The Measurement of an NMR Signal with Halbach Arrays

The Measurement of an NMR Signal

with Halbach Arrays

Progressing Towards Low-Budget MRI Using Permanent

Magnets

THESIS

submitted in partial fulfillment of the requirements for the degree of

MASTER OFSCIENCE

in PHYSICS

Author : Wico Breimer

Student ID : s1023284

Supervisor : Andrew G. Webb 2ndcorrector : Tjerk H. Oosterkamp

The Measurement of an NMR Signal

with Halbach Arrays

Progressing Towards Low-Budget MRI Using Permanent

Magnets

Wico Breimer

Huygens-Kamerlingh Onnes Laboratory, Leiden University P.O. Box 9500, 2300 RA Leiden, The Netherlands

April 2, 2019

Abstract

The generally high costs of the in vivo imaging technique Magnetic Resonance Imaging (MRI) leads to a low availability of the technology in developing countries. However, to reduce the costs of MRI, a novel approach can be used where permanent

magnets in Halbach arrays replace the superconducting magnet normally used in MRI. In this research, a magnet consisting of 4 Halbach rings is constructed to create a magnetic field of 59 mT corresponding to a Larmor frequency of 2.5 MHz for protons. With this new setup, spin echo measurements are performed where a signal-to-noise

ratio of 70 is achieved. After that, spin echo trains were successfully measured. The setup can be used to work towards the creation of 2D pediatric brain images with an

Contents

1 Introduction 1

1.1 MRI in General 1

1.2 The Downsides of MRI 1

1.3 Hydrocephalus 2

1.4 Lowering the Costs of MRI 3

1.5 The History of this Project 5

1.6 The Outline of this Thesis 5

2 Theory 7

2.1 Magnetic Resonance Imaging 7

2.1.1 Magnetization 7

2.1.2 RF Pulse, FID and Relaxation Times 9

2.1.3 Gradients 10

2.1.4 Image Formation 10

2.1.5 Pulse Sequences 11

2.2 MRI in Low Inhomogeneous Fields 12

2.2.1 Homogeneity 12

2.2.2 SNR 13

2.3 Halbach arrays 14

2.3.1 Permanent magnets 14

2.3.2 The Definition of a Halbach magnet 17 2.3.3 Segmenting the Halbach Array 17

2.3.4 Simulating the Magnets 17

3 The Development of the Experimental Setup 19

3.1 Setup 19 3.2 Magnets 20 3.3 RF Coils 21 3.4 RF Pulse 23 3.5 Preamp 24 3.6 Power Amplifier 25 3.7 Switches 26 3.8 RF Shield 27

vi CONTENTS

4.1 Spin-Echo 30

4.2 Carr-Purcell-Meiboom-Gill Sequence 31

5 Discussion 33

6 Conclusion and Future Perspectives 37

6.1 Conclusion 37

Chapter

1

Introduction

1.1

MRI in General

The introduction of magnetic resonance imaging (MRI) caused immense change for medical imaging. With MRI, body parts are studied in great detail utilizing electro-magnetic fields. This goes in contrast with the harmful high energy radiation used in the other in vivo imaging technique: computed tomography (CT). The electromagnetic fields in MRI cause, when used well, no dangers to the investigated patient. In gen-eral, one also acquires more spatial information with MRI than e.g. ultrasonography, where the user works with ultrasound to construct the images.

The first signs of MRI evolved in the 1970s from nuclear magnetic resonance (NMR). Significant progress was made during the decades after the invention. The pioneering human body scans by Damadian et al. in 1977 used a magnetic field of around 50.8 mT.[1] By comparison, a common MRI machine in the average hospital used for diag-nosis uses magnetic fields up to 3 T. Nowadays, images can reach spatial resolutions of several micrometers. Also, a growing number of MRI techniques are developed that give a multiplicity of insights in the human body, like local tissue structures, blood perfusion, and brain activity.

1.2

The Downsides of MRI

The aforementioned benefits make MRI a very powerful technique, but there are rea-sons that make it inconvenient.

One major downside is the high price of MRI. The magnet needs to be strong enough to make images of quality. High electronic currents must power a solenoid to create the strong magnetic fields. Every material has electrical resistance at room tempera-ture and in these situations electrical current creates heat. Currents of this magnitude would damage the solenoid. Instead, liquid helium cools niobium-titanium cables down to below -264◦C. The cables become superconductive and can now handle the

2 Introduction

high current level. Helium is expensive. One liter of the used helium costs around€10 and an average MRI system utilizes 1,700 liters of helium.

There are other costs that emerge around the purchase of one MRI machine. A big metal shield has to repress radiofrequency (RF) radiation and magnetic fields going in and out of the machine for safety and avoiding noise sources. Renting and maintain-ing the space and keepmaintain-ing the software up-to-date also has its costs. Then there are taxes, insurance, energy, employees, teaching and training that are other continuous expenses. All these costs summed up makes an MRI machine worth roughly 1 million Euro’s per achieved Tesla.[2]

Another inconvenience is the low mobility of MRI machines. There is a great variety of hardware that needs the help professionals to install. For example, to charge or terminate the magnetic field in a superconductive magnet, a professional has to be hired. Active and passive shielding techniques limit the stray field of the magnet. Advanced shimming technologies have to be installed to maintain a magnetic field of high quality. Then there are the surrounding cooling systems, gradients, amplifiers, and computer systems. The MRI system and the surrounding hardware consumes a lot of space and weight. Moving MRI systems, therefore, takes planning and effort. The next disadvantage is the high power consumption. The cooling system, gradient amplification and the RF transmitters all use a lot of power. Charging or terminating the superconducting magnet takes a lot of power, although it does not need regular maintenance afterwards. The total power used in an operating MRI system can go up to 100 kW.[2] This would make an MRI system hard to implement at places with an unstable power supply.

The high costs of MRI have serious consequences. The World Health Organization (WHO) published information about the abundance of medical imaging devices in 2009 in several countries. It showed how developing countries have a small number of MRI scanners.[3] Uganda, a developing country, has in total 1 public MRI for a pop-ulation of 33 million people in 2009. This contrasts with the 382 MRI scanners to Spain, which is a country with a better economy and a population of 45 million in 2009. This results in a painful comparison: Uganda has 0.03 MRI systems per million population, while Spain has 8.5 MRI scanners per million population. That is almost 300 times as high. The health problems in developing countries could be encountered if diagnostic tools like MRI would be available. The low accessibility of advanced medical tech-nologies like MRI is one of the major healthcare problems for the developing world. Affordable imaging machines would increase this accessibility and have great use.

1.3

Hydrocephalus

One important application of MRI in developing countries would be the diagnosis of hydrocephalus.

Hydrocephalus is a pediatric, neurological disease, where cerebrospinal fluid (CSF) ac-cumulates in the brain.[4] This accumulation causes pressure and consequently results in symptoms like immense headaches and the pupils of the eyes going downwards, also known as sunsetting. In the case of newborns, the head grows since they only

1.4 Lowering the Costs of MRI 3

have the soft fontanelles connecting the bones in their skull. The head of an infant with hydrocephalus can grow up to unusually large sizes. If these symptoms are not treated with care, the disease can have lethal consequences.

