetic moment (or its Larmor frequency) the nucleus gains energy from the external force *If energy is delivered at a different frequency to that os the Larmor frequency, resonance does not occur, and the nucleus does not gain energy -Resonance is achieved by transmitting an RF pulse called RF excitation pulse

Some particles in the atom possess and electrical charge.

-Protons have a positive electrical charge -Neutrons have not net charge -Electrons have a negative electrical charge

Alignment: Quantum Theory

-Quantum theory uses the energy level of the spins to illustrate alignment -Protons of hydrogen nuclei couple with the external magnetic field B0 (Zeeman interaction) cause a discrete number of energy states For hydrogen there are only 2 types of energy states

B0

-Refers to the large magnetic field of the scanner, is the static magnetic field -The static magnetic field is measures in teslas (T) -B is the universally accepted notion for magnetic flux density, and the zero annotation indicates that this is the primary magnetic field of the scanner *There are other magnetic fields, graded or sloped (called gradients, used to produce images) and an oscillating magnetic field that causes a phenomenon called resonance *This oscillating filed is termed B1, it has a magnitude several orders lower than B0 (millitesla vs. Teslas)

Phase

-Refers to the position of magnetic moments on their precessional path at any moment in time -Unit of phase is radian * a magnetic moment travel through 360 rad or 360° during one rotation

Net Magnetic Moment (NMV)

-Reflects the relative balance between spin up and spin down nuclei **It is the sum of all magnetic moments of excess spin up nuclei, and is measurable (microtesla) -It aligns in the same direction as the main magnetic filed in the longitudinal plane or z-axis -The number os spins that constitute this small excess depends on the number of molecules per gram os tissue and the strength of B0

Oscillating Magnetic Field B1

-The B1 field is applied at 90° to B0 at a narrow range or bandwidth of frequencies, centered around a central frequency (transmit bandwidth) -The magnetic field associated with the RF excitation pulse B1 is very weak compared with the main external field B0

B0 vs. B1

-The RF excitation pulse is characterized by its amplitude (B1) and its frequency -For resonance to occur, the frequency of the RF excitation pulse must equal the Larmor frequency of magnetic moments of hydrogen nuclei If match occurs, B1 causes magnetic moments of the hydrogen nuclei to precess in the transverse plane How fast they precess in transverse plane is derived from the Larmor equation (States that precessional frequency is proportional to the field strength) As B1 is much smaller than B0 magnetic moments of the hydrogen nuclei precess at a much lower frequency than they do before resonance when affected only by B0 Before resonance, not only do they precess faster but their magnetic moments are out of phase (incoherent) and therefore have no net transverse component When B1 field is applied in the transverse plane, magnetic moments align with this field and gain phase coherence Causes an increase in transverse magnetization The combination of development of phase coherence and nutation results in coherent magnetization that precesses in the transverse plane During the RF excitation pulse, the transverse magnetization precesses at a frequency dependent on the amplitude of the B1 field

Magnetic Moment

-The magnetic moment of each nucleus has vector properties size (magnitude) and direction -The total magnetic moment of the nucleus is the vector sum of all the magnetic moments of protons in the nucleus

Flip angle

-The magnitude of the flip angle depends on the amplitude and duration of the RF excitation pulse -Usually, the flip angle is 90°, the NMV is given enough energy by the RF excitation pulse to move through 90° relative to B0 -With a flip angle of 90° the nuclei are given sufficient energy so that the longitudinal NMV is completely transferred into a transverse NMV -When a flip angle less than or more than 90° are used, only a portion of the NMV is transferred to the transverse plane -The flip angle depends on the strength of the B1 field and for how long it is applied

Spinning direction

-The principles of MRI rely on the spinning motion of specific nuclei present in biological tissue -There are a limited number of spin values depending on the atomic and mass numbers -A nucleus has NO spin if it has an EVEN atomic and mass number EX| 6 protons, 6 neutrons mass number 12 -In nuclei that have an even mass number caused by an even number of protons and neutrons, half of the nucleons spin in one direction and half in the other (the forces of rotation cancel out, and the nucleus itself has not net spin) -Nuclei with ODD number of protons and ODD number of neutrons, or ODD number of both, the spin directions are not equal and opposite so the nucleus itself HAS a net spin (angular motion)

