1. Magnetic Resonance Imaging Glenn Pierce, King’s College London, Department of Physics Introduction Edward Purcell and Felix Bloch were both awarded the Nobel Prize in 1952 for their independent discovery of Nuclear Magnetic Resonance also known as NMR. In 1971 Raymond Damadian showed that the nuclear magnetic relaxation times of tissues and tumours differed. This allowed magnetic resonance to be used for the detection of disease. The force that acts upon the dipole is proportional to the strength of the field in which it is placed and the magnitude of the moment. The proton has a large magnetic moment and has a strong tendency to align with an external magnetic field. Precession If the particles were perfect dipoles the particle moments would all line up with the external field to minimise the energy. However, In the case of nuclei with spin, the randomly orientated dipole moments precess around the axis of the magnetic field. The angle between the external field and the spin axis of the particle depends simply upon the initial spin axis before the external field is applied. The rate at which this precession occurs is known as the Lamor relationship and is given by the equation If the particle absorbs the energy corresponding to the Lamor frequency the nuclei can undergo a transition between the two energy states. A particle in the lower energy state that absorbs a photon can undergo transition to the higher energy state. Therefore the energy corresponding to the Lamor frequency is equal to the difference between the two energy states of the system. In clinical MRI, is typically between 15 and 80 MHz for hydrogen imaging and thus the frequency of the photon is in the radio frequency (RF) range. This is the resonance in MRI. Nuclei have the property of spin. Spin is a fundamental intrinsic property of particles. The spin of an electrically charged particle which moves creates a magnetic moment. The hydrogen nucleus is the most important nucleus in the field of NMR as the proton has a large magnetic moment and has a strong tendency to align with an external magnetic field. It is also highly abundant in the water and fat of the human body. Hydrogen nuclei magnetic moments are randomly oriented in the absence of an external magnetic field and are considered to have a net magnetization of zero. Once hydrogen protons are placed in the presence of an external magnetic field these alignments are quantized. In the case of protons two alignments are possible. They will orientate parallel or anti-parallel to the field. This is shown in figure 1. Figure 2 shows the energy separation between the two spin states of the nuclei in a magnetic field. It shows that spin states which are orientated towards being parallel with the magnetic field are in a lower energy state than those states that are anti-parallel to the magnetic field. Here beta is the magnetic field and gamma is the gyromagnetic ratio that depends on the type of nucleus. If the Lamor frequency is negative then the precession is clockwise when looking against the magnetic field as show in figure 3. For a positive Lamor frequency the direction of precession is in the anti clockwise direction. The spins in thermal equilibrium are distributed among the two states according to the Boltzmann distribution. The ratio of the nuclei in the spin-down state to the spin up state is given by The upper and lower energy spin states are almost equally populated with only a very small excess in the lower energy state. It is only measurable because of large number of hydrogen nuclei in organic tissue. T1 Process When the system is in equilibrium the net magnetization vector aligns with the direction of the applied magnetic field. This is known as the equilibrium magnetization. If the system is exposed to energy of a frequency equal to the energy difference between the spin states the net magnetization can be changed. The energy absorbed by a nucleus must exactly equal that defined by the Lamor frequency. After the net magnetization is changed it will eventually return to its equilibrium value. For a nucleus to transition from the high energy state to that of the low energy state a discrete amount of energy has to be transferred to the lattice of the sample. The energy difference between the low and high energy states results in a greater probability of transition to the low energy state. The time constant which describes how the longitudinal magnetization returns to equilibrium is called the spin lattice relaxation time, also known as T1 relaxation time or longitudinal relaxation. The rate at which the relaxation occurs is given by T2 Process T1 and T2 processes occur at the same time. As stated when an external magnetic field is applied to a sample the nuclei will precess around the external field. After an radio frequency pulse, hydrogen nuclei will be spinning in unison or in-phase with each other. As the magnetic fields of all the nuclei interact with each other, energy is exchanged between those nuclei. As each of the nuclei is experiencing a slightly different magnetic field and rotates at its own Larmor frequency an exponential decrease or decay in transverse magnetization occurs. This process is know as T2 relaxation or spin-spin relaxation as the decay is the result of the exchange of energy between spinning hydrogen nuclei, as T2 decay occurs, the MR signal dies out. Due to T1 and T2 relaxation, it is possible differentiate between various tissues in the body. Various tissues have different T1 and T2 values. For example due to the slow molecular motion of fat nuclei, T1 relaxation occurs more rapidly than water nuclei. This is due to the fact that water nuclei do not give up their energy to the lattice as quickly as fat due to the high kinetic energy of the water molecules. Figure 6 shows two MRI images, one shows a T1 weighted image and the other T2 weighted. Fig. 1 Shows how hydrogen nuclei align themselves along or against an external magnetic field. Fig 2 shows the energy differerence for hydrogen nuclei that are aligned in opposing directions in a magnetic field. As the magnetic field strength increases so does the energy separation between states. Fig 3 shows the precession of a proton at an angular velocity w around an external magnetic field B. Fig 4 shows the T1 recovery for two different tissues. Tissue A is shown to return to the equilibrium magnetism faster than tissue B. Fig 5 shows the T2 decay rate for two different tissues. The fat sample here is shown to have a faster T2 decay rate than cerebrospinal fluid. Fig 6 shows two images. The first is a T1 weighted image that is used to compare T1 relaxation times between tissues. The second is T2 weighted that is used to compare T2 relaxation times between tissues. Spin Tissue Contrast Literature cited Basic Priciples of MRI, Margaret M King, http://www.erads.com/mrimod.htm, Last accessed 11-06-04 Malcolm H. Levit. Spin Dynamics Basics of Nucler Magnetic Resonace. John Wiley and Sons, 1998. Acknowledgments I would like to thank Alan Michette for allowing me to undertake the course "Xrays and Imaging" at Kings College.