density, ρ ( x → ) )} . fundamentally, the signal is derived from faraday's law of induction: s ( t ) = ρ ~ e f f ( k → ( t ) ) ≡ ∫ − ∞ ∞ d x → ρ ( x → ) ⋅ e 2 π i k → ( t ) ⋅ x → _ }\left((t)\right)\equiv \int _^\mathrm \ \rho ()\cdot e^(t)\cdot where: k → ( t ) ≡ ∫ 0 t g → ( τ ) d τ (t)\equiv \int _^(\tau )\ \mathrm \tau } in other words, as time progresses the signal traces out a trajectory in k-space with the velocity vector of the trajectory proportional to the vector of the applied magnetic field gradient. by the term effective spin density we mean the true spin density ρ ( x → ) )} corrected for the effects of t1 preparation, t2 decay, dephasing due to field inhomogeneity, flow, diffusion, etc. and any other phenomena that affect that amount of transverse magnetization available to induce signal in the rf probe or its phase with respect to the receiving coil' s electromagnetic field. from the basic k-space formula, it follows immediately that we reconstruct an image i ( x → ) )} by taking the inverse fourier transform of the sampled data, viz. i ( x → ) = ∫ − ∞ ∞ d k → s ( k → ( t ) ) ⋅ e − 2 π i k → ( t ) ⋅ x → \right)=\int _^\mathrm \ s\left((t)\right)\cdot e^(t)\cdot using the k-space formalism, a number of seemingly complex ideas became simple. for example, it becomes very easy (for physicists, in particular) to understand the role of phase encoding (the so-called spin-warp method). in a standard spin echo or gradient echo scan, where the readout (or view) gradient is constant (e.g., g), a single line of k-space is scanned per rf excitation. when the phase encoding gradient is zero, the line scanned is the kx axis. when a non-zero phase-encoding pulse is added in between the rf excitation and the commencement of the readout gradient, this line moves up or down in k-space, i.e., we scan the line ky = constant. the k-space formalism also makes it very easy to compare different scanning techniques. in single-shot epi, all of k-space is scanned in a single shot, following either a sinusoidal or zig-zag trajectory. since alternating lines of k-space are scanned in opposite directions, this must be taken into account in the reconstruction. multi-shot epi and fast spin echo techniques acquire only part of k-space per excitation. in each shot, a different interleaved segment is acquired, and the shots are repeated until k-space is sufficiently well-covered. since the data at the center of k-space represent lower spatial frequencies than the data at the edges of k-space, the te value for the center of k-space determines the image's t2 contrast. the importance of the center of k-space in determining image contrast can be exploited in more advanced imaging techniques. one such technique is spiral acquisition—a rotating magnetic field gradient is applied, causing the trajectory in k-space to spiral out from the center to the edge. due to t2 and t*2 decay the signal is greatest at the start of the acquisition, hence acquiring the center of k-space first improves contrast to noise ratio (cnr) when compared to conventional zig-zag acquisitions, especially in the presence of rapid movement. since x → and k → are conjugate variables (with respect to the fourier transform) we can use the nyquist theorem to show that a step in k-space determines the field of view of the image (maximum frequency that is correctly sampled) and the maximum value of k sampled determines the resolution; i.e., f o v ∝ 1 δ k r e s o l u t i o n ∝ | k max | . \propto \qquad \mathrm \propto |k_|\ .} (these relationships apply to each axis independently.) example of a pulse sequence simplified timing diagram for two-dimensional-fourier-transform (2dft) spin echo (se) pulse sequence in the timing diagram, the horizontal axis represents time. the vertical axis represents: (top row) amplitude of radio frequency pulses; (middle rows) amplitudes of the three orthogonal magnetic field gradient pulses; and (bottom row) receiver analog-to-digital converter (adc). radio frequencies are transmitted at the larmor frequency of the nuclide to be imaged. for example, for 1h in a magnetic field of 1 t, a frequency of 42.5781 mhz would be employed. the three field gradients are labeled gx (typically corresponding to a patient's left-to-right direction and colored red in diagram), gy (typically corresponding to a patient's front-to-back direction and colored green in diagram), and gz (typically corresponding to a patient's head-to-toe direction and colored blue in diagram). where negative-going gradient pulses are shown, they represent reversal of the gradient direction, i.e., right-to-left, back-to-front or toe-to-head. for human scanning, gradient strengths of 1–100 mt/m are employed: higher gradient strengths permit better resolution and faster imaging. the pulse sequence shown here would produce a transverse (axial) image. the first part of the pulse sequence, ss, achieves "slice selection". a shaped pulse (shown here with a sinc modulation) causes a 90° nutation of longitudinal nuclear magnetization within a slab, or slice, creating transverse magnetization. the second part of the pulse sequence, pe, imparts a phase shift upon the slice-selected nuclear magnetization, varying with its location in the y direction. the third part of the pulse sequence, another slice selection (of the same slice) uses another shaped pulse to cause a 180° rotation of transverse nuclear magnetization within the slice. this transverse magnetisation refocuses to form a spin echo at a time te. during the spin echo, a frequency-encoding (fe) or readout gradient is applied, making the resonant frequency of the nuclear magnetization vary with its location in the x direction. the signal is sampled nfe times by the adc during this period, as represented by the vertical lines. typically nfe of between 128 and 512 samples are taken. the longitudinal magnetisation is then allowed to recover somewhat and after a time tr the whole sequence is repeated npe times, but with the phase-encoding gradient incremented (indicated by the horizontal hatching in the green gradient block). typically npe of between 128 and 512 repetitions are made. the negative-going lobes in gx and gz are imposed to ensure that, at time te (the spin echo maximum), phase only encodes spatial location in the y direction. typically te is between 5 ms and 100 ms, while tr is between 100 ms and 2000 ms. after the two-dimensional matrix (typical dimension between 128 × 128 and 512 × 512) has been acquired, producing the so-called