The Concept of MRI Physics, from Water to Signal to Image

The Concept of MRI Physics, from Water to Signal to Image Ali Alhamud, PhD alkk1973@gmail.com

Magnetic Resonance Imaging (MRI) Yes we know MRI does not use ionizing radiation and it is good for imaging soft tissues including blood. Is that all for MRI? MRI has powerful features whereas other imaging techniques, such as CT and PET, are relatively limited. These features of MRI include several protocol parameters by which indigenous contrast and image quality can be manipulated in unlimited ways. For example by changing TE and TR we can generate different MRI contrasts.

Magnetic Resonance Imaging (MRI) Other sequences have special parameters such as inversion time in IR sequence Selective Tissue Suppression using IR http://mriquestions.com/why-use-ir.html

MRI Protocol Parameters It is important to understand MRI protocol parameters and their changes, to do so the basic physics of MRI must be understood. Small FOV bad Contrast Bad resolution (partial volume) Different flip angles Receiver bandwidth (BW)

Review of Vectors Several phenomena (force, velocity etc) in our life can be represented as vectors but in MRI we are only interested in magnetic fields. A vector can be represented by an arrow or two components (horizontal and vertical components ). (1) Horizontal vector What is the resultant vector of the following: 2 2 Out of phase (2) Vertical vector 2 2 In phase How to reach to this point? What are the total horizontal and vertical components for these oblique vectors? (3) Oblique vector

MRI Radio Signals An MRI scanner uses radio signals with frequencies in the range of megahertz (MHz). You have to therefore exercise extreme caution in relation to any source of communication systems (mobile, radio, train..etc) near the MRI scanner or the building. FM 90.4 FM 94.5

Signal Representation Let s imagine a signal as though it was the motion of a hand clock. In MRI, we will see how magnetic field vectors rotate in the same manner as a hand clock. time Two dimensional representation One dimensional representation

Signal Parameters (Magnitude, Frequency and Phase) (1) Magnitude The length of the clock s hand Which ones are in phase and which are out of phase? (2) Frequency: How fast the clock s hand is rotating around the face of the clock (number of cycles per second). (3) Phase: the location of the clock s hand at a specific time

Lecture 1 Signal Creation

The Static Magnetic Field (the B0 Field) Why do we have to place our patient in the bore of the MRI scanner? There has to be a source of magnetism in our body! B0 A superconducting electromagnet, which is immersed in liquid Helium, is capable of producing a very powerful magnetic field such as 3 Tesla. 1 Tesla = 10,000 Gauss Earth s B field ~ 0.5 Gauss (50 µt) Refrigerator magnet ~ 5 mt The blue arrow or vector represents the magnitude and direction of the B0 field

The Source of Magnetism in the Human Body Different elements in the human body can be used as the source of magnetism such as Hydrogen 1, Carbon 13, Sodium 23 and Phosphorus 31. However, due to the abundance of 1 H nuclei (spins) in water and fat-based tissues of the human body, 1 H is the most commonly used element in clinical MRI. Nucleus (like the core of the earth) Water (H 2 O) Magnetic moment (µ) 1 H possesses: Spin angular momentum (Spin) Spin A magnetic dipole moment (µ) In MRI, hydrogen nuclei are referred to as spins.

Active and Stable Nuclei MRI active nuclei have a property of spin greater than zero which enables them to interact with the external B0 field. Nuclei must have one of the following: Odd protons. Odd neutrons. Odd (protons + neutrons). Examples: 1 H, 23 Na, 13 C, 31 P Stable nuclei, with nuclear spin equalling zero, cannot undergo an MRI experiment: Examples: 4 He, 12 C, 16 O and 32 S

Outside the MRI Scanner (Spins with Random Orientations) Outside the MRI scanner, human tissue is not magnetised The net magnetization (M) = 0

Quantum Behaviour of Hydrogen in the B0 Field (Energy States) 1 H nuclei have only two energy states in the presence of the B0 field; spin up (lower energy state) or spin down (higher energy state). Spin up Spin down Higher energy state Lower energy state 1/2 γb0h -1/2 γb0h γb0h Although there are 2 energy states, we do not know what the exact state of the hydrogen is at any time, it is actually in all possible states simultaneously (quantum superposition). Quantum mechanics can tell us what happens to a large number of 1 H nuclei in the B0 field at the thermal equilibrium. γ: gyromagnetic ratio and h: Planck's constant

Quantum Behaviour of Hydrogen in the B0 Field (Energy States) Higher energy state Lower energy state Spin up The ratio is roughly 100,000 to 100,006 per Tesla of B 0 At thermal equilibrium (body temperature ~ 27 Cº), there is almost equal distribution of spins in the two states but with a very small excess in the lower energy state. The small excess in the lower energy state is only visible for MRI measurement. Spin down The population is given by the Boltzmann factor: N+/N = exp [ γb0h / kt] --- magnetic energy / thermal energy At absolute temperature (-273.15 Cº) most nuclei reside at the lower energy state. 27 Cº -273.15 Cº Increasing the field strength also increases spins in the lower energy state.

