SIMULATED MRI-SCANNING

Transcription

1 SAHLGRENSKA ACADEMY SIMULATED MRI-SCANNING Visualising signal sampling and image reconstruction of a human brain M.Sc. Thesis Jens Johansson Essay/Thesis: Program and/or course: Level: Semester/year: Supervisor: Examiner: 30 hp Medical Physics Programme Second Cycle St/2017 Göran Starck & Jonathan Arvidsson Magnus Båth

2 Abstract Essay/Thesis: Program and/or course: Level: Semester/year: Supervisor: Examiner: Keyword: 30 hp Medical Physics Programme Second Cycle St/2017 Göran Starck & Jonathan Arvidsson Magnus Båth MRI, Simulation, Image reconstruction The image formation process is a key concept in MRI and understanding how it works gives a solid foundation for further studies in the field. For example, it can be helpful for understanding various scan protocols, how to modify them or even create new ones. How various artefacts appear and how to best avoid them will also be easier to comprehend with this foundation. To understand image formation however, is not simple and most people struggle to conceptualize it 1. By visualising the scan process in a MRI scanner and illustrate how the image is formed during a scan, the purpose of this project is to change that. Functions for describing and visualising signal sampling and image reconstruction were added to an existing simulation and thus enabled it to produce educational videos. These videos illustrate signal sampling along with image formation during an MRI scan. Two pulse sequences were implemented for the use in the simulation, a single-shot EPI and a GE sequence. Further concepts such as Nyquist ghosting, water-fat shift and half scan were also implemented to have the possibility of demonstrating wellknown scenarios and artefacts. In vivo data (T1, T2 and M0 maps) of a brain was implemented by scanning two volunteers with a Philips Ingenia 3T. These maps represent the scanned object in the simulation. These videos, demonstrating image formation during an MRI scan in progress, can be used as a complement to today s course material in MRI courses and thereby help students to better understand and embrace these concepts.

3 Svensk sammanfattning Bildformationen i MR-kameran är en komplex och fundamental process och det underlättar för vidare studier inom fältet att ha god kännedom om hur det fungerar. Den här kunskapen är en viktig grundförutsättning för en djupare förståelse, exempelvis vad gäller bildartefakter, optimering av skannprotokoll och olika samplingstrategier. Syftet med projektet är att bidra till att öka förståelsen kring bildformationsprocessen genom visualisering av skannprocessen i en MR-kamera. Genom implementering av signalsampling och bildrekonstruktion i en befintlig Blochsimulering möjliggjordes skapandet av korta utbildningsfilmer. Filmerna demonstrerar signalsampling i k-rummet, rekonstruktion av varje taget sampel och hur bilden formas genom summan av rekonstruerade sampel. En single-shot EPI-sekvens och en GE-sekvens har implementerats i simuleringen. Demonstration av artefakter och scenarion möjliggjordes genom implementering av Nyquist spöke, vatten-fett skifte och half-scan. In-vivo data av den mänskliga hjärnan har använts för att beskriva det skannade och rekonstruerade objektet. Filmerna, skapade genom simuleringen, kan användas som ett komplement till dagens undervisningsmaterial i MR-kurser och därmed underlätta för studerande att ta till sig och förstå hur bilden formas i en MR-kamera.

4 Clearly, the major role of simulation has been, and will continue to be, to educate, train, and provide rehearsal for those preparing for or working in the delivery of health care D M Gaba.

5 Table of content Introduction... 1 Background... 1 Purpose/Aim... 1 Theory... 1 Simulation... 1 Pulse sequences and k-space... 3 Chemical shift... 5 Nyquist N/2 Ghost... 6 Half scan... 6 Mapping... 7 Method... 8 The simulation... 8 Added sections... 8 Chemical shift... 8 Gradient strengths, k-space and Bandwidth... 8 Signal sampling... 9 EPI sequence GE sequence Image reconstruction Simulation process Load external object In vivo measurements and mapping Scanning Mapping Videos and images Results Signal sampling Image reconstruction Sequences In vivo data set Video Discussion Conclusion Acknowledgements Reference list Appendix

