Which of the following statements concerning power and influence is most likely false?

• Spin
• Precession
• Resonance
• Relaxation I - Physics
• Relaxation II - Clinical

1. Concerning nuclear spin (I), which of the following is true?

   Spin is a fundamental quantum property of subatomic particles and does not result from their physical rotation. Many subatomic particles besides the proton have spin, including the neutrons and electrons. Spin is quantized and can take on a limited number of discrete values, so c) is true. When placed in an external magnetic field, nuclear spin results in precession, but spin and precession are not the same. Link to Q&A discussion

2. Which of the following spins (I) could a nucleus not possess?

   Quantum mechanics restricts nuclear spin to only integer or half-integer (1/2, 3/2, 5/2, etc) values, so I = 3/4 is not permitted. Link to Q&A discussion

3. Concerning nuclear spin (I), which of the following statements is false?

   The hydrogen (¹H) nucleus contains only a single proton surrounded by an electron cloud, so d) is false. The other statements are all true. Link to Q&A discussion

4. Concerning nuclear spin (I), which of the following statements is false?

   Net nuclear spin (I) does depend on the total number of protons and neutrons, but no simple formula for I exists as interactions between more elementary components (quarks and gluons) must be considered. The other statements — a), c) and d) — are all true. Link to Q&A discussion

5. Concerning nuclear spin (I) and NMR, which of the following statements is false?

   Only nuclei with non-zero spins can undergo NMR, so d) is false. The other statements are all true. Link to Q&A discussion

6. Which of the following statements concerning the magnetic dipole moment is false?

   The magnetic dipole moment (μ) will experience a torque causing it to align with an externally applied magnetic field, but will not precess around the field. Link to Q&A discussion

7. Which of the following statements about a magnetic dipole placed in an external magnetic field is false?

   The dipole (μ) experiences a torque (τ) given by the vector cross-product τ = μ x B0. In terms of scalar magnitudes: ||τ|| = ||μ|| ||B0|| sin θ, where θ is the angle between them. The energy (E) is defined by the dot product, E = −μ • B0 = −||μ|| ||B0|| cos θ. The energy is at its maximum (not a minimum), when the dipole points opposite the field (θ = 180°), so answer a) is false, . Link to Q&A discussion

8. The dipole magnetic moment (μ) is directly proportional to nuclear spin (I), connected by a constant called the

   The two are connected by the gyromagnetic ratio (γ), described through the relationship: μ = γI Link to Q&A discussion

9. Which of the following statements about the gyromagnetic ratio (γ) is false?

   The gyromagnetic ratio (γ) is a constant of proportionality between the dipole magnetic moment (μ) and nuclear spin (I). It is commonly expressed in units of MHz/T. Although usually a positive number, it may be negative. A negative value for γ means that the magnetic moment and spin point in opposite directions. The gyromagnetic ratio (γ) is different for every isotope of every element, so answer d) is false. Link to Q&A discussion

10. The ¹H nucleus has a spin (I) = ½. When placed in an external magnetic field, its number of measurable spin states (eigenstates) will be

    The number of observable spin states for a nucleus with spin I equals 2I +1. So the ¹H nucleus has 2(½) + 1 = 2 possible spin states. Link to Q&A discussion

11. Besides ¹H, two nuclei commonly studied by NMR spectroscopy are ³¹P and ¹³C. The fact that all three isotopes have identical nuclear spins (I) = ½ means that when placed in an external magnetic field

    All spin-½ particles will exhibit two discrete energy states when placed in an external magnetic field, so answer b) is true. The isotopes will have different gyromagnetic ratios (γ), different resonant frequencies, and different energy levels, however. Link to Q&A discussion

12. ²³Na is another NMR active isotope used for imaging research. It has a nuclear spin (I) = 3/2. Compared to the ¹H nucleus with I = 1/2, in an external magnetic field

    The number of observable energy states for a nucleus with spin I equals 2I +1. The ²³Na nucleus therefore has 2(3/2) + 1 = 4 possible spin states, so answer d) is correct. The gyromagnetic ratio (γ) and hence resonance frequency do not depend on I. Link to Q&A discussion

13. The famous experiment demonstrating how spin-½ particles can be physically separated into two groups by a magnetic field was performed in 1922 by

    This is a description of the Stern-Gerlach experiment, often provided as tangible proof for the quantization of nuclear angular momentum visible in the macroscopic world. Link to Q&A discussion

