PSY3419 - Structural Imaging Notes

X-ray-based Computerised Tomography (CT)

• Tomography: Creation of images in slices or sections.
• CT (Computerised Tomography): Based on X-ray technology.
• X-rays: Electromagnetic radiation with short wavelength and high energy, sharing properties with visible light, notably absorbance.
• Contrast in Projection: Depends on tissue absorbance of X-rays; some X-rays pass through, others are absorbed. The contrast results from these differences.

2D X-ray Images

• Limitation: Unable to distinguish between small high-absorbance and large low-absorbance tissues because they absorb similar amounts of radiation.

Solution: Computerised Axial Tomography (CAT/CT)

• Method: Rotate the X-ray emitting source and detectors around the object, obtaining projections from different angles and integrating these projections.
• Advantage of 3D Tomography: Helps differentiate between smaller high-absorbance objects and larger low-absorbance objects.

CT: Advantages and Drawbacks

• Advantages:
  • Lower cost compared to MRI.
  • Better at identifying certain abnormalities like bone fractures.
• Drawbacks:
  • Ionising X-ray radiation poses health risks, limiting exposure.
  • Lower spatial resolution and contrast than MRI.
  • Less versatility than MRI.
• Current Status: MRI is becoming the norm in structural imaging for both research and routine diagnostics.

Magnetic Resonance Imaging (MRI)

Spin

• Nuclear Spin: Nuclear particles (protons and neutrons) have spin, considered an intrinsic property.
• Spin Pairing: Protons and neutrons pair with opposite spins, canceling each other out. Only nuclei with an odd number of protons and neutrons have a net spin.
• Hydrogen (H): Nucleus has one proton and no neutrons, resulting in a net spin. Abundant in the body.

Magnetization and Spin

• Magnetic Moment: Nuclear spin is associated with a magnetic moment; nuclei behave like dipole magnets with an axis parallel to the spin axis.
• External Magnetic Field (B0): When nuclei are placed in a strong external magnetic field $B_0$, the field exerts torque, aligning the nuclei's axes of spin with the field's axis.

Magnetisation: Before and After Applying a Large Static Magnetic Field

• H nuclei align with the magnetic field until their magnetization reaches equilibrium.

Equilibrium Magnetization

• Definition: Overall magnetization of H nuclei when maximally aligned with the large field.
• Detection: Equilibrium magnetization is a weak local magnetic field resulting from the sum of each of the H nuclei's magnetic fields. It is undetectable because it aligns with $B<em>0$ and is much smaller. To detect it, it must be tipped out of alignment with $B</em>0$.

Magnetic Resonance (MR)

• Discovery: During WWII, it was discovered that spatially aligned hydrogen responds (resonates) with a detectable magnetic signal when a magnetic field that changes over time (oscillates) is applied.

Tipping the Nuclei Away from $B_0$

• Process: Applying an oscillating magnetic field perpendicularly to the static field $B<em>0$ tips the magnetic field of the hydrogen nuclei away from $B</em>0$.
• Excitation Field: The oscillating field must have the same frequency as the nuclear precession around the axis of $B_0$ (Larmor frequency).
• Radio Frequency (RF): A field oscillating in the radio frequency range is used.

Flip Angle (α)

• Definition: The angle to which the local magnetization (M) of H nuclei is tipped away from field $B_0$.
• Dependence: Depends on the amplitude of the RF pulse ($B_1$) and its duration.
• Excitation Pulse: The RF field is called the 'excitation pulse' because its energy is absorbed by the H nuclei, resulting in the MR signal.
• Realignment: After the excitation pulse is switched off, the static field pulls the H nuclei back into alignment.