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7 Introduction Working with simulations instead of real life experiments has several benefits. Complex systems and physical phenomena for example can be studied under ideal and fully controlled conditions without the need of expensive lab equipment. It can also be used as a tool to give students a better understanding of a specific system and how different scenarios affects that system. Simulations has an important role when it comes to education of people preparing to work in health care. It has a use in all levels of education, from the earliest to the more experienced level 2. Background An existing Bloch simulation in 2D has been used in Magnetic Resonance Imaging (MRI) courses at the Sahlgrenska Academy to provide students with a better understanding regarding the fundamental properties of magnetic resonance imaging. The simulation calculates and shows the behaviour of the longitudinal and transversal magnetisation under the influence of a pulse sequence. This simulation was developed by G. Starck and has been used as a tool to create educational videos, which demonstrate what happens with the magnetisation during a sequence of Radio Frequencies (RF) and gradient pulses. Image formation in MRI is a concept that is neither simple nor obvious to understand and most people find it difficult to grasp 1. Therefore, it is beneficial to be able to visualise how image formation works and how various artefacts appear and behave. A simulation that can demonstrate signal sampling and image reconstruction can give students a better way to learn these concepts. Functions needed for the simulation to enable visualisation of scanning and image formation include signal sampling and image reconstruction. The section that handles signal sampling stores the complex signal samples along with their corresponding k-space positions. The sampling and reconstruction process can then be visualised by showing the image while it is formed from the ongoing k-space sampling. The image, formed by the sum of frequency components, will over time begin to appear as more and more k-space points are sampled and the corresponding reconstructed frequency component is added to the image. Sequences with scanning and reconstruction from rectilinear, radial and spiral sampling schemes can be implemented. Potential scenarios to add and demonstrate are various MRI artefacts and techniques for speeding up the sampling. With these possibilities implemented, the simulation has the potential of bringing several interesting concepts in the field of MRI for demonstration. Purpose/Aim The purpose of this project was to provide a simulation tool to aid teachers in MRI-courses to better explain the concepts of image formation in MRI and in the process, help students to better understand and embrace these concepts. The first specific aim was to extend the existing simulation with scanning and image reconstruction and thus enabling it to create educational videos showing how the image formation works in a MRI-scanner. The second aim was to simulate a number of MR experiments and produce videos capturing and visualising scanning and reconstruction. These videos can then be used as a complement to today s course materials and the simulation can be used to study various scanning and reconstruction scenarios. Theory Simulation The existing simulation follows the magnetisation in an infinite coaxial cylinder over time as it is subject to a pulse sequence in an MRI scanner. Bloch equations 3 are used to calculate the regrowth of the 1

8 longitudinal magnetisation and the signal decay of the transversal magnetisation after an RF-pulse, see eq. 1 and 2. M "#$% (t) = M + + M "#$% 0. M + e M 267$8 t = M 267$8 0 e where t, T1 and T2 are the time after an RF-pulse, the spin-lattice and spin-spin relaxations times and M 0, M long (0+), M trans and M long the net magnetisation, longitudinal magnetisation immediately after a RF pulse, transversal and longitudinal magnetisation. Different gradients, defined in the pulse sequence, will add a linear variation in the static magnetic field strength and thus affect the object magnetisation, which will start to de-phase. These gradients are needed to acquire spatial information and does so by changing the frequency and phase of the spins in the object. After applying a gradient, G(t), for a time t, the phase, j, is given by, φ t = γr G t? dt? 0 t 3 where g and r are the gyromagnetic ratio and the spatial position respectively. The phase, eq.3, is added to the expression for the transversal magnetisation, eq.2, which now describes both the signal decay and dephasing of the transversal component, eq.4. M 267$8 t = M 267$8 0 e e 1DE(2) 4 All spins in each volume element will create a net magnetisation, aligned with the B0-field, that after an RF pulse is flipped to the transversal axis creating the transversal magnetisation component. The transversal component, giving rise to the signal induced from each volume element, is proportional to the spin density, M trans (r)» r(r). In an MRI scanner, the signal induced in the RF-coil, is the sum of the transversal magnetisation components from all locations in the object and the total signal, S(t), is given by, S t = ρ r e 1DIr t G 2J K2 0 J dr r 5 which is the time-dependent signal from the entire object where the relaxation has been excluded. As described by Ljunggren , the time integral over the gradient can be replaced and written as, k t = γ 2π + 2 G t? dt? 6 The k-space definition from eq.6 is substituted into eq.5 and the total signal from the object is now expressed as, S t = r ρ r e 1DPQ r k dr 7 When looking closer at eq. 7 one realises that S(t) is proportional to the Fourier transform, FT, of the spin density r(r), S(k), and k is the vector of origin in Fourier space, which is often referred to as k- 2

9 space. The signal, S(t), at any time t, will correspond to a certain location in k-space, on which the signal value will be stored. The signal collected during an MRI scan is a discrete sampling of k-space and the signal S(t) in eq. 7 can be replaced by S(k), see eq. 8. This sampling procedure collects complex signal values point-by-point during the scanning and by taking the inverse Fourier transform of these k-space values, S(k), an image of r(r) is obtained. The image, ρ(r), and its Fourier transform, S(k), are mapped over the spatial coordinates, [x, y], and k-space coordinates, [k x, k y ] respectively 5. Image reconstruction is performed by taking the inverse Fourier transform of the sampled data according to, ρ r = FT 1V [S(k)] = FT -1 denoting the inverse Fourier transform. k S(k)e DPQ r k dk 8 Equation 8 shows the continuous ideal case. Since sampling in MRI is discrete, the sum of the frequency components is also discrete. This leads to the use of the discrete Fourier transform, DFT, for reconstruction of the image. Images are often reconstructed and displayed as 2-dimensional images leading to the use of the 2-dimensional inverse DFT. Analogue with eq. 8, the inverse DFT is given by, ρ r [, r ] = S(k [, k ] )e DPQ (6 _`_.6 a`a) 9 `_ `a where the continuous integration in eq. 8 has been replaced by a discrete summation, giving the reconstructed image. An example of the k-space with the corresponding image is given in figure 1. Figure 1: The image, ρ(r), is reconstructed by taking the inverse discrete Fourier Transform of the raw-data in k- space, S(k). The logarithm of values in S(k) has been taken for displaying. Pulse sequences and k-space A pulse sequence is a set of gradients and RF-pulses that describes how a specific MRI scan will be carried out. The strengths, directions and execution times regarding each gradient along with the flip angles for each RF-pulse are defined and stored in the sequence. The first gradients, light-blue in figure 2-3a, applied after an RF-pulse will take the trajectory out in k-space to the position where the signal sampling will start. When sampling occurs, the trajectory will follow a path determined by the read-out gradients, the dark-blue gradients in figure 2-3a. The light-blue and dark-blue coloured gradients correspond to the light-blue and dark-blue trajectories in figure 2-3b. 3