k-space data, a two-dimensional inverse fourier transform is performed to provide the familiar mr image. either the magnitude or phase of the fourier transform can be taken, the former being far more common. overview of main sequences main article: mri sequence this table does not include uncommon and experimental sequences. groupsequenceabbr.physicsmain clinical distinctionsexample spin echot1 weightedt1measuring spin–lattice relaxation by using a short repetition time (tr) and echo time (te). lower signal for more water content, as in edema, tumor, infarction, inflammation, infection, hyperacute or chronic hemorrhage. high signal for fat high signal for paramagnetic substances, such as mri contrast agents standard foundation and comparison for other sequences t2 weightedt2measuring spin–spin relaxation by using long tr and te times higher signal for more water content low signal for fat − note that this only applies to standard spin echo (se) sequences and not the more modern fast spin echo (fse) sequence (also referred to as turbo spin echo, tse), which is the most commonly used technique today. in fse/tse, fat will have a high signal. low signal for paramagnetic substances standard foundation and comparison for other sequences proton density weightedpdlong tr (to reduce t1) and short te (to minimize t2). joint disease and injury. high signal from meniscus tears. (pictured) gradient echo (gre)steady-state free precessionssfpmaintenance of a steady, residual transverse magnetisation over successive cycles.creation of cardiac mri videos (pictured). effective t2 or "t2-star"t2*spoiled gradient recalled echo (gre) with a long echo time and small flip anglelow signal from hemosiderin deposits (pictured) and hemorrhages. susceptibility-weightedswispoiled gradient recalled echo (gre), fully flow compensated, long echo time, combines phase image with magnitude image detecting small amounts of hemorrhage (diffuse axonal injury pictured) or calcium. inversion recovery short tau inversion recoverystirfat suppression by setting an inversion time where the signal of fat is zero. high signal in edema, such as in more severe stress fracture. shin splints pictured: fluid-attenuated inversion recoveryflairfluid suppression by setting an inversion time that nulls fluidshigh signal in lacunar infarction, multiple sclerosis (ms) plaques, subarachnoid haemorrhage and meningitis (pictured). double inversion recoverydirsimultaneous suppression of cerebrospinal fluid and white matter by two inversion times. high signal of multiple sclerosis plaques (pictured). diffusion weighted (dwi)conventionaldwimeasure of brownian motion of water molecules. high signal within minutes of cerebral infarction (pictured). apparent diffusion coefficientadcreduced t2 weighting by taking multiple conventional dwi images with different dwi weighting, and the change corresponds to diffusion. low signal minutes after cerebral infarction (pictured). diffusion tensordtimainly tractography (pictured) by an overall greater brownian motion of water molecules in the directions of nerve fibers. evaluating white matter deformation by tumors reduced fractional anisotropy may indicate dementia. perfusion weighted (pwi) dynamic susceptibility contrastdscmeasures changes over time in susceptibility-induced signal loss due to gadolinium contrast injection. provides measurements of blood flow in cerebral infarction, the infarcted core and the penumbra have decreased perfusion and delayed contrast arrival (pictured). arterial spin labellingaslmagnetic labeling of arterial blood below the imaging slab, which subsequently enters the region of interest. it does not need gadolinium contrast. dynamic contrast enhanceddcemeasures changes over time in the shortening of the spin–lattice relaxation (t1) induced by a gadolinium contrast bolus. faster gd contrast uptake along with other features is suggestive of malignancy (pictured). functional mri (fmri)blood-oxygen-level dependent imagingboldchanges in oxygen saturation-dependent magnetism of hemoglobin reflects tissue activity. localizing brain activity from performing an assigned task (e.g. talking, moving fingers) before surgery, also used in research of cognition. magnetic resonance angiography (mra) and venographytime-of-flighttofblood entering the imaged area is not yet magnetically saturated, giving it a much higher signal when using short echo time and flow compensation. detection of aneurysm, stenosis, or dissection phase-contrast magnetic resonance imagingpc-mratwo gradients with equal magnitude, but opposite direction, are used to encode a phase shift, which is proportional to the velocity of spins. detection of aneurysm, stenosis, or dissection (pictured). (vipr) mri scanner construction and operation schematic of construction of a cylindrical superconducting mr scanner the major components of an mri scanner are: the main magnet, which polarizes the sample, the shim coils for correcting inhomogeneities in the main magnetic field, the gradient system which is used to localize the mr signal and the rf system, which excites the sample and detects the resulting nmr signal. the whole system is controlled by one or more computers. magnet a mobile mri unit visiting glebefields health centre, tipton, england the magnet is the largest and most expensive component of the scanner, and the remainder of the scanner is built around it. the strength of the magnet is measured in teslas (t). clinical magnets generally have a field strength in the range 0.1–3.0 t, with research systems available up to 9.4 t for human use and 21 t for animal systems. in the united states, field strengths up to 4 t have been approved by the fda for clinical use. just as important as the strength of the main magnet is its precision. the straightness of the magnetic lines within the center (or, as it is technically known, the iso-center) of the magnet needs to be near-perfect. this is known as homogeneity. fluctuations (inhomogeneities in the field strength) within the scan region should be less than three parts per million (3 ppm). three types of magnets have been used: permanent magnet: conventional magnets made from ferromagnetic materials (e.g., steel alloys containing rare-earth elements such as neodymium) can be used to provide the static magnetic field. a permanent magnet that is powerful enough to be used in an mri will be extremely large and bulky; they can weigh over 100 tonnes. permanent magnet mris are very inexpensive to maintain; this