Presentation on theme: "Introduction to fMRI physics for dummies (like me!)."— Presentation transcript:
1Introduction to fMRI physics for dummies (like me!).
2Outline History of NMR to MRI to fMRI Physics of protons (1H in particular)Creating MRI imagesFrom MRI to fMRI
3History of Nuclear Magnetic Resonance NMR = nuclear magnetic resonanceFelix Block and Edward Purcell1946: atomic nuclei absorb and re-emit radio frequency energy1952: Nobel prize in physicsnuclear: properties of nuclei of atomsmagnetic: magnetic field requiredresonance: interaction between magnetic field and radio frequencyBlochPurcellNMR MRISource: Jody Culham’s web slides
4History of fMRIMRI-1973: Lauterbur suggests NMR could be used to form images-1977: clinical MRI scanner patented-1977: Mansfield proposes echo-planar imaging (EPI) to acquire images fasterfMRI-1990: Ogawa observes BOLD effect with T2*blood vessels became more visible as blood oxygen decreased-1991: Belliveau observes first functional images using a contrast agent-1992: Ogawa & Kwong publish first functional images using BOLD signalSource: Jody Culham’s web slides
5Some terms to knowB0 – this is used to denote the main magnetic field – also known as longitudinal magnetizationobjects placed within B0 will gradually align to this field (longitudinal relaxation)M0 – this is used to denote the net magnetization of an object within B0it is the M0 which is ‘tipped’ out of alignment with B0 to create the MR image – so M0 is now measured as transverse magnetizationRF pulse – radio frequency pulse – not to be confused with ‘resonant frequency’to read M0 it must be tipped out of alignment with B0 – this is achieved by sending an RF pulse at certain resonant frequencies and gradients
6Some more terms to knowMagnet – the big magnet that we allocate the Tesla value to that creates B0Gradient Coil – smaller magnets that are used to tip the net magnetization of the subject (M0) out of alignment with B0There are actually three gradient coils orthogonal to one another so that gradients can be applied in the x, y and z planesRF coil – radio frequency coil – these are typically receive only coils and are used to measure M0 at some time after the RF pulses have been applied. Send/receive coils are also available
7Physics of protons.motion of electrically charged particles results in a magnetic force orthogonal to the direction of motionprotons (nuclear constituent of atom) have a property of angular momentum known as spinAngular momentum (spin) of a proton.
8Protons aligning within a magnetic field In “field free” spacerandomly orientedInside magnetic fieldoriented with or against B0M = net magnetizationMApplied MagneticField (B0)when placed in a magnetic field (B0; e.g., our MRI machines) protons will either align with the magnetic field or orthogonal to it (process of reaching magnetic equilibrium)there is a small difference (10:1 million) in the number of protons in the low and high energy states – with more in the low state leading to a net magnetization (M)Source: Mark Cohen’s web slidesSource: Robert Cox’s web slidesSource: Jody Culham’s web slides
9Precession – the spinning top analogy. What is actually aligned with the B0 is the axis around which the protonprecesses – the decay of precession (i.e., it is the rate of precession out ofalignment with B0 together with the proton density of the tissue concernedthat is crucial in MRI)Source: Cohen and Bookheimer article
10Larmor Frequency Larmor equation f = B0 the energy difference between the high (oriented with B0) and low (oriented against B0) energy protons is measurable and is expressed in the Larmor equationLarmor equationf = B0 = MHz/TAt 1.5T, f = MHzAt 4T, f = MHzField Strength (Tesla)ResonanceFrequency for 1H170.3220.127.116.11
11RF Excitationprotons can flip between low and high energy states (i.e., flip between being aligned with or against B0)to do so the energy transfer must be of a precise amount and must be facilitated by another force (e.g., other protons or molecules)in MRI, RF (radio frequency) pulses are used to excite the RF field – the Swing analogy – tipping the net magnetization out of alignment with B0
12Cox’s Swing AnalogySource: Robert Cox’s web slides
13RF Excitation Excite Radio Frequency (RF) field transmission coil: apply magnetic field along B1 (perpendicular to B0) for ~3 msoscillating field at Larmor frequencyfrequencies in range of radio transmissionsB1 is small: ~1/10,000 Ttips M to transverse plane – spirals downanalogies: guitar string (Noll), swing (Cox)final angle between B0 and B1 is the flip angleB1B0Source: Robert Cox’s web slides
14Longitudinal relaxation and T1. temperature influences the number of collisions (and hence the rate at which protons flip between low and high energy states)so magnetic equilibrium (M0), or the rate at which a body placed inside B0 becomes magnetized depends on temperature – this is known as longitudinal relaxationthe T1-weighted image (usually used for anatomical images) measures the rate at which the object placed in B0 (the unsuspecting subject in our case) goes from a non-magnetized to a magnetized state – the longitudinal relaxationdifferent types of molecules (and by extension tissue) approach M0 at different rates allowing us to differentiate things like white and grey matter – we creep close towards the image!!!
