1 A look at the utility of pulsed NMR Katherine Magat and Vasudev Mandyam Physics 173 Spring 2004 Prof Kleinfeld Introduction Pulsed nuclear magnetic resonance NMR was first introduced in the 1940 s by Felix Bloch and Edward Purcell Bloch and Purcell developed methods for determining the magnetic moments of nuclei in solids and liquids One can use pulsed NMR to identify characteristic properties of various samples More recently the technique of functional magnetic resonance imaging fMRI has contributed a lot to non invasive brain research Our goal has been to use pulsed NMR to detect the difference between oxygenated and deoxygenated blood The difference between these two blood states arises from their unique magnetic properties which can be probed with our apparatus Along the way we examined glycerin and water samples as well in order to refine our measurement techniques and learn more about NMR Background Nuclear spins The nuclei of certain elements have a spin angular momentum associated with a magnetic moment In the z presence of an external magnetic field the orientations of the spins will either align or Mo Bo anti align with the field with a majority of the spins in the aligned state 5 Each orientation corresponds to a particular energy level and NMR involves transitions between these energy levels In our case we are measuring y the spins of water protons Each spin moment precesses around Fig 1 alignment of spins the axis of the magnetic field see Fig 1 The x frequency of precession called the Larmour frequency is proportional to the strength of the field f B0 where is the gyromagnetic ratio of the material and B0 is the static field strength Resonance A resonance condition occurs when there is an RF field applied transverse to the static field at the precession frequency The transient field will rotate the ensemble of magnetic moments away from the static field axis The static field is assumed to be in the z direction the pulsed field thus rotates the magnetization into the xy plane see Fig 2 3 2 Fig 2 Upon application of an RF pulse net magnetization is knocked out of the z axis and gains a component in the xy direction Free Induction Decay With the absorption of the RF energy the population of nuclei in the equilibrium state decreases while the population in the higher energy state increases until a saturation level is reached The magnetization vector now lying in the xy plane quickly spreads out and decays due to longitudinal and transverse relaxation effects to be discussed later When looking at a signal after an RF pulse one observes this decay known as the free induction decay or FID see Fig 3 Fig 3 free induction decay We speak of delivering RF pulses to the system These are short bursts of RF energy which rotate the spins by a certain amount away from the z axis For instance a 90o pulse will knock the spins from the z direction into the xyplane A 180o pulse will knock the spins all the way to the z direction The spins will then begin to decay back to their original orientation The pulse s angle is determined by its duration a o o 180 pulse is thus twice as long as a 90 pulse There are two relaxation processes involved in spin decay the longitudinal or spin lattice relaxation and the transverse or spin spin relaxation First in longitudinal relaxation the z component of the magnetization exponentially decays to its equilibrium value with characteristic time constant T1 see Fig 4 3 Fig 4 T1 relaxation The magnetization moment shown as being spread out over the entire xy plane decays back to its original orientation along the z direction Transverse relaxation refers to the exponential decay of the xy component of the net magnetic moment and is characterized by time constant T2 There are actually two sub 3 processes at work in T2 namely T2 inhomogeneous and T2 pure T2 pure is often just called T2 These add to form T2 1 T2 1 T2 pure 1 T2 inhomogeneous Note that an FID results from a combination of T2 and T1 effects T2 inhomogeneous arises from local inhomogeneities in the static B field Once the spins have been knocked away from the z axis they begin to precess with a given frequency However some moments experience different local field strengths due to an imperfect field and thus precess faster or slower than others The net result is that the spins de phase and spread apart in the xy plane T2 inhomogeneous is the dominant effect The pure T2 effect takes a lot longer than the inhomogeneous one and is a result of random molecular interactions These break up the alignment of the spins also causing a net de phasing in the xy plane see Fig 5 3 Fig 5 de phasing of magnetization in the xy plane which is the T2 effect Now we can look at how these relaxation times are measured T1 measurement uses a 90 90 pulse sequence as seen in the following figure Fig 6 Pulse sequence for T1 Two 90o pulses are delivered in succession The first pulse kicks the spins into the xyplane after which they begin to decay The second pulse rotates them another 90 degrees leaving only a small xy component remaining One can measure the FID amplitude of the second pulse as a function of the time between pulses Notice that the FID will approach a maximum value with longer and longer delay times Measuring T2 is slightly more complicated In order to eliminate T2inhomogeneous one uses the spin echo technique Figs 6 7 3 Here a 90o pulse knocks the spins into the xy plane at which point they start to de phase After a certain 4 time t a 180o pulse rotates all the spins over keeping them in the xy plane Spins that were precessing faster are now behind of the rest and spins that were precessing slower are now ahead of the rest Therefore after an equivalent time t the spins will all catch up to each other creating a large signal called the spin echo We measure this echo as a function of the time between the pulses giving us a value for T2 Fig 6 Diagram of de phased magnetization undergoing 180 pulse and then re phasing Fig 7 Pulse sequence for T2 Diffusion Typically T1 and T2 are first order exponential graphs of the form Y A B Exp t T However in the case of less viscous fluids such as water diffusion causes additional effects6 Over the course of a measurement a given water proton will move within the sample thus experiencing different local field strengths This causes a change in precession frequency and thus a change in the signal To compensate for this one can introduce a cubic term into the equation Y A B