10 The phase-encoding gradient, G PE, is applied in the vertical y-axis while the frequency-encoding gradient, G FE, is applied in the horizontal x-axis for the examples shown in figure 2-3. These x- and y- axes in the spatial domain correspond to the k-space axes k x and k y respectively. The phase-encoding gradient will therefore change the trajectory in the k y -direction, while the frequency-encoding gradient changes the trajectory in the k x -direction. The sign of the gradient dictates the direction of the k-space trajectory, i.e. a positive gradient will extend the trajectory in a positive direction. Usually there is also a third gradient called the slice-selective gradient present in MRI. This gradient is used for slice selection in a three-dimensional object. In the simulation however, the object is defined in two dimensions, i.e. one slice, and a slice-selective gradient is therefore redundant. Figure 2 and figure 3 show a single-shot Echo Planar Imaging (EPI) and a Gradient Echo (GE) sequence respectively, along with their corresponding k-space trajectories. These sequences are very common in clinical MRI scans. A single-shot EPI sequence is a fast sequence that will sample a complete set of lines in k-space following a single RF-pulse. The k-space trajectory will follow a zig-zag pattern due to bipolar read-out gradients, see figure 2b. In a GE sequence, however, only one line in k-space is sampled after each RFpulse and repetition of this procedure will sample multiple lines. Between the repetitions, the phaseencoding gradient amplitude will change leading to a different line in k-space being sampled each repetition, see figure 3. The time between two RF-pulses is called repetition time (TR). Echo formation will always occur when the trajectory is closest to origo, independently of the choice of sequence. The time it takes for reaching echo formation is called echo time (TE) 1. (a) (b) Figure 2: Typical EPI sequence used in MRI scans (a) and the path the trajectory will follow in k-space (b) under the influence of the gradients. G FE and G PE are the frequency-encoding and phase-encoding gradients corresponding to the k x and k y directions in (b) respectively. Figure (a) shows amplitude vertically and time horizontally. 4

11 (a) (b) Figure 3: Ordinary Gradient Echo, GE, sequence (a), which samples the k-space (b) one line at a time during each repetition. Which line on the k y -axis is being sampled depends on the strength of the phase-encoding gradient, which changes each repetition. Figure (a) shows amplitude vertically and time horizontally, Chemical shift A change in resonance frequency, due to different molecular environment, is called chemical shift 6. Electron clouds surrounding the protons will give rise to a shielding effect resulting in an experienced magnetic field for the protons that differs from the main magnetic field. The strength of the shielding effect will determine the size of the field strength difference. Protons in water and fat, having a different molecular environment and thus different electron clouds, will be affected by this phenomenon. The protons in fat are more shielded compared to those in water. This leads to the experience of a slightly weaker magnetic field and thus a lower resonance frequency for protons in fat compared to those in water. These differences in frequencies are very small and measured in parts per million. For example, protons in fat will rotate at a frequency 3.5 ppm less than those in water in a magnetic field of 1.5 T. This leads to an absolute difference of approximately 220 Hz given by, Df = γ 2π B + σ 10 where s is the chemical shift given in ppm and B 0 the external magnetic field strength. The difference in frequency increases with increasing magnetic field strength. The water-fat shift artifact arises due to these differences in the precessional frequency. The fat signal will be shifted a number of pixels in the frequency direction. This can be interpreted as the frequency encoding being fooled to believe that the fat is located in a different position than it actually is. The size of this shift depends on the strength of the frequency encoding gradient, which determines the frequency bandwidth across the pixels. Water-fat shift is seen in the frequency encoding direction with one exception occurring in the EPI sequence, where it will appear in the phase encoding direction. This is due to the very low bandwidth used in the phase-encoding direction in EPI sequences. The artefact may appear as light and/or dark bands around organs that are surrounded by fat, see figure 4. Light bands appear in the areas where the fat signal is added to the water signal, whereas the dark band appear in the areas where no signal is acquired owing to the fact that the fat signal has been shifted away from that area. 5

12 Figure 4: Example of the water-fat shift artefact. The fat tissue is shifted due to the lower precession frequency compared to water. The fat is shifted towards the red arrows in the example above and the characteristic light and dark band appears. Nyquist N/2 Ghost A common artefact in EPI sequences is the Nyquist N/2 ghost, figure 5. It will appear as a ghost image displaced by exactly one-half the field of view, hence the name N/2 7. This is a special case of the phasewrap artefact, and arises due to timing errors between echoes on every other frequency line. These timing errors can result from several reasons including imperfections in the bipolar gradients or induction of eddy currents. Figure 5: Example of the Nyquist N/2 ghost. The ghost is mismapped exactly half the field of view, hence the name N/2. Half scan Half scan is a technique that will speed up the imaging time in an MRI scanner. Time is saved by only scanning the lower or upper part of the k-space, i.e. only scanning half the k-space 1. In practise half scan is usually done by scanning approximately 60 % of the k-space, just going over the centre line in k- space, see figure 6. 6