Nutation

-The transition results in a spiral motion downward of the NMV from the longitudinal to the transverse plane This spiral motion is called nutation and is caused by two precessional motions that happen simultaneously (1) precession around B0 (2) much slower precession around B1

Avogadro's Law

-There are 6 x 10 ^ 23 molecules per gram of tissue -Number of excess spins is in the order of 6 x 10 ^ 17 per gram pf tissue

Alignment in thermal equalibrium

-There are a greater proportion o spins with their magnetic moments aligned in the same direction as B0 than against it -As there is a larger number aligned parallel, there is always a small excess in this direction that produces a net magnetic moment (NMV)

RF excitation pulse

-This is produced by a transmit coil -It consists of an electric and magnetic field that propagate in waves at 90° to each other -These waves have a frequency that resides in the RF band of the electromagnetic spectrum -The RF excitation pulse is derived from the magnetic component only (the electric field produces heat) and unlike the B0 (static magnetic field, which is stationary) the RF excitation pulse produces an oscillating magnetic field, termed B1

Things to remember: Alignment

-When placed in an external magnetic field, the magnetic moments of hydrogen align in a spin-up, low-energy or spin-down, high-energy orientation -At thermal equilibrium, there are more spin-up low-energy than spin-don high-energy spins so the net magnetic vector (NMV) of the patient is orientated in the same direction as B0 -The difference in energy between these populations is mainly determined by the strength of B0 -As B0 increased the energy difference between the two populations also increase as the number of spin-up low-energy spins increases relative to the number of spin-down high-energy spins -The signal-to-noise ration (SNR) increases at higher values of B0

Faraday's Law

A changing magnetic field causes movement of charged particles; electrons This flow of electrons is a current, and if a receiver coil or any conductive loop is pace in a moving magnetic field (magnetization precessing in the transverse plane) a voltage generated by this current is induced in the receiver coil. This voltage is called a signal And is produced when coherent (in phase) magnetization cuts across the coil The frequency of signal depends on the frequency of rotation of the magnetic field - the magnitude of signal depends on the amount of coherent magnetization present in the transverse plane

Hydrogen Precessional Frequencies

1.5 T = 63.87 MHz (42.58 MHz x 1.5 T) 1.0 T = 42.57 MHz (42.58 MHz x 1.0 T) 1.5 T = 21.29 MHz (42.58 MHz x 0.5 T) *These frequencies fall into the radio-frequency (RF) band of the electromagnetic spectrum

Number of excess spins at 1.5 T 3 T

1.5 T, the number in excess is about 4.5 for every million protons 3T increase t about 10 million

Antiparallel alignment

Alignment of magnetic moments in the opposite direction to the main B0 field (also referred to as spin down)

Parallel alignment

Alignment of magnetic moments in the same direction as the main B0 field (also referred to as spin up)

What does the Larmor equation tell us?

All MR-active nuclei have their own unique gyromagnetic constant or ratio, so that when they are exposed to the same field strength, their magnetic moments precess at different frequencies -Magnetic moments of hydrogen precess at a different frequency to magnetic moments of either fluorine, or carbon -This allows specific imaging of hydrogen *As the gyromagnetic ratio is a constant of proportionality, B0 is proportional to the Larmor frequency -Therefore if B0 increases the Larmor frequency increases proportionally and vice versa

Electrons

Are particles that spin around the nucleus

For Resonance of hydrogen to occur

As magnetic moments of hydrogen nuclei precess in the RF (radio-frequency) band of the electromagnetic spectrum, and RF pulse of energy is applied at the Larmor frequency of hydrogen

Free Induction Decay (FID) signal

As the magnitude of transverse coherent magnetization decreases, so does the magnitude of the voltage induced in the receiver coil The induction of decaying voltage This is because spins freely precess influence only by B0, signal decays with time, and magnetic moments of the spins induce a current in the receiver coil

All things are made up of?

Atoms

When are atoms electrically stable?