Quantum Behaviour of Hydrogen in the B0 Field The net magnetisation (M) > 0 Since there is an excess number of nuclei in the lower energy state, the thermal equilibrium magnetisation M (net magnetisation) > 0 Spin up

Quantum Behaviour of Hydrogen in the B0 Field (Precession or Larmor Frequency) B0 spin Spin up Since 1 H possesses spin, it precesses around B0 with Larmor frequency which depends on the field strength: ω 0 = γ * B0 γ: gyromagnetic ratio of hydrogen (42.58 MHz/T) At 3 Tesla ω 0 = 127 MHz Larmor or the precessional frequency equation (ω 0 =γ*b0) is the most important equation in MRI and you should memorize it. http://www.xrayphysics.com/sequences.html

Longitudinal (M z ) and Transverse (M xy ) Magnetisation Components Classical mechanic s view of precession: The net magnetization vector (M) of all hydrogen nuclei aligns along the B0 field (z axis) and it is called the longitudinal magnetisation component (M z ). In the xy plane, the transverse magnetisation component (M xy )= 0. The precession is said to be frozen or invisible in the classical view. M xy =0 Transverse xy plane

Resonance Condition We place our subject in the MRI scanner to generate some longitudinal magnetization (M z ) which is parallel to the B0 field. How do we measure M 0? Fact: M 0 is extremely small and there is no existing device which can measure it directly. Subject in the MRI bore M = 0 M z Subject out of the MRI bore B0 field

ω 0 = γ * B0 Resonance Condition (Excitation) We have to manipulate (excite) the system by adding energy. This is done by applying an oscillating magnetic field (much smaller than B0) known as the B1 field (RF pulse). Fact: the B1 field is not static like B0 but it alters its direction (+ to -) at Larmor frequency. When spins absorb this energy (resonance condition), (1) Spins transfer from lower energy state to higher energy state. (2) M z starts to rotate to the xy plane (transverse plane). (3) Spins are brought into phase in the xy plane B1 field (90 RF pulse) M xy M = 0 M z B0 field z direction

Frames of Reference Let us imagine how M z rotates during the application of B1 field (RF pulse): On a dark night, imagine you are holding a flash light and standing on a merry go round that is moving. Try to flip/rotate the flashlight. If someone from outside is watching you, what is the trajectory of the light (a or b)? If someone is with you on the merry go round, what is the trajectory of the light (a or b)? How is the trajectory when the flashlight is rotated 90? 90 RF pulse M z =0 M xy = M 0 a) The laboratory frame of reference. b) The rotating frame of reference rotating about z. Most MRI analyses are performed in the rotating frame to simplify the complex motion of precessing spins.

Detecting an MRI Signal We applied a 90 RF pulse (B1 field), for a short period of time, to rotate M z completely to the transverse plane. M z in the transverse plane is called the transverse magnetisation component (M xy ) which is the only component which is visible for measurement. Since M xy in the transverse plane precesses at the Larmor frequency,by placing a loop of wire around the imaged subject (an MRI coil), we can detect M xy as a free induction decay signal (FID). Z axis M xy in the transverse plane is not static but it is rotates or precesses at Larmor frequency. Voltage can then be produced due to the motion of M xy (Faraday's Law). M xy MRI coil Fact: M xy is the only component which can be measured by the MRI coil. Transverse plane (xy)

Free Induction Decay (FID) Signal The received MRI signal (FID) decays quite rapidly due to relaxation. The excited spins need to return back to the thermal equilibrium state along the longitudinal axis (z-axis) Energy exchange (T1 relaxation). However, the rate of decay is much faster than the required time to return to the thermal equilibrium state. spin-spin magnetic fields interaction (T2 relaxation) field inhomogeneity (T2*) SI( M xy ) time

The Composed MRI Signal (FID) What we receive in the MRI coil is only one signal (the composed signal) that is the sum of the contribution of all 1 H nuclei. What frequency does the FID signal have (spins all see B0 field)? ω0 = γ * B0 Which part of the human body does the FID signal come from (liver, heart, brain, limbs..etc)?