13 Figure 6: The k-space is scanned approximately 60 % when half scan is enabled, represented by the blue arrows. The green area represents the part in k-space that is omitted during the sampling procedure to save time. Mapping Mapping is a technique used for calculating images, which represents a tissue property value in each pixel. Example of such tissue property are the T1 and T2 parameters. Images, containing the T1 and T2 values for the different tissues in the image, are often referred to maps, hence the name mapping. 7

14 Method All programming was performed in MATLAB R2016a, The MathWorks, Inc., Natick, Massachusetts, United States. Signal sampling and image reconstruction as well as several different sequences and scenarios have been added to the existing simulation. Sequences that have been implemented are a GE sequence and an EPI sequence with half scan. Scenarios demonstrating water-fat shift, N/2 ghost and geometric distortion were created. In vivo data sets of the human brain from MRI scans have also been added to the simulation. The simulation During execution of the simulation, the Bloch equations are used to calculate changes in the transversal and longitudinal components of the objects magnetisation under the influence of RF- and gradientpulses. Simulation of a two-dimensional object requires that the three maps T1, T2 and M0 are present, which, in the context of the simulation, fully describe the object and contain the T1, T2 and M0 values in every given location in the object. Changes in the magnetisation after an RF-pulse are due to T1- and T2-relaxation and free precession during which different gradients are applied. RF and gradient events occurring during the simulation are predefined in the pulse sequence, chosen by the user. The pulse sequence and the object to be simulated are setup and stored in the computer memory before execution of the simulation. User input, such as acquisition matrix, bandwidth and FOV, is available to alter the sequence, which then calculates and holds all events. The events defined in the pulse sequence include gradient pulses, RF-pulses and sampling events. Added sections Chemical shift Chemical shift for water and fat has been implemented. Two sets of T1, T2 and M 0 maps are used to simulate this artefact, one set describing the fat tissue and the other describing the water tissue. A second calculation channel is added which enables the possibility to follow the fat and water magnetisations separately. One channel follows and updates the magnetisation in the fat tissue while the other channel does the equivalent for the water tissue. The calculation is the same for the water and fat maps apart from a non-zero chemical shift for the fat. This chemical shift is added to the expression for the phase difference. The phase difference, a part of Bloch equation for calculation of the transversal magnetisation, see eq. 4, is calculated by, φ = γ B + G + σb + J t 11 where the deviation from the external magnetic field, due to the shielding effect, is calculated by multiplying the field strength, B 0, with the chemical shift, s. J is an all-ones matrix with the same dimensions as G. The term, DB, describes the deviation from the external field due to susceptibilities in every given location. The chemical shift is set to 3.5 ppm and 0 ppm for the fat and water tissue respectively. Gradient strengths, k-space and Bandwidth The size of the acquisition matrix, n kx n ky, the bandwidth (BW) and the image Field of view (FOV) will together determine the time spacing between two samples, known as the dwell time, and the time and strength for all the gradients. The bandwidth is defined as the range of frequencies in the scanned 8

15 object and is measured in hertz per meter. The gradient strengths in the frequency and phase encoding direction are calculated by, G = 2π γ k 1 t d 12 where Dk is the length between two samples in k-space and t d is the dwell time determined by, and k [,] = 1 FOV [,] 13 1 t K = BW FOV 14 where FOV and BW are given in the units meter, [m], and hertz per meter, [Hz/m], respectively, leading to the units one per meter, [1/m], and seconds, [s] for Dk and t d respectively. The gradient strengths will then be given in the unit tesla per meter [T/m]. How far out in k-space the trajectory moves is dictated by the step size, Dk, and the matrix size n. The field of view in k-space, kfov, in k x - and k y - directions is given by, kfov`_,`a = k [,] (n`_,`a 1) 15 The minus one is there because the number of spacing, Dk, between all samples will be one less than the actual number of samples. In the case of an even number of samples, all the k-space lines will be shifted towards the positive side in k-space for the centre line to be sampled. When there is an odd number of samples the lines will be spread out evenly on both side of the centre line without the need of any shift. It is important to sample the centre line as it contains a majority of the signal and therefore dictates the signal-to-noise and contrast of the resulting image. Signal sampling The signal, given by eq. 7, is continuous and defined at all time points in time. The sampling is a discretisation of this continuous signal and the data is sampled at discrete time points during the influence of the read-out gradient. When a sampling event occurs, the signal from the entire object is summed and stored along with the current position in k-space. This sum is calculated by, S k = ρ r [, r ], k 16 6 _ 6 a where r(r) is the spin density matrix containing the signals at each location (r x, r y ) in space. The signals, having an amplitude and phase, will be represented by complex numbers. The position in k-space, according to the different gradients being applied, is known at any given time according to eq. 6. In the simulation, the k-space position is updated by using the analogue discrete version of eq. 6 given by, k = γ 2π G t 17 where Dk is the calculated step size taken in k-space according to the gradient, G, and time interval Dt. 9