Compared to other parts of the world, the incidence of hydrocephalus in children is very high in sub-Saharan Africa (SSA).[5] Nutrition deficiency, low weight at birth and delay in diagnosis are all explanations of this higher incidence. Infection after birth causes 70% of all the cases in SSA, where in developed countries hydrocephalus mostly develops after a hemorrhage.[6] No reliable study has been done due date that show these numbers, but there are estimates that hint at rates reaching 200,000 new cases per year under infants in SSA.[7] The economic benefits of treating the hydro-cephalus patients for one year are estimated to be at least 1.4 billion US dollars in the long-term.[7]

Multiple treatments exist for hydrocephalus and differ per individual case. The most frequently used treatments are the placement of a shunt or doing an endoscopy. Endoscopic third ventriculostomy (ETV) has been very successful in developing countries.[5] Every treatment for hydrocephalus includes infiltration of the fragile in-fant’s skull. Therefore, choosing the right treatment relies on good information sur-rounding the diagnosis and the anatomy of the patient’s brain. Having non-infiltrating imaging tools like CT, ultrasound or MRI provides this information in this process. The diagnosis of hydrocephalus is mostly done using brain imaging.[4] When the in-fant has an open fontanelle, cranial ultrasonography can be used to observe the growth of the ventricle. But, this technique does not give sufficient information about the anatomy of the brain and cause of the disease, which is important when choosing the treatment. One commonly used technique for a diagnosis in developing countries is CT. The high energy radiation used for CT scans causes higher risk to cancer in later stages of life, especially when used for young children.[8] It is therefore suggested to limit the use of CT for infants. Using MRI does not have negative influences on the patient’s health and also provides information about the structure of the brain. In practice, MRI is almost never used in SSA for diagnosing hydrocephalus because of the low availability and the other reasons mentioned before.

1.4

Lowering the Costs of MRI

Drastically lowering the costs of MRI would increase the availability of MRI in de-veloping countries. The costs would be limited by reducing the magnitude of the magnetic field. Other technologies can be used then to create the magnetic field than the expensive superconducting coil. This also opens doors to make an MRI machine that is portable and easy to install on site. A lower magnetic field would also lower the signal compared to the noise. This can be tolerated, since CSF and brain tissue have a high contrast and are distinguishable. The localization of accumulation areas can be done with low spatial resolution. Thus, diagnosing a hydrocephalus patient might be possible using these alternative MRI techniques.

There are multiple examples of researches that attempt to lower the costs of MRI with electromagnets. One research from Saracanie et al. was published, where ultra-low

4 Introduction

frequency MRI was used.[9] In the research, an electromagnet was constructed that created the magnetic fields. The achieved magnetic field had an intensity of 6.5 mT, which is 450 times lower than a clinical MRI. With this setup, they managed to make 3D images of the brain with enough signal and low amount of artifacts. The reason that this worked mainly has to do to the acquisition techniques and pulse sequences they used. The image is then constructed using different sampling techniques and more sensitive technology to pick up the signals. Also, the materials used for this setup would amount to less than 50,000 dollars. A significant decrease of costs.

Using permanent magnets instead to create the magnetic field could be a solution for the costs of MRI. Permanent magnets are widely available, cheap, and can produce strong magnetic fields. One advantage would be the passive creation of the magnetic field. The magnets do not have to be cooled to low temperatures and do not consume any power. This would make this new kind of MRI system easier to install on set and portable as well. Specific geometrical designs have to be used to create the right magnetic field. Even with these designs, the magnetic field will not be as strong nor homogeneous, i.e. the same magnetic field intensity at every position within a certain range, as with a superconducting electromagnet. The design that is used in this re-search is the Halbach design.[10] A Halbach magnet consists of magnetic material that continually changes in magnetic orientation with that material, which creates a mag-netic field on only one side of the material. It can be made as a circular array magnet, consisting of idential magnetic pieces placed along the circumference. This creates a magnetic field that has a relatively high homogeneity and magnetic field within the magnet, and has low stray fields i.e. low magnetic field outside the magnet.

One study at Massachusetts Institute of Technology (MIT) by Cooley et al. focused on the use of permanent magnets to perform MRI.[11] In this study, a Halbach magnet was fabricated (figure 1.1a) that produced a magnetic field of 77.3 mT at the center. The system was under 100 kg and did not produce a lot of sound while in use. They created the 2D-image of a MIT logo phantom shown in figure using their own system to emit pulses and to analyze the data (figure 1.1b). For the future, they were already working on methods to make 3D-imaging techniques like e.g. Transmit Array Spatial

(a) (b)

Figure 1.1: (a) The setup used by Cooley et al. that includes an Halbach array. (b) One image of a phantom made with the setup.

1.5 The History of this Project 5

Encoding (TRASE).[12] The research will be used as a baseline for the research in this thesis.

1.5

The History of this Project

In 2015, Leiden University Medical Center (LUMC) agreed to take part in the Open-Source Imaging Initiative (OSI2).[13] The goal of the initiative is to develop a portable imaging technique that can be fabricated at low costs. The designs and software of this new system would then be shared on the website of OSI2to make it accessible for every interested person.[14] This would avoid systems that are hard to use, maintain, and repair. This will make it easier to operate in developing countries, which was also suggested by pediatric neurosurgeons operating locally.[15] Multiple universities have agreed to work in this initiative, where a collaboration between Delft University of Technology (TU Delft) and the LUMC was born.

With the two universities collaborating, knowledge about the physics, mathematics, and electrical engineering surrounding coincide. The whole project has three goals. The first goal is to make a mobile low-field MRI using Halbach arrays that can make 2D images of an infant’s head. Second is to have the costs to fabricate one system not exceed 50,000 US dollars, already a significant drop in costs in comparison to the average CT and MRI systems. Third is to make all the designs and software open access, so that anyone can make and use the setup and suggest adjustments.

Another collaboration is with Penn State University, where the neurosurgery group develops a pre-polarized MRI (PMRI) system. In PMRI, a low magnetic field magne-tizes a sample, where temporary pulses enhance this magnetic field, where the rest of the imaging part is done during the exponential decay of the increased magnetization. The research group also functions as the communication bridge between the collab-orating universities and the CURE hospital in Uganda where the new techniques are implemented. In the Berlin Ultrahigh Field Faculty (BUFF), similar experiments are done and Halbach arrays are also produced to make MRI possible. This group is the source of OSI2and is our reference point for the open-source community.

The project in the LUMC is now in process since 2016. Jelle Hockx started constructing most of the setup and the electronics for the first fabricated Halbach rings.[16] Koen van Deelen characterized the Halbach magnets using simulations done with ComSol Multiphysics.[17] The research now focuses on finishing the first setup and producing the first signals using commercial software instead of open-source.

1.6

The Outline of this Thesis

The goal of the thesis is to summarize the construction of a setup for low-field MRI us-ing Halbach configurations. The main thought is to make a setup that can be tweaked in the future for the measurement of the first NMR signal and, eventually, the first 2D-image.