14. Which of the following names refers to the highest energy spin state of an ¹H nucleus in a magnetic field?

    The highest energy state occurs when the spin has a direction opposite that of the main magnetic field and is denoted spin-down (correct answer), anti-parallel, or |−½>. Link to Q&A discussion

15. Why don't all the nuclear spins simply fall to their lowest energy states to minimize total system energy?

    The natural tendency for spins to fall to lower energy states is offset by thermal collisions that tend to equalize the two energy levels. The result is a compromise predicted by the Boltzmann distribution. Link to Q&A discussion

16. According to quantum mechanical (QM) theory and experiment, which statement is true?

    Quantum mechanics does not require a proton to exist exclusively in one of its two primary (eigen)states, only a linear combination of the two. Thus answer a) is false. The Stern Gerlach experiment only shows that when a measurement is made a group of spin-½ particles that one of two results becomes physically manifest. This does not speak to the underlying quantum reality prior to measurement, however, so b) is also false. Haroche and Weinland, working independently, were awarded the Nobel Prize for Physics in 2012 for their experiments trapping and manipulating spins in superposition states, so c) is true. The Copenhagen Interpretation of QM, while still the most popular, is far from being universally accepted, so d) is false. Recent polls of quantum physicists found the Many Worlds Interpretation gaining significant ground. Of course, neither may be correct! Link to Q&A discussion

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1. Nuclear precession can be considered the result of a "twisting force" or torque (τ) on a spin's angular momentum as it interacts with an externally applied magnetic field. The orientation of this torque is

   The torque (τ) is perpendicular to both the spin angular momentum and the magnetic field. This creates a "twisting force" that can be thought of as "pushing the spin from the side" resulting in nuclear precession rather than alignment with the field. Link to Q&A discussion

2. Precession may be expressed in either angular (ω0) or cyclic (f0) frequency. The two are are related by the equation

   The correct equation is a). Angular frequency (ω0) is measured in radians per second, where 2 π radians/sec = 360°/sec = 1 cycle (or revolution) per second = 1 Hertz (Hz). Thus the cyclic frequency (f0) must be multiplied by 2 π to obtain angular frequency (ω0). Link to Q&A discussion

3. The conventional units for angular frequency (ω0) are

   The correct answer is c), radians per second. The other options are used to express cyclic frequency (f0). Link to Q&A discussion

4. Which of the following is the correct form of the Larmor equation?

   The correct answer is a), f0 = γ B0. Link to Q&A discussion

5. What is the approximate gyromagnetic ratio (γ) of the ¹H nucleus?

   The correct answer is b), 42.6 MHz/Tesla. I don't think you need to memorize this number, but it can easily be retrieved as I do believe everyone involved with MRI should know that a 1.5T scanner has a resonance frequency of about 64 MHz. Thus γ ≈ 64 MHz ÷ 1.5 Tesla, giving a γ of about 42.6 MHz/T. Link to Q&A discussion

6. If the ¹H resonance frequency in a 1.5T scanner is about 64 MHz, what is the approximate ¹H resonance frequency at 7T?

   Resonance frequency is directly proportional to field strength. So the ¹H resonant frequency at 7.0T can be calculated as 64 MHz x (7.0/1.5) ≈ 298 MHz. Link to Q&A discussion

7. The gyromagnetic ratio (γ) of the ¹³C nucleus is about 10.7 MHz/T. What is the ¹³C resonance frequency at 3.0T?

   By the Larmor equation: f0 = γ B0 = (10.7 MHz/T) x 3.0T = 32.1 MHz. Link to Q&A discussion

8. Sir Joseph Larmor developed his famous equation to allow calculation of NMR resonance frequencies in different magnetic fields.