16 The trajectory during sampling is parallel to the k x -axis, i.e. frequency direction, in all cases for the sequences implemented in this work. All samples are taken on this parallel path with equidistance length, Dk x, between every two adjacent samples. EPI sequence The implemented EPI sequence is a single shot EPI, which means that the entire raw data set is acquired after a single RF-pulse with no repetition, see figure 2. The following parameters are a portion of the available parameters for the user to set: the bandwidth in phase and frequency direction, the FOV and the size of the acquisitions matrix. With these parameters, the different times and gradient strengths are calculated according to eq Nyquist N/2 ghosting and half scan have been implemented and made available for demonstration for the EPI sequence. To simulate Nyquist ghosting the size of the shift, Dk shift, must be set, which is given as an integer multiple of the step size Dk. The time shift error for the echo is then given by the dwell time, t d, multiplied with the same integer multiple as one step size Dk corresponds to one dwell time. The shift is introduced on every other line in k-space, figure 7a. All lines first shifted is shifted back before reconstruction, going from the sampled k-space in figure 7a to the k-space in figure 7b. All samples are then reconstructed as if they were collected on a trajectory shown in figure 7b, although they were actually collected on the trajectory in figure 7a. Figure 7: When Nyquist ghost is simulated every other line in k-space is shifted (a). During reconstruction, these lines are shifted back to introduce a time shift error. The reconstruction will then believe that the echoes were collected as in (b). If half-scan is to be simulated two parameters must be set. The first parameter is the percentage of k- space that will be sampled. The second determines if the upper or lower part of k-space is acquired. The scenarios Nyquist Ghosting and half scan are user options. GE sequence The implemented gradient echo sequence use a rectilinear sampling scheme, see figure 3. Available parameters to set is equal to that for the EPI sequence with one exception, the bandwidth in phase direction, which will be infinite large for the GE sequence. This is due to that only one echo is collected per repetition time, TR, with the same echo times, TE, for all repetitions. This leads to a dwell time of zero and thus an infinite large bandwidth, see eq. 14. The user options available for the two sequences are listed in table 1. 10

17 Table 1: The user options available for the two pulse sequences. Single-shot EPI Linear GE sfov Yes Yes Bandwidth, freq Yes Yes Bandwidth, phase Yes No Size of acq. matrix Yes Yes Nyquist ghost artefact Yes No Half scan Yes No Reconstruction resolution Yes Yes Water-fat shift Yes Yes The bandwidth for the EPI sequence is defined in the two directions, frequency and phase, whereas it is only defined in the frequency direction for the GE sequence Image reconstruction The raw-data, collected during the current sampling event, is reconstructed to the corresponding frequency component. The image is formed from the sum of all previously reconstructed frequency components and each newly reconstructed component is added to the sum. Each frequency component contributes with a certain frequency, phase and amplitude to the sum. The reconstruction of a frequency component, ρ(r, k), from a single sample, S(k), is given by, ρ(r, k) = S(k) e DPQ `_6 _. `a6 a 18 where k x, k y and r x, r y are k-space and spatial positions respectively. The image is then formed by adding together the spatial frequencies according to q ρ(r) = S k $ e DPQr k p $rv 19 where ρ(r) is calculated for all pixel coordinates in the image. Each single reconstructed frequency component originating from one sample is displayed along with the k-space trajectory and the frequency summation. In this way, an overview of the frequency component reconstructed from the most recent sample along with the current position in k-space and the ongoing summation is given. The frequency pattern, originating from the current sample, can be chosen to be displayed on top of the object or as a frequency pattern in space. Simulation process The simulation is performed in a loop, figure 8, that iterates through all time points until the simulation ends, defined by the last time point. All events executed during the simulation with the corresponding times are defined and stored in the pulse sequence. While the simulation is executing, the time that has elapsed since the last iteration is calculated at the start of each loop-turn. The eventuated changes in the magnetisation during the elapsed time is calculated and the object s magnetisation state is updated. The nuclear magnetisation in every given location in the object is followed and updated separately. The simulation-resolution, describing the number of magnetisation compartments the object is divided in, is set by the user. 11

18 Several if-statements check whether any event should be executed. If there is an event occurring at the current time, these if-statements will recognize and executes those events. The different events that may occur are gradient amplitude changes, RF-pulses, sampling events and reconstruction. The display section will display the images while the video section save the current frame for the making of a video. There are several combinations to choose from regarding which images shall be displayed. The images available are the k-space trajectory, the single frequency component, the frequency sum (i.e. the object image), the pulse sequence and the object s transversal and longitudinal magnetisation. Which images being displayed are chosen by the user before running the simulation. Most effort, as far as programming is concerned, was given to the implementation of signal sampling, image reconstruction and new pulse sequences, blue sections in figure 8. Figure 8: The simulation procedure. After the magnetisation is updated and all events on the current time has been executed the display section is next. This section will display the various images, such as the k-space, the single frequency or the frequency sum. Which images being displayed are chosen by the user before the simulation starts. All events, with the corresponding times, are defined and stored in the pulse sequence. Load external object The T1, T2 and M0 maps, describing the object, are stored in separate files and the user chooses which file to be loaded before execution of the simulation. The file must contain all three maps for both water and fat along with the chemical shift for each given in ppm. The ppm for fat and water is set to 3.5 ppm and 0 ppm respectively. During setup, these maps are loaded in the data memory. 12