Lecture 2 MRI Pulse Sequences

The Concept of Echo in MRI As we mentioned, the MR scanner can only detect a single signal (the composed signal) in the transverse plane. We applied a 90 RF pulse, then after some time (echo time TE ), we recorded the FID signal. The FID signal declines due to the fact that spins need to go back to the lower energy state (T1 relaxation). However, the rate of decay is much faster than T1 relaxation due to T2/T2* relaxation. Free Induction ecay )FID) TE

Signal Intensity (SI) Field Inhomogeneity (T2*) Initially, we assume all spins experience only the B0 field, so each spin precesses at the same Larmor frequency (ω 0 =γ*b0). However, in the transverse plane, the magnetic field of each spin can interact with the B0 field and this causes changes in the precessional frequency of other spins (T2 relaxation). Also, the B0 field may not be homogeneous at all points in the space (T2 relaxation). The affect of T2 and T2 (T prime) is called T2*. This figure shows how the MRI signal decays (T2) even faster due to T2*. T2* T2 time

The Concept of Echo in MRI In order to minimise the rate of decay to some degree due to T2, we can add 180 RF pulse after the 90 pulse to generate an "echo" that occurs later in time. This is referred to as the spin echo. The 180 RF pulse only reduces the rate of decay due to the inhomogeneity in B0 (T2 ) and not due to T2. Please be aware that spin echo sequences can not recover all inhomogeneity in the B0 field. Maximum signal Losing signal FID: free induction decay If you are in a cave and start shouting. You will hear your voice come back due to reflection of sound. This is called an echo.

Spin Echo (SE) (Hahn Echo) Experiment: (1) Take two pens and flip them to 90 from the longitudinal axis to the transverse plane. (2) In the transverse plan, move one pen faster than the other. You will notice that they are out of phase (dephased) (3) After some time (TE/2), rotate the two dephased pens by 180 RF pulse (4) In this case, the faster pen will be behind the slower pen. (5) If you wait the same time (TE/2) and the same speed, you will notice that both pens will come back in phase. Even spin echo minimizes the rate of decay due to T2, the echo is still affected by the rate of T2. http://www.slideshare.net/drpsdeb/mri-basics

http://www.revisemri.com/questions/pulse_sequences/se_ge_differences The Concept of an MRI Pulse Sequence Timing Diagram An MRI pulse sequence consists of several horizontal lines. Each line shows a specific event of when RF-pulses are applied, an MR signal is generated, and gradients are turned on and off. Time is on the horizontal axis. To generate an MRI image, we have to repeat the excitation process (RF pulse) many times, which depends on the number of phase encoding steps (N phase ). The time used to repeat the excitation is called the repetition time (TR). TE TR N phase TR: how often we repeat the RF excitation pulse TE: the time between the centre of the RF pulse and the centre of the echo. N Phase N frequency Signal ADC Echo ADC: Analogue to Digital Converter

The Main Components of an MRI pulse Sequence Most MRI pulse sequences have the following components: TE TR (1) An RF excitation pulse is applied in the presence of slice selection gradient (G ss ) to generate M xy from a specific slice (2) A frequency encoding gradient (G f ) to create a 1D image (3) A phase encoding gradient (G p ) to create the second dimension in the image (4) A signal or ADC where our echo is recorded Signal ADC FID Echo

Gradient Recalled Echo (GRE) Pulse Sequence SE vs GRE What differences can you observe? http://www.revisemri.com/questions/pulse_sequences/se_ge_differences

Spin Echo (SE) Pulse Sequence TE TR The spin echo pulse sequence has : (1) A 90 excitation pulse with Slice selection gradient (G ss ) to generate M xy from a specific slice (2) A frequency encoding gradient (G f ) to create 1D image (3) A phase encoding gradient (G p ) to create the second dimension in the image (4) A 180 pulse (refocusing pulse) used to refocus the dephased spins (T2 ) (5) Signal or ADC where our echo is recorded The typical TR in SE is around 2 s and N phase = 256. Total scan time to acquire one slice = TR * Nphase = 2 *256 = 8.3 minute ADC FID Echo

Gradient Recalled Echo (GRE) Pulse Sequence GRE is identical to SE pulse sequence except that there is no 180 RF pulse. While the SE sequence generates an echo using a 180 RF pulse, in the GRE, the echo is generated using the gradient reversal approach. Following the 90 RF pulse, the first negative lobe of the gradient (dephasing lobe) causes a rapid phase dispersion of the precessing spins. When this gradient is reversed (rephasing lobe), the spins refocus and form a gradient (recalled) echo. Although GRE does not correct for T2, GRE has two main features, the echo can be recorded much more quickly and with less RF power. dephasing lobe rephasing lobe For clarity, other sequence components are not shown.

