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Introduction to fMRI physics for dummies (like me!).

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1 Introduction to fMRI physics for dummies (like me!).

2 Outline History of NMR to MRI to fMRI Physics of protons (1H in particular) Creating MRI images From MRI to fMRI

3 History of Nuclear Magnetic Resonance NMR = nuclear magnetic resonance Felix Block and Edward Purcell 1946: atomic nuclei absorb and re- emit radio frequency energy 1952: Nobel prize in physics nuclear: properties of nuclei of atoms magnetic: magnetic field required resonance: interaction between magnetic field and radio frequency BlochPurcell NMR  MRI Source: Jody Culham’s web slidesweb slides

4 History of fMRI MRI -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 faster fMRI -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 signal Source: Jody Culham’s web slidesweb slides

5 Some terms to know B 0 – this is used to denote the main magnetic field – also known as longitudinal magnetization objects placed within B 0 will gradually align to this field (longitudinal relaxation) M 0 – this is used to denote the net magnetization of an object within B 0 it is the M 0 which is ‘tipped’ out of alignment with B 0 to create the MR image – so M 0 is now measured as transverse magnetization RF pulse – radio frequency pulse – not to be confused with ‘resonant frequency’ to read M 0 it must be tipped out of alignment with B 0 – this is achieved by sending an RF pulse at certain resonant frequencies and gradients

6 Some more terms to know Magnet – the big magnet that we allocate the Tesla value to that creates B 0 Gradient Coil – smaller magnets that are used to tip the net magnetization of the subject (M 0 ) out of alignment with B 0 There are actually three gradient coils orthogonal to one another so that gradients can be applied in the x, y and z planes RF coil – radio frequency coil – these are typically receive only coils and are used to measure M 0 at some time after the RF pulses have been applied. Send/receive coils are also available

7 Physics of protons. motion of electrically charged particles results in a magnetic force orthogonal to the direction of motion protons (nuclear constituent of atom) have a property of angular momentum known as spin Angular momentum (spin) of a proton.

8 Protons aligning within a magnetic field In “field free” space randomly oriented Source: Mark Cohen’s web slidesMark Cohen’s web slidesSource: Robert Cox’s web slidesRobert Cox’s web slidesSource: Jody Culham’s web slidesweb slides when placed in a magnetic field (B 0 ; 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) Inside magnetic field oriented with or against B 0 M = net magnetization M Applied Magnetic Field (B 0 )

9 Precession – the spinning top analogy. Source: Cohen and Bookheimer articleCohen and Bookheimer article What is actually aligned with the B 0 is the axis around which the proton precesses – the decay of precession (i.e., it is the rate of precession out of alignment with B 0 together with the proton density of the tissue concerned that is crucial in MRI)

10 Larmor Frequency Larmor equation f =  B 0  = MHz/T At 1.5T, f = MHz At 4T, f = MHz Field Strength (Tesla) Resonance Frequency for 1H the energy difference between the high (oriented with B 0 ) and low (oriented against B 0 ) energy protons is measurable and is expressed in the Larmor equation

11 RF Excitation protons can flip between low and high energy states (i.e., flip between being aligned with or against B 0 ) 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 B 0

12 Cox’s Swing Analogy Source: Robert Cox’s web slidesRobert Cox’s web slides

13 RF Excitation Excite Radio Frequency (RF) field transmission coil: apply magnetic field along B1 (perpendicular to B 0 ) for ~3 ms oscillating field at Larmor frequency frequencies in range of radio transmissions B 1 is small: ~1/10,000 T tips M to transverse plane – spirals down analogies: guitar string (Noll), swing (Cox) final angle between B 0 and B 1 is the flip angle B1B1 B0B0 Source: Robert Cox’s web slidesRobert Cox’s web slides

14 Longitudinal 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 (M 0 ), or the rate at which a body placed inside B 0 becomes magnetized depends on temperature – this is known as longitudinal relaxation the T1-weighted image (usually used for anatomical images) measures the rate at which the object placed in B 0 (the unsuspecting subject in our case) goes from a non-magnetized to a magnetized state – the longitudinal relaxation different types of molecules (and by extension tissue) approach M 0 at different rates allowing us to differentiate things like white and grey matter – we creep close towards the image!!!