19 In vivo measurements and mapping In vivo measurements of a human brain were carried out on two volunteer test subjects. They were scanned with a Dixon sequence (see appendix) on an Ingenia 3T (Philips Best, the Netherlands) to acquire separate water and fat images. Several scans with different combinations of TE and TR was performed and the images from these different combinations were used to estimate T1, T2 and M 0 values. Scanning A multipoint Dixon turbo spin echo sequence with an asymmetric profile order, a TSE-factor of 8 and an acquisition matrix of 200x225 (frequency x phase) was used in all scans. A B0 scan, with same geometry as the Dixon scans, was performed for every test subject and geometry, i.e. transversal and sagittal. A B0 map, showing the heterogeneity of the magnetic field, could be used for simulating susceptibility effects. Parameters set for the scans can be found in the appendix section. Three and five Dixon scans, with different combinations of TE and TR, were carried out for the first and second test subject respectively. Two scans were added for the second test subject in an attempt to obtain slightly more accurate estimates of the T1, T2 and M0 values. The test subjects were scanned for both transversal and sagittal images. Separate images of water and fat for all scans were acquired. The various combinations of TE and TR for all scans are presented in table 2 and 3. The shortest and longest echo time available on the scanner was 6.8 ms and 53 ms respectively. Table 2: The combinations of TE and TR for the first test subject scanned. Separate fat and water images were acquired for every combination. Transversal & Sagittal Scan nr TR [ms] TE [ms] Table 3: The combinations of TE and TR for the second test subject, for which five scans were carried out. Separate water and fat images were acquired for all combinations. Transversal images Sagittal images Scan nr TR [ms] TE [ms] TR [ms] TE [ms] Mapping A non-linear fitting procedure for estimating T1, T2 and M 0 -values was performed. The different combinations of TE and TR along with the corresponding signal intensities were used as input. The fitting was carried out with a built-in function in Matlab called fit. The data were fitted to the function, M(TR, TE) = M + 1 e 13u 3V e 13v 3P 20 13

20 where M, TR and TE are the input values known prior to the fitting. A set of T1, T2 and M0 maps, describing a transversal slice was acquired for the first test subject, whereas a set of maps describing a sagittal slice was acquired from the images of the second subject. The fitting procedure was carried out with the data available from each dataset shown in table 2 and 3. Before fitting the model, some pre-processing of the images was required. First the standard deviation for the noise was calculated and multiplied with a factor to obtain a cut-off value. This cut-off value was then used to filter out the noise in the images, where all pixel values with a lower value than the cut-off value was set to zero. After this a mask was created to filter out those pixels that did not have a nonzero signal value in the same pixels for all the images inserted to the fitting function. After these steps were taken the fitting procedure was carried out. After the estimation, a constant was added to all the values in the estimated M0 map. This was done in order to obtain the correct ratio, 100 %, 82% and 70 % 8, between the proton densities for CSF, grey matter and white matter, respectively. The relaxation times in the T1 and T2 map for the fat tissue were set to 382 ms and 68 ms respectively 9. Videos and images With the set of maps inserted and all functions up and running, the performance of the simulation was tested. Images demonstrating geometric distortion, water-fat shift and Nyquist ghosting were formed as well as T1-, T2- and PD-weighted images. Simulations demonstrating increasing image resolution for increasing acquisition matrices were also executed. And finally, four videos showing both the EPI and the GE sequence, without any artefacts present, were recorded. 14

21 Results The resulting simulation is capable of scanning and reconstructing any object as well as simulating chemical shift. In order to execute an MRI simulation of an external object; T1, T2 and M0 maps of the object must be provided by the user. The scanned object is reconstructed as the scan progresses and can be shown on the subsecond scale. Execution of the simulation can also be done in the background, only presenting the resulting reconstructed image at the end of the scan. These following functions were added to make this possible; signal sampling, image reconstruction, a second calculation channel and an in vivo reference set of T1, T2 and M0 maps. Several images demonstrating the capabilities and performance of the simulation are presented throughout this section. Images originating from the different pulse sequences, with various sequence parameters and with different artefacts demonstrated are all present. Signal sampling A function that handles signal sampling has been added. This function determines whether a sample is acquired on the current time point or not. The data collected for each sample are the object s signal along with the corresponding position in k-space. A sampling event is executed at each time point in accordance with a binary vector, predefined in the sequence setup file. Image reconstruction A function that handles image reconstruction has also been added. This function reconstructs each sample right after it has been collected. Each sample is reconstructed to a single spatial frequency component which then is added to the sum of frequency components, successively building the image. As the frequency sum increases an image will slowly start to appear. Spatial resolution and the FOV of the reconstructed image is specified by the user in the sequence setup file. Sequences Two pulse sequences have been implemented within the simulation, one single shot EPI sequence and one linear Gradient Echo sequence, GE. Images of the cylinder scanned with both the EPI and GE sequence are illustrated in figure 9. The grey areas in figure 9a are water whereas the dark area is air. The cylinder in figure 9a is scanned with an EPI sequence without any susceptibility added to it. Figure 9b-c present the cylinder with an added susceptibility of 3 ppm, scanned with the EPI sequence (9b) and the GE sequence (9c). The bandwidth in the phase and frequency direction for the EPI and GE sequence respectively, was set to Hz/m. Frequency direction is left-right and the phase direction is up-down in figure 9a-b, whereas it is the opposite in figure 9c. The geometric distortion, due to susceptibility, is clearly visible in figure 9b-c. 15