Precession

• Process: Nuclei “wobble” around the axis of the magnetic field at the Larmor frequency (w) proportional to the magnetic field ($B_0$).
• Larmor Frequency Equation: $w = γ ". " B<em>0$, where γ is the gyromagnetic constant (different for different chemical elements, but constant within a chemical element, like H). Note: Gyromagnetic constant is always the same for MRI (only uses H) and can be ignored. Hence, $w$ depends exclusively on the strength of $B</em>0$.
• Spinning Top Analogy: As a spinning top wobbles before tipping over, the nuclei start “wobbling” around the axis of the magnetic field

Longitudinal Relaxation

• Signal Regeneration: The signal can be re-generated via a new RF pulse.
• Repetition Time (TR): Time at which the RF pulse is repeated.
• Effect on Nuclei: The RF pulse has less effect on nuclei that are not maximally aligned with the static field $B_0$.
• Recovery: The equilibrium magnetization of H nuclei must ‘recover’ in the longitudinal plane for the next RF pulse to have a measurable effect.
• T1: The recovery is described by the time constant $T<em>1$, which is different for different tissues (hence, $T</em>1$-weighted contrast).

T1-weighted Contrast

• Sensitivity: For the image to be sensitive to $T<em>1$, TR must be shorter than the $T</em>1$ constants for the tissues of interest.
• Signal Recovery: The signal from different tissues recovers at different rates, depending on their $T_1$.

Density-weighted Contrast

• Long TR: If TR is considerably longer than $T_1$, the MR signal is fully recovered at the time of the next RF pulse.
• Sensitivity: The MR signal is not be sensitive to longitudinal relaxation (little $T_1$ weighting).
• Measurement: The signal can be measured very soon after the RF excitation pulse is switched off, so it does not decay/dissipate.
• Hydrogen Density: Instead, it would be sensitive to hydrogen density.

Transverse Magnetization

• Definition: The component of nuclear magnetization tipped over (orthogonal to the stationary field $B_0$).

MRI Signal Decay

• Coherent Precession: At the point of excitation (just after RF pulse), H nuclei precess coherently (in phase).
• Decay Cause: The signal starts decaying because of loss of phase coherence between nuclei, due to local random variations of the field (thermal motions dependent on molecular structure of the tissue).
• T2: The decay, described by the constant $T_2$, is referred to as transverse relaxation.
• Transverse: Because the transverse magnetization decays.
• Relaxation: Because the tipped nuclei are in a higher energy state and they eventually reach a lower energy state in which they ‘relax’.

Exponential Decay of MR Signal

• Formula: The proportion of signal left in a given tissue at acquisition time t is calculated by $e^{-t/T_2}$, where $e$ is Euler’s number (~2.72).
• Example 1: Signal left at 100 ms in a tissue with $T<em>2$ of 100 ms ( $t = T</em>2 = 100 ms$) is ~ 37% or $2.72^{-100/100} = 2.72^{-1} = 1/2.72 ≈ 0.37$.
• Example 2: Signal left at 200 ms in a tissue with $T<em>2$ of 100 ms ( $t = 200 ms; T</em>2 = 100 ms$) is ~ 14% or $2.72^{-200/100} = 2.72^{-2} = 1/2.72^2 ≈ 0.14$.

T2-weighted Contrast

• Sensitivity: To be sensitive to $T_2$, the MR signal should be measured after some delay, not immediately after the RF pulse.
• Contrast: Differences in decay time between tissues cause some tissues to decay sooner than others, creating contrast.

T2* Decay

• T2* Decay: The decay of the transverse MR signal is more rapid than that described by $T<em>2$, and is described by the time constant $T</em>2^*$.
• Cause: This rapid decay is due to static (constant) magnetic field inhomogeneities, in addition to random inhomogeneities. Variations in the strength of the magnetic field across tissue boundaries (boundary inhomogeneity) lead to different precession rates and rapid decay.
• T2-weighted Image: To get a $T_2$-weighted image, one needs to cancel (remove) the effect of static inhomogeneities.

Spin Echoes

• Process: After tipping the magnetization into the transverse plane, H protons acquire a phase difference due to static field inhomogeneities, causing them to fan out and reducing the net signal.
• 180° RF Pulse: A $180°$ RF pulse (refocusing pulse) flips the transverse plane, causing protons with higher precession rates to fall behind those with lower precession rates.
• Spin-Echo Formation: Eventually, the faster protons catch up with the slower ones, and for a moment, they are back in-phase, forming a spin-echo.