6 Introduction

The thesis is split into several chapters. Following this introduction, one can read about the theory in chapter 2. Afterwards, chapter 3 describes the hardware used and characterizes every part of the setup. Then chapter 4 summarizes the experiments and the results. This is followed by the discussion in chapter 5, where possibilities are given on what to do after the conducted research. Chapter 6 finishes this thesis with a summary of the research, where a conclusion about the achievement is given, and lists the recommendations for future research. Enjoy reading.

Chapter

2

Theory

2.1

Magnetic Resonance Imaging

With MRI, one develops in vivo images of an object or body part. This is done study-ing the energy transitions in a material. A strong homogeneous magnetic field mag-netizes the studied object to create an energy difference within the material. Then, a separate oscillating magnetic field—called the radio frequency (RF) pulse— that is formed by a transmit coil flips the orientation of the magnetization, where the consec-utive relaxation process induces an electronic signal in the receive coils. The decaying behaviour of this signal provides information about the studied material, and a three-dimensional image is formed after a sequence of RF pulses using three additional gra-dient magnetic fields to encode the dimensions.

The theory behind MRI is introduced and explained in this section. This was done studying the material in [18] and [19], and will be referred to if one wants to broaden his or her knowledge about conventional MRI.

2.1.1

Magnetization

The magnetization determines the signal strength in MRI directly and is one of of the most important factors in good image quality. Every proton has spin angular momen-tum I, creating a magnetic moment~µi determined by the proton’s orientation mI. The

magnetization is defined as the sum of the magnetic moments in a material, which can be written as M=     

∑

_i ~ µi      . (2.1)

The magnetization of an organic material appears to be zero in a natural environment, since the protons are randomly oriented throughout the material. This is shown in figure 2.1a. It becomes interesting when a strong external magnetic field comes into practice. Let us sketch the situation in a conventional MRI system.

8 Theory

An object is placed in an external magnetic field B0aligned with the length of the bore,

the z-axis. Subsequently, the spins of protons orient in two directions: parallel or anti-parallel to the z-axis (figure 2.1a). The magnetic field perturbs the potential energy of the protons. The additional energy becomes

E = mIγhB0

2π , (2.2)

where the constant γ represents the gyromagnetic ratio and h Planck’s constant. With mI = ±1/2 for the two possible orientations of protons, the energy difference∆E is

∆E= γhB0

2π . (2.3)

The magnetization is determined by the population difference between the states. This is calculated using the Boltzmann distribution principle, which states that the proba-bility of a particle being in a certain state is dependent on the state’s energy and on the cumulative energy of all the possible states. The ratio between the number of particles in state i and the total population is

Ni

Ntot

= e

−ei/kBT

e∑i−ei/kBT, (2.4)

where, for a state i, Niis the number of particles and eiis the energy. Summing over the

number of particles in every state results in the total number of particles: Ntot =∑iNi.

Now, let us go back to the situation in MRI. Like said earlier, there are two possible states (mI = ±1/2). The ratio between the particle numbers of the two states is then

found using equation 2.4: Nap

Np

=e−∆E/kBT _≈1− γhB0

2πkBT. (2.5)

The approximation in the last step uses the first order Taylor expansion e−x = ∞

∑

n=0 (−1)nxn n! ≈1−x, (2.6) since the term in the exponential is very small. Equation 2.3 is used to replace∆E. The population difference∆N can be calculated using the following approach:

∆N =Np−Nap = Np  1− Nap Np  = γhB0 4πkBT Ntot. (2.7)

The total number of particles is approximated using Np ≈Ntot/2.

The magnetic moment is described as µi = ±_4πγh. The magnetization is then completed:

M=

∑

i µi = γh 4π∆N = γ2h2B0Ntot 16π2_k BT . (2.8)

2.1 Magnetic Resonance Imaging 9

(a)

(b)

Figure 2.1: (a)The orientation of the spins before and after the application of an external mag-netic field (B0). Before the magnetic field is applied, the spins are randomly oriented, having

zero net magnetization. After the application of the magnetic field, the spins align parallel or anti-parallel to the direction of the magnetic field, causing a magnetization that is calculated in equation 2.8.[18] (b) The changed magnetization orientation in a material when a RF-pulse is applied. The RF-pulse has to oscillate at the Larmor frequency f0 to be able to influence

the spins. In this case, the pulse is long enough to flip the spins to the angle π/2. After the RF pulse, the magnetization relaxes towards its original position, where the processes are de-scribed by the Bloch equations. [19]

2.1.2

RF Pulse, FID and Relaxation Times

The magnetization alone does not create a signal. In electromagnetism, it is known that a change in magnetic flux induces electromotive force (emf) in a loop that is measured as a voltage. If the magnetization of the material changes in orientation, a signal would be created in adjacent conductive loops. To accomplish this, the orientation of the magnetization is changed with another magnetic field—the RF pulse—to create this change in flux.

The RF pulse creates an electromagnetic B1 field in a coil placed around the object of

interest. The B1field oscillates around the z-axis at the same frequency as the atoms in

the magnetic field,

f0 =2πγB0, (2.9)

which is known as the Larmor frequency. The reason that the pulse has to oscillate at the Larmor frequency is to press the orientation of the spins directed along the z-axis towards the xy-plane, still rotating around the z-axis.

The magnetization orients with an angle from the z-axis after the application of an RF pulse and oscillates around the z-axis right after this application. After the RF pulse is applied, the spins go back to their original position. This relaxation process causes the signal in a pickup loop placed around the object, creating an oscillating decaying electronic current. The change in the magnetization M is described by the~

10 Theory Bloch equations: dMx(t) dt =γ My(t)Bz(t) −Mz(t)By(t)
− Mx(t) T2 , (2.10) dMy(t) dt =γ(Mz(t)Bx(t) −Mx(t)Bz(t)) − My(t) T2 , (2.11) dMz(t) dt =γ Mx(t)By(t) −My(t)Bx(t)
− Mz(t) −M0 T1 . (2.12) Two time constants are introduced here that give information about the relaxation pro-cess. The first time constant, called the spin-lattice relaxation time (T1), describes the

relaxation process of the spins to their original orientation. The second time constant describes how the spins dephase and is called the spin-spin relaxation time (T2). Since

inconsistencies in the magnetic field cause faster dephasing, a shorter relaxation con-stant T₂∗is what one would measure instead of T2. It is known that T2is always shorter

than T1.

Every material has different time constants and has different proton densities. These parameters provide information about tissue in the human body and one can thus study specific subjects by letting one of these parameters dominate in weight.

2.1.3

Gradients

It is now of importance to get a full image. A voxel is selected using three magnetic field gradients. One for slice selection, one for phase encoding, and one for frequency encoding.

First a slice is selected using the z-gradient. When the gradient is applied, the magnetic field is characterized as

B(z) = B0+Gzz (2.13)

The additional frequency ωs of the pulse equals ωs = γGzz. The slice is then selected

by applying an RF pulse with a small bandwidth ∆ωs, which determines the slice

thickness:

T= 2∆ω

γGz. (2.14)

Now that the protons in a selected slice are excited, a phase gradient creates frequency differences in the y-direction. After applying this gradient for a time τpe, the atoms are

left with a phase difference. Lastly, another gradient in the x-direction is used during the readout, where the gradient creates differences in the Larmor frequencies in the x-direction.