22 Figure 9: Images of the cylinder with (b-c) and without (a) added susceptibility. The frequency and phase directions are left-right and up-down for (a)-(b) respectively. The opposite is true for (c). Image (a): EPI, 256x256 matrix, TE=128 ms. Image (b): EPI, 256x256, BW phase = 10000Hz/m, TE = 128 ms. Image (c): GE, 191x191, BW frequency = 10000Hz/m, TR = 10000ms, TE = 191 ms. In vivo data set Separate water and fat images were acquired for all scans given in table 2 and 3. Two sets of T1, T2 and M0 maps extracted from these images are presented in figure 10 and 11. Figure 10 presents the maps for the transversal slice from the first test subject, while figure 11 presents the maps for the sagittal slice from the second test subject. Figure 10a - c and figure 10d - e show the T1, T2 and M0 maps for the water and fat respectively. Figure 11 shows the maps in equal manner for the sagittal slice. Figure 10: The upper row shows the maps for the water tissue and the bottom row the maps for the fat tissue. T1 maps, (a) and (d), T2 maps, (b) and (e), and M0 maps, (c) and (f), were calculated from experimental data. These maps are one set of maps used in the simulation and which, in the context of the simulation, fully describe the object. 16

23 Figure 11: The upper row shows the maps for the water tissue and the bottom row the maps for the fat tissue. T1 maps, (a) and (d), T2 maps, (b) and (e), and M0 maps, (c) and (f), were acquired. These maps, in the context of the simulation, fully describe the object. Mean values and standard deviations of the estimated T1 and T2 relaxation times for the transversal and sagittal maps are presented in table 4. The values originate from regions of interest (ROIs) drawn in the water images, figure 10a-b and figure 11a-b. Table 4: Estimated T1 and T2 values for the transversal and sagittal images. The values in bold are the mean values for the different tissues in the images from figure The standard deviations are shown along with reference values in parenthesis. CSF Grey matter White matter Transversal T1 [ms] 4885 ± 385 (3120) ± 182 (1331) ± 43 (832) 11 T2 [ms] 2665 ± 1869 (160) ± 10 (110) ± 4 (79.6) 11 Sagittal T1 [ms] 7314 ± 1967 (3120) ± 386 (1331) ± 95 (832) 11 T2 [ms] 3771 ± 1918 (160) ± 17 (110) ± 5 (79.6) 11 Figure 12 demonstrates the increase in resolution for increasing acquisition matrix using the EPI sequence. The echo time was 50 ms for all images and the acquisition matrices sizes in figure a-d are 32x32, 64x64, 128x128 and 256x256. The spacing between samples, Dk, was equal for all the scans. 17

24 Figure 12: Images acquired from the EPI sequence with various acquisition matrices. The sizes, through a d, are 32x32, 64x64, 128x128 and 256x256. The echo time is 50 ms in all images. Figure 13 visualises the artefact water-fat shift and the Nyquist N/2 ghost simulated with the EPI sequence. The left image, showing the water-fat shift, was acquired with the bandwidth in the phasedirection set to Hz/m. The magnetic field strength was set to 1.5 T, given rise to a frequency difference for the fat of approximately 220 Hz. This led to the fat being shifted ~2,2 cm in the phase encoding direction, with the FOV set to 24 cm, as seen by the high intensity band across the image. The right image, showing the Nyquist ghost, was acquired with the shift set to 3Dk, which in this case led to a time shift of ms. Figure 13: The water-fat shift artefact, left image, as a result from an EPI simulation with the phase bandwidth set to 10000Hz/m and an echo time of 32 ms. The phase direction is up-down. The Nyquist ghost, right image, appearing as a result from an EPI simulation with an echo time of 25 ms and the shift set to 3Dk, corresponding to a time shift of ms. The acquisition matrix was set to 128x128 in both simulation. T1-, T2- and PD-weighted images originating from simulations using the GE sequence are presented in figure 14a-c. The acquisition matrix and resolution were both set to 191x191 for all scans in figure 14. Figure 14: The same object scanned with the GE sequence with various combinations of TE and TR. T1- weighted (a) with TE = 20ms and TR = 750ms, T2-weighted (b) with TE =145ms and TR = 6000ms and PDweighted (c) with TE = 20ms and TR = 6000ms. 18

25 The various arrangements of display windows available for the creation of a video are shown in figure The windows in figure 15 are, from left to right, the current transversal magnetisation configuration in the object, the current longitudinal magnetisation configuration in the object, the reconstructed frequency component from the most recent sample, the k-space trajectory and the frequency sum in its current state. Above these the pulse sequence is shown. Variations in the layout of these windows, of which the user can choose from, are presented throughout figure The layout presented in figure 18 shows those windows directly related to image formation. Figure 15: The image, from left to right, shows: the transversal magnetisation in the object, the longitudinal magnetisation in the object, the current spatial frequency component, the k-space trajectory and the frequency sum. The pulse sequence is displayed on the top. This display shows all windows available. Figure 16: This combination shows all windows from figure 15, except the longitudinal magnetisation component. 19

26 Figure 17: The k-space, current spatial frequency component and the frequency sum along with the pulse sequence. The top image shows the spatial frequency pattern in space, while the bottom image shows the frequency patter on top of the object being scanned. Figure 18: This layout shows the parts only concerning image formation. The layout from left to right: acquired raw-data in k-space, frequency pattern reconstructed from the most recent sample and the image composed of the frequency component sum. Video Four videos illustrating the signal sampling and image formation is uploaded to Vimeo and can be seen by following the links below. Video 1: A 32x32 EPI scan with the arrangement in figure 18; Video 2: A 128x128 EPI scan with the arrangement in figure 18; Video 3: A 31x31 GE scan with the arrangement in figure 15 (except the pulse diagram); Video 4: A 32x32 EPI scan with the arrangement in figure 16; 20