Multislice Imaging Since TR in SE sequence is quite long, a large number of slices can be excited in the free time within the same TR. This approach is implemented to speed up the imaging acquisition. TR TE SE Sequence echo Free time Multislice SE Sequence Slice 1 Slice 2 Slice 40 Slice 1

Turbo/Fast Spin Echo (TSE) TSE is an extension of multislice imaging TSE uses a series of 180 refocusing pulses after a single 90 pulse to generate a train of echoes for the same slice. echo1 The number of echoes acquired in a given TR interval is known as the echo train length (ETL) or turbo factor. echo1 echo2 echo3 echo4 If a SE sequence with a certain TR/TE/spatial resolution takes 8 minutes to perform, a TSE sequence with ETL=8 would take only 1 minute.

Turbo/Fast Spin Echo (TSE) TSE FID Echo1 Echo2 Echo3 Echo4 http://mriquestions.com/fse-parameters.html http://www.revisemri.com/questions/pulse_sequences/tse

Inversion Recovery (IR) Pulse Sequence What differences can you observe between SE pulse sequence and the second sequence?

Inversion Recovery (IR) Pulse Sequence In our SE pulse sequence, what happens if we add a 180 RF pulse at the start of the sequence? SE IR B 0 B 0 180 RF 90 RF -z

Inversion Recovery (IR) Pulse Sequence The time between the first 180 RF pulse and the 90 RF pulse is called inversion time (TI). TI is one of the most important protocol parameters in MRI by which a signal from any tissue can be suppressed (STIR and FLAIR). TI TE TR FACT: there was a technique called FIRM Fast Inversion Recovery Myeline which was used to suppress the signal from myelinated brain white matter. The point where we apply the 90 RF pulse is called the nulling or bouncing point http://mriquestions.com/why-use-ir.html

Lecture 3 Image Contrasts (T1, T2/T2* and PD) in MRI

Spin Relaxation Let s look at the example below. A heater is similar to the RF excitation pulse. The RF gives energy to spins (hydrogen nuclei). The heater provides the two cats with heat (energy). Let s take the heater away. Where do you think this energy goes? (1) Energy exchanges between the two cats (2) Energy exchanges between each cat and the surroundings (3) Cats will keep their energy The process of energy exchange is called relaxation.

Spin Relaxation Once we switch the RF pulse (heater) off, spins need to move back to the lower energy state or thermal equilibrium along the longitudinal z axis. Keep in mind that we are only able to measure the magnetization (M xy ) in the transverse plan. While we are busy measuring our FID signal, the relaxation process takes place simultaneously, causing the signal to decay very rapidly. The excitation trajectory is different to the relaxation trajectory! Maximum signal Losing signal M 0 During excitation FID: free induction decay M z During relaxation TE M xy Coil

Spins In phase and Out of Phase The phase of spins (magnetizations vectors of spins) are one of the most important concepts in MRI by which the signal decay is determined. If spins in the transverse plane (xy plane) are in phase (spins point in the same direction), the MRI signal intensity (SI) will be maximum (a). If spins in the transverse plane (xy plane) have different orientations (out of phase or dephase), the MRI signal will be weak (b) and it becomes extremely weak as the dephasing aggravates. SI a b c time The spins dephasing mainly arises from T2 relaxation and aggravates with T2* relaxation.

Spin-Spin Relaxation (T2 Relaxation) T2 relaxation is the process by which the transverse component of magnetization (Mxy) decays very rapidly. This is due to the spins dephasing (spins get out of step from one another in random ways). This is shown in the figure below (arrows with different orientations). + + + + Spins magnetic fields interaction M 0 SI 37% of M 0 T2 time The exponential decay of M xy is governed by a time T2. Thus T2 is the time required for the signal to fall to approximately 63% of its initial value (when there is only 37% of the signal left) http://mriquestions.com/what-is-t2.html

Inhomogeneity in the B0 Field (T2* relaxation) Once we place our subject in the bore of the MRI scanner, the field becomes inhomogeneous. This is due to the different levels of susceptibility of human tissue. This causes a very slight variation in B0 field strength (variation in the precession frequency) from point to point. This will cause the transverse magnetisation to decay even faster. In this case, the time governing this decay is not T2 but T2*. The T2* is the sum of T2 and T2. T2 prime (T2 ) is due to the inhomogeneity in the B0 field. In reality, we measure our signal weighted by T2* relaxation. Luckily, there is a way to generate an MRI signal weighted by T2. This is done by minimising, to some degree, the affect of T2 using spin echo with 180 RF pulse. SI M 0 Fact: T2* can be useful in MRI. There are many applications which use MRI based on T2* such as fmri. 37% of M 0 T2* T2 time

