Advanced signal processing algorithms for fMRI

1.1.1 Magnetic Resonance Imaging – A Brief History 1 1.1.2 Functional Magnetic Resonance Imaging 4 2.1.2 Radio Frequency Pulse and Precession 11 2.2.1 Functional Magnetic Resonance Imagi

ADVANCED SIGNAL PROCESSING ALGORITHMS FOR fMRI

TEY ENG TIAN

NATIONAL UNIVERSITY OF SINGAPORE

2003

ADVANCED SIGNAL PROCESSING ALGORITHMS FOR fMRI

TEY ENG TIAN

(B.Eng.(Hons.), NUS)

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

ACKNOWLEDGEMENT

I would like to thank everyone who has given me help and guidance throughout the duration of this project In particular, special thanks go to

i My supervisor, Dr Sadasivan Puthusserypady

ii The fMRI Data Center for providing the fMRI data set, with speed and ease, free of charges too

iii Researchers who have given me guidance through email like, Prof Christian Jutten, Prof Juha Karhunen, Asst Prof M.J McKeown and

1.1.1 Magnetic Resonance Imaging – A Brief History 1

1.1.2 Functional Magnetic Resonance Imaging 4

2.1.2 Radio Frequency Pulse and Precession 11

2.2.1 Functional Magnetic Resonance Imaging Data Formation and

Terminology 29 2.2.2 Blood Oxygenation Level Dependent (BOLD) Signal 31

2.2.3 Oxygen Limitation Model and Balloon Model 34

2.3.1 Linear Independent Component Analysis 38 2.3.2 Nonlinear Independent Component Analysis 40 2.3.3 Post-Nonlinear Independent Component Analysis 41

2.5 Independent Component Analysis of fMRI data 45

3.4 Linear Independent Component Analysis on fMRI 53 3.5 Post-Nonlinear Independent Component Analysis on fMRI 55 3.5.1 Modification of the Original PNL-ICA Algorithm 55 3.5.2 Verification of Modified Kernel Density Estimation 57 3.5.3 Testing of Modified PNL-ICA Algorithm 62 3.5.4 Modified PNL-ICA Algorithm on fMRI data 66 3.5.5 Computational Complexity of the PNL-ICA Algorithm 66

REFERENCES 87

fMRI is a new technique for localising brain activity and independent component analysis (ICA) is a relatively new technique for blind source separation (BSS) The principle of brain modularity states that different regions of the brain perform different functions independently Thus, spatial ICA can be applied on fMRI to localise the functions of the brain Brain signal has long been shown to be nonlinear,

so applying a nonlinear ICA method to analyse fMRI signals should yield improved results However nonlinear ICA yields non-unique solutions, therefore alternative methods are needed The post-nonlinear (PNL) ICA model has been used here because of its close resemblance to a simplified balloon model The balloon model is

a biomechanical model of the haemodynamic system, which includes transient states Both linear and PNL-ICA was applied to the fMRI data

There are two purposes of applying linear ICA to fMRI data Firstly, it served to familiarise fMRI data and ICA algorithms Secondly, it provides a reference for

decompose the fMRI signals into their respective independent components in this study The results also indicate that the choice of algorithm could be important to the success of decomposition PNL-ICA was subsequently applied to the fMRI data and the results were compared with those from the linear ICA The results of PNL-ICA were less satisfactory

There are two possible reasons for this The simplest possibility is that the assumptions used to represent the simplified balloon model with the PNL model are incorrect Another less likely possibility is that the PNL model cannot sufficiently represent the simplified balloon model, even though the simplified balloon model is correct However to ascertain this, we need data sets with the CBF, CBV, CMRO2 and BOLD signal to compare the effect of simplifying the balloon model Although the results obtained are not as encouraging as expected, it is premature to disregard the PNL-ICA technique for fMRI signal deconvolution Further studies need to be conducted on more definitive fMRI data sets before any concrete conclusions can be drawn on the method tested