2.1.4

Image Formation

For the image formation, the Fourier transformation and the inverse Fourier transform have to be introduced: F(ω) = 1 2π Z ∞ −∞ f(t)e iωt dt f(t) = Z ∞ −∞F(ω)e −iωt dω (2.15)

2.1 Magnetic Resonance Imaging 11

The previous formula is working with angle frequencies (ω). One can use regular frequencies (ν) replacing ω =2πν.

After the MRI acquired the signals of the selected slice, the voxels are found using the phase and frequency differences created with the gradients. The signal is dependent on the gradients Gxand Gyand the time of application t and τpe

S(Gx, t, Gy, τpe) =

Z Z

ρ(x, y)eiGyτpeyeiGxtxdxdy (2.16) ρ(x, y)is the proton density, which relates to the number of particles in equation 2.7 in

a voxel area. This is the unknown parameter that is calculated to form the image. But to achieve the image from the signals, another step needs to be performed. The so-called k-space parameters are now defined as kx = G_2πxt and ky = G_2πyτpe. Giving the

new formula

S(kx, ky) =

Z Z

ρ(x, y)ei2πkxxei2πkyydxdy (2.17)

This is now looking similar to the Fourier transform of equation 2.15, but then in the spatial domain. Finally, the image can be calculated doing the inverse Fourier trans-form: ρ(x, y) = Z ∞ −∞ Z ∞ −∞S(kx, ky)e −i2πkxx−i2πkyy_dk xdky (2.18)

which gives the spatial information of the proton density and results as the MRI im-ages that are normally seen.

2.1.5

Pulse Sequences

Like described in section 2.1.2, information about the studied material can be found in the time constants. The time constants can be acquired by using different kinds of pulse sequences, which come in handy during the experiments described in chapter 4. There are three pulse sequences that are used for the experiments in this thesis. The most primitive sequence is simply applying a pulse and observe how the signal proceeds. The resulting signal—the free induction decay (FID)—is described as a sine function oscillating at the Larmor frequency decaying exponentially through time. The T₂∗ is then found by fitting the maxima of the signal with the exponential e−t/T2∗.

This does not give any information about the two other time constants. To compensate for the static magnetic field inhomogeneities, an additional π-pulse has to be applied after the π/2. This results in the resynchronization of the spins, which consequently creates a signal—an echo. This is called the spin-echo sequence. The time between RF pulses is called the repetition time (TR), and the time between the RF pulse and the echo is called the echo time (TE). When the sequence comprises two pulses that are not π/2 and π, subsequently, an echo signal is still the result. This is called a Hahn echo sequence. The signal intensity I(x, y)of the spin-echo produces is dependent on the parameters of the pulses TR and TE and behaves as

I(x, y) ∝ ρ(x, y)



1−e−TRT1



12 Theory

The last equation gives an insight how one can use the parameters of the pulses. First, when TE is in the order of T2and TR much longer than T1, the signal is T2-weighted.

If TR is long and TE is much shorter than T2, the signal depends on T1.

When the signal is strong enough, one can perform an echo train to find T2. This is

called the Carr-Purcell-Meiboom-Gill (CPMG) sequence.

2.2

MRI in Low Inhomogeneous Fields

After knowing the theory of conventional MRI, we can now focus on the permanent magnet situation. These permanent magnets create a low inhomogeneous magnetic field—how this happens will be the focus of section 2.3. It will be interesting to know the outcome of MRI experiments using these magnetic fields. The low inhomogeneous field will probably cause a weak signal, which makes information about the signal de-pendency crucial. As one will see, the system’s properties make a significant difference in the signal-to-noise ratio (SNR). This section goes over the terminology of both ho-mogeneity and SNR to help the reader to understand some of these dependencies in the experiment.

2.2.1

Homogeneity

The homogeneity of the magnetic field, i.e, the parameter that tells how much the mag-netic field is the same in a certain volume, is an essential part of MRI. The homogeneity

η is defined over a sample volume V as

η = pvar(B0)V

hB0iV

×106, (2.20)

which is expressed in parts-per-million (ppm). In conventional MRI, a homogeneity of 10 ppm is achieved as a bare minimum in the field of view (FOV) using passive and active shimming techniques.[20]

The expected homogeneity of the magnetic field in the magnetic field of the perma-nent magnets are orders of magnitude higher: 1000 or even 10000 ppm. One wants to avoid such an inhomogeneity for multiple reasons. Large differences in the magnetic field require a larger bandwidth in the RF-pulse to excite the same amount of spins. The larger bandwidth then increases the amount of noise that is received in the ex-periment. This will be elaborated in section 2.2.2. Then there is the loss of signal due to a smaller amount of protons that is excited by the same bandwidth. Also, the T₂∗ relaxation time is shortened by inhomogeneities in the magnetic field, which means that the experimental setup needs to switch fast between transmit and receive. It is therefore important to limit the inhomogeneity as much as possible.

2.2 MRI in Low Inhomogeneous Fields 13

2.2.2

SNR

The distinction between signal and noise is quantified with the signal-to-noise ratio (SNR) and an estimation of the quality of the image can be estimated. High image contrast and resolution are only possible with a high SNR. With low signal strengths and high noise levels expected in the low inhomogeneous field situation, optimizing the SNR is therefore essential.

It is good to mention that there is a difference between intrinsic SNR and image SNR. The image SNR gives the difference between the background noise voxels and the signal voxels in the FOV, carefully selected for the calculation. The intrinsic SNR gives the limit of the signal that one can measure in an experiment. The term SNR used in this section refers to the intrinsic SNR.

It is hard to derive a fundamental equation for the SNR, especially since there is a high number of factors that is involved in the SNR. Also, there are factors involved which are hard to measure, like the geometry of the coil and the ratio between the volume of the sample and the coil. There is still a fair amount of research done to define the SNR of MRI.[20–25] In one paper by Hoult et al., a formula was formulated to estimate the dependency of the SNR in NMR experiments. Back then, this was done to understand the disappointing signal improvement as a consequence of the increasing used magnetic fields. By reasoning, the SNR was derived.[26]

The SNR depends, like stated in the previous paragraph, on multiple factors. It is best to start with the signal. There are two main reasons why a higher magnetic field improves the signal strength. First, the higher magnetic fields increases the energy level difference, thus increasing the population difference like stated in 2.7, which then causes a stronger signal. Second, the Larmor frequency increases proportion-ally with the magnetic field, thus increasing the voltage that is induced. This explains the B₀2dependency of the signal strength. Another important factor in the SNR is the sensitivity of the RF coil, which is expressed in the receiving B₁− magnetic field. This mostly has to do with coil geometry which itself depends on the region of interest and the homogeneity of the B0magnetic field. The following signal dependency is found:

S∝ B−₁ B₀2 (2.21) Then there is the thermal noise coming from the system, also known as Johnson noise or Nyquist noise. This has to do with thermal fluctuations that cause small signals. The variation of the voltage of the thermal noise measured over a bandwidth ∆ f is defined as:

σth =p4kBTcR∆ f (2.22)

Where R =Rc+Rs is a combination of the resistance from the coil and the resistance

that the sample creates in the coil originating from eddy currents in the sample’s tis-sue. kB is the Boltzmann constant and T is the temperature of the coil and the sample.