Spin Lattice Relaxation (T1 relaxation) T1 relaxation is the process by which the net magnetisation (M) returns to its initial maximum value (Mo) parallel to Bo. + Energy exchange between spins and the surroundings. M z M 0 63% of M 0 tissue The rate of recovery is governed by time T1. T1 can be viewed as the time required for the z-component of M z to reach about 63% of its maximum value (Mo). T1 time http://mriquestions.com/what-is-t2.html

Fact: T1 is much longer than T2/T2*. Each tissue has a unique T1 and T2 Spin Relaxation Times (T1, T2 and T2*) I usually like to imagine T1 and T2 curves as a mountain with a slope It takes a longer time to climb a mountain (T1) than to slide down it (T2/T2*). T1 T2/T2* When you go to a higher magnetic field, for example from 1.5 T to 3 T, the mountain becomes higher. This means the signal is much higher but T1 is longer. http://www.slideshare.net/drpsdeb/mri-basics

List of Relaxation Times for some Tissue at 1.5 T and 3 T List of relaxation times by tissue type and main magnetic field strength (Gati et al., 1997; Kruger et al., 2001; Lu et al., 2005; Wu and Wong, 2006).

GRE vs SE GRE generates an MRI image weighted by T2* (T2,T2 ). SE vs GRE SE generates an MRI image weighted by T2. But why do we have to use GRE if it generates such a low signal? hemorrhage, calcification, and iron deposition in various tissues and lesions. ADC FID Echo ADC FID Echo

T2/T2* and PD Contrasts M Z Recovery curve TR long T2w MRI Long TR Long TE PD Long TR Short TE fat tissue With a shorter TE, we have a higher signal but no T2 contrast Difference in T1 contrast almost 0 Time Decay curve Image contrast is a function of all T1,T2/T2* and PD. The important point is how to minimise one contrast and maximize the other one. SI (M xy ) TE TR fat PD tissue TE T2 Time With a longer TE there is more T2 contrast but a lower signal

SE Signal Intensity vs TE What do you observe in terms of signal brightness and contrast? SE brain images with TR = 1500 ms and various TE s Source from chapter 3 "MRI from picture to proton"

How to Measure T2 Relaxation Time of a Tissue This is done using SE sequence by acquiring different acquisitions with varying TEs. Each acquisition is applied with the same TR (very long). For each acquisition and for the same location, we measure the mean signal intensity (SI). We then plot these values and determine the time where the maximum SI falls to 37% of its initial value. SI Initial value (M) 37% of M 0 T2 time

An example of T2 vs T2* T2 T2* Spin echo gradient echo T2* includes T2 and T2. T2 is due to the variability in the B0 field. While spin echo recovers to some degree T2, gradient echo accumulates both T2 and T2.

T1 Contrast TR short Difference in T1 contrast T1w MRI Short TR Short TE M Z fat tissue Yes with a short TR we generate a T1 contrast but also a less amount of Mz is rotated to the transverse plane (xy) Time Image contrast is a function of all T1,T2/T2* and PD. The important point is how to minimise one contrast and maximize the other one T1 contrast SI (M xy ) fat Contrast reverse tissue T1 TE T2+T1

SE Signal Intensity vs TR What do you observe in terms of signal brightness and contrast? SE brain images with TE = 10 ms and varies TR Source from chapter 3 "MRI from picture to proton"

The GRE Pulse Sequence and the Modified Flip Angle Some applications require the use of a very short TR to speed up the scan time. In this case, the optimal flip angle to generate a maximum signal is not 90 RF pulse. http://mriquestions.com/4-or-more-rf-pulses.html

GRE with Short TR and Varying Flip Angles The choice of flip angle is critical for determining both signal intensity as well as image contrast. Which flip angle gives: (1) the maximum signal intensity for a given tissue? the Ernst angle provides maximum signal intensity (2) the maximum contrast? GRE with fixed TR (150 ms) and TE (4.6 ms) and various flip angles The exact shape of this curve depends on the specific T1 value of the tissue and the TR interval. Source from chapter 3 "MRI from picture to proton"

Contrast Enhanced MRI Image There are ways to manipulate the relaxation time of tissues. In other words, how to speed up the energy exchange between spins and the surroundings. For example when gadolinium (Gd) is injected, the T1 relaxation time is dramatically shortened. This causes the MRI signal to be brighter or whiter in the image. Inject Gd Tumour Normal tissue TR M Z Tumour-Gd Tumour Effect of contrast agent on images tissue https://en.wikipedia.org/wiki/mri_contrast_agent Tumour and normal tissue have both almost same T1 (contrast ~ 0) With Gd inserted, the contrast becomes much better