27 Discussion The simulation is now able to demonstrate and visualise signal sampling along with image reconstruction on a subsecond level during execution of a specified scan. It is also capable of demonstrating several interesting scenarios such as water-fat shift, Nyquist ghosting, half scan, geometric distortion and the production of T1-, T2- and PD-weighted images. Educational videos demonstrating any of these concepts can easily be created with the simulation. The different scenarios are available as user options and predefined before execution. Beside that two pulse sequences were implemented, more sequences with different sampling schemes can easily be implemented. However, if a sequence with a non-cartesian sampling scheme would be implemented some filtering may be required before the acquired raw-data are reconstructed with eq.19. This was not needed for the implemented sequences and the focus was laid on implementing the EPI and GE sequence owing to the reason that students most likely will encounter these sequences during an MRI course. The extra calculation channel, added for enabling demonstration of chemical shift, makes it possible to simulate Dixon scans in the future. Regarding the different layout arrangements for the video, figure 15-18, I would recommend using figure 18 as a start to showing image formation to students. This arrangement has the fewest windows and is therefore the easiest to comprehend for a student new to MRI. As their knowledge in the field of MRI increases, the pulse diagram and the transversal component can be added, as seen in the arrangement in figure 16. A student who is able to understand all that is happening in figure 16 and how the windows correlate with each other, has reached a higher level of knowledge regarding the image formation of MRI. Dixon sequences were chosen for the in vivo measurement to acquire separate water and fat images to later have the possibility to demonstrate the water-fat shift artefact. With the data sets, acquired from the in vivo scans, inserted and used in the simulation a more interesting object than a coaxial cylinder can be scanned and reconstructed. With the two set of maps of the transversal and sagittal slice now available in the simulation, the demonstration of image formation will be more interesting and can hopefully help bringing students attention to it. When looking closer to figure 14 an artefact is apparent across the middle of the images. It is a small stripe with alternating intensities, which only appears during execution of the GE sequence. At present I have no explanation for the source of this artefact. An effort to find the bug in the code, responsible for this artefact has been made without any success. As the artefact does not appear in the EPI images, the source for the artefact most certainly originates somewhere in the setup file for the GE sequence. Future work includes the rewriting of this sequence in order to fix this problem. The echo time is currently not a user option and instead a consequence of the chosen bandwidth, acquisition matrix and the time between the RF-pulse and the start of the first sampling event. There is a possibility to indirectly change the echo time by changing these parameters and then check the effect on the echo time. This must be done manually and is quite cumbersome. Implementation of the feature of choosing the echo time will also be done in the future. B0 scans were performed on all test subjects. The intention was to use these acquired B0 maps in the simulation to enable demonstration of geometric distortion due to susceptibility effects. This can be done when the heterogeneity of the magnetic field in each voxel of the simulated object is known. However, we were unable to interpret the values in the B0 maps. There lies a possibility that the dicomtags for the slope and intercept were incorrect and/or that an unknown scaling factor was used for the intercept that we were unable to find. If a correct B0 map, however, is provided to the simulation, the demonstration of the susceptibility effect for the external objects is already implemented. 21

28 The geometric distortion in figure 9b-c does not appear as we expected. The mismapping of the middle area of the cylinder should only be stretched out in the up-down direction. However, it is also stretched out in the left-right direction. The susceptibility in the cylinder in the middle where the air and the water meet is calculated with a model according to Chu et al. 12 This susceptibility was already implemented when this project started and unfortunately there has been no time to review it. The underlying mechanism behind this effect was not further investigated due to time limitations and the deviation from the main scope of the project. The estimated values of T1 and T2 for grey and white matter in the transversal slice and the T2 values in the sagittal slice coincide well with the values measured by Wansapura et al. 11, see table 4. Estimated T1 values for CSF, grey and white matter and T2 values for CSF, however do not coincide well with reference data. No article with reference data concerning T1 and T2 values for the CSF was found, instead reference-data from the Philips Ingenia 3T scanner was used. The fact that it was necessary to add a constant to acquire correct proton densities ratios, indicates an inconsistency regarding the dicom scale values. This can be an explanation for the inconsistencies recorded in the T1- and T2-values. All the mean values presented in table 4 originate from ROIs drawn by hand in the maps. This procedure can introduce a bias error, meaning that the values presented in table 4 may not be the optimal values representing the maps. A point should be made that it was not our top priority to obtain highly correct values for the maps. The main goal for the mapping procedure was to acquire maps with values that were good enough to be used in the simulation for illustrating image formation. This has been achieved. Despite the various issues discussed above the main goal, which was to add signal sampling and image formation and thereby visualise these concepts, has been reached. The simulation is now fully capable of visualisation of image formation and a few videos illustrating this has been produced. All students are individuals with different preferred ways for acquiring information. Some may prefer to read text books, while other may favour solving equations or listen to spoken presentations as their preferred way to acquire knowledge. I think the educational videos presented in this project will benefit all these individuals. One individual can look at the videos and reach a level of understanding without the need of solving equations, whereas others can find it helpful to see what the equations really describe. Hopefully the simulation and the videos will be of good used for the teachers in their lectures and thereby give students all the benefits possible from this project. 22