If the magnetic field is very low, the coil’s resistance is higher than the sample’s re-sistance. This would be called a coil noise dominated situation. In conventional MRI, the sample resistance is dominant, which gives so-called loading problems.[27] In the low-field situation, it is more important to choose the coil properties in such a way that the resistance is mitigated. This can be done by taking the thickness and the con-ductivity of the wire into account, and thus make a coil with a high quality factor Q,

14 Theory which is defined as Q = fres ∆ f = 2π fresL R (2.23)

fres is the resonance frequency of the coil tuned to the Larmor frequency, ∆ f is the

bandwidth at the resonance frequency, R is the resistance, and L is the inductance of the coil. One problem then arises relating to the inhomogeneity of the B0 magnetic

field. Like stated in section 2.2.1, a higher bandwidth from the coil is necessary to ex-cite a larger volume and therefore creating a higher signal. To get a higher bandwidth, a lower Q is needed or a higher resistance, which would then lead to more noise. It is therefore important to find the balance in this conundrum, creating a sufficient band-width without creating unnecessary noise.

In the end, it is the image SNR that really matters. This can deviate much from the intrinsic SNR.[21] This comes from losses during the transmission of the signals, but also losses in the system. For a good image, the pixel size should be chosen as such that the pixel SNR should be above 20.

2.3

Halbach arrays

In this research, Halbach arrays are used for the creation of the magnetic fields. Hal-bach magnets were defined for the first time in 1973 by Mallinson [28]. It was then further characterized by its namesake Halbach in 1979.[29] This section elaborates on magnetism, Halbach arrays, and simulations of magnets.

2.3.1

Permanent magnets

When a material is targeted by an external magnetic field, it magnetizes and creates a magnetic field on its own. This happens due to the crystal structures within the ma-terial, where every atom has a magnetic moment, like one remembers from section 2.1.1. The magnetization of a material magnetizes from summation of magnetic mo-ments of the atoms. Since the materials have different crystal structures, this causes the different kinds of magnetisms like e.g. ferromagnetism, ferrimagnetism, and anti-ferromagnetism. Ferromagnetic origins in the parallel alignment of spins in the mate-rial, where the spins are aligned even without an external magnetic field. This is the origin of permanent magnets.

The relationship between the magnetic field H, magnetization M, and magnetic flux density B is

~

H = ~B

µ0

+ ~M. (2.24)

The response of a material on a magnetic field can be showed in a magnetization plot (figure 2.2).[30] When a magnetic field is applied on a material, it magnetizes and creates its own magnetic field. This behavior saturates at higher magnetic fields. If the external magnetic field is terminated, the material still produces a magnetic field, which is known as the remanence magnetic field Br(1 to 2). Afterwards, this effect can

2.3 Halbach arrays 15

Figure 2.2: Magnetization plot of a ferromagnetic material. Without the application of an external magnetic field H, the remaining magnetic field becomes the remanance magnetic field Br. The coercivity magnetic field Hc gives the ammount of magnetic field that is needed to

demagnetize the magnet.[30]

of the material go to zero (2 to 3). This point is called the coercivity magnetic field. Afterwards, the same saturation behavior can be observed if the negative magnetic field is increased (3 to 4). If the external magnetic field is then increased again, the material goes towards its original magnetization (4 to 1). The behavior of the material is called a hysteresis, where the material memorizes its past magnetic state and the original magnetization behavior (0 to 1) cannot be determined.

In the 20th century, new ferromagnetic materials were created and introduced. The first example that were discovered before that time were the three metals cobalt, iron, and nickel. But with the development of specific alloys, materials with stronger mag-netic properties were discovered. Nowadays, there are two majorly used magmag-netic alloys: Semarium cobalt (SmCo) and Neodymium (NdFeB).

The strength of a magnet is defined by the remanence magnetic field Br. This is

de-fined as the magnetic field that remains after the magnetization of the magnet, and is measured as the magnetic field at the surface of the magnet.

Neodymium magnets generally have the strongest magnetization, where the highest achieved remnant magnetic field that can be bought at shops is Br = 1.3T, which is

16 Theory

θ

α

(a) (b)

(c) (d)

Figure 2.3: Multiple aspects of Halbach designs. (a) is the definition of the magnetization angle of the magnet at one point, depicted here as a cube magnet. θ is the spatial angle of the magnet with the vertical axis of the magnet formation, where α, the magnetization angle, is then defined as(m+1)θ, where m is the number of modes or the polarity of the Halbach

magnet. (b) is the result of a dipole Halbach magnet consisting of a continuously magnetized cylinder of infinite length. The vector lines within the magnet would be the resulting magnetic field, where within the magnet there is a strong homogeneous magnetic field and outside the magnet there is no stray field. (c) and (d) are examples of the mandhala design, where the continuously magnetized material is replaced by identical (c) cube or (d) octagon magnets. The resulting magnetic field is similar to the magnetic field in (b), but with less homogeneity, a lower magnitude, and a small stray field.

2.3 Halbach arrays 17

2.3.2

The Definition of a Halbach magnet

It is the orientation of the magnetization within a permanent magnet that defines the magnetic field outside the material. The Halbach array is defined as such that the angle of the magnetization at a position is the number of modes in the magnetic field times the spatial angle. Better said, the definition of the angle of the magnetization is:

α = (m+1)θ; m ∈Z (2.25)

where α is m the angle of the magnetization and θ is the angle of the magnets position. is the number of modes or the polarity—m = 1 is a dipole, m = 2 a quadrupolar, m = 3 a sextupolar, and so forth. Negative values of m result in Halbach magnets with outward magnetic fields and positive values of m result in Halbach magnets with inward magnetic fields.[10]

Halbach defined a formula for the magnetic field of an infinitely long cylinder Halbach magnet using the scalar magnetic potential:[29]

B= Brln rin

rout



(2.26) Where Br is the remanence magnetic field of the material.[29]

In this way, strong magnetic fields can be achieved using Halbach arrays, where ex-amples exist where magnetic fields are achieved of 5 T.[31]

2.3.3

Segmenting the Halbach Array

In the last section, only theoretic models were explained. In reality, a continuous mag-netized material with changing orientation of magnetization is practically impossible to make. The solution for this problem is segmenting the Halbach magnet, creating an array of magnets.

Various methods to segment the Halbach magnet have been proposed and verified be-fore. One method is dividing magnet in segments with the magnetization oriented in one direction, summing up to an array that approaches a Halbach magnet. One prob-lem of this approach is that the instalment can be hard and different eprob-lements have to be used. The most common sequence of magnets, called the Magnet Arrangement for Novel Discrete Halbach Layout (MANDHaLa), consists of polygon or cubic shaped magnets. The design was introduced by Raich and Bl ¨umler.[32] Octogon shaped mag-nets result in the best magnetic field which can be used well in practice, since the cor-ners of the magnets can help to keep the orientation of the magnet.[10] Cubic shaped magnets are easy to get and affordable, and thus chosen for the research.