15T1 and T2T1 measures the longitudinal relaxation (along B0) – or the rate at which the subject (and the various different constituents of that subject) reaches magnetic equilibriumT2 measures the transverse relaxation (along B1) – or the rate of decay of the signal after an RF pulse is deliveredT1 – recovery to state of magnetic equilibriumT2 – rate of decay after excitationTissue T2 decay times (in 1.5 T magnet)white matter 70 msecgrey matter 90 msecCSF msec
16Reading M0RF coils receive the net magnetization from the object placed within the coil (e.g., a subject’s head)can also have send / receive RF coils that also deliver the RF pulse (to get the swing going) – usually the pulse is delivered by gradient coils
17Proton density, recovery (T1) and decay (T2 and T2*) times. T1 weightedDensity weightedT2 weightedBy ‘weighting’ the pulse sequence (and point at which data is collected) different images of the brain are obtainedWeighting is achieved by manipulating TE (time to echo) and TR (time to repetition of the pulse sequence)
18Precession In and Out of Phase all nuclei aligned and precessingin the same direction.nuclei not aligned but still precessingin the same direction.So MR signal will start off strong but as protons begin to precess out of phase the signal will decay.Source: Mark Cohen’s web slides
19T1 and TRT1 = recovery of longitudinal (B0) magnetization after the RF pulseused in anatomical images~ msec (longer with bigger B0)TR (repetition time) = time to wait after excitation before sampling T1Source: Mark Cohen’s web slides
20T2 and TE T2 = decay of transverse magnetization after RF pulse TE (time to echo) = time to wait to measure T2 or T2* (after re-focusing with spin echo)Source: Mark Cohen’s web slides
21T1 vs. T2effectively, T1 and T2 images are the inverse of one another, with T1 typically used to form anatomical images and T2* used in fMRIT1 and TR
22T2*T2: intrinsic decay of transverse magnetization over microscopic region (~5-10 microns)~ msec (shorter with bigger B0)T2*: overall decay of transverse magnetization over macroscopic region (~mm)decays more quickly than T2 (by factor of ~2)Source: Robert Cox’s web slides
24Repetition and echo time dependence. Source: Buxton book Ch. 8
25Spatial localisation of the signal – creating the 1D image. A spatially variant B1 leads to a spatially variant distribution of RFs.Frequency analysis is used to discriminate different spatial locations.PULSE SEQUENCEtimeRF pulseGx (x – gradient)data acquisition
26Spatial Coding Gradient coil add a gradient to the main magnetic field Field Strength (T) ~ z positionFreqGradient coiladd a gradient to the main magnetic fieldexcite only frequencies corresponding to slice planeGradient magnetic field = applied in theslice plane (i.e., the x direction) thus Gx
27Spatial localisation of the signal – creating the 2D image. Can’t simply turn on 2 gradients.Instead the 2 gradients need a precise sequence.The 1D sequence already shown is known as frequency encoding.A different pulse sequence can be used in the y-direction to create the 2D image – phase encoding.This method is known as echo-planar imaging or EPI and is the most common method used in fMRI.
