physics of magnetic resonance imaging physics of magnetic resonance imaging the physics of magnetic resonance imaging (mri) concerns fundamental physical considerations of mri techniques and technological aspects of mri devices. mri is a medical imaging technique mostly used in radiology and nuclear medicine in order to investigate the anatomy and physiology of the body, and to detect pathologies including tumors, inflammation, neurological conditions such as stroke, disorders of muscles and joints, and abnormalities in the heart and blood vessels among others. contrast agents may be injected intravenously or into a joint to enhance the image and facilitate diagnosis. unlike ct and x-ray, mri uses no ionizing radiation and is, therefore, a safe procedure suitable for diagnosis in children and repeated runs. patients with specific non-ferromagnetic metal implants, cochlear implants, and cardiac pacemakers nowadays may also have an mri in spite of effects of the strong magnetic fields. this does not apply on older devices, and details for medical professionals are provided by the device's manufacturer. modern 3 tesla clinical mri scanner. certain atomic nuclei are able to absorb and emit radio frequency energy when placed in an external magnetic field. in clinical and research mri, hydrogen atoms are most often used to generate a detectable radio-frequency signal that is received by antennas in close proximity to the anatomy being examined. hydrogen atoms are naturally abundant in people and other biological organisms, particularly in water and fat. for this reason, most mri scans essentially map the location of water and fat in the body. pulses of radio waves excite the nuclear spin energy transition, and magnetic field gradients localize the signal in space. by varying the parameters of the pulse sequence, different contrasts may be generated between tissues based on the relaxation properties of the hydrogen atoms therein. when inside the magnetic field (b0) of the scanner, the magnetic moments of the protons align to be either parallel or anti-parallel to the direction of the field. while each individual proton can only have one of two alignments, the collection of protons appear to behave as though they can have any alignment. most protons align parallel to b0 as this is a lower energy state. a radio frequency pulse is then applied, which can excite protons from parallel to anti-parallel alignment, only the latter are relevant to the rest of the discussion. in response to the force bringing them back to their equilibrium orientation, the protons undergo a rotating motion (precession), much like a spun wheel under the effect of gravity. the protons will return to the low energy state by the process of spin-lattice relaxation. this appears as a magnetic flux, which yields a changing voltage in receiver coils to give the signal. the frequency at which a proton or group of protons in a voxel resonates depends on the strength of the local magnetic field around the proton or group of protons, a stronger field corresponds to a larger energy difference and higher frequency photons. by applying additional magnetic fields (gradients) that vary linearly over space, specific slices to be imaged can be selected, and an image is obtained by taking the 2-d fourier transform of the spatial frequencies of the signal (k-space). due to the magnetic lorentz force from b0 on the current flowing in the gradient coils, the gradient coils will try to move producing loud knocking sounds, for which patients require hearing protection. history the mri scanner was developed from 1975 to 1977 at the university of nottingham by prof raymond andrew frs frse following from his research into nuclear magnetic resonance. the full body scanner was created in 1978. nuclear magnetism subatomic particles have the quantum mechanical property of spin. certain nuclei such as 1h (protons), 2h, 3he, 23na or 31p, have a non–zero spin and therefore a magnetic moment. in the case of the so-called spin-1⁄2 nuclei, such as 1h, there are two spin states, sometimes referred to as up and down. nuclei such as 12c have no unpaired neutrons or protons, and no net spin; however, the isotope 13c does. when these spins are placed in a strong external magnetic field they precess around an axis along the direction of the field. protons align in two energy eigenstates (the zeeman effect): one low-energy and one high-energy, which are separated by a very small splitting energy. resonance and relaxation quantum mechanics is required to accurately model the behaviour of a single proton. however, classical mechanics can be used to describe the behaviour of an ensemble of protons adequately. as with other spin 1 / 2 particles, whenever the spin of a single proton is measured it can only have one of two results commonly called parallel and anti-parallel. when we discuss the state of a proton or protons we are referring to the wave function of that proton which is a linear combination of the parallel and anti-parallel states. in the presence of the magnetic field, b0, the protons will appear to precess at the larmor frequency determined by the particle's gyro-magnetic ratio and the strength of the field. the static fields used most commonly in mri cause precession which corresponds to a radiofrequency (rf) photon. the net longitudinal magnetization in thermodynamic equilibrium is due to a tiny excess of protons in the lower energy state. this gives a net polarization that is parallel to the external field. application of an rf pulse can tip this net polarization vector sideways (with, i.e., a so-called 90° pulse), or even reverse it (with a so-called 180° pulse). the protons will come into phase with the rf pulse and therefore each other. the recovery of longitudinal magnetization is called longitudinal or t1 relaxation and occurs exponentially with a time constant t1. the loss of phase coherence in the transverse plane is called transverse or t2 relaxation. t1 is thus associated with the enthalpy of the spin system, or the number of nuclei with parallel versus anti-parallel spin. t2 on the other hand is associated with the entropy of the system, or the number of nuclei in phase. when the radio frequency pulse is turned off, the transverse vector component produces an oscillating magnetic field which induces a small current in the receiver coil. this signal is called the free induction decay (fid). in an idealized nuclear magnetic resonance experiment, the fid decays approximately