fMRI Methods Lecture2 – MRI Physics

magnetized materials and moving electric charges. Magnetic fields magnetized materials and moving electric charges.

Electric induction Similarly a moving magnetic field can be used to create electric current (moving charge).

Or you could use an electric current to move a magnet… Electric induction Or you could use an electric current to move a magnet…

Force and field directions Right hand rule Force and field directions

Nuclear spins Protons are positively charged atomic particles that spin about themselves because of thermal energy.

Magnetic moment μ (magnetic moment) = the torque (turning force) felt by a moving electrical charge as it is put in a magnet field. The size of a magnetic moment depends on how much electrical charge is moving and the strength of the magnetic field it is in. A Hydrogen proton has a constant electrical charge.

Spin alignment Earth’s magnetic field is relatively small (0.00005 Tesla), so the spins happen in different directions and cancel out.

But when in a strong external magnetic field (e.g. 1.5 Tesla). Spin alignment But when in a strong external magnetic field (e.g. 1.5 Tesla).

Net magnetization (M) Sum of magnetic moments in a sample with a particular volume at a given time.

Precession Hydrogen protons not only spin. They also precess around the axis of the magnetic field. Magnetic field direction True for all atoms with an odd number of protons

Precession speed Two factors govern the speed of precession (Larmor frequency): magnetic field strength & gyromagnetic ratio Larmor frequency = Bo * /2π

Gyromagnetic ratio Gyromagnetic ratio ( ) Magnetic moment / Angular momentum Combination of electromagnetic and mechanical forces. Angular momentum is dependant on the mass of the atom.

Different atoms have different gyromagnetic ratios: Nucleus Gyromagnetic ratio (γ) 1H 267.513 7Li 103.962 13C 67.262 19F 251.662 23Na 70.761 31P 108.291

Larmor Frequency at 1 Tesla Different atoms placed in the same magnetic field have different Larmor frequencies: “Tune in” to the Hydrogen frequency. Nucleus Larmor Frequency at 1 Tesla 1H 42.576 MGHz 7Li 16.546 MGHz 13C 10.705 MGHz 19F 40.053 MGHz 23Na 11.262 MGHz 31P 17.235 MGHz

The hydrogen atoms are precessing around z (direction of B0) Longitudinal & transverse directions The hydrogen atoms are precessing around z (direction of B0)

Net magnetization is all pointing in the z direction Steady state Net magnetization is all pointing in the z direction

Applying a perpendicular magnetic field “flips” the protons Excitation pulses Applying a perpendicular magnetic field “flips” the protons

Excitation & Relaxation Excite the sample in a perpendicular direction and let it relax. Net magnetization of the sample changes as it relaxes, inducing current to move in a near by coil. Larmor frequency

Flip angle Defined by the strength of B1 pulse and how long it lasts (T) θ = *B1*T This is one of the parameters we set during a scan It defines how far we “flip” the protons… x y z <900 pulse x y z 900 pulse x y z >900 pulse x y z 1800 pulse

Changes in the direction of the sample’s net magnetization T1 and T2/T2* T1: relaxation in the longitudinal direction T2*: relaxation in the transverse plane Changes in the direction of the sample’s net magnetization

Realignment of net magnetization with main magnetic field direction Before excitation At excitation Relaxation Net magnetization along the longitudinal direction

T1 T1 = 63% recovery of original magnetization value M0

What influences T1? Has something to do with the surroundings of the excited atom. The excited hydrogen needs to “pass on” its energy to its surroundings (the lattice) in order to relax. Different tissues offer different surroundings and have different T1 relaxation times… We can also introduce external molecules to a particular tissue and change its relaxation time. These are called “contrast agents”…

Loss of net magnetization phase in the transverse plain T2*/T2 Loss of net magnetization phase in the transverse plain Before excitation At excitation Relaxation Net magnetization in the transverse plain

T2/T2* T2 = 63% decay of magnetization in transverse plain

T2* = T2 - T2’ Two main factors effect transverse relaxation: 1. Intrinsic (T2): spin-spin interactions. Mechanical and electromagnetic interactions. 2. Extrinsic (T2’): Magnetic field inhomogeneity. Local fluctuations in the strength of the magnetic field experienced by different spins.

Magnetic field inhomogeneities Examples of causes: Transition to air filled cavities (sinusoids) Paramagnetic materials like cavity fillings Most importantly – Deoxygenated hemoglobin

What influences T2? Again, has to do with the molecular neighborhood affecting the amount and quality of spin-spin interactions. Different tissues will have different T2 relaxation times. The stronger the static magnetic field, the more interactions there are, quicker T2 decay.

