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The Role of Diffusion in NMR Proton Relaxation Enhancement by Ferritin

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The Role of Diffusion in NMR Proton Relaxation Enhancement by Ferritin DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Michael A. Boss, B.S. Physics, M.S. Physics Graduate Program in Physics The Ohio State University 2010 Dissertation Committee: Professor P. Chris Hammel, Advisor Professor Klaus Honscheid Professor Thomas Lemberger Professor Nandini Trivedi c Copyright by Michael A. Boss 2010 Abstract By using binary solutions of water and glycerol, we controlled diffusion so as to better understand its role in the relaxation rate enhancement of protons in the vicinity of ferritin at 7 tesla. The slower diffusion rates and higher external magnetic field used in these experiments are more consistent with the conditions expected in MRI experiments. New data was obtained on the diffusion coefficients of water and glycerol in binary solutions with relatively dilute amounts of glycerol. The effects of chemical exchange in such systems was also quantified. Two main relaxation mechanisms have been proposed for protons in the vicinity of ferritin: an outer-sphere mechanism (OS) in which spins diffuse past ferritin and experience a changing Larmor frequency by moving through the ferritin's magnetic field, and a proton exchange dephasing mechanism (PE), where protons temporarily reside on the surface of the ferritin core and sample a single, enhanced, Larmor frequency. At high-field, the OS mechanism becomes increasingly important because of a quadratic dependence on field strength, versus linear for the competing mechanism involving proton exchange. It was found that the relaxation enhancement of protons of both water and glycerol in the presence of ferritin was inversely proportional to their diffusion coefficients, in agreement with the OS model of relaxation enhancement. The strength of the relaxation enhancement on inverse diffusion coefficient was weaker for slow-diffusing glycerol than for water: glycerol molecules spent more time in a weaker magnetic field, indicating that glycerol did not approach the ferritin core as closely as water, ii potentially answering questions about molecular intake into the ferritin structure. The results of these experiments have important implications for the quantification of brain iron in vivo. iii Para mis abuelos. iv Acknowledgments I have many people to thank for many reasons. I begin with my parents, because they began me, and have been behind me during all the trials and tribulations of graduate school. Thank you to my advisor, Chris Hammel, who took me in when things were looking most dire for continuing my research in NMR, and has guided me in understand what it means to be a physicist and a good scientist. Thank you to Denis Pelekhov for his assistance throughout the years, and to Yuri Obukhov for many fruitful discussions of NMR, in particular regarding chemical exchange. Thank you to Susan Olesik for providing me with the opportunities to teach outside of OSU, giving me valuable experience both professionally and in terms of social awareness, while also giving me valuable financial support to continue my studies. I am grateful to the many students with whom I have worked on problems, both in class and in the lab, and there are more than I can name here. To Seongjin Choi, I owe much for the many conversations about NMR and MRI we had over the years. Thanks to Don Burdette and Jeff Stevens for helping maintain my sanity by making me laugh when times were tough. To KC Fong, Steve Avery, and James Morris for general physics discussions and help with LATEX. To my hundreds of FEH students who let me practice explaining physics for hundreds of hours. To Kay Chapman for helping me find references in the Health Sciences Library. And to all my fellow graduate students who have have been such good listeners and friends. Thank you. v Vita October 25, 1977 . Born - Bedford, Ohio May 2000 . .B.S. in Physics, Cum Laude, Case Western Reserve University, Cleveland, Ohio May 2002 . .M.S. in Physics, University of Illinois, Urbana-Champaign September 2002-present . PhD student in Physics, The Ohio State University, Columbus, OH Fields of Study Major Field: Physics vi Table of Contents Page Abstract . ii Dedication . iv Acknowledgments . .v Vita......................................... vi List of Figures ..................................x List of Tables ................................... xii Chapters 1 Introduction and Overview 1 1.1 Motivation: Non-invasive Detection and Quantification of Iron . 