exponentially with a time constant t2. however, in practical mri there are small differences in the static magnetic field at different spatial locations ("inhomogeneities") that cause the larmor frequency to vary across the body. this creates destructive interference, which shortens the fid. the time constant for the observed decay of the fid is called the t*2 relaxation time, and is always shorter than t2. at the same time, the longitudinal magnetization starts to recover exponentially with a time constant t1 which is much larger than t2 (see below). in mri, the static magnetic field is augmented by a field gradient coil to vary across the scanned region, so that different spatial locations become associated with different precession frequencies. only those regions where the field is such that the precession frequencies match the rf frequency will experience excitation. usually, these field gradients are modulated to sweep across the region to be scanned, and it is the almost infinite variety of rf and gradient pulse sequences that gives mri its versatility. change of field gradient spreads the responding fid signal in the frequency domain, but this can be recovered and measured by a refocusing gradient (to create a so-called "gradient echo"), or by a radio frequency pulse (to create a so-called "spin-echo"), or in digital post-processing of the spread signal. the whole process can be repeated when some t1-relaxation has occurred and the thermal equilibrium of the spins has been more or less restored. the repetition time (tr) is the time between two successive excitations of the same slice. typically, in soft tissues t1 is around one second while t2 and t*2 are a few tens of milliseconds. however, these values can vary widely between different tissues, as well as between different external magnetic fields. this behavior is one factor giving mri its tremendous soft tissue contrast. mri contrast agents, such as those containing gadolinium(iii) work by altering (shortening) the relaxation parameters, especially t1. imaging imaging schemes a number of schemes have been devised for combining field gradients and radio frequency excitation to create an image: 2d or 3d reconstruction from projections, such as in computed tomography. building the image point-by-point or line-by-line. gradients in the rf field rather than the static field. although each of these schemes is occasionally used in specialist applications, the majority of mr images today are created either by the two-dimensional fourier transform (2dft) technique with slice selection, or by the three-dimensional fourier transform (3dft) technique. another name for 2dft is spin-warp. what follows here is a description of the 2dft technique with slice selection. the 3dft technique is rather similar except that there is no slice selection and phase-encoding is performed in two separate directions. echo-planar imaging another scheme which is sometimes used, especially in brain scanning or where images are needed very rapidly, is called echo-planar imaging (epi): in this case, each rf excitation is followed by a train of gradient echoes with different spatial encoding. multiplexed-epi is even faster, e.g., for whole brain functional mri (fmri) or diffusion mri. image contrast and contrast enhancement image contrast is created by differences in the strength of the nmr signal recovered from different locations within the sample. this depends upon the relative density of excited nuclei (usually water protons), on differences in relaxation times (t1, t2, and t*2) of those nuclei after the pulse sequence, and often on other parameters discussed under specialized mr scans. contrast in most mr images is actually a mixture of all these effects, but careful design of the imaging pulse sequence allows one contrast mechanism to be emphasized while the others are minimized. the ability to choose different contrast mechanisms gives mri tremendous flexibility. in the brain, t1-weighting causes the nerve connections of white matter to appear white, and the congregations of neurons of gray matter to appear gray, while cerebrospinal fluid (csf) appears dark. the contrast of white matter, gray matter and cerebrospinal fluid is reversed using t2 or t*2 imaging, whereas proton-density-weighted imaging provides little contrast in healthy subjects. additionally, functional parameters such as cerebral blood flow (cbf), cerebral blood volume (cbv) or blood oxygenation can affect t1, t2, and t*2 and so can be encoded with suitable pulse sequences. in some situations it is not possible to generate enough image contrast to adequately show the anatomy or pathology of interest by adjusting the imaging parameters alone, in which case a contrast agent may be administered. this can be as simple as water, taken orally, for imaging the stomach and small bowel. however, most contrast agents used in mri are selected for their specific magnetic properties. most commonly, a paramagnetic contrast agent (usually a gadolinium compound) is given. gadolinium-enhanced tissues and fluids appear extremely bright on t1-weighted images. this provides high sensitivity for detection of vascular tissues (e.g., tumors) and permits assessment of brain perfusion (e.g., in stroke). there have been concerns raised recently regarding the toxicity of gadolinium-based contrast agents and their impact on persons with impaired kidney function. (see safety/contrast agents below.) more recently, superparamagnetic contrast agents, e.g., iron oxide nanoparticles, have become available. these agents appear very dark on t*2-weighted images and may be used for liver imaging, as normal liver tissue retains the agent, but abnormal areas (e.g., scars, tumors) do not. they can also be taken orally, to improve visualization of the gastrointestinal tract, and to prevent water in the gastrointestinal tract from obscuring other organs (e.g., the pancreas). diamagnetic agents such as barium sulfate have also been studied for potential use in the gastrointestinal tract, but are less frequently used. k-space main article: k-space (mri) in 1983, ljunggren and twieg independently introduced the k-space formalism, a technique that proved invaluable in unifying different mr imaging techniques. they showed that the demodulated mr signal s(t) generated by the interaction between an ensemble of freely precessing nuclear spins in the presence of a linear magnetic field gradient g and a receiver-coil equals the fourier transform of the effective spin