15 T1 and T2 T1 measures the longitudinal relaxation (along B 0 ) – or the rate at which the subject (and the various different constituents of that subject) reaches magnetic equilibrium T2 measures the transverse relaxation (along B 1 ) – or the rate of decay of the signal after an RF pulse is delivered T1 – recovery to state of magnetic equilibrium T2 – rate of decay after excitation TissueT2 decay times (in 1.5 T magnet) white matter70 msec grey matter90 msec CSF400 msec

16 Reading M 0 RF 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

17 Proton density, recovery (T1) and decay (T2 and T2*) times. By ‘weighting’ the pulse sequence (and point at which data is collected) different images of the brain are obtained Weighting is achieved by manipulating TE (time to echo) and TR (time to repetition of the pulse sequence) T1 weightedDensity weightedT2 weighted

18 Precession In and Out of Phase Source: Mark Cohen’s web slidesMark Cohen’s web slides all nuclei aligned and precessing in the same direction. nuclei not aligned but still precessing in the same direction. So MR signal will start off strong but as protons begin to precess out of phase the signal will decay.

19 T1 and TR Source: Mark Cohen’s web slidesMark Cohen’s web slides T1 = recovery of longitudinal (B 0 ) magnetization after the RF pulse used in anatomical images ~ msec (longer with bigger B 0 ) TR (repetition time) = time to wait after excitation before sampling T1

20 T2 and TE Source: Mark Cohen’s web slidesMark Cohen’s web slides 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)

21 T1 vs. T2 effectively, T1 and T2 images are the inverse of one another, with T1 typically used to form anatomical images and T2* used in fMRI T1 and TR

22 T2* T2: intrinsic decay of transverse magnetization over microscopic region (~5-10 microns) ~ msec (shorter with bigger B 0 ) T2*: overall decay of transverse magnetization over macroscopic region (~mm) decays more quickly than T2 (by factor of ~2) Source: Robert Cox’s web slidesRobert Cox’s web slides

23 T1 vs. T2 Source: Mark Cohen’s web slidesMark Cohen’s web slides

24 Repetition and echo time dependence. Source: Buxton book Ch. 8

25 Spatial localisation of the signal – creating the 1D image. A spatially variant B 1 leads to a spatially variant distribution of RFs. Frequency analysis is used to discriminate different spatial locations. time RF pulse Gx (x – gradient) data acquisition PULSE SEQUENCE

26 Spatial Coding excite only frequencies corresponding to slice plane Field Strength (T) ~ z position Freq Gradient coil add a gradient to the main magnetic field Gradient magnetic field = applied in the slice plane (i.e., the x direction) thus Gx

27 Spatial 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.

28 Spatial 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

29 Spatial localisation of the signal – creating the 3D image frequ. encode phase encode Source: Buxton book Ch. 10

30 Echos Source: Buxton book All RF pulses create an ‘echo’ of the M 0 signal obtained by the pulse. T2* signals decay more rapidly than T2 A refocusing pulse is used to create a transient echo of the signal – a spin echo Multiple refocussing pulses create multiple echoes

31 Echos Source: Mark Cohen’s web slidesMark Cohen’s web slides Echos – refocussing of signal Spin echo: when “fast” regions get ahead in phase, make them go to the back and catch up - measure T2 - ideally TE = average T2 Gradient echo: make “fast” regions become “slow” and vice-versa - measure T2* - ideally TE ~ average T2* pulse sequence: series of excitations, gradient triggers and readouts

32 EPI 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 wavelengths The different spatial frequencies of these wavelengths are denoted as k- space – the inverse of the wavelengths small k value = low spatial frequency / long wavelength large k value = high spatial frequency / short wavelength k-space is what is actually measured in MRI (i.e., the signal from M 0 is transformed into x and y values via k-space)