2.3.4

Simulating the Magnets

There are multiple techniques to simulate the magnetic fields of Halbach arrays, and multiple studies are done about the verification of the techniques. One approach one

18 Theory

can make is by using Finite Element Methods (FEM) simulations, which can be done using e.g. software packages in ComSol Multiphysics. Another approach would be to use infinitesimally small dipole magnets, which magnetic field can be defined as:

~_{B(~r) =} µ0 4π  ~ m×~r r3  (2.27) ~

m is the dipole moment, ~B is the magnetic field, and~r is the spatial coordinate with respect to the dipole.[33]

Figure 2.4:Simulations of a segmented 2D Halbach ring with radius R = 4 arbitrary units (AU) using equation 2.27. The direction and size of the arrows relate to the direction and magnitude of the created magnetic field, respectively. The axes are displayed in arbitrary units.

Chapter

3

The Development of the Experimental

Setup

With the theory of the last chapter in mind, the next subject will be the development of setup. The prototype has been modified several times throughout this research before it was used to measure the first results. This chapter summarizes the most important changes of the major parts of the setup. A description of the setup will be given before by calling up all the components to give an overview. It is assumed that the reader has basic knowledge about RF electronics.

3.1

Setup

The setup has to meet up the requirement to pick up signals and process them for analysis. This setup is made only for the creation of a signal over a large volume. The sketch in figure 3.1 gives an insight about how this has been done. Let us go through the sketch to give an idea about how the setup works.

First, a pulse with a frequency in the RF range is emitted from a computer with a specialized, pre-installed card and software. A power amplifier increases the voltage of this pulse, so that it has sufficient power to excite the sample. Then a switch that works passively directs the current towards a coil that then emits an RF-pulse. This RF-pulse excites a sample placed within the magnetic field. This consequently creates a signal in the same coil. The signal transports itself again through the switch, where it is guided towards some filters and a preamplifier. Afterwards, the computer receives the signal, where it is processed and analyzed.

The goal of the research states that the eventually developed device needs to be easy to use and modify. For the development of the first setup it was chosen to first make the prototype perform succesful measurements, where some of the part designs were chosen for convenience. Also commercial software and hardware were chosen instead of open-source software for now, ensuring that the transmission and reception of sig-nals is possible. Whenever the first setup is finished, these parts can be simplified and fabricated with open-source software and hardware.

20 The Development of the Experimental Setup

Figure 3.1: A basic flow-chart of the setup. The RF system creates the RF pulse, which gains in amplitude through an amplifier. After its amplification, the T/R switch flows the pulse towards the solenoid coil, which excites the sample. After the excitement of the sample’s spins, a signal is creates consecutively in the same solenoid coil and goes through the T/R switch towards the preamplifier. The preamplifier then increases the voltage of the signal, after which it can be analyzed again in the RF system after passing a filter. The data can then be processed as such that a signal can be read out.

3.2

Magnets

Previously, multiple Halbach rings and alternative magnet designs were fabricated. These were made using a laser cutter and PMMA moulds and small commercial

mag-(a)

(b)

Figure 3.2: Early examples of constructing a magnet using (a) cylinder magnets and (b) cube magnets.

3.3 RF Coils 21

nets. By measuring the magnetic field within these rings using a Hall probe, one could see how efficient one design was. One of these fabricated Halbach magnet arrays (fig-ure 3.2b) consisted of 24 small NdFeB N52 magnet cubes. They produce very small magnetic fields at the center and are also very inhomogeneous. One of the alternative magnet designs consists of cylinder magnets with the magnetization along the mag-nets length (figure 3.2a). This design has a strong magnetic field along the length of the bore, but a very strong stray field is present outside of the array.

After experimenting with Halbach designs, the fabrication of a stronger magnet was started at TU Delft. This design consisted of 4 aluminium rings where 24 N52 NdFeB cubes were placed in each ring. The radius of the bore is 13 cm and the length of the bore is 18 cm. Between the rings is a spacing of 2.5 cm. After the fabrication, the magnetic fields within the bore were measured with an automated 3D Hall probe. The center of the magnet had a magnetic field of 59 mT, which corresponds to a Larmor frequency of 2.5 MHz. This is more than 50 times smaller than the magnetic field of a conventional 3 T MRI. 4 cm from the center, the frequency has already shifted with 100 kHz, already a 4% increase. Outside the magnet, the stray fields decay fast. The 5 Gauss boundary normally used to avoid interferance with devices, is less than a meter from the magnet. The aluminium housing of the magnet made the construction light enough to carry.

3.3

RF Coils

For the new constructed magnet, an RF coil had to be made with a resonance frequency of 2.5 MHz. The radial direction of the magnetic field, makes it important that the B1

field is directed in the longitudinal direction. This made the choice for a solenoid coil obvious, since that design has a good B1 homogeneity and is sensitive to signals. In

(a)

(b)

Figure 3.3: (a)The constructed magnet containing four Halbach rings each filled with 24 N52 NdFeB cube magnets. (b) The magnetic field distribution in the xy-plane at the center of the magnet, where at the center a magnetic field of 59 mT was measured. This corresponds to a Larmor frequency of 2.5 MHz.

22 The Development of the Experimental Setup

(a)

(b)

Figure 3.4: (a)The RF-coil plus the circuit. (b) Equivalent lumped circuit of the RF coil, where the coil is showed as a combination of an inductance Lc, a resistance Rc, and a stray capacitance

Cc. The tuning cap is used to adjust the resonance frequency, and the matching caps Cm are

used to match the impedance with the characteristic impedance of the coax cable Z0 =50Ω to

allow maximum power transfer.

this situation, the coil was used for both transmission and receiving.

In figure 3.4b, one can see the electronic circuit used for the coil. The circuit includes two important capacitors: one tuning capacitors Ct to tune the coil to the resonance

frequency and one matching capacitor Cm to match the circuit to the characteristic

impedance Z0 = 50 Ω. Matching is important to get the highest power transfer and

avoid reflections of power, where the latter results in a lower B1 fields and possible

damage to the hardware. The assigned coil itself is shown as an inductance Lc and

a resistance Rc in series, and a stray capacitance Cc in parallel with Lc and Rc. The

combination of the capacitors and inductors gives an effective impedance of: Ztot = ZL ZL−ZC = 1 1− ZC ZL (3.1) Where the total impedance impedance is a combination of impedances ZC = iωC1 and

ZL =iωL. This is basically a parallel LC filter, where the impedance has a peak when

the ratio between capacitance and inductor equals one: ZC

ZL

= 1

ω2LC =1 (3.2)

The resonance frequency fres =2πωres then becomes

fres = 1

3.4 RF Pulse 23

(a)

(b)

Figure 3.5: (a)The Radioprocessor-G that is placed in a computer. (b) The python code used to perform the measurements.

PMMA cylinders were used as a mould to wind a copper wire around, giving it the structure of the coil. For the number of windings N, the following formula for the inductance L was taken as an estimation using the permeability of the core µ, length of the solenoid l, and the cross-sectional area A:

L = µN

2_A

l (3.4)

After the coil was made, the capacitors were chosen to get the right resonance fre-quency and match the 50Ω impedance. When the coil was finished, it was attached to the network, where it had a resonance frequency at 2.6 MHZ. The calculated electro-magnetic wavelength in air would be λ= c_f =115 m. This is long enough to avoid RF effects like e.g. cable coupling, so one does not have to make baluns to limit common mode currents and balance the coils.