LIST OF ABBREVIATIONS

BCI Brain Computer Interface

BIRCH Balanced Iterative Reducing and Clustering using Hierarchies

BOLD Blood Oxygenation Level Dependent

BSS Blind Source Separation

CBV Cerebral Blood Volume

CMRO2 Cerebral Metabolic Rate of Oxygen

CSF Cerebral Spinal Fluid

EEG Electroencephalogram

EPI Echo planar imaging

FDA Food and Drug Administration

fMRI Functional Magnetic Resonance Imaging

FSE Fast Spin Echo

GUI Graphic User Interface

HRF Haemodynamic Response Function

ICA Independent Component Analysis

MRI Magnetic Resonance Imaging

NMR Nuclear Magnetic Resonance

PCA Principal Component Analysis

PDW Proton Density Weighted

PET Positron Emission Tomography

PNL Post-Nonlinear

rCBF Regional Cerebral Blood Flow

RF Radiofrequency

SPECT Single Photon Emission Computed Tomography

SPM Statistical Parametric Mapping

LIST OF FIGURES

Figure 1.1 Timeline of the development of fMRI 2

Figure 2.2 (a) Proton rotate about its own axis (b) When external magnetic

field, B0, is applied, the proton not only rotate about its own axis,

Figure 2.3 Illustration of the nuclei’s alignment at equilibrium (a) before and

Figure 2.4 Net magnetisation (a) before and (b) after the RF pulse is applied 13

Figure 2.5 Illustration of nutation, the spiral motion of Mnet from z-axis

Figure 2.6 Illustration of the spin dephasing (a) Mxy just after RF pulse is

removed, (b) spin-spin interaction caused inhomogeneities in

magnetic field, (c) spins completely out of phase, with no net

Figure 2.7 Illustration of the spin echo pulse sequence 20

Figure 2.8 Illustration of the gradient echo pulse sequence 22

Figure 2.9 Usual direction of axes in a MRI machine 23

Figure 2.10 Illustration of the changes (a) in phases when a phase encoding

gradient is applied, (b) in precessional frequencies when a

frequency encoding gradient is applied, and (c) in both phases and

precessional frequencies when both phase and frequency encoding

Figure 2.11 Chart showing the spatial, temporal resolution and invasive nature

of various functional brain mapping technique 29

Figure 2.12 Illustration of fMRI scanning procedure and signal collected 30

Figure 2.13 Illustration of oxy and deoxy-haemoglobin concentration in blood

vessels 33

Figure 2.14 BOLD signal strength vs time during stimulant onset 33

Figure 2.15 Block diagram of the balloon model 35

Figure 2.18 Relationship between BOLD-CBF and CMRO2 37

Figure 2.19 Mixing and demixing stage of the linear ICA model 38

Figure 2.20 Mixing stage of signals and demixing stage of the nonlinear ICA

model 40

Figure 2.22 Basic ideology of ICA, applied on fMRI data 46

Figure 2.23 The IC maps are linearly mixed, forming the measured signals 46

Figure 2.24 Plot of applied stimulant vs volume 47

Figure 3.2 HRF model using a simple rectangular function 51

Figure 3.3 HRF model using difference of two gamma function 52

Figure 3.5 Reference Wave derived from rectangular HRF 53

Figure 3.6 Reference Wave derived from gamma HRF 53

Figure 3.7 Density estimation of 20,000 randomly generated Gaussian data 59

Figure 3.8 Density estimation of 20,000 randomly generated bi-Gaussian data 60

Figure 3.9 Magnified view of the Gaussian density estimation 60

Figure 3.10 Plot of computational time of the three algorithms 61

Figure 3.11 Plot of actual fMRI data density estimation 61

Figure 3.12 Plots showing the original signals and the mixed signals 63

Figure 3.13 Plot comparing the results of original and modified PNL-ICA

algorithm 64 Figure 3.14 FastICA with Gaussian nonlinearity on PNL mixture 65

Figure 3.15 FastICA with tanh nonlinearity on PNL mixture 65

Figure 3.16 Plot of number of flops vs number of voxels 67

Figure 3.17 GUI displaying time course and reference wave of a single IC map 68

Figure 3.18 Magnified view of the GUI control 69

Figure 3.19 Scatter plot of correlation coefficient of components maps 70

Figure 4.1 Scatter plot of the correlation coefficient (a) before and (b) after

Figure 4.2 Time course of Subject 01 with tanh nonlinearity 75 Figure 4.3 Time course of Subject 01 with Gaussian nonlinearity 75 Figure 4.4 Correlation coefficient of unfiltered task related IC map from

Figure 4.12 Correlation coefficient of the unfiltered timecourse of Subject 11 84

LIST OF TABLES

Table 1.1 FDA guidelines on the safety limits 5

Table 2.1 Spin properties and natural abundance of various nuclei 10

Table 2.2 Image contrast and their respective TR and TE 19

Table 3.1 Computational Time and the mean square error of the various

algorithms 61 Table 3.2 Average computation time per iteration for the simulated data 64