Inversion Recovery (IR) Pulse Sequence In our SE pulse sequence, what happens if we add a 180 RF pulse at the start of the sequence? SE IR B 0 B 0 90 RF 180 RF -z

Inversion Recovery (IR) Pulse Sequence Observations: (1) Since we applied a 180 RF inversion pulse, all the longitudinal magnetization (M z ) will be transferred completely from +z to -z direction. (2) Once we switch the 180 RF inversion pulse off, the spins tend to relax back to the lower energy state. (3) It turns out that spins are relaxed by shrinking along the z direction (- to +). This means that there is no magnetization appearing at the transverse plane (M xy =0, no signal) at any time. (4) Since there is no M xy during and after the 180 RF pulse, a 90 RF excitation pulse is then applied to generate M xy. During excitation (180 ) Inversion pulse Excitation pulse Refocusing pulse During relaxation TE

STIR FLAIR Selective Tissue Suppression using IR The time between the 1 st 180 and 90 RF pulses is called Time to inversion (TI) or tau (τ). This time determines how much M xy is generated in the transverse plan. TI is one of the most important parameters in the MRI protocol for suppressing a signal from a specific tissue. Short tau inversion recovery (STIR ): it is used to null fat at a very short TI (why). Fluid attenuation inversion recovery (FLAIR): it is used to null fluid at a very long TI (why). Fact: if you know the bouncing point of a tissue then you can determine the T1 of the tissue (T1 TI/ 0.69) TI http://mriquestions.com/why-use-ir.html Nulling or bouncing point

Selective Tissue Suppression using IR

How to Measure T1 Relaxation Time of a Tissue This is done by acquiring different acquisitions with varying TIs. Each acquisition is applied with the same TR (usually very long ~ 9000 ms). For each acquisition and for the same location, we measure the mean signal intensity (SI). Then we plot these values and determine TI where the curve crosses zero (bouncing or nulling point) The T1 of a tissue = TI bouncing_point /0.69 SI TI TI = Bouncing point Time

Lecture 4 Imaging Gradients

The Composed MRI Signal (FID) What we receive in the MRI coil is only one signal (the composed signal). If we excite a human body (subject) with a 90 RF pulse for a period of time, then we start measuring the FID or echo signal: Which part of the human body does the FID/echo signal come from (liver, heart, brain, limbs..etc)? What frequency does the FID/echo signal have? The RF coil measures only one signal which is the sum of the contribution from all spins ( 1 H nuclei). B0 field Composed signal

Spatial Encoding The FID/echo signal comes from everywhere (all spins) and we have absolutely no clue how to tell how much of the signal is coming from the brain, heart, toes, liver etc. This is therefore not a useful piece of information. In MRI, magnetic field gradients encode spatial position in precessional frequency. FOV phase FOV base FOV: Field Of View

Magnetic Field Gradients The gradient is an additional magnetic field which varies over space. Gradient adds to B 0, so the field depends on the position Precessional frequency varies with position (ω = γb0+ γg.r) Spins at each position precess at a different frequency The RF coil hears all of the spins at once Differentiate material at a given position by selectively listening to that frequency High field Fast precession Low field Slow precession B0

The Components of Spatial Encoding How does an MRI scanner create an MRI image? 1) Select information (M xy ) from a single slice. 2) Then address, in sequence, the localization in the plane of that slice. The in plane localization uses two different techniques: - Frequency encoding - Phase encoding

Slice Selection We have to keep in mind that the direction of slice selection will always be perpendicular to the net gradient magnetic field Any MRI scanner comes with three magnetic field gradients: Magnetic field gradient in X direction, Magnetic field gradient in Y direction and Magnetic field gradient in Z direction.

Slice Selection How do we: 1) Select a slice in any plane (axial, sagittal, coronal) 2) Select a slice in any location in the plane 3) Select a slice with a specific thickness 4) Select a slice in any orientation

Slice Selection In GRE Pulse Sequence TE TR Slice selection gradient Rephase lobe for Gs Signal ADC FID Echo

Slice Selection RF 0 frequency Isocenter where all gradient magnetic fields are zero. Gs gradient How to write Larmor frequency in the presence of slice selection gradient that varies linearly in z direction: ω = γb0+ γgz Along the bore of the magnet (z direction) excited slice

Slice Selection Which gradient do you select to image in the coronal or sagittal plane? In lumbar spine imaging, we usually want slices parallel to disk spaces at different oblique angles. This can be achieved by turning on more than one gradient simultaneously. http://mriprotocol.blogspot.co.za/2012/01/mri-lumbar-spine-protocol.html