3.4

RF Pulse

Previously, a software defined radio (SDR) was used to create a RF pulse. SDR’s are relatively cheap in costs and the associated software GNU Radio is open-source. This makes SDR’s ideal for the cause of this project. A USRP1 was used for the first experi-ments. The motherboard can be expanded by including daughterboards with specific functions, like gradients, TTL, RF-in and RF-out. The outputs of these cards ranged between -1 and 1 V. The software GNU Radio programmed using logic and function blocks. It is also possible to include own functions into the program by coding it your-self using Python and/or C++. A program was previously made that outputs a single RF pulse. A scope to monitor the receiving and transmitting signals in the software caused problems and another issue of the system was the production of an output file with results. This made it impossible to visualize and analyze the experimental results.

It was then chosen to use commercial hardware. The advantages of using commercial hardware is the involvement of help from professionals and included soft- and hard-ware that has been used for other researches. There are also some drawbacks of using commercial hardware. One would be the high costs that are involved. Another is that commercial hardware includes software that is not open-source and non-adjustable

24 The Development of the Experimental Setup

Figure 3.6:The used preamp. It is feeded with a +15 V source from a power supply.

(most of the time). This would consequently not make it possible to easily share the software. A RadioProcessor-G was bought to use for the experiments. This is a board that is installed into a PCI port in the computer’s motherboard. It has four BNC ports of which one in, one out, and two transistor-transitor logic (TTL) ports. The RF-out puts RF-out maximum 1.2 V. The TTL ports put RF-out 2.5 V. There are also three SMA gradient ports available, that output 3.3 V.[34]

The software of the RadioProcessor-G includes multiple pulse files that could be downloaded from the company’s website. These files were executable, where another configuration file included all the parameters of the experiment. It is impossible to modify the .c files that compiles to the executable files. This made it not possible to create our own pulse programs. This was one severe disadvantage coming with the card. A Python program was produced that emitted one pulse (figure 3.5a). This gave the option to automate the experiment, sweeping over a certain range of parameter values using different pulse sequences. There was no log-file available, so the out-put of a text file with important parameter values was manually programmed into the Python code.

3.5

Preamp

A preamp is included in the network. Preamps are mainly used to amplify a weak signal, where in this case probably signals of the level of µV have to be amplified. It also filters noise around the frequencies, since it only amplifies a certain bandwidth of frequencies. This is done to make the SNR larger. A Miteq AU-1054 is used, which is turned on with a 15 V voltage. It has a amplification of 30 dB between 1 and 500 MHz. It also shows saturation effects when it has an input voltage of around 50 mV.

3.6 Power Amplifier 25

(a)

(b) (c)

Figure 3.7: (a)The power amplifier fabricated by TU Delft. (b) The amplification of the am-plifier expressed in dB. (c) The amplification at diffent voltages expressed in Vpp. The

perfor-mance is still stable just above 10 MHz with a amplification of 50 dB, but quickly degrades near 20 MHz.

3.6

Power Amplifier

A power amplifier is necessary to get large amounts of current to excite the sample. Three different power amplifiers were used through the course of this research. These were different in their frequency range, noise levels, and handling. The first device was an old amplifier ENI 310L, which had large noise levels. The second device was a Barthel power amplifier, where 5 V voltage enables the amplification. These two amplifiers did not work at the frequency of the constructed magnet of 3.3, and were thus not used.

Then an amplifier was developed in collaboration with TU Delft. This made it easier to get an amplifier that worked on the requirements of the experiments. The device

26 The Development of the Experimental Setup

(a) (b)

Figure 3.8: (a)An early example of an active switch. Using a PIN diode that is switched on with a DC signal, most of the RF power is shorted. (b) The T/R switch that is used during the experiments. It contains both passive switching elements—crossed diodes and π-filters to create a 90/_{circ phase shift in the pulse[35]—and active elements in the form of PIN diodes}

that are switched on with a TTL signal.

worked at frequencies between 500 kHz and 12 MHz. In figure 3.7, the amplification values are shown in a graph. The amplifier only works with another enabler of 5 V. Since the TTL ports of the RadioProcessor-G puts out 2.5 V, two devices were build to get to these requirements. The first one is a leveller, causing a constant 5 V voltage. The second one was used to match with the high input impedance of the enable port.

3.7

Switches

A passive switch was used to direct most of the current into the coil and to protect the preamp. The diodes have a cut-off voltage of 0.6 V, so the two crossed diodes placed do not let the signal pass. This was done with the inclusion of crossed diodes and the

λ/4 idea of Lowe and Tarr.[35] The λ/4-line is used to eliminate most of the current

into a ground. To simulate the same effect, the length of the line was replaced with a pi-section filter. This filter is a capacitor with two inductors placed in parallel that leads to the ground.

The second switch of the setup involved an active switch. This is important, since it protects the input channel of the hardware and can be actively be controlled from the control system. Since the passive switch has a cut-off voltage of 0.6 V, this last bit of current has to be lead to the ground before it goes to the preamp. There are multiple ways to fabricate an active switch. These include PIN diode, which functions as a short for RF voltages that is activated with a positive DC current and blocked even more with a negative DC current. These circuits can be seen in figure 3.8a. The circuit that was eventually used was the one in figure 3.8b. The fabricated version can be seen in figure 3.8. This involved the network that is crossed. One side is the input of the RF signal that passes a capacitor blocking the DC-current. Another side is the DC current that passes a large RF choke inductance. Then one side is for the PIN diode that is activated if there is a positive DC current. This PIN diode can also be directed

3.8 RF Shield 27

Figure 3.9: The RF shield that covers the RF coil and the sample during the experiments to block noise from the environment.

in the opposite direction, then it is activated by a negative DC current. The output side includes a capacitor to block the DC current again, after which the RF signal is lead towards the preamp.

3.8

RF Shield

One of the large problems during the experiments are noise sources that emit electro-magnetic radiation. These sources, like explained in section 2.2.2, can come from the sample or the system. System noise sources can be the computer, electric network, cellphones, wifi-networks, lights in the room, but also the electronics used during the experiment. RF-shields can be used to protect the setup for these sources. RF radiation cannot penetrate these shields. This is done by using a conductive copper sheet that is wrapped around a PMMA cylinder within the magnets. The PMMA boxes containing the circuit boards were also wrapped with copper sheets.

Chapter

4

Experiments and Results

Doing experiments is essential to test the capability of the system. One of the problems conducting these experiments are the parameters of the experiments. The amplitude and and homogeneity of the magnetic field has influence on the relaxation times, and since these time constants are not known for the magnetic fields of this system, a search for the right parameters was started. The first experiments conducted were a simple RF pulse applied to the sample to subsequently measure the FID. What was not taken into account is the ring-down of the coils, which had a similar relationship as an FID. The FID mostly depeneds on the T₂∗, which is extremely short due to the inhomogene-ity of the magnetic field. An FID was thus impossible to measure, and another pulse sequence was used instead.

30 Experiments and Results

(a) (b)

Figure 4.2: (a)A spin echo measurement with TE = 1 ms. (b) The same measurement with TE = 5 ms.