33 EPI imaging and k-space Source: Traveler’s Guide to K-space (C.A. Mistretta)Traveler’s Guide to K-space x = frequency and y = phase or angle

34 Fourier transformation. k-space is magically transformed into our image via a Fourier transformation. Source: Buxton book Ch 5

35 EPI imaging and k-space Source: Buxton book Ch 10

36 EPI imaging and k-space Source: Buxton book Ch 10

37 k-space and sampling methods. The EPI pulse sequence zig-zags across k-space, slowly in the x-direction and rapidly in the y-direction. The G z gradient shifts this process to the next slice to be imaged. Source: Buxton book Ch 11

38 A Walk Through K-space k-space can be sampled in many “shots” 2 shot or 4 shot less time between samples of slices allows interpolation more shots = increased spatial resolution both halves of k-space in 1 sec 1 st half of k-space in 0.5 sec 2 nd half of k-space in 0.5 sec vs. single shottwo shot 1st volume in 1 sec interpolated image Note: The above is k-space, not slices 1 st half of k-space in 0.5 sec 2 nd half of k-space in 0.5 sec 2nd volume in 1 sec

39 Voila! The MRI! But what about activation?

40 Vascular Network Arterioles –Y=95% at rest. –Y=100% during activation. –25  m diameter. –<15% blood volume of cortical tissue. Venules –Y=60% at rest. –Y=90% during activation. –25-50  m diameter. –40% blood volume of cortical tissue. Red blood cell –6  m wide and 1-2  m thick. –Delivers O 2 in form of oxyhemoglobin. Capillaries –Y=80% at rest. –Y=90% during activation. –8  m diameter. –40% blood volume of cortical tissue. –Primary site of O 2 exchange with tissue. Transit Time = 2-3 s Source: Chris Thomas’ Slides

41 Vascular network and BOLD Source: Buxton book Ch 2

42 Susceptibility and Susceptibility Artifacts Source: Robert Cox’s web slidesRobert Cox’s web slides Adding a nonuniform object (like a person) to B 0 will make the total magnetic field B nonuniform This is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external field For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimming Susceptibility Artifact -occurs near junctions between air and tissue sinuses, ear canals sinuses ear canals

43 How Susceptibility Affects Signal Source: Robert Cox’s web slidesRobert Cox’s web slides Susceptibility  nonuniform precession frequencies RF signals from different regions that are at different frequencies will get out of phase and thus tend to cancel out Sum of 500 Cosines with Random Frequencies Starts off large when all phases are about equal Decays away as different components get different phases

44 Susceptibility and BOLD fMRI Magnetic susceptibility (  ) refers to magnetic response of a material when placed in B 0. Red blood cells exhibit a change in  during ‘activation’ Basically, oxyhaemoglobin in the RBC (HbO 2 ) becomes deoxyhaemoglobin (Hb): –Becomes paramagnetic. –Susceptibility difference between venous vasculature and surroundings (susceptibility induced field shifts).

45 BOLD signal Source: Buxton book Ch 17 Blood Oxygen Level Dependent signal

46 BOLD signal Blood Oxygen Level Dependent signal CBF, CBV, and CMRO 2 have different effects on HbO 2 concentration: Interaction of these 3 produce BOLD response –They change [Hb] which affects magnetic environment. (delivery of more HbO 2 -> less Hb on venous side if excess O 2 not used) CMRO 2 CBV CBF Local Hb Content Local Hb Content Local Hb Content (extraction of O 2 -> HbO 2 becomes Hb) (more Hb in a given imaging voxel)

47 BOLD signal Source: Doug Noll’s primer

48 First Functional Images Source: Kwong et al., 1992

49 Hemodynamic Response Function % signal change = (point – baseline)/baseline usually 0.5-3% initial dip -more focal -somewhat elusive so far time to rise signal begins to rise soon after stimulus begins time to peak signal peaks 4-6 sec after stimulus begins post stimulus undershoot signal suppressed after stimulation ends

50 And now we can all get some sleep!


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