Atoms are electrically stable if the number of negatively charged electrons equals the number of positively charged protons -This balance is sometimes altered by applying energy to knock out electrons from the atom -This produces a deficit in the number of electrons compared with protons and causes electrical instability

Ions

Atoms in which electrical instability occurs

MR Signal

Because of resonance, in-phase r coherent magnetization precesses in the transverse plane *this changing magnetic field generates an electric current Faraday's Law of induction explains this The change of magnetic flux through a closed circuit induces and electromotive force (emf) in the circuit

Alignment: Classical Theory

Classical theory uses the direction of the magnetic moments of spins (hydrogen nuclei) to illustrate alignment (1) Parallel alignment (2) Antiparallel alignment

Transverse plane or x-y-axis

Classical theory: application of the B1 field in a plane at 90° to B0, causes magnetic moments of the spins to precess around this axis rather than about the longitudinal plane or z-axis

Atoms mass

Come mainly from particles called nucleons, which are subdivided into protons and neutrons

Law of Electromagnetic Induction

Determined by Michael Faraday in 1833 Refers to the connection between electric and magnetic fields and motion -Determines that a moving electric field produces a magnetic field and visa versa -A magnetic field is created by a charged moving particle (that creates an electric field)

High-Energy Nuclei

Do have enough energy to oppose the main B0 field, These are nuclei that align their magnetic moments antiparallel or spin-down to the main B0 field in the classical description

E = hω0

E = is the energy of a photon (Joules, J) h = is Planck's constant (6.626 x 10 ^ 34 J/s) ω0 = is the frequency of an electromagnetic wave (Hz) **Planck's constant relates the energy of a photon of electromagnetic radiation to its frequency. Photons are particles that possess energy and at the same time behave like waves that have frequency (wave-particle duality)

Stationary vs. Rotating frame of Reference

EX| A good example of this is to imagine what happens during an RF excitation pulse. If you were to observe this from the stationary frame of reference, them you would observe nutation (spiral motion, result of precession around B0 and much slower precession around B1 happening at same time) of the NMV (net magnetic vector) around B0 and simultaneously around B1. As B0 is larger than B1 the outside observer sees fast precession around B0 and a much slower spiraling down onto the transverse plane around B1. If, however, you were to observe this from inside the rotating frame of reference, then you would see something different. Imagine that you are riding along with the NMV inside the rotation system at the frequency associated with B0. You would then only observe the slow precession of the NMV from the z-axis onto the x-y-axis caused by B1

Watch analogy

Frequency is the time is takes the hour hand to make one revolution of the watch face i.e. 12 hours The unit of frequency is Hz, 1 Hz is one cycle or rotation per second Frequency of the hour hand is 1/4320 s = 0.0000231 Hz as it moves around the watch face once every 12 h The phase of the hour hand, measured in degrees or radians, is the time on the watch e.g. 1 o'clock, 2 o'clock which corresponds to its position around the watch face when you look to see what time it is. The phase of the hour hands depends on its frequency (speed) If the frequency is correct, than the hour hand always tells the correct time. If the watch goes fast or slow i.e. the frequency either increases or decreases, then the watch tells an incorrect time

The most abundant atom in the human body?

Hydrogen Hydrogen is most commonly found in molecules of water and fat

The energy and frequency of electromagnetic radiation (including RF) are related to each other -

If just the right amount of energy is absorbed, the NMV lies in the transverse plane at 90° to B0 When it does it has moved through a flip or tip angle of 90° -consequently the frequency required to cause resonance is related to the difference in energy between the high-energy and low-energy populations and this the strength of B0 As the field strength increases, the energy difference between the two populations increases so that more energy (higher frequencies) is required to produce resonance

Saturation

In quantum mechanics, a 180° RF pulse produces an inversion of the spin populations, i.e. all the low-energy spins have enough energy to locate in the high-energy population and all the high-energy spins have been stimulated to give up their energy and locate in the low-energy population. Is caused when the spins are unable to absorb more energy or to be stimulated and release more energy -The amount of RF needed to produce a 90° flip angle is half of this value and relates to equalizing the high and low energy spins

Electromotive force (emf)

Is defined as the energy available from a unit of charge traveling once around a loop of wire. The emf drives a current in the circuit and is the result of a changing magnetic field inducing an electric field