Formation of a Spin Echo

• 90° pulse sets up the signal.
• Spin de-phasing occurs.
• 180° pulse flips the spins.
• Spin re-phasing occurs.
• Echo is formed.

T2 Constant

• Accuracy: The decay of the MR signal around the echo peaks is accurately characterized by the $T_2$ constant.
• Reproduction of T2 Decay: To reproduce the ‘true’ $T_2$ decay, several refocusing pulses are generated at equal intervals.
• Line Through Peaks: A line through the spin echo peaks reproduces what the MR signal would be without the effect of static inhomogeneities.

MRI Contrasts

• T1-weighted: (TR=600, TE=11)
• Density-weighted: (TR=3000, TE=17)
• T2-weighted: (TR=3800, TE=102)
• TE: Time at which the signal is measured

Imaging in 3-D

• Differentiation: To measure a 3-Dimensional contrast, one needs to introduce differentiation between protons in 3 dimensions.
• Precession Frequency: The precession frequency of protons is proportional to the magnetic field strength: $w = γB$.

Gradient Fields

• Spatial Variation: Varying the strength of the magnetic field in space gives protons in each spatial location their own precession frequency.
• Gradient Fields: This is accomplished via magnetic fields that vary in strength from one spatial location to another.
• Gradient Equation: $w = γ(B<em>0 + B</em>1)$, where $B_1$ is the gradient field.

Slice Selection

• Process: A gradient field is switched on prior to the RF pulse.
• Frequency Variation: At the time of the pulse, the transverse magnetization precesses at different frequencies along the gradient field.
• Thin Band Response: Only a thin band (slice) of nuclei will respond to the RF pulse—those that precess at the same frequency as the RF pulse.
• Measured Signal: Thus, all the measured signal will come from that slice of the brain.

Concepts 1

• Spin: Intrinsic rotation-like property of all electrons, protons, and neutrons.
• Equilibrium Magnetisation: The net (summed) magnetization of H protons in a large static magnetic field in the scanner ($B_0$).
• Precession: The “wobbling” of H protons prior to alignment to a large magnetic field. Coherent precession is the source of the MRI signal.
• Larmor Frequency: The frequency of precession; it depends of the type of nucleus and field strength. It is fixed for H nuclei for a given field strength.
• Excitation Pulse: An oscillating magnetic field of a frequency in the RF (radio frequency) range that tips over the magnetism of protons away from the large static field of the scanner into the transverse plane.
• Flip Angle: The angle to which protons are tipped by the excitation pulse.
• Magnetic Resonance (MR) Signal: The signal resulting from resonant (coherent) precession of protons after being tipped over by the RF pulse.
• Longitudinal Relaxation: The realignment of protons with the static magnetic field $B_0$ after being tipped over by the RF pulse.
• TR: Time of the repetition of the RF pulse.
• T1: A time constant that describes the speed of longitudinal relaxation.

Concepts 2

• T1-weighted Contrast: The contrast obtained when TR is considerably shorter than $T_1$. The contrast comes from a more complete longitudinal relaxation in some tissues than other tissues.
• Transverse Relaxation: The decay of the MR signal due to loss of precession coherence (dephasing).
• T2: Time constant describing transverse relaxation. It describes the rate of decay due to random inhomogeneities.
• T2-weighted Contrast: Comes from some tissues decaying more rapidly than others; the MR signal should be measured at some delay after the RF pulse.
• T2*: Time constant describing decay due to both random and static inhomogeneities.
• Spin Echo Sequence: Imaging sequence that uses $180°$ refocusing pulses to bring spins dephased by static inhomogeneities back into phase.
• Spin Echo: The re-focusing (re-generation) of the MR signal when proton precession is re-synchronised following the $180°$ refocusing pulse.
• TE (Time to Echo): TE is in the middle of the data acquisition window. Effectively refers to the data acquisition time (the middle of that period).
• Magnetic Gradient: Magnetic field whose strength is constant in time but varies in space.