Table 3.3 Average computation time per iteration for fMRI data 66

Table 4.1 Linear ICA result using tanh nonlinearity in fastICA 73

Table 4.2 Linear ICA result using Gaussian nonlinearity in fastICA 73

Table 4.3 Maximum correlation coefficient of the unfiltered timecourse of

CHAPTER 1 INTRODUCTON

1.1 Background

Medical imaging has helped doctors in their daily diagnosis, since the application of X-ray in medical diagnosis [1] There have been vast improvements to the imaging techniques and quality of the medical image since then Imaging has improved from the simple two dimensional (2D) X-ray to three dimensional (3D) and four dimensional (4D) scans X-ray, computer tomography (CT) and magnetic resonance imaging (MRI) are some examples of anatomical scans Later, technology advanced such that functional image of the body could be taken, using Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) Unfortunately, all of these scans are either radioactive or invasive1 in nature [2] Radioactive substances emit energetic particles and photons by disintegration of the nucleus These energetic particles are harmful to the body especially in high exposure; hence, there is a limit to the number of scans which can be performed Functional magnetic resonance imaging (fMRI), where a high Tesla magnetic field (combined with radiofrequency (RF) pulse and magnetic gradient) is used to image the patient’s brain, based on the principle of nuclear magnetic resonance (NMR) It is neither radioactive nor invasive with few known side effects

1.1.1 Magnetic Resonance Imaging – A Brief History

The brief history of the development of magnetic resonance imaging (MRI), leading

to functional MRI (fMRI), is discussed here The text is taken from “Naked to the

Bone: Medical Imaging in the Twentieth Century” by Kevles [1] It covers historical developments of medical imaging (including CT, PET, ultrasound MRI etc) since the X-ray years A timeline for the major events is also provided on page 304 of the book, the major events leading to the development of fMRI are noted in Figure 1.1

Paul Lauterbur extracts an image from NMR signals.

Richard Ernst introduces 2D NMR.

Damadian announces first whole body NMR scanner.

Mansfield introduces echoplanar MRI.

Seiji Ogawa introduces BOLD contrast agents in fMRI

MRI used clinically fMRI used in brain mapping

Figure 1.1 Timeline of the development of fMRI

In 1924, Wolfgang Pauli suggested that protons or neutrons (or both) move with angular momentum and become magnetic under certain condition In 1937, Isador Rabi actually measured the magnetic moment of the nucleus, for which he called it NMR In the late 1960s, Raymond Damadian showed interest in the then controversial theory of biologist Gilbert Ling, who argued that water in malignant cell differs in organisation from water in healthy cell He subsequently produced NMR spectra of

rats’ tumour in 1970, which showed different T1 and T2 readings for cancerous tissue and healthy tissue However, it is Paul Lauterbur, who succeeded in producing the first NMR image in 1973, before Raymond Damadian, who subsequently produced the first human NMR image in 1976 By the early 1980s, most MRI hardware had been developed and the four theoretical contributions that explain why magnetic resonance (MR) can produce images of the body’s interior were at hand They are namely, (i) Paul Lauterbur’s discovery that an image can be extracted for NMR using single-line projection data – 1D MRI, (ii) Richard Ernst’s implementation of the mathematics of Fourier transform that brought on data from 2D, (iii) Peter Mansfield showed how practical imaging could be developed using echoplanar technique, that leds to functional, or fast, magnetic resonance imaging a decade later, and (iv) Raymond Damadian’s design for a practical whole body magnet capable for performing imaging and spectroscopy

Ordinary MRI data is acquired line by line, whereas echoplanar method acquires and processes data from an entire plane at one time This will be described in detail in Section 2.1.6 Speed has the advantage of avoiding distortions caused by the motions

of breathing, heartbeats, blood flow, and intestinal moments, or movements of patient The initial breakthrough for fMRI came from Seiji Ogawa when he investigated the radiofrequency (RF) signals when the brain functions [3] He worked with the knowledge that activated brain cells used more oxygen than cells at rest The deoxy-haemoglobin is paramagnetic and changes the magnetic field around it This distortion of the magnetic field, in turn, affects the magnetic resonance of nearby water protons amplifying their signal as much as 10,000 times Ogawa called this

paper in 1990 [4] The BOLD contrast image is exceptionally good when acquired with magnet stronger than 4 Tesla Ogawa’s discovery leads to the development of effective fMRI

1.1.2 Functional Magnetic Resonance Imaging

fMRI is a technique for localising brain activity An fMRI machine is basically an advance magnetic resonance imaging (MRI) machine that is programmed to detect a functional signal rather than a structural signal fMRI usually measures the blood oxygenation level dependent (BOLD) signal on a voxel by voxel basis, which increases with increased brain activity With the availability of a functional scan, it is possible to develop a method which can monitor a patient’s health continuously This

is especially so in the case of a coma patient, where communication with the doctors

is not possible The brain controls the whole body functions Thus, a continuous monitoring of the patient’s brain should tell a lot about the patient’s health