Frequency

Is the rate of change phase of magnetic moments, i.e. it is a measure of how quickly the phase position of a magnetic moment changes over time *In MRI, the relative phase positions of all magnetic moments of hydrogen are important

TR

Is the time from the application of one RF excitation pulse to the application of the next RF excitation pulse for each slice and is measures in millisecond. The TR determines the amount of longitudinal relaxation that occurs between the end of one RF excitation pulse and application of the next The TR thus determines the amount of T1 relaxation that has occurred when signal is read

TE

Is the time from the application of the RF excitation pulse to the peak of signal induced in the receiver coil and is also measure in millisecond The TE determines how much decay of transverse magnetization occurs TE thus controls the amount of T2 relaxation that occurred when signal is read

Angular motion

Nuclei that have an odd number of protons (odd atomic number) or an odd mass number, thus the nucleus itself has a net spin -This means that their spin has a half-integral value 1/2, 5/2 -Only nuclei with an odd mass number or atomic weight are used in MRI (MRI-active nuclei)

Ionization

Process of knocking out electrons from the atom

What is the isotope of hydrogen?

Protium *Most commonly used MR-active nucleus in MRI -Has a mass and atomic number of 1, so the nucleus consists of a single proton and has no neutrons -Hydrogen is most abundant in human body, and the solitary proton gives it a relatively large magnetic moment

Stationary Frame of Reference

Refers to the observer (you) viewing something moving. You and the room you are situation in are stationary, and what you are observing moves. You are an outsider looking in

Rotating Frame of Reference

Refers to the observer viewing this from a different perspective. Imagine you are "the thing" that moves: what would the room look? You are stationary, and the room would appear to move around you because you are now part of the rotating system

Number of energy states = 2S + 1

S is the spin quantum number The value S for hydrogen is 1/2 -This equation explains why hydrogen can only possess two energy states. If S = 1/2 then the number of energy states is 2 x 1/2 + 1 = 2

How many types of motion are present within an atom?

Three (1) Electrons spinning on their own axis (2) Electrons orbiting the nucleus (3) The nucleus itself spinning about its own axis

Learning Tip: Vectors

The NMV is a vector quantity It is created by two components at 90° to each other These two components are (1) Magnetization in the longitudinal plane (2) Magnetization in the transverse plane Before resonance, there is full longitudinal magnetization parallel to B0 After the application of the RF pulse (and assuming a flip angle of 90°) the NMV is flipped fully into the transverse plane **There is now a full transverse magnetization and 0 longitudinal magnetization Once the RF excitation pulse is removed, the NMV recovers As this occurs, the longitudinal component of magnetization grows again while the transverse component decreases As the received signal amplitude is related to the magnitude of the coherent transverse component, signal in the coil decays as relaxation occurs

When the RF excitation pulse is switched off

The NMV is influenced only by B0, and it tries to realign with it Once the RF excitation pulse is removed, the NMV recovers To do so, the hydrogen nuclei lose energy given to them by the RF excitation pulse As relaxation occurs, the NMV returns to realign with B0 because some of this high-energy nuclei return to the low-energy population and therefore align their magnetic moments in the spin-up direction At the same time, the magnetic moments of hydrogen los coherency due to de-phasing

Results of Resonance - Quantum Theory

The RF excitation pulse gives energy to hydrogen nuclei and causes a net increase in the number of high-energy, spin-down nuclei -This is because the spin-up low-energy hydrogen nuclei absorb energy from the RD excitation pulse and move into the high-energy population -At the same time, the spin-down high-energy nuclei are stimulated to release energy and return to the lo-energy state *Because there are more low-energy spins, the net effect is of energy absorption

Precessional Path

The course these magnetic moments take (circularly) and the speed at which they precess around B0 is the precessional frequency

N+/N- = e ^ (-Change in E/kT)

This means the magnetic moments of hydrogen spins only align in the parallel or antiparallel directions. They cannot orientate themselves in any other direction. The number of spins in each energy level is predicted by the Botlzmann equation N+ and N-: are the number of spins in the high and low energy populations Change or difference in E: is the energy difference between the high and low energy population in Joules (J) k: is Boltzmann's constant (1.381 x 10 ^ -23 J/K) T: is the temperature of the tissue in Kelvin (K) *This equation enables prediction of the number of spins in the high and low energy populations and how this is dependent on temperature