90 RF pulse Interslice Gap (Distance Factor) An interslice gap is a small space between two adjacent slices. Because the resultant slice profiles of the B1 field (90 RF excitation pulse) are not perfectly rectangular, two adjacent slices overlap at their edges when closely spaced. In this case, the RF pulse for one slice also excites spins in adjacent slices. This interference is known as cross-talk. Cross-talk produces saturation effects and thus reduces SNR tails Most clinical applications use an interslice gap of 25 50% of the slice thickness. Effect of cross-talk on image contrast. SE (with (TR/TE 2000/20) image with (a) 50% gap and (b) 0% gap demonstrating impaired contrast. http://mriquestions.com/cross-talk.html

Interleaved Acquisition for 100% gap The interleaved approach allows us to acquire contiguous slices without cross talk artefacts. This is done firstly by acquiring odd-numbered slices and this is followed by acquiring even-numbered slices. Slice interleaving to allow contiguous slices without cross-talk. Odd-numbered slices (with 100% gaps) are obtained in one acquisition, followed by a second acquisition of even-numbered slices. http://mriquestions.com/cross-talk.html

In Plane Localization Both an RF pulse with Gs is turned on for a period of time to knock the longitudinal magnetization (M z ) from a specific slice to the transverse plane (M xy ). At time (TE), the MRI signal is recorded. Where does the FID signal come from? Gs

Phase encoding direction In Plane Localization We know it comes from the excited slice but we have no idea which part of the slice it is originating from. There are two steps for in plane localisation. One dimension is encoded using the frequency encoding gradient while the other dimension is encoded using the phase encoding gradient. An MRI image of a slice Frequency encoding direction Frequency encoding gradient

Fourier Theory Fourier s theory can find the receipt of an image. Fourier demonstrates that an image can be made from ingredients called signals. Each signal has a different spatial frequency. Signals with different spatial frequencies are generated by magnetic field gradients. Recipe (spatial frequencies) K-space Real Image

Frequency Encoding Gradient (Gf) (FOV x and base resolution) 1. Gf generates range of frequencies along the frequency encoding direction. B0±G x.x 2. The range of frequencies determine the FOV x 3. The period of Gf depends on the base resolution in the frequency encoding direction. Range of frequencies (FOV x )

Frequency Encoding in GRE Pulse Sequence TR TE lobe2 lobe1 Time during Gf is on Spatial frequency: Signal ADC FID Echo k x (t) = Gf(t) dt

Phase encoding direction Phase Encoding to Create the Second Dimension Now we need to find Fourier s recipe for the other dimension One of the most difficult challenges in MRI is phase encoding to locate signals with different frequencies along the phase encoding direction. A,B and C experience the same frequency (a). The same with D, E and F, they see (b). a b Frequency encoding direction http://mriquestions.com/frequency-encoding.html

Phase Encoding Gradient (Gp) (FOV y and phase resolution) To differentiate each pixel along the phase encoding direction, the excitation process has to be repeated, which depends on the matrix size of the image along the phase encoding direction. TE TR Gp is applied with different amplitudes. This has several dramatic complications in MRI: (1) A substantial increase in the scan time, (2) Limiting image resolution, Spatial frequency: k y (t) = Gp (t) dt Signal ADC FID Echo

Phase Encoding Gradient (Gp) (FOV y and phase resolution) In MRI, the normal spatial resolution in the phase encoding direction (N phase ) is about 128 or 256. Let s say in spin echo we use a very long TR such as 2 seconds and N phase =256 (for simplicity we assume we have one slice) The total scan time = TR * N phase = 256 * 2 = 8.5 minutes The time to acquire one slice takes 8.5 minutes. Imagine we have 50 slices. Do not forget we can still minimize the total scan time using Multislice Imaging (slide 35) or Turbo/Fast Spin Echo (TSE) (slide 36) techniques.

Lecture 5 Imaging Formation

Sampling an MRI Signal (Echo) Using magnetic field gradients in the x, y and z directions, we were able: (1) To localise our signal to a specific slice (RF excitation pulse together with Gs) (2) To encode one dimension in that slice using the frequency encoding gradient (Gf). (3) To encode the other dimension of the slice using the phase encoding gradient (Gp) multiple times. (4) Each time we repeat (TR) with different Gp, we collect an echo with Gf. (5) The echo data is placed in a special grid called K-space. Signal ADC FID TE TR Echo

Sampling an MRI Signal (Echo) Remember that what we receive in the MRI coil is only one signal (the composed signal or an echo). Since we are dealing with a digital system, each echo has to be digitized. Gp 1 RF G S Coil Gf Where does each point in the echo come from? Gp 2 RF G S Coil Gf

