Chapter 1 Flashcards
What are the two main ways to explain MRI principles?
Classical Theory (Newtonian): Uses mass, spin, and angular momentum.
Quantum Theory (Planck, Einstein, Dirac): Explains MRI at the subatomic level, focusing on energy levels of protons, neutrons, and electrons.
Why is classical theory used more often in MRI explanations?
Because it is easier to understand than quantum mechanics for describing large-scale MRI concepts.
What are the two ways to characterize an atom?
Atomic number = Number of protons in the nucleus (defines chemical identity).
Mass number (atomic weight) = Sum of protons + neutrons in the nucleus.
What are isotopes?
Atoms with the same number of protons but a different number of neutrons.
What are the charges of atomic particles?
Protons = Positive charge (+1).
Neutrons = No charge (neutral).
Electrons = Negative charge (-1).
What are ions?
Atoms that have lost or gained electrons, becoming electrically unstable.
What are the three types of atomic motion?
- Electrons spinning on their own axis.
- Electrons orbiting the nucleus.
- Nucleus spinning about its own axis.
What determines whether an atomic nucleus has spin?
Even atomic and mass number → No net spin (e.g., Carbon-12).
Odd atomic/mass number → Has spin (e.g., Hydrogen-1, Oxygen-17).
What are MR-active nuclei?
Nuclei that have angular momentum (spin) and a net electrical charge, allowing them to interact with a magnetic field.
What law explains how MR-active nuclei acquire a magnetic field?
Faraday’s Law of Electromagnetic Induction – A moving electric charge creates a magnetic field.
What are examples of MR-active nuclei?
¹H (Hydrogen), ¹³C (Carbon), ¹⁵N (Nitrogen), ¹⁷O (Oxygen), ¹⁹F (Fluorine), ²³Na (Sodium).
Why is hydrogen used in MRI?
Most abundant element in the human body.
Single proton gives it a large magnetic moment.
What is Faraday’s Law of Electromagnetic Induction?
A moving electric charge (like a spinning hydrogen proton) creates a magnetic field.
How is the hydrogen nucleus represented in MRI diagrams?
As an arrow called the magnetic moment:
Length = Magnitude of magnetic field.
Direction = Alignment with the external magnetic field (B₀).
What happens to hydrogen nuclei when placed in a strong external magnetic field (B₀)?
Their magnetic moments align with the field, a process called alignment.
What are the two types of alignment?
Parallel alignment (spin-up) → Low-energy state (aligned with B₀).
Antiparallel alignment (spin-down) → High-energy state (opposed to B₀).
What determines the number of energy states a nucleus can have?
Equation: Number of energy states = 2S + 1 (S = Spin quantum number).
For hydrogen (S = ½): 2(½) + 1 = 2 energy states (parallel and antiparallel).
The spin quantum number can only be two numbers:
- +½ → This means the electron is spinning up (↿).
- -½ → This means the electron is spinning down (⇂).
What is Zeeman Interaction?
The process where protons couple with the external magnetic field (B₀), resulting in two distinct energy states.
spin up or spin down
What is the net magnetic vector (NMV)?
The sum of all magnetic moments in the body, representing the small excess of spin-up nuclei in alignment with B₀.
there are always more magnetic moments parellel than anti parallel
Why does the NMV align with B₀?
Because there are always more spin-up nuclei than spin-down nuclei, creating a measurable net magnetization in the longitudinal (z-axis) direction.
What is the most abundant element in the body?
Hydrogen.
Which nuclei are used in MRI?
Nuclei with a net spin.
Why do spinning nuclei create a magnetic field?
Due to Faraday’s Law (a moving charge induces a magnetic field).
How is a nucleus’s magnetic field represented?
By a magnetic moment (arrow).
According to Avogadro’s law, how many molecules are present per gram of tissue?
6 × 10²³ molecules per gram of tissue
How many excess spins are present per gram of tissue?
6 × 10¹⁷ excess spins per gram of tissue
How does increasing B₀ affect the number of spin-up (low-energy) and spin-down (high-energy) nuclei?
Increasing B₀ increases the number of spin-up (low-energy) nuclei and decreases the number of spin-down (high-energy) nuclei
What is the equation for the ratio of spin-up (N⁺) to spin-down (N⁻) populations?
N⁺ / N⁻ = e^(-ΔE / kT)
What does the variable ΔE represent in the Boltzmann equation?
The energy difference between high- and low-energy populations (in Joules)
What is the value of Boltzmann’s constant (k)?
1.381 × 10⁻²³ J/K
Why does SNR increase at higher B₀ values?
Higher B₀ increases the NMV, leading to a greater signal-to-noise ratio (SNR)
What is precession?
The wobbling motion of magnetic moments around B₀ due to its influence
What is the Larmor frequency (ω₀)?
The rate at which magnetic moments precess around B₀
What is the equation for Larmor frequency?
ω₀ = γB₀
What does the gyromagnetic ratio (γ) represent?
The relationship between angular momentum and the magnetic moment of MR-active nuclei
What are the units of Larmor frequency?
Megahertz (MHz)
What is the gyromagnetic ratio of hydrogen?
42.58 MHz/T
What is the precessional frequency of hydrogen at 1.5T?
63.87 MHz (42.58 × 1.5)
What is the precessional frequency of hydrogen at 1.0T?
42.58 MHz (42.58 × 1.0)
What is the precessional frequency of hydrogen at 0.5T?
21.29 MHz (42.58 × 0.5)
What is the precessional frequency of hydrogen at 3.0T?
127.74 MHz (42.58 × 3.0)
What is the gyromagnetic ratio of ¹³C (carbon-13)?
10.71 MHz/T
What is the precessional frequency of carbon at 1.5T?
16.06 MHz (10.71 × 1.5)
What is the gyromagnetic ratio of ¹⁵N (nitrogen-15)?
4.32 MHz/T
What is the precessional frequency of nitrogen at 1.5T?
6.48 MHz (4.32 × 1.5)
Why is hydrogen (¹H) primarily used in MRI instead of other MR-active nuclei?
It has the highest abundance in the body and a large magnetic moment
What does phase refer to in MRI?
The position of magnetic moments on their precessional path at any moment in time
What does out of phase (incoherent) mean?
Magnetic moments of hydrogen are at different places on the precessional path
What does in phase (coherent) mean?
Magnetic moments of hydrogen are at the same place on the precessional path
What happens to precessional frequency when B₀ is increased?
Larmor frequency increases proportionally
How does the Larmor equation explain the specificity of MRI?
Different MR-active nuclei have unique gyromagnetic ratios, allowing MRI to selectively image hydrogen while ignoring other nuclei
What is the equation for calculating the ratio of spin-up to spin-down nuclei?
N⁺ / N⁻ = e^(-ΔE / kT)
What happens to the NMV when the external magnetic field (B₀) increases?
Increases
What is the gyromagnetic ratio of nitrogen-15?
4.32 MHz/T
Which of the following is NOT a correct description of precession?
It occurs due to thermal energy transfer
What is the precessional frequency of hydrogen at 1.5T?
63.87 MHz
What is resonance in MRI?
A phenomenon where a nucleus absorbs energy when exposed to an RF pulse at its Larmor frequency.
What happens if the applied RF pulse is not at the Larmor frequency of hydrogen?
Resonance does not occur, and the nucleus does not absorb energy.
Why do other MR-active nuclei not resonate with the RF pulse used for hydrogen imaging?
Their gyromagnetic ratios are different, leading to different precessional frequencies.
What is B₁ in MRI?
The weak oscillating magnetic field created by the RF excitation pulse, applied perpendicular to B₀.
How is B₁ different from B₀?
B₀ is a strong, static magnetic field, while B₁ is a weak, oscillating magnetic field applied at 90° to B₀.
According to classical theory, what happens when an RF excitation pulse is applied?
The NMV spirals from the longitudinal plane to the transverse plane (nutation).
What is nutation?
A spiral motion caused by the NMV transitioning from the longitudinal to the transverse plane.
According to quantum theory, what does RF excitation do?
It increases the number of high-energy (spin-down) hydrogen nuclei.
Why does the net effect of RF excitation result in energy absorption?
Because there are initially more low-energy spins, causing an overall shift toward high-energy states.
What happens to the phase of magnetic moments after RF excitation?
They become in-phase (coherent), leading to a detectable MRI signal.
What is Planck’s equation for energy absorption?
E = hω₀
What does the variable h represent in Planck’s equation?
Planck’s constant (6.626 × 10⁻³⁴ J/s).
How does increasing B₀ affect the energy required for resonance?
A stronger B₀ increases the energy difference (ΔE) between spin-up and spin-down states.
What happens to ω₀ (Larmor frequency) as B₀ increases?
ω₀ increases proportionally.
What is the relationship between B₀ and resonance frequency?
Higher B₀ leads to a higher resonance frequency, requiring a higher RF pulse frequency for excitation.
What is the typical flip angle for a 90° RF pulse?
π/2 radians.
What is the typical flip angle for a 180° RF pulse?
π radians.
How is flip angle calculated?
θ = γB₁τ
What happens to magnetization at a 90° flip angle?
The NMV is completely transferred into the transverse plane.
What happens at a 180° flip angle?
The NMV is completely inverted, saturating the system.
What is the principle behind MR signal generation?
Faraday’s Law of Electromagnetic Induction.
What does Faraday’s Law state?
A changing magnetic field induces an electromotive force (emf) in a closed circuit.
What equation describes electromagnetic induction?
ε = -N (dΦ/dt)
In the equation ε = -N (dΦ/dt), what does Φ represent?
Magnetic flux.
How is MR signal detected?
By placing a receiver coil in the path of precessing transverse magnetization.
What happens when the RF excitation pulse is turned off?
The NMV begins to realign with B₀, causing relaxation.
What is the Free Induction Decay (FID) signal?
A decaying MR signal induced in the receiver coil due to dephasing of spins.
What causes the loss of transverse magnetization after RF excitation?
Dephasing due to inhomogeneities in B₀ and spin-spin interactions.
Why does MR signal fade over time after excitation?
Due to transverse relaxation and spin dephasing.
What happens to the NMV as relaxation occurs?
It gradually returns to the longitudinal axis.
What must be true for resonance to occur in MRI?
The RF excitation pulse must match the Larmor frequency.
What is the role of B₁ in MRI?
It provides the oscillating field needed for resonance.
According to quantum theory, what happens during RF excitation?
The number of low-energy spins decreases.
What equation describes the energy difference between spin-up and spin-down states?
ΔE = hγB₀.
What happens to magnetization at a 180° flip angle?
The NMV is inverted, fully saturating the system.
What is the equation for calculating the flip angle?
θ = γB₁τ.
What happens when an RF pulse is applied at the Larmor frequency?
Resonance occurs, and hydrogen nuclei absorb energy, moving into a high-energy state.
What is excitation in MRI?
The net absorption of RF energy, causing a shift in spin populations and creating transverse magnetization.