Unfortunately, due to the cost of the equipment and shielding requirements, it is not economical or practical to use fMRI for continuous monitoring Furthermore, it is technically impossible, as the BOLD signal will saturate under long exposure of a constant strong magnetic field Moreover, the use of RF pulses also restricts the duration of scan on patients Specific absorption rate (SAR) is the physiological measure of the intensity of RF energy measured in Watts/kg (W/kg) Table 1.1 shows the United States Food and Drug Administration (FDA) guideline on the safety exposure limits on the RF and magnetic field [5]

Table 1.12 FDA guidelines on the safety limits Type of exposure FDA limits

Static magnetic field 2 T

Magnetic Field Transient magnetic field 3.0 T/s

2 Table 1.1 is extracted from [5], Chapter 29

3 Magnitude of twisting depends on several factors, like strength of static magnetic field, degree of ferromagnetism, and size, shape and mass of the surgical clip [5]

The principle of brain modularity states that different regions of the brain perform different functions and hence measured brain signals should be able to decomposed into their independent sources [8] Independent component analysis (ICA) is a powerful signal processing technique for blind source separation (BSS) which can decompose mixed signals into their independent sources [9,10] Therefore, ICA can

be applied to fMRI data for extracting the independent components The fMRI signals comprise effects from the applied stimulant, background activities (breathing, heartbeat etc) and motion of patient etc These effects are deemed to be independent events, which could be separated using ICA Linear ICA, because of its simplicity, has been applied to fMRI brain signal data and has shown reasonably good results for separating the brain’s activations due to stimulant from other causes (which are considered as noise) [8]

However, EEG are widely accepted as nonlinear [11,12] and the BOLD signal has also shown to be nonlinear [13,14] This coincides with the balloon model, which shows that the haemodynamic system is nonlinear [15] The balloon model is a biomechanical model of the haemodynamic system Hence, a nonlinear algorithm should be able to achieve a better decomposition of the fMRI data than a linear one

1.2 Motivation

Currently, researchers especially in the medical field are using hybrid-techniques (e.g fMRI & EEG and fMRI & PET), where two or more different techniques are combined to achieve better imaging qualities [16-18] A hybrid method could prove to

be possible to achieve the desired continuous monitoring especially in an intensive care unit environment Electroencephalogram (EEG) is a well-established method to

understand the conditions of the brain using 1D/2D signal processing techniques It was suggested that it might be possible to combine the two techniques (fMRI with EEG) [16,18] for better understanding of brain function These two techniques complement each other; fMRI has a high spatial but low temporal resolution, whereas EEG has a low spatial but high temporal resolution The hybrid scheme might then result in high spatial and temporal resolution Besides, EEG can be used for continuous monitoring of the brain without any harmful effects to the patient The strategy is to use the high spatial resolution property of fMRI to map out the location that generates the respective EEG signal From there, it might be able to gauge the health of the patient; perhaps even determine the state of coma and the chance of the patient waking up from coma This is especially so in view of the recent development

in brain computer interface (BCI) for completely paralysed patients [19]

From the background study, it is hypothesized that applying nonlinear ICA to the fMRI signal data will result in better source separation of signals by their spatial origin of fMRI signals than linear ICA algorithm For this study, the PNL-ICA algorithm was applied to fMRI signal data and the results was compared to that from linear ICA algorithms for this application This project is focused on the development

of nonlinear ICA algorithms

CHAPTER 2 THEORY AND LITERATURE REVIEW

2.1 Magnetic Resonance Imaging

As the name implies, magnetic resonance imaging (MRI) makes use of resonance of the atomic nucleus as signal for imaging Atomic nuclei possess angular moment, known as spin This spin depends on the number of neutrons and protons in the nucleus Any nucleus with an even atomic mass number and even charge number has

no spin and hence has no nuclear magnetic resonance (MR) signal Fortunately, hydrogen-1, which has one of strongest spins, is relatively abundant in human body This section is mostly referenced from the book, “MRI – the basics” [20]

Magnetic susceptibility is the measure of how magnetised the substance is under a magnetic field Different substances have different degree of magnetisation; this difference is the basis of image contrast in the MRI There are three categories of magnetic susceptibility commonly dealt with in MRI They are diamagnetic, paramagnetic and ferromagnetic Diamagnetic substances have no unpaired electrons

When place under an external magnetic field, B0, they have a weak induced magnetic

field, M, in the opposite direction to B0, thereby reducing the net magnetic field Paramagnetic substances have unpaired electrons Under an external magnetic field,

B0, they produce an induced magnetic field, M, in the direction of B0, thereby increasing the net magnetic field Both diamagnetic and paramagnetic substances will

lose their magnetisation when the external magnetic field, B0, is removed In contrast, ferromagnetic substances retain their magnetisation even after the external field is removed and are strongly attracted to the magnetic field

