University of Moratuwa PC - BASED IMAGE RECONSTRUCTION FOR MR IMAGING Dissertation submitted in partial fulfilment for the degree of Master of Engineering in Electronic and Telecommunication e®)OOQ. S. N. Hettiwatte 0 7 2 3 5 7 University of Moratuwa June 2000 7 2 3 5 7 The work presented in this dissertation has not been submitted for the fulfilment of any other degree. S. N. Hettiwatte Candidate Dr. J. A. K. S. Jayasinghe Supervisor Mr. B. S. Samarasiri Co-Supervisor 1* Acknowledgements I wish to convey my gratitude to all those persons who supported me in carrying out this project. In particular, I wish to thank my supervisor, Dr. J. A. K. S. Jayasinghe for the guidance, advice and the overall supervision of the project and my co-supervisor, Mr. B. S. Samarasiri, for the literature provided during Medical Electronics classes. Those printed materials were very useful during the literature review phase of this project. I also wish to thank Dr. Pawel F. Tokarczuk of Imaging Science and Biomedical Engineering Research Group at the University of Manchester for sending me some MRI data from Prof. Kunio Takaya's office at the University of Saskatchewan in Canada. Without those data my project would not have taken off the ground. Finally, I wish to convey my gratitude to my employer, the Open University of Sri Lanka, for sponsorship. Abstract Reconstruction is the abstract rebuilding of something that has been torn apart. In the medical imaging context, it is often necessary to acquire data from methods that essentially tear data apart in order to be able to view what is inside. Also, a big part of reconstruction is then being able to view, or visualise, all the data once it is been put back together again. In MRI, the imaging device acquires data of a cross-sectional plane of the tissue being studied. The process of reconstruction then involves rebuilding of the cross-sectional view of that plane from the acquired data. Usually, the imaging device acquires data from a number of cross-sectional planes of the tissue being examined. Then, in reconstruction, all these planes are stacked back together to obtain a complete picture of the tissue. Image reconstruction in MRI is usually performed by dedicated hardware. A typical system usually consists of multi-processors, application specific integrated circuits (ASIC) and uses parallel processing techniques. These systems are capable of high­ speed image reconstruction, both 2D and 3D, high resolution image display and manipulation. Obviously, these systems are fairly expensive. In this project a general purpose PC operating on Microsoft® Windows® 98 operating system was used to reconstruct a 2D image of a slice through the human head, using head scan data available from a MRI scanner. The FID signals from the scanner were available as projection data, which have been collected by suitably rotating the magnetic gradients. The filtered back-projection algorithm with nearest neighbour interpolation scheme was used in the reconstruction program, which was written in Matlab®. The resulting image from this system is acceptable. With the ever-increasing processor power of PC's and cost of PC's coming down, PC-based image reconstruction would find its way in a cost effective MRI system. i List of Figures 1. A typical MRI system 1 2. Typical MR imaging systems in use today 4 3. Randomly oriented nuclear magnetic moments 5 4. Magnetic moments in the presence of an external magnetic field 6 5. RF energy at the Larmor frequency acts as a second magnetic field 7 6. Free Induction Decay (FID) signal induced in the receiver coil 7 7. Flipping a magnetic moment 8 8. Three different gradients are used to measure the FT of an object 11 9. Projection geometry 14 10. Projection of an object at an angle 9 15 11. Frequency response of filter 19 12. Transfer function of filter 22 13. Flow chart of filtered back-projection algorithm 26 14. Frequency response of a Ram-Lak filter obtained using Matlab 27 15. Frequency response of filters obtained using Matlab 28 16. FID projection data 29 17. Reconstructed image with the filter used 30 ii List of Tables 1. Comparison of time for reconstruction 31 iii List of Abbreviations Used A/D Analog to Digital ASIC Application Specific Integrated Circuit CT Computerised Tomography DFT Discrete Fourier Transform EPI Echo Planar Imaging FFT Fast Fourier Transform FID Free Induction Decay FT Fourier Transform GB Giga Bytes GUI Graphical User Interface IFFT Inverse Fast Fourier Transform KB Kilo Bytes MB Mega Bytes MMX® Multi Media Extension MR Magnetic Resonance MRI Magnetic Resonance Imaging NMR Nuclear Magnetic Resonance NMRI Nuclear Magnetic Resonance Imaging PC Personal Computer RF Radio Frequency SIMD Single Instruction Multiple Data SNR Signal to Noise Ratio ZP Zero Pad Contents Abstract List of Figures List of Tables List of Abbreviations Used 1. Introduction 1.1 Project Objectives 1.2 PC Configuration 1.2.1 Operating System 1.2.2 Application Software 2. Brief History on MR Imaging and Present Systems 3. Basic Theory of Magnetic Resonance 3.1 Magnetic Moments 3.2 RF Magnetic Field 3.3 The Free Induction Decay (FID) Signal 3.4 Magnetic Field Gradient 3.5 Frequency Encoding 3.6 Slice Selection 4. Current Reconstruction Practice 4.1 Fourier Imaging and Spin Warp Imaging 4.2 Zeugmatography 4.3 Echo Planar Imaging (EPI) 5. Projection Reconstruction as used in this Project 5.1 Fourier Slice Theorem 5.2 Derivation of the Filtered Back-Projection Algorithm 5.3 Discrete Representation 19 5.4 Implementation on a Personal Computer (PC) 21 5.5 Implementation using Matlab 27 6. Results 29 7. Discussion and Conclusions 32 7.1 Conclusions 32 * 7.2 Scope for Further Work 32 References 34 Appendix I Matlab m-file for Implementing Filtered Back-Projection Algorithm 36 Appendix II GUI Designed with Matlab 39 GUI Layout and Call-Backs 40 i f Appendix III Matlab Functions used in the Program and GUI 41 vi