   False. Larmor developed his equation in the late 19th Century before NMR was even discovered. He was investigating the splitting of optical spectra by magnetic fields, and his equation described the precession of orbital electrons. In the 20th Century the Larmor equation was found to apply to any particle with spin angular momentum and was hence fully applicable to NMR. Link to Q&A discussion

9. Which of the following statements about nuclear precession is true?

   Nuclear precession occurs spontaneously when protons are placed in any magnetic field. No energy input is required to start or sustain precession. Precession occurs even in the tiniest magnetic fields, including that of the earth, so answer c) is true. In fact, crude MR images using the earth's magnetic field alone have been obtained. Link to Q&A discussion

10. The slight difference in resonant frequencies noted between ¹H-nuclei in different molecular environments is due to

    This question concerns the origin of chemical shift. Variable shielding and deshielding of ¹H-nuclei by molecular electron clouds results in slightly different local magnetic fields that each nucleus experiences. These different local fields alter resonance frequencies slightly. Link to Q&A discussion

11. Chemical shifts (δ) are typically reported in units of

    Chemical shifts are typically reported in ppm, which is independent of field strength. Note that ppm, like %, is dimensionless. Link to Q&A discussion

12. The abbreviation "ppm" stands for

    The correct answer is d), "parts per million", the commonly used field-independent method to report chemical shifts. Link to Q&A discussion

13. The chemical shift (δ) between water and fat protons measured at 1.5T is approximately 3.5 ppm. What would their chemical shift be at 3.0T?

    The chemical shift (δ) in ppm is independent of field strength, so b) is correct. Link to Q&A discussion

14. The methyl protons of two brain metabolites, N-acetyl aspartate (NAA) and Creatine (Cr), have a chemical shift difference of 1.0 ppm. At a field strength of 1.5 T (where the water Larmor frequency is 64 MHz), their difference in frequency would be about

The frequency difference is just the Larmor frequency x the chemical shift = 64 MHz x 1 ppm = (64 x 106 Hz) x (1.0 x 10−6) = 64 Hz. Link to Q&A discussion

1. Which of scientist first experimentally demonstrated the NMR phenomenon in the 1930's and gave it its name?

   Isidor Rabi is credited with naming NMR and being the first to demonstrate its existence experimentally in a molecular beam of LiCl. Link to Q&A discussion

2. Which of the following statements about the NMR discoveries of Felix Bloch and Edward Purcell is true?

   Bloch performed his research at Stanford at the same time Purcell was working independently at MIT. Their experimental setups were quite different, Bloch detecting an induction signal from water and Purcell measuring energy absorption in solid paraffin wax. Their initial reports were published simultaneously in the January, 1946 issue of the journal Physical Review, so answer c) is true. Bloch and Purcell jointly received the Nobel Prize for Physics in 1952. Link to Q&A discussion

3. The radiofrequency (RF) field used to inject energy into a spin system to induce nuclear resonance is called

   The correct answer is B1. B0 is the main magnetic field and Mxy are the transverse components of net magnetization induced by B1. There is no field called B2. Link to Q&A discussion

4. For resonance to occur, B1 must be applied exactly at the Larmor frequency.

   The B1 must only be applied reasonably close to the Larmor frequency, not exactly. Energy transfer is optimized when B1 is precisely on resonance, but appreciable tipping of M will still occur even if the frequency is not perfect. Link to Q&A discussion

5. For resonance to occur, B1 must be applied exactly perpendicularly to B0.

   The only requirement is that B1 not be collinear with B0 and have have some perpendicular components. Energy transfer is optimized when B1 is perfectly orthogonal to B0, however. Link to Q&A discussion

6. Which of the following statements about flip angle using conventional RF-pulses is false?

   Flip angle is measured relative to the direction of B0, not B1. The other statements are all true. Link to Q&A discussion

7. (Advanced) Which of the following statements concerning the spin-system immediately after a 90°-pulse is true?

   This is a pretty tricky question that really probes one's understanding of the NMR phenomenon. Only a) is true. If the longitudinal angular momentum of all spins were measured (by passing them through all Stern-Gerlach device, for example), an equal distribution of spin-up and spin-down states would be observed. Remember that spins do not exist in pure eigenstates, so it is not correct to say there are an equal number of spin-up and spin-down protons (though that statement is commonly found in textbooks). But the idea is much the same. Option b) is false, but only barely so. Precession after a 90°-pulse occurs around the direction of B0, just as it did prior to the RF-pulse. During the application of the RF-pulse, however, procession occurs around both B0 and B1, described in more detail in the Q&A's about the rotating frame. Option c) is false, as no "magical" locking together of spins occurs. What we call "phase coherence" is simply the same initially skewed longitudinal distribution of spin energies that have been rotated into the transverse plane by the RF-pulse. Finally, option d) is false. By the Heisenberg uncertainty principle we cannot know the direction a spin is "pointing", so the statement is meaningless. But I'm pretty sure the spins would not all be "pointing" horizontally if we were able to know! Link to Q&A discussion

8. When stimulated to higher energy levels by RF-excitation, protons spontaneously release this energy and fall back to lower levels.