We only have one measurement: MR signal We only have one measurement: Measurement of the net magnetization in the transverse plain as the sample relaxes. Once T2* relaxation is complete Protons precess out of phase in the transverse plain Net magnetization in transverse plain = 0

TR and TE Two important scanning parameters: TR – repetition time between excitation pulses. TE – time between excitation pulse and data acquisition (“read out”). Creating scanning protocols with different TR and TE lengths will allow us to derive T1 and T2/T2* relaxation times.

Short TR = weaker MR signal on consecutive pulses. TR length & MR signal strength Short TR = weaker MR signal on consecutive pulses. With short TRs relaxation in the longitudinal direction will not be complete. So there will be fewer relaxed protons to excite.

TE: when to measure MR signal We can measure the amplitude of net magnetization immediately after excitation or we can wait a bit. Longer TEs will allow more transverse relaxation to happen and the MR signal will be weaker.

Different image contrasts We can scan the brain using different pulse sequences by choosing particular TR and TE values to create images with different contrasts. TR length will determine how much time the sample has had to relax in the longitudinal direction. TE will determine how much time the sample has had to relax (loose phase) in the transverse plain.

Proton density contrast Measuring the amount of hydrogen in the voxels regardless of their T1 or T2 relaxation constants. This is done using a very long TR and very short TE

Higher intensity in voxels containing more hydrogen protons Proton density Higher intensity in voxels containing more hydrogen protons

T1 contrast Measuring how T1 relaxation differs between voxels. This is done using a medium TR and very short TE You need to know when largest difference between the tissues will take place…

T1 contrast Images have high intensity in voxels with shorter T1 constants (faster relaxation/recovery = release of more energy) CSF: 1800 ms Gray matter: 650 ms White matter: 500 ms Muscle: 400 ms Fat: 200 ms

We can combine a T2 acquisition with proton density… T2/T2* contrast Measuring how T2 relaxation differs between voxels. This is done using a long TR and medium TE We can combine a T2 acquisition with proton density…

T2 contrast Images have high intensity in voxels with longer T2 constants (slower relaxation = more detectable energy) CSF: 200 ms Gray Matter: 80 ms White Matter: 60 ms Muscle: 50 ms Fat: 50 ms

Same as T2 only smaller numbers (faster relaxation) T2* contrast Same as T2 only smaller numbers (faster relaxation) CSF: 100 ms Gray Matter: 40 ms White Matter: 30 ms Fat: 25 ms

T2* and BOLD fMRI T2* = T2 +T2’ T2: Spin-spin interactions T2’: field inhomogeneities Exposed iron (heme) molecules create local magnetic inhomogeneities BOLD – blood oxygen level dependant Assuming everything else stays constant during a scan one can measure BOLD changes across time…

T2* and BOLD More deoxygenated blood = more inhomogeneity more inhomogeneity = faster relaxation (shorter T2*) Shorter T2* = weaker energy/signal (image intensity) So what would increased neural activity cause?

So what happened in particular time points of this scan? T2* and BOLD So what happened in particular time points of this scan?

Bloch equation

MR images So far we’ve talked about a bunch of forces and energies changing in a sample across time… How can we differentiate locations in space and create an image? 2004 Nobel prize in Medicine Paul Lauterbur Peter Mansfield

Spatial gradients Create magnetic fields in each direction (x,y,z) that move from stronger to weaker (hence gradient).

Spatial gradients Different magnetic fields at different points in space. Hydrogen will precess at a different speed in each spatial location. By “tunning in” on the specific precession speed we can separate different spatial locations. Similarly to how we “tunned in” on hydrogen atoms…

Spatial gradients (-) 62 MHz 63 MHz 64 MHz G 65 MHz 66 MHz (+)

Spatial gradients Lot’s of Fourier transforms. Work in k-space (a vectorial space that keeps track of the spin phase & frequency variation across magnet space). It’s possible to turn gradients on and off very quickly (ms). Image reconstruction Pulse sequences

The magnet

Main static field Extremely large electric charge spinning on a helium cooled (-271o c) super conducting coil. Earth’s magnetic field 30-60 microtesla. MRI magnets suitable for scanning humans 1.5-7 T.

Main coils The bulk of the structure contains the coils generating the static magnetic field and the gradient magnetic fields.

RF coil Transmit and receive RF coils located close to the sample do the actual excitation and “read out”.

Homework! Read Chapters 3-5 of Huettel et. al. Explain how a spin-echo pulse does the magic of separating T2 relaxation from T2* relaxation. You can include figures/drawings if you like.