In MRI, a constant magnetic field, B0, is applied to the patient Then a RF pulse of a specific frequency (resonance frequency of the tissue being examined) is directed at

the patient; this induces an oscillating magnetic field, B1, in the patient The nuclei of

the tissue will be realigned due to the B1 After the RF pulse is removed, the nuclei return to their original position, releasing a signal as they do so This signal is captured as the MR signal from the tissue Figure 2.1 illustrate this basic concept of MRI Three orthogonal gradient coils are used to change the magnetic field’s homogeneity applied to the patient This is to allow spatial encoding of the received signal

Figure 2.15 Basic ideology of MRI 2.1.1 Larmor Frequency

In a magnetic field, the nucleus with a spin number, I, will have (2I + 1) discrete

energy levels [21] Using hydrogen-1 as an example, it will have two energy states Hence, in a magnetic field, the hydrogen-1 nucleus will align either in parallel (lower energy state) with the magnetic field or opposite (higher energy state) to it However,

by applying a radiofrequency magnetic field, it is possible to attain a transition energy

state in between the highest and the lowest energy states The Larmor equation,

Equation (2.1) below, shows this relationship

γ

=

where, ω is the Larmor frequency in MHz, γ is the gyromagnetic ratio in MHz/Telsa

and B is the magnetic field strength in Tesla Table 2.1 shows the various properties

and relative abundance of nuclei found in the human body

Table 2.16 Spin properties and natural abundance of various nuclei

Without any external magnetic field, the proton only rotates about its own axis, as

shown in Figure 2.2(a) When a magnetic field, B0, is applied to the proton, besides

rotating about its own axis, it will also precess about the axis of the axis of B0, as

shown in Figure 2.2(b) Protons spin much faster along their own axis than around the

axis of B0, that is, ωspin is much faster than ω0 ω0 is the Larmor frequency

corresponding to B0 as shown in Equation (2.1)

6 Table 2.1 is extracted from [21], Chapter 3

Nucleus Natural Abundance (%) Spin Frequency/Tesla (MHz/T)

B0

spin

Figure 2.2 (a) A proton rotates about its own axis (b) When external magnetic field, B0, is applied, the

proton not only rotates about its own axis, but also rotates about the axis of B0

2.1.2 Radio Frequency Pulse and Precession

Figure 2.3 illustrates the nuclei’s alignment at equilibrium (a) before and (b) after a longitudinal magnetic field, B0, is applied to an ensemble of hydrogen-1 nuclei As seen in Figure 2.3(a), the nuclei are randomly aligned; thus there is no net magnetisation However, in Figure 2.3(b) when B0 is applied to the ensemble of nuclei, they align in parallel with this magnetic field At equilibrium, a small majority

of the hydrogen-1 nuclei align in the direction of B0, thus forming a single net magnetisation, M0 in the direction of B0 Note that there is no net transverse magnetic field perpendicular to B0, since the nuclei do not precess in phase with each other

Figure 2.3 Illustration of the nuclei’s alignment at equilibrium (a) before and (b) after B0 is applied

Figure 2.4(a) shows 3D coordinate system to depict the net magnetisation of the system after B0 was applied but before the RF pulse was transmitted In Figure 2.4(b),

an RF pulse perpendicular to B0, is transmitted to the ensemble of nuclei The RF pulse, being an electromagnetic wave, will also have an oscillating magnetic field, B1, perpendicular to B0 Note that the strength of B0 (≥1T) is much greater than B1

(~50mT) Figure 2.4(b) also shows the presence of transverse magnetic field, Mxy, and the flipping of net magnetisation7, Mnet, at an angle of θ away from z-axis The causes of flipping of Mnet and degree of flipping, θ, will be explained below

7 Note that B1 causes the flipping of the individual spins, Mnet flips because of the summation of these individual spins The text will refers these flippings of individual spins collectively as the flipping of

Mnet

RF p se

Figure 2.4 Net magnetisation (a) before and (b) after the RF pulse is applied

When B0 is applied towards the z-axis, the nuclei will precess about the z-axis Similarly, when B1 is applied along the x-axis, the nuclei will precess about the x-axis The only difference is their frequency of precession Since B0 is stronger than B1, ω0

will be higher than ω1, where ω0 and ω1 are the precessional frequencies about B0 and

B1 respectively This can be determined using the Larmor equation As the nuclei precess about the both axes (z-axis and x-axis) at the same time, this results a spiral motion of the M0 from z-axis towards the x-y plane This is known as nutation, as shown in Figure 2.5

Figure 2.58 Illustration of nutation, the spiral motion of Mnet from z-axis towards x-y plane

However, it must be noted that the RF pulse transmitted must be at the Larmor

frequency (precessional frequency) of the nuclei for resonance to occur In this case,