   Spontaneous emission of absorbed energy is extremely improbable at the (MHz) frequencies where NMR occurs. Virtually all energy release by an NMR spin system must be induced by direct interaction with its external environment. This is the principle underlying T1 relaxation. Link to Q&A discussion

9. The complex motion of the net magnetization vector (M) when acted upon by both B0 and B1 can be simplified by considering the system in the

   The rotating frame of reference allows the motion of (M) to be simplified by removing the simple Larmor precession around B0. It's like riding on a merry-go-round instead of watching it from stationary ground nearby. Link to Q&A discussion

10. (Advanced) What happens if the B1 field is not applied exactly at the Larmor frequency?

    The correct answer is c). It describes the "off-resonance" condition which is commonly encountered in MR imaging where a span of RF-frequencies is transmitted and gradients affect Larmor frequencies across the object being imaged. Link to Q&A discussion

11. (Advanced) Which of the following statements about adiabatic excitation is false?

    All statements are true except d). Unlike "conventional" RF-pulses, the flip angle of an adiabatic pulse is NOT proportional to its magnitude and duration. An adiabatic pulse cannot be easily scaled or stretched to change its effect. Link to Q&A discussion

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1. Which of the following is not a synonym for T1 relaxation?

   Spin-spin relaxation is a synonym for T2 relaxation. Link to Q&A discussion

2. Which of the following is/are synonyms for T2 relaxation?

   Thermal relaxation is a synonym for T1. Link to Q&A discussion

3. Which of the following statements about T1 relaxation is false?

   All are true except d). T1 relaxation requires release of absorbed energy from the spin system to the external environment, but this such energy transfer must be stimulated by interaction with a fluctuating field near the Larmor frequency arising from a nearby proton or molecule. Link to Q&A discussion

4. When an unmagnetized sample is placed in a magnetic field, an internal magnetization (M) will develop and grow to a maximum value in the longitudinal direction (M0). The first order exponential time constant for this growth is defined as

   This is the definition of T1 as described by Felix Bloch. Link to Q&A discussion

5. T1 is the time required for the longitudinal magnetization Mz to grow from zero to about ____ of its maximum value (M0)

   The equation for exponential regrowth is Mz = M0 (1 − e−t/T1). After one time constant (i.e., at t = T1), Mz will have reached (1 − e−1) or about 63% of its maximum value (M0). Link to Q&A discussion

6. T2 is the time required for the transverse components of magnetization M0 to decay to approximately ____ from their maximum initial value after a 90°-pulse.

   The equation for exponential decay of transverse magnetization immediately after a 90°-pulse where the initial magnetization (M0) has been tipped into the transverse plane is given by: Mxy = M0 e−t/T2. After one time constant (i.e., at t = T2), Mxy will have decayed by (e−1) or to about 37% of its initial value. Link to Q&A discussion

7. Which of the following statements concerning T2 relaxation is false?

   Only a) is false, but its converse is true, "Any process causing T1 relaxation also results in T2 relaxation". The other options are correct. Link to Q&A discussion

8. If the T1 relaxation time for brain tissue is 1000 ms, what is its relaxation rate (R1)?

   Relaxation rate is merely the inverse of relaxation time. So R1 = 1/T1 = 1/1000 msec = 1/(1 sec) = 1 sec−1 Link to Q&A discussion

9. Which of the following statements concerning T1 and T2 relaxation times in tissues at 1.5T are correct?

   These basic facts and relationships about tissue T1 and T2 values should be known by anyone involved with MR imaging. Link to Q&A discussion

10. Which of the following relaxation time pairs for tissue is impossible?

    Because every process that causes T1 relaxation also causes T2 relaxation, but T2 relaxation can occur without T1 relaxation, T2 is always less than or equal to T1. Thus the combination in choice d) is impossible. Link to Q&A discussion

11. Which of the following biological materials would be expected to have the shortest T2 values?

    T2 relaxation occurs most quickly when local static magnetic fields are present that dephase the spins. The more "solid" and "drier" the tissue, the shorter is its T2 value. Of the choices above, tendon has the shortest T2. Link to Q&A discussion

