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 OF SCIENCE in PHYSICS Author : Wico Breimer Student ID : s1023284 Supervisor : Andrew G. Webb 2nd corrector : Tjerk H. Oosterkamp Leiden, The Netherlands, April 2, 2019 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 affordable, portable MRI system that will not exceed the costs of 50,000 US dollars. Contents 1 Introduction 1 1.1 MRI in General1 1.2 The Downsides of MRI1 1.3 Hydrocephalus2 1.4 Lowering the Costs of MRI3 1.5 The History of this Project5 1.6 The Outline of this Thesis5 2 Theory 7 2.1 Magnetic Resonance Imaging7 2.1.1 Magnetization7 2.1.2 RF Pulse, FID and Relaxation Times9 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 4 Experiments and Results 29 v 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 6.2 Future Perspectives 38 vi 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 1 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 keeping 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 2 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.