ω0 is the resonance frequency Resonance is necessary for the nuclei to absorb the

energy transmitted by the RF pulse The oscillating magnetic field, B1, caused the

nuclei to precess in phase about the z-axis (compared with Figure 2.3(b), the nuclei

precess out of phase without the RF pulse) This generates a transverse magnetic field,

Mxy, which also contributes to the flipping of Mnet Meanwhile, some nuclei would

attain a higher energy level and aligned in opposite direction as B0 This will slightly

decrease Mz and cause slightly more flipping This creates the NMR RF signal, which

will be released when the RF pulse is removed and the system shifted back to

equilibrium

The degree of flipping, θ, depends on a number of factors as stated in Equation (2.2)

1 1

θ γ τ τ

where τ is the duration of the RF pulse Thus, to have a larger flip angle, we could

increase either the strength of the RF pulse or the duration of the RF pulse

Conversely, the same flip angle can be achieved by using a shorter duration and

stronger pulse or longer duration and weaker pulse There are three common flip

angles used in medical imaging, namely, 90° flip, 180° flip and partial flip

The 90° flip occurs when Mnet flips into the x-y plane and Mz is equal to zero This

happens because the nuclei absorb energy from the RF pulse, causeing the number of

nuclei at higher energy level and lower energy level to be equal Meanwhile, the RF

pulse also causes the nuclei to precess in phase with each other, thereby generating a

transverse magnetic field The RF pulse that causes this 90° flip is known as the 90°

RF pulse From Equation (2.2), the time needed for the 90° flip is given by,

The 180° RF pulse has either twice the power or the duration of the 90° RF pulse The

180° RF pulse causes more nuclei to be in the higher energy level that points towards

the negative z-axis After the 180° RF pulse, the final net magnetisation is -M0, in the

opposite direction of B0 Note that the 180° RF pulse does not induce any phase

coherence, thus no transverse magnetisation Similarly to Equation (2.3), the duration

of the 180° RF pulse is given by,

Partial flip is defined as being less than 90° and is achieved by having less power or a

shorter pulse duration, as defined in Equation (2.2) The final magnitude of Mxy is less

than the magnitude of M0 and is given by,

xy = θ

2.1.3 T1, T2 and T2 * Relaxation Times

T1 and T2 relaxation times are inherent properties of the substances, and are fixed for

a specific substances Another signal decay time constant, T2*, also depends on the

inhomogeneities of the magnetic field The term “relaxation” means going back to the

equilibrium state, which is the lowest energy state

T1 relaxation time is called the longitudinal relaxation time or the spin-lattice

relaxation time T1 is the time constant taken for the longitudinal magnetic field, Mz,

to return to the magnitude of (1-e-1)M0 after the RF pulse is removed It is also the

time taken for the spins to return the energy (absorbed from RF pulse) back to the

surrounding lattice The recovery of Mz to its initial magnetisation M0 is characterised

by the time constant, T1, as shown in Equation (2.6)

Besides returning to the lower energy state, the spins will also start to precess out of

phase with each other These result in the rapid decrease of Mxy and the slow recovery

of Mz T2 relaxation time is also known as the transverse relaxation time or spin-spin relaxation time, because the dephasing of the spins is due to the spin-spin interaction within the ensemble of nuclei Figure 2.6 illustrates this spin dephasing process Figure 2.6(a) shows the net transverse just after the RF pulse is removed Figure 2.6(b)

illustrates that after the RF pulse is removed, spins that are aligned with B0 will have a

slightly stronger magnetic field, Mstronger, for their neighbours, whereas spins that are

aligned against B0 will have a slightly weaker field, Mweaker, for their neighbours These cause slight inhomogeneities in the magnetic field experience by the spins Those spins that are exposed to higher magnetic field will have a higher precessional frequency; likewise, those in the weaker magnetic field will have a lower precessional

frequency Thus, this results in a smaller Mxy In time, the spins will get completely out of phase with each other, resulting in a zero net transverse magnetic field, as shown in Figure 2.6(c) This magnetic inhomogeneity caused by spin-spin interactions

is an inherent property of any tissue In the MR system, T2 decays 5 to 10 times faster than T1 recovery

Figure 2.6 Illustration of the spin dephasing (a) Mxy just after RF pulse is removed, (b) spin-spin interaction caused inhomogeneities in magnetic field, (c) spins completely out of phase, with no net

transverse magnetic field

Another factor causing spin dephasing is external magnetic field inhomogeneities

magnet T2* relaxation time accounts for these external magnetic field

inhomogeneities, as shown in Equation (2.8)

Sample components with very different magnetic susceptibility will have very rapid

local T2* relaxation This difference is also seen in blood vessels due to differences in

vascular and extravascular concentration of haemoglobin iron bound in different

oxidation states, which is the basis of the BOLD effect It is clear that if these

inhomogeneities are removed, then T2* will be equal to T2

As mentioned earlier, a RF signal is released from the sample along with the decay of

the transverse magnetic field, Mxy Free induction decay (FID) is the signal picked up

by the MRI RF receiver (usually the coil acts both as a transmitter and a receiver)