1 1.2 Nuclear Magnetic Resonance Overview . 3 1.3 Ferritin: Role, Physical and Magnetic Properties . 5 1.4 Ferritin-induced Relaxation Enhancement . 11 1.4.1 Outer-sphere mechanism . 11 1.4.2 Proton exchange mechanism . 13 1.4.3 Two relaxation mechanisms . 14 1.5 Chapter Outline . 16 2 Nuclear Magnetic Resonance 19 2.1 Signal Source- Equilibrium Polarization . 19 2.2 Excitation and Detection . 21 2.2.1 Excitation and the rotating frame . 22 2.2.2 Signal detection . 24 2.3 Magnetization: Equations of Motion . 24 2.4 Physics of Relaxation . 25 2.4.1 Autocorrelation function and spectral density . 26 2.5 Spectroscopy . 28 2.6 Experimental Techniques . 29 2.6.1 Spin echoes . 31 2.6.2 Inversion recovery . 33 2.6.3 Saturation recovery . 33 vii 2.6.4 Carr-Purcell . 35 2.6.5 Carr-Purcell-Meiboom-Gill . 36 2.7 Diffusion . 37 2.7.1 Pulsed Gradient Spin Echo (PGSE) . 38 2.7.2 Pulsed Gradient Stimulated Echo (PGStE) . 40 3 Magnetic Resonance Apparatus 42 3.1 Probe Overview . 42 3.1.1 Radiofrequency and gradient board assembly . 43 3.1.2 Electronics . 44 3.2 Radiofrequency Coils . 45 3.2.1 Construction . 45 3.2.2 Tuning . 47 3.3 Gradients . 48 3.3.1 Coil design and modeling . 48 3.3.2 Assembly material . 50 4 Diffusion Data 53 4.1 Introduction and Premise . 53 4.2 Discerning Mechanisms of Dephasing: The Role of Diffusion . 54 4.2.1 Relaxation mechanism dependencies . 55 4.2.2 In vivo environment . 55 4.3 Controlling and Measuring Diffusion . 57 4.3.1 Extracting diffusion coefficients . 57 4.3.2 Water-glycerol samples . 60 4.4 Gradient Calibration . 61 4.5 Experimental Diffusion Data . 64 4.5.1 Pure solvents: water and glycerol . 64 4.5.2 Diffusion in binary mixtures . 66 4.6 Summary of Experimental Results . 71 5 Relaxation Data 76 5.1 Introduction and Premise . 76 5.2 Methodology and Experimental Results . 77 5.2.1 Longitudinal relaxation and saturation recovery . 77 5.2.2 Transverse relaxation (R2) and fast CPMG sequence . 81 5.2.3 Distinguishing water and glycerol relaxation . 89 5.2.4 Chemical exchange and T2 dispersion . 89 6 Discussion 98 6.1 Relaxation Enhancement, ∆R2 ..................... 98 6.2 ∆R2 as a Function of OH concentration . 101 6.3 ∆R2 as a Function of Diffusion . 102 6.3.1 Water enhancement . 102 viii 6.3.2 Glycerol enhancement . 102 6.3.3 Water vs glycerol- distance of closest approach . 104 6.4 Conclusions . 106 ix List of Figures Figure Page 1.1 Perl's stain and MRI of the brain stem of a 44 year old male. 4 1.2 Physical structure of apoferritin . 6 1.3 Ferritin magnetic structure . 8 1.4 Ferritin- canted AFM sublattices and defects . 9 1.5 Ferritin- magnetization vs applied field . 10 1.6 R2 vs B0 .................................. 15 2.1 Zeeman splitting . 20 2.2 Precession of the magnetic moment in an external field . 22 2.3 Magnetization in the rotating frame . 23 2.4 Spectral density plot . 28 2.5 NMR spectrum of glycerol . 29 2.6 Free induction decay of water. 30 2.7 Spin echo pulse sequence . 31 2.8 Spin echo rephasing . 32 2.9 Inversion recovery pulse sequence . 33 2.10 Saturation recovery pulse sequence . 34 2.11 Carr-Purcell train . 36 2.12 CPMG pulse sequence . 37 2.13 Effects of imperfect 180◦ pulse and correction via CPMG sequence . 38 2.14 PGSE sequence . 39 2.15 PGStE sequence . 41 3.1 Assembled NMR probe . 43 3.2 Assembled NMR probe . 44 3.3 Bare RF board . 46 3.4 RF board with electronic . 47 3.5 Gradient board wire geometry . 49 3.6 Gradient board magnetic field . 50 3.7 Gradient board constructed with thermal epoxy . 52 x 4.1 3 dimensional representation of a glycerol molecule. 58 4.2 Gradient calibration . 63 4.3 Diffusion of pure glycerol at room temperature . 67 4.4 Diffusion of pure water at room temperature. 68 4.5 Water diffusion compared to literature . 69 4.6 Glycerol diffusion compared to literature . 70 4.7 Diffusion in a binary mixture of water and glycerol . 72 4.8 Diffusion in a binary mixture of water and glycerol with ferritin . 73 4.9 Water diffusion as a function of composition . 74 5.1 Saturation recovery data, water . 79 5.2 Saturation recovery data, glycerol . 80 5.3 Saturation recovery for a water-glycerol mixture . 82 5.4 CPMG results of water . 86 5.5 CPMG results of glycerol . 87 5.6 Effects of long τCP on water-glycerol CPMG experiment . 90 5.7 Effects of long τCP on water-glycerol CPMG experiment . 91 5.8 Transverse relaxation in water-glycerol with ferritin . ..
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