Sampling and Receiver Bandwidth (BW) Since each echo is composed of waveforms with different spatial frequencies, to record the echo efficiently we have to sample as fast as possible to avoid aliasing (wrap-around) or chemical shift artefacts. The protocol s parameter, which determines the sampling efficiency, is called receiver bandwidth (BW = 1 / t d ) TE TR We sample an echo while Gf is turning on http://mriquestions.com/receiver-bandwidth.html Fact: since we work on a digital computer, we have to sample a signal Signal ADC FID Echo

Narrow Receiver Bandwidth Chemical shift of fat signal Wrap-around

Sampling in K-space Each time we acquire and sample an echo, we place the samples of each echo in a line, in a special grid called k-space. k-space is an array of numbers representing spatial frequencies in both directions (k x,k y ) of the MR image. In each pixel in the k-space, where does the signal intensity for each sample come from? K-space Echo 1 Echo 2 Echo 3 K y Echo n Kx

Two Dimensional Fourier Transform (2DFT) Since each sample in k-space represents the Fourier relationship between the signal at a spatial frequency and the signal in real space, by taking the inverse Fourier, we can generate an MRI image. K-space Real image

Sampling K-space In each pixel in the k-space, where does the signal intensity for each sample come from? TR What is the total scan time? TE What determines how many echoes we have in k-space? What determines the number of samples in both directions? K-space Echo 1 Echo 2 Echo 3 K y Echo n Each generated echo is placed in one line in k-space Signal ADC FID Echo We sample an echo while Gf is turning on Kx

http://mriquestions.com/locations-in-k-space.html The Properties of K-space

k-space k-space relations: FOV and Resolution Image Full sampling Full-FOV, high-res Reduce k max 2DFT Full-FOV, low-res: blurred Increase k Low-FOV, high-res: may be aliased This is related to the receiver BW. With a smaller BW, a smaller ranges of frequencies are sampled. http://users.fmrib.ox.ac.uk/~karla/teaching/image_formation.ppt

Partial Fourier in K-space The k-space data have special properties where the upper part is a mirror to the lower part. This is only correct if there are no aretfacts influencing the acquired data. With partial Fourier, not all of the phase-encoding values are acquired. The phase-encoding values that are not collected are approximated from those that are. This can be translated into a reduction in imaging time. Example: In the Siemens scanner, If you choose the partial Fourier to be 7/8: We are only acquiring 75 % of the lines of k-space (N phase ) Total scan time to acquire one slice = TR * Nphase * partial Fourier

http://link.springer.com/chapter/10.1007%2f978-3-540-37845-7_5#page-1 Factors Affecting the Signal-to-Noise Ratio (SNR) The SNR is defined in terms of voxel volume, number of measurements and receiver bandwidth. K is a constant that is related to the hardware system, FOV x and FOV y are the field-of-view in the x and y directions, N x and N y are the number of frequency and phase encoding steps, Δz is the slice thickness, NEX is the number of excitation (number of signal averages), and BW is the receiver bandwidth. FOV y FOV x FOV: Field Of View In this example N x =5 N y = 5 Δz

30 cm FOVy SNR - Field of View (FOV) and the Imaging Matrix Size The matrix should be as large as possible in order to produce high spatial resolution. But the minimum pixel size is limited by the fact that, in general, SNR decreases with the size of the voxel. What is the pixel size in each figure? a b c d e 15 cm FOV 30 cm FOV x 15 cm FOV x Effect of the FOV on pixel size with the matrix size held constant A smaller matrix size with the FOV held constant results in larger pixels and thus a poorer spatial resolution

SNR - Slice Thickness Thinner slices are better for image resolution. Thinner slices are associated with more noise ( SNR). Thicker slices are associated with other problems such as an increase in partial volume effects.

SNR - Receiver Bandwidth Increasing receiver bandwidth reduces SNR as more noise is included.

SNR Number of Excitations (NEX) NEX is also called the number of signal averages (NSA). NSA refers to how many times a signal from a given slice is measured. The SNR, which is proportional to the square root of the NEX, improves as the NEX increases, but scan time also increases linearly with the NEX. Scan time = TR number of phase-encoding steps number of signal averages (NSA).

SNR TR and TE The SNR increases with the longer TR, but the T1 effect is lost. The SNR decreases as the TE increases, but with a short TE, the T2 contrast is lost.

SNR Magnetic Field At higher field strength the longitudinal magnetisation is increased (more spins align along the B0 field), resulting in an increase in SNR. The disadvantages of the higher field are RF and longer T1.

SNR MRI Coils There is another way to improve SNR without increasing voxel size or lengthening scan time, this is by selecting an appropriate radiofrequency (RF) coil. An RF coil should be as close as possible to the anatomy being imaged and should surround the target organ.