This is the result of the oscillating spins generating oscillating magnetic field and the

decay of the transverse magnetic field, given by Equation (2.9), where ω0 is the

Repetition Time (TR) is the time between the two successive RF pulses applied Echo

Time or Echo Delay Time (TE) is the time delay before measurement was taken, after

the RF pulse was applied The choice of TR and TE can determine the image contrast

Image contrast is commonly termed T1 weighted (T1W), T2 weighted (T2W) and

Proton density weighted (PDW) Intuitively, T1W and T2W contrast are based on T1

and T2 relaxation time respectively, whilst PDW contrast emphasises the proton

density They are termed “weighted” because it is impossible to remove the other

effects; T2 relaxation time will have some effects on T1W contrast and vice versa Table 2.2 shows the durations of TR and TE for the various types of weighted images

Table 2.29 Image contrast and their respective TR and TE

From Figure 2.6, we can see that spin dephasing effects take place after the removal

of the 90° pulse In order to remove the effect of the external magnetic field inhomogeneities, a 180° refocusing or rephasing pulse is applied along the xy-plane Figure 2.7 illustrates the SE pulse sequence From Figure 2.7,

i The 90° RF pulse is applied at time 0 and removed at time τ

ii The 180° refocusing pulse is applied at time t after the application of 90° pulse (at time 0) The spins are flipped about the xy-plane, in this case, about the

y-axis This flip brings the faster spins (Mstronger) behind the slower spins

(Mweaker) Therefore, the faster spins will have to travel a longer distance back

to the initial point, while the slower spins needs to travel a shorter distance

iii Hence, the spins are able to refocus again at time 2t The time 2t is also known

as the echo time (TE)

Using this method, the effects of T2* is removed and a true T2W contrast can be achieved [7]

Figure 2.7 Illustration of the spin echo pulse sequence

Using a simple modification, inversion recovery (IR) imaging is able to attain a better T1W image A 180° RF pulse is used to flip the longitudinal net magnetisation to the negative z-axis, before starting the SE pulse sequence As the net magnetisation recovers, it will pass through the null point before returning to the positive z-axis Different tissues’ magnetisation will cross the null point at different time because they have different T1 relaxation time By starting the SE pulse sequence at the time where

a particular tissue’s magnetisation is at the null point, the effect of this tissue (on the final MRI image) can be removed

GE was introduced in 1984 because of the desire for faster imaging [5] GE uses a partial flip angle, α, smaller than 90°, therefore it can use a shorter TR than SE

However, since the longitudinal magnetisation, Mz, will be large, the 180° refocusing

RF pulse cannot be used This is because Mz will be flipped onto the negative z-axis, thus requiring a long recovery time In place of the 180° refocusing RF pulse, a bipolar magnetic field gradient is used to refocus the spins The flip angle chosen is optimised for the T1 of the desired tissue This optimal flip angle, where the maximum signal can be achieved, is known as the Ernst angle [5]

A bipolar magnetic gradient is applied at time t, when the spins start to dephase, that

is, when the FID occurs Firstly, the negative magnetic gradient speeds up the dephasing process (which leads to a shorter TR) Secondly, a positive magnetic gradient is applied for twice the duration of the negative magnetic gradient The spins will start to rephase for the first half of the positive magnetic gradient, being fully in phase at the end of the first half Then the positive magnetic gradient will cause the spins to dephase again, becoming fully dephased at the end of the positive magnetic gradient This is illustrated in Figure 2.8

Figure 2.8 Illustration of the gradient echo pulse sequence

As a magnetic gradient was used to accelerate the dephasing process, the signal intensity is predominated by T2* relaxation, rather than the T2 relaxation Thus, a T2* weighted (T2*W) image is obtained instead10

10 Note that the GE method does not fully correct for static inhomogenities in the sample or the external field, on ly for spins that are precessing

2.1.5 Spatial Encoding

Figure 2.911 Usual direction of axes in a MRI machine

Figure 2.9 shows the usual direction of the axes used in the MRI machine By

applying a magnetic gradient, Gz, along the z-axis, the MRI machine changes the Larmor frequency of the tissue according to the Larmor equation, Equation (2.1) Thus, the desired slice of the subject can be selected by varying the frequency of the

RF pulse A slice is divided into a 2D matrix, where each element is known as a voxel (volume element), analogues to pixel (picture element) in a 2D image It is called a voxel because each slice consists of certain thickness, instead of being flat as in a 2D picture After locating the desired slice, the exact location of the voxel is determined

by two more magnetic gradient fields, one for each axis They are known as the frequency encoding gradient and phase encoding gradient