28Spatial localisation of the signal – creating the 3D image The RF field must be at the same resonant frequency as the nucleus being scanned.For the 2D image we have selected only one resonant frequency in one particular z-plane (and used EPI to sequences to obtain the x and y-planes).So we simply apply a gradient at different levels (slices) in the z-plane to create the 3D image.slices in the z-plane
29Spatial localisation of the signal – creating the 3D image frequ.encodephaseencodeSource: Buxton book Ch. 10
30EchosAll RF pulses create an ‘echo’ of the M0 signal obtained by the pulse.T2* signals decay more rapidly than T2A refocusing pulse is used to create a transient echo of the signal – a spin echoMultiple refocussing pulses create multiple echoesSource: Buxton book
31Echospulse sequence: series of excitations, gradient triggers and readoutsEchos – refocussing of signalSpin echo: when “fast” regions get ahead in phase, make them go to the back and catch upmeasure T2ideally TE = average T2Gradient echo: make “fast” regions become “slow” and vice-versameasure T2*ideally TE ~ average T2*Source: Mark Cohen’s web slides
32EPI imaging and k-space Any net signal produced by proton spins can be expressed as a sum of the sine and cosine waves of different wavelengthsThe different spatial frequencies of these wavelengths are denoted as k-space – the inverse of the wavelengthssmall k value = low spatial frequency / long wavelengthlarge k value = high spatial frequency / short wavelengthk-space is what is actually measured in MRI (i.e., the signal from M0 is transformed into x and y values via k-space)
33EPI imaging and k-space x = frequency and y = phase or angleSource: Traveler’s Guide to K-space (C.A. Mistretta)
34Fourier transformation. k-space is magically transformed into our image via a Fourier transformation.Source: Buxton book Ch 5
35EPI imaging and k-space Source: Buxton book Ch 10
36EPI imaging and k-space Source: Buxton book Ch 10
37k-space and sampling methods. The EPI pulse sequence zig-zags acrossk-space, slowly in the x-direction andrapidly in the y-direction.The Gz gradient shifts this process to thenext slice to be imaged.Source: Buxton book Ch 11
38A Walk Through K-space single shot two shot k-space can be sampled in many “shots”2 shot or 4 shotless time between samples of slicesallows interpolationmore shots = increased spatial resolutionNote: The above is k-space, not slicesboth halves of k-space in 1 sec1st half of k-spacein 0.5 sec2nd half of k-spacein 0.5 sec1st half of k-spacein 0.5 sec2nd half of k-space2nd volume in 1 secvs.interpolatedimage1st volume in 1 sec
39But what about activation? Voila! The MRI!But what about activation?
40Vascular Network Transit Time = 2-3 s Arterioles Capillaries Venules Y=95% at rest.Y=100% during activation.25 mm diameter.<15% blood volume of cortical tissue.VenulesY=60% at rest.Y=90% during activation.25-50 mm diameter.40% blood volume of cortical tissue.Red blood cell6 mm wide and 1-2 mm thick.Delivers O2 in form of oxyhemoglobin.CapillariesY=80% at rest.Y=90% during activation.8 mm diameter.40% blood volume of cortical tissue.Primary site of O2 exchange with tissue.Transit Time = 2-3 sSource: Chris Thomas’ Slides
41Vascular network and BOLD Source: Buxton book Ch 2
42Susceptibility and Susceptibility Artifacts Adding a nonuniform object (like a person) to B0 will make the total magnetic field B nonuniformThis is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external fieldFor large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimmingSusceptibility Artifact-occurs near junctions between air and tissuesinuses, ear canalssinusesearcanalsSource: Robert Cox’s web slides
43How Susceptibility Affects Signal Susceptibility nonuniform precession frequenciesRF signals from different regions that are at different frequencies will get out of phase and thus tend to cancel outSum of 500 Cosines with Random FrequenciesStarts off large when all phases are about equalDecays away as differentcomponents get different phasesSource: Robert Cox’s web slides
44Susceptibility and BOLD fMRI Magnetic susceptibility (c) refers to magnetic response of a material when placed in B0.Red blood cells exhibit a change in c during ‘activation’Basically, oxyhaemoglobin in the RBC (HbO2) becomes deoxyhaemoglobin (Hb):Becomes paramagnetic.Susceptibility difference between venous vasculature and surroundings (susceptibility induced field shifts).
45BOLD signal Blood Oxygen Level Dependent signal Source: Buxton book Ch 17
46BOLD signalCBF, CBV, and CMRO2 have different effects on HbO2 concentration:Interaction of these 3 produce BOLD responseThey change [Hb] which affects magnetic environment.Blood Oxygen Level Dependent signalLocal HbContent(delivery of more HbO2 -> less Hb on venous side if excess O2 not used)CBFLocal HbContent(extraction of O2-> HbO2 becomes Hb)CMRO2Local HbContentCBV(more Hb in a given imaging voxel)
48First Functional Images Source: Kwong et al., 1992
49Hemodynamic Response Function % signal change= (point – baseline)/baselineusually 0.5-3%initial dip-more focal-somewhat elusive so fartime to risesignal begins to rise soon after stimulus beginstime to peaksignal peaks 4-6 sec after stimulus beginspost stimulus undershootsignal suppressed after stimulation ends