4.1

Spin-Echo

The alternative was a spin-echo sequence. The setup was used with a bottle of oil. The oil was used because of its low diffusion, having less influence on the T₂∗. The se-quence is basically dependent on three parameters: the echo time (TE), the repetition time (TR), and the amplititude of the pulse (A). The amplitude A will be represented as a ratio between the used voltage and the maximum voltage of the RadioProcessor-G. These three parameters were randomly changed to see the differences in the results. The output was a frequency-dependent graph, which was then Fourier transformed to get a time-dependent signal. The expected frequency of the signal would be the reso-nance frequency of the magnetic field. The pulses were all applied with the resoreso-nance frequency at the center of the magnet fres =2.5 MHz.

In figure 4.1, one can see the results of a normal spin-echo experiment without post-processing. These was the result of an spin-echo sequence with TE = 1 ms and a pulse time of 200 µs. There is an abundance of noise, where the exponential decline at the be-ginning of the graph is the result of the ring-down. Clearly, no signal can be distincted from this graph. First, multiple noise sources were searched for in the system. These noise levels were made lower by using a special circuit to decrease ring-down effects. Another influence on the noise levels were from external system sources, which were eliminated using RF shields like explained in section 3.8.

After the elimination of most of the noise sources the next step is the post-processing of the signal to increase the SNR. This was done using a digital filter for which signals other then the resonance frequency is filtered out. The result can be seen in figure 4.2a. This graph was the result of TE = 1 ms and a pulse time = 200 µs. Where before, no signal could be found because of the extreme noise levels, now there is a small peak exactly two times the echo time, which is the predicted time of measuring. To see if this peak is really the signal, the echo time was adjusted to 5 ms. The result is seen in figure 4.2b. The peak has shifted exactly as far as the echo time had gone. This gave the conclusion that is the signal from the sample. The following step was to optimize the parameters and to estimate the relaxation times in this setup. This was done by sweeping over TE and A to find exactly the parameters for a π/2-pulse and a π-pulse.

4.2 Carr-Purcell-Meiboom-Gill Sequence 31

4.2

Carr-Purcell-Meiboom-Gill Sequence

The last experiment conducted was a Carr-Purcell-Meiboom-Gill sequence (CPMG) sequence. This is basically a spin-echo sequence, but then repeating the pi-pulses to get sequence of signals with a delay of 2×TE between them. This result can be seen in figure 4.3. There is a clear delay between the signal of the echoes.

Figure 4.3: The resulting graph from a CPMG sequence, where clear echoes exponentially decreasing in magnitude are observed.

Chapter

5

Discussion

Let us first summarize the work that is done. We gathered all the theory needed to start building the setup. This meant that there were some expectations about the direction B0 field and consequently the design of the coil. Then we build the setup improving

the designs and the hardware that was fabricated before. A Halbach magnet was fab-ricated consisting of 4 seperate rings made of cubic magnets to create the B0magnetic

field. A commercial RF system was used to emit pulses. And the electronics were build. In the end some experiments were done. The reproduction of an FID seemed impossible due to the long coil ring-down and the short T₂∗. Instead, spin-echo se-quences were performed. The combination of noise reduction and digital filters made the first measurements of an echo possible. After that, a CPMG was performed as well with results. The setup works and now the next steps can be made to get towards a 2D image. Let us discuss the results of this research in this chapter to get insights of the quality of the research. This knowledge can then be used to see what can be done in the future.

First the quality of the measured signals. The most important subject of the results is the SNR. 2D-imaging with clear contrasts will only become possible with a high SNR. As can be seen in chapter 4, the SNR at this moment is not very high. Especially when taken into account that the sample size is quite big and the excitation volume is still larger than one voxel would be in the ideal case. It was expected in section 2.2.2 that the SNR would be in the order of per voxel. An acceptable SNR per voxel would be around 5, so that there is still a great distinction between signal and noise. It is still the question what the influence of the experiments will be on the signal strength. Different pulse sequences have to be used while one is imaging. For now, the SNR has to be improved before the sample can be made smaller or one can start with 2D-imaging. At this moment the parameters of the sequences are being optimalized. After this step has been done, there are multiple parts that has to be improved in the setup. First, the design of the magnets can be modified, so that the homogeneity and the magnetitude of the B0field improves. Another step would be to use a different RF system. Also the

electronics can be modified. Let us focus first on the desing of the magnets. Another step would be to improve the SNR. Another technique used now to improve the SNR is by averaging the signals. If this has to be done for every voxel in the infant’s head, this would cause problematic duration of scanning time. It is essential to optimize the

34 Discussion

SNR, if one wants to scan without it taking hours. Still, while changing the designs it most important that an infant’s head would still fit inside of this magnet, coil and all, where there is an opening at the beginning of the bore.

One other problem is the area of excitation. The coil is designed to excite a larger band-width. Since the homogeneity is so bad, this would mean that a smaller volume can be excited. One of the most important features that has to be improved is the homo-geneity of the magnets. There are multiple ways to improve this. The first solution is to use other designs for the whole apparatus. The second solution is to use shimming techniques. Shimming can be used both passively and actively. It is advantageous to use passive techniques, since active shimming would include more electronics that will consume power. There are multiple shimming techniques that are used for NMR experiments with Halbach designs. Some of these shimming techniques are described by Bl ¨umler.[10] This would become something like the placement of external cube magnets to correct a mapped magnetic field.

It would definitely be helpful to simulate magnetic designs beforehand to estimate the homogeneity and magnitude of the magnetic field. Using simulations, it could also be possible to find optimal formations of cube magnets with different magnetization, like done recently by Cooley et al.[36] This could be done using ComSol software pro-grammed with Matlab-code, like done in the thesis of Koen van Deelen.[17]. These simulations match well with real life values. There are great examples of studies that simulate the characteristics of different Halbach designs.[37] Using Python or Matlab, also different magnet formations could be explored.

One design change would be to close the gap at the end of the bore of the magnet. Magnetic flux is lost this way, and this is also done by Cooley.[11] Most ideal would be to use bar magnets instead of cube magnets with the orientation of the magnetiza-tion along the width of the bar magnets, although it could be hard to find companies that sell these kind of magnets on the free market. A lot of magnetic flux is now lost within the bore, since there is a separation between the rings. This is a situation that is comparable with the use of Helmholtz coils instead of a solenoid coil. This change would improve the magnitude and homogeneity of the magnetic field.

One other problem that will arise in the future, when the experiments will include more sensitive coils is the differences in the magnetization it the magnets. Perma-nent magnets do not have a very stable magnetization. To elaborate the last sentence, this means that first the fabrication of commercial magnets already has quite a large variation within the magnetization of every magnet. Then, the magnetization is also dependent on the temperature, which would cause temperature drifts in the magnetic field. If one has a good idea how the magnetic field is mapped at one point in time, the magnetic field homogeneity can have changed drastically at another. For this, it is important to start to actively map the field while one is scanning. This could also be in hand for the use in conventional MRI scanners.

The sample used now is oil. The goal is to make images of an infant’s head, so the ideal experiment would be performed on a more realistic phantom. If it would be replaced with water, it would give different results, since the T₂∗ would get shorter due to the diffusion within the fluid, and the signal strength will probably drop. It would be reasonable to start using different sizes of oil first to see the influence on the signal