Assume a slice is divided into a simple 3x3 matrix, forming nine voxels as seen in

Figure 2.10 When a phase encoding gradient, Gy, is applied along the y-axis, as shown in Figure 2.10(a), it causes changes to the phases of precession along the row

of the matrix The magnetic gradient is applied in such a way that the top row experienced higher magnetic field, the middle row experience no magnetic field, whereas the bottom row experiences a lower magnetic field Therefore, according to the Larmor equation, the top row will precess faster, the middle row will be

unchanged and the bottom row will precess slower After sometime, Gy is turned off and all the spins will precess at the same frequency again Nonetheless, a permanent phase shift has been created between the rows Thus, the middle row has no change in precessional phase (ω0), whereas the top row has a positive precessional phase shift (ω0+θ) and the bottom row has a negative precessional phase shift (ω0-θ) Note that the precessional frequency, ω0, remains unchanged

The frequency encoding gradient, Gx, is applied along the x-axis, as shown in Figure

2.10(b) Gx affects the precessional frequency across the column of the matrix The column on the left will experience a lower magnetic field, the middle column experiences no magnetic field and finally, the right column will experience a higher magnetic field Hence the left column will have a lower precessional frequency, the middle column no change in the precessional frequency and the right column will have a faster precessional frequency Therefore combining both phase and frequency encoding makes it possible to differentiate the exact location of the voxels in the slice From Figure 2.10(c), it is clear that each voxel has a unique combination of precessional phase and frequency

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-2.1.6 Echo Planar Imaging

K-space is the spatial-frequency domain whereby the detected echoes from the MRI scan are stored during the MRI scan A single k-space data set represents each individual slice of the MRI scan The k-space is represented as a 2D area, where the vertical axis represents the phase axis and the horizontal axis represents the frequency This area will be divided into a matrix space (e.g 256x256), with size depending on the resolution of the scan Each echo will fill up a single horizontal row, so a 256x256 image requires 256 echoes to fill up k-space Conventional SE and GE take one TR

to get one echo, thus it will require 256 TR to fill the entire slice Faster scan methods12, like multi-slice techniques and multi-echo techniques obtain more echoes within a single TR, hence the k-space can be filled up faster [22] These techniques are briefly described below, using SE as the pulse sequence

i Multi-slice techniques – Within a single TR, a successive 90° and 180° RF

pulse of different frequency is delivered, exciting a series of up to 32 different slices (depends on pulse sequence) before repeated the first slice The shorter the TE as compared to the TR, the more slices can be interleaved Interleaving avoids cross-talk and eliminates the need for a gap between the slices

ii Multi-echo techniques – After each 90° RF pulses, two or more successive

180° RF pulses produce successive echoes with increasing TE The peak amplitudes of the successive echoes decrease with time constant T2 Interleaving is also possible

Multi-slice and multi-echo techniques usually fill up k-space line by line Fast spin echo (FSE) uses the multi-echo technique, except that each echo is phase encoded with a different phase-encoding gradient In this way, the k-space is filled with Necho

12 There are other variants of fast acquisition methods; however, they will not be discussed here

lines within a single TR, where Necho is the number of echoes However, the number

of slices that can be acquired is reduced This reduces the acquisition time of a single slice by a factor of the Necho For example, if the FSE receives 8 echoes within the TR, then it will only require 32 (256/8) repetitions to acquire an entire slice

EPI is the fastest MRI technique available [20] It can fill up the entire k-space using a single RF excitation (in one TR), however this ability requires extremely fast and high amplitude gradient switching, and rapid data acquisition [5] The early versions of EPI filled k-space in zigzag manner, which leads to some artefacts during the Fourier transformation compared to conventional k-space trajectories Blipped EPI, a newer version of EPI that fills the k-space in a rectilinear fashion, solves this problem There are two types of EPI, single-shot and multi-shot EPI As the name implies, single-shot EPI fills k-space with a single RF pulse, while multi-shot EPI uses multiple RF pulses Multi-shot EPI requires less demanding hardware because the gradient switching can

be slower, but it will take longer to acquire an image slice compared to single-shot EPI Thus, multi-shot EPI is also more prone to motion artefacts

The relatively high temporal resolution of EPI13 is required to make fMRI effective The fast acquisition is required because of the signal stability over time [21] During neural activities, cerebral blood flow (CBF) increases in response to these activities This haemodynamic response occurs over a few seconds, ans so to resolve this MRI must be performed over a similar period EPI can be obtained at radiographic speed, approximately at 50ms [5] The image contrast is provide by blood, through an effect known as blood oxygen level dependent (BOLD) signal, which will be discussed in