The magnetic moments of hydrogen nuclei align with B0 not hydrogen nuclei themselves

The hydrogen nucleus does not change direction but merely spins on its axis

Pulse sequences

The magnitude and timing of the RF pulses for part of pulse sequences, Which are the basis of contrast generation in MRI

After alignment, there are always more spins with their magnetic moments aligned parallel than antiparallel

The net magnetism of the patient (Net magnetic vector NMV) is aligned parallel to the main B0 field in the longitudinal plane or z-axis

Isotopes

The number of neutrons and protons in a nucleus is usually balanced so that the mass number is even, however, there are slightly more or fewer neutrons than protons. -Atoms of elements with the same number of protons but a different number of neutrons

Thermal equilibrium

The patients temperature is usually similar inside and outside the magnetic field

Larmor frequency

The precessional frequency, because this frequency is determined by Larmor equation -The unit of precessional frequency hertz (Hz) -Where 1 Hx is one cycle or rotatinon per second (s) -1 Megahertz (MHz) is one million cycles or rotations per second (s) *The magnetic moments of all spin-up and spin-down nuclei precess around B0 (static magnetic field) on a precessional path that a Larmor frequency determined by B0 ω0 = γB0

Relaxation

The process by which hydrogen loses this energy

Heisenberg's Uncertainty Principle

Traditionally, electrons spinning around the nucleus is thought of as analogous to planets orbiting around the sun with electrons moving in distinct shells. However, according to quantum theory, the position of an electron is not predictable as it depends on the energy of an individual electron at any moment in time

How many ways are there of explaining the fundamentals of MRI?

Two (1) Classical theory and (2) Quantum Physics

Atoms are characterized in how many ways?

Two (1) The atomic number is the sum of the protons in the nucleus. This number gives an atom its chemical identity (2) The mass number or atomic weight is the sum of the protons and neutrons in the nucleus

How many types of energy states are there for hydrogen?

Two -Low-energy nuclei -High-energy nuclei

ε = -NdΦ / dt

ε = is the emf in volts (V) N = is the number of turns in a coil dΦ = is changing magnetic flux in a single loop (V/s) dt = is changing time (s) **This equation shows that the amount of induced current in a coil is related to the rate of change of magnetic flux (how fast the magnetic lines of flux are crossed) and the number of turns in the coil

θ = ω1 τ Therefore from the Larmor equation θ = γB1 τ 90° = π/2 = γB1 τ 180° = π = γB1 τ

θ = is the flip angle (°) ω1 = is the precessional frequency of B1 (μT) B1 = is the magnetic field associated with the RF excitation pulse (mT) τ = is the duration of the RF excitation pulse (ms) **This equation shows that the flip angle is determined by the strength of the B1 field and the duration of the pulse. In trigonometry, a factor of 2π represents 360°, a flip angle of 90° can therefore be written as π/2; a flip angle of 180° is π. Replacing θ with these values shows that and RF pulse producing a flip angle of 90° has either half the power or half the duration of an 180° RF pulse -A flip angle of 180° is used when the RF excitation pulse is twice the magnitude of that used to produce a 90° flip angle

ω0 = γB0/2π simplified to ω0 = γB0

ω0 = is the precessional or Larmor frequency (MHz) γ = is the gyromagnetic ration (MHz/T) B0 = is the strength os the external magnetic field (T) -This is the Larmor equation. The 2π function enables the conversion of ω0 from angular to cyclical frequency. As γ us a constant, for a given MR-active nucleus ω0 is proportional to B0

∆E = hω0 = hγB0

∆E = is the energy difference between the spin-up and spin-down populations h = is Planck's constant (6.626 x 10 ^ 34 J/s) ω0 = is the precessional or Larmor frequency (MHz) γ = is the gyromagnetic ration (MHz/T) **This equation shows that when the energy of the photon matches the energy difference between the spin-down populations, energy absorption occurs. This is proportional to the magnetic field strength B0