12. Which of the following biological materials would be expected to have the shortest T1 values?

    Because of their size and shape, triglycerides (the main component of adipose tissue as in scalp fat) have a relatively large fraction of molecular motions near the Larmor frequency, making them efficient at T1 relaxation. So the correct answer is a). Yellow bone marrow has relatively short T1 due to fat deposition, but red marrow has much less fat and is filled with water-containing hematopoietic cells. Link to Q&A discussion

13. Which of the following biological materials would be expected to have the longest T2 values?

    "Free" or "unbound" water molecules tumble most rapidly averaging out static dipolar interactions and hence have the longest T2 values. So pure liquids like spinal fluid and urine have the longest T2 values. Link to Q&A discussion

14. Which of the following statements about T2* is false?

    T2* includes not only "true" T2 effects but also effects of magnetic field inhomogeneities. Link to Q&A discussion

15. Which of the following molecular mechanisms is the most important for causing T1 and T2 relaxation in ¹H NMR?

    All these mechanisms make contributions, but the dipole-dipole interaction is the most important. Dipole-dipole interactions are "through space" magnetic field disturbances typically occurring between nuclear or electron spins on the same or closely apposed molecules. Link to Q&A discussion

16. Because they each have spin = ½, electrons and protons are equally effective at producing dipole-dipole interactions.

    Due to its small size, the electron has a much greater charge to mass ratio and hence a much larger gyromagnetic ratio (γ). The electron is thus many thousand times more powerful than the proton at dipole-dipole interactions. Link to Q&A discussion

17. Intramolecular dipole-dipole interactions are more powerful than intermolecular ones.

    The strength of the dipolar interaction is inversely proportional to the sixth power of the distance between spins (1/r6). Thus dipole-dipole interactions between spins on the same molecule (intramolecular) are more powerful than more distantly spaced spins on different molecules (intermolecular). Link to Q&A discussion

18. In dipole-dipole interactions, T1 relaxation is most efficient (and T1 values are shortest) for

    Since T1 relaxation requires stimulated energy exchange at the Larmor frequency, spins on molecules tumbling at near the Larmor frequency are most efficient at T1 relaxation. Link to Q&A discussion

19. In dipole-dipole interactions, T2 relaxation is most efficient (and T2 values are shortest) for

    Stationary local magnetic fields are most effective at inducing T2 relaxation, so nearly immobile macromolecules (especially those bound to bones, cell membrane, or collagen) have the shortest relaxation times of all. Small, rapidly tumbling molecules have very long T2 values. Link to Q&A discussion

20. Considering the effects of macromolecules on relaxation times, which of the following is false

    Only c) is false. The bound water molecules interact and exchange magnetization both with the macromolecules and the free water pool. Link to Q&A discussion

21. Which of the following ¹H-containing molecules account for nearly 100% of the signal recorded within the brain parenchyma using routine MRI sequences?

    Triglcerides are present in scalp fat, but not in the brain parenchyma itself. Myelin is present in the brain, but as an immobile macromolecule has an extremely short T2 and whose signal thus decays too rapidly to be detected using conventional MRI sequences. NAA is the brain metabolite with the largest peak seen on MR spectroscopy of the brain, but its concentration is many thousand times lower than that of water. Link to Q&A discussion

22. By irradiating tissue with an off-resonance RF-pulse it is possible to affect image contrast by transferring energy between macromolecular and free-water pools. This process is known as

    This is a brief description of MT. Link to Q&A discussion

23. As field strength increases from 0.5T to 3.0T, the T1 of most tissues

    For most biological tissues, empirical measurements suggest that T1 increases approximately as B0⅓. Therefore, measured T1 values of most tissues will approximately double as field strength is raised from 0.3 T to 3.0 T. Link to Q&A discussion

24. As field strength increase from 0.5T to 3.0T, the T2 of most tissues

    The effect varies depending on tissue type, but generally there is relatively little change in T2 values over the 0.5T to 3.0T range. T2 definitely shortens for fields > 3.0T, however. Link to Q&A discussion

25. NMR relaxation theory from basic science nearly completely explains T1 and T2 values observed in tissues.

    Basic science relaxation theory adequately explains the T1 and T2 behavior of simple homogenous materials and solutions, but is far from explaining the observed relaxation times observed in biological tissues. Multi-compartment models may give some insights, but no fully comprehensive